Orbital interactions symmetry-adapted

Molecular orbitals are not unique. The same exact wave function could be expressed an infinite number of ways with different, but equivalent orbitals. Two commonly used sets of orbitals are localized orbitals and symmetry-adapted orbitals (also called canonical orbitals). Localized orbitals are sometimes used because they look very much like a chemist s qualitative models of molecular bonds, lone-pair electrons, core electrons, and the like. Symmetry-adapted orbitals are more commonly used because they allow the calculation to be executed much more quickly for high-symmetry molecules. Localized orbitals can give the fastest calculations for very large molecules without symmetry due to many long-distance interactions becoming negligible. 

An explanation of the direct 4s contribution to the charge density at the nucleus requires MO calculations. A simple MO diagram for octahedral complexes is shown in Fig. 4.4. The a-interaction of metal /-orbitals and symmetry-adapted ligand orbitals usually yields the major part to the stability of the bonds. According... 

Williams HL, Chabalowski CF (2001) Using Kohn-Sham orbitals in symmetry-adapted perturbation theory to investigate intermolecular interactions. J Phys Chem A 105 646-659... 

The interpretation of the results is straight forward. Due to the through space interaction of the two ns orbitals, the symmetry adapted linear combinations n = l/v (nsi nsa) are split. The observed energy difference is between 0.3 eV and 0.5 eV, corresponding to the quantity 21/31, where /3 is the resonance integral between the basis orbitals nsi and ngi in a simple Zero-Differential-Overlap (ZDO) model. A decrease of the center of gravity, indicated by a dot in Fig. 11, is observed with increasing size of the alkyl moiety. 

However, due to the availability of numerous techniques, it is important to point out here the differences and equivalence between schemes. To summarize, two EDA families can be applied to force field parametrization. The first EDA type of approach is labelled SAPT (Symmetry Adapted Perturbation Theory). It uses non orthogonal orbitals and recomputes the total interaction upon perturbation theory. As computations can be performed up to the Coupled-Cluster Singles Doubles (CCSD) level, SAPT can be seen as a reference method. However, due to the cost of the use of non-orthogonal molecular orbitals, pure SAPT approaches remain limited... 

Multipole analysis with high-resolution X-ray data for [Ni(thmbtacn)]2+ was carried out to determine the electron configuration in the C3 symmetry-adapted orbitals of the Ni ion, confirming a higher occupancy of the crystal field-stabilized t2g orbitals relative to the destabilized eg orbitals. This is interpreted in terms of a predominantly ionic metal-ligand interaction.1424... 

FIGURE 18. The symmetry-adapted, orthogonal linear combinations of the localized a-orbitals of norbornadiene 75 belonging to the irreducible representations / and 62 of the point group C2v- The A] and B2 combinations are the relay orbitals for through-bond interaction between jra and 7Tb which define, according to equation 56, the orbitals jt and jt... 

FIGURE 21. Top Photoelectron spectrum of (Z,Z,Z)-cyclonona-l,4,7-triene 189. Bottom Diagram showing the homoconjugative a/n-interaction between the symmetry-adapted linear combinations of the 7T- and of the methylene cr-orbitals... 

A very similar approach can be used to interpret the UPS of bis-chelate complexes of acac, hfa, and related monothio and bisthio analogues (45, 51). Monomeric Ni(acac)2 has been found to possess D2h symmetry in the vapor phase (258), and this geometry is assumed here for the other bis-chelates. In D2d symmetry the rr3, +, and n- MOs of each 0-diketonate ligand combine to afford the symmetry-adapted combinations shown in Fig. 44. Introduction of the metal d orbitals, which transform as ag(d2 ), ag(dx> yz), blg(dxy), bigidxz), and b2g(dyz), completes the scheme. By analogy with the tris-chelates, the strongest interaction anticipated is that between the dxy orbital and the antisymmetric lone pair combination of b g symmetry. 

It is possible to use as the basis functions symmetry-adapted combinations of primitive basis functions. This affords a decomposition of the orbital interaction energy of Eq. [21] according to irreducible representations of the point group... 

In the earlier sections of this chapter we reviewed the many-electron formulation of the symmetry-adapted perturbation theory of two-body interactions. As we saw, all physically important contributions to the potential could be identified and computed separately. We follow the same program for the three-body forces and discuss a triple perturbation theory for interactions in trimers. We show how the pure three-body effects can be separated out and give working equations for the components in terms of molecular integrals and linear and quadratic response functions. These formulas have a clear, partly classical, partly quantum mechanical interpretation. The exchange terms are also classified for the explicit orbital formulas we refer to Ref. (302). 

Current hybrid functionals do not improve this situation. Their non-local component (Hartree-Fock exchange) cannot give rise to any attraction. To describe quantitatively the long-range interactions, either a non-local approximation to Exc[p] must be applied within the Kohn-Sham framework or methods using other-than-Kohn-Sham formalism should be used. Some of such approaches will be discussed in the last section of this review. Here, we mention an especially promising combination of symmetry adapted perturbation theory with of the Kohn-Sham orbitals.125... 

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