Potential energy surface variational approach

The presence or absence of a homoaromatic interaction is often based solely on the distance between the non-bonded atoms. Distances greatly over 2.0 A are thought to lead to a p-p overlap that is too small to make any significant contribution. This simplistic approach is not necessarily reliable as shown by Cremer et al. (1991). Their calculations on the homotropylium cation [12] indicate a double-minimum potential energy surface with respect to variations of the C(l)-C(7) distance at the Hartree-Fock level of theory. At the MP4(SDQ) level of theory, only a single-minimum curve was found with the minimum at 2.03 A. The calculated potential energy curves are quite flat in this region. 

The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches. 

Fig. 5.40 The distribution of electron density (charge density) p for an atom the nucleus is at the origin of the coordinate system, (a) Variation of p with distance from the nucleus. Moving away from the nucleus p decreases from its maximum value and fades asymptotically toward zero, (b) Variation of — p with distance from the nucleus —p becomes less negative and approaches zero as we move away from the nucleus. The —p picture is useful for molecules (Fig. 5.41) because it makes clearer analogies with a potential energy surface, (c) A 4-D picture (p vs x, y, z) of the variation of p in an atom the density of the dots (number of dots per unit volume) indicates qualitatively electron density p in various regions...

The ab initio spin-coupled valence bond (SCVB) approach continues to provide accurate ground and excited state potential energy surfaces for use in a variety of subsequent applications, with particular emphasis on intermolecular forces and reactive systems. The compactness of the various wavefunctions allows direct and clear interpretation of the correlated electronic structure of molecular systems. Recent developments, in the form of SCVB and MR-SCVB, involve the optimization of virtual orbitals via an approximate energy expression. These improved virtuals lead to still higher accuracy for the final variational wavefunctions, but with even more compact wavefunctions. 

The treatment of the vibrational NLO properties in the previous sections employed either the Bishop-Kirtman perturbational theory (BKPT) or the finite field-nuclear relaxation (FF-NR) approach. These approaches may fail for molecules containing large amplitude anharmonic motions, as indeed was suspected to happen in Li C6o-In such cases a more recently proposed variational method, based on analytical response theory [78, 79], would in principle be applicable, but is computationally extremely expensive, as it requires an accurate numerical description of the potential energy surface (PES), at least if the anharmonicity is so large that a power series expansion of the PES is inadequate [80]. 

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