The quasidiabatic, coupled electronic state, fully quadratic Hamiltonian (Hd), suitable for the simulation of spectra exhibiting strong vibronic couplings and constructed using a recently introduced pseudonormal equations approach, is studied. The flexibility inherent in the normal equations approach is shown to provide a robust means for (i) improving the accuracy of Hd, (ii) extending its domain of utility, and (iii) determining the limits of the fully quadratic model. The two lowest electronic states of pyrrolyl which are coupled by conical intersections are used as a test case. The requisite ab initio data are obtained from large multireference configuration interaction expansions comprised of 108.5×106 configuration state functions and based on polarized triple zeta quality atomic orbital bases.

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