Cumulative atomic multipole moments

Sokalski, W. A., K. Maruszewski, P. C. Hariharan, and J. J. Kaufman. 1989. Library of Cumulative Atomic Multipole Moments II. Neutral and Charged Amino Acids. Int. J. Quantum Chem. Quantum Biol. Symp. 16,119-164. 

Recently, Sokalski et al. presented distributed point charge models (PCM) for some small molecules, which were derived from cumulative atomic multipole moments (CAM Ms) or from cumulative multicenter multipole moments (CMMMs) [89,90] (see Sect. 3.2). For this method the starting point can be any atomic charge system. In their procedure only analytical formulas are used,... 

These atomic contributions depend on the choice of the coordinate origin. A space invariant form can be obtained using the cumulative approach [93, 94]. The space invariant cumulative atomic multipole moments (CAMMs) do not contain contributions from lower moments. The definition of the CAMMs is as follows ... 

Sokalski WA, Sawaryn A (1987) Correlated molecular and cumulative atomic multipole moments. J Chem Phys 87 526-534... 

W. A. Sokalski and A. Sawaryn,/. Chem. Phys., 87, 526 (1987). Correlated Molecular and Cumulative Atomic Multipole Moments. 

The marching-cube algorithm has been used also by Kolle and Jug (1995) to define the tesserae of isodensity surfaces. The procedure is implemented in the semiempirical SINDOl program (INDO with Slater-type orbitals, Li et al., 1992). To compute AS charges the asymptotic density model ADM (Koster et al., 1993) is used. This is an approximation to the calculation of molecular electrostatic potentials based on the cumulative atomic multipole moment procedure (CAMM, Sokalski et al., 1992). 

A. Sawaryn and W. A. Sokalski, Comput. Phys. Commun., 52, 397 (1989). Cumulative Atomic Multipole Moments and Point Charge. Models Describing Molecular Charge Distribution. 

It is seen that when the origins are located on atoms, we have an intermediary situation, and it might be sufficient to have a few multipoles per atom. This is what the concept of the so-called cumulative atomic multipole moments is all about (CAMM ). Besides the isotropic... 

P-27 - Cumulative coordinates for approximations of atomic multipole moments in cationic forms of aluminosilicates... 

With this asymptotic density model (ADM) an advantage over the standard multipole expansion can be achieved, so that the MESP is well approximated not only outside the molecule, but also near the atoms. This scheme has been implemented in SINDOl for first- and second-row elements. The evolving expansion has been truncated after the cumulative dipole moments terms. The three-center integrals have been approximated on the NDDO level. In order to achieve good agreement with ab initio based MESPs, the atomic hybrid moments had to be scaled. In the application to. solvation energies the atomic electronic charges had to be scaled too. 

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