Energy total overlap

Fig. 11 0 Competition by ligands for Ihe ir bonding d orbilul of a central metal atom. Relative overtop is symbolized by the shaded areas, (a) Equal aod strong tr bonds resulting from equal and good overlap of Ihe two carbon monoxide sr orbitals with the meial J orbital (b) Superior overlap of carbon monoxide t orbital wilh polarized metal d orbiial compared lo poorer overlap between ligand <1 and metal d orbitals. Polarization (mixing of higher energy wave functions) occurs so as to maximize total overlap Recall that the overlap integral includes both spatial and intensive properties Ihe represemation above is a graphic simplification.

Table 9. Effective charges (QM, total overlap populations (OP), dipole moments (p), dielectric dipole polarizabilities (a), ionization potentials (IP) and atomization energies (DJ for MO,Cl (M - Tc, Re, and Bh). From [ 1131. ...

Finally the most sensitive scheme to differentiate between the shapes of closely related conformers is by comparison of the total overlap energy [148]. It extends the calculation of electrostatic overlap energy (5.8.1) over all pairs of atoms in the molecule. This procedure mimics the calculation of molecular quantum potential even more closely than MM and eliminates the scaling of different types of steric energy. 

A calculation has also been made on the relative energies of Pt(7r-MeC=CH)(PH3)2 and PtH(C=CMe)(PHg)2 (295). Consideration of total overlap population showed that the Tr-complex is definitely less stable than either the cis or trans oxidative adduct. The acetylenic hydrogen on the 7r-complex is considered to be almost completely hydridic, and it is proposed that the monosubstituted 7r-acetylene complex rearranges to the hydroacetylide complex via an S l (lim) mechanism involving loss of hydride, rearrangement to a new cationic complex, and recombination. The rearrangement reaction is visualized as follows ... 

Total Overlap Population. While the above study of the individual bond overlap populations is helpful in following the changes occurring in the proposed mechanism steps, the total overlap population, presented in Table V, does not appear to be a useful value. The total overlap population is the sum over all pairs of atoms A and B of the overlap population 0P B defined above. All intermediates and products haveDlower total overlap than the reactants, and the apparently lower energy acid catalyzed pathway does not have the largest total overlap of the three pathways studied. 

Total Overlap Energy. However, while total overlap population does not appear to be a useful parameter, the calculated total overlap energy, as presented in Table VI, does. The total overlap energy is the sum over all pairs of atoms A and B of the overlap energy, 0E.., which is defined similarly to the overlap population above, but elements of the H-matrix are used in place of elements of the overlap matrix ... 

Total Overlap Energy (g-kcal/mole, relative to reactants)... 

A recent comparison (33.) of quantities calculated from molecular electronic wave functions for pyrrole and pyrazole indicated that ARCANA values compared more favorably with large-scale ab initio values than those calculated by other non-rigorous methods in the case of orbital energies of occupied molecular orbitals, gross atomic populations of heteroatoms, and total overlap populations including negative overlap populations between nonbonded atoms. 

If both the M0DP0T and VRDD0 approximations are introduced, the accuracy [ see footnote page Ul9] with respect to the reference calculations is about the same as that obtained using only the M0DP0T approximation. The maximum error in the orbital energies is 0.012 a.u., in the gross atomic populations is 0.009> in the total overlap populations is 0.027 and in the dipole moment is 0.009 a.u. 

The repulsion energy, Erep, is modeled as proportional to intermolecular overlap. The total overlap integral between the charge densities of any two molecules, Sab, is calculated by numerical integration over the original uncondensed densities, and is... 

Preliminary studies for Te4 indicate different orbital exponents, 2.12 or 2.45, depending on the choice of total overlap energy or total overlap population as the criterion of stationary property. Further calculations for Sc4 with a 3d STO produce a flatter curve similar to that of Figure 1. 

Figure 5 - Change in total energy and overlap population for concerted reductive elimination of ethane and propene.

---