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Akin to the traditional quasi-classical trajectory method for investigating the dynamics on a single adiabatic potential energy surface for an elementary chemical reaction, we carry out the dynamics on a 2-state ab initio potential energy surface including nonadiabatic coupling terms as friction terms for D + + H 2 collisions. It is shown that the resulting dynamics correctly accounts for nonreactive charge transfer, reactive non-charge transfer and reactive charge transfer processes. In addition, it leads to the formation of triatomic DH 2 + species as well.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (1 2 A', 2 2 A', and 1 2 A″) of the F + H 2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [ J. Chem. Phys. 2020 , 153 , 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state ( v = 0, j = 0) of the H 2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

First-principles based beyond Born-Oppenheimer theory has been employed to construct multistate global Potential-Energy Surfaces (PESs) for the HeH 2 + system by explicitly incorporating the Nonadiabatic Coupling Terms (NACTs). Adiabatic PESs and NACTs for the lowest four electronic states (1 2 A', 2 2 A', 3 2 A' and 4 2 A') are evaluated as functions of hyperangles for a grid of fixed values of the hyperradius in hyperspherical coordinates. Conical intersection between different states are validated by integrating the NACTs along appropriately chosen contours. Subsequently, adiabatic-to-diabatic (ADT) transformation angles are determined by solving the ADT equations to construct the diabatic potential matrix for the HeH 2 + system which are smooth, single-valued, continuous, and symmetric and are suitable for performing accurate scattering calculations for the titled system.

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H 2 /D 2 reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum ( J ) quantum numbers. For two different reactant diatomic molecules (H 2 and D 2 ) initially at their respective ground roto-vibrational state ( v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H 2 and F + D 2 reactions are presented along with previous theoretical and experimental results.

The dynamics of the H + H 2 + reaction has been analyzed from the electronically first excited state of diabatic potential energy surfaces constructed by employing the Beyond Born-Oppenheimer theory [ J. Chem. Phys . 2014 , 141 , 204306]. We have employed the coupled 3D time-dependent wavepacket formalism in hyperspherical coordinates for multisurface reactive scattering problems. To be specific, the charge transfer processes have been investigated extensively by calculating state-to-state as well as total reaction probabilities and integral cross sections, when the reaction process is initiated from the first excited electronic state (2 1 A'). We have depicted the convergence profiles of reaction probabilities for the competing charge transfer processes, namely, reactive charge transfer (RCT) and nonreactive charge transfer (NRCT) processes for different total energies with respect to total angular momentum, J . Total and state-to-state integral cross sections are calculated as a function of total energy for the initial rovibrational state, namely, v = 0, j = 0 level of H 2 + ( 2 Σ g + ) molecule and are compared with previous theoretical calculations. Finally, we have calculated temperature-dependent rate constants using our presently evaluated cross sections and compared their average with the experimentally measured one.

The major bottleneck of first principle based beyond Born-Oppenheimer (BBO) treatment originates from large number and complicated expressions of adiabatic to diabatic transformation (ADT) equations for higher dimensional sub-Hilbert spaces. In order to overcome such shortcoming, we develop a generalized algorithm, "ADT" to generate the nonadiabatic equations through symbolic manipulation and to construct highly accurate diabatic surfaces for molecular processes involving excited electronic states. It is noteworthy to mention that the nonadiabatic coupling terms (NACTs) often become singular (removable) at degenerate point(s) or along a seam in the nuclear configuration space (CS) and thereby, a unitary transformation is required to convert the kinetically coupled (adiabatic) Hamiltonian to a potentially (diabatic) one to avoid such singularity(ies). The "ADT" program can be efficiently used to (a) formulate analytic functional forms of differential equations for ADT angles and diabatic potential energy matrix and (b) solve the set of coupled differential equations numerically to evaluate ADT angles, residue due to singularity(ies), ADT matrices, and finally, diabatic potential energy surfaces (PESs). For the numerical case, user can directly provide ab initio data (adiabatic PESs and NACTs) as input files to this software or can generate those input files through in-built python codes interfacing MOLPRO followed by ADT calculation. In order to establish the workability of our program package, we selectively choose six realistic molecular species, namely, NO 2 radical, H 3 + , F + H 2 , NO 3 radical, C 6 H 6 + radical cation, and 1,3,5-C 6 H 3 F 3 + radical cation, where two, three, five and six electronic states exhibit profound nonadiabatic interactions and are employed to compute diabatic PESs by using ab initio calculated adiabatic PESs and NACTs. The "ADT" package released under the GNU General Public License v3.0 (GPLv3) is available at https://github.com/AdhikariLAB/ADT-Program and also as the Supporting Information of this article.

We carry out detailed investigation for topological effects of two molecular systems, NO 3 radical and C 6 H 6 + (Bz + ) radical cation, where the dressed adiabatic, dressed diabatic, and adiabatic-via-dressed diabatic potential energy curves (PECs) are generated employing ab initio calculated adiabatic and diabatic potential energy surfaces (PESs). We have implemented beyond Born-Oppenheimer (BBO) theory for constructing smooth, single-valued, and continuous diabatic PESs for five coupled electronic states [ J. Phys. Chem. A 2017, 121, 6314-6326]. In the case of NO 3 radical, the nonadiabatic coupling terms (NACTs) among the low-lying five electronic states, namely, X̃ 2 A 2 ' (1 2 B 2 ), A ~ 2 E″ (1 2 A 2 and 1 2 B 1 ), and B ~ 2 E' (1 2 A 1 and 2 2 B 2 ), bear the signature of Jahn-Teller (JT) interactions, pseudo JT (PJT) interactions, and accidental conical intersections (CIs). Similarly, Bz + radical cation also exhibits JT, PJT, and accidental CIs in the interested domain of nuclear configuration space. In order to generate dressed PECs, two components of degenerate in-plane asymmetric stretching modes are selectively chosen for both the molecular species ( Q 3 x - Q 3 y pair for NO 3 radical and Q 16 x - Q 16 y pair for Bz + radical cation). The JT coupling between the electronic states is essentially originated through the asymmetric stretching normal mode pair, where the coupling elements exhibit symmetric and nonlinear functional behavior along Q 3 x and Q 16 x normal modes., Competing Interests: The authors declare no competing financial interest.

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 NO 3 and C 6 H 6 + (Bz + ) are selectively chosen for the demonstration of workability of those equations. We examine the NACTs among the lowest five electronic states of the NO 3 radical [X̃ 2 A 2 ' (1 2 B 2 ), Ã 2 E″ (1 2 A 2 and 1 2 B 1 ) and B̃ 2 E' (1 2 A 1 and 2 2 B 2 )], 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 + [X̃ 2 E 1g (1 2 B 3g and 1 2 B 2g ), B̃ 2 E 2g (1 2 A g and 1 2 B 1g ), and C̃ 2 A 2u (1 2 B 1u )] depict similar kind of complex feature of non-adiabatic effects. For NO 3 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.

We implement a coupled three-dimensional (3D) time-dependent wave packet formalism for the 4D reactive scattering problem in hyperspherical coordinates on the accurate double many body expansion (DMBE) potential energy surface (PES) for the ground and first two singlet states (1(1)A', 2(1)A', and 3(1)A') to account for nonadiabatic processes in the D(+) + H2 reaction for both zero and nonzero values of the total angular momentum (J). As the long-range interactions in D(+) + H2 contribute significantly due to nonadiabatic effects, the convergence profiles of reaction probabilities for the reactive noncharge transfer (RNCT), nonreactive charge transfer (NRCT), and reactive charge transfer (RCT) processes are shown for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. The total and state-to-state cross sections are presented as a function of the collision energy for the initial rovibrational state v = 0, j = 0 of the diatom, and the calculated cross sections compared with other theoretical and experimental results.

The major portion of the algorithm of the time-dependent discrete variable representation (TDDVR) method is recently parallelized using the shared-memory parallelization scheme with the aim of performing dynamics on relatively large molecular systems. Because of the astronomical importance of naphthalene and anthracene, we have investigated their radical cations as models for theoretical simulation of complex photoelectron spectra and nonradiative decay process using the newly implemented parallel TDDVR code. The strong vibronic coupling among the six lowest doublet electronic states makes these polynuclear hydrocarbons dynamically important. The aim of the present investigation is to show the efficiency of our current TDDVR algorithm to perform dynamics on large dimensional quantum systems in vibronically coupled electronic manifold. Both the sequential and the parallelized TDDVR algorithms are almost linear scalable for an increase in number of processors. Because a significant speed-up is achieved by cycling in the correct way over arrays, all of the simulations are performed within a reasonable wall clock time. Our theoretical spectra well reproduce the features of the corresponding experimental analog. The dynamical outcomes, for example, population, photoelectron spectra, and diffused interstellar bands, etc., of our quantum-classical approach show good agreement with the findings of the well-established quantum dynamical method, that is, multi configuration time-dependent Hartree (MCTDH) approach.

We explore a coupled three-dimensional (3D) time-dependent wave packet formalism in hyperspherical coordinates for a 4D reactive scattering problem on the lowest adiabatic singlet surface (1(1)A') of the D(+) + H2 reaction. The coupling among the wavepackets arises through quantization of the rotation matrix, which represents the orientation of the three particles in space. The required transformation from Jacobi to hyperspherical coordinates and vice versa during initialization and projection of the wave packet on the asymptotic state(s), and the coupled equations of motion, are briefly discussed. With the long-range potential known to contribute significantly on the D(+) + H2 system, we demonstrate the workability of our approach, where the convergence profiles of the reaction probability for the reactive noncharge transfer (RNCT) process [D(+) + H2(v=0, j=0,1) → HD(v',j') + H(+)] are shown for three different collisional energies (1.7, 2.1, and 2.5 eV) with respect to the helicity (K) and total angular momentum (J) quantum numbers. The calculated reactive cross-section is presented as a function of the collision energy for two different initial states of the diatom (v = 0, j = 0, 1).

We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (2(2)E' and 1(2)A1') of Na3 cluster, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO). The signs of the NACTs at each point of the configuration space (CS) are determined by employing appropriate irreducible representations (IREPs) arising due to MS group, and such terms are incorporated into the adiabatic to diabatic transformation (ADT) equations to obtain the ADT angles. Since those sign corrected NACTs and the corresponding ADT angles demonstrate the validity of curl condition for the existence of three-state (2(2)E' and 1(2)A1') sub-Hilbert space, it becomes possible to construct the continuous, single-valued, symmetric, and smooth 3 × 3 diabatic Hamiltonian matrix. Finally, nuclear dynamics has been carried out on such diabatic surfaces to explore whether our MS-based treatment of diabatization can reproduce the pattern of the experimental spectrum for system B of Na3 cluster.

We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H(2)(v,j)/D(2)(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the "stochastic" treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D⊗2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H(2)(v,j)-Cu(100) system, and dissociative chemisorption-physisorption for both H(2)(v,j)-Cu(100) and D(2)(v,j)-Cu(111) systems. Calculated sticking probabilities by either 4D⊗2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D⊗2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H(2) molecule substantially, and (b) the sticking probabilities due to the collision of H(2) on Cu(100) and D(2) on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D)., (© 2011 American Chemical Society)