1
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Orozco-Ic M, Soriano-Agueda L, Sundholm D, Matito E, Merino G. Core-electron contributions to the magnetic response of molecules with heavy elements and their significance in aromaticity assessments. Chem Sci 2024; 15:12906-12921. [PMID: 39148783 PMCID: PMC11323299 DOI: 10.1039/d4sc02269f] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2024] [Accepted: 07/07/2024] [Indexed: 08/17/2024] Open
Abstract
This study delves into the magnetic response of core electrons and their influence on the global magnetic response of planar and three-dimensional systems containing heavy elements, employing the removing valence electron (RVE) approximation. We also explore electronic aromaticity indices to understand the potential role of core electrons on electron delocalization in the absence of an external perturbation. The study reveals that core electrons significantly contribute to the overall magnetic response, especially to the magnetic shielding, affecting the interpretation of aromaticity. In contrast, the calculation of the electronic aromaticity indices suggests a negligible participation of the core electrons on electron delocalization. Despite their widespread use, the study emphasizes caution in labeling systems as strongly aromatic based solely on shielding function computations. It is noteworthy to emphasize the limitations associated with each aromaticity criterion; particularly in the context of magnetic shielding function calculations, the core-electron effect contamination is undeniable. Hence, the integration of various criteria becomes imperative for attaining a comprehensive understanding of magnetic responses within complex systems.
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Affiliation(s)
- Mesías Orozco-Ic
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
| | | | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki P.O. Box 55, A. I. Virtasen aukio 1 FIN-00014 Helsinki Finland
| | - Eduard Matito
- Donostia International Physics Center (DIPC) 20018 Donostia Euskadi Spain
| | - Gabriel Merino
- Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados Unidad Mérida. Km 6 Antigua Carretera a Progreso. Apdo. Postal 73, Cordemex 97310 Mérida Yuc. Mexico
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2
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Schrader SE, Kristiansen HE, Pedersen TB, Kvaal S. Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets. J Chem Phys 2024; 161:044105. [PMID: 39037132 DOI: 10.1063/5.0213576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Accepted: 07/05/2024] [Indexed: 07/23/2024] Open
Abstract
Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to 5 × 1014 W/cm2. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation.
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Affiliation(s)
- Simon Elias Schrader
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Håkon Emil Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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3
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Sun S, Gu B, Hu H, Lu L, Tang D, Chernyak VY, Li X, Mukamel S. Direct Probe of Conical Intersection Photochemistry by Time-Resolved X-ray Magnetic Circular Dichroism. J Am Chem Soc 2024; 146:19863-19873. [PMID: 38989850 DOI: 10.1021/jacs.4c03033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/12/2024]
Abstract
The direct probing of photochemical dynamics by detecting the electronic coherence generated during passage through conical intersections is an intriguing challenge. The weak coherence signal and the difficulty in preparing purely excited wave packets that exclude coherence from other sources make it experimentally challenging. We propose to use time-resolved X-ray magnetic circular dichroism to probe the wave packet dynamics around the conical intersection. The magnetic field amplifies the relative strength of the electronic coherence signal compared to populations through the magnetic field response anisotropy. More importantly, since the excited state relaxation through conical intersections involves a change of parity, the magnetic coupling matches the symmetry of the response function with the electronic coherence, making the coherence signal only sensitive to the conical intersection induced coherence and excludes the pump pulse induced coherence between the ground state and excited state. In this theoretical study, we apply this technique to the photodissociation dynamics of a pyrrole molecule and demonstrate its capability of probing electronic coherence at a conical intersection as well as population transfer. We demonstrate that a magnetic field can be effectively used to extract novel information about electron and nuclear molecular dynamics.
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Affiliation(s)
- Shichao Sun
- Department of Chemistry, University of California, Irvine, California 92697, United states
- Departmnet of Physics and Astronomy, University of California, Irvine, California 92697, United States
| | - Bing Gu
- Department of Chemistry and Department of Physics, Westlake University, Hangzhou, Zhejiang 310030, China
| | - Hang Hu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Diandong Tang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Vladimir Y Chernyak
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, United States
- Department of Mathematics, Wayne State University, 656 West Kirby, Detroit, Michigan 48202, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Shaul Mukamel
- Department of Chemistry, University of California, Irvine, California 92697, United states
- Departmnet of Physics and Astronomy, University of California, Irvine, California 92697, United States
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4
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Blaschke S, Stopkowicz S, Pausch A. Efficient approximate screening techniques for integrals over London atomic orbitals. J Chem Phys 2024; 161:024117. [PMID: 38995080 DOI: 10.1063/5.0217246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2024] [Accepted: 06/19/2024] [Indexed: 07/13/2024] Open
Abstract
Efficient integral screening techniques are essential for the investigation of extended molecular structures. This work presents a critical assessment of well-established approximate screening techniques and extends them for integrals over London atomic orbitals, which are required in the presence of strong, external magnetic fields. Through the examination of helium clusters in such extreme environments, we demonstrate that seemingly straightforward extensions of field-free screening techniques as proposed in the recent literature can lead to significant errors. To rectify this, we propose two alternative screening techniques that lead to the desired speedups while still maintaining strict error control.
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Affiliation(s)
- Simon Blaschke
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
- Fachrichtung Chemie, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Stella Stopkowicz
- Fachrichtung Chemie, Universität des Saarlandes, D-66123 Saarbrücken, Germany
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, N-0315 Oslo, Norway
| | - Ansgar Pausch
- Theoretical Chemistry, Vrije Universiteit Amsterdam, 1081HV Amsterdam, The Netherlands
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5
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Wibowo-Teale M, Huynh BC, Wibowo-Teale AM, De Proft F, Geerlings P. Symmetry and reactivity of π-systems in electric and magnetic fields: a perspective from conceptual DFT. Phys Chem Chem Phys 2024; 26:15156-15180. [PMID: 38747576 PMCID: PMC11135622 DOI: 10.1039/d4cp00799a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 04/30/2024] [Indexed: 05/30/2024]
Abstract
The extension of conceptual density-functional theory (conceptual DFT) to include external electromagnetic fields in chemical systems is utilised to investigate the effects of strong magnetic fields on the electronic charge distribution and its consequences on the reactivity of π-systems. Formaldehyde, H2CO, is considered as a prototypical example and current-density-functional theory (current-DFT) calculations are used to evaluate the electric dipole moment together with two principal local conceptual DFT descriptors, the electron density and the Fukui functions, which provide insight into how H2CO behaves chemically in a magnetic field. In particular, the symmetry properties of these quantities are analysed on the basis of group, representation, and corepresentation theories using a recently developed automatic program for symbolic symmetry analysis, QSYM2. This allows us to leverage the simple symmetry constraints on the macroscopic electric dipole moment components to make profound predictions on the more nuanced symmetry transformation properties of the microscopic frontier molecular orbitals (MOs), electron densities, and Fukui functions. This is especially useful for complex-valued MOs in magnetic fields whose detailed symmetry analyses lead us to define the new concepts of modular and phasal symmetry breaking. Through these concepts, the deep connection between the vanishing constraints on the electric dipole moment components and the symmetry of electron densities and Fukui functions can be formalised, and the inability of the magnetic field in all three principal orientations considered to induce asymmetry with respect to the molecular plane of H2CO can be understood from a molecular perspective. Furthermore, the detailed forms of the Fukui functions reveal a remarkable reversal in the direction of the dipole moment along the CO bond in the presence of a parallel or perpendicular magnetic field, the origin of which can be attributed to the mixing between the frontier MOs due to their subduced symmetries in magnetic fields. The findings in this work are also discussed in the wider context of a long-standing debate on the possibility to create enantioselectivity by external fields.
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Affiliation(s)
- Meilani Wibowo-Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Bang C Huynh
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Andrew M Wibowo-Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Frank De Proft
- Research group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Paul Geerlings
- Research group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
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6
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Kitsaras MP, Grazioli L, Stopkowicz S. The approximate coupled-cluster methods CC2 and CC3 in a finite magnetic field. J Chem Phys 2024; 160:094112. [PMID: 38441261 DOI: 10.1063/5.0189350] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Accepted: 01/18/2024] [Indexed: 08/16/2024] Open
Abstract
In this paper, we report on the implementation of CC2 and CC3 in the context of molecules in finite magnetic fields. The methods are applied to the investigation of atoms and molecules through spectroscopic predictions and geometry optimizations for the study of the atmosphere of highly magnetized White Dwarf stars. We show that ground-state finite-field (ff) CC2 is a reasonable alternative to CCSD for energies and, in particular, for geometrical properties. For excited states, ff-CC2 is shown to perform well for states with predominant single-excitation character. Yet, for cases in which the excited state wavefunction has double-excitation character with respect to the reference, ff-CC2 can easily lead to completely unphysical results. Ff-CC3, however, is shown to reproduce the CCSDT behavior very well and enables the treatment of larger systems at a high accuracy.
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Affiliation(s)
- Marios-Petros Kitsaras
- Fachrichtung Chemie, Universität des Saarlandes, Campus B2.2, D-66123 Saarbrücken, Germany
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Laura Grazioli
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Stella Stopkowicz
- Fachrichtung Chemie, Universität des Saarlandes, Campus B2.2, D-66123 Saarbrücken, Germany
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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7
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Åström H, Lehtola S. Insight on Gaussian Basis Set Truncation Errors in Weak to Intermediate Magnetic Fields with an Approximate Hamiltonian. J Phys Chem A 2023; 127:10872-10888. [PMID: 38103024 PMCID: PMC10758122 DOI: 10.1021/acs.jpca.3c04531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Revised: 11/01/2023] [Accepted: 11/20/2023] [Indexed: 12/17/2023]
Abstract
Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structures of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with Gaussian basis sets designed for zero field, leading to large basis set truncation errors [Lehtola et al., Mol. Phys. 2020, 118, e1597989]. In this work, we aim to identify the failures of the Gaussian basis sets in atomic calculations to guide the design of new basis sets for strong magnetic fields. We achieve this by performing fully numerical electronic structure calculations at the complete basis set (CBS) limit for the ground state and low lying excited states of the atoms 1 ≤ Z ≤ 18 in weak to intermediate magnetic fields. We also carry out finite-field calculations for a variety of Gaussian basis sets, introducing a real-orbital approximation for the magnetic-field Hamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has been used in many works in the literature. A study of the differences in total energies of the fully numerical CBS limit calculations and the approximate Gaussian basis calculations is carried out to provide insight into basis set truncation errors. Examining a variety of states over the range of magnetic field strengths from B = 0 to B = 0.6B0, we observe significant differences for the aug-cc-pVTZ basis set, while much smaller errors are afforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys. 2020, 152, 134108]. This suggests that there is considerable room to improve Gaussian basis sets for calculations at finite magnetic fields.
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Affiliation(s)
- Hugo Åström
- Department of Chemistry,
Faculty of Science, University of Helsinki, P.O. Box 55 (A.I. Virtanens plats 1), Helsinki FI-00014, Finland
| | - Susi Lehtola
- Department of Chemistry,
Faculty of Science, University of Helsinki, P.O. Box 55 (A.I. Virtanens plats 1), Helsinki FI-00014, Finland
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8
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Alonso M, Bettens T, Eeckhoudt J, Geerlings P, De Proft F. Wandering through quantum-mechanochemistry: from concepts to reactivity and switches. Phys Chem Chem Phys 2023; 26:21-35. [PMID: 38086672 DOI: 10.1039/d3cp04907h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2023]
Abstract
Mechanochemistry has experienced a renaissance in recent years witnessing, at the molecular level, a remarkable interplay between theory and experiment. Molecular mechanochemistry has welcomed a broad spectrum of quantum-chemical methods to evaluate the influence of an external mechanical force on molecular properties. In this contribution, an overview is given on recent work on quantum mechanochemistry in the Brussels Quantum Chemistry group (ALGC). The effect of an external force was scrutinized both in fundamental topics, like reactivity descriptors in Conceptual DFT, and in applied topics, such as designing molecular force probes and tuning the stereoselectivity of certain types of reactions. In the conceptual part, a brief overview of the techniques introducing mechanical forces into a quantum-mechanical description of a molecule is followed by an introduction to conceptual DFT. The evolution of the electronic chemical potential (or electronegativity), chemical hardness and electrophilicity are investigated when a chemical bond in a series of diatomics is put under mechanical stress. Its counterpart, the influence of mechanical stress on bond angles, is analyzed by varying the strain present in alkyne triple bonds by applying a bending force, taking the strain promoted alkyne-azide coupling cycloaddition as an example. The increase of reactivity of the alkyne upon bending is probed by Fukui functions and the local softness. In the applied part, a new molecular force probe is presented based on an intramolecular 6π-electrocyclization in constrained polyenes operating under thermal conditions. A cyclic process is conceived where ring opening and closure are triggered by applying or removing an external pulling force. The efficiency of mechanical activation strongly depends on the magnitude of the applied force and the distance between the pulling points. The idea of pulling point distances as a tool to identify new mechanochemical processes is then tested in [28]hexaphyrins with an intricate equilibrium between Möbius aromatic and Hückel antiaromatic topologies. A mechanical force is shown to trigger the interconversion between the two topologies, using the distance matrix as a guide to select appropriate pulling points. In a final application, the Felkin-Anh model for the addition of nucleophiles to chiral carbonyls under the presence of an external mechanical force is scrutinized. By applying a force for restricting the conformational freedom of the chiral ketone, otherwise inaccessible reaction pathways are promoted on the force-modified potential energy surfaces resulting in a diastereoselectivity different from the force-free reaction.
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Affiliation(s)
- Mercedes Alonso
- Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium.
| | - Tom Bettens
- Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium.
| | - Jochen Eeckhoudt
- Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium.
| | - Paul Geerlings
- Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium.
| | - Frank De Proft
- Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium.
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9
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Ofstad BS, Wibowo-Teale M, Kristiansen HE, Aurbakken E, Kitsaras MP, Schøyen ØS, Hauge E, Irons TJP, Kvaal S, Stopkowicz S, Wibowo-Teale AM, Pedersen TB. Magnetic optical rotation from real-time simulations in finite magnetic fields. J Chem Phys 2023; 159:204109. [PMID: 38018753 DOI: 10.1063/5.0171927] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 11/01/2023] [Indexed: 11/30/2023] Open
Abstract
We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.
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Affiliation(s)
- Benedicte Sverdrup Ofstad
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Meilani Wibowo-Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Håkon Emil Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Einar Aurbakken
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Marios Petros Kitsaras
- Physical and Theoretical Chemistry, Saarland University, Campus B2.2, 66123 Saarbruecken, Germany
| | | | - Eirill Hauge
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, 0164 Oslo, Norway
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Stella Stopkowicz
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Physical and Theoretical Chemistry, Saarland University, Campus B2.2, 66123 Saarbruecken, Germany
| | - Andrew M Wibowo-Teale
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
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10
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Culpitt T, Tellgren EI, Pavošević F. Unitary coupled-cluster for quantum computation of molecular properties in a strong magnetic field. J Chem Phys 2023; 159:204101. [PMID: 37991157 DOI: 10.1063/5.0177417] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 10/20/2023] [Indexed: 11/23/2023] Open
Abstract
In truncated coupled-cluster (CC) theories, non-variational and/or generally complex ground-state energies can occur. This is due to the non-Hermitian nature of the similarity transformed Hamiltonian matrix in combination with CC truncation. For chemical problems that deal with real-valued Hamiltonian matrices, complex CC energies rarely occur. However, for complex-valued Hamiltonian matrices, such as those that arise in the presence of strong magnetic fields, complex CC energies can be regularly observed unless certain symmetry conditions are fulfilled. Therefore, in the presence of magnetic fields, it is desirable to pursue CC methods that are guaranteed to give upper-bound, real-valued energies. In this work, we present the first application of unitary CC to chemical systems in a strong magnetic field. This is achieved utilizing the variational quantum eigensolver algorithm applied to the unitary coupled-cluster singles and doubles (UCCSD) method. We benchmark the method on the H2 molecule in a strong magnetic field and then calculate UCCSD energies for the H4 molecule as a function of both geometry and field angle. We show that while standard CCSD can yield generally complex energies that are not an upper-bound to the true energy, UCCSD always results in variational and real-valued energies. We also show that the imaginary components of the CCSD energy are largest in the strongly correlated region. Last, the UCCSD calculations capture a large percentage of the correlation energy.
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Affiliation(s)
- Tanner Culpitt
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Ave., Madison, Wisconsin 53706, USA
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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11
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Franzke Y, Holzer C, Andersen JH, Begušić T, Bruder F, Coriani S, Della Sala F, Fabiano E, Fedotov DA, Fürst S, Gillhuber S, Grotjahn R, Kaupp M, Kehry M, Krstić M, Mack F, Majumdar S, Nguyen BD, Parker SM, Pauly F, Pausch A, Perlt E, Phun GS, Rajabi A, Rappoport D, Samal B, Schrader T, Sharma M, Tapavicza E, Treß RS, Voora V, Wodyński A, Yu JM, Zerulla B, Furche F, Hättig C, Sierka M, Tew DP, Weigend F. TURBOMOLE: Today and Tomorrow. J Chem Theory Comput 2023; 19:6859-6890. [PMID: 37382508 PMCID: PMC10601488 DOI: 10.1021/acs.jctc.3c00347] [Citation(s) in RCA: 50] [Impact Index Per Article: 50.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Indexed: 06/30/2023]
Abstract
TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.
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Affiliation(s)
- Yannick
J. Franzke
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Josefine H. Andersen
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Tomislav Begušić
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Florian Bruder
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Sonia Coriani
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Daniil A. Fedotov
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Susanne Fürst
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Sebastian Gillhuber
- Institute
of Inorganic Chemistry, Karlsruhe Institute
of Technology (KIT), Engesserstr. 15, 76131 Karlsruhe, Germany
| | - Robin Grotjahn
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Max Kehry
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Marjan Krstić
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Sourav Majumdar
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Brian D. Nguyen
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Shane M. Parker
- Department
of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106 United States
| | - Fabian Pauly
- Institute
of Physics, University of Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany
| | - Ansgar Pausch
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Eva Perlt
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Gabriel S. Phun
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Ahmadreza Rajabi
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dmitrij Rappoport
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Bibek Samal
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Tim Schrader
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Manas Sharma
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Enrico Tapavicza
- Department
of Chemistry and Biochemistry, California
State University, Long Beach, 1250 Bellflower Boulevard, Long
Beach, California 90840-9507, United States
| | - Robert S. Treß
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Vamsee Voora
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Jason M. Yu
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Benedikt Zerulla
- Institute
of Nanotechnology, Karlsruhe Institute of
Technology (KIT), Hermann-von-Helmholtz-Platz
1, 76344 Eggenstein-Leopoldshafen Germany
| | - Filipp Furche
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Christof Hättig
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Marek Sierka
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - David P. Tew
- Physical
and Theoretical Chemistry Laboratory, University
of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | - Florian Weigend
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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12
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Bhattacharjee I, Ghosh D, Paul A. Eliminating all bonds from the ground state gives rise to ionic bonding in high-spin states of heterodiatomics. Phys Chem Chem Phys 2023; 25:26060-26064. [PMID: 37728064 DOI: 10.1039/d3cp01781h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/21/2023]
Abstract
Understanding chemical bonding in second-row diatomics has been central to elucidating the basics of bonding itself. Bond strength and the number of bonds are the two factors that decide the reactivity of molecules. While bond strengths have been theoretically computed accurately and experimentally determined, the number of bonds is a more contentious issue, especially for complicated multi-reference systems like C2. We have developed an experimentally verifiable approach to determine bond numbers from excited spin state potential energy surfaces. On applying this to a series of second-row heterodiatomics, we obtain the surprising phenomenon of an inverted charge transfer ionic state after all the ground state bonds are broken via higher spin states. These ionic states are ubiquitous in all heterodiatomics and unexpected in non-metallic systems.
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Affiliation(s)
- Ishita Bhattacharjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India.
| | - Debashree Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India.
| | - Ankan Paul
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India.
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13
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Cheng CY, Wibowo-Teale AM. Semiempirical Methods for Molecular Systems in Strong Magnetic Fields. J Chem Theory Comput 2023; 19:6226-6241. [PMID: 37672773 PMCID: PMC10536997 DOI: 10.1021/acs.jctc.3c00671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Indexed: 09/08/2023]
Abstract
A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, |B | ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, |B | > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.
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Affiliation(s)
- Chi Y. Cheng
- School
of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
| | - Andrew M. Wibowo-Teale
- School
of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O.
Box 1033, Blindern, N-0315 Oslo, Norway
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14
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Holzer C. Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References. J Chem Theory Comput 2023. [PMID: 37183702 DOI: 10.1021/acs.jctc.3c00156] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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15
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Karachi SS, Eskandari K. Bonding in the high spin lithium clusters: Non-nuclear attractors play a crucial role. J Comput Chem 2023; 44:962-968. [PMID: 36573786 DOI: 10.1002/jcc.27056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 11/29/2022] [Accepted: 12/01/2022] [Indexed: 12/28/2022]
Abstract
The bonding in lithium high-spin clusters contradicts the usual chemical bonding concept since there are no electron pairs between the atoms, and they are bound with parallel spin electrons. Quantum theory of atoms in molecules and interacting quantum atom analysis (IQA) were used to investigate the nature of bonding in the high-spin Li n n + 1 n = 2 - 5 clusters. Our findings demonstrate that the non-nuclear attractors (NNAs) are an essential component of the high-spin lithium clusters and play a key role in keeping them stable. Based on IQA energy terms, an electrostatic destabilizing interaction between the lithium atoms works against the cluster formation. On the other hand, the interactions between lithium atoms and NNA basins are stabilizing and outweigh the lithium-lithium destabilizing effects. In fact, NNAs tend to draw lithium atoms together and stabilize the resulting cluster. The high-spin clusters of lithium can be regarded as electrostatically driven compounds since the electrostatic components are primarily responsible for the stabilizing interactions between NNAs and Li atoms. The only exception is 3 Li2 , which lacks NNA and has a non-repellent lithium-lithium interaction. Indeed, in the 3 Li2 , the interatomic electrostatic component is negligibly small, and the exchange-correlation term leads to a weak bonding interaction.
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Affiliation(s)
- Sara Sadat Karachi
- Department of Chemistry, Isfahan University of Technology, Isfahan, Iran
| | - Kiamars Eskandari
- Department of Chemistry, Isfahan University of Technology, Isfahan, Iran
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16
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Tellgren EI, Culpitt T, Peters LDM, Helgaker T. Molecular vibrations in the presence of velocity-dependent forces. J Chem Phys 2023; 158:124124. [PMID: 37003779 DOI: 10.1063/5.0139684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023] Open
Abstract
A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise-for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.
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Affiliation(s)
- Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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17
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Culpitt T, Peters LDM, Tellgren EI, Helgaker T. Time-dependent nuclear-electronic orbital Hartree-Fock theory in a strong uniform magnetic field. J Chem Phys 2023; 158:114115. [PMID: 36948801 DOI: 10.1063/5.0139675] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023] Open
Abstract
In an ultrastrong magnetic field, with field strength B ≈ B0 = 2.35 × 105 T, molecular structure and dynamics differ strongly from that observed on the Earth. Within the Born-Oppenheimer (BO) approximation, for example, frequent (near) crossings of electronic energy surfaces are induced by the field, suggesting that nonadiabatic phenomena and processes may play a more important role in this mixed-field regime than in the weak-field regime on Earth. To understand the chemistry in the mixed regime, it therefore becomes important to explore non-BO methods. In this work, the nuclear-electronic orbital (NEO) method is employed to study protonic vibrational excitation energies in the presence of a strong magnetic field. The NEO generalized Hartree-Fock theory and time-dependent Hartree-Fock (TDHF) theory are derived and implemented, accounting for all terms that result as a consequence of the nonperturbative treatment of molecular systems in a magnetic field. The NEO results for HCN and FHF- with clamped heavy nuclei are compared against the quadratic eigenvalue problem. Each molecule has three semi-classical modes owing to the hydrogen-two precession modes that are degenerate in the absence of a field and one stretching mode. The NEO-TDHF model is found to perform well; in particular, it automatically captures the screening effects of the electrons on the nuclei, which are quantified through the difference in energy of the precession modes.
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Affiliation(s)
- Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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18
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Geerlings P, De Proft F. External fields in conceptual density functional theory. J Comput Chem 2023; 44:442-455. [PMID: 36054623 DOI: 10.1002/jcc.26978] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 06/30/2022] [Accepted: 07/13/2022] [Indexed: 12/31/2022]
Abstract
The necessity of the recent incorporation of new external variables in the context of conceptual DFT (CDFT) is discussed based on the ever-increasing portfolio of experimental reaction conditions in the endeavor of experimentalists to synthesize new molecules with unprecedented properties. Electric and magnetic fields (ε and B), mechanical forces (F), and confinement are proposed as valuable new variables, extending conventional CDFT and its associated response functions. A finite field approach is used to calculate the evolution of both global and local descriptors in a selected series of atomic and molecular applications, and from it derive new response function involving, with one exception, the first derivative to the field considered. The electric field results, displaying, for example, a case of a field-induced enantioselectivity in the Fukui function, may be instrumental in the recent upsurge of chemistry in oriented external electric fields. The study of atomic electronegativity and hardness in magnetic fields displays a piecewise behavior, associated to configurational jumps upon increasing field strength and reveals an overall compression of their ranges for stronger fields, which may be guiding upon investigating chemistry in extremely high fields like in white dwarfs. The evolution of the electronegativity and hardness of diatomics under mechanical force can elegantly be traced back to differences in their equilibrium distance in the neutral, cationic, and anionic state. The well-known reduction of the polarizability under confinement can be seen as a fore-runner of the increasing hardness of atoms under pressure, presently under investigation. Periodicity showing up in a spontaneous way in the variety of properties is a leitmotiv in this study, as well as the interconnections/analogies between the different response functions.
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Affiliation(s)
- Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel, Brussels, Belgium
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel, Brussels, Belgium
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19
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Peters LDM, Culpitt T, Tellgren EI, Helgaker T. Berry Population Analysis: Atomic Charges from the Berry Curvature in a Magnetic Field. J Chem Theory Comput 2023; 19:1231-1242. [PMID: 36705605 PMCID: PMC9979605 DOI: 10.1021/acs.jctc.2c01138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
The Berry curvature is essential in Born-Oppenheimer molecular dynamics, describing the screening of the nuclei by the electrons in a magnetic field. Parts of the Berry curvature can be understood as the external magnetic field multiplied by an effective charge so that the resulting Berry force behaves like a Lorentz force during the simulations. Here, we investigate whether these effective charges can provide insight into the electronic structure of a given molecule or, in other words, whether we can perform a population analysis based on the Berry curvature. To develop our approach, we first rewrite the Berry curvature in terms of charges that partially capture the effective charges and their dependencies on the nuclear velocities. With these Berry charges and charge fluctuations, we then construct our population analysis yielding atomic charges and overlap populations. Calculations at the Hartree-Fock level reveal that the atomic charges are similar to those obtained from atomic polar tensors. However, since we additionally obtain an estimate for the fluctuations of the charges and a partitioning of the atomic charges into contributions from all atoms, we conclude that the Berry population analysis is a useful alternative tool to analyze the electronic structures of molecules.
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20
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Speake BT, Irons TJP, Wibowo M, Johnson AG, David G, Teale AM. An Embedded Fragment Method for Molecules in Strong Magnetic Fields. J Chem Theory Comput 2022; 18:7412-7427. [PMID: 36414537 DOI: 10.1021/acs.jctc.2c00865] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
An extension of the embedded fragment method for calculations on molecular clusters is presented, which includes strong external magnetic fields. The approach is flexible, allowing for calculations at the Hartree-Fock, current-density-functional theory, Møller-Plesset perturbation theory, and coupled-cluster levels using London atomic orbitals. For systems consisting of discrete molecular subunits, calculations using London atomic orbitals can be performed in a computationally tractable manner for systems beyond the reach of conventional calculations, even those accelerated by resolution-of-the-identity or Cholesky decomposition methods. To assess the applicability of the approach, applications to water clusters are presented, showing how strong magnetic fields enhance binding within the clusters. However, our calculations suggest that, contrary to previous suggestions in the literature, this enhanced binding may not be directly attributable to strengthening of hydrogen bonding. Instead, these results suggest that this arises for larger field strengths as a response of the system to the presence of the external field, which induces a charge density build up between the monomer units. The approach is embarrassingly parallel and its computational tractability is demonstrated for clusters of up to 103 water molecules in triple-ζ basis sets, which would correspond to conventional calculations with more than 12 000 basis functions.
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Affiliation(s)
- Benjamin T Speake
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Meilani Wibowo
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Andrew G Johnson
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Grégoire David
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom.,Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226, F-35000 Rennes, France
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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21
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Wibowo M, Huynh BC, Cheng CY, Irons TJP, Teale AM. Understanding ground and excited-state molecular structure in strong magnetic fields using the maximum overlap method. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2152748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Meilani Wibowo
- School of Chemistry, University of Nottingham, University Park, Nottingham, UK
| | - Bang C. Huynh
- School of Chemistry, University of Nottingham, University Park, Nottingham, UK
| | - Chi Y. Cheng
- School of Chemistry, University of Nottingham, University Park, Nottingham, UK
| | - Tom J. P. Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, UK
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, UK
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Blindern, Oslo, Norway
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22
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Irons TJP, Huynh BC, Teale AM, De Proft F, Geerlings P. Molecular charge distributions in strong magnetic fields: a conceptual and current DFT study. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2145245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Tom J. P. Irons
- School of Chemistry, University of Nottingham, Nottingham, UK
| | - Bang C. Huynh
- School of Chemistry, University of Nottingham, Nottingham, UK
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, Nottingham, UK
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel, Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel, Brussels, Belgium
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23
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Paranthaman S, Vedamanickam N, Ganesan M, Sampathkumar S. Structure, Stability, Electronic and Magnetic Properties of FemBin (m + n = 2–4) Clusters: A DFT Study. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2022. [DOI: 10.1134/s0036024422110279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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24
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Peters LDM, Culpitt T, Tellgren EI, Helgaker T. Magnetic-translational sum rule and approximate models of the molecular Berry curvature. J Chem Phys 2022; 157:134108. [PMID: 36208997 DOI: 10.1063/5.0112943] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct center-of-mass motion during molecular dynamics in these environments. In this work, we demonstrate how these properties of the Berry connection and curvature arise from the translational symmetry of the electronic wave function and how they are fully captured by a finite basis set of London orbitals but not by standard Gaussian basis sets. This is illustrated by a series of Hartree-Fock calculations on small molecules in different basis sets. Based on the resulting physical interpretation of the Berry curvature as the shielding of the nuclei by the electrons, we introduce and test a series of approximations using the Mulliken fragmentation scheme of the electron density. These approximations will be particularly useful in ab initio molecular dynamics calculations in a magnetic field since they reduce the computational cost, while recovering the correct physics and up to 95% of the exact Berry curvature.
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Affiliation(s)
- Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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25
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Hutcheon MJ, Teale AM. Topological Analysis of Functions on Arbitrary Grids: Applications to Quantum Chemistry. J Chem Theory Comput 2022; 18:6077-6091. [PMID: 36070593 PMCID: PMC9558314 DOI: 10.1021/acs.jctc.2c00649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighborhood graph, allowing the topological analysis to be recast as a problem in the graph theory. The flexibility of the approach is demonstrated for various applications involving analysis of the charge and magnetically induced current densities in molecules, where features of the neighborhood graph are found to correspond to chemically relevant topographical properties, such as Bader charges. These properties converge using orders of magnitude fewer grid points than uniform-grid approaches while exhibiting an appealing O[N log(N)] scaling of the computational cost. The issue of grid bias is discussed in the context of graph-based algorithms and strategies for avoiding this bias are presented. Python implementations of the algorithms are provided.
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Affiliation(s)
- Michael J Hutcheon
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K
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26
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Shaik S, Danovich D, Hiberty PC. On The Nature of the Chemical Bond in Valence Bond Theory. J Chem Phys 2022; 157:090901. [DOI: 10.1063/5.0095953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This perspective outlines a panoramic description of the nature of the chemical bond according to valence bond theory. It describes single bonds, and charge-shift bonds (CSBs) in which the entire/most of the bond energy arises from the resonance between the covalent and ionic structures of the bond. Many CSBs are homonuclear bonds. Hypervalent molecules are CSBs. Then we describe multiply bonded molecules with emphasis on C2 and 3O2. The perspective outlines an effective methodology of peeling the electronic structure to the necessary minimum: a structure with a quadruple bond, and two minor structures with double bonds, which stabilize the quadruple bond by resonance. 3O2 is chosen because it is a persistent diradical. The persistence of 3O2 is due to the large CSB resonance interaction of the π-3-electron bonds. Subsequently, we describe the roles of π vs. σ in the geometric preferences in unsaturated molecules, and their Si-based analogs. Then, the perspective discusses bonding in clusters of univalent metal-atoms, which possess only parallel spins, and are nevertheless bonded due to multiple resonance interactions. The bond energy reaches ~40 kcal/mol for a pair of atoms (in n+1Cun; n~10-12). The final subsection discusses singlet excited states in ethene, ozone and SO2. It demonstrates the capability of the breathing-orbital VB method to yield an accurate description of a variety of excited states using 10 or less VB structures. Furthermore, the method underscores covalent structures which play a key role in the correct description and bonding of these excited states.
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Affiliation(s)
- Sason Shaik
- Hebrew University of Jerusalem Institute of Chemistry, Israel
| | - David Danovich
- Hebrew University of Jerusalem Institute of Chemistry, Israel
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27
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Monzel L, Pausch A, Peters L, Tellgren E, Helgaker T, Klopper W. Molecular Dynamics of Linear Molecules in Strong Magnetic Fields. J Chem Phys 2022; 157:054106. [DOI: 10.1063/5.0097800] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born-Oppenheimer potential energy surfaces are calculated at the Hartree-Fock and MP2 levels of theory, using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.
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Affiliation(s)
- Laurenz Monzel
- Karlsruhe Institute of Technology Institute of Physical Chemistry, Germany
| | - Ansgar Pausch
- Karlsruhe Institute of Technology Faculty of Chemistry and Biosciences, Germany
| | | | | | | | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology Faculty of Chemistry and Biosciences, Germany
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28
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Pemberton MJ, Irons TJP, Helgaker T, Teale AM. Revealing the exotic structure of molecules in strong magnetic fields. J Chem Phys 2022; 156:204113. [DOI: 10.1063/5.0092520] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
A novel implementation for the calculation of molecular gradients under strong magnetic fields is employed at the current-density functional theory level to optimize the geometries of molecular structures, which change significantly under these conditions. An analog of the ab initio random structure search is utilized to determine the ground-state equilibrium geometries for He n and CH n systems at high magnetic field strengths, revealing the most stable structures to be those in high-spin states with a planar geometry aligned perpendicular to the field. The electron and current densities for these systems have also been investigated to develop an explanation of chemical bonding in the strong field regime, providing an insight into the exotic chemistry present in these extreme environments.
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Affiliation(s)
- Miles J. Pemberton
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Tom J. P. Irons
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
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29
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Lemmens L, De Vriendt X, Bultinck P, Acke G. Analyzing the Behavior of Spin Phases in External Magnetic Fields by Means of Spin-Constrained States. J Chem Theory Comput 2022; 18:3364-3376. [PMID: 35611406 DOI: 10.1021/acs.jctc.1c00953] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
During molecular dissociation in the presence of an external uniform magnetic field, electrons flip their spin antiparallel to the magnetic field because of the stabilizing influence of the spin Zeeman operator. Although generalized Hartree-Fock descriptions furnish the optimal mean-field energetic description of such bond-breaking processes, they are allowed to break Ŝz symmetry, leading to intricate and unexpected spin phases and phase transitions. In this work, we show that the behavior of these molecular spin phases can be interpreted in terms of spin phase diagrams constructed by constraining states to target expectation values of projected spin. The underlying constrained states offer a complete electronic characterization of the spin phases and spin phase transitions, as they can be analyzed using standard quantum chemical tools. Because the constrained states effectively span the entire phase space, they could provide an excellent starting point for post-Hartree-Fock methods aimed at gaining more electron correlation or regaining spin symmetry.
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Affiliation(s)
- Laurent Lemmens
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Ghent, Belgium
| | - Xeno De Vriendt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Ghent, Belgium
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Ghent, Belgium
| | - Guillaume Acke
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Ghent, Belgium
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30
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Culpitt T, Peters LDM, Tellgren EI, Helgaker T. Analytic calculation of the Berry curvature and diagonal Born–Oppenheimer correction for molecular systems in uniform magnetic fields. J Chem Phys 2022; 156:044121. [DOI: 10.1063/5.0079304] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D. M. Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I. Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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31
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Blaschke S, Stopkowicz S. Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields. J Chem Phys 2022; 156:044115. [DOI: 10.1063/5.0076588] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Simon Blaschke
- Department Chemie, Johannes Gutenberg-Unversität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Unversität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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32
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Francotte R, Irons TJP, Teale AM, de Proft F, Geerlings P. Extending conceptual DFT to include external variables: the influence of magnetic fields. Chem Sci 2022; 13:5311-5324. [PMID: 35655570 PMCID: PMC9093152 DOI: 10.1039/d1sc07263c] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Accepted: 03/24/2022] [Indexed: 11/21/2022] Open
Abstract
An extension of conceptual DFT to include the influence of an external magnetic field is proposed in the context of a program set up to cope with the ever increasing variability of reaction conditions and concomitant reactivity.
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Affiliation(s)
- Robin Francotte
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Tom J. P. Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Frank de Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
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33
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Holzer C, Pausch A, Klopper W. The GW/BSE Method in Magnetic Fields. Front Chem 2021; 9:746162. [PMID: 34900932 PMCID: PMC8655096 DOI: 10.3389/fchem.2021.746162] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 10/19/2021] [Indexed: 11/16/2022] Open
Abstract
The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, Germany
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34
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Pausch A, Gebele M, Klopper W. Molecular point groups and symmetry in external magnetic fields. J Chem Phys 2021; 155:201101. [PMID: 34852467 DOI: 10.1063/5.0069859] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
As quantum-chemical calculations of molecules in static external magnetic fields are becoming increasingly popular, the description of molecular symmetry under such conditions is also becoming more and more relevant. Using group theory, a general scheme of identifying the molecular point group in an external magnetic field is constructed. For both point groups that are non-existent in the absence of a field (C∞ and C∞ h) and their double groups, the character tables are presented. General properties of all possible point groups are discussed, and it is mathematically proven that they are all Abelian.
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Affiliation(s)
- Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Melanie Gebele
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
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35
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Sundholm D, Dimitrova M, Berger RJF. Current density and molecular magnetic properties. Chem Commun (Camb) 2021; 57:12362-12378. [PMID: 34726205 DOI: 10.1039/d1cc03350f] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We give an overview of the molecular response to an external magnetic field perturbing quantum mechanical systems. We present state-of-the-art methods for calculating magnetically-induced current-density susceptibilities. We discuss the essence and properties of current-density susceptibilities and how molecular magnetic properties can be calculated from them. We also review the theory of spin-current densities, how relativity affects current densities and magnetic properties. An overview of the magnetic ring-current criterion for aromaticity is given, which has implications on theoretical and experimental research. The recently reported theory of antiaromaticity and how molecular symmetry affects the magnetic response are discussed and applied to closed-shell paramagnetic molecules. The topology of magnetically induced current densities and its consequences for molecular magnetic properties are also presented with twisted and toroidal molecules as examples.
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Affiliation(s)
- Dage Sundholm
- Department of Chemistry, Faculty of Science, FI-00014 University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, Finland.
| | - Maria Dimitrova
- Department of Chemistry, Faculty of Science, FI-00014 University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, Finland. .,Chemistry of Materials, Paris-Lodron University of Salzburg, Jakob-Haringerstr. 2A, A-5020 Salzburg, Austria
| | - Raphael J F Berger
- Chemistry of Materials, Paris-Lodron University of Salzburg, Jakob-Haringerstr. 2A, A-5020 Salzburg, Austria
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36
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On the chemical bond complexity of the H2+ in 1-D: The ground-state avoided crossing. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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37
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David G, Irons TJP, Fouda AEA, Furness JW, Teale AM. Self-Consistent Field Methods for Excited States in Strong Magnetic Fields: a Comparison between Energy- and Variance-Based Approaches. J Chem Theory Comput 2021; 17:5492-5508. [PMID: 34517708 DOI: 10.1021/acs.jctc.1c00236] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Self-consistent field methods for excited states offer an attractive low-cost route to study not only excitation energies but also properties of excited states. Here, we present the generalization of two self-consistent field methods, the maximum overlap method (MOM) and the σ-SCF method, to calculate excited states in strong magnetic fields and investigate their stability and accuracy in this context. These methods use different strategies to overcome the well-known variational collapse of energy-based optimizations to the lowest solution of a given symmetry. The MOM tackles this problem in the definition of the orbital occupations to constrain the self-consistent field procedure to converge on excited states, while the σ-SCF method is based on the minimization of the variance instead of the energy. To overcome the high computational cost of the variance minimization, we present a new implementation of the σ-SCF method with the resolution of identity approximation, allowing the use of large basis sets, which is an important requirement for calculations in strong magnetic fields. The accuracy of these methods is assessed by comparison with the benchmark literature data for He, H2, and CH+. The results reveal severe limitations of the variance-based scheme, which become more acute in large basis sets. In particular, many states are not accessible using variance optimization. Detailed analysis shows that this is a general feature of variance optimization approaches due to the masking of local minima in the optimization. In contrast, the MOM shows promising performance for computing excited states under these conditions, yielding results consistent with available benchmark data for a diverse range of electronic states.
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Affiliation(s)
- Grégoire David
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K
| | - Adam E A Fouda
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K.,Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 S Cass Avenue, Lemont, Illinois 60439, United States
| | - James W Furness
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, U.K.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
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38
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Peters LDM, Culpitt T, Monzel L, Tellgren EI, Helgaker T. Ab Initio molecular dynamics with screened Lorentz forces. II. Efficient propagators and rovibrational spectra in strong magnetic fields. J Chem Phys 2021; 155:024105. [PMID: 34266256 DOI: 10.1063/5.0056235] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes in the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we analyze simulations of He and H2 at two field strengths characteristic of magnetic white dwarfs (0.1 B0 = 2.35 × 104 T and B0 = 2.35 × 105 T). While the He simulations clearly demonstrate the importance of electron screening of the Lorentz force in the dynamics, the extracted rovibrational spectra of H2 reveal a number of fascinating features not observed in the field-free case: couplings of rotations/vibrations with the cyclotron rotation, overtones with unusual selection rules, and hindered rotations that transmute into librations with increasing field strength. We conclude that our presented framework is a powerful tool to investigate molecules in these extreme environments.
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Affiliation(s)
- Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurenz Monzel
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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39
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Culpitt T, Peters LDM, Tellgren EI, Helgaker T. Ab initio molecular dynamics with screened Lorentz forces. I. Calculation and atomic charge interpretation of Berry curvature. J Chem Phys 2021; 155:024104. [PMID: 34266267 DOI: 10.1063/5.0055388] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
The dynamics of a molecule in a magnetic field is significantly different from its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically using a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H2 at the restricted and unrestricted Hartree-Fock levels of theory and for CH+ as a function of the magnetic field strength at the restricted Hartree-Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In this paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. The calculation of the Berry curvature allows for its inclusion in ab initio molecular dynamics simulations in a magnetic field.
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Affiliation(s)
- Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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40
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Irons TJP, David G, Teale AM. Optimizing Molecular Geometries in Strong Magnetic Fields. J Chem Theory Comput 2021; 17:2166-2185. [PMID: 33724812 PMCID: PMC8047810 DOI: 10.1021/acs.jctc.0c01297] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Indexed: 11/28/2022]
Abstract
An efficient implementation of geometrical derivatives at the Hartree-Fock (HF) and current-density functional theory (CDFT) levels is presented for the study of molecular structure in strong magnetic fields. The required integral derivatives are constructed using a hybrid McMurchie-Davidson and Rys quadrature approach, which combines the amenability of the former to the evaluation of derivative integrals with the efficiency of the latter for basis sets with high angular momentum. In addition to its application to evaluating derivatives of four-center integrals, this approach is also applied to gradients using the resolution-of-the-identity approximation, enabling efficient optimization of molecular structure for many-electron systems under a strong magnetic field. The CDFT contributions have been implemented for a wide range of density functionals up to and including the meta-GGA level with current-density dependent contributions and (range-separated) hybrids for the first time. Illustrative applications are presented to the OH and benzene molecules, revealing the rich and complex chemistry induced by the presence of an external magnetic field. Challenges for geometry optimization in strong fields are highlighted, along with the requirement for careful analysis of the resulting electronic structure at each stationary point. The importance of correlation effects is examined by comparison of results at the HF and CDFT levels. The present implementation of molecular gradients at the CDFT level provides a cost-effective approach to the study of molecular structure under strong magnetic fields, opening up many new possibilities for the study of chemistry in this regime.
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Affiliation(s)
- Tom J. P. Irons
- School
of Chemistry, University of Nottingham,
University Park, Nottingham NG7 2RD, United Kingdom
| | - Grégoire David
- School
of Chemistry, University of Nottingham,
University Park, Nottingham NG7 2RD, United Kingdom
| | - Andrew M. Teale
- School
of Chemistry, University of Nottingham,
University Park, Nottingham NG7 2RD, United Kingdom
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.
O. Box 1033 Blindern, N-0315 Oslo, Norway
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41
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Wibowo M, Irons TJP, Teale AM. Modeling Ultrafast Electron Dynamics in Strong Magnetic Fields Using Real-Time Time-Dependent Electronic Structure Methods. J Chem Theory Comput 2021; 17:2137-2165. [PMID: 33724806 PMCID: PMC8047917 DOI: 10.1021/acs.jctc.0c01269] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
![]()
An implementation
of real-time time-dependent Hartree–Fock
(RT-TDHF) and current density functional theory (RT-TDCDFT) for molecules
in strong uniform magnetic fields is presented. In contrast to earlier
implementations, the present work enables the use of the RT-TDCDFT
formalism, which explicitly includes field-dependent terms in the
exchange–correlation functional. A range of current-dependent
exchange–correlation functionals based on the TPSS functional
are considered, including a range-separated variant, which is particularly
suitable for application to excited state calculations. The performance
of a wide range of propagator algorithms for real-time methods is
investigated in this context. A recently proposed molecular orbital
pair decomposition analysis allows for assignment of electronic transitions,
providing detailed information about which molecular orbitals are
involved in each excitation. The application of these methods is demonstrated
for the electronic absorption spectra of N2 and H2O both in the absence and in the presence of a magnetic field. The
dependence of electronic spectra on the magnetic field strength and
its orientation relative to the molecule is studied. The complex evolution
of the absorption spectra with magnetic field is rationalized using
the molecular orbital pair decomposition analysis, which provides
crucial insight in strong fields where the spectra are radically different
from their zero-field counterparts.
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Affiliation(s)
- Meilani Wibowo
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway
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42
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Sen S, Tellgren EI. Benchmarking Density Functional Approximations for Diamagnetic and Paramagnetic Molecules in Nonuniform Magnetic Fields. J Chem Theory Comput 2021; 17:1480-1496. [PMID: 33576625 PMCID: PMC7948255 DOI: 10.1021/acs.jctc.0c01222] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Indexed: 11/28/2022]
Abstract
In this article, correlated studies on a test set of 36 small molecules are carried out with both wavefunction (HF, MP2, CCSD) and density functional (LDA, KT3, cTPSS, cM06-L) methods. The effect of correlation on exotic response properties such as molecular electronic anapole susceptibilities is studied and the performance of the various density functional approximations are benchmarked against CCSD and/or MP2. Atoms and molecules are traditionally classified into "diamagnetic" and "paramagnetic" based on their isotropic response to uniform magnetic fields. However, in this article, we propose a more fine-grained classification of molecular systems on the basis of their response to generally nonuniform magnetic fields. The relation of orientation to different qualitative responses is also considered.
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Affiliation(s)
- Sangita Sen
- Department
of Chemical Sciences, Indian Institute of
Science, Education and Research, Kolkata 741246, India
| | - Erik I. Tellgren
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway
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Adamowicz L, Stanke M, Tellgren E, Helgaker T. A quantum-mechanical non-Born–Oppenheimer model of a molecule in a strong magnetic field. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.138041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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44
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Bhattacharjee I, Ghosh D, Paul A. Comprehending the quadruple bonding conundrum in C 2 from excited state potential energy curves. Chem Sci 2020; 11:7009-7014. [PMID: 33033605 PMCID: PMC7499457 DOI: 10.1039/d0sc02336a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 06/10/2020] [Indexed: 11/28/2022] Open
Abstract
The question of quadruple bonding in C2 has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory.
The question of quadruple bonding in C2 has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C2, N2, Be2 and HC
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CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the 2S+1Σg/u (with 2S + 1 = 1, 3, 5, 7, 9) states of C2 and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case of N2 and HC
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CH, the presence of a deep minimum in the 7Σ+ state of C2 and CN+ suggests a latent quadruple bonding nature in these two dimers. Our investigations reveal that the number of bonds in the ground state can be determined for 2nd row dimers by figuring out at what value of spin symmetry a purely dissociative PEC is obtained. For N2 and HC
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CH the purely dissociative PEC appears for the septet spin symmetry as compared to that for the nonet in C2. This is indicative of a higher number of bonds between the two 2nd row atoms in C2 as compared to those of N2 and HC
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CH. Hence, we have struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be experimentally verified, thus providing the window so that the narrative can move beyond theoretical conjectures.
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Affiliation(s)
- Ishita Bhattacharjee
- School of Chemical Sciences , Indian Association for the Cultivation of Science , Jadavpur , India . ;
| | - Debashree Ghosh
- School of Chemical Sciences , Indian Association for the Cultivation of Science , Jadavpur , India . ;
| | - Ankan Paul
- School of Chemical Sciences , Indian Association for the Cultivation of Science , Jadavpur , India . ;
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45
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Matthews DA, Cheng L, Harding ME, Lipparini F, Stopkowicz S, Jagau TC, Szalay PG, Gauss J, Stanton JF. Coupled-cluster techniques for computational chemistry: The CFOUR program package. J Chem Phys 2020; 152:214108. [DOI: 10.1063/5.0004837] [Citation(s) in RCA: 214] [Impact Index Per Article: 53.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Devin A. Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, USA
| | - Lan Cheng
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Michael E. Harding
- Institut für Physikalische Chemie, Karlsruher Institut für Technologie (KIT), Kaiserstr. 12, D-76131 Karlsruhe, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Thomas-C. Jagau
- Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - John F. Stanton
- Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, USA
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46
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Loos PF, Fromager E. A weight-dependent local correlation density-functional approximation for ensembles. J Chem Phys 2020; 152:214101. [DOI: 10.1063/5.0007388] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS, Université de Strasbourg, Strasbourg, France
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47
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Sun S, Li X. Relativistic Effects in Magnetic Circular Dichroism: Restricted Magnetic Balance and Temperature Dependence. J Chem Theory Comput 2020; 16:4533-4542. [DOI: 10.1021/acs.jctc.0c00287] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shichao Sun
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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48
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Pausch A, Klopper W. Efficient evaluation of three-centre two-electron integrals over London orbitals. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1736675] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Centre for Advanced Study (CAS), The Norwegian Academy of Science and Letters, Oslo, Norway
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49
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Guo R, Uddin MN, Price LS, Price SL. Calculation of Diamagnetic Susceptibility Tensors of Organic Crystals: From Coronene to Pharmaceutical Polymorphs. J Phys Chem A 2020; 124:1409-1420. [PMID: 31951408 PMCID: PMC7145345 DOI: 10.1021/acs.jpca.9b07104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
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Understanding
why crystallization in strong magnetic fields can
lead to new polymorphs requires methods to calculate the diamagnetic
response of organic molecular crystals. We develop the calculation
of the macroscopic diamagnetic susceptibility tensor, χcryst, for organic molecular crystals using periodic density
functional methods. The crystal magnetic susceptibility tensor, χcryst, for all experimentally known polymorphs,
and its molecular counterpart, χmol,
are calculated for flexible pharmaceuticals such as carbamazepine,
flufenamic acid, and chalcones, and rigid molecules, such as benzene,
pyridine, acridine, anthracene, and coronene, whose molecular magnetic
properties have been traditionally studied. A tensor addition method
is developed to approximate the crystal diamagnetic susceptibility
tensor, χcryst, from the molecular one, χmol, giving good agreement with those calculated
directly using the more costly periodic density functional method
for χcryst. The response of pharmaceutical
molecules and crystals to magnetic fields, as embodied by χcryst, is largely determined by the packing in the crystal,
as well as the molecular conformation. The anisotropy of χcryst can vary considerably between polymorphs though
the isotropic terms are fairly constant. The implications for developing
a computational method for predicting whether crystallization in a
magnetic field could produce a novel or different polymorph are discussed.
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Affiliation(s)
- Rui Guo
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
| | - M Nadia Uddin
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
| | - Louise S Price
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
| | - Sarah L Price
- Department of Chemistry , University College London , 20 Gordon Street , London WC1H 0AJ , U.K
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50
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Leon RCC, Yang CH, Hwang JCC, Lemyre JC, Tanttu T, Huang W, Chan KW, Tan KY, Hudson FE, Itoh KM, Morello A, Laucht A, Pioro-Ladrière M, Saraiva A, Dzurak AS. Coherent spin control of s-, p-, d- and f-electrons in a silicon quantum dot. Nat Commun 2020; 11:797. [PMID: 32047151 PMCID: PMC7012832 DOI: 10.1038/s41467-019-14053-w] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Accepted: 12/11/2019] [Indexed: 11/09/2022] Open
Abstract
Once the periodic properties of elements were unveiled, chemical behaviour could be understood in terms of the valence of atoms. Ideally, this rationale would extend to quantum dots, and quantum computation could be performed by merely controlling the outer-shell electrons of dot-based qubits. Imperfections in semiconductor materials disrupt this analogy, so real devices seldom display a systematic many-electron arrangement. We demonstrate here an electrostatically confined quantum dot that reveals a well defined shell structure. We observe four shells (31 electrons) with multiplicities given by spin and valley degrees of freedom. Various fillings containing a single valence electron-namely 1, 5, 13 and 25 electrons-are found to be potential qubits. An integrated micromagnet allows us to perform electrically-driven spin resonance (EDSR), leading to faster Rabi rotations and higher fidelity single qubit gates at higher shell states. We investigate the impact of orbital excitations on single qubits as a function of the dot deformation and exploit it for faster qubit control.
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Affiliation(s)
- R C C Leon
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia.
| | - C H Yang
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - J C C Hwang
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
- Research and Prototype Foundry, The University of Sydney, Sydney, NSW, 2006, Australia
| | - J Camirand Lemyre
- Institut Quantique et Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
| | - T Tanttu
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - W Huang
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - K W Chan
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - K Y Tan
- QCD Labs COMP Centre of Excellence, Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - F E Hudson
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - K M Itoh
- School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohokuku, Yokohama, 223-8522, Japan
| | - A Morello
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - A Laucht
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - M Pioro-Ladrière
- Institut Quantique et Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
- Quantum Information Science Program, Canadian Institute for Advanced Research, Toronto, ON, M5G 1Z8, Canada
| | - A Saraiva
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia.
| | - A S Dzurak
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, 2052, Australia.
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