By John R. Sabin and Erkki Brändas (Eds.)
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Extra info for Combining Quantum Mechanics and Molecular Mechanics. Some Recent Progresses in QM/MM Methods
Barone et al. improved by increasing the limit for the number of integrals computed for each class of transitions: NImax . A higher number of allowed transitions obviously yields a better spectrum convergence but also directly increases the required computational time and memory usage. Skipping prefactors and the dependence on the frequency, the intensity of a given transition is equal to Iðn; n 0 Þ ¼ jhnjmif ðQ0 Þjn 0 ij2 and summing over all the possible final states one gets X X a Itot ¼ jh n j mif ðQ0 Þ jn 0 ij2 ¼ hnj2if R ðQ0 Þ j ni; ð26Þ 0 R¼x;y;z where the superscript a indicates that the sum has been carried out analytically by exploiting the closure relation.
According to several other methodologies [45–52] developed in the framework of QM continuum models, we have also treated WdispÀrep as a classical mean force potential not perturbing the system electronic density. In particular, WdispÀrep is obtained from an effective empirical procedure parametrized on structural and thermodynamic properties originally presented in Ref.  and further developed in Ref.  (see also Refs. [35 and 31] for applications in the context of MM and QM/MM MD simulations, respectively).
While this approximation is known to lead to very good results in many cases, it becomes not satisfactory for the dipole-forbidden [mif ðQ00 Þ ¼ 0] or weakly allowed transitions. In these cases, one needs to improve the model and to add the second term [Herzberg–Teller (HT) term]. Then, a limited change in the structure during the transition is taken into account. For many studied systems, the FC and HT approximations are sufficient to correctly describe both absorption and emission spectra, but for symmetry-forbidden transitions a correct reproduction of intensity of weak bands may require the inclusion of higher order terms .