Overlap densities

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

The NDDO (Neglect of Diatomic Differential Overlap) approximation is the basis for the MNDO, AMI, and PM3 methods. In addition to the integralsused in the INDO methods, they have an additional class of electron repulsion integrals. This class includes the overlap density between two orbitals centered on the same atom interacting with the overlap density between two orbitals also centered on a single (but possibly different) atom. This is a significant step toward calculatin g th e effects of electron -electron in teraction s on different atoms. 

The two eflPects above constitute what is called central field covalency since they aflFect both the a and the tt orbitals on the metal to the same extent. There is also, of course, symmetry restricted covalency which acts difiFerently on metal orbitals of diflFerent symmetries. This type of covalency shows up in optical absorption spectra as differences in the values of Ps and p -, as compared with 35. The first two s refer to transitions within a given symmetry subshell while 635 refers to transitions between the two subshells. This evidence of covalency almost of necessity forces one to admit the existence of chemical bonds since it is difficult to explain on a solely electrostatic model. The expansion of the metal orbitals can be caused either by backbonding to vacant ligand orbitals, or it may be a result of more or less extensive overlap of ligand electron density in the bond region. Whether or not this overlap density can properly be assigned metal 3d character is what we questioned above. At any... 

The ability to use precisely the same basis set parameters in the relativistic and non-relativistic calculations means that the basis set truncation error in either calculation cancels, to an excellent approximation, when we calculate the relativistic energy correction by taking the difference. The cancellation is not exact, because the relativistic calculation contains additional symmetry-types in the small component basis set, but the small-component overlap density of molecular spinors involving basis functions whose origin of coordinates are located at different centres is so small as to be negligible. The non-relativistic molecular structure calculation is, for all practical purposes, a precise counterpoise correction to the four-component relativistic molecular... 

Zimmerman, H. E. Alabugin, I. V. Energy Distribution and Redistribution and Chemical Reactivity. The Generalized Delta Overlap-Density Method for Ground State and Electron Transfer Reactions A New Quantitative Counterpart of Electron-Pushing. J. Am. Chem. Soc. 2001, 123, 2265-2270. 

The summation of Eq. (3.7) contains one- and two-center terms for which (/> and 0V are centered on the same, and on different nuclei, respectively. The two-center terms represent the overlap density in a bond they can only give a significant contribution to the density if and < v(r) have an appreciable value in the same region of space, and are therefore not important for distant atoms. 

That the positive bias in the scale factors correlates with an increase in thermal parameters is evident from comparison of X-ray and neutron results (Coppens 1968). The apparent increase in thermal parameters of some of the atoms may be interpreted as the response of the spherical-atom model to the existence of overlap density. Because of the positive correlation between the temperature parameters and k, this increase is accompanied by a positive bias in k. 

For HF, the F atom in the oriented reference state of the chemical deformation density has 1.414 e (rather than 5/3 = 1.67 e in the spherical atom, or 1 e in the oriented atom) in the pa orbital, and 1.793 e (rather than 1.67 e in the spherical atom, or 2 e in the oriented atom) in each of the pn orbitals. As in Fig. 5.4(b) and (c), the trough along the bond axis of the total deformation density disappears, and the overlap density becomes evident. 

Figure 6.1 shows the stockholder decomposition of the theoretical deformation density of the cyanoacetylene molecule, H—Cs=C—C=N (Hirshfeld 1977b). The overlap density in the bonds is distributed between the bonded atoms. The assignment of part of the density near the hydrogen nucleus to the adjacent carbon atom manifests the difference between fuzzy and discrete boundary partitioning methods. 

That the vibrational displacements of the valence shell electrons may be smaller than those of the core electrons can be qualitatively understood by considering the vibrations of two identical, strongly bonded atoms. When the atoms vibrate in phase, they behave as a rigid body, so all shells will vibrate equally. But when they vibrate out of phase, the density near the center of the bond will be stationary, assuming the average static overlap density to be independent of the vibrations. This apparently invariant component of the valence density would contribute to a lowering of the outer-shell temperature... 

Goulomb interaction integrals over molecular orbitals can be written as a sum of similar interaction integrals with G-spinor overlap densities and... 

The J v matrix elements represent the classical interaction energy of the overlap density pfi, with the electron distribution. Following Almlof [20], we can write this in the form... 

It is possible to assume that the absorption intensity originates mainly from the locally excited zero-order state since the AB+ zero-order state should barely contribute at all owing to the small overlap density of donor and acceptor orbitals. Therefore, the S, or T( should be reached at planar geometries by vertical excitation into the dominantly locally excited states. Only for the best donor-acceptor subunit combinations and high-lying locally excited states, a motion from planar minimum toward twisted minimum in S, or T, will be barrierless. Otherwise, a thermal activation is needed to overcome the barrier caused by crossings of zero-order states. 

Since we neglected overlap between orbitals of subunits, overlap densities a(l)b(l) and a (2)b (2) are negligible. The matrix element //, for the singlet state can be approximated by the electrostatic interaction between transition densities aa on subunit A and bb on subunit B ... 

If the overlap between two subunits is negligible, the overlap densities a(l)6(l) and a 2)b 2) are negligible and H2 matrix element vanishes as well. 

The monomer-monomer correlation functions of flexible polyelectrolytes exhibit qualitatively the same behavior as those for rod-like molecules. The conformational changes, however, result in more pronounced and shifted peaks. From Fig. 8 we deduce a shift of the peaks of flexible chains to larger distances compared to those of rod-like chains. This is a consequence of a smaller overlap between flexible chains compared to the one between rodlike molecules. Naturally, the effect is most pronounced for densities larger than the overlap densities. The increased peak intensity corresponds to a more pronounced order in the system of flexible chains, and is a result of the more compact structure of a polymer coil. (The structural properties of flexible polyelectrolytes without medium-induced potential have been studied in [48].)... 

Becke exchange and LYP correlation functional Complete Active Space Self-Consistent Field Configuration Interaction Complete Neglect Differential Overlap Density Functional Theory... 

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