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Fauser S, Drontschenko V, Ochsenfeld C, Görling A. Accurate NMR Shieldings with σ-Functionals. J Chem Theory Comput 2024; 20:6028-6036. [PMID: 38967385 DOI: 10.1021/acs.jctc.4c00512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/06/2024]
Abstract
In recent years, density-functional methods relying on a new type of fifth-rung correlation functionals called σ-functionals have been introduced. σ-Functionals are technically closely related to the random phase approximation and require the same computational effort but yield distinctively higher accuracies for reaction and transition state energies of main group chemistry and even outperform double-hybrid functionals for these energies. In this work, we systematically investigate how accurate σ-functionals can describe nuclear magnetic resonance (NMR) shieldings. It turns out that σ-functionals yield very accurate NMR shieldings, even though in their optimization, exclusively, energies are employed as reference data and response properties such as NMR shieldings are not involved at all. This shows that σ-functionals combine universal applicability with accuracy. Indeed, the NMR shieldings from a σ-functional using input orbitals and eigenvalues from Kohn-Sham calculations with the exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE) turned out to be the most accurate ones among the NMR shieldings calculated with various density-functional methods including methods using double-hybrid functionals. That σ-functionals can be used for calculating both reliable energies and response properties like NMR shieldings characterizes them as all-purpose functionals, which is appealing from an application point of view.
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Affiliation(s)
- Steffen Fauser
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
- Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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Fauser S, Förster A, Redeker L, Neiss C, Erhard J, Trushin E, Görling A. Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals. J Chem Theory Comput 2024; 20:2404-2422. [PMID: 38466924 DOI: 10.1021/acs.jctc.3c01132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.
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Affiliation(s)
- Steffen Fauser
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
| | - Leon Redeker
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Christian Neiss
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Jannis Erhard
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
- Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
- Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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Drontschenko V, Bangerter FH, Ochsenfeld C. Analytical Second-Order Properties for the Random Phase Approximation: Nuclear Magnetic Resonance Shieldings. J Chem Theory Comput 2023; 19:7542-7554. [PMID: 37863033 DOI: 10.1021/acs.jctc.3c00542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2023]
Abstract
A method for the analytical computation of nuclear magnetic resonance (NMR) shieldings within the direct random phase approximation (RPA) is presented. As a starting point, we use the RPA ground-state energy expression within the resolution-of-the-identity approximation in the atomic-orbital formalism. As has been shown in a recent benchmark study using numerical second derivatives [Glasbrenner, M. J. Chem. Theory Comput. 2022, 18, 192], RPA based on a Hartree-Fock reference shows accuracies comparable to coupled cluster singles and doubles (CCSD) for NMR chemical shieldings. Together with the much lower computational cost of RPA, it has emerged as an accurate method for the computation of NMR shieldings. Therefore, we aim to extend the applicability of RPA NMR to larger systems by introducing analytical second-order derivatives, making it a viable method for the accurate and efficient computation of NMR chemical shieldings.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Felix H Bangerter
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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Drontschenko V, Graf D, Laqua H, Ochsenfeld C. Efficient Method for the Computation of Frozen-Core Nuclear Gradients within the Random Phase Approximation. J Chem Theory Comput 2022; 18:7359-7372. [PMID: 36331398 DOI: 10.1021/acs.jctc.2c00774] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
A method for the evaluation of analytical frozen-core gradients within the random phase approximation is presented. We outline an efficient way to evaluate the response of the density of active electrons arising only when introducing the frozen-core approximation and constituting the main difficulty, together with the response of the standard Kohn-Sham density. The general framework allows to extend the outlined procedure to related electron correlation methods in the atomic orbital basis that require the evaluation of density responses, such as second-order Møller-Plesset perturbation theory or coupled cluster variants. By using Cholesky decomposed densities─which reintroduce the occupied index in the time-determining steps─we are able to achieve speedups of 20-30% (depending on the size of the basis set) by using the frozen-core approximation, which is of similar magnitude as for molecular orbital formulations. We further show that the errors introduced by the frozen-core approximation are practically insignificant for molecular geometries.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Henryk Laqua
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany.,Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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