Beyond Born–Oppenheimer based diabatic surfaces of 1,3,5-C₆H₃F₃⁺ to generate the photoelectron spectra using time-dependent discrete variable representation approach

Abstract

In this article, Beyond Born-Oppenheimer (BBO) treatment is implemented to construct diabatic potential energy surfaces (PESs) of 1,3,5-C6H3F3+ over a series [eighteen (18)] of two-dimensional (2D) nuclear planes constituted with...

Curl condition: Existence of sub‐Hilbert space for molecular species or chemical processes

“…While exploring the existence of three state SHS (, ) for the above two sets of normal mode pairs, we compute the Mathematical Curls () and ADT Curls () using their explicit expressions as functions of ADT angles [30,49] (see Subsections S3.3.2 and S3.2.2 of SI). One‐dimensional (1D) variation of those quantities ( and ) are presented along the coordinate for various values of in Figure 1.…”

“…The calculated ADT angles [49] are used to compute Mathematical Curls (Z ij ρϕ ) and ADT Curls (C ij ρϕ ) using their explicit expressions in terms of those mixing angles (see Subsections S3.3.5 and S3.2.5 of SI). Figure 4 Since Ti 4þ center of TiO 8À 6 (Titanate) unit in BaTiO 3 crystal is a d 0 system, the ground state of the titled system belongs to 1 A 1g symmetry and the immediate next three excited states are triply degenerate ( 1 T 1u ), which shows JT couplings within excited states ( 1 T 1u ) and exhibits feeble PJT interactions with 1 A 1g state through g-symmetric normal mode pairs, like Q t1gx À Q t1gy .…”

Construction of Beyond Born‐Oppenheimer Based Diabatic Surfaces and Generation of Photoabsorption Spectra: The Touchstone Pyrazine (C4N2H4)

“…Our earlier studies [22,[63][64][65][66][67][68]76,90] have firmly established that if the adiabatic PESs and NACTs exhibit even-parity functional forms along some nuclear DOFs, the associated diabatic PESs and couplings also retain the (even) parity. Such unique feature is observed along one of the components in most of the degenerate pair of asymmetric stretching/bending modes or even some specific non-degenerate normal modes.…”

“…9 and 14]. Since those pathdependent diabatic matrices are connected through an orthogonal transformation matrix, [65,76] the calculated observables from those matrices appear to be path-independent. In Section S2 of SI, we present a brief discussion on the theoretical outline of path-dependence of diabatic PESs matrix and their equivalence with each other.…”

“…Our group has utilized such an elegant theory to compute high resolution spectral bands of a variety of floppy molecules of spectroscopic interest [20–24,72–75] . In our recent works, TDDVR dynamics has been carried out over BBO based diabatic PESs of benzene (C 6 H$${{}_{6}^{+}}$$ ) [22] and trifluorobenzene (1,3,5‐C 6 H 3 F$${{}_{3}^{+}}$$ ) [76] radical cations with the aim of computing the photoelectron (PE) spectra of their neutral counterparts.…”