Amit Kumar Paul

The multistate multimode vibronic dynamics of benzene radical cation with a realistic model Hamiltonian using a parallelized algorithm of the quantumclassical approach

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.

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

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.

Zero-Point Energy Constraint for Unimolecular Dissociation Reactions. Giving Trajectories Multiple Chances To Dissociate Correctly

A zero-point energy (ZPE) constraint model is proposed for classical trajectory simulations of unimolecular decomposition and applied to CH4* → H + CH3 decomposition. With this model trajectories are not allowed to dissociate unless they have ZPE in the CH3 product. If not, they are returned to the CH4* region of phase space and, if necessary, given additional opportunities to dissociate with ZPE. The lifetime for dissociation of an individual trajectory is the time it takes to dissociate with ZPE in CH3, including multiple possible returns to CH4*. With this ZPE constraint the dissociation of CH4* is exponential in time as expected for intrinsic RRKM dynamics and the resulting rate constant is in good agreement with the harmonic quantum value of RRKM theory. In contrast, a model that discards trajectories without ZPE in the reaction products gives a CH4* → H + CH3 rate constant that agrees with the classical and not quantum RRKM value. The rate constant for the purely classical simulation indicates that anharmonicity may be important and the rate constant from the ZPE constrained classical trajectory simulation may not represent the complete anharmonicity of the RRKM quantum dynamics. The ZPE constraint model proposed here is compared with previous models for restricting ZPE flow in intramolecular dynamics, and connecting product and reactant/product quantum energy levels in chemical dynamics simulations.

Photodissociation of H2(+) upon exposure to an intense pulsed photonic Fock state.

Producing and controlling nonclassical light states are now the subject of intense experimental efforts. In this paper we consider the interaction of such a light state with a small molecule. Specifically, we develop the theory and apply it numerically to calculate in detail how a short pulse of nonclassical light, such as the high intensity Fock state, induces photodissociation in H(2)(+). We compare the kinetic energy distributions and photodissociation yields with the analogous results of quasi-classical light, namely a coherent state. We find that Fock-state light decreases the overall probability of dissociation for low vibrational states of H(2)(+) as well as the location of peaks and line shapes in the kinetic energy distribution of the nuclei.

A parallelised quantum-classical approach to the molecular dynamics of allene ( ) radical cation

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 ( ) where its two electronic surfaces (A 2 E and B 2 B 2) 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 A 2 E 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 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.

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.

Chemical Dynamics Simulations of Benzene Dimer Dissociation

Classical chemical dynamics simulations were performed to study the intramolecular and unimolecular dissociation dynamics of the benzene dimer, Bz2 → 2 Bz. The dissociation of microcanonical ensembles of Bz2 vibrational states, at energies E corresponding to temperatures T of 700-1500 K, were simulated. For the large Bz2 energies and large number of Bz2 vibrational degrees of freedom, s, the classical microcanonical (RRKM) and canonical (TST) rate constant expressions become identical. The dissociation rate constant for each T is determined from the initial rate dN(t)/dt of Bz2 dissociation, and the k(T) are well-represented by the Arrhenius eq k(T) = A exp(-E(a)/RT). The E(a) of 2.02 kcal/mol agrees well with the Bz2 dissociation energy of 2.32 kcal/mol, and the A-factor of 2.43 × 10(12) s(-1) is of the expected order-of-magnitude. The form of N(t) is nonexponential, resulting from weak coupling between the Bz2 intramolecular and intermolecular modes. With this weak coupling, large Bz2 vibrational excitation, and low Bz2 dissociation energy, most of the trajectories dissociate directly. Simulations, with only the Bz2 intramolecular modes excited at 1000 K, were also performed to study intramolecular vibrational energy redistribution (IVR) between the intramolecular and intermolecular modes. Because of restricted IVR, the initial dissociation is quite slow, but N(t) ultimately becomes exponential, suggesting an IVR time of 20.7 ps.

Dynamics of Na+(Benzene) + Benzene Association and Ensuing Na+(Benzene)2* Dissociation

Chemical dynamics simulations were used to study Bz + Na(+)(Bz) → Na(+)(Bz)2* association and the ensuing dissociation of the Na(+)(Bz)2* cluster (Bz = benzene). An interesting and unexpected reaction found from the simulations is direct displacement, for which the colliding Bz molecule displaces the Bz molecule attached to Na(+), forming Na(+)(Bz). The rate constant for Bz + Na(+)(Bz) association was calculated at 750 and 1000 K, and found to decrease with increase in temperature. By contrast, the direct displacement rate constant increases with temperature. The cross section and rate constant for direct displacement are approximately an order of magnitude lower than those for association. The Na(+)(Bz)2* cluster, formed by association, dissociates with a biexponential probability, with the rate constant for the short-time component approximately an order of magnitude larger than that for the longer time component. The latter rate constant agrees with that of Rice-Ramsperger-Kassel-Marcus (RRKM) theory, consistent with rapid intramolecular vibrational energy redistribution (IVR) and intrinsic RRKM dynamics for the Na(+)(Bz)2* cluster. A coupled phase space model was used to analyze the biexponential dissociation probability.

Models for Intrinsic Non-RRKM Dynamics. Decomposition of the SN2 Intermediate Cl––CH3Br

Abstract Chemical dynamics simulations, based on both an analytic potential energy surface (PES) and direct dynamics, were used to investigate the intrinsic non-RRKM dynamics of the Cl−–CH3Br ion-dipole complex, an important intermediate in the Cl− + CH3Br SN2 nucleophilic substitution reaction. This intermediate may dissociate to Cl− + CH3Br or isomerize to the ClCH3–Br− ion-dipole complex. The decomposition of microcanonical ensembles of the Cl−–CH3Br intermediate were simulated, and the ensuing populations vs. time of the excited intermediate and Cl− + CH3Br and ClCH3–Br− products were fit with multi-exponential functions. The intrinsic non-RRKM dynamics is more pronounced for the simulations with the analytic PES than by direct dynamics, with the populations for the former and latter primarily represented by tri- and bi-exponential functions, respectively. For the analytic PES and direct dynamics simulations, the intrinsic non-RRKM dynamics is more important for the isomerization pathway to form ClCH3–Br− than for dissociation to Cl− + CH3Br. Since the decomposition probability of Cl−–CH3Br is non-exponential, the Cl−–CH3Br unimolecular rate constant depends on pressure, with both high and low pressure limits. The high pressure limit is the RRKM rate constant and for the simulations with the analytic PES the rate constant decreased by a factor of 3.0, 5.6, and 4.3 in going from the high to low pressure limit for total energies of 40, 60, and 80 kcal/mol. For the direct dynamics simulations these respective factors are 2.4, 1.4, and 1.2. A separable phase space model with intermolecular and intramolecular complexes describes some of the simulation results, but overall models advanced for intrinsic non-RRKM dynamics give incomplete representations of the intermediate and product populations vs. time determined from the simulations.

Chemical Dynamics Simulations of Intermolecular Energy Transfer: Azulene + N2 Collisions

Chemical dynamics simulations were performed to investigate collisional energy transfer from highly vibrationally excited azulene (Az*) in a N2 bath. The intermolecular potential between Az and N2, used for the simulations, was determined from MP2/6-31+G* ab initio calculations. Az* is prepared with an 87.5 kcal/mol excitation energy by using quantum microcanonical sampling, including its 95.7 kcal/mol zero-point energy. The average energy of Az* versus time, obtained from the simulations, shows different rates of Az* deactivation depending on the N2 bath density. Using the N2 bath density and Lennard-Jones collision number, the average energy transfer per collision ⟨ΔEc⟩ was obtained for Az* as it is collisionally relaxed. By comparing ⟨ΔEc⟩ versus the bath density, the single collision limiting density was found for energy transfer. The resulting ⟨ΔEc⟩, for an 87.5 kcal/mol excitation energy, is 0.30 ± 0.01 and 0.32 ± 0.01 kcal/mol for harmonic and anharmonic Az potentials, respectively. For comparison, the experimental value is 0.57 ± 0.11 kcal/mol. During Az* relaxation there is no appreciable energy transfer to Az translation and rotation, and the energy transfer is to the N2 bath.