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The effect of surface mode vibrations on the reactive scattering of D2, initialized in the ground rovibrational state (v = 0, j = 0), from a Cu(111) surface is investigated for different surface temperature situations. We adopt a time and temperature dependent effective Hamiltonian [Dutta et al., J. Chem. Phys. 154, 104103 (2021)] constructed by combining the linearly coupled many oscillator model [Sahoo et al., J. Chem. Phys. 136, 084306 (2012)] and the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)] potential within the mean-field approach. Such an effective Hamiltonian is employed for six-dimensional quantum dynamical calculations to obtain temperature dependent reaction and state-to-state scattering probability profiles as a function of incidence energy of colliding D2 molecules. As reported in the experimental studies, the movements of surface atoms modify the dissociative scattering dynamics at higher surface temperature by exhibiting vibrational quantum and surface atoms' recoil effects in the low and high collision energy domains, respectively. Finally, we compare our present theoretical results with the experimental and other theoretical outcomes, as well as discuss the novelty of our findings. [ABSTRACT FROM AUTHOR]

We present explicit forms of nonadiabatic coupling (NAC) elements of nuclear Schrödinger equation (SE) for a coupled three-state electronic manifold in terms of mixing angles of real electronic basis functions. If the adiabatic-diabatic transformation (ADT) angles are the mixing angles of electronic bases, ADT matrix transforms away the NAC terms and brings diabatic form of SE. ADT and NAC matrices are shown to satisfy a curl condition with nonzero divergence. We have demonstrated that the formulation of extended Born-Oppenheimer (EBO) equation from any three-state BO system is possible only when there exists a coordinate-independent ratio of the gradients for each pair of mixing angles. On the contrary, since such relations among the mixing angles lead to zero curl, we explore its validity analytically around conical intersection(s) and support numerically considering two nuclear-coordinate-dependent three surface BO models. Numerical calculations are performed by using newly derived diabatic and EBO equations and expected transition probabilities are obtained. [ABSTRACT FROM AUTHOR]

We report quantum dynamics calculations of the O + OH → H + O 2 reaction on the CHIPR (Varandas, 2013) and DMBE IV (Pastrana et al., 1990) potential energy surfaces (PESs) for ground-state HO 2 using the 3D time-dependent wavepacket formalism based on hyperspherical coordinates. Reaction probabilities for J = 0 are calculated for several initial rovibrational states of the OH radical ( v = 0; j = 0–5). The J-shifting approximation is used to obtain initial state selected rate-coefficients in the range 0–400 K. Total and state-to-state rate-coefficients are predicted in good agreement with recent experimental studies and theoretical calculations. [ABSTRACT FROM AUTHOR]

The effect of surface atom vibrations on H2 scattering from a Cu(111) surface at different temperatures is being investigated for hydrogen molecules in their rovibrational ground state (v = 0, j = 0). We assume weakly correlated interactions between molecular degrees of freedom and surface modes through a Hartree product type wavefunction. While constructing the six-dimensional effective Hamiltonian, we employ (a) a chemically accurate potential energy surface according to the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)]; (b) normal mode frequencies and displacement vectors calculated with different surface atom interaction potentials within a cluster approximation; and (c) initial state distributions for the vibrational modes according to Bose–Einstein probability factors. We carry out 6D quantum dynamics with the so-constructed effective Hamiltonian and analyze sticking and state-to-state scattering probabilities. The surface atom vibrations affect the chemisorption dynamics. The results show physically meaningful trends for both reaction and scattering probabilities compared to experimental and other theoretical results. [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]

The collision of a hydrogen molecule with a copper surface has been studied using a semiclassical theory. The four molecular coordinates, the distance from the surface, the vibrational coordinate, and the polar angles, are treated quantum mechanically using a grid method. The kinetic energy is evaluated by a fast Fourier transformation (FFT) technique and the wave function propagated by a Lanczos iterative method. Two translational degrees of freedom for motion at the lattice are treated classically, whereas the normal modes of the solid are quantized using a quantum boson approach. The present calculation indicates that rotational state distributions of the scattered molecule and dissociative chemisorption of the diatom on the metal surface are significantly affected by the phonon coupling. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We perform four-dimensional (4Dx2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for D2(v, j)-Cu(111) system, where such effective potential has been derived through a mean-field approach between molecular degrees of freedom and surface modes with Bose-Einstein probability factor for their initial state distribution. We present the convergence of the theoretically calculated sticking probabilities employing 4Dx2D quantum dynamics with increasing number of surface atoms as well as layers for rigid surface and the surface at a particular temperature, where the temperature-dependent sticking probabilities appear exclusively dictated by those surface modes directed along the Z-axis. The sticking and state-to-state transition probabilities obtained from 6D quantum dynamics are shown as a function of initial kinetic energy of the diatom at different surface temperature. Theoretically calculated sticking probabilities display the similar trend with the experimentally measured one. [ABSTRACT FROM AUTHOR]

We investigate the molecular dynamics of pyrazine after excitation to the S2 electronic state by using the time-dependent discrete variable representation (TDDVR) method. The investigation has been carried out with a realistic 24-mode model Hamiltonian consisting of all the vibrational degrees of freedom of pyrazine molecule. First, we perform the simulation on a basic four-mode model, and then by including additional eight important modes and finally, by introducing 20 bath modes on the basic model. This sequential inclusion of bath modes demonstrates the effect of weak modes on the subsystem, where the calculations of energy and population transfer from basic model to the bath quantify the same effect. The spectral profile obtained by using TDDVR approach shows reasonably good agreement with the results calculated by quantum mechanical approach. It appears that the TDDVR approach for those large systems where quantum mechanical description is needed in a restricted region is a good compromise between accuracy and speed. [ABSTRACT FROM AUTHOR]

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn–Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrödinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born–Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

[Display omitted] The effect of surface temperature on the scattering and dissociation processes of D 2 (v = 0, j = 0)/D 2 (v = 0, j = 2) on Cu(111) metal plane is investigated by formulating a time and temperature dependent effective Hamiltonian within mean-field approach, where the molecular degrees of freedom and surface mode vibrations are assumed to be weakly coupled with each other. While constructing such effective Hamiltonian with a Hartree product type wavefunction, we incorporate: (i) an operator algebra method to circumscribe higher order-quadratic (anharmonic) molecular DOFs-surface modes couplings over the linear coupling case implemented previously [Adhikari and coworkers, J. Chem. Phys. 154 , 104103 (2021)]; (ii) surface temperature by considering Bose–Einstein or Maxwell–Boltzmann probability factors for the initial state distribution of the surface vibrational modes. Finally, a six-dimensional (6D) quantum dynamical (QD) calculation is performed with such newly formulated effective Hartree potential and calculated transition/dissociation probabilities at various surface temperature situations. The quadratic (anharmonic) molecular DOFs-surface modes couplings modify the reaction and transition probabilities substantially with change of surface temperature, which indicates the crucial role of surface mode vibrations on the molecule-surface scattering phenomena. [ABSTRACT FROM AUTHOR]

The approach to calculate improved, two-state, adiabatic-to-diabatic transformation angles (also known as mixing angles), presented before (see Das et al., J Chem Phys 2010, 133, 084107), was used here while studying the F + H2 system. However, this study is characterized by two new features: (a) it is the first of its kind in which is studied the interplay between Renner-Teller (RT) and Jahn-Teller (JT) nonadiabatic coupling terms (NACT); (b) it is the first of its kind in which is reported the effect of an upper singular RT-NACT on a lower two-state (JT) mixing angle. The fact that the upper NACT is singular (it is shown to be a quasi-Dirac δ-function) enables a semi-analytical solution for this perturbed mixing angle. The present treatment, performed for the F + H2 system, revealed the existence of a novel parameter, η, the Jahn-Renner coupling parameter (JRCP), which yields, in an unambiguous way, the right intensity of the RT coupling (as resembled, in this case, by the quasi-Dirac δ-function) responsible for the fact that the final end-of-the contour angle (identified with the Berry phase) is properly quantized. This study implies that the numerical value of this parameter is a pure number (independent of the molecular system): η = $ 2\sqrt 2 /\pi $ (= 0.9003) and that there is a good possibility that this value is a novel characteristic molecular constant for a certain class of tri-atomic systems. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 [ABSTRACT FROM AUTHOR]

The time-dependent discrete variable representation (TDDVR) of a wave function with grid points defined by the Hermite part of the Gauss–Hermite (G-H) basis set introduces quantum corrections to classical mechanics. The grid points in this method follow classical trajectory and the approach converges to the exact quantum formulation with sufficient trajectories (TDDVR points) but just with a single grid point; only classical mechanics performs the dynamics. This newly formulated approach (developed for handling time-dependent molecular quantum dynamics) has been explored to calculate vibrational transitions in the inelastic scattering processes. Traditional quantum mechanical results exhibit an excellent agreement with TDDVR profiles during the entire propagation when enough grid points are included in the quantum-classical dynamics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [ABSTRACT FROM AUTHOR]

We demonstrate the workability of a parallelized algorithm of the time-dependent discrete variable representation (TDDVR) method to explore the detailed dynamical aspects of vibronic interaction in two three-state model Hamiltonians (X 2E1g, B 2E2g, C 2A2u and B 2E2g, D 2E1u, E 2B2u) of benzene radical cation along with a preliminary investigation on its five electronic states (X 2E1g, B 2E2g, C 2A2u, D 2E1u, and E2B2u). Since those electronic states are interconnected through a series of conical intersections, we have used six and nine vibronically important modes for the three- and five-state Hamiltonians, respectively, in order to perform the quantum dynamics on such system. The population profiles calculated by using our TDDVR approach show reasonably good agreement with the results obtained by exact quantum mechanical (multiconfiguration time-dependent Hartree) method, whereas the corresponding (calculated) photoabsorption spectra originating from various electronic states agree well with the experimental ones. It is important to note that the parallelized algorithm of our TDDVR approach reduces the computation cost by more than an order of magnitude compared to its serial analog. The TDDVR approach appears to be a good compromise between accuracy and speed for such large molecular system, where quantum mechanical description is needed in a restricted region. [ABSTRACT FROM AUTHOR]

[Display omitted] We employ trajectory surface hopping (TSH) formalism [Chem. Phys. 349 (2008) 334, J. Chem. Phys. 142 (2015) 144307] to compute cross-sections or/and rate constants of D+ + H 2 (v = 0 , j = 0) and H + H 2 + (v = 0 , j = 0) reactions initiating from ground and first excited electronic state of H 3 + , respectively. While solving Hamilton's equations over adiabatic potential energy surfaces (PESs), switching probabilities are calculated by ab initio nonadiabatic coupling terms for the first time. During hopping, momenta are adjusted to fulfil total energy conservation, where a scaling factor is introduced to explore the conservation of linear momentum. For non-charge transfer process, quasi-classical cross-sections match well with quantum results obtained from diabatic PESs of H 3 + and experimental findings, but deviations are observed at the energy domain of conical intersection driven hopping for charge-transfer processes. Calculated results indicate the origin of limitations of TSH algorithm as well as depict computational advantage with respect to quantum dynamics. [ABSTRACT FROM AUTHOR]

We carry out both four-dimensional (4D×2D) and six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for H2/D2(v= 0,j= 0)–Ni(100) collision process. Such an effective potential was derived within a theoretical framework of mean-field approximation by considering weakly correlated interaction between molecular degrees of freedom, phonon modes and electron– hole pair (elhp) coupling through a Hartree-product-type wave function, where the initial state distribution of the surface modes and elhp coupling were introduced through Bose– Einstein and Fermi– Dirac probability factor, respectively. The temperature-dependent dissociation and state-to-state transition probabilities for H2/D2(v= 0,j= 0)–Ni(100) system are depicted as a function of initial kinetic energ of the incoming diatom. Though such effect appears negligibly small for H2(v= 0,j= 0)–Ni(100) system, it is prominent in the case of D2(v= 0,j= 0)–Ni(100) collision. It appears that the change of dissociation and transition probabilities of D2with the increase of surface temperature is exclusively dictated by the phonon modes directed alongZ-axis, but the effect of elhp coupling particularly for transition probabilities is insignificant. [ABSTRACT FROM AUTHOR]

Time-Dependent Discrete Variable Representation (TDDVR) method was implemented by involving "classical" trajectories on each degrees of freedom (DOF) for the dynamics of multi-surface multi-mode Hamiltonian. The major focus of this article is to explore the efficiency of the serial and parallelized TDDVR algorithm for relatively large dimensional quantum dynamics in presence of non-adiabaticity among the electronic states. As a model system, the complex photoelectron spectra and non-radiative decay dynamics of trifluoroacetonitrile radical cation (CF3CN+) are theoretically simulated with the aid of such parallelized algorithm, where the five lowest electronic states (X²E, A²A1, B²A2, C²A1, and D²E) of the Hamiltonian are interconnected through several conical intersections in the vicinity of Frank-Condon region with twelve (12) active vibrational modes. The Jahn-Teller splitting of the X²E and D²E states makes the coupled five-surface system to a more challenging quantum dynamical seven-surface twelve-mode model. The results obtained from the TDDVR approach show very good agreement with the profiles of both Multi Configuration Time-Dependent Hartree (MCTDH) methodology and experimental technique, where its' sequencial and parallelized algorithm depict closely linear scalability with the increasing number of basis set vis-a-vis DOFs. [ABSTRACT FROM AUTHOR]