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We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas–metal interaction potential obtained for 0 K. Unlike in that work, we now explicitly account for surface expansion at 925 K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0 K and (ii) slab models resulting in phonons at 0 and 925 K according to the quasi-harmonic approximation—all consistently calculated at the density functional theory level with the same exchange–correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)–Cu(111) system employing Hartree potential constructed with 925 K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v′ = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v′ = 1) display a higher magnitude since the 925 K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface. [ABSTRACT FROM AUTHOR]

A model Hamiltonian for centrifugally stabilized electronic-vibrational motion of a cubic perturbed upper "Mexican hat" potential surface for a Mn3+ ion in an octahedral symmetry is formulated, and its eigenspectrum is explored. Theoretically calculated eigenvalues for cubic perturbed ground and excited electronic states are employed to interpret the origin of higher energy narrow side bands (satellite transitions) appearing in the dielectric function spectra of the LaMnO3 complex, which exhibit anomalous temperature dependence in the vicinity of the Néel temperature, TN ≃ 140 K [N. N. Kovaleva et al., J. Exp. Theor. Phys. 122, 890 (2016)]. [ABSTRACT FROM AUTHOR]

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He + H 2 + → HeH + + H on the ground electronic adiabatic potential energy surface and on the lowest two electronic states of newly constructed ab initio calculated diabatic potential energy surfaces for the system [Naskar et al., J. Phys. Chem. A 127, 3832 (2023)]. With the reactant diatom ( H 2 + ) in its roto-vibrational ground state (v = 0, j = 0), the calculations have been carried out in hyperspherical coordinates to obtain the reaction attributes. Convergence profiles of the reaction probability with respect to the total angular momentum quantum number at different collision energies are presented for the title reaction. State-to-state as well as initial state selected integral reaction cross sections are calculated from the fully converged reaction probabilities over a range of collision energies. The integral cross section values computed using the two-state diabatic potential energy surfaces are significantly lower than those obtained using the ground electronic state adiabatic potential energy surface and are in much better agreement with the available experimental results than the latter for total energy greater than 1.1 eV. Therefore, it becomes clear that it is important to include the nonadiabatic coupling terms for a quantitative prediction of the dynamical observables. [ABSTRACT FROM AUTHOR]

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]

In this article we consider a molecular system exposed to an intense short-pulsed external field. It is a continuation of a previous publication [A. K. Paul, S. Adhikari, D. Mukhopadhyay et al., J. Phys. Chem. A 113, 7331 (2009)] in which a theory is presented that treats quantum effects due to nonclassical photon states (known also as Fock states). Since these states became recently a subject of intense experimental efforts we thought that they can be treated properly within the existing quantum formulation of dynamical processes. This was achieved by incorporating them in the Born–Oppenheimer (BO) treatment with time-dependent coefficients. The extension of the BO treatment to include the Fock states results in a formidable enhancement in numerical efforts expressed, in particular, in a significant increase in CPU time. In the present article we discuss an approach that yields an efficient and reliable approximation with only negligible losses in accuracy. The approximation is tested in detail for the dissociation process of H2+ as caused by a laser field. [ABSTRACT FROM AUTHOR]

This second article in the two back-to-back articles presents a numerical application to support and strengthen two theoretical findings extensively discussed in the previous article (article I). In I, we found that introducing the space-time contours enables to distinguish between N, the number of nuclear Schrödinger equations to be solved, and L, the number of field-free states that become populated by the external field (in the ordinary, perturbative approaches this distinction is not apparent). In the numerical study we show, employing the electronic transition probability matrix P(s,t) [which closely is related to the transformation matrix ω(s,t)—see Eqs. (21) and (25) in I], that the N=L case is rare and in most cases we have N≤L. Since the perturbative approach can be shown to follow when N=L (see Sec. III C in I) the numerical study implies that in most cases the perturbative approach is not reliable. The second issue that is studied is related to the diabatization process. It is shown, numerically, that the N≥L case, in general, does not lead to field-dressed diabatic potentials which are single valued. However, if N is chosen to be identical to the number of field-free states that yield field-free single-valued diabatic potentials in a given spatial region then the corresponding N field-dressed states also yield single-valued (field-dressed) diabatic potentials. This result is independent of L. The numerical study is carried out for an eigenvalue problem based on the Mathieu equation. [ABSTRACT FROM AUTHOR]

A molecular system exposed to an intense external field is considered. The strength of the field is measured by the number L of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced space-time contours [R. Baer, et al., J. Chem. Phys. 119, 6998 (2003)], to form N coupled Schrödinger equations where N≤L, which maintains the effects due to the remaining (L-N) populated states. It is shown that whereas the size of L is unlimited, the main requirement concerning N is that the original group of N field-free states forms a Hilbert subspace in the spatial region of interest. From previous studies it is known that a group of states forms a Hilbert subspace if and only if the corresponding topological D matrix is diagonal [M. Baer, et al., Farad, Discuss 127, 337 (2004)] [ABSTRACT FROM AUTHOR]

In this article the authors relate the possibility that an intense electric field affects topological features of a molecular system. For this purpose they studied a model based on the Mathieu equation. They found that such a field may affect the spatial distribution of the nonadiabatic coupling terms but not the position of the intersections. In other words an intense electric field does not create or annihilate conical intersections. It is shown that this conclusion is valid as long as the field is an analytic function of the coordinates in the region of interest. These findings can be extended to magnetic fields (or electromagnetic fields) as long as they are analytic functions in the region of interest. [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 have investigated the dynamics of a reaction coordinate with or without coupling to a heat bath of harmonic oscillators using a novel time-dependent discrete variable representation (TDDVR) method. The proposed method is semiclassical in nature, theoretically rigorous, and rather straightforward to implement. Excellent agreement of the computed tunneling probabilities and time-averaged tunneling rates with the corresponding exact results demonstrates the efficacy of the proposed approach. Most of the semiclassical calculations reported here have been performed by using classical force, whereas, in a few cases, the quantum force (QF) has been taken into account. It appears that among the TDDVR formulations, it was the first time we have derived a rigorous form of QF from the first principle. [ABSTRACT FROM AUTHOR]

Demonstrates the Hermite correction method for nonadiabatic transitions. Use of molecular dynamics simulations on a system where electronic transitions are allowed anywhere in configuration space among any number of coupled states; Use of a classical path theory based on the Hermite correction to the Gaussian wave packet expansion; Initialization, propagation, and projection of the wave function.

Studies the extended Jahn-Teller model using a time-dependent wave packet approach to see symmetry effects on scattering processes. Symmetry of nuclear wave function due to conical intersections between Born-Oppenheimer potential energy surfaces; Introduction of a vector potential in nuclear Hamiltonian; Incorporation of a phase factor in nuclear wave function.

Focuses on the hyperspherical formulation of the vector potential arising due to the presence of a conical intersection in the adiabatic potential energy hypersurface of an A + B[sub 2] type reactive system. Difference in the absolute peak position of rotational distributions obtained by quasiclassical trajectory calculations.

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]

While carrying out Beyond Born–Oppenheimer theory based diabatization, the solutions of adiabatic-to-diabatic transformation equations depend on the paths of integration over two-dimensional cross-sections of multi-dimensional space of nuclear degrees of freedom. It is shown that such path-dependent solutions leading to diabatic potential energy surface matrices computed along any two different paths are related through an orthogonal matrix, and thereby, those surface matrices should provide unique observables. While exploring the numerical validity of the theoretical framework, we construct diabatic Hamiltonians for the five low-lying electronic states ( X ̃ 2 E 1 g , B ̃ 2 E 2 g , and C ̃ 2 A 2 u ) of benzene radical cation ( C 6 H 6 + ) along three different approaches of contour integration over two dimensional nuclear planes constituted by seven non-adiabatically active normal modes. Three different diabatic surface matrices are further employed to generate the photoelectron spectra of the benzene molecule (C6H6). It is interesting to note that the spectral peak positions and intensity patterns for all three cases are almost close to each other and also exhibit very good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

We calculate the adiabatic potential energy surfaces (PESs) and the non-adiabatic coupling terms (NACTs) for the excited electronic states of K 3 cluster by MRCI approach using MOLPRO. The NACTs are adapted with molecular symmetry to assign appropriate IREPs so that the elements of the Hamiltonian matrix are totally symmetric. We incorporate those NACTs into three-state adiabatic-to-diabatic transformation (ADT) equations to obtain ADT angles for constructing continuous, single-valued, smooth and symmetric diabatic Hamiltonian matrix, where its elements are fitted with analytic functions. Finally, we demonstrate that the dressed diabatic and adiabatic-via-dressed diabatic PECs show prominent topological effect over dressed adiabatic curves. [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]

Abstract: In this review, we consider two gauges: one, the field-free gauge, is formed by the field-free electronic eigenstates and the other, the field-dressed gauge, is formed by the field-dressed electronic basis set. The field-free gauge is used, of course, in the case of time-independent systems but then it is also the more common one to be used in the case of molecular systems exposed to external fields. This gauge is conceptually simple and therefore numerically friendly — two features which make it versatile for numerical application. The field-dressed gauge is, eventually, more involved but yields deeper insight which might lead to a better understanding of the complicated interaction between a molecular system and external fields. In addition, these features can be exploited to develop efficient and reliable approximations that may save CPU (computer processing unit) time in numerical applications. These two gauges are the main topics of the present review. Once the general derivation of the two gauges is completed, two additional issues are discussed: (i) we extend these gauges to include external fields formed by non-classical photon-state distributions (also known as non-coherent Fock-state distributions). These photon state distributions, recently considered for the first time for molecular systems [A.K. Paul, S. Adhikari, M. Baer, R. Baer, Phys. Rev. A 81 (2010) 013412], are interesting on their own footing. Although here they mainly serve as a vehicle to test the above-mentioned novel approximations, we also devote part of the review to studying the importance of non-coherent Fock states for obtaining an unbiased correct understanding of the interaction of molecular systems with strong, short-pulsed laser fields. For this purpose, we study the photo-dissociation process of and show (a) that the approximations, recently introduced, diminish the CPU time by about one order of magnitude with minimal loss of accuracy and (b) indeed non-coherent Fock states are found to affect molecular systems in a unique way. (ii) As mentioned, the field-dressed gauge contributes to the understanding of effects due to external fields. In the present review, we analyze the interplay between the electronic non-adiabatic coupling terms and these external interactions. This analysis relates directly to the open question whether external fields are capable of eliminating (or creating) conical intersections. [Copyright &y& Elsevier]

If a coupled three-state electronic manifold forms a sub-Hilbert space, it is possible to express the non-adiabatic coupling (NAC) elements in terms of adiabatic–diabatic transformation (ADT) angles. Consequently, we demonstrate: (a) Those explicit forms of the NAC terms satisfy the Curl conditions with non-zero Divergences; (b) The formulation of extended Born-Oppenheimer (EBO) equation for any three-state BO system is possible only when there exists coordinate independent ratio of the gradients for each pair of ADT angles leading to zero Curls at and around the conical intersection(s). With these analytic advancements, we formulate a rigorous EBO equation and explore its validity as well as necessity with respect to the approximate one (Sarkar and Adhikari, J Chem Phys 2006, 124, 074101) by performing numerical calculations on two different models constructed with different chosen forms of the NAC elements. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

In this article, we apply a novel time-dependent discrete variable representation (TDDVR) method proposed by Barkakaty and Adhikari to investigate tunneling through an Eckart barrier. This semi-classical method is theoretically rigorous and straightforward to implement. Among the TDDVR formulations, this report presents the first derivation of a rigorous form of quantum force (QF) for the present perspective. The validity of this semi-classical approach is demanded based on the excellent agreement of the tunneling probability with the corresponding quantum results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 [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 have developed a novel discrete variable representation (DVR) method where not only the amplitudes of the wave function at the DVR grid points can change but also the positions of these grid points can move as a function of time. Since the Gauss-Hermite basis set is used as the primitive basis functions (PBF) to construct the DVR basis set, the method appears as a semiclassical one with a small number of PBF but converges very fast to the quantum with an increasing PBF. We have investigated the dynamics of a reaction coordinate with or without coupling to a heat bath of harmonic oscillators to demonstrate the validity of the proposed method. The excellent agreement of the calculated tunneling probabilities with numbers obtained by traditional quantum grid method (FFT) and the fast computability of the present method compared to the latter are remarkable. © 2000 American Institute of Physics. [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]

A recently proposed coupled three-dimensional time-dependent wave-packet formalism in hyperspherical coordinates is shown to yield accurate results for the reactive non-charge transfer process in the title system at collision energies as low as 100 K, where the lowest sheet of the accurate double many body expansion form for the singlet H+3 is used. The results are compared with available experimental data as well as time-independent calculations, and the agreement shown to be generally good. [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]

The "accuracy" of diabatic Hamiltonian matrix elements solely depends on the level of ab initio calculation and on the included set of coupled electronic manifold forming a "true" sub‐Hilbert space (SHS). If ab initio calculations are performed with enough accuracy, existence of SHS can be validated only when the Curl Condition attains zero within numerical precision. For the first time, we depict a theoretical and algorithmic formulation on the calculation of Curl Condition to demonstrate the existence of SHS on molecular processes or chemical reactions. [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]

The tetra-atomic C2H2+ cation is known to form Renner–Teller-type intersections along its collinear axis. Not too long ago, we studied the nonadiabatic coupling terms (NACTs) of this molecule [G. J. Halász et al., J. Chem. Phys. 126, 154309 (2007)] and revealed two kinds of intersections. (i) By employing one of the hydrogens as a test particle, we revealed the fact that indeed the corresponding (angular) NACTs produce topological (Berry) phases that are equal to 2π, which is a result anticipated in the case of Renner–Teller intersections. (ii) However, to our big surprise, repeating this study when one of the atoms (in this case a hydrogen) is shifted from the collinear arrangement yields for the corresponding topological phase a value that equals π (and not 2π). In other words, shifting (even slightly) one of the atoms from the collinear arrangement causes the intersection to change its character and become a Jahn–Teller intersection. This somewhat unexpected novel result was later further analyzed and confirmed by other groups [e.g., T. Vertesi and R. Englman, J. Phys. B 41, 025102 (2008)]. The present article is devoted to another tetra-atomic molecule, namely, the H2CN molecule, which just like the C2H2+ ion, is characterized by Renner–Teller intersections along its collinear axis. Indeed, we revealed the existence of Renner–Teller intersections along the collinear axis, but in contrast to the C2H2+ case a shift of one atom from the collinear arrangement did not form Jahn–Teller intersections. What we found instead is that the noncollinear molecule was not affected by the shift and kept its Renner–Teller character. Another issue treated in this article is the extension of (the two-state) Berry (topological) phase to situations with numerous strongly interacting states. So far the relevance of the Berry phase was tested for systems characterized by two isolated interacting states, although it is defined for any number of interacting states [M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984)]. We intend to show how to overcome this limitation and get a valid, fully justified definition of a Berry phase for an isolated system of any number of interacting states (as is expected). [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]

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]

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]

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]

A theoretical investigation of selective bond dissociation of O–H or O–D bond of HOD molecule is carried out by optimally designed electromagnetic field where optimisation is performed by Genetic Algorithm (GA). Two strategies depending upon the objective function and variable space for optimisation have been followed to achieve selective photodissociation. InStrategy Iflux along a particular channel (JH + O-D/JD + O-H) in the repulsive excited state of HOD is considered in defining the objective function with a polychromatic IR pulse of eight components and a UV radiation of two components being optimally found out by GA. The polychromatic IR pulse distributes the population among the low quanta vibrational states of O–H or O–D stretching mode in ground electronic state and the subsequent UV pulse transfers the population to the excited state where photodissociation occurs. According to the direction of population along O–H or O–D stretch in ground electronic state, fluxes in the channels may be expected. We have obtained a maximum value of 92.38% and 74.12% alongJH + O-DandJD + O-Hchannels, respectively. TheStrategy IIis the conventional strategy of selective vibrational excitation followed by population transfer to excited state by single UV pulse. In this case, the polychromatic IR fields are optimised by GA to achieve selective vibrational excitation on |1, 0⟩, |2, 0⟩, |0, 1⟩ and |0, 2⟩ states and the matching single UV pulse is fired for electronic excitation. The first two states correspond to the O–H stretch and population transfer from these states to excited state result in predominant flux along H+O–D channel and similar scheme from the last two states result in D+O–H dissociation as they are effectively of O–D character. The best values ofJH + O-DandJD + O-Hare 86.91% and 65.94% obtained by usingStrategy II. [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]

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 (1¹A', 2¹A', and 3¹A') 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. [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]

We explore a coupled three-dimensional(3D) time-dependent wavepacket formalism in hyperspherical coordinates for a 4D reactive scatteringproblem on the lowest adiabatic singlet surface (11A′)of the D++ H2reaction. The coupling amongthe 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 coordinatesand vice versa during initialization and projection of the wave packeton the asymptotic state(s), and the coupled equations of motion, arebriefly discussed. With the long-range potential known to contributesignificantly on the D++ H2system, we demonstratethe workability of our approach, where the convergence profiles ofthe 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 collisionalenergies (1.7, 2.1, and 2.5 eV) with respect to the helicity (K) and total angular momentum (J) quantumnumbers. The calculated reactive cross-section is presented as a functionof the collision energy for two different initial states of the diatom(v= 0, j= 0, 1). [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]

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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]

Vibrational excitation cross-sections $\sigma_{\nu_f \leftarrow \nu_i } (E)$ in resonant e-F and HCl scattering are calculated from transition matrix elements $T_{\nu_f \leftarrow \nu_i } (E)$ obtained using Fourier transform of the cross correlation function $\left\langle {\phi_{\nu_f } \left( R \right)\vert \Psi_{\nu_i } \left( {R,t} \right)} \right\rangle $ where $\Psi_{\nu_i } \left( {R,t} \right)\approx e^{-i\hbar H_{AB^-} \left( R \right)t}\phi_{\nu { }_i} \left( R \right)$. Time evolution under the influence of the resonance anionic Hamiltonian H- (AB=F/HCl) is effected using Lanczos reduction technique followed by fast Fourier transform and the target (AB) vibrational eigenfunctions $\phi _{\nu_i } \left( R \right)$ and $\phi_{\nu_f } \left( R \right)$ are calculated using Fourier grid Hamiltonian method applied to potential energy (PE) curve of the neutral target. The resulting vibrational excitation cross-sections provide reasonable agreement with experimental and other theoretical results. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

Abstract: We present a study of the non-adiabatic coupling terms (NACTs) and the corresponding diabatic potentials for the reactive H2 +F system in the entrance channel. The study reveals two conical intersections (ci): (I) A Jahn–Teller (1,2) ci, located at a point on the collinear HHF axis close to the minimum energy path; (II) A Renner–Teller line of (2,3) cis, along the collinear HHF axis. To form the diabatic potentials we consider only the two lower adiabatic potentials and the quantized Born–Oppenheimer mixing angles that guarantee single-valued diabatic potentials. [Copyright &y& Elsevier]

Abstract: We have investigated the molecular dynamics of after excitation from the ground to different electronically excited states by using our parallelized Time Dependent Discrete Variable Representation method. Since the system consists of five electronic states with several conical intersections, a complex dynamical phenomena arises. TDDVR calculated population dynamics and various spectra, namely photoelectron, mass analyzed threshold ionization and photoinduced Rydberg ionization, etc. show good agreement with the results obtained by multiconfiguration time-dependent Hartree method as well as experimental findings. The parallelized TDDVR algorithm reduces the computation time drastically and appears to be a good compromise between accuracy and speed for such large molecular system. [ABSTRACT FROM AUTHOR]

We are investigating the molecular dynamics of the allene system using a parallelised Time Dependent Discrete Variable Representation (TDDVR) methodology by employing a corresponding cation ( [image omitted]) where its two electronic surfaces (A2E and B2B2) are vibronically coupled with each other. In fact the allene radical cation exhibits a three-surface system due to the presence of degeneracy in the A2E state. Our initial investigation is carried out on a linear vibronically coupled model Hamiltonian consisting of 11 vibrationally active modes with two potential energy surfaces. We included both the bilinear and quadratic coupled terms in the effective three-surface Hamiltonian of the [image omitted] radical cation. The spectral profiles obtained from the higher order Hamiltonian show better agreement with the experimental spectrum than the result corresponding to the linearly coupled one. Along with the spectral calculation, we also analyse the nuclear cum population dynamics of the same system. The TDDVR calculated spectral profile as well as the population dynamics show reasonably good agreement with the results calculated by an exact quantum mechanical (multiconfiguration time-dependent Hartree, MCTDH) approach as well as experimental measurement. It appears that the TDDVR approach for those large systems where the quantum mechanical description is needed in a restricted region, is a good compromise between accuracy and speed. [ABSTRACT FROM AUTHOR]

Abstract: The inclusion of the geometric phase effects through the addition of vector potential is well known. We present the formulation of DVR and TDDVR matrix equations for any 2-D system with vector potential. The effective potential appears as the complex hermitian matrix in the DVR/TDDVR representation where in case of TDDVR, matrices associated with “classical” momentum also plays an important role in the dynamics. We derive the rigorous expressions of “classical” equations of motion from Dirac–Frenkel variational principle without introducing the “classical” path as such. Numerical calculations by using DVR/TDDVR equations have been carried out to obtain the signature of geometric phase on the reactive and non-reactive scattering processes. TDDVR appears to be better compromise between speed and accuracy than traditional quantum dynamics numerical methodologies (DVR/FFT). [Copyright &y& Elsevier]

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 have carried out molecular dynamics simulations of non-adiabatic processes with the help of a newly formulated potentially exact quantum-classical approach derived from a method proposed earlier [J. Chem. Phys. 118 (2003) 5302]. In this method, time-dependent Schroedinger equation is solved by representing Ψ on a moving Gauss–Hermite DVR grid, the motion of grid-centre being handled classically, but self consistently with the quantum evolution of the wavefunction. Electronic transitions are allowed anywhere in the configuration space among any number of coupled states. We have tested the method on three model problems proposed by J.C. Tully [J. Chem. Phys. 93 (1990) 1061]. These models are relevant to a wide range of gas-phase and condensed-phase phenomena occurring even at low energies. Excellent agreement of computed transition probabilities with corresponding quantum mechanical (DVR/FFT) results even in the deep quantum regime and its cost-efficiency (computational) are encouraging. [Copyright &y& Elsevier]

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]