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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]

A thorough investigation has been performed for electronic structure, topological effect, and nuclear dynamics of NO2 molecule, where the adiabatic potential energy surfaces (PESs), conical intersections between the ground (X²A1) and the first excited state (A²B2), and the corresponding non-adiabatic coupling terms between those states are recalculated [Chem. Phys. 416, 11 (2013)] to achieve enough accuracy in dynamics. We employ beyond Born-Oppenheimer theory for these two state sub-Hilbert space to carry out adiabatic to diabatic transformation (ADT) to obtain the ADT angles and thereby, to construct single-valued, smooth, and continuous diabatic PESs. The analytic expressions for the adiabatic PESs and ADT angles are provided to represent a two-state three-mode diabatic Hamiltonian of NO2 for performing nuclear dynamics to calculate the photoelectron spectra of its anion. It appears that not only Jahn-Teller type coupling but also Renner-Teller interaction contributes significantly on the overall spectrum. The coupling between the electronic states (X²A1 and A²B2) of NO2 is essentially through the asymmetric stretching mode, where the functional form of such interaction is distinctly symmetric and non-linear. [ABSTRACT FROM AUTHOR]

We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non-Adiabatic Coupling Terms (NACTs) for the three lowest singlet states of H+3 in hyperspherical coordinates as functions of hyperangles (θ and ɸ) for a grid of fixed values of hyperradius (1.5 ≤ ρ ≤ 20 bohrs) using the MRCI level of methodology employing ab initio quantum chemistry package (MOLPRO). The NACT between the ground and the first excited state translates along the seams on the θ - ɸ space, i.e., there are six Conical Intersections (CIs) at each θ (60° ≤ θ ≤ 90°) within the domain, 0 ≤ ɸ ≤ 2p. While transforming the adiabatic PESs to the diabatic ones, such surfaces show up six crossings along those seams. Our beyond Born-Oppenheimer approach could incorporate the effect of NACTs accurately and construct single-valued, continuous, smooth, and symmetric diabatic PESs. Since the location of CIs and the spatial amplitudes of NACTs are most prominent around ρ = 10 bohrs, generally only those results are depicted. [ABSTRACT FROM AUTHOR]

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na3 cluster and present the adiabatic PESs for the electronic states 22E′ and 12A1′, and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 22E′ and 12A1′ demonstrate the numerical validity of so called 'Curl Condition,' such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the 'adiabatic-diabatic transformation (ADT)' equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation. [ABSTRACT FROM AUTHOR]

We have performed a nuclear dynamics simulation to calculate photoelectron spectra and population profiles of benzene radical cation (CH $_6^+$) employing the parallelized Time Dependent Discrete Variable Representation (TDDVR) approach. For this purpose, we have considered two multi-state multi-mode model Hamiltonians of CH $_6^+$ with degeneracy among the eectronic states: (a) One consists of three states and eight modes, which in turn leads to a five state thirteen mode Hamiltonian ( XE- BE- CA) due to the degeneracy; and (b) The other is constituted of three states and thirteen modes which is basically a five state twenty mode Hamiltonian ( BE- DE- EB) for the same reason. Since these electronic states are interconnected by several conical intersections in the vicinity of the Franck Condon region, it will be challenging to pursue such large dynamical calculation in the presence of nonadiabaticity among the electronic states. The spectral as well as population profiles calculated with the advent of TDDVR approach show reasonably good agreement with the results obtained by the Multi Configuration Time Dependent Hartree (MCTDH) methodology. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

Molecular electronic ground-state theories, whether ab initio, or semiempirical are most often formulated as a variational principle, where the electronic ground-state energy, considered a linear or nonlinear functional of a reduced density matrix, obtains a constrained minimum. In this communication, we present a Lagrangian analysis of the self-consistent-field electronic structure problem, which does not resort to the concept of orthogonal molecular orbitals. We also develop a method of constrained minimization efficiently applicable to nonlinear energy functional minimization, as well as to linear models such as tight-binding. The method is able to treat large molecules with an effort that scales linearly with the system size. It has built-in robustness and leads directly to the desired minimal solution. Performance is demonstrated on linear alkane and polyene chains. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non-Adiabatic Coupling Terms (NACTs) for the three lowest singlet states of H+3 in hyperspherical coordinates as functions of hyperangles (θ and ɸ) for a grid of fixed values of hyperradius (1.5 ≤ ρ ≤ 20 bohrs) using the MRCI level of methodology employing ab initio quantum chemistry package (MOLPRO). The NACT between the ground and the first excited state translates along the seams on the θ - ɸ space, i.e., there are six Conical Intersections (CIs) at each θ (60° ≤ θ ≤ 90°) within the domain, 0 ≤ ɸ ≤ 2p. While transforming the adiabatic PESs to the diabatic ones, such surfaces show up six crossings along those seams. Our beyond Born-Oppenheimer approach could incorporate the effect of NACTs accurately and construct single-valued, continuous, smooth, and symmetric diabatic PESs. Since the location of CIs and the spatial amplitudes of NACTs are most prominent around ρ = 10 bohrs, generally only those results are depicted. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract A five-state multimode non-adiabatic dynamics has been performed on NO 3 by constructing accurate diabatic potential energy surfaces (PESs) in vibronically coupled manifold using beyond Born-Oppenheimer (BBO) theory. In this article, we have considered the photodetachment of NO 3 - to the doublet states ( X ∼ 2 A 2 ′ , A ∼ 2 E ″ and B ∼ 2 E ′ ) of NO 3 and determined the vibronic couplings and conical intersections of the latter. Using ab initio calculated adiabatic PESs and Non-adiabatic Coupling Terms, we have carried out adiabatic-to-diabatic transformation (ADT) in five-state sub-Hilbert space to obtain ADT angles and thereby, constructed single-valued, smooth, symmetric and continuous diabatic PESs. The explicit analytic expressions for diabatic PESs and coupling elements are provided. Subsequently, we have performed nuclear dynamics starting from the electronic ground state of NO 3 - to simulate photodetachment spectra. The overall spectral profiles for 2 A 2 ′ and 2 E ″ states show reasonably good agreement with experimental results and that of 2 E ′ state with other theoretical calculations. [ABSTRACT FROM AUTHOR]