1
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Drontschenko V, Ochsenfeld C. Low-Scaling, Efficient and Memory Optimized Computation of Nuclear Magnetic Resonance Shieldings within the Random Phase Approximation Using Cholesky-Decomposed Densities and an Attenuated Coulomb Metric. J Phys Chem A 2024; 128:7950-7965. [PMID: 39239944 PMCID: PMC11421095 DOI: 10.1021/acs.jpca.4c02773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2024] [Revised: 08/12/2024] [Accepted: 08/19/2024] [Indexed: 09/07/2024]
Abstract
An efficient method for the computation of nuclear magnetic resonance (NMR) shielding tensors within the random phase approximation (RPA) is presented based on our recently introduced resolution-of-the-identity (RI) atomic orbital RPA NMR method [Drontschenko, V. J. Chem. Theory Comput. 2023, 19, 7542-7554] utilizing Cholesky decomposed density type matrices and employing an attenuated Coulomb RI metric. The introduced sparsity is efficiently exploited using sparse matrix algebra. This allows for an efficient and low-scaling computation of RPA NMR shielding tensors. Furthermore, we introduce a batching method for the computation of memory demanding intermediates that accounts for their sparsity. This extends the applicability of our method to even larger systems that would have been out of reach before, such as, e.g., a DNA strand with 260 atoms and 3408 atomic orbital basis functions.
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Affiliation(s)
- 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
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2
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Ramos SA, Mueller LJ, Beran GJO. The interplay of density functional selection and crystal structure for accurate NMR chemical shift predictions. Faraday Discuss 2024. [PMID: 39258864 DOI: 10.1039/d4fd00072b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/12/2024]
Abstract
Ab initio chemical shift prediction plays a central role in nuclear magnetic resonance (NMR) crystallography, and the accuracy with which chemical shifts can be predicted relative to experiment impacts the confidence with which structures can be assigned. For organic crystals, periodic density functional theory calculations with the gauge-including projector augmented wave (GIPAW) approximation and the PBE functional are widely used at present. Many previous studies have examined how using more advanced density functionals can increase the accuracy of predicted chemical shifts relative to experiment, but nearly all of those studies employed crystal structures that were optimized with generalized-gradient approximation (GGA) functionals. Here, we investigate how the accuracy of the predicted chemical shifts in organic crystals is affected by replacing GGA-level PBE-D3(BJ) crystal geometries with more accurate hybrid functional PBE0-D3(BJ) ones. Based on benchmark data sets containing 132 13C and 35 15N chemical shifts, plus case studies on testosterone, acetaminophen, and phenobarbital, we find that switching from GGA-level geometries and chemical shifts to hybrid-functional ones reduces 13C and 15N chemical shift errors by ∼40-60% versus experiment. However, most of the improvement stems from the use of the hybrid functional for the chemical shift calculations, rather than from the refined geometries. In addition, even with the improved geometries, we find that double-hybrid functionals still do not systematically increase chemical shift agreement with experiment beyond what hybrid functionals provide. In the end, these results suggest that the combination of GGA-level crystal structures and hybrid-functional chemical shifts represents a particularly cost-effective combination for NMR crystallography in organic systems.
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Affiliation(s)
- Sebastian A Ramos
- Department of Chemistry, University of California Riverside, Riverside, CA 92521, USA.
| | - Leonard J Mueller
- Department of Chemistry, University of California Riverside, Riverside, CA 92521, USA.
| | - Gregory J O Beran
- Department of Chemistry, University of California Riverside, Riverside, CA 92521, USA.
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3
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Zhang X, Li C, Ye HZ, Berkelbach TC, Chan GKL. Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics. J Chem Phys 2024; 161:014109. [PMID: 38949583 DOI: 10.1063/5.0212274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.
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Affiliation(s)
- Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Chenghan Li
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | | | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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4
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Wilhelmer R, Diez M, Krondorfer JK, Hauser AW. Molecular Pseudorotation in Phthalocyanines as a Tool for Magnetic Field Control at the Nanoscale. J Am Chem Soc 2024; 146:14620-14632. [PMID: 38743819 PMCID: PMC11140746 DOI: 10.1021/jacs.4c01915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Revised: 04/29/2024] [Accepted: 04/30/2024] [Indexed: 05/16/2024]
Abstract
Metal phthalocyanines, a highly versatile class of aromatic, planar, macrocyclic molecules with a chelated central metal ion, are topical objects of ongoing research and particularly interesting due to their magnetic properties. However, while the current focus lies almost exclusively on spin-Zeeman-related effects, the high symmetry of the molecule and its circular shape suggests the exploitation of light-induced excitation of 2-fold degenerate vibrational states in order to generate, switch, and manipulate magnetic fields at the nanoscale. The underlying mechanism is a molecular pseudorotation that can be triggered by infrared pulses and gives rise to a quantized, small, but controllable magnetic dipole moment. We investigate the optical stimulation of vibrationally induced molecular magnetism and estimate changes in the magnetic shielding constants for confirmation by future experiments.
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Affiliation(s)
- Raphael Wilhelmer
- Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria
| | - Matthias Diez
- Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria
| | - Johannes K Krondorfer
- Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria
| | - Andreas W Hauser
- Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria
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5
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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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6
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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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7
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Iuliucci RJ, Hartman JD, Beran GJO. Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids? J Phys Chem A 2023; 127:2846-2858. [PMID: 36940431 DOI: 10.1021/acs.jpca.2c07657] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/22/2023]
Abstract
Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller-Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental 13C and 15N chemical shifts and 114 17O and 14N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew-Burke-Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.
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Affiliation(s)
- Robbie J Iuliucci
- Department of Chemistry, Washington and Jefferson College, Washington, Pennsylvania 15301 United States
| | - Joshua D Hartman
- Department of Chemistry, University of California, Riverside, California 92521 United States
| | - Gregory J O Beran
- Department of Chemistry, University of California, Riverside, California 92521 United States
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8
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DFT calculations of 1H- and 13C-NMR chemical shifts of 3-methyl-1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine in solution. Sci Rep 2022; 12:17798. [PMID: 36273019 PMCID: PMC9588065 DOI: 10.1038/s41598-022-22900-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Accepted: 10/20/2022] [Indexed: 01/19/2023] Open
Abstract
Geometries of the 3-methyl-1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine azo-dye compound and its tautomer were optimized using B3LYP and M06-2X functionals in coupling with TZVP and 6-311 + G(d,p) basis sets. The 1H- and 13C-NMR chemical shifts of all species were predicted using 13 density functional theory (DFT) approaches in coupling with TZVP and 6-311 + G(d,p) basis sets at the different optimized geometries by applying the using GIAO method using the eight geometries. The selected functionals are characterized by having different amount of Hartree-Fock exchange. The selected DFT methods were B3LYP, M06-2X, BP86, B97XD, TPSSTPSS, PBE1PBE, CAM-B3LYP, wB97XD, LSDA, HSEH1PBE, PW91PW91, LC-WPBE, and B3PW91. The results obtained were compared with the available experimental data using different statistical descriptors such as root mean square error (RMSE) and maximum absolute error (MAE). Results revealed that the prediction of the 1H-NMR chemical shifts has more significant dependence on the applied geometry than that of the prediction of the 13C-NMR chemical shifts. Among all the examined functionals, B97D and TPSSTPSS functionals were found to be the most accurate ones, while the M06-2X functional is the least accurate one. Results also revealed that the prediction of NMR chemical shifts using TZVP basis sets results is more accurate results than 6-311 + G(2d,p) basis set.
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9
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Yan W, Xu X. Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals. J Chem Theory Comput 2022; 18:2931-2946. [PMID: 35467852 DOI: 10.1021/acs.jctc.2c00055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for 13C, 15N, 17O, 19F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for 1H and 13C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental 13C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.
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Affiliation(s)
- Wenjie Yan
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
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10
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Poidevin C, Stoychev GL, Riplinger C, Auer AA. High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants. J Chem Theory Comput 2022; 18:2408-2417. [PMID: 35353527 PMCID: PMC9009078 DOI: 10.1021/acs.jctc.1c01095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2021] [Indexed: 11/29/2022]
Abstract
In this work, we present a quantum mechanics/molecular mechanics (QM/MM) approach for the computation of solid-state nuclear magnetic resonance (SS-NMR) shielding constants (SCs) for molecular crystals. Besides applying standard-DFT functionals like GGAs (PBE), meta-GGAs (TPSS), and hybrids (B3LYP), we apply a double-hybrid (DSD-PBEP86) functional as well as MP2, using the domain-based local pair natural orbital (DLPNO) formalism, to calculate the NMR SCs of six amino acid crystals. All the electronic structure methods used exhibit good correlation of the NMR shieldings with respect to experimental chemical shifts for both 1H and 13C. We also find that local electronic structure is much more important than the long-range electrostatic effects for these systems, implying that cluster approaches using all-electron/Gaussian basis set methods might offer great potential for predictive computations of solid-state NMR parameters for organic solids.
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Affiliation(s)
- Corentin Poidevin
- Institut
des Sciences Chimiques de Rennes, Av. Général Leclerc, 357000 Rennes, France
| | - Georgi L. Stoychev
- Max-Planck-Institut
für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | | | - Alexander A. Auer
- Max-Planck-Institut
für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
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11
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Glasbrenner M, Vogler S, Ochsenfeld C. Efficient low-scaling computation of NMR shieldings at the second-order Møller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric. J Chem Phys 2021; 155:224107. [PMID: 34911319 DOI: 10.1063/5.0069956] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller-Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller-Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Sigurd Vogler
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
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12
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Glasbrenner M, Graf D, Ochsenfeld C. Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings. J Chem Theory Comput 2021; 18:192-205. [PMID: 34898213 DOI: 10.1021/acs.jctc.1c00866] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A method for computing NMR shieldings with the direct random phase approximation (RPA) and the closely related σ-functionals [Trushin, E.; Thierbach, A.; Görling, A. Toward chemical accuracy at low computational cost: density functional theory with σ-functionals for the correlation energy. J. Chem. Phys. 2021, 154, 014104] is presented, which is based on a finite-difference approach. The accuracy is evaluated in benchmark calculations using high-quality coupled cluster values as a reference. Our results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional. NMR shieldings computed with direct RPA using a Hartree-Fock reference are significantly more accurate than MP2 shieldings and comparable to CCSD shieldings. Also, the basis set convergence is analyzed and it is shown that at least triple-zeta basis sets are required for reliable results.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany.,Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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13
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Mauksch M, Tsogoeva SB. Disclosure of Ground-State Zimmerman-Möbius Aromaticity in the Radical Anion of [6]Helicene and Evidence for 4π Periodic Aromatic Ring Currents in a Molecular "Metallic" Möbius Strip. Chemistry 2021; 27:14660-14671. [PMID: 34375466 PMCID: PMC8596793 DOI: 10.1002/chem.202102230] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Indexed: 12/19/2022]
Abstract
In 1966, Zimmerman proposed a type of Möbius aromaticity that involves through-space electron delocalization; it has since been widely applied to explain reactivity in pericyclic reactions, but is considered to be limited to transition-state structures. Although the easily accessible hexahelicene radical anion has been known for more than half a century, it was overlooked that it exhibits a ground-state minimum and robust Zimmerman-Möbius aromaticity in its central noose-like opening, becoming, hence, the oldest existing Möbius aromatic system and with smallest Möbius cycle known. Despite its overall aromatic stabilization energy of 13.6 kcal mol-1 (at B3LYP/6-311+G**), the radical also features a strong, globally induced paramagnetic ring current along its outer edge. Exclusive global paramagnetic currents can also be found in other fully delocalized radical anions of 4N+2 π-electron aromatic polycyclic benzenoid hydrocarbons (PAH), thus questioning the established magnetic criterion of antiaromaticity. As an example of a PAH with nontrivial topology, we studied a novel Möbius[16]cyclacene that has a non-orientable surface manifold and a stable closed-shell singlet ground state at several density functional theory levels. Its metallic monoanion radical (0.0095 eV band gap at HSE06/6-31G* level) is also wave-function stable and displays an unusual 4π-periodic, magnetically induced ring current (reminiscent of the transformation behaviour of spinors under spatial rotation), thus indicating the existence of a new, Hückel-rule-evading type of aromaticity.
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Affiliation(s)
- Michael Mauksch
- Department of Chemistry and PharmacyInstitute of Theoretical ChemistryComputer Chemistry CenterFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)Nägelsbachstrasse 25a91052ErlangenGermany
| | - Svetlana B. Tsogoeva
- Department of Chemistry and PharmacyOrganic Chemistry Chair I andInterdisciplinary Center for Molecular Materials (ICMM)Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)Nikolaus-Fiebinger Str. 1091058ErlangenGermany
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14
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Stauch T, Ganoe B, Wong J, Lee J, Rettig A, Liang J, Li J, Epifanovsky E, Head-Gordon T, Head-Gordon M. Molecular magnetisabilities computed via finite fields: assessing alternatives to MP2 and revisiting magnetic exaltations in aromatic and antiaromatic species. Mol Phys 2021; 119. [DOI: 10.1080/00268976.2021.1990426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Tim Stauch
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Brad Ganoe
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Jonathan Wong
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Joonho Lee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Adam Rettig
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Jiashu Liang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Jie Li
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | | | - Teresa Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
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15
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Burger S, Lipparini F, Gauss J, Stopkowicz S. NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals. J Chem Phys 2021; 155:074105. [PMID: 34418917 DOI: 10.1063/5.0059633] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We report on a formulation and implementation of a scheme to compute nuclear magnetic resonance (NMR) shieldings at second-order Møller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed and perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field and for the computed NMR shieldings, before we illustrate the applicability of our CD-based GIAO-MP2 scheme in calculations involving up to about 100 atoms and more than 1000 basis functions.
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Affiliation(s)
- Sophia Burger
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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16
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Stoychev GL, Auer AA, Gauss J, Neese F. DLPNO-MP2 second derivatives for the computation of polarizabilities and NMR shieldings. J Chem Phys 2021; 154:164110. [PMID: 33940835 DOI: 10.1063/5.0047125] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole polarizabilities. Relative deviations from the resolution of the identity-based MP2 (RI-MP2) reference for both properties are below 0.5% with the default truncation thresholds. For large systems, our implementation achieves quadratic effective scaling, is more efficient than RI-MP2 starting at 280 correlated electrons, and is never more than 5-20 times slower than the equivalent Hartree-Fock property calculation. The largest calculation performed here was on the vancomycin molecule with 176 atoms, 542 correlated electrons, and 4700 basis functions and took 3.3 days on 12 central processing unit cores.
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Affiliation(s)
- Georgi L Stoychev
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Alexander A Auer
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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17
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Dittmer A, Stoychev GL, Maganas D, Auer AA, Neese F. Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2. J Chem Theory Comput 2020; 16:6950-6967. [PMID: 32966067 PMCID: PMC7659039 DOI: 10.1021/acs.jctc.0c00067] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
In
this work, we explore the accuracy of post-Hartree–Fock
(HF) methods and double-hybrid density functional theory (DFT) for
the computation of solid-state NMR chemical shifts. We apply an embedded
cluster approach and investigate the convergence with cluster size
and embedding for a series of inorganic solids with long-range electrostatic
interactions. In a systematic study, we discuss the cluster design,
the embedding procedure, and basis set convergence using gauge-including
atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of
theory. We demonstrate that the accuracy obtained for the prediction
of NMR chemical shifts, which can be achieved for molecular systems,
can be carried over to solid systems. An appropriate embedded cluster
approach allows one to apply methods beyond standard DFT even for
systems for which long-range electrostatic effects are important. We find that an embedded
cluster should include at least one sphere of explicit neighbors around
the nuclei of interest, given that a sufficiently large point charge
and boundary effective potential embedding is applied. Using the pcSseg-3
basis set and GIAOs for the computation of nuclear shielding constants,
accuracies of 1.6 ppm for 7Li, 1.5 ppm for 23Na, and 5.1 ppm for 39K as well as 9.3 ppm for 19F, 6.5 ppm for 35Cl, 7.4 ppm for 79Br, and
7.5 ppm for 25Mg as well as 3.8 ppm for 67Zn
can be achieved with MP2. Comparing various DFT functionals with HF
and MP2, we report the superior quality of results for methods that
include post-HF correlation like MP2 and double-hybrid DFT.
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Affiliation(s)
- Anneke Dittmer
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Georgi L Stoychev
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Dimitrios Maganas
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Alexander A Auer
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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18
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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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19
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Pinski P, Neese F. Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2). J Chem Phys 2019; 150:164102. [DOI: 10.1063/1.5086544] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Peter Pinski
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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20
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Dornbach M, Werner HJ. Analytical energy gradients for local second-order Møller-Plesset perturbation theory using intrinsic bond orbitals. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1537529] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Mark Dornbach
- Institut für Theoretische Chemie, Universität Stuttgart, Stuttgart, Germany
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21
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Stoychev GL, Auer AA, Neese F. Efficient and Accurate Prediction of Nuclear Magnetic Resonance Shielding Tensors with Double-Hybrid Density Functional Theory. J Chem Theory Comput 2018; 14:4756-4771. [DOI: 10.1021/acs.jctc.8b00624] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Georgi L. Stoychev
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr 45470, Germany
| | - Alexander A. Auer
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr 45470, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr 45470, Germany
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22
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Pinski P, Neese F. Communication: Exact analytical derivatives for the domain-based local pair natural orbital MP2 method (DLPNO-MP2). J Chem Phys 2018; 148:031101. [PMID: 29352787 DOI: 10.1063/1.5011204] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electron correlation methods based on pair natural orbitals (PNOs) have gained an increasing degree of interest in recent years, as they permit energy calculations to be performed on systems containing up to many hundred atoms, while maintaining chemical accuracy for reaction energies. We present an approach for taking exact analytical first derivatives of the energy contributions in the simplest method of the family of Domain-based Local Pair Natural Orbital (DLPNO) methods, closed-shell DLPNO-MP2. The Lagrangian function contains constraints to account for the relaxation of PNOs. RI-MP2 reference geometries are reproduced accurately, as exemplified for four systems with a substantial degree of nonbonding interactions. By the example of electric field gradients, we demonstrate that omitting PNO-specific constraints can lead to dramatic errors for orbital-relaxed properties.
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Affiliation(s)
- Peter Pinski
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
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23
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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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24
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Nagy PR, Kállay M. Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform. J Chem Phys 2017; 146:214106. [PMID: 28576082 PMCID: PMC5453808 DOI: 10.1063/1.4984322] [Citation(s) in RCA: 70] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2017] [Accepted: 05/05/2017] [Indexed: 01/30/2023] Open
Abstract
An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.
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Affiliation(s)
- Péter R Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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25
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Hoffmann F, Li DW, Sebastiani D, Brüschweiler R. Improved Quantum Chemical NMR Chemical Shift Prediction of Metabolites in Aqueous Solution toward the Validation of Unknowns. J Phys Chem A 2017; 121:3071-3078. [PMID: 28388058 DOI: 10.1021/acs.jpca.7b01954] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
A quantum-chemistry based protocol, termed MOSS-DFT, is presented for the prediction of 13C and 1H NMR chemical shifts of a wide range of organic molecules in aqueous solution, including metabolites. Molecular motif-specific linear scaling parameters are reported for five different density functional theory (DFT) methods (B97-2/pcS-1, B97-2/pcS-2, B97-2/pcS-3, B3LYP/pcS-2, and BLYP/pcS-2), which were applied to a large set of 176 metabolite molecules. The chemical shift root-mean-square deviations (RMSD) for the best method, B97-2/pcS-3, are 1.93 and 0.154 ppm for 13C and 1H chemical shifts, respectively. Excellent results have been obtained for chemical shifts of methyl and aromatic 13C and 1H that are not directly bonded to a heteroatom (O, N, S, or P) with RMSD values of 1.15/0.079 and 1.31/0.118 ppm, respectively. This study not only demonstrates how NMR chemical shift in aqueous environment can be improved over the commonly used global linear scaling approach, but also allows for motif-specific error estimates, which are useful for an improved chemical shift-based verification of metabolite candidates of metabolomics samples containing unknown components.
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Affiliation(s)
- Felix Hoffmann
- Institute of Chemistry, Martin-Luther-University Halle-Wittenberg , von-Danckelmann-Platz 4, 06120 Halle, Germany
| | - Da-Wei Li
- Campus Chemical Instrument Center, The Ohio State University , Columbus, Ohio 43210, United States
| | - Daniel Sebastiani
- Institute of Chemistry, Martin-Luther-University Halle-Wittenberg , von-Danckelmann-Platz 4, 06120 Halle, Germany
| | - Rafael Brüschweiler
- Campus Chemical Instrument Center, The Ohio State University , Columbus, Ohio 43210, United States.,Department of Chemistry and Biochemistry, The Ohio State University , Columbus, Ohio 43210, United States.,Department of Biological Chemistry and Pharmacology, The Ohio State University , Columbus, Ohio 43210, United States
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26
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Jose KVJ, Raghavachari K. Fragment-Based Approach for the Evaluation of NMR Chemical Shifts for Large Biomolecules Incorporating the Effects of the Solvent Environment. J Chem Theory Comput 2017; 13:1147-1158. [DOI: 10.1021/acs.jctc.6b00922] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- K. V. Jovan Jose
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Krishnan Raghavachari
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
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27
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Kumar C, Kjærgaard T, Helgaker T, Fliegl H. Nuclei-selected atomic-orbital response-theory formulation for the calculation of NMR shielding tensors using density-fitting. J Chem Phys 2016; 145:234108. [DOI: 10.1063/1.4972212] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Chandan Kumar
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
| | - Thomas Kjærgaard
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Trygve Helgaker
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
| | - Heike Fliegl
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
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28
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Hartman J, Day GM, Beran GJO. Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions. CRYSTAL GROWTH & DESIGN 2016; 16:6479-6493. [PMID: 27829821 PMCID: PMC5095663 DOI: 10.1021/acs.cgd.6b01157] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2016] [Revised: 09/09/2016] [Indexed: 05/10/2023]
Abstract
Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state 13C and 15N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.
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Affiliation(s)
- Joshua
D. Hartman
- Department
of Chemistry, University of California, Riverside, California 92521 United States
| | - Graeme M. Day
- School
of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Gregory J. O. Beran
- Department
of Chemistry, University of California, Riverside, California 92521 United States
- E-mail:
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29
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Nagy PR, Samu G, Kállay M. An Integral-Direct Linear-Scaling Second-Order Møller-Plesset Approach. J Chem Theory Comput 2016; 12:4897-4914. [PMID: 27618512 DOI: 10.1021/acs.jctc.6b00732] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An integral-direct, iteration-free, linear-scaling, local second-order Møller-Plesset (MP2) approach is presented, which is also useful for spin-scaled MP2 calculations as well as for the efficient evaluation of the perturbative terms of double-hybrid density functionals. The method is based on a fragmentation approximation: the correlation contributions of the individual electron pairs are evaluated in domains constructed for the corresponding localized orbitals, and the correlation energies of distant electron pairs are computed with multipole expansions. The required electron repulsion integrals are calculated directly invoking the density fitting approximation; the storage of integrals and intermediates is avoided. The approach also utilizes natural auxiliary functions to reduce the size of the auxiliary basis of the domains and thereby the operation count and memory requirement. Our test calculations show that the approach recovers 99.9% of the canonical MP2 correlation energy and reproduces reaction energies with an average (maximum) error below 1 kJ/mol (4 kJ/mol). Our benchmark calculations demonstrate that the new method enables MP2 calculations for molecules with more than 2300 atoms and 26000 basis functions on a single processor.
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Affiliation(s)
- Péter R Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics , P.O. Box 91, Budapest H-1521, Hungary
| | - Gyula Samu
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics , P.O. Box 91, Budapest H-1521, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics , P.O. Box 91, Budapest H-1521, Hungary
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30
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Sumowski CV, Hanni M, Schweizer S, Ochsenfeld C. Sensitivity of ab Initio vs Empirical Methods in Computing Structural Effects on NMR Chemical Shifts for the Example of Peptides. J Chem Theory Comput 2015; 10:122-33. [PMID: 26579896 DOI: 10.1021/ct400713t] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The structural sensitivity of NMR chemical shifts as computed by quantum chemical methods is compared to a variety of empirical approaches for the example of a prototypical peptide, the 38-residue kaliotoxin KTX comprising 573 atoms. Despite the simplicity of empirical chemical shift prediction programs, the agreement with experimental results is rather good, underlining their usefulness. However, we show in our present work that they are highly insensitive to structural changes, which renders their use for validating predicted structures questionable. In contrast, quantum chemical methods show the expected high sensitivity to structural and electronic changes. This appears to be independent of the quantum chemical approach or the inclusion of solvent effects. For the latter, explicit solvent simulations with increasing number of snapshots were performed for two conformers of an eight amino acid sequence. In conclusion, the empirical approaches neither provide the expected magnitude nor the patterns of NMR chemical shifts determined by the clearly more costly ab initio methods upon structural changes. This restricts the use of empirical prediction programs in studies where peptide and protein structures are utilized for the NMR chemical shift evaluation such as in NMR refinement processes, structural model verifications, or calculations of NMR nuclear spin relaxation rates.
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Affiliation(s)
- Chris Vanessa Sumowski
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 Munich, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Matti Hanni
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 Munich, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Sabine Schweizer
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 Munich, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 Munich, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 Munich, Germany
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31
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Hartman JD, Beran GJO. Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals. J Chem Theory Comput 2015; 10:4862-72. [PMID: 26584373 DOI: 10.1021/ct500749h] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.
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Affiliation(s)
- Joshua D Hartman
- Department of Chemistry, University of California , Riverside, California 92521, United States
| | - Gregory J O Beran
- Department of Chemistry, University of California , Riverside, California 92521, United States
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32
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Hartman JD, Monaco S, Schatschneider B, Beran GJO. Fragment-based (13)C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods. J Chem Phys 2015; 143:102809. [PMID: 26374002 DOI: 10.1063/1.4922649] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.
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Affiliation(s)
- Joshua D Hartman
- Department of Chemistry, University of California, Riverside, California 92521, USA
| | - Stephen Monaco
- The Pennsylvania State University, The Eberly Campus, 2201 University Dr, Lemont Furnace, Pennsylvania 15456, USA
| | - Bohdan Schatschneider
- The Pennsylvania State University, The Eberly Campus, 2201 University Dr, Lemont Furnace, Pennsylvania 15456, USA
| | - Gregory J O Beran
- Department of Chemistry, University of California, Riverside, California 92521, USA
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33
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Usvyat D, Maschio L, Schütz M. Periodic local MP2 method employing orbital specific virtuals. J Chem Phys 2015; 143:102805. [DOI: 10.1063/1.4921301] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Denis Usvyat
- Institute for Physical and Theoretical Chemistry, Universität Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
| | - Lorenzo Maschio
- Dipartimento di Chimica, and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via Giuria 5, I-10125 Torino, Italy
| | - Martin Schütz
- Institute for Physical and Theoretical Chemistry, Universität Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
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34
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Ledermüller K, Schütz M. Local CC2 response method based on the Laplace transform: analytic energy gradients for ground and excited states. J Chem Phys 2015; 140:164113. [PMID: 24784259 DOI: 10.1063/1.4872169] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
A multistate local CC2 response method for the calculation of analytic energy gradients with respect to nuclear displacements is presented for ground and electronically excited states. The gradient enables the search for equilibrium geometries of extended molecular systems. Laplace transform is used to partition the eigenvalue problem in order to obtain an effective singles eigenvalue problem and adaptive, state-specific local approximations. This leads to an approximation in the energy Lagrangian, which however is shown (by comparison with the corresponding gradient method without Laplace transform) to be of no concern for geometry optimizations. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated by application calculations devoted to a photocatalytic decarboxylation process of present interest.
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Affiliation(s)
- Katrin Ledermüller
- Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
| | - Martin Schütz
- Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
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35
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Maurer M, Ochsenfeld C. Spin component-scaled second-order Møller-Plesset perturbation theory for calculating NMR shieldings. J Chem Theory Comput 2015; 11:37-44. [PMID: 26574201 DOI: 10.1021/ct5007295] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Spin component-scaled and scaled opposite-spin second-order Møller-Plesset perturbation approaches (SCS-MP2 and SOS-MP2) are introduced for calculating NMR chemical shifts in analogy to the well-established scaled approaches for MP2 energies. Gauge-including atomic orbitals (GIAO) are employed throughout this work. The GIAO-SCS-MP2 and GIAO-SOS-MP2 methods typically show superior performance to nonscaled MP2 and are closer to the coupled-cluster singles doubles perturbative triples (CCSD(T))/cc-pVQZ reference values. In addition, the pragmatic use of mixed basis sets for the Hartree-Fock and the correlated part of NMR chemical shift calculations is shown to be beneficial.
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Affiliation(s)
- Marina Maurer
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 7, D-81377 Munich, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 7, D-81377 Munich, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 5-13, D-81377 Munich, Germany
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36
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Reynolds RD, Shiozaki T. Fully relativistic self-consistent field under a magnetic field. Phys Chem Chem Phys 2015; 17:14280-3. [DOI: 10.1039/c4cp04027a] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Four-component Dirac–Hartree–Fock method with gauge-including atomic orbitals.
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Affiliation(s)
| | - Toru Shiozaki
- Department of Chemistry
- Northwestern University
- Evanston
- USA
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37
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Loibl S, Schütz M. Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals. J Chem Phys 2014; 141:024108. [DOI: 10.1063/1.4884959] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Stefan Loibl
- Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
| | - Martin Schütz
- Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
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38
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Rolik Z, Szegedy L, Ladjánszki I, Ladóczki B, Kállay M. An efficient linear-scaling CCSD(T) method based on local natural orbitals. J Chem Phys 2014; 139:094105. [PMID: 24028100 DOI: 10.1063/1.4819401] [Citation(s) in RCA: 288] [Impact Index Per Article: 28.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.
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Affiliation(s)
- Zoltán Rolik
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, P.O. Box 91, Hungary
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39
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Ledermüller K, Kats D, Schütz M. Local CC2 response method based on the Laplace transform: orbital-relaxed first-order properties for excited states. J Chem Phys 2014; 139:084111. [PMID: 24006978 DOI: 10.1063/1.4818586] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
A multistate local CC2 response method for the calculation of orbital-relaxed first order properties is presented for ground and electronically excited states. It enables the treatment of excited state properties including orbital relaxation for extended molecular systems and is a major step on the way towards analytic gradients with respect to nuclear displacements. The Laplace transform method is employed to partition the eigenvalue problem and the lambda equations, i.e., the doubles parts of these equations are inverted on-the-fly, leaving only the corresponding effective singles equations to be solved iteratively. Furthermore, the state specific local approximations are adaptive. Density-fitting is utilized to decompose the electron-repulsion integrals. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated on the example of an organic sensitizer for solar-cell applications, which consists of about 100 atoms.
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Affiliation(s)
- Katrin Ledermüller
- Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany
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40
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Maurer M, Ochsenfeld C. A linear- and sublinear-scaling method for calculating NMR shieldings in atomic orbital-based second-order Møller-Plesset perturbation theory. J Chem Phys 2013; 138:174104. [PMID: 23656111 DOI: 10.1063/1.4801084] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
An atomic-orbital (AO) based formulation for calculating nuclear magnetic resonance chemical shieldings at the second-order Møller-Plesset perturbation theory level is introduced, which provides a basis for reducing the scaling of the computational effort with the molecular size from the fifth power to linear and for a specific nucleus to sublinear. The latter sublinear scaling in the rate-determining steps becomes possible by avoiding global perturbations with respect to the magnetic field and by solving for quantities that involve the local nuclear magnetic spin perturbation instead. For avoiding the calculation of the second-order perturbed density matrix, we extend our AO-based reformulation of the Z-vector method within a density matrix-based scheme. Our pilot implementation illustrates the fast convergence with respect to the required number of Laplace points and the asymptotic scaling behavior in the rate-determining steps.
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Affiliation(s)
- Marina Maurer
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich, Butenandtstr. 7, D-81377 Munich, Germany
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