Charge distribution, molecular,

Stone A J 1981 Distributed multipole analysis or how to describe a molecular charge distribution Chem. Phys. Lett. 83 233... 

Stone A J 1981. Distributed Multipole Analysis, or How to Describe a Molecular Charge Distribution. Chemical Physics Letters 83 233-239. 

Gaussian also predicts dipole moments and higher multipole moments (through hexadecapole). The dipole moment is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution, and is given as a vector in three dimensions. For Hartree-Fock calculations, this is equivalent to the expectation value of X, Y, and Z, which are the quantities reported in the output. 

Electrostatic Potential Maps and Molecular Charge Distributions... 

The potential from the surface charge is given by the molecular charge distribution (eq. (16.44)), but also enters the Hamiltonian and thus influences the molecular wave function. The procedure is therefore iterative. 

The charge distribution of neutral polar molecules is characterized by a dipole moment which is defined classically by jx = E, , , where the molecular charge distribution is defined in terms of the residual charges (qt) at the position r,. The observed molecular dipole moment provides useful information about the charge distribution of the ground state and its ionic character. 

Geerhngs, P., De Proft, F., Martin, J. M. L., 1996, Density Functional Theory Concepts and Techniques for Studying Molecular Charge Distributions and Related Properties , in Recent Developments and Applications of Modem Density Functional, Seminario, J. M. (ed.), Elsevier, Amsterdam. 

Qa and Qc are the charges obtained from the multipolar expansion of the interacting A and C molecular charge distributions, NyAL and NyAL being their respective number of valence electrons. Wa and Wc are the A and C atoms effective van der Waals radii. Kac is a proportionality factor tabulated upon the atomic numbers of the A and C atoms, a is a constant fixed to 12.35. The same treatment is applied to the others terms of the repulsion energy. 

Vigne-Maeder F, Claverie P (1988) The exact multicenter multipolar part of a molecular charge distribution and its simplified representations. J Chem Phys 88 4934... 

Taking the difference of Eqs. (9-68) and (9-69) yields an expression for the response of the molecular charge distribution to the external field... 

Gatti, C., P. J. MacDougall, and R. F. W. Bader. 1988. Effect of Electron Correlation on the Topological Properties of Molecular Charge Distributions. J. Chem. Phys. 88, 3792. 

Sokalski, W. A., D. A. Keller, R. L. Ornstein, and R. Rein. 1993. Multipole Correction of Atomic Monopole Models of Molecular Charge Distribution. I. Peptides. J. Comput. Chem. 14, 970-976. 

Other electrostatic processes studied include proton binding [43] and changing the molecular charge distribution [44], The free energy expansion formula (12.5) was used, including terms up to second order... 

In contrast, Lambert has proposed that the shift is due to the Stark effect exerted by the electric field at the inner Helmholtz plane on the intra-molecular charge distribution of the adsorbed CO molecule (19). 

In discussing gross atomic charges it must be realized that a given pattern of atomic charge densities in a molecule can be imposed by several factors. We identify three effects responsible for a molecular charge distribution ... 

By = xiytZi) and spin coordinates of individual electrons, n represents the number of electrons in the molecule. For many cases it is appropriate to include nuclear charges as well and to define a molecular charge distribution Q (R) ... 

The theory of molecular structure based on the topology of molecular charge distribution, developed by Bader and co-workers (83MI2 85ACR9), enables certain features to be revealed that are characteristic of the systems with aromatic cyclic electron delocalization. To describe the structure of a molecule, it is necessary to determine the number and kind of critical points in its electronic charge distribution, i.e., the points where for the gradient vector of the charge density the condition Vp = 0 is fulfilled. 

The summation in Eq. (8.53) is slowly converging if a molecular charge distribution is represented by a single set of moments. However, the expression can be written as the summation over the distributed moments, centered at the nuclei j, which is precisely the information available from the multipole analysis ... 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

This chapter introduces a number of useful graphical models, including molecular orbitals, electron densities, spin densities, electrostatic potentials and local ionization potentials, and relates these models both to molecular size and shape and molecular charge distributions. The chapter also introduces and illustrates property maps which simultaneously depict molecular size and shape in addition to a molecular property. Properties include the electrostatic potential, the value of the LUMO, the local ionization potential and the spin density. 

Clearly not Atomic charges are not molecular properties, and it is not possible to provide a unique definition (or even a definition which will satisfy all). It is possible to calculate (and measure using X-ray diffraction) molecular charge distributions, that is, the number of electrons in a particular volume of space, but it is not possible to uniquely partition them among the atomic centers. 

Polarization Potential. Afimction describing the energy of electronic relaxation of a molecular charge distribution following interaction with a point positive charge. The polarization potential may be added to the Electrostatic Potential to provide a more accurate account of the interaction of a point-positive charge and a molecule. 

SMART (Solvent Measurement, Assessment, and Revamping Tool) is a software program that allows assessment of solvents used for batch processing based on both empirical data and property estimation methods (Modi et al., 1996). This system includes a new conjugation based method for the estimation of reaction rates in solution, which is based on the concept that the absolute reaction rate coefficient can be obtained from a function dependent on the change in molecular charge distribution between reactants and activated complex (Sherman et al., 1998). Table 9.2 provides a list of solvent substitution resources available on the World Wide Web. 

One of the most useful features of a QM model is its ability to provide information about the molecular charge distribution. It is a general rule of thumb that even very low quality QM methods tend to give reasonable charge distributions. For neutral molecules, the dominant moment in the overall charge distribution is the usually dipole moment (unless symmetry renders the dipole moment zero). For a 125-molecule test set including H, C, N, O, F, Al, Si, P, S, Cl, Br, and I functionality, Stewart found mean unsigned errors in dipole moments... 

Homonuclear molecules have a center of inversion symmetry. Molecular charge distributions of such symmetry are inconsistent with a permanent... 

---