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First principles based beyond Born–Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin–orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A′, 22A′, and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn–Teller (JT) type conical intersections between the two A′ states translate along C2 v and linear geometries in F + H2. In addition, A′ and A″ states undergo Renner–Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system. [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]

The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H3+ system (1¹A', 2¹A', and 3¹A') using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D+ +H2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H3+. We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results. [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]

It is shown that the Born–Oppenheimer–Huang non-adiabatic coupling terms (NACTs) in a molecular Hamiltonian can be considered as equivalent to a friction force in classical mechanics and consequently responsible for the formation of triatomic species like HeH 2 + . The classical equation of motion is solved accordingly for a test case of a helium atom approaching an H 2 + molecule at its potential minimum along the collinear axis and lines parallel to it and also for the C 2 v geometry. It is shown that the singular NACTs between the first two excited states slow down the motion of the three quasi-ions (He, H, H) + while approaching each other and result in substantial loss of kinetic energy in the collision process. These results have profound implications for the formation of di- and triatomic species in the early universe, during the chemical synthesis epoch following the nucleosynthesis that followed the Big Bang. [ABSTRACT FROM AUTHOR]

By computing the non-adiabatic coupling terms and the adiabatic-to-diabatic transformation angle along closed contours in nuclear configuration space using the CASSCF method and the aug-cc-pVTZ basis set for the lowest three electronic states of HeH2+, we explore the conical intersection between states in near collinear and noncollinear geometries, particularly in the C2v geometry. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Validity of curl τ ̃ ≃ 0 ̃ at the close vicinity of conical intersection points is explored. • The magnitudes of curl arising from Jahn-Teller interactions are either zero or negligible. • The other curls due to pseudo Jahn-Teller couplings attain reasonably higher magnitude. • The eigenvalues of nonadiabatic coupling matrix are found to be gauge invariant. Abstract Formulation of single-surface extended Born-Oppenheimer (EBO) equation is a long-standing problem for three or higher dimensional sub-Hilbert space mainly due to the difficulty to include the contribution of off-diagonal elements of anti-symmetric nonadiabatic coupling matrix ( τ → ) as the diagonal ones. Diagonalization of a vector matrix is possible only when its components commute with each other (i.e. curl τ → = 0 → ) and thereby, that vector matrix ( τ → ) can be expressed as a product of a vector function and an antisymmetric scalar matrix. For two electronic state sub-Hilbert space (Abelian case), since curl τ → = 0 → naturally, such factorization is readily obtained. In non-Abelian cases, for systems with three or more than three sub-Hilbert space, such factorization of nonadiabatic coupling matrix (NACM) may be achievable approximately (Sarkar and Adhikari, 2006; Sarkar and Adhikari, 2008), which will be explored further both theoretically and numerically. In this article, we take an attempt to generalize the single-surface EBO equations for higher dimensional sub-Hilbert space by selecting two realistic molecular systems containing Jahn-Teller (JT) conical intersections (CIs). The curl equations and gauge invariance (GI) of the eigenvalues of the NACM for NO 3 radical and 1,3,5-C 6 H 3 F 3 + (TFBZ+) radical cation are computed numerically, which clearly indicates the possibility to formulate single-surface EBO equations. [ABSTRACT FROM AUTHOR]

The present study is devoted to the possibility that tri-atomic molecules were formed during or shortly after the Big Bang. For this purpose, we consider the ordinary H3+ and H3 molecular systems and the primitive tri-atomic molecular system, H3++, which, as is shown, behaves differently. The study is carried out by comparing the topological features of these systems as they are reflected through their non-adiabatic coupling terms. Although H3++ is not known to exist as a molecule, we found that it behaves as such at intermediate distances. However, this illusion breaks down as its asymptotic region is reached. Our study indicates that whereas H3+ and H3 dissociate smoothly, the H3++ does not seem to do so. Nevertheless, the fact that H3++ is capable of living as a molecule on borrowed time enables it to catch an electron and form a molecule via the reaction H3++ + e → H3+ that may dissociate properly: Thus, the two unique features acquired by H3++, namely, that it is the most primitive system formed by three protons and one electron and topologically, still remain for an instant a molecule, may make it the sole candidate for becoming the cornerstone for creating the molecules. [ABSTRACT FROM AUTHOR]

In order to explore spectroscopic properties of a floppy molecule, it is necessary to compute accurate diabatic potential energy surfaces (PESs) around the Franck–Condon region of nuclear configuration space. In such cases, it is desirable to include the non-adiabatic coupling terms (NACTs) through Jahn–Teller (JT) and pseudo Jahn–Teller (PJT) effects as well as other accidental conical intersections (CIs) prevailing among the electronic states of the molecule. In this work, we investigate NACTs among the five lowest doublet electronic states of NO3radical [and 22B2)], in which all those effects (JT, PJT and CIs) have prominent contributions. The study is carried out in terms of normal modes (Qis) of NO3and the CIs (JT and accidental) are located in a plane of nuclear configuration space of two such coordinates (QiandQj). We have calculatedab initioadiabatic PESs and NACTs of those five states of NO3at the MRCI level as functions of pairwiseQis. Further, to explore the nature of a given CI in terms of normal coordinates contributing to NACTs within a particular planeQi-Qj, we have performed CP-MCSCF study computing analytic NACTs and characterised their contributions along variousQks. [ABSTRACT FROM PUBLISHER]

We present explicit form of Adiabatic to Diabatic Transformation (ADT) equations and expressions of non-adiabatic coupling terms (NACTs) for a coupled five-state electronic manifold in terms of ADT angles between electronic wave functions. ADT matrices eliminate the numerical instability arising from singularity of NACTs and transform the adiabatic Schrödinger equation to its diabatic form. Two real molecular systems NO3 and C6H6+ (Bz+) are selectively chosen for the demonstration of workability of those equations. We examine the NACTs among the lowest five electronic states of the NO3 radical [X˜2A2' (12B2), Ã2E" (12A2 and 12B1) and B˜2E' (12A1 and 22B2)], in which all types of non-adiabatic interactions, that is, Jahn-Teller (JT) interactions, Pseudo Jahn-Teller (PJT) interactions, and accidental conical intersections (CIs) are present. On the other hand, lowest five electronic states of Bz+ [X˜2E1g (12B3g and 12B2g), B˜2E2g (12Ag and 12B1g), and C˜2A2u (12B1u)] depict similar kind of complex feature of non-adiabatic effects. For NO3 radical, the two components of degenerate in-plane asymmetric stretching mode are taken as a plane of nuclear configuration space (CS), whereas in case of Bz+, two pairs are chosen: One is the pair of components of degenerate in-plane asymmetric stretching mode, and the other one is constituted with one of the components each from out-of-plane degenerate bend and in-plane degenerate asymmetric stretching modes. We calculate ab initio adiabatic potential energy surfaces (PESs) and NACTs among the lowest five electronic states at the CASSCF level using MOLPRO quantum chemistry package. Subsequently, the ADT is performed using those newly developed equations to validate the positions of the CIs, evaluate the ADT angles and construct smooth, symmetric, and continuous diabatic PESs for both the molecular systems. [ABSTRACT FROM AUTHOR]

This article continues a previous study (Int. J. Quantum Chem.114, 1645 (2014)) in which is presented a theory that discusses the possibility to induce a novel field – to be called molecular field – via the interaction of an external electro-magnetic (EM) field and a molecular system. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from three time-space curl equations and one time-space divergence equation to a set of decoupled wave equations usually encountered for fields. In the present study, wave equations are derived for an external field having two features: (1) the field intensity is relativelyhigh enough; (2) the duration of the interaction isshort enough. For this situation, the study reveals that the just mentioned interaction creates two fields that coexist within a molecule: one is just a scalar EM field essentially identical to the external EM field and the other, a vectorial field, produced by the non-adiabatic coupling terms. In addition, we mention that the wave velocities related to these two fields are identical to the wave velocity, c, of the external EM field. [ABSTRACT FROM PUBLISHER]

In the present article are analyzed the non‐adiabatic coupling terms (NACT) for two molecular systems, namely H3+ and H3. In contrast to previous occasions in which the NACTs are studied along (closed) circular contours usually surrounding conical intersections (ci), in the present article are studied distribution of the NACTs in (planar) configuration spaces (CS). The motivation for this study has to do with a novel idea being mentioned earlier (Molec. Phys., 116, 2435 [2018]; ArXiv:1801.00103) that NACTs are like a Glue (eventually) associated with the ability of creating molecules and/or protecting them from breaking up. It was found that the distributions of the NACTs due to the two molecules are similar as long as the attention is given to regions close to their equilateral cis, but then they behave significantly different in other regions. In case of H3+, the NACTs are distributed rather uniformly whereas, in case of H3 they become spiky the closer they approach the diatom axis. The main conclusion of this study is that the glue which has its origin in the NACTs is most likely to be effective in case of H3+ that explains the creation and later survival of this molecule. [ABSTRACT FROM AUTHOR]

It is shown that the Born–Oppenheimer–Huang non-adiabatic coupling terms (NACTs) in a molecular Hamiltonian can be considered as equivalent to a friction force in classical mechanics and consequently responsible for the formation of triatomic species like HeH 2 + . The classical equation of motion is solved accordingly for a test case of a helium atom approaching an H 2 + molecule at its potential minimum along the collinear axis and lines parallel to it and also for the C 2 v geometry. It is shown that the singular NACTs between the first two excited states slow down the motion of the three quasi-ions (He, H, H) + while approaching each other and result in substantial loss of kinetic energy in the collision process. These results have profound implications for the formation of di- and triatomic species in the early universe, during the chemical synthesis epoch following the nucleosynthesis that followed the Big Bang. [ABSTRACT FROM AUTHOR]

By computing the non-adiabatic coupling terms and the adiabatic-to-diabatic transformation angle along closed contours in nuclear configuration space using the CASSCF method and the aug-cc-pVTZ basis set for the lowest three electronic states of HeH2+, we explore the conical intersection between states in near collinear and noncollinear geometries, particularly in the C2v geometry. [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 (X̃ 2 E '' , Ã 2 A 2 '' , B̃ 2 E ' , and C̃ 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 (Q 9x , Q 9y , Q 10x , Q 10y , Q 12x , and Q 12y ) 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.

The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H 3 + system (1 1 A ' , 2 1 A ' , and 3 1 ) using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D ' ) using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D + + H 2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H 3 + . We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H 2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results.