Investigation of the interaction between molecules at medium distances

Otto, P.; Ladik, J.

doi:10.1016/0301-0104(75)80107-8

Cited by 135 publications

(66 citation statements)

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“…In the original 1975 implementation of MCF by Otto and Ladik, 50 the wave function of a fragment was polarized by a partner fragment through modifying the Fock operator by the Coulomb potential of a partner. A simple monopole approximation was used originally to represent the electrostatic potential; HF equations for a pair of fragments were solved until selfconsistency.…”

Section: Introductionmentioning

confidence: 99%

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

et al. 2011

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Theoretical chemists have always strived to perform quantum mechanics (QM) calculations on larger and larger molecules and molecular systems, as well as condensed phase species, that are frequently much larger than the current state-of-the-art would suggest is possible. The desire to study species (with acceptable accuracy) that are larger than appears to be feasible has naturally led to the development of novel methods, including semiempirical approaches, reduced scaling methods, and fragmentation methods. The focus of the present review is on fragmentation methods, in which a large molecule or molecular system is made more computationally tractable by explicitly considering only one part (fragment) of the whole in any particular calculation. If one can divide a species of interest into fragments, employ some level of ab initio QM to calculate the wave function, energy, and properties of each fragment, and then combine the results from the fragment calculations to predict the same properties for the whole, the possibility exists that the accuracy of the outcome can approach that which would be obtained from a full (nonfragmented) calculation. It is this goal that drives the development of fragmentation methods. Disciplines Chemistry CommentsReprinted (adapted) with permission from Chemical Reviews 112 (2012): 632,

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Section: Introductionmentioning

confidence: 99%

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

et al. 2011

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“…In this subsection, the electrostatic dimer (ES-DIM) approximation for the fully analytic energy gradients is introduced, and it is shown that the response terms arising from the ES-DIM approximation need not be considered, because they cancel out with the response term from Eq. (19).…”

Section: Application To the Electrostatic Dimer Approximationmentioning

confidence: 99%

“…It is important to numerically verify that the gradients are fully analytic using U a = 0 [Eq. (19)]. …”

Section: A Fully Analytic Energy Gradients Without Approximationsmentioning

confidence: 99%

“…Considerable efforts are invested in developing linear scaling or O(N ) methods. 14,15 The fragmentation methods have a fairly long history [16][17][18][19][20][21][22] and now it is an active area of research. 13, 23-32 a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, in order to realize linear scaling, approximations have been proposed for the time-consuming ESP calculation in FMO 34,37 and other methods. 10 The fragment self-consistent procedure employed in FMO has been used in somewhat different forms in other methods, 18,19,9,38,39 while the many-body expansion of the energy is conceptually related to the theory of intermolecular interactions 16 or the density expansion method. 20 Over the past decade, the FMO method has become one of the most extensively developed fragmentation methods for the calculation of accurate chemical properties, such as the total energy, the dipole moment, and the interaction energy between fragments in large systems.…”

Section: Introductionmentioning

confidence: 99%

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Fully analytic energy gradient in the fragment molecular orbital method

Brorsen¹,

Fedorov²

2011

The Journal of Chemical Physics

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The Z-vector equations are derived and implemented for solving the response term due to the external electrostatic potentials, and the corresponding contribution is added to the energy gradients in the framework of the fragment molecular orbital (FMO) method. To practically solve the equations for large molecules like proteins, the equations are decoupled by taking advantage of the local nature of fragments in the FMO method and establishing the self-consistent Z-vector method. The resulting gradients are compared with numerical gradients for the test molecular systems: (H 2 O) 64 , alanine decamer, hydrated chignolin with the protein data bank (PDB) ID of 1UAO, and a Trp-cage miniprotein construct (PDB ID: 1L2Y). The computation time for calculating the response contribution is comparable to or less than that of the FMO selfconsistent charge calculation. It is also shown that the energy gradients for the electrostatic dimer approximation are fully analytic, which significantly reduces the computational costs. The fully analytic FMO gradient is parallelized with an efficiency of about 98% on 32 nodes. KeywordsPolymers, Electrostatics, Chemical bonds, Proteins, Density functional theory Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 134 (2011) The Z-vector equations are derived and implemented for solving the response term due to the external electrostatic potentials, and the corresponding contribution is added to the energy gradients in the framework of the fragment molecular orbital (FMO) method. To practically solve the equations for large molecules like proteins, the equations are decoupled by taking advantage of the local nature of fragments in the FMO method and establishing the self-consistent Z-vector method. The resulting gradients are compared with numerical gradients for the test molecular systems: (H 2 O) 64 , alanine decamer, hydrated chignolin with the protein data bank (PDB) ID of 1UAO, and a Trp-cage miniprotein construct (PDB ID: 1L2Y). The computation time for calculating the response contribution is comparable to or less than that of the FMO self-consistent charge calculation. It is also shown that the energy gradients for the electrostatic dimer approximation are fully analytic, which significantly reduces the computational costs. The fully analytic FMO gradient is parallelized with an efficiency of about 98% on 32 nodes.

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Modeling and Visualization for the Fragment Molecular Orbital Method with the Graphical User Interface FU, and Analyses of Protein–Ligand Binding

Fedorov

Kitaura²

2017

Fragmentation

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Investigation of the interaction between molecules at medium distances

Cited by 135 publications

References 11 publications

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

Fully analytic energy gradient in the fragment molecular orbital method

Modeling and Visualization for the Fragment Molecular Orbital Method with the Graphical User Interface FU, and Analyses of Protein–Ligand Binding

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