Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy

Li, Hui; Jensen, Jan H.

doi:10.1007/s00214-001-0317-7

Cited by 122 publications

(85 citation statements)

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“…Subsequently, harmonic vibrational frequencies of acetophenone in the seven solvents were computed by diagonalizing the Hessian matrix for the quantum region in the fixed environment, also known as a partial normal mode analysis. 64 The C==O stretching mode is a rather localized mode, and thus, it can be reasonably well described within the vibrationally decoupled solute-solvent picture provided by a partial Hessian analysis. 65 We note that a basis set of triple-ζ quality is generally recommended for geometry optimizations and harmonic vibrational frequencies when using the B3LYP exchangecorrelation functional.…”

Section: Frequency Calculationsmentioning

confidence: 96%

Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

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Beerepoot

Olsen

et al. 2015

The Journal of Chemical Physics

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We present an implementation of analytical quantum mechanical molecular gradients within the polarizable embedding (PE) model to allow for efficient geometry optimizations and vibrational analysis of molecules embedded in large, geometrically frozen environments. We consider a variational ansatz for the quantum region, covering (multiconfigurational) self-consistent-field and Kohn-Sham density functional theory. As the first application of the implementation, we consider the internal vibrational Stark effect of the C==O group of acetophenone in different solvents and derive its vibrational linear Stark tuning rate using harmonic frequencies calculated from analytical gradients and computed local electric fields. Comparisons to PE calculations employing an enlarged quantum region as well as to a non-polarizable embedding scheme show that the inclusion of mutual polarization between acetophenone and water is essential in order to capture the structural modifications and the associated frequency shifts observed in water. For more apolar solvents, a proper description of dispersion and exchange-repulsion becomes increasingly important, and the quality of the optimized structures relies to a larger extent on the quality of the Lennard-Jones parameters. C 2015 AIP Publishing LLC. [http://dx

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Section: Frequency Calculationsmentioning

confidence: 96%

Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

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Beerepoot

Olsen

et al. 2015

The Journal of Chemical Physics

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“…Such a partial geometry optimization with fixed hydrogens asks for an adapted NMA method: the saturating hydrogens should also be kept fixed during the vibrational analysis to ensure consistency. This is accomplished by the Partial Hessian Vibrational Analysis (PHVA), where first the rows and columns corresponding to the fixed atoms are deleted from the Hessian and then this smaller submatrix is diagonalized [39,40,41,42,43]. This NMA scheme is labeled as PHVA H , referring to the hydrogens as the fixed atoms.…”

Section: Theoretical Simulationsmentioning

confidence: 99%

“…In the latter work, large finite clusters and a hybrid QM/MM ONIOM calculation scheme were applied. The large finite clusters were saturated with fixed outer hydrogens and a normal mode analysis was hence performed using the partial hessian vibrational analysis (PHVA) method [39,40,41,42,43]. In addition to the PHVA scheme, other vibrational analysis schemes can be applied to study extended systems.…”

Section: Introductionmentioning

confidence: 99%

Experimental and theoretical IR study of methanol and ethanol conversion over H-SAPO-34

Hemelsoet

Ghysels

et al. 2011

Catalysis Today

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Theoretical and experimental IR data are combined to gain insight into the methanol and ethanol conversion over an acidic H-SAPO-34 catalyst. The theoretical simulations use a large finite cluster and the initial physisorption energy of both alcohols is calculated.Dispersive contributions turn out to be vital and the final adsorption of ethanol is predicted to be stronger compared to methanol (difference of 14 kJ mol −1 ). Calculated IR spectra of the alcohols and of formed aromatic cations upon conversion are also analyzed and support the peak assignment of the experimental in situ DRIFT spectra, in particular for the C-H and C=C regions. Theoretical IR spectra of the gas phase compounds are compared with those of the molecules loaded in a SAPO cluster and the observed shifts of the peak positions are discussed. To get a better understanding of these framework-guest interactions, a new theoretical procedure is proposed based on a normal mode analysis.A cumulative overlap function is defined and enables the characterization of individual peaks as well as induced frequency shifts upon adsorption.

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“…17 To accelerate the Hessian evaluation for a subset of atoms, usually, in a numeric fashion, a number of partial schemes is available. [18][19][20][21] The linearscaling QM algorithms [22][23][24][25] have primarily been developed for energy and gradient evaluations; the efficiency of Hessian computations has also been improved. [26][27][28] Some fragment based approaches [29][30][31][32][33][34][35][36][37][38][39][40] feature analytic second derivatives.…”

Section: Introductionmentioning

confidence: 99%

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

Nakata

Fedorov

Zahariev

et al. 2015

The Journal of Chemical Physics

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Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented. KeywordsProteins, Polymers, Free energy, Raman spectra, Biochemical reactions Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 142 (2015) Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted HartreeFock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S N 2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented. C 2015 AIP Publishing LLC.[http://dx

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Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy

Cited by 122 publications

References 1 publication

Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

Experimental and theoretical IR study of methanol and ethanol conversion over H-SAPO-34

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

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