Equilibrium Geometry Model

VSEPR model, the dihalides of Be and Mg and the heavier halides of Ca and Sr are essentially linear. However, the other dihalides are appreciably bent, e.g. Cap2 145°, Srp2 -- 120°, Bap2 108° SrCl2 - 130°, BaCh - 115° BaBri -115° Bah 105°. The uncertainties on these bond angles are often quite large ( 10°) and the molecules are rather flexible, but there seems little doubt that the equilibrium geometry is substantially non-linear. This has been interpreted in terms of sd (rather than sp) hybridization or by a suitable id hoc modification of the VSEPR theory. ... 

The model is that the ground-state PES is first altered by the electronic excitations (on-diagonal coupling leads to a change in equilibrium geometry and frequency), and these smooth diabatic states are then further altered by vibronic (off-diagonal) coupling. 

We restrict ourselves again to symmetric tetraatomic molecules (ABBA) with linear equilibrium geometry. After integrating over electronic spatial and spin coordinates we obtain for A electronic states in the lowest order (quartic) approximation the effective model Hamiltonian H = Ho + //, which zeroth-order part is given by Eq. (A.4) and the perturbative part of it of the form... 

The equilibrium geometry and three-center NBOs of the protonated ethylene model are displayed in Fig 3.97. The qualitative similarities to the diborane bridge bond (Fig. 3.93) are evident. Thus, the 7t—s model (cf. Fig. 3.91) may be considered a useful descriptive picture of three-center T-bond formation in diborane. 

Kettle and his co-workers (39—42) used a model rather similar to the AOM to discuss stereochemistry. A perturbation approach led to the proportionality of MO energies (relative to the unperturbed orbitals) to squared overlap integrals, as in the AOM. For systems where the valence shell orbitals are evenly occupied, the total stabilization energy shows no angular dependence, suggesting that steric forces determine the equilibrium geometry. 

In order to understand the origin of the breakdown of the SR methods away from equilibrium, consider the torsional potential in ethylene (Figure 2). While at its equilibrium geometry ethylene is a well-behaved closed-shell molecule whose ground and n-valence excited states can be described accurately by SR models (except for the doubly excited Z-state), it becomes a diradical at the barrier, when the Jt-bond is completely broken (13). Thus, at the twisted geometry all of ethylene s Jt-valence states (N, T, V, and Z) are two-configurational, except for the high-spin components of the triplet. 

This model has the advantage that the atomic polar tensor elements can be determined at the equilibrium geometry from a single molecular orbital calculation. Coupled with a set of trajectories (3R /3G)o obtained from a normal coordinate analysis, the IR and VCD intensities of all the normal modes of a molecule can be obtained in one calculation. In contrast, the other MO models require a separate MO calculation for each normal mode, since the (3p,/3G)o contributions for each unit are determined by finite displacement of the molecule along each normal coordinate. Both the APT and FPC models are useful in readily assessing how changes in geometry or refinements in the vibrational force field affect the frequencies and intensities of all the vibrational modes of a molecule. 

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