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Wong J, Ganoe B, Liu X, Neudecker T, Lee J, Liang J, Wang Z, Li J, Rettig A, Head-Gordon T, Head-Gordon M. An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3. J Chem Phys 2023; 158:164116. [PMID: 37114707 PMCID: PMC10148725 DOI: 10.1063/5.0145130] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Accepted: 04/10/2023] [Indexed: 04/29/2023] Open
Abstract
We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.
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Affiliation(s)
- Jonathan Wong
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Brad Ganoe
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Xiao Liu
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Tim Neudecker
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Joonho Lee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Jiashu Liang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Zhe Wang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Jie Li
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Adam Rettig
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
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Manian A, Hudson RJ, Ramkissoon P, Smith TA, Russo SP. Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants. J Chem Theory Comput 2023; 19:271-292. [PMID: 36490305 DOI: 10.1021/acs.jctc.2c00888] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S1 → S0 transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 106-1016 s-1 compared with an experimental rate of the order 107 s-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.
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Affiliation(s)
- Anjay Manian
- ARC Centre of Excellence in Exciton Science, School of Science, RMIT University, Melbourne3000, Australia
| | - Rohan J Hudson
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Melbourne, Parkville3010, Australia
| | - Pria Ramkissoon
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Melbourne, Parkville3010, Australia
| | - Trevor A Smith
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Melbourne, Parkville3010, Australia
| | - Salvy P Russo
- ARC Centre of Excellence in Exciton Science, School of Science, RMIT University, Melbourne3000, Australia
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Franzke YJ, Holzer C. Communication: Impact of the current density on paramagnetic NMR properties. J Chem Phys 2022; 157:031102. [DOI: 10.1063/5.0103898] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals generally depend on the kinetic energy density τ. For magnetic properties, this necessitates generalizations to ensure gauge invariance. In most implementations, τ is generalized by incorporating the external magnetic field. However, this introduces artifacts in the response of the density matrix and does not satisfy the iso-orbital constraint. Here, we extend previous approaches based on the current density to paramagnetic NMR shieldings and EPR g-tensors. The impact is assessed for main-group compounds and transition-metal complexes considering 25 density functional approximations. It is shown that the current density leads to substantial improvements-especially for the popular Minnesota and SCAN functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs.
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Affiliation(s)
- Yannick J. Franzke
- Fachbereich Chemie, Philipps-Universität Marburg Fachbereich Chemie, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruher Institut für Technologie Fakultät für Physik, Germany
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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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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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Summa FF, Monaco G, Zanasi R, Lazzeretti P. Dynamic Toroidisability as Ubiquitous Property of Atoms and Molecules in Optical Electric Fields. J Chem Phys 2022; 156:054106. [DOI: 10.1063/5.0082731] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Guglielmo Monaco
- Dipartimento di Chimica, Università degli Studi di Salerno Dipartimento di Chimica e Biologia, Italy
| | - Riccardo Zanasi
- Chemistry and Biology, University of Salerno Department of Chemistry and Biology, Italy
| | - Paolo Lazzeretti
- University of Salerno Department of Chemistry and Biology, Italy
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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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Summa FF, Monaco G, Lazzeretti P, Zanasi R. Assessment of the performance of DFT functionals in the fulfillment of off-diagonal hypervirial relationships. Phys Chem Chem Phys 2021; 23:15268-15274. [PMID: 34240095 DOI: 10.1039/d1cp01298c] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way to test electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relationships were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen for this purpose, adopting a large basis set to ensure high quality results. A partial agreement with previous benchmarks is observed.
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Affiliation(s)
- Francesco F Summa
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
| | - Guglielmo Monaco
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
| | - Paolo Lazzeretti
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
| | - Riccardo Zanasi
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
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