Doubly excited molecules

It was assumed that the quasiresonant transfer of excitation with the rates Wss or Wsr is due to the multipolar interaction between the excited molecules and the decay of the doubly excited molecules 1,3 A is practically instantaneous [263]. 

The dissociation problem is solved in the case of a full Cl wave function. As seen from eq. (4.19), the ionic term can be made to disappear by setting ai = —no- The full Cl wave function generates the lowest possible energy (within the limitations of the chosen basis set) at all distances, with the optimum weights of the HF and doubly excited determinants determined by the variational principle. In the general case of a polyatomic molecule and a large basis set, correct dissociation of all bonds can be achieved if the Cl wave function contains all determinants generated by a full Cl in the valence orbital space. The latter corresponds to a full Cl if a minimum basis is employed, but is much smaller than a full Cl if an extended basis is used. 

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. 

If the CISD wave functions for two identical molecules are multiplied, to give the wave function for the pair of molecules, there are terms in the resulting wave function in which both molecules are doubly excited. Since these terms represent quadruple excitations from the HF configuration, they are not included in the CISD wave function for two identical molecules at infinity. Consequently, the CISD energy for a pair of identical molecules is higher than twice the CISD energy for an individual molecule. 

If one mode alone is doubly excited, this transition is called the first overtone of the fundamental if one mode alone is triply excited, this is called the second overtone, and so on. Transitions in which two or more modes are simultaneously excited (by one or more units each) are called combination tones. If the molecule initially has one or more fundamentals in an excited (n > 0) state, any transitions that it makes are called hot transitions. 

CIS does not improve on the Hartree-Fock energy, as there is no interaction between the fundamental state and the singly excited states (Brillouin theorem). In CISD, the singly excited states can interact with the fundamental state through the intermediacy of the doubly excited states. We have met a similar situation in three orbital interactions (p. 27) two MOs belonging to the same molecule can interact if perturbed by a third MO belonging to another molecule. 

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