1
|
Hanson-Heine MWD. Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study. J Phys Chem A 2022; 126:7273-7282. [PMID: 36164938 PMCID: PMC9574917 DOI: 10.1021/acs.jpca.2c05881] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.
Collapse
|
2
|
Yagi K, Sugita Y. Anharmonic Vibrational Calculations Based on Group-Localized Coordinates: Applications to Internal Water Molecules in Bacteriorhodopsin. J Chem Theory Comput 2021; 17:5007-5020. [PMID: 34296615 PMCID: PMC10986902 DOI: 10.1021/acs.jctc.1c00060] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
An efficient anharmonic vibrational method is developed exploiting the locality of molecular vibration. Vibrational coordinates localized to a group of atoms are employed to divide the potential energy surface (PES) of a system into intra- and inter-group contributions. Then, the vibrational Schrödinger equation is solved based on a PES, in which the inter-group coupling is truncated at the harmonic level while accounting for the intra-group anharmonicity. The method is applied to a pentagonal hydrogen bond network (HBN) composed of internal water molecules and charged residues in a membrane protein, bacteriorhodopsin. The PES is calculated by the quantum mechanics/molecular mechanics (QM/MM) calculation at the level of B3LYP-D3/aug-cc-pVDZ. The infrared (IR) spectrum is computed using a set of coordinates localized to each water molecule and amino acid residue by second-order vibrational quasi-degenerate perturbation theory (VQDPT2). Benchmark calculations show that the proposed method yields the N-D/O-D stretching frequencies with an error of 7 cm-1 at the cost reduced by more than five times. In contrast, the harmonic approximation results in a severe error of 150 cm-1. Furthermore, the size of QM regions is carefully assessed to find that the QM regions should include not only the pentagonal HBN itself but also its HB partners. VQDPT2 calculations starting from transient structures obtained by molecular dynamics simulations have shown that the structural sampling has a significant impact on the calculated IR spectrum. The incorporation of anharmonicity, sufficiently large QM regions, and structural samplings are of essential importance to reproduce the experimental IR spectrum. The computational spectrum paves the way for decoding the IR signal of strong HBNs and helps elucidate their functional roles in biomolecules.
Collapse
Affiliation(s)
- Kiyoshi Yagi
- Theoretical
Molecular Science Laboratory, RIKEN Cluster
for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Yuji Sugita
- Theoretical
Molecular Science Laboratory, RIKEN Cluster
for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Computational
Biophysics Research Team, RIKEN Center for
Computational Science, 7-1-26 Minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
- Laboratory
for Biomolecular Function Simulation, RIKEN
Center for Biosystems Dynamics Research, 1-6-5 Minatojima-Minamimachi,
Chuo-ku, Kobe, Hyogo 650-0047, Japan
| |
Collapse
|
3
|
Hanson-Heine MWD. Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates. J Chem Theory Comput 2021; 17:4383-4391. [PMID: 34087068 DOI: 10.1021/acs.jctc.1c00314] [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
Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.
Collapse
|
4
|
Yagi K, Yamada K, Kobayashi C, Sugita Y. Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations. J Chem Theory Comput 2019; 15:1924-1938. [PMID: 30730746 PMCID: PMC8864611 DOI: 10.1021/acs.jctc.8b01193] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
![]()
Quantum
mechanics/molecular mechanics (QM/MM) calculations are
applied for anharmonic vibrational analyses of biomolecules and solvated
molecules. The QM/MM method is implemented into a molecular dynamics
(MD) program, GENESIS, by interfacing with external electronic structure
programs. Following the geometry optimization and the harmonic normal-mode
analysis based on a partial Hessian, the anharmonic potential energy
surface (PES) is generated from QM/MM energies and gradients calculated
at grid points. The PES is used for vibrational self-consistent field
(VSCF) and post-VSCF calculations to compute the vibrational spectrum.
The method is first applied to a phosphate ion in solution. With both
the ion and neighboring water molecules taken as a QM region, IR spectra
of representative hydration structures are calculated by the second-order
vibrational quasi-degenerate perturbation theory (VQDPT2) at the level
of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra
over the structures reproduces the experimental spectrum with a mean
absolute deviation of 16 cm–1. Then, the method
is applied to an enzyme, P450 nitric oxide reductase (P450nor), with
the NO molecule bound to a ferric (FeIII) heme. Starting
from snapshot structures obtained from MD simulations of P450nor in
solution, QM/MM calculations have been carried out at the level of
B3LYP-D3/def2-SVP(D). The spin state of FeIII(NO) is likely
a closed-shell singlet state based on a ratio of N–O and Fe–NO
stretching frequencies (νN–O and νFe–NO) calculated for closed- and open-shell singlet
states. The calculated νN–O and νFe–NO overestimate the experimental ones by 120 and
75 cm–1, respectively. The electronic structure
and solvation of FeIII(NO) affect the structure around
the heme of P450nor leading to an increase in νN–O and νFe–NO.
Collapse
Affiliation(s)
- Kiyoshi Yagi
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Kenta Yamada
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Chigusa Kobayashi
- Computational Biophysics Research Team, RIKEN Center for Computational Science, 7-1-26 Minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Yuji Sugita
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Computational Biophysics Research Team, RIKEN Center for Computational Science, 7-1-26 Minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, 1-6-5 Minatojima-Minamimachi,
Chuo-ku, Kobe, Hyogo 650-0047, Japan
| |
Collapse
|
5
|
Hanson-Heine MWD. Reduced Basis Set Dependence in Anharmonic Frequency Calculations Involving Localized Coordinates. J Chem Theory Comput 2018; 14:1277-1285. [PMID: 29385338 DOI: 10.1021/acs.jctc.7b01075] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Localized normal coordinates are known to be effective in speeding up anharmonic frequency calculations by reducing the complexity of the nuclear Hamiltonian and wave function. Displacing atoms in localized coordinates can also cause relatively small changes in the electronic structure, which can be exploited for further computational efficiency improvements during ab initio electronic structure calculations of the potential energy surface by reducing the electronic basis set dependence. Three different schemes for reducing the basis set dependence have been investigated in this work. These include combining localized coordinate schemes with general mixed basis sets, distance based force-field reductions, and using coordinate specific basis sets. The importance of accurately describing electronic interactions is found to diminish both for multicoordinate terms involving the displacement of remote atoms and when describing the interactions between more remote atoms within specific coordinates.
Collapse
|
6
|
Thomsen B, Kawakami T, Shigemoto I, Sugita Y, Yagi K. Weight-Averaged Anharmonic Vibrational Analysis of Hydration Structures of Polyamide 6. J Phys Chem B 2017; 121:6050-6063. [DOI: 10.1021/acs.jpcb.7b00372] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bo Thomsen
- Theoretical
Molecular Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Tomonori Kawakami
- Advanced
Materials Research Laboratories, Toray Industries, Inc., 2-1 Sonoyama 3-chome, Otsu, Shiga 520-0842, Japan
| | - Isamu Shigemoto
- Advanced
Materials Research Laboratories, Toray Industries, Inc., 2-1 Sonoyama 3-chome, Otsu, Shiga 520-0842, Japan
| | - Yuji Sugita
- Theoretical
Molecular Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- RIKEN iTHES, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- RIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-Minamimachi,
Chuo-ku, Kobe, Hyogo 650-0047, Japan
- RIKEN Quantitative Biology Center, 6-7-1 Minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Kiyoshi Yagi
- Theoretical
Molecular Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- RIKEN iTHES, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| |
Collapse
|
7
|
Hanson-Heine MWD. Intermediate vibrational coordinate localization with harmonic coupling constraints. J Chem Phys 2017; 144:204116. [PMID: 27250288 DOI: 10.1063/1.4951011] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.
Collapse
Affiliation(s)
- Magnus W D Hanson-Heine
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
8
|
Affiliation(s)
- Robin N. Perutz
- Department of Chemistry, University of York, York YO10 5DD, United Kingdom
| | - Barbara Procacci
- Department of Chemistry, University of York, York YO10 5DD, United Kingdom
| |
Collapse
|
9
|
Hanson-Heine MWD. Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates. J Chem Phys 2016; 143:164104. [PMID: 26520495 DOI: 10.1063/1.4934234] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.
Collapse
Affiliation(s)
- Magnus W D Hanson-Heine
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
10
|
Hanson-Heine MWD, Wriglesworth A, Uroos M, Calladine JA, Murphy TS, Hamilton M, Clark IP, Towrie M, Dowden J, Besley NA, George MW. Calculating singlet excited states: Comparison with fast time-resolved infrared spectroscopy of coumarins. J Chem Phys 2015; 142:154119. [DOI: 10.1063/1.4917311] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
11
|
Do H, Besley NA. Calculation of the vibrational frequencies of carbon clusters and fullerenes with empirical potentials. Phys Chem Chem Phys 2015; 17:3898-908. [DOI: 10.1039/c4cp05424e] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Empirical potentials are assessed and optimized for the calculation of the vibrational frequencies of fullerenes and nanotubes.
Collapse
Affiliation(s)
- Hainam Do
- School of Chemistry
- University of Nottingham
- University Park
- Nottingham
- UK
| | | |
Collapse
|
12
|
Wang Y, Xie X, Lu H, Chen F, Liu H, Li W. Harmonic and anharmonic analysis of the IR and Raman spectrum of macrocyclic dioxopolyamine. J Mol Struct 2014. [DOI: 10.1016/j.molstruc.2014.06.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
13
|
Hanson-Heine MWD, George MW, Besley NA. Calculating excited state properties using Kohn-Sham density functional theory. J Chem Phys 2013; 138:064101. [PMID: 23425455 DOI: 10.1063/1.4789813] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The accuracy of excited states calculated with Kohn-Sham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for open-shell singlet excited states. The computed Kohn-Sham adiabatic excitation energies are improved significantly by post self-consistent field spin-purification, but remain too low compared with experiment with a larger error than time-dependent density functional theory. Excited state structures and vibrational frequencies are also improved by spin-purification. The structures show a comparable accuracy to time-dependent density functional theory, while the harmonic vibrational frequencies are found to be more accurate for the majority of vibrational modes. The computed harmonic vibrational frequencies are also further improved by perturbative anharmonic corrections, suggesting a good description of the potential energy surface. Overall, excited state Kohn-Sham density functional theory is shown to provide an efficient method for the calculation of excited state structures and vibrational frequencies in open-shell singlet systems and provides a promising technique that can be applied to study large systems.
Collapse
Affiliation(s)
- Magnus W D Hanson-Heine
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | | | | |
Collapse
|
14
|
Hudecová J, Profant V, Novotná P, Baumruk V, Urbanová M, Bouř P. CH Stretching Region: Computational Modeling of Vibrational Optical Activity. J Chem Theory Comput 2013; 9:3096-108. [PMID: 26583989 DOI: 10.1021/ct400285n] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Most organic compounds provide vibrational spectra within the CH stretching region, yet the signal is difficult to interpret because of multiple difficulties in experiment and modeling. To better understand various factors involved, the ability of several harmonic and anharmonic computational approaches to describe these vibrations was explored for α-pinene, fenchone, and camphor as test compounds. Raman, Raman optical activity (ROA), infrared absorption (IR), and vibrational circular dichroism (VCD) spectra were measured and compared to quantum chemical computations. Surprisingly, the harmonic vibrational approach reasonably well reproduced the measured spectral patterns, including the vibrational optical activity (VOA). The CH stretching, however, appeared to be more sensitive to the basis set and solvent variations than lower-frequency vibrations. For a higher accuracy in frequencies and spectral shapes, anharmonic corrections were necessary. Accurate harmonic and anharmonic force fields were obtained with the mPW2PLYP double-hybrid functional. A limited vibrational configuration interaction (LVCI) where the CH stretching motion was decoupled from other vibrations provided the best simulated spectra. A balanced harmonic oscillator basis set had to be used, containing also states indirectly interacting with fundamental vibrations. A simpler second-order perturbational approach (PT2) appeared less useful. The modeling provided unprecedented agreement with experimental vibrational frequencies; spectral shapes were reproduced less faithfully. The possibility of ab initio interpretation of the CH spectral region for relatively large molecules further broadens the application span of vibrational spectroscopy.
Collapse
Affiliation(s)
- Jana Hudecová
- Faculty of Mathematics and Physics, Institute of Physics, Charles University , Ke Karlovu 5, 12116, Prague 2, Czech Republic.,Institute of Organic Chemistry and Biochemistry, Academy of Sciences , Flemingovo náměstí 2, 16610 Prague, Czech Republic
| | - Václav Profant
- Faculty of Mathematics and Physics, Institute of Physics, Charles University , Ke Karlovu 5, 12116, Prague 2, Czech Republic
| | - Pavlína Novotná
- Department of Physics and Measurements and Department of Analytical Chemistry, Institute of Chemical Technology , Technická 5, 16628 Prague, Czech Republic
| | - Vladimír Baumruk
- Faculty of Mathematics and Physics, Institute of Physics, Charles University , Ke Karlovu 5, 12116, Prague 2, Czech Republic
| | - Marie Urbanová
- Department of Physics and Measurements and Department of Analytical Chemistry, Institute of Chemical Technology , Technická 5, 16628 Prague, Czech Republic
| | - Petr Bouř
- Institute of Organic Chemistry and Biochemistry, Academy of Sciences , Flemingovo náměstí 2, 16610 Prague, Czech Republic
| |
Collapse
|