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While carrying out Beyond Born–Oppenheimer theory based diabatization, the solutions of adiabatic-to-diabatic transformation equations depend on the paths of integration over two-dimensional cross-sections of multi-dimensional space of nuclear degrees of freedom. It is shown that such path-dependent solutions leading to diabatic potential energy surface matrices computed along any two different paths are related through an orthogonal matrix, and thereby, those surface matrices should provide unique observables. While exploring the numerical validity of the theoretical framework, we construct diabatic Hamiltonians for the five low-lying electronic states ( X ̃ 2 E 1 g , B ̃ 2 E 2 g , and C ̃ 2 A 2 u ) of benzene radical cation ( C 6 H 6 + ) along three different approaches of contour integration over two dimensional nuclear planes constituted by seven non-adiabatically active normal modes. Three different diabatic surface matrices are further employed to generate the photoelectron spectra of the benzene molecule (C6H6). It is interesting to note that the spectral peak positions and intensity patterns for all three cases are almost close to each other and also exhibit very good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

We employ theoretically "exact" and numerically "accurate" Beyond Born–Oppenheimer (BBO) treatment to construct diabatic potential energy surfaces (PESs) of the benzene radical cation ( C 6 H 6 + ) for the first time and explore the workability of the time-dependent discrete variable representation (TDDVR) method for carrying out dynamical calculations to evaluate the photoelectron (PE) spectra of its neutral analog. Ab initio adiabatic PESs and nonadiabatic coupling terms are computed over a series of pairwise normal modes, which exhibit rich nonadiabatic interactions starting from Jahn–Teller interactions and accidental conical intersections/seams to pseudo Jahn–Teller couplings. Once the electronic structure calculation is completed on the low-lying five doublet electronic states ( X ̃ 2 E 1 g , B ̃ 2 E 2 g , and C ̃ 2 A 2 u ) of the cationic species, diabatization is carried out employing the adiabatic-to-diabatic transformation (ADT) equations for the five-state sub-Hilbert space to compute highly accurate ADT angles, and thereby, single-valued, smooth, symmetric, and continuous diabatic PESs and couplings are constructed. Subsequently, such surface matrices are used to perform multi-state multi-mode nuclear dynamics for simulating PE spectra of benzene. Our theoretical findings clearly depict that the spectra for X ̃ 2 E 1 g and B ̃ 2 E 2 g − C ̃ 2 A 2 u states obtained from BBO treatment and TDDVR dynamics exhibit reasonably good agreement with the experimental results as well as with the findings of other theoretical approaches. [ABSTRACT FROM AUTHOR]

In order to circumvent numerical inaccuracy originating from the singularity of nonadiabatic coupling terms (NACTs), we need to perform kinetically coupled adiabatic to potentially coupled diabatic transformation of the nuclear Schrödinger Equation. Such a transformation is difficult to achieve for higher dimensional sub-Hilbert spaces due to inherent complicacy of adiabatic to diabatic transformation (ADT) equations. Nevertheless, detailed expressions of ADT equations are formulated for six coupled electronic states for the first time and their validity is extensively examined for a well-known radical cation, namely, 1,3,5- C 6 H 3 F 3 + (TFBZ+). While implementing this formulation, we compute ab initio adiabatic potential energy surfaces (PESs) and NACTs within the low-lying six electronic states ( X ̃ 2 E ′ ′ , Ã 2 A 2 ′ ′ , B ̃ 2 E ′ , and C ̃ 2 A 2 ′ ), where several types of nonadiabatic interactions, like Jahn-Teller conical intersections (CI), accidental CIs, accidental seams (series of degenerate points), and pseudo Jahn-Teller interactions can be observed over the Franck-Condon region of nuclear configuration space. Those interactions are depicted by exploring degenerate components of C–C asymmetric stretching, C–C symmetric stretching, and C–C–C scissoring motion (Q9x, Q9y, Q10x, Q10y, Q12x, and Q12y) to compute complete active space self-consistent field level adiabatic PESs and NACTs as implemented in the MOLPRO quantum chemistry package. Subsequently, we perform the ADT using our newly devised fifteen (15) ADT equations to locate the position of CIs, verify the quantization of NACTs, and to construct highly accurate diabatic PESs. [ABSTRACT FROM AUTHOR]

We review our development on beyond Born–Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years. The theoretical formulation leading to the BBO equations are thoroughly discussed with ab initio calculations. We have employed first principle based BBO theory not only to formulate single surface extended Born–Oppenheimer equation to understand the nature of nonadiabatic effect but also to construct accurate diabatic potential energy surfaces (PESs) for important spectroscopic systems, namely, NO 2 radical, Na 3 and K 3 clusters, NO 3 radical, benzene and 1,3,5-trifluorobenzene radical cations ( C 6 H 6 + and C 6 H 3 F 3 + ) as well as triatomic reactive scattering systems like H + + H 2 and F + H 2 . The nonadiabatic phenomena like Jahn–Teller (JT), Renner–Teller, pseudo Jahn–Teller effects and the accidental conical intersections are the key players in dictating spectroscopic and reactive scattering profiles. The nature of diabatic coupling elements derived from ab initio data with BBO theory for molecular processes in Franck-Condon region has been analysed in the context of linearly and bilinearly coupled JT model Hamiltonian. The results obtained from quantum dynamical calculations on BBO based diabatic PESs of the above molecular systems are found to be in accord with available experimental outcomes. [ABSTRACT FROM AUTHOR]