Multipole representation

When the non-electrostatic terms are semiempirical, they also make up in an average way for systematic deficiencies in the treatment of electrostatics, e.g., for the truncation of the distributed multipole representation of the solute charge density at the monopole term on each center. 

Sokalski WA, Poirier RA (1983) Cumulative atomic multipole representation of the molecular charge distribution and its basis set dependence. Chem Phys Lett 98 86-92... 

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. 

The accuracy of a distributed multipole representation can always be tested by evaluating the effect on the calculated electrostatic energies in the region of interest of increasing the number of interaction sites (e.g., by adding sites at the midpoints of bonds) or the order of multipoles. Similarly, simplifications of the model, such as removing small multipole components, can be evaluated. However, the accuracy of the calculated electrostatic energies is inevitably limited by the quality of the wavefunction and the absence of penetration effects. 

Finally, supposing the origin to be at the center of the sphere, we can expand u(oo) at ill) in a multipole representation in terms of the values of u(co) and higher-order derivatives of u(co) at the position occupied by the center of the sphere ... 

W. A. Sokalski, C/zem, Phys. Lerf., 98, 86 (1983). Cumulative Atomic Multipole Representation of the Molecular Charge Distribution and Its Basis Set Dependence. 

The model of molecule visualized in virtually all popular computer programs shows spherical atoms and chemical bonds as shining rods connecting them. First of aU, atoms are not spherical, as is revealed by Bader analysis (p. 667) or atomic multipole representations (see Appendix S available at booksite.elsevier.com/978-0-444-59436-5). Second, a chemical bond resembles more a rope (higher values) of electronic density than a cylindrical rod. The tope is not quite straight and is slimmest at a critical point (see p. 671). Moreover, the rope, when cut... 

Electrostatic Energy in the Multipole Representation Plus the Pmetiation Enagy Induction Energy in the Multipole Representation Dispersion Energy in the Multipole Representation Dispersion Energy Model-Calculation on Fingers... 

Electrostatic Energy in the Multipole Representation Plus the Penetration Energy... 

The goal of the present section is to take apart the induction mechanism by showing its multipole components. If we insert the multipole representation of V into the induction energy B), then... 

After inserting V in the multipole representation into the expression for the dispersion energy, we obtain... 

Electrostatic energy in the multipole representation and the penetration energy... 

Dispersion energy in the multipole representation Symmetry-Adapted Perturbation Theories (SAPT) ( U )... 

ELECTROSTATIC ENERGY IN THE MULTIPOLE REPRESENTATION AND THE PENETRATION ENERGY... 

Electrostatic energy (p. 693) represents the first-order correction in polarization perturbational theory and is the mean value of V with the product wave function = a,o b,o- Because we have the multipole representation of V, we may insert it into formula (13.5). 

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