Inter-state coupling constant

Eor the inter-state coupling constants, displacement along a single normal coordinate Qi usually leads to a coupling of two component states only, with a 2 x 2 coupling matrix lE of the following form [6] ... 

In practical applications of the theory, the computational problem is simplified by restricting the electronic Hilbert space to just two or three electronic states of interest, e.g. the ground state and two excited states. A further significant simpiification arises from symmetry selection rules. It follows from the definition (10) that the first-order intra-state coupling constants can be nonzero only for totally symmetric modes. Wnn (0) is zero if and transform according to different irreducible representations. The first-order inter-state coupling constant A is nonzero only for modes which transform according to the irreducible representation Tq which fulfils... 

The computation of the inter-state coupling constants being defined as first derivatives of off-diagonal elements of the electronic Hamiltonian in the diabatic representation (see Eq. (11)), appears at first sight to be more difficult. It can be shown, however, by analj ng the adiabatic PE functions associated with the vibronic-coupling Hamiltonian (13) that the A -"" can be determined from second derivatives of the adiabatic energies with respect to the nontotally symmetric coordinate Qj. For an electronic two-state system, the following simple formula results ... 

Since commutes with the molecular Hamiltonian in the absence of electronic inter-state couplings, P it) becomes a constant of motion in this limit. Correspondingly, P (t) becomes a constant of motion if the nona-diabatic coupling operators are neglected. The populations P (t) are thus a direct measure of nonadiabatic transitions in either the diabatic or the adiabatic representation. ... 

A reliable electronic-structure model which provides a balanced description of the electronic states of interest is required for the computation of inter-state vibronic coupling constants. In particular, artifactual symmetrybreaking effects in the electronic wave function should be avoided. For excited electronic states, a CASSCF/MRCI description with appropriately chosen active space is generally to be recommended. For ionized states, the OVGF method, the ADC(3) method or the EOM-CC method have been found to be appropriate tools. 

A reliable electronic-structure model which provides a balanced description of the electronic states of interest is required for the computation of inter-state vibronic coupling constants. In particular, artifactual symmetry-breaking effects in the... 

Significant inter-ring bond torsional (twisting) coupling to the ground state could occur, resulting in a large radiationless rate constant for Ti —> So... 

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