1
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Hurtado A, Sekino H, Harrison RJ. Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis. J Chem Theory Comput 2024; 20:5145-5156. [PMID: 38842252 PMCID: PMC11209939 DOI: 10.1021/acs.jctc.4c00394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Revised: 05/20/2024] [Accepted: 05/21/2024] [Indexed: 06/07/2024]
Abstract
This paper presents the first converged frequency-dependent HF polarizability results for general molecules, on a set of 89 closed-shell atoms and molecules. The solver employs multiresolution analysis (MRA) in a multiwavelet basis to compute both ground and response states to a guaranteed precision, which are validated against independent numerical grid calculations on atoms and linear molecules. The MRA ground-state energies and response properties are used to evaluate results in correlation-consistent basis sets up to 5Z augmented with either single or double diffuse functions and core-polarization functions. Systematic trends are revealed through consideration of chemical composition as well as the use of machine learning to cluster convergence trends, the latter suggesting the possibility of learning and correcting basis-set error.
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Affiliation(s)
- Adrian Hurtado
- Department
of Materials Science and Chemical Engineering, Stony Brook University, Stony
Brook, New York 11794-2275, United States
| | - Hideo Sekino
- Institute
for Advanced Computational Science, Stony
Brook University, Stony
Brook, New York 11794-5250, United States
| | - Robert J. Harrison
- Institute
for Advanced Computational Science, Stony
Brook University, Stony
Brook, New York 11794-5250, United States
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2
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Brakestad A, Jensen SR, Tantardini C, Pitteloud Q, Wind P, Užulis J, Gulans A, Hopmann KH, Frediani L. Scalar Relativistic Effects with Multiwavelets: Implementation and Benchmark. J Chem Theory Comput 2024; 20:728-737. [PMID: 38181377 PMCID: PMC10809714 DOI: 10.1021/acs.jctc.3c01095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Revised: 12/18/2023] [Accepted: 12/19/2023] [Indexed: 01/07/2024]
Abstract
The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.
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Affiliation(s)
- Anders Brakestad
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Stig Rune Jensen
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Christian Tantardini
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
- Department
of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, United States
| | - Quentin Pitteloud
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Peter Wind
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
| | - Jānis Užulis
- Department
of Physics, University of Latvia, Jelgavas iela 3, Riga, Latvia 1004, Latvia
| | - Andris Gulans
- Department
of Physics, University of Latvia, Jelgavas iela 3, Riga, Latvia 1004, Latvia
| | | | - Luca Frediani
- Hylleraas
Centre for Quantum Molecular Sciences, UiT
The Arctic University of Norway, Tromsø 9037, Norway
- Department
of Chemistry, UiT The Arctic University
of Norway, Tromsø 9037, Norway
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3
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Tantardini C, Di Remigio Eikås R, Bjørgve M, Jensen SR, Frediani L. Full Breit Hamiltonian in the Multiwavelets Framework. J Chem Theory Comput 2024; 20:882-890. [PMID: 38163290 PMCID: PMC10809419 DOI: 10.1021/acs.jctc.3c01056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2023] [Revised: 12/06/2023] [Accepted: 12/15/2023] [Indexed: 01/03/2024]
Abstract
New techniques in core-electron spectroscopy are necessary to resolve the structures of oxides of f-elements and other strongly correlated materials that are present only as powders and not as single crystals. Thus, accurate quantum chemical methods must be developed to calculate core spectroscopic properties in such materials. In this contribution, we present an important development in this direction, extending our fully adaptive real-space multiwavelet basis framework to tackle the four-component Dirac-Coulomb-Breit Hamiltonian. We show that multiwavelets can reproduce one-dimensional grid-based approaches. They are however a fully three-dimensional approach which can later be extended to molecules and materials. Our multiwavelet implementation attained precise results irrespective of the chosen nuclear model, provided that the error threshold is tight enough and that the chosen polynomial basis is sufficiently large. Furthermore, our results confirmed that in two-electron species, the magnetic and Gauge contributions from s-orbitals are identical in magnitude and can account for the experimental evidence from K and L edges.
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Affiliation(s)
- Christian Tantardini
- Hylleraas
Centre, UiT The Arctic University of Norway, P.O. Box 6050 Langnes, N-9037 Tromsø, Norway
- Department
of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, United States
| | - Roberto Di Remigio Eikås
- Hylleraas
Centre, UiT The Arctic University of Norway, P.O. Box 6050 Langnes, N-9037 Tromsø, Norway
- Algorithmiq
Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Magnar Bjørgve
- Hylleraas
Centre, UiT The Arctic University of Norway, P.O. Box 6050 Langnes, N-9037 Tromsø, Norway
| | - Stig Rune Jensen
- Hylleraas
Centre, UiT The Arctic University of Norway, P.O. Box 6050 Langnes, N-9037 Tromsø, Norway
| | - Luca Frediani
- Hylleraas
Centre, UiT The Arctic University of Norway, P.O. Box 6050 Langnes, N-9037 Tromsø, Norway
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4
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Valeev EF, Harrison RJ, Holmes AA, Peterson CC, Penchoff DA. Direct Determination of Optimal Real-Space Orbitals for Correlated Electronic Structure of Molecules. J Chem Theory Comput 2023; 19:7230-7241. [PMID: 37791808 DOI: 10.1021/acs.jctc.3c00732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for the evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction (CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the orbital sets of the same rank expanded in Gaussian AO bases, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials.
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Affiliation(s)
- Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Robert J Harrison
- Department of Applied Mathematics & Statistics, Stony Brook University, Stony Brook, New York 11794, United States
| | - Adam A Holmes
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Charles C Peterson
- Office of Advanced Research Computing, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Deborah A Penchoff
- UT Innovative Computing Laboratory, University of Tennessee, Knoxville, Tennessee 37996, United States
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5
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Wilson DJD. Extreme NMR shielding in fluoro-nitrogen cations. Phys Chem Chem Phys 2023; 25:25420-25434. [PMID: 37706351 DOI: 10.1039/d3cp03399f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
The structure and NMR shielding of a set of N-F containing cations is reported to near-quantitative accuracy from extensive ab initio calculations. Currently, the shortest experimentally confirmed N-F bond is 1.2461(10) Å in NNF+, however CCSD(T)-F12b/cc-pVQZ-F12 optimised geometries suggest that even shorter N-F bonds are possible for both monocations (1.236 Å, HNF+) and dications (1.098 Å, NF2+). NMR shielding constants have been calculated in a composite manner with individual components from coupled-cluster expansions up to CCSDTQP and basis sets up to aug-cc-pCV8Z, together with vibrational and relativistic corrections. 15N and 19F NMR chemical shifts correlate well with available experimental data. Extreme 19F chemical shifts are predicted for HNF+ (1628.9 ppm) and NH2F2+ (1298.0 ppm), which are by far the largest 19F chemical shifts ever reported and well outside the known range of +865 ppm (F2O2) to -448 ppm (ClF). The 15N chemical shift of -1283.07 ppm in HNF+ is similarly extreme, being well outside the known range of 15N chemical shifts of -730 to 260 ppm (CH3NO2 reference). This work highlights the application of state-of-the-art theoretical techniques, and provides accurate NMR properties of both isolated and yet unknown N-F cations, which can serve to guide and supplement NMR experimentation.
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Affiliation(s)
- David J D Wilson
- Department of Chemistry, La Trobe Institute for Molecular Science, La Trobe University, Melbourne, Victoria 3086, Australia.
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6
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Lehtola S, Marques MAL. Reproducibility of density functional approximations: How new functionals should be reported. J Chem Phys 2023; 159:114116. [PMID: 37725491 DOI: 10.1063/5.0167763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 08/28/2023] [Indexed: 09/21/2023] Open
Abstract
Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations are published every year. To become available in program packages, the novel density functional approximations (DFAs) need to be (re)implemented. However, according to our experience as developers of Libxc [Lehtola et al., SoftwareX 7, 1 (2018)], a constant problem in this task is verification due to the lack of reliable reference data. As we discuss in this work, this lack has led to several non-equivalent implementations of functionals such as Becke-Perdew 1986, Perdew-Wang 1991, Perdew-Burke-Ernzerhof, and Becke's three-parameter hybrid functional with Lee-Yang-Parr correlation across various program packages, yielding different total energies. Through careful verification, we have also found many issues with incorrect functional forms in recent DFAs. The goal of this work is to ensure the reproducibility of DFAs. DFAs must be verifiable in order to prevent the reappearance of the above-mentioned errors and incompatibilities. A common framework for verification and testing is, therefore, needed. We suggest several ways in which reference energies can be produced with free and open source software, either with non-self-consistent calculations with tabulated atomic densities or via self-consistent calculations with various program packages. The employed numerical parameters-especially the quadrature grid-need to be converged to guarantee a ≲0.1 μEh precision in the total energy, which is nowadays routinely achievable in fully numerical calculations. Moreover, as such sub-μEh level agreement can only be achieved when fully equivalent implementations of the DFA are used, the source code of the reference implementation should also be made available in any publication describing a new DFA.
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Affiliation(s)
- Susi Lehtola
- Molecular Sciences Software Institute, Blacksburg, Virginia 24061, USA
- Department of Chemistry, University of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
| | - Miguel A L Marques
- Research Center Future Energy Materials and Systems of the University Alliance Ruhr, Faculty of Mechanical Engineering, Ruhr University Bochum, Universitätsstraße 150, D-44801 Bochum, Germany
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7
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Höynälänmaa T, Rantala TT. Electronic structure calculations with interpolating tensor product wavelet basis. Phys Rev E 2023; 108:025307. [PMID: 37723814 DOI: 10.1103/physreve.108.025307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 08/04/2023] [Indexed: 09/20/2023]
Abstract
We introduce a basis set consisting of three-dimensional Deslauriers-Dubuc wavelets and solve numerically the Schrödinger equations of H and He atoms and molecules H_{2}, H_{2}^{+}, and LiH with Hartree-Fock and density functional theory (DFT) methods. We also compute the 2s and 2p excited states of hydrogen. The Coulomb singularity at the nucleus is handled by using a pseudopotential. The eigenvalue problem is solved with Arnoldi and Lanczos methods, Poisson equation with generalized minimal residual method and conjugate gradient on the normal equations methods, and matrix elements are computed using the biorthogonality relations of the interpolating wavelets. Performance is compared with those of CCCBDB and bigdft.
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Affiliation(s)
- Tommi Höynälänmaa
- Computational Physics, P. O. Box 692, FI-33014 Tampere University, Finland
| | - Tapio T Rantala
- Computational Physics, P. O. Box 692, FI-33014 Tampere University, Finland
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8
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Gerez S GA, Di Remigio Eikås R, Jensen SR, Bjørgve M, Frediani L. Cavity-Free Continuum Solvation: Implementation and Parametrization in a Multiwavelet Framework. J Chem Theory Comput 2023; 19:1986-1997. [PMID: 36933225 PMCID: PMC10100532 DOI: 10.1021/acs.jctc.2c01098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
Abstract
We present a multiwavelet-based implementation of a quantum/classical polarizable continuum model. The solvent model uses a diffuse solute-solvent boundary and a position-dependent permittivity, lifting the sharp-boundary assumption underlying many existing continuum solvation models. We are able to include both surface and volume polarization effects in the quantum/classical coupling, with guaranteed precision, due to the adaptive refinement strategies of our multiwavelet implementation. The model can account for complex solvent environments and does not need a posteriori corrections for volume polarization effects. We validate our results against a sharp-boundary continuum model and find a very good correlation of the polarization energies computed for the Minnesota solvation database.
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Affiliation(s)
- Gabriel A Gerez S
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | | | - Stig Rune Jensen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Magnar Bjørgve
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Luca Frediani
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
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9
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Liang J, Wang Z, Li J, Wong J, Liu X, Ganoe B, Head-Gordon T, Head-Gordon M. Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets. J Chem Theory Comput 2023. [PMID: 36594660 DOI: 10.1021/acs.jctc.2c00933] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.
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Affiliation(s)
- Jiashu Liang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Zhe Wang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Jie Li
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Jonathan Wong
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Xiao Liu
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Brad Ganoe
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Teresa Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
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10
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Lehtola S, Karttunen AJ. Free and open source software for computational chemistry education. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Susi Lehtola
- Molecular Sciences Software Institute Blacksburg Virginia USA
| | - Antti J. Karttunen
- Department of Chemistry and Materials Science Aalto University Espoo Finland
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11
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de Wijs GA, Kresse G, Havenith RWA, Marsman M. Comparing GIPAW with numerically exact chemical shieldings: The role of two-center contributions to the induced current. J Chem Phys 2021; 155:234101. [PMID: 34937373 DOI: 10.1063/5.0069637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this study, we benchmark density functional theory gauge-including projector-augmented-wave (GIPAW) chemical shieldings against molecular shieldings for which basis set completeness has been achieved [Jensen et al., Phys. Chem. Chem. Phys. 18, 21145 (2016)]. We demonstrate the importance of two-center corrections for GIPAW hydrogen shieldings. For the other nuclei studied, standard GIPAW is sufficiently accurate. We find that GIPAW can be pushed to closely approach the basis set limit. The only source of small inaccuracies lies in the contribution to the shielding that is caused by surface currents, which we estimate comparing GIPAW susceptibilities to converged molecular magnetizabilities.
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Affiliation(s)
- Gilles A de Wijs
- Radboud University, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands
| | - Georg Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Remco W A Havenith
- Stratingh Institute for Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
| | - Martijn Marsman
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Kolingasse 14-16, A-1090 Vienna, Austria
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12
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Brakestad A, Wind P, Jensen SR, Frediani L, Hopmann KH. Multiwavelets applied to metal-ligand interactions: Energies free from basis set errors. J Chem Phys 2021; 154:214302. [PMID: 34240981 DOI: 10.1063/5.0046023] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Transition metal-catalyzed reactions invariably include steps where ligands associate or dissociate. In order to obtain reliable energies for such reactions, sufficiently large basis sets need to be employed. In this paper, we have used high-precision multiwavelet calculations to compute the metal-ligand association energies for 27 transition metal complexes with common ligands, such as H2, CO, olefins, and solvent molecules. By comparing our multiwavelet results to a variety of frequently used Gaussian-type basis sets, we show that counterpoise corrections, which are widely employed to correct for basis set superposition errors, often lead to underbinding. Additionally, counterpoise corrections are difficult to employ when the association step also involves a chemical transformation. Multiwavelets, which can be conveniently applied to all types of reactions, provide a promising alternative for computing electronic interaction energies free from any basis set errors.
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Affiliation(s)
- Anders Brakestad
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Peter Wind
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Stig Rune Jensen
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Luca Frediani
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
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13
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Kottmann JS, Schleich P, Tamayo-Mendoza T, Aspuru-Guzik A. Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach. J Phys Chem Lett 2021; 12:663-673. [PMID: 33393305 DOI: 10.1021/acs.jpclett.0c03410] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 22 qubits where conventional representation would for the same systems require 40-100 or more qubits. We further demonstrate reductions in the quantum circuits through the structure of the pair-natural orbitals.
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Affiliation(s)
- Jakob S Kottmann
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada
- Department of Computer Science, University of Toronto, Toronto, Canada
| | - Philipp Schleich
- Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany
| | - Teresa Tamayo-Mendoza
- Department of Computer Science, University of Toronto, Toronto, Canada
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, United States
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada
- Department of Computer Science, University of Toronto, Toronto, Canada
- Vector Institute for Artificial Intelligence, Toronto, Canada
- Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow, Toronto, Canada
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14
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Jaszuński M, Sauer SPA, Faber R, Wilson DJD. NMR parameters of FNNF as a test for coupled-cluster methods: CCSDT shielding and CC3 spin-spin coupling. Phys Chem Chem Phys 2020; 22:21350-21359. [PMID: 32936148 DOI: 10.1039/d0cp02730h] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
NMR shielding and spin-spin coupling constants of cis and trans isomers of FNNF have been determined to near-quantitative accuracy from ab initio calculations. The FNNF system, containing multiple N-F bonds and fluorine atoms, provides a severe test of computational methods. Coupled-cluster methods were used with large basis sets and complete basis set (CBS) extrapolations of the equilibrium geometry results, with vibrational and relativistic corrections. Shielding constants were calculated with basis sets as large as aug-cc-pCV7Z, together with coupled-cluster expansions up to CCSDT, at the all-electron CCSD(T)/aug-cc-pCVQZ optimized geometries. Spin-spin coupling constants have been determined with specialized versions of the correlation consistent basis sets ccJ-pVXZ, further augmented with diffuse functions. All-electron coupled-cluster methods up to CC3 were applied in these calculations. The results of this work highlight the application of state-of-the-art theoretical techniques, and provide the most accurate NMR properties of FNNF to date, which can serve to guide and supplement NMR experimentation.
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Affiliation(s)
- Michał Jaszuński
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44-52, 01-224 Warsaw, Poland
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15
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Brakestad A, Jensen SR, Wind P, D'Alessandro M, Genovese L, Hopmann KH, Frediani L. Static Polarizabilities at the Basis Set Limit: A Benchmark of 124 Species. J Chem Theory Comput 2020; 16:4874-4882. [PMID: 32544327 PMCID: PMC7467643 DOI: 10.1021/acs.jctc.0c00128] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Abstract
![]()
Benchmarking molecular properties
with Gaussian-type orbital (GTO)
basis sets can be challenging, because one has to assume that the
computed property is at the complete basis set (CBS) limit, without
a robust measure of the error. Multiwavelet (MW) bases can be systematically
improved with a controllable error, which eliminates the need for
such assumptions. In this work, we have used MWs within Kohn–Sham
density functional theory to compute static polarizabilities for a
set of 92 closed-shell and 32 open-shell species. The results are
compared to recent benchmark calculations employing the GTO-type aug-pc4
basis set. We observe discrepancies between GTO and MW results for
several species, with open-shell systems showing the largest deviations.
Based on linear response calculations, we show that these discrepancies
originate from artifacts caused by the field strength and that several
polarizabilies from a previous study were contaminated by higher order
responses (hyperpolarizabilities). Based on our MW benchmark results,
we can affirm that aug-pc4 is able to provide results close to the
CBS limit, as long as finite difference effects can be controlled.
However, we suggest that a better approach is to use MWs, which are
able to yield precise finite difference polarizabilities even with
small field strengths.
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Affiliation(s)
- Anders Brakestad
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT, The Arctic University of Norway, 9037 Tromsø, Norway
| | - Stig Rune Jensen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT, The Arctic University of Norway, 9037 Tromsø, Norway
| | - Peter Wind
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT, The Arctic University of Norway, 9037 Tromsø, Norway
| | - Marco D'Alessandro
- Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italia
| | - Luigi Genovese
- Laboratoire de Simulation Atomistique, Université Grenoble Alpes, CEA, INAC-MEM, 38000 Grenoble, France
| | - Kathrin Helen Hopmann
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT, The Arctic University of Norway, 9037 Tromsø, Norway
| | - Luca Frediani
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT, The Arctic University of Norway, 9037 Tromsø, Norway
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16
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Cheeseman S, Christofferson AJ, Kariuki R, Cozzolino D, Daeneke T, Crawford RJ, Truong VK, Chapman J, Elbourne A. Antimicrobial Metal Nanomaterials: From Passive to Stimuli-Activated Applications. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2020; 7:1902913. [PMID: 32440470 PMCID: PMC7237851 DOI: 10.1002/advs.201902913] [Citation(s) in RCA: 124] [Impact Index Per Article: 31.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Revised: 01/23/2020] [Accepted: 02/22/2020] [Indexed: 05/20/2023]
Abstract
The development of antimicrobial drug resistance among pathogenic bacteria and fungi is one of the most significant health issues of the 21st century. Recently, advances in nanotechnology have led to the development of nanomaterials, particularly metals that exhibit antimicrobial properties. These metal nanomaterials have emerged as promising alternatives to traditional antimicrobial therapies. In this review, a broad overview of metal nanomaterials, their synthesis, properties, and interactions with pathogenic micro-organisms is first provided. Secondly, the range of nanomaterials that demonstrate passive antimicrobial properties are outlined and in-depth analysis and comparison of stimuli-responsive antimicrobial nanomaterials are provided, which represent the next generation of microbiocidal nanomaterials. The stimulus applied to activate such nanomaterials includes light (including photocatalytic and photothermal) and magnetic fields, which can induce magnetic hyperthermia and kinetically driven magnetic activation. Broadly, this review aims to summarize the currently available research and provide future scope for the development of metal nanomaterial-based antimicrobial technologies, particularly those that can be activated through externally applied stimuli.
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Affiliation(s)
- Samuel Cheeseman
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Nanobiotechnology LaboratorySchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
| | - Andrew J. Christofferson
- School of EngineeringRMIT UniversityMelbourneVIC3001Australia
- Food Science and TechnologyBundoora CampusSchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3086Australia
| | - Rashad Kariuki
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Nanobiotechnology LaboratorySchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
| | - Daniel Cozzolino
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Food Science and TechnologyBundoora CampusSchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3086Australia
| | - Torben Daeneke
- School of EngineeringRMIT UniversityMelbourneVIC3001Australia
| | - Russell J. Crawford
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Nanobiotechnology LaboratorySchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
| | - Vi Khanh Truong
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Nanobiotechnology LaboratorySchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
| | - James Chapman
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Nanobiotechnology LaboratorySchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
| | - Aaron Elbourne
- School of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
- Nanobiotechnology LaboratorySchool of ScienceCollege of ScienceEngineering and HealthRMIT UniversityMelbourneVIC3001Australia
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17
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Kang S, Woo J, Kim J, Kim H, Kim Y, Lim J, Choi S, Kim WY. ACE-Molecule: An open-source real-space quantum chemistry package. J Chem Phys 2020; 152:124110. [DOI: 10.1063/5.0002959] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sungwoo Kang
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Jeheon Woo
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Jaewook Kim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Hyeonsu Kim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Yongjun Kim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Jaechang Lim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Sunghwan Choi
- National Institute of Supercomputing and Network, Korea Institute of Science and Technology Information, 245 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Woo Youn Kim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
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18
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Lehtola S, Dimitrova M, Sundholm D. Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1597989] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Susi Lehtola
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| | - Maria Dimitrova
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki, Helsinki, Finland
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19
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Bischoff FA. Computing accurate molecular properties in real space using multiresolution analysis. ADVANCES IN QUANTUM CHEMISTRY 2019. [DOI: 10.1016/bs.aiq.2019.04.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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20
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Parkkinen P, Xu WH, Solala E, Sundholm D. Density Functional Theory under the Bubbles and Cube Numerical Framework. J Chem Theory Comput 2018; 14:4237-4245. [PMID: 29944363 PMCID: PMC6150645 DOI: 10.1021/acs.jctc.8b00456] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Density functional theory within the Kohn-Sham density functional theory (KS-DFT) ansatz has been implemented into our bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional (1D) numerical grids multiplied with spherical harmonics (bubbles). The remainder, i.e., the cube, which is the cusp-free and smooth difference between the atomic one-center contributions and the exact molecular function, is represented on a three-dimensional (3D) equidistant grid by using a tractable number of grid points. The implementation of the methods is demonstrated by performing 3D numerical KS-DFT calculations on light atoms and small molecules. The accuracy is assessed by comparing the obtained energies with the best available reference energies.
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Affiliation(s)
- Pauli Parkkinen
- Department of Chemistry , University of Helsinki , P.O. Box 55 ( A. I. Virtanens plats 1 ), FIN-00014 Helsinki , Finland
| | - Wen-Hua Xu
- Department of Chemistry , University of Helsinki , P.O. Box 55 ( A. I. Virtanens plats 1 ), FIN-00014 Helsinki , Finland.,College of Chemistry and Materials Science , Northwest University , Xi'an 710069 , China
| | - Eelis Solala
- Department of Chemistry , University of Helsinki , P.O. Box 55 ( A. I. Virtanens plats 1 ), FIN-00014 Helsinki , Finland
| | - Dage Sundholm
- Department of Chemistry , University of Helsinki , P.O. Box 55 ( A. I. Virtanens plats 1 ), FIN-00014 Helsinki , Finland.,Centre for Advanced Study at the Norwegian Academy of Science and Letters , Drammensveien 78 , N-0271 Oslo , Norway
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21
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Morgan WJ, Matthews DA, Ringholm M, Agarwal J, Gong JZ, Ruud K, Allen WD, Stanton JF, Schaefer HF. Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde. J Chem Theory Comput 2018; 14:1333-1350. [DOI: 10.1021/acs.jctc.7b01138] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- W. James Morgan
- Center for Computational Quantum Chemistry (CCQC), University of Georgia, Athens, Georgia 30602, United States
| | - Devin A. Matthews
- Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, Texas 78712, United States
| | - Magnus Ringholm
- Hylleraas Centre for Quantum Molecular Science, Department of Chemistry, University of Tromsø − The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Jay Agarwal
- Center for Computational Quantum Chemistry (CCQC), University of Georgia, Athens, Georgia 30602, United States
| | - Justin Z. Gong
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Kenneth Ruud
- Hylleraas Centre for Quantum Molecular Science, Department of Chemistry, University of Tromsø − The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Wesley D. Allen
- Center for Computational Quantum Chemistry (CCQC), University of Georgia, Athens, Georgia 30602, United States
| | - John F. Stanton
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry (CCQC), University of Georgia, Athens, Georgia 30602, United States
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22
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Stoychev GL, Auer AA, Izsák R, Neese F. Self-Consistent Field Calculation of Nuclear Magnetic Resonance Chemical Shielding Constants Using Gauge-Including Atomic Orbitals and Approximate Two-Electron Integrals. J Chem Theory Comput 2018; 14:619-637. [DOI: 10.1021/acs.jctc.7b01006] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Georgi L. Stoychev
- Max Planck Institute for Chemical Energy Conversion, 45470 Mülheim an der Ruhr, Germany
| | - Alexander A. Auer
- Max Planck Institute for Chemical Energy Conversion, 45470 Mülheim an der Ruhr, Germany
| | - Róbert Izsák
- Max Planck Institute for Chemical Energy Conversion, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max Planck Institute for Chemical Energy Conversion, 45470 Mülheim an der Ruhr, Germany
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23
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Field-Theodore TE, Olejniczak M, Jaszuński M, Wilson DJD. NMR shielding constants in group 15 trifluorides. Phys Chem Chem Phys 2018; 20:23025-23033. [DOI: 10.1039/c8cp04056g] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
By combining large basis and complete basis set (CBS) extrapolations of the coupled-cluster equilibrium geometry results with rovibrational and relativistic corrections, we demonstrate that it is possible to achieve near-quantitative accuracy for the NMR shielding constants in three group 15 trifluorides – NF3, PF3 and AsF3.
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Affiliation(s)
- Terri E. Field-Theodore
- Department of Chemistry and Physics
- La Trobe Institute for Molecular Science
- La Trobe University
- Melbourne
- Australia
| | | | - Michał Jaszuński
- Institute of Organic Chemistry
- Polish Academy of Sciences
- 01-224 Warszawa
- Poland
| | - David J. D. Wilson
- Department of Chemistry and Physics
- La Trobe Institute for Molecular Science
- La Trobe University
- Melbourne
- Australia
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24
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Kottmann JS, Bischoff FA. Coupled-Cluster in Real Space. 1. CC2 Ground State Energies Using Multiresolution Analysis. J Chem Theory Comput 2017; 13:5945-5955. [PMID: 28902997 DOI: 10.1021/acs.jctc.7b00694] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A framework to calculate CC2 approximated coupled-cluster ground state correlation energies in a multiresolution basis is derived and implemented into the MADNESS library. The CC2 working equations are formulated in first quantization which makes them suitable for real-space methods. The first quantized equations can be interpreted diagrammatically using the usual diagrams from second quantization with adjusted interpretation rules. Singularities arising from the nuclear and electronic potentials are regularized by explicitly taking the nuclear and electronic cusps into account. The regularized three- and six-dimensional cluster functions are represented directly on an adaptive grid. The resulting equations are free of singularities and virtual orbitals, which results in a low intrinsic scaling. Correlation energies close to the basis set limit are computed for small molecules. This work is the first step toward CC2 excitation energies in a multiresolution basis.
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Affiliation(s)
- Jakob S Kottmann
- Institut für Chemie, Humboldt-Universität zu Berlin , Unter den Linden 6, D-10099 Berlin, Germany
| | - Florian A Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin , Unter den Linden 6, D-10099 Berlin, Germany
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25
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Kottmann JS, Bischoff FA. Coupled-Cluster in Real Space. 2. CC2 Excited States Using Multiresolution Analysis. J Chem Theory Comput 2017; 13:5956-5965. [DOI: 10.1021/acs.jctc.7b00695] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jakob S. Kottmann
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
| | - Florian A. Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
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26
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Jensen SR, Saha S, Flores-Livas JA, Huhn W, Blum V, Goedecker S, Frediani L. The Elephant in the Room of Density Functional Theory Calculations. J Phys Chem Lett 2017; 8:1449-1457. [PMID: 28291362 DOI: 10.1021/acs.jpclett.7b00255] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.
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Affiliation(s)
- Stig Rune Jensen
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT - The Arctic University of Norway , N-9037 Tromsø, Norway
| | - Santanu Saha
- Department of Physics, Universität Basel , Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - José A Flores-Livas
- Department of Physics, Universität Basel , Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - William Huhn
- Department of Mechanical Engineering and Materials Science, Duke University , Durham, North Carolina 27708, United States
| | - Volker Blum
- Department of Mechanical Engineering and Materials Science, Duke University , Durham, North Carolina 27708, United States
| | - Stefan Goedecker
- Department of Physics, Universität Basel , Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Luca Frediani
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT - The Arctic University of Norway , N-9037 Tromsø, Norway
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27
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Bischoff FA. Analytic second nuclear derivatives of Hartree-Fock and DFT using multi-resolution analysis. J Chem Phys 2017; 146:124126. [PMID: 28388127 DOI: 10.1063/1.4978957] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We present the formalism, implementation, and numerical results for the computation of second derivatives with respect to nuclear displacements of molecules in the formalism of multi-resolution analysis. The highly singular nuclear potentials are partially regularized to improve the numerical stability. Vibrational frequencies are well reproduced to within an RMS of a few cm-1 compared to large basis set LCAO (linear combination of atomic orbitals) calculations. Intermolecular modes, hindered rotations, and heavy atoms may lead to loss of precision. Tight precision thresholds are therefore necessary to converge to numerically stable results.
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Affiliation(s)
- Florian A Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
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28
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Solala E, Losilla SA, Sundholm D, Xu W, Parkkinen P. Optimization of numerical orbitals using the Helmholtz kernel. J Chem Phys 2017; 146:084102. [PMID: 28249419 DOI: 10.1063/1.4976557] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present an integration scheme for optimizing the orbitals in numerical electronic structure calculations on general molecules. The orbital optimization is performed by integrating the Helmholtz kernel in the double bubble and cube basis, where bubbles represent the steep part of the functions in the vicinity of the nuclei, whereas the remaining cube part is expanded on an equidistant three-dimensional grid. The bubbles' part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kinds. The angular part of the bubble functions can be integrated analytically, whereas the radial part is integrated numerically. The cube part is integrated using a similar method as we previously implemented for numerically integrating two-electron potentials. The behavior of the integrand of the auxiliary dimension introduced by the integral transformation of the Helmholtz kernel has also been investigated. The correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations on H2, H2O, and CO. The obtained energies are compared with reference values in the literature showing that an accuracy of 10-4 to 10-7 Eh can be obtained with our approach.
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Affiliation(s)
- Eelis Solala
- Department of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats 1, FIN-00014 Helsinki, Finland
| | - Sergio A Losilla
- Department of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats 1, FIN-00014 Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats 1, FIN-00014 Helsinki, Finland
| | - Wenhua Xu
- Department of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats 1, FIN-00014 Helsinki, Finland
| | - Pauli Parkkinen
- Department of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats 1, FIN-00014 Helsinki, Finland
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29
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de Wijs GA, Laskowski R, Blaha P, Havenith RWA, Kresse G, Marsman M. NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations. J Chem Phys 2017; 146:064115. [DOI: 10.1063/1.4975122] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- G. A. de Wijs
- Radboud University, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands
| | - R. Laskowski
- Institute of High Performance Computing, A∗STAR, 1 Fusionopolis Way, #16-16, Connexis, Singapore 138632
| | - P. Blaha
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - R. W. A. Havenith
- Zernike Institute for Advanced Materials, Stratingh Institute for Chemistry, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
- Ghent Quantum Chemistry Group, Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - G. Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Sensengasse 8/12, A-1090 Vienna, Austria
| | - M. Marsman
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Sensengasse 8/12, A-1090 Vienna, Austria
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30
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Parkkinen P, Losilla SA, Solala E, Toivanen EA, Xu WH, Sundholm D. A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels. J Chem Theory Comput 2017; 13:654-665. [PMID: 28094984 DOI: 10.1021/acs.jctc.6b01207] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid. The integration of the bubbles part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H2, H2O, and CO. Our calculations show that an accuracy of 10-4 to 10-7 Eh can be reached in HF-SCF calculations on general molecules.
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Affiliation(s)
- Pauli Parkkinen
- Department of Chemistry, University of Helsinki , P.O. Box 55, A. I. Virtanens plats 1, Helsinki FIN-00014, Finland
| | - Sergio A Losilla
- Department of Chemistry, University of Helsinki , P.O. Box 55, A. I. Virtanens plats 1, Helsinki FIN-00014, Finland
| | - Eelis Solala
- Department of Chemistry, University of Helsinki , P.O. Box 55, A. I. Virtanens plats 1, Helsinki FIN-00014, Finland
| | - Elias A Toivanen
- Department of Chemistry, University of Helsinki , P.O. Box 55, A. I. Virtanens plats 1, Helsinki FIN-00014, Finland
| | - Wen-Hua Xu
- Department of Chemistry, University of Helsinki , P.O. Box 55, A. I. Virtanens plats 1, Helsinki FIN-00014, Finland
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki , P.O. Box 55, A. I. Virtanens plats 1, Helsinki FIN-00014, Finland
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31
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Anelli M, Ringholm M, Ruud K. Gauge-origin independent calculations of electric-field-induced second-harmonic generation circular intensity difference using London atomic orbitals. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1249979] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Marco Anelli
- Center for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø, Tromsø, Norway
| | - Magnus Ringholm
- Center for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø, Tromsø, Norway
| | - Kenneth Ruud
- Center for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromsø, Tromsø, Norway
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32
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Amos R, Kobayashi R. Ab Initio NMR Chemical Shift Calculations Using Fragment Molecular Orbitals and Locally Dense Basis Sets. J Phys Chem A 2016; 120:8907-8915. [DOI: 10.1021/acs.jpca.6b09190] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Roger Amos
- Australian National University, Leonard Huxley Bldg 56, Mills Rd, Canberra, ACT 2601, Australia
| | - Rika Kobayashi
- Australian National University, Leonard Huxley Bldg 56, Mills Rd, Canberra, ACT 2601, Australia
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