Effective fragment potential method

EFP parameters for a particular fragment are generated for a given atomic basis set, they can be used in a variety of applications. The various components of the non-bonded interactions between molecules are evaluated using the EFP2 generated parameters. The procedure has been described in elsewhere [36] only the main points are summarized below. 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

The exchange repulsion energy in EFP2 is derived as an expansion in the intermolecular overlap. When this overlap expansion is expressed in terms of frozen LMOs on each fragment, the expansion can reliably be truncated at the quadratic term [44], This term does require that each EFP carries a basis set, and the smallest recommended basis set is 6-31-1— -G(d,p) [45] for acceptable results. Since the basis set is used only to calculate overlap integrals, the computation is very fast and quite large basis sets are realistic. 

The dispersion interaction can be expressed as the familiar inverse R expansion, 

The coefficients Cn may be derived from the (imaginary) frequency dependent polarizabilities summed over the entire frequency range [46]. If one employs only dipole polarizabilities the dispersion expansion is truncated at the leading term, with n = 6. In the current EFP2 code, an estimate is used for the n = 8 term, in addition to the explicitly derived n = 6 term. Rather than express a molecular C as a sum over atomic interaction terms, the EFP2 dispersion is expressed in terms of LMO-LMO 

Department of Chemistry, Purdue University, West Lafayette, IN 47906, USA lslipchenko gmail.com 

The effective fragment potential (EFP) method emerged as a promising compromise between computational efficiency and rigorous ab initio-based formulation of interaction energy in weakly interacting systems [1-6]. The EFP method decomposes 

Many-Body Effects and Electrostatics in Biomolecules Edited by Qjang Cui, Markus Meuwly, and Pengyu Ren Copyright 2016 Pan Stanford Publishing Pte. Ltd. 

The EFPl models faithfully reproduce the parent methods, HF or DFT, and suffer from the limitations of those, e.g., neglecting the dispersion interactions. 

The screening function /damp may be represented using Tang-Toennies expression [17] or using intermolecular overlap integrals pq [15] 

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Keywords Coarse-graining, Force-matching, Effective fragment potential method, Molecular... 

M.S. Gordon, M.A. Freitag, P. Bandyopadhyay, J.H. Jensen, V. Kairys, W.J. Stevens, The effective fragment potential method A QM-based MM approach to modeling environmental effects in chemistry, J. Phys. Chem. A105 (2001) 293. 

Methanol-water mixtures were studied by Adamovic and Gordon who used the so called effective-fragment-potential method, an approach of the type discussed in section IID, for finite (Me0H/H20) clusters with n = 2,3,. .., 8. Some of their findings were tested by using accurate, parameter-free, electronic-structure methods. The main outcome is the organization of the H2O and MeOH molecules relative to each other, which then is expected to be representative for macroscopic mixtures of water and methanol. 

Inclusion of dispersion effect in the MP2 based effective fragment potential method (EFP1).132... 

Ohta K, Yoshioka Y, Morokuma K, Kitaura K (1983) The effective fragment potential method an approximate ab initio MO method for large molecules. Chem Phys Lett 101 12-17... 

Jensen JH, Gordon MS. An approximate formula for the intermolecular Pauli repulsion between closed shell molecules II. Application to the effective fragment potential method. J Chem Phys 1998 108 4772-4782. 

Flick, J. C., Kosenkov, D., Hohenstein, E. G Sherrill, C. D., and Slipchenko, L. V. (2012]. Accurate prediction of noncovalent interaction energies with the effective fragment potential method Comparison of energy components to symmetry-adapted perturbation theory for the S22 test set,/. Chem. Theory Comput 8, pp. 2835-2843, doi 10.1021/ct200673a. 

Slipchenko, L. V, and Gordon, M. S. Electrostatic energy in the effective fragment potential method Theory and application to benzene dimer. /. Comput Chem., 28, 276-291 (2007). 

Gordon, M. S., Freitag, M. A., Bandyopadhyay R, Jensen, J. H., Kairys, V., Stevens, W. J. (2001). The Effective Fragment Potential Method A QM-Based MM Approach to Modeling Environmental Effects in Chemistry J. Phys. Chem. A, 105, 293-307. 

Noncovalent Interactions in Extended Systems Described by the Effective Fragment Potential Method Theory and Application to Nucleobase Oligomers,/. Phys. Chem. A, 114,12739-12754. 

Jensen, J. H., Gordon, M. S. (1998). An Approximate Formula for the Intermolecular Pauli Repulsion between Closed Shell Molecules. II. Application to the Effective Fragment Potential Method, / Chem. Phys., 108,4772-4782. 

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