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 include the effect of the phonon modes originating from the three layers of Cu(1nn) surface atoms on the dynamics of incoming 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 potential by considering Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes calculated within harmonic approximation. Such time and temperature dependent effective Hamiltonian is further subdivided assuming a weak coupling between the two sets of molecular DOFs, namely, (x, y, z, Z) and (X, Y), respectively, in particular, to reduce the computational cost and the corresponding coupled quantum dynamical equations of motion have been formulated in terms of Time Dependent Discrete Variable Representation (TDDVR) approach. We demonstrate the workability of TDDVR method to investigate the scattering of H(2)(v, j) on Cu(1nn) surface by calculating the reaction probabilities and scattering cross-sections. Calculated results show that the phonon modes affect (a) the state-to-state transition probabilities of the scattered H(2) molecule substantially but chemisorption and physisorption processes negligibly and (b) the reaction probability of the incoming D(2) molecule noticeably.
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 (2)E(1g), B (2)E(2g), C (2)A(2u) and B (2)E(2g), D (2)E(1u), E (2)B(2u)) of benzene radical cation along with a preliminary investigation on its five electronic states (X (2)E(1g), B (2)E(2g), C (2)A(2u), D (2)E(1u), and E(2)B(2u)). 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.
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-C6H3F3+ (TFBZ+). While implementing this formulation, we compute ab initio adiabatic potential energy surfaces (PESs) and NACTs within the low-lying six electronic states (X̃2E′′, Ã2A2′′, B̃2E′, and C̃2A2′), 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.
We are investigating the molecular dynamics of the butatriene cation after excitation from the ground state (X(2)B(2g)) to the first excited electronic state (A(2)B(2u)) by using the time-dependent discrete variable representation (TDDVR) method. The investigation is being carried out with a realistic 18-mode model Hamiltonian consisting of all the vibrational degrees of freedom of the butatriene molecule. First, we perform the simulation on a basic five mode model, and then by including additional thirteen modes as bath on the basic model. This sequential inclusion of bath modes demonstrates the effect of so called weak modes on the subsystem, where the calculations of energy and population transfer from the basic model to the bath quantify the same effect. The spectral profile obtained by using the TDDVR approach shows reasonably good agreement with the results calculated by the quantum mechanical approach/experimental measurement. 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.