Potential-derived atomic multipole

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. 

A class of improved population analysis schemes has been designed to reproduce the total dipole moment of the molecule when calculated by point charges. Such a dipole moment conserving procedure was proposed e.g. by Jug [99] and by Thole and van Duijnen [100]. A more general multipole fitted scheme has also been derived [101]. A slightly different approach is to determine potential derived atomic charges which are fitted to reproduce the values of the electrostatic potential outside the van der Waals envelope of the molecule [102, 103]. 

Stone s DMA method has been applied in several other papers. Our review cannot be exhaustive but we would like to quote two additional papers using this approach because they give additional information on the basic problems of the electrostatic approach. Price, Harrison and Guest [89] examined the DMA description of the MEP of a large molecule, with formula C63H113N11O12, obtained from a 3-21G SCF wavefunction. The description of the electrostatic potential obtained in such a way is comparable to that obtained with potential derived atomic charges (PD-AC) to which we shall refer later on in more detail. The superiority of a distribute multipole description, in describing the anisotropic contributions to the MEP on the van der Waals surface is shown clearly. 

Tel. 502-852-5975, fax 502-852-8149, e-mail dewO 1 uxray5. chem.louisville.edu Electric Potential Derived Multipoles method to find optimized net atomic charges and other site multipole representations. Accepts input from Gaussian 92. UNIX workstations and VAX. 

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. 

J. Kong and J.-M. Van, Int. ]. Quantum Chem., 46, 239 (1993). The Effects of Atomic Multipole Moments Obtained by the Potential-Derived Method on Hydrogen Bonding. 

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. 

W. A. Sokalski and R. A, Poirer, Chem. Phys, Lett., 98, 86 (1983). Cumulative Atomic Multipole Representation of the Molecular Charge Distribution and Its Basis Set Dependence. D. E. Williams and D. J. Craycroft, J. Phys, Chem., 89, 1461 (1985). Estimation of Dimer Coulombic Intermolecular Energy and Site Charge Polarization by the Potential-derived Method. 

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. 

To evaluate this expression for distributions expressed in terms of their multipolar density functions, the potential <1> and its derivatives must be expressed in terms of the multipole moments. The expression for charge distribution has been given in chapter 8 [Eq. (8.54)]. Since the potential and its derivatives are additive, a sum over the contributions of the atom-centered multipoles is again used. The resulting equation contains all pairwise interactions between the moments of the distributions A and B, and is listed in appendix J. 

A factor -2 included in the last term here compensates for the use of Rydberg units and for the omission of the negative electronic charge in potential functions derived from Eq. (7.14). Hence the electrostatic multipole moments of atomic cell r/( are... 

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