Fully analytic energy gradient in the fragment molecular orbital method

Brorsen, Kurt R.; Fedorov, Dmitri G.

doi:10.1063/1.3568010

Cited by 99 publications

(15 citation statements)

References 99 publications

(141 reference statements)

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“…A comparison of the accuracy of two and three-body expansions of DFT for the energy and gradient is found elsewhere, 65 and the cost scaling of FMO with system size has already been discussed in general. 48 The FMO analytic energy gradient has been developed for closed and open-shell Hartree-Fock (HF) [66][67][68][69][70][71] and DFT. 72 The analytic second derivative, which can be used to evaluate Raman activities, 73 has been developed only for HF 46,74 at the two-body level (FMO2).…”

Section: Introductionmentioning

confidence: 99%

“…(7)- (14) into Eq. (6) 46,67 is that the sum of all orbital response terms cancels out in FMO2 gradients and Hessians if the ESP point charge (PC) approximation, ESP-PC, is applied to all ESPs, or if the ESP-PC approximation is not used at all; 80,81 otherwise, the orbital response terms need to be evaluated. 82 Now, it is shown that the orbital response terms U ab, X,Y also cancel out for FMO3, for the same two conditions.…”

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confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

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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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“…We used the first structure available in each of the downloaded structures. For comparison, we performed two-body Fragment Molecular Orbital (FMO) (Fedorov & Kitaura, 2007) geometry optimizations using RHF/6-31G(d) (Francl et al, 1982; Gordon et al, 1982; Hariharan & Pople, 1973; Nagata et al, 2011) and the D3 dispersion correction (Grimme et al, 2010; Peverati & Baldridge, 2008). …”

Section: Methodsmentioning

confidence: 99%

A third-generation dispersion and third-generation hydrogen bonding corrected PM6 method: PM6-D3H+

Kromann

Christensen

Steinmann

et al. 2014

PeerJ

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We present new dispersion and hydrogen bond corrections to the PM6 method, PM6-D3H+, and its implementation in the GAMESS program. The method combines the DFT-D3 dispersion correction by Grimme et al. with a modified version of the H+ hydrogen bond correction by Korth. Overall, the interaction energy of PM6-D3H+ is very similar to PM6-DH2 and PM6-DH+, with RMSD and MAD values within 0.02 kcal/mol of one another. The main difference is that the geometry optimizations of 88 complexes result in 82, 6, 0, and 0 geometries with 0, 1, 2, and 3 or more imaginary frequencies using PM6-D3H+ implemented in GAMESS, while the corresponding numbers for PM6-DH+ implemented in MOPAC are 54, 17, 15, and 2. The PM6-D3H+ method as implemented in GAMESS offers an attractive alternative to PM6-DH+ in MOPAC in cases where the LBFGS optimizer must be used and a vibrational analysis is needed, e.g., when computing vibrational free energies. While the GAMESS implementation is up to 10 times slower for geometry optimizations of proteins in bulk solvent, compared to MOPAC, it is sufficiently fast to make geometry optimizations of small proteins practically feasible.

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“…Consequently, it is expected that the use of the variational X-Pol energy as the monomer energy reference state in many-body energy expansion should lead to smaller corrections than other alternatives. 14 Although it is possible to obtain analytic gradients for the nonvariational, charge-embedding approaches, 35 it generally involves solution of coupled-perturbed self-consistent field equations. Sometimes the response terms in fragment-based methods have been neglected.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Explicit Polarization: A Quantum Mechanical Framework for Developing Next Generation Force Fields

et al. 2014

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ConspectusMolecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF).X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems (“fragments”) to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples involving water clusters (which show the power of two-body corrections), ethylmethylimidazolium acetate ionic liquids (which reveal that the amount of charge transfer between anion and cation is much smaller than what has been assumed in some classical simulations), and a solvated protein in aqueous solution (which shows that the average charge distribution of carbonyl groups along the polypeptide chain depends strongly on their position in the sequence, whereas they are fixed in most classical force fields). The development of QMFFs also offers an opportunity to extend the accuracy of biochemical simulations to areas where classical force fields are often insufficient, especially in the areas of spectroscopy, reactivity, and enzyme catalysis.

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Fully analytic energy gradient in the fragment molecular orbital method

Cited by 99 publications

References 99 publications

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

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

A third-generation dispersion and third-generation hydrogen bonding corrected PM6 method: PM6-D3H+

Explicit Polarization: A Quantum Mechanical Framework for Developing Next Generation Force Fields

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