Many-body polarizable potential

Ding YB, Bernardo DN, Kroghjespersen K, Levy RM (1995) Solvation free-energies of small amides and amines from molecular-dynamics free-energy perturbation simulations using pairwise additive and many-body polarizable potentials. J Phys Chem 99(29) 11575—11583... 

Solvation Free Energies of Small Amides and Amines from Molecular Dynamics/Free Energy Perturbation Simulations Using Pairwise Additive and Many-Body Polarizable Potentials. 

Y. Ding, D. N. Bernardo, K. Krogh-Jespersen, and R. M. Levy, /. Phys. Chem., 99,11575 (1995). Solvation Free Energies of Small Amides and Amines from Molecular Dynamics/ Free foergy Perturbation Simulations Using Pairwise Additive and Many-Body Polarizable Potentials. 

The role of many-body polarizable potentials in MD-based predictions of electronic spectra at the water liquid/vapor interface was examined by Benjamin " for a model dipolar solute. The peak absorption spectrum was found to be more sensitive to the solvent polarizability than to the solute polarizability. The contribution of many-body polarizabilities was found to be more pronounced as the excited state dipole was increased, and more in the bulk than at the interface. 

Many of the fixes or modifications necessary to make an effective water potential work can be traced back to the influence of polarization of the molecular charge distribution. Recent efforts in the development of water potentials have considered the explicit inclusion of a many-body polarizability term. The problem of including polarization is that it is not decomposable into pairwise additive terms. If one water molecule becomes polarized by an electric field generated by other surrounding water molecules, the extra induced moment will in turn affect the charge distribution of the surrounding water, which in turn will change the induced moment on the central water molecule, and so on. 

Some years ago our group has proposed a new method, based on the supermolecular approach and the polarizable continuum model (PCM) [128a, 128b] to include many-body effects in a potential, keeping at the same time the computational convenience and simplicity of two-body functions [129]. 

Beside the empirical or semiempirical models described above, the need for inclusion of many-body effects, polarizability at least, in water-water potentials has also been recognized in the development of more recent ab initio potentials [45,75,103-108]. 

Recently, there were many attempts of MD simulations for the vibrational dynamics of ice. In these calculations more realistic, either non-rigid or polarizable, potentials were used. One such calculation was made by Itoh et al [72] using the KKY potential [9] which has three separate pair-wise terms yoo(r), VoH(r), VnH(r) and an extra three-body term for H-O-H and H-0—H bending. These calculations produced the all the fundamental modes up to 450 meV (or 3622 cm" ). The resulting spectra show very similar features to results from the MCY and TIP4P potentials in the translational and librational regions (see Fig. 16 and 17). 

Recently, a new theoretical method of calculating potential energy and dipole/polarizability surfaces for van der Waals molecules based on symmetry-adapted perturbation theory (sapt) of intermolecular forces (12)— (15) has been developed (16)-(24). In this method, referred to as many-body symmetry-adapted perturbation theory, all physically important contributions to the potential and the interaction-induced properties, such as electrostatics, exchange, induction, and dispersion are identified and computed separately. By making a perturbation expansion in the intermolecular interaction as well as in the intramolecular electronic correlation, it is possible to sum the correlation contributions to the different physical... 

The presence of solvent molecules between solute molecules affects all the interaction energies. We have seen that the presence of solvent molecules changes the molecular polarizabilities of solutes in Section 2.5.3 and decreases the strength of van der Waals interactions (Section 2.6.4) and the total intermolecular pair potential energies (Section 2.7.4). When two molecules interact in a condensed liquid medium, there are many solvent molecules interfering in this interaction. Now, this becomes a many-body interaction and we have to consider some important new effects ... 

This includes the Pauli repulsion and (attractive) dispersion terms. The polarizability of the ions is included using the shell model (Dick and Overhauser, 1964) which, as discussed in Chapter 3, models the polarizability using a massive core linked to a mass-less shell by a spring. The theoretical basis of this model is uncertain, but its practical success has been attested over 20 years. Probably the best way to consider it is as a sensible model for linking the electronic polarizability of the ions to the forces exerted by the surrounding lattice. It is therefore a many-body term, a fact that should be remembered if one wishes to consider three-body potentials in the description of the crystal. A recent development in the field has been the use of quantum calculations. These are discussed in detail elsewhere (Chapter 8) but some results will be compared with the classical simulations in this chapter. 

A many-body perturbation theory (MBPT) approach has been combined with the polarizable continuum model (PCM) of the electrostatic solvation. The first approximation called by authors the perturbation theory at energy level (PTE) consists of the solution of the PCM problem at the Hartree-Fock level to find the solvent reaction potential and the wavefunction for the calculation of the MBPT correction to the energy. In the second approximation, called the perturbation theory at the density matrix level only (PTD), the calculation of the reaction potential and electrostatic free energy is based on the MBPT corrected wavefunction for the isolated molecule. At the next approximation (perturbation theory at the energy and density matrix level, PTED), both the energy and the wave function are solvent reaction field and MBPT corrected. The self-consistent reaction field model has been also applied within the complete active space self-consistent field (CAS SCF) theory and the eomplete aetive space second-order perturbation theory. ... 

Potentials that treat the polarization and ionization are important for modeling a number of metal oxide systems. This is difficult since polarization in solids is a many-body effect with various components and depends strongly upon changes in the electronic structure as a function of structure and forces on the ions. One of the most widely used approaches to simulate polarizability effects is that of the Shell model which uses a massless shell of charge (electron density) I 1. 

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