Potential-derived atomic multipole models

J. P. Ritchie and A. S. Copenhaver, J. Comput. Chem., 16, 777 (1995). Comparison of Potential-Derived Charge and Atomic Multipole Models in Calculating Electrostatic Potentials and Energies of Some Nucleic Acid Bases and Pairs. 

D. E. Williams, J. Comput. Chem., 9, 745 (1988). Representation of the Molecular Electrostatic Potential by Atomic Multipole and Bond Dipole Models. D. E. Williams, Biopolymers, 29, 1367 (1990). Alanyl Dipeptide Potential-Derived Net Atmnic Charges and Bond Dipoles, and Their Variation with Molecular Conformation. 

D. E. Williams and J.-M. Yan, Adv. Atomic Mol. Phys., 23, 87 (1988). Point-Charge Models for Molecules Derived from Least-Squares Fitting of the Electric Potential. See also, D. E. Williams, this volume. Net Atomic Charge and Multipole Models for the ab Initio Molecular Electric Potential. 

The solute charge distribution can be represented by atom centered point charges or as multipole expansions. Of course, if the solute is treated quantum mechanically the charge distribution can be obtained directly from its wave function. Depending on the solvation model, the electrostatic potential derived from the wave function is fitted to atomic charges or multipoles that are then used to construct the solvent reaction field. 

It is has been known that the atomic multipole moments for atoms in AMOEBA model can be calculated through quantum mechanics method and Stone s distributed multipole analysis [61]. Thus, it is straightforward to obtain the parameters of electric multipole potentials based on the distributed multipole analysis after the EMP sites of Gay-Berne particles are decided or directly from AMOEBA force field. However, the EMP parameters of Gay-Berne particles need to be optimized because they are derived based on the gas-phase ab initio quantum mechanics. One possible solution would be to match GBEMP and AMOEBA results for the electrostatic energies between CG particles and water molecules, or between CG particle dimers, at various separations and/or in different orientations. 

In another approach, He et al. (He et al., 2013) proposed a 2-site per nucleotide (NARES-2P, nucleic acid united residue 2-point model) CG model where chain connectivity, excluded volume and base dipole interactions are sufficient to form helical DNA and RNA structures. This model was parametrized using a bottom-up strategy by employing a set of statistical potentials, derived from DNA and RNA structures from the Protein Data Bank, and the Boltzmann inversion method to reproduce the structural features. The base-base interactions were parametrized by fitting the potential of mean force to detailed all-atoms MD simulations using also the Boltzmann inversion approach. The respective potentials do not explicitly define the nucleic-acid structure, dynamics and thermod3mamics, but are derived as potentials of mean force. By detailed analysis of the different contribution to the Hamiltonian, the authors determined that the multipole-multipole interactions are the principal factor responsible for the formation of regular structures, such as the double helical structures. 

A classical description of M can for example be a standard force field with (partial) atomic charges, while a quantum description involves calculation of the electronic wave function. The latter may be either a semi-empirical model, such as AMI or PM3, or any of the ab initio methods, i.e. HF, MCSCF, CISD, MP2 etc. Although the electrostatic potential can be derived directly from the electronic wave function, it is usually fitted to a set of atomic charges or multipoles, as discussed in Section 9.2, which then are used in the actual solvent model. 

Another method is to calculate the molecular electronic electrostatic potential by replacing p(r ) in Eq. 19 by its multipole formulation (Eq. 8). The quantity obtained represents the electrostatic potential of a molecule removed from the crystal lattice. First calculations have been performed by the Pittsburgh group (Stewart, Craven, He, and co-workers) [43] electrostatic potential calculations were also derived from the Hansen Coppens [lib] electron density model [41,44], The atomic total electrostatic potential including nuclear contribution may be calculated as ... 

Another simpler systematic potential was derived for chlorine, using the two atomic sites for the distributed multipoles and dispersion coefficients. The anisotropic atom-atom repulsion potential was derived from the overlap model, with the proportionality constant and one major anisotropic coefficient being adjusted by empirical fitting to the crystal structure. This empirical adjustment appeared to effectively absorb the missing contributions, including the many-body effects, because the potential was able to reproduce a wide range of properties of the solid and liquid from Monte Carlo simulations. 

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