Molecular Dynamics With Quantum Transitions Research Articles

Hybrid Quantum/Classical Simulations of the Vibrational Relaxation of the Amide I Mode of N-Methylacetamide in D2O Solution

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

Dissociative ionization of neon clusters Nen, n=3 to 14: A realistic multisurface dynamical study

The molecular dynamics with quantum transitions (MDQT) method is applied to study the fragmentation dynamics of neon clusters following vertical ionization of neutral clusters with 3 to 14 atoms. The motion of the neon atoms is treated classically, while transitions between the adiabatic electronic states of the ionic clusters are treated quantum mechanically. The potential energy surfaces are described by the diatomics-in-molecules model in a minimal basis set consisting of the effective 2p orbitals on each neon atom for the missing electron. The fragmentation mechanism is found to be rather explosive, with a large number of events where several atoms simultaneously dissociate. This is in contrast with evaporative atom by atom fragmentation. The dynamics are highly nonadiabatic, especially at shorter times and for the larger clusters. Initial excitation of the neutral clusters does not affect the fragmentation pattern. The influence of spin-orbit coupling is also examined and found to be small, except for the smaller size systems for which the proportion of the Ne+ fragment is increased up to 43%. From the methodological point of view, most of the usual momentum adjustment methods at hopping events are shown to induce nonconservation of the total nuclear angular momentum because of the nonzero electronic to rotation coupling in these systems. A new method for separating out this coupling and enforcing the conservation of the total nuclear momentum is proposed. It is applied here to the MDQT method of Tully but it is very general and can be applied to other surface hopping methods.

Molecular dynamics with quantum transitions for proton transfer: Quantum treatment of hydrogen and donor–acceptor motions

The mixed quantum/classical molecular dynamics with quantum transitions (MDQT) method is extended to treat the donor–acceptor vibrational motion as well as the hydrogen motion quantum mechanically for proton transfer reactions. The quantum treatment of both the hydrogen and the donor–acceptor motions requires the calculation of two-dimensional vibrational wave functions. The MDQT surface hopping method incorporates nonadiabatic transitions among these adiabatic vibrational states. This approach is applied to a model representing intramolecular proton transfer within a phenol-amine complex in liquid methyl chloride. For this model, the rates and kinetic isotope effects are the same within statistical uncertainty for simulations in which only the hydrogen motion is treated quantum mechanically and simulations in which both the hydrogen and the donor–acceptor vibrational motions are treated quantum mechanically. The analysis of these simulations elucidates the fundamental issues arising from a quantum mechanical treatment of the donor–acceptor vibrational motion as well as the hydrogen motion. This insight is relevant to future mixed quantum/classical molecular dynamics simulations of proton and hydride transfer reactions in solution and in enzymes.

Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.

Hybrid approach for the dynamical simulation of proton and hydride transfer in solution and proteins

A hybrid approach for simulating proton and hydride transfer reactions in solution and proteins is described. The electronic quantum effects are incorporated with an empirical valence bond potential. The nuclear quantum effects are included with a mixed quantum‐classical molecular dynamics method in which the transferring hydrogen nuclei are represented by multidimensional vibrational wavefunctions. The free energy profiles are obtained as functions of a collective reaction coordinate, and a mapping or umbrella potential is utilized to drive the reaction over the barrier for infrequent events. The vibrationally adiabatic nuclear quantum effects are incorporated into the free energy profiles. The dynamics are described with the molecular dynamics with quantum transitions (MDQT) surface hopping method, which incorporates vibrationally non-adiabatic effects. The MDQT method is combined with a reactive flux approach to calculate the transmission coefficient and to investigate the real-time dynamics of reactive trajectories. Nuclear quantum effects such as zero point energy, hydrogen tunnelling and non-adiabatic transitions, as well as the dynamics of the solvent and protein environment, are included during the generation of the free energy profiles and dynamical trajectories. This methodology provides detailed mechanistic information at the molecular level and allows the calculation of rates and kinetic isotope effects. The feasibility of this approach is illustrated through an application to hydride transfer in the enzyme liver alcohol dehydrogenase. This approach may be extended for use with mixed quantum mechanical‐molecular mechanical potentials and alternative mixed quantum‐classical molecular dynamics methods. It has also been generalized for multiple proton and protoncoupled electron transfer reactions.

Hybrid approach for including electronic and nuclear quantum effects in molecular dynamics simulations of hydrogen transfer reactions in enzymes

A hybrid approach for simulating proton and hydride transfer reactions in enzymes is presented. The electronic quantum effects are incorporated with an empirical valence bond approach. The nuclear quantum effects of the transferring hydrogen are included with a mixed quantum/classical molecular dynamics method in which the hydrogen nucleus is described as a multidimensional vibrational wave function. The free energy profiles are obtained as functions of a collective reaction coordinate. A perturbation formula is derived to incorporate the vibrationally adiabatic nuclear quantum effects into the free energy profiles. The dynamical effects are studied with the molecular dynamics with quantum transitions (MDQT) surface hopping method, which incorporates nonadiabatic transitions among the adiabatic hydrogen vibrational states. The MDQT method is combined with a reactive flux approach to calculate the transmission coefficient and to investigate the real-time dynamics of reactive trajectories. This hybrid approach includes nuclear quantum effects such as zero point energy, hydrogen tunneling, and excited vibrational states, as well as the dynamics of the complete enzyme and solvent. The nuclear quantum effects are incorporated during the generation of the free energy profiles and dynamical trajectories rather than subsequently added as corrections. Moreover, this methodology provides detailed mechanistic information at the molecular level and allows the calculation of rates and kinetic isotope effects. An initial application of this approach to the enzyme liver alcohol dehydrogenase is also presented.

Caging and excited state emission of ICN trapped in cryogenic matrices: experiment and theory

We discuss the cage induced stabilisation of fragments in excited electronic states following the UV-dissociation of ICN in cryogenic matrices. Emission spectra recorded upon Ã-band excitation of ICN in solid neon, argon and krypton exhibit a long progression of broad bands due to a weakly bound electronically excited state, presumably one of the low-lying triplet states 3Π1 or 3Π2 of ICN. A lifetime analysis favours the 3Π2 state. Molecular dynamics with quantum transitions (MDQT) simulations were conducted on six coupled electronic potential energy surfaces in a matrix of 498 argon atoms. Although a complete potential energy surface for the 3Π2 state is not available, it is known to be very similar to the 3Π1 one. Therefore only the 6 available [3Π1 (A′, A″), 3Π0+, 1Π1 (A′, A″), X 1Σ+] ab initio electronic potential energy surfaces were considered. The results predict a 2% probability of stabilisation in the shallow minimum of the triplet excited state. The molecule adopts a linear ICN configuration with a mean value of the I–CN distance far away from the absorption Franck–Condon region. The simulations also deliver insight into the mechanism of cage-induced population trapping in excited state surfaces, which is not accessible in the gas phase.

Improvement of the Internal Consistency in Trajectory Surface Hopping

This paper addresses the issue of internal consistency in the molecular dynamics with quantum transitions (MDQT) surface hopping method. The MDQT method is based on Tully's fewest switches algorithm, which is designed to ensure that the fraction of trajectories on each surface is equivalent to the corresponding average quantum probability determined by coherent propagation of the quantum amplitudes. For many systems, however, this internal consistency is not maintained. Two reasons for this discrepancy are the existence of classically forbidden transitions and the divergence of the independent trajectories. This paper presents a modified MDQT method that improves the internal consistency. The classically forbidden switches are eliminated by utilizing modified velocities for the integration of the quantum amplitudes, and the difficulties due to divergent trajectories are alleviated by removing the coherence of the quantum amplitudes when each trajectory leaves a nonadiabatic coupling region. The standard and modified MDQT methods are compared to fully quantum calculations for a classic model for ultrafast electronic relaxation (i.e., a two-state three-mode model of the conically intersecting S1 and S2 excited states of pyrazine). The standard MDQT calculations exhibit significant discrepancies between the fraction of trajectories in each state and the corresponding average quantum probability. The modified MDQT method leads to remarkable internal consistency for this model system.

Intramolecular vibrational redistribution and fragmentation dynamics of I2 ⋯ Nen (n=2–6) clusters

Intramolecular vibrational energy redistribution and fragmentation dynamics in I2(B,v=22) ⋯ Nen (n=2–6) and I2(B,v=21) ⋯ Nen (n=2–5) clusters is studied by hybrid quantum/classical techniques and the results are compared with experiments. A vibrational version of the molecular dynamics with quantum transitions (MDQT) treatment is used in which the vibrational degree of freedom of I2 is treated quantum mechanically while all the other degrees of freedom are treated classically. The potential energy surface is represented as a sum of pairwise interactions with parameters taken from the literature. The calculated product state distributions are in very good agreement with the experiments. Fragmentation lifetimes were also calculated and agree reasonably well with those measured in time-dependent experiments. Fragmentation proceeds via sequential ejection of Ne monomers through three different mechanisms: (i) sequential intramolecular vibrational redistribution plus vibrational predissociation (in which the I2 molecule loses more than one quantum of vibration); (ii) direct vibrational predissociation (in which the I2 molecule loses only one quantum of vibration); (iii) evaporation (in which the I2 molecule remains in the same vibrational state).

Comparison of surface hopping and mean field approaches for model proton transfer reactions

This paper presents a comparison of surface hopping and mean field approaches for simulating proton transfer reactions. In these mixed quantum/classical simulations, the transferring proton(s) are treated quantum mechanically, while the remaining nuclei are treated classically. The surface hopping method used for these calculations is the molecular dynamics with quantum transitions (MDQT) method based on Tully’s fewest switches algorithm. In addition, this paper describes a modified MDQT method (denoted MDQT*) that eliminates classically forbidden transitions to promote consistency between the quantum probabilities and the fraction of trajectories in each adiabatic state. The MDQT, MDQT*, mean field, and fully quantum dynamical methods are applied to one-dimensional model single and double proton transfer reactions. Both the MDQT and MDQT* calculations agree remarkably well with the fully quantum dynamical calculations, while the mean field calculations exhibit qualitatively incorrect behavior.

Competition between electronic and vibrational predissociation in Ar–I2(B): a molecular dynamics with quantum transitions study

Abstract A theoretical study of the competition between vibrational and electronic predissociation of the Van der Waals complex Ar⋯I 2 ( B ) using the Molecular Dynamics with Quantum Transitions (MDQT) method of Tully, is presented. The electronic predissociation is modeled by surface hopping from the B to the a state with probabilities given by the Franck–Condon factors between them. The vibration of I 2 is treated quantum mechanically using a Discrete Variable Representation (DVR) while the relative motion of the Ar atom with respect to I 2 is treated classically. The agreement between calculated and measured predissociation rates is very good. Analysis of the results indicate that first order rate equations are not adequate to describe the time dependent signals. This is due to the dependance of the electronic predissociation rates on the vibrational quantum number of the intermediate states of the process.

Mixed Quantum/Classical Dynamics of Hydrogen Transfer Reactions

This article presents the methodology we have developed for the simulation of hydrogen transfer reactions, including multiple proton transfer and proton-coupled electron transfer reactions. The central method discussed is molecular dynamics with quantum transitions (MDQT), which is a mixed quantum/classical surface hopping method that incorporates nonadiabatic transitions between the proton vibrational and/or electronic states. The advantages of MDQT are that it accurately describes branching processes (i.e., processes involving multiple pathways), is valid in the adiabatic and nonadiabatic limits and the intermediate regime, and provides real-time dynamical information. The multiconfigurational MDQT (MC-MDQT) method combines MDQT with an MC-SCF formulation of the vibrational modes for the simulation of processes involving multiple quantum modes (e.g., for multiple proton transfer reactions). MC-MDQT incorporates the significant correlation between the quantum modes in a computationally practical way and ...

Vibrational predissociation of the I2⋯Ne2 cluster: A molecular dynamics with quantum transitions study

The MDQT (molecular dynamics with quantum transitions) method of Tully is applied to the vibrational predissociation of a Van der Waals cluster containing a diatomic molecule and two rare gas atoms, I2⋯Ne2. The vibrational degree of freedom of the diatomic is treated quantum mechanically using DVR (discrete variable representation) while all the other degrees of freedom are treated classically. The results are in very good agreement with the experimentally measured lifetimes and product state distributions. In particular, the final vibrational state distribution of I2, which could not be satisfactorily reproduced in quasiclassical studies, is well described. Based on these results a different kinetic scheme for interpreting the vibrational predissociation in this system is proposed. In addition, this work shows that the method is very promising for the study of clusters containing more rare gas atoms.

A theoretical study of photofragmentation and geminate recombination of ICN in solid Ar

Photodissociation of ICN in an Ar matrix is studied by molecular dynamics with quantum transitions (MDQT) with the motion of the nuclei treated classically and the electronic motion quantum mechanically. Four electronic surfaces and their corresponding couplings are included in the calculations. The coupling between electronic states at large I-CN internuclear distances is modeled using a diatomic in molecules (DIM) treatment of the mixing of the different spin-orbit states of iodine induced by the Ar atoms. For a total propagation time of 3 ps, no cage exit is found and 44% of the trajectories recombine to the ground electronic state. The principal mechanism for geminate recombination involves the reaction path 3Π0+→1Π1→1Σ0++.

Application of trajectory surface hopping to vibrational predissociation

The recent MDQT (molecular dynamics with quantum transitions) trajectory surface hopping technique developped by Tully is applied to vibrational predissociation of the Van der Waals complex Ar⋯I 2. The vibration of I 2 is treated quantum mechanically while the relative motion of the Ar atom with respect to I 2 is treated classically. The results show that even for this extreme case where no actual crossings between quantum potential energy surfaces exist, the method provides satisfactorily results for the vibrational predissociation rates.