Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations

An Exhaustive Quantum-Classical Study of C6F6+ Using the Newly Formulated Parallel TDDVR Method

We recently implemented our parallelized quantum-classical dynamical approach, known as the Time-Dependent Discrete Variable Representation (TDDVR) method, which is applied to the spectroscopically important hexafluorobenzene (HFBz) radical cation, where several conical intersections exist in their seven lowest excited electronic states (S11B2u, S21E1g, S31B1u, S41E1u, and S51A2u) considering degeneracy among potential energy surfaces (PESs), to demonstrate their various dynamical aspects. This new parallel version shows almost linear scalability with increasing number of computing processors. To get photoelectron (PE) spectra, Mass-Analyzed Threshold Ionization (MATI) spectra, population dynamics, and many other dynamical observables, the first-principles dynamics is applied at the state-of-the-art level to the corresponding Hamiltonian, where the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type interactions are involved in those coupled seven electronic states. The quantum-classical method is used to thoroughly analyze the effects of these couplings on the nuclear dynamics of the involved electronic states, and the findings are compared with those observables obtained from experiments. Intrinsic dynamical properties are explained using the reduced densities of the wave packet (WP) in a coupled electronic manifold. The PE and MATI spectra of HFBz computed using TDDVR are found to be in good agreement with earlier experimental data and other theoretically simulated spectra.

Jahn-Teller Effect in Orthorhombic Manganites: Ab Initio Hamiltonian and Roto-vibrational Spectrum

For the first time, using three different electronic structure methodologies, namely, CASSCF, RS2c, and MRCI(SD), we construct ab initio adiabatic potential energy surfaces (APESs) and nonadiabatic coupling term (NACT) of two electronic states (⁵E_g) of MnO₆^9- unit, where eight such units share one La atom in LaMnO₃ crystal. While fitting those APESs with analytic functions of normal modes (Q_x, Q_y), an empirical scaling factor is introduced considering the mass ratio of eight MnO₆^9- units with and without one La atom to explore the environmental (mass) effect on MnO₆^9- unit. When the roto-vibrational levels of MnO₆^9- Hamiltonian are calculated, peak positions computed from ab initio constructed excited APESs are found to be enough close with the experimental satellite transitions [ J. Exp. Theor. Phys. 2016, 122, 890-901] endorsing our earlier model results [ J. Chem. Phys. 2019, 150, 064703]. In order to explore the electron-nuclear coupling in an alternate way, theoretically "exact" and numerically "accurate" beyond Born-Oppenheimer (BBO) theory based diabatic potential energy surfaces (PESs) of MnO₆^9- are constructed to generate the photoelectron (PE) spectra. The PE spectral band also exhibits good peak by peak correspondence with the higher satellite transitions in the dielectric function spectra of the LaMnO₃ complex.

Stochastic wave packet approach to nonadiabatic scattering of diatomic molecules from metals

In this contribution, we present a quantum dynamical approach to study inelastic scattering of diatomic molecules from metal surfaces at normal incidence. The dissipative dynamics obeys a stochastic Schrödinger equation describing the time-evolution of the system as a piecewise deterministic process. Energy exchange between the molecular vibrational degrees of freedom and the metal electrons is represented using operators in tensor product form, which are coupled via anharmonic transition rates calculated from first-order perturbation theory. Full dimensional observables are obtained by averaging over simulations in 4D-including the internal stretch, the distance to the surface, and the orientation angles-at different surface sites. The method is applied to the state-resolved scattering of vibrationally excited NO from Au(111), revealing important channels for quantized energy relaxation.

Classical blended quantum formulation of the parallel TDDVR method to the dynamics on furan

A major portion (∼98%) of the quantum-classical molecular dynamics approach, namely, Time-Dependent Discrete Variable Representation (TDDVR) method, is recently parallelized using shared-memory parallelization scheme with the aim of performing dynamics on relatively large molecular systems. Therefore, we have chosen the furan as a model system for dynamical simulation. Four lowest singlet excited electronic states 1A2(3s), 1B2(V), 1A1(V*), and 1B1(3p) of furan are vibronically coupled through several conical intersections in the vicinity of Frank-Condon region. The major focus of the present paper is to explore the efficiency of our newly implemented parallelized TDDVR algorithm to perform dynamics on large dimensional quantum systems in vibronically coupled electronic manifold. The present version of parallelized TDDVR algorithm show closely linear speed up with increasing number of computing processors. As a significant speed up is achieved by cycling in the correct way over arrays, all dynamical simulations are performed within a reasonable wall clock time. The photoelectron spectra calculated by the TDDVR method show peak by peak correspondence with the experimental spectra. The TDDVR calculated quantum-classical dynamical outcomes, viz., population and photoelectron spectra, etc. show good agreement with the findings of the well-established quantum dynamical method, i.e. Multi Configuration Time-Dependent Hartree (MCTDH) approach.

NEARLY LINEAR SCALABILITY OF TIME-DEPENDENT DISCRETE VARIABLE REPRESENTATION (TDDVR) METHOD FOR THE DYNAMICS OF MULTI-SURFACE MULTI-MODE HAMILTONIAN

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.

Space-time contours to treat intense field-dressed molecular states

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 H(2) (+) as caused by a laser field.

Intralines of quasi-conical intersections on torsion planes: methylamine as a case study

Recently we reported on a novel feature associated with the intersection of the two lowest states (1)A' and (1)A'' of the methylamine (J. Chem. Phys. 2008, 128, 244302). We established the existence of a finite (closed) line of conical intersections (ci), namely, a finite seam, located in the HC-NHH symmetry plane, a line that is formed by moving a single hydrogen on that plane while locking the positions of the (six) other atoms. In the present article, this study is extended to the corresponding torsion planes formed by rotating the methyl group around the CN axis. The torsion planes, in contrast with the HC-NHH symmetry plane, do not satisfy the symmetry feature that enables the seam just mentioned. Nevertheless, the calculated nonadiabatic coupling terms (NACTs) resemble features similar to those encountered in the HC-NHH symmetry plane. Following a tedious numerical study supported by a theoretical model (Section III), it was verified that these NACTs may become similar to those on the symmetry plane, sometimes even to the level of almost no distinction, but lack one basic feature; namely, they are not singular and therefore do not form topological effects.

Space-time contours to treat intense field-dressed molecular states. I. Theory

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 Schrodinger 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)].

Renner-Teller/Jahn-Teller intersections along the collinear axes of polyatomic molecules: C2H2+ as a case study

Recently we discussed the Renner-Teller effect in triatomic molecules [J. Chem. Phys. 125, 094102 (2006)]. In that article the main message is that the Renner-Teller phenomenon, just like the Jahn-Teller phenomenon, is a topological effect. Now we extend this study to a tetra-atomic system, namely, the C(2)H(2) (+) ion, for which topological effects are revealed when one atom surrounds the triatom axis or when two atoms surround (at a time) the two-atom axis. The present study not only supports the findings of the previous study, in particular, the crucial role played by the topological D matrix for diabatization, but it also reveals new features which are expected to be more and more pronounced the larger the original collinear molecule. As already implied, shifting away two atoms from the collinear molecular axis does not necessarily abolish the ability of the remaining two atoms to form topological effects. Moreover, the study indicates that when the two hydrogens are shifted away, the CC axis produces two kinds of topological effects: (1) a Renner-Teller effect (characterized by a topological phase of 2pi) which is revealed when the two hydrogens surround, rigidly, this axis (as mentioned above), and (2) a Jahn-Teller effect (characterized by a topological phase of pi) which is revealed when one of the hydrogens surrounds this axis while the other hydrogen is clamped to its position.

Do intense electromagnetic fields annihilate∕create conical intersections?

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.

A quantum-classical approach to the molecular dynamics of pyrazine with a realistic model Hamiltonian

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.

D matrix analysis of the Renner-Teller effect: An accurate three-state diabatization for NH2

Some time ago we published our first article on the Renner-Teller (RT) model to treat the electronic interaction for a triatomic molecule [J. Chem. Phys. 124, 081106 (2006)]. The main purpose of that Communication was to suggest considering the RT phenomenon as a topological effect, just like the Jahn-Teller phenomenon. However, whereas in the first publication we just summarized a few basic features to support that idea, here in the present article, we extend the topological approach and show that all the expected features that characterize a three (multi) state RT-type'3 system of a triatomic molecule can be studied and analyzed within the framework of that approach. This, among other things, enables us to employ the topological D matrix [Phys. Rev. A 62, 032506 (2000)] to determine, a priori, under what conditions a three-state system can be diabatized. The theoretical presentation is accompanied by a detailed numerical study as carried out for the HNH system. The D-matrix analysis shows that the two original electronic states 2A1 and 2B1 (evolving from the collinear degenerate Pi doublet), frequently used to study this Renner-Teller-type system, are insufficient for diabatization. This is true, in particular, for the stable ground-state configurations of the HNH molecule. However, by including just one additional electronic state--a B state (originating from a collinear Sigma state)--it is found that a rigorous, meaningful three-state diabatization can be carried out for large regions of configuration space, particularly for those, near the stable configuration of NH2. This opens the way for an accurate study of this important molecule even where the electronic angular momentum deviates significantly from an integer value.

Extended Born-Oppenheimer equation for a three-state system

We present explicit forms of nonadiabatic coupling (NAC) elements of nuclear Schrodinger 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.

A quantum-classical approach to the photoabsorption spectrum of pyrazine

We have used the time-dependent discrete variable representation (TDDVR) method to simulate the photoabsorption spectrum of pyrazine. The time-dependent molecular dynamics of pyrazine after excitation to the S2 electronic state is considered as a benchmark to investigate the S2 absorption spectrum. We have carried out the dynamics on a basic four-mode model of pyrazine with the inclusion of five major modes as well as the rest of the vibrational modes as bath modes. Investigations reveal the effect of bath modes such as energy and population transfer from the subsystem to the bath. Calculated results demonstrate excellent agreement with traditional quantum-mechanical findings during the entire propagation and converge to the exact quantum results when enough gridpoints are used. It appears that TDDVR, as a numerical quantum dynamics methodology, is a good compromise between accuracy and speed.