Sampling the proton transfer reaction coordinate in mixed quantum-classical molecular dynamics simulations

An umbrella sampling approach based on the vibrational energy gap is presented and examined for exploring the reaction coordinate for a proton transfer (PT) reaction. The technique exploits the fact that for a PT reaction the energy gap between the vibrational ground and excited states of the transferring proton reaches a minimum at the transition state. Umbrella sampling is used within mixed quantum-classical simulations to identify the transition state configurations and explore the reaction free energy curve and vibrationally nonadiabatic coupling. The method is illustrated by application to a model phenol-amine proton transfer reaction complex in a nanoconfined solvent. The results from this new umbrella sampling approach are consistent with those obtained from previous umbrella sampling calculations based on a collective solvent coordinate. This sampling approach further provides insight into the vibrationally nonadiabatic coupling for the proton transfer reaction and has potential for simulating vibrational spectra of PT reaction complexes in solution.     

Umbrella sampling of solute vibrational line shifts in mixed quantum-classical molecular dynamics simulations

An umbrella sampling approach for vibrational frequency line shifts is presented. The technique allows for efficient sampling of the solvent configurations corresponding to frequency shifts of a solute in mixed quantum-classical simulations. The approach is generally applicable and can also be used within traditional perturbation theory calculations of frequency shifts. It is particularly useful in the extraction of detailed mechanistic information about the solute-solvent interactions giving rise to the frequency shifts. The method is illustrated by application to the simple I2 in a liquid Xe system, and the advantages are discussed.     

Nonadiabatic deactivation of 9H-adenine: a comprehensive picture based on mixed quantum-classical dynamics

Mixed quantum-classical dynamics simulations at the multireference configuration interaction (MR-CIS) level were performed for 9 H-adenine in order to understand its ultrafast nonradiative decay process. Dynamics simulations were also performed for the model system 6-aminopyrimidine. MR-CIS and complete active space perturbation theory (CASPT2) have been employed to characterize a large variety of qualitatively different conical intersections, the branches of the crossing seam connecting them, and the reaction paths from the Franck-Condon region for 9 H-adenine. The results show a two-step process consisting of ultrashort deactivation from S 3 to S 1 and a longer exponential decay step corresponding to the conversion from S 1 to S 0.     

A hybrid hydrodynamic-Liouvillian approach to mixed quantum-classical dynamics: application to tunneling in a double well

The hybrid quantum-classical approach of Burghardt and Parlant [Burghardt, I.; Parlant, G. J. Chem. Phys. 2004, 120, 3055], referred to here as the quantum-classical moment (QCM) approach, is demonstrated for the dynamics of a quantum double well coupled to a classical harmonic coordinate. The approach combines the quantum hydrodynamic and classical Liouvillian representations by the construction of a particular type of moments (that is, partial hydrodynamic moments) whose evolution is determined by a hierarchy of coupled equations. For pure states, which are at the center of the present study, this hierarchy terminates at the first order. In the Lagrangian picture, the deterministic trajectories result in dynamics which is Hamiltonian in the classical subspace, while the projection onto the quantum subspace evolves under a generalized hydrodynamic force. Importantly, this force also depends upon the classical (Q, P) variables. The present application demonstrates the tunneling dynamics in both the Eulerian and Lagrangian representations. The method is exact if the classical subspace is harmonic, as is the case for the systems studied here.     

A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism

We show that the mixed quantum-classical Liouville equation is equivalent to linearizing the forward-backward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantum-classical Liouville equation for calculating the memory kernel of the generalized quantum master equation is also presented. The accuracy and computational feasibility of such an approach is demonstrated in the case of a two-level system nonlinearly coupled to an anharmonic bath.     

Photodynamics and time-resolved fluorescence of azobenzene in solution: a mixed quantum-classical simulation

We have simulated the photodynamics of azobenzene by means of the Surface Hopping method. We have considered both the trans → cis and the cis → trans processes, caused by excitation in the n → π* band (S(1) state). To bring out the solvent effects on the excited state dynamics, we have run simulations in four different environments: in vacuo, in n-hexane, in methanol, and in ethylene glycol. Our simulations reproduce very well the measured quantum yields and the time dependence of the intensity and anisotropy of the transient fluorescence. Both the photoisomerization and the S(1) → S(0) internal conversion require the torsion of the N═N double bond, but the N-C bond rotations and the NNC bending vibrations also play a role. In the trans → cis photoconversion the N═N torsional motion and the excited state decay are delayed by increasing the solvent viscosity, while the cis → trans processes are less affected. The analysis of the simulation results allows the experimental observations to be explained in detail, and in particular the counterintuitive increase of the trans → cis quantum yield with viscosity, as well as the relationship between the excited state dynamics and the solvent effects on the fluorescence lifetimes and depolarization.     

A non-adiabatic quantum-classical dynamics study of the intramolecular excited state hydrogen transfer in ortho-nitrobenzaldehyde

Ab initio surface-hopping dynamics calculations have been performed to simulate the intramolecular excited state hydrogen transfer dynamics of ortho-nitrobenzaldehyde (o-NBA) in the gas phase from the electronic S(1) excited state. Upon UV excitation, the hydrogen is transferred from the aldehyde substituent to the nitro group, generating o-nitrosobenzoic acid through a ketene intermediate. The semiclassical propagations show that the deactivation from the S(1) is ultrafast, in agreement with the experimental measurements, which detect the ketene in less than 400 fs. The trajectories show that the deactivation mechanism involves two different conical intersections. The first one, a planar configuration with the hydrogen partially transferred, is responsible for the branching between the formation of a biradical intermediate and the regeneration of the starting material. The conversion of the biradical to the ketene corresponds to the passage through a second intersection region in which the ketene group is formed.     

Mixed quantum-classical molecular dynamics analysis of the molecular-level mechanisms of vibrational frequency shifts

A detailed analysis of the origins of vibrational frequency shifts of diatomic molecules (I2 and ICl) in a rare gas (Xe) liquid is presented. Specifically, vibrationally adiabatic mixed quantum-classical molecular dynamics simulations are used to obtain the instantaneous frequency shifts and correlate the shifts to solvent configurations. With this approach, important mechanistic questions are addressed, including the following: How many solvent atoms determine the frequency shift? What solvent atom configurations lead to blue shifts, and which lead to red shifts? What is the effect of solute asymmetry? The mechanistic analysis can be generally applied and should be useful in understanding what information is provided by infrared and Raman spectra about the environment of the probed vibrational mode.     

Anharmonic infrared and Raman spectra in Car-Parrinello molecular dynamics simulations

The infrared and Raman spectra of naphthalene crystal with inclusion of anharmonic effects have been calculated by adopting the generalized variational density functional perturbation theory in the framework of Car-Parrinello molecular dynamics simulations. The computational approach has been generalized for cells of arbitrary shape. The intermolecular interactions have been analyzed with and without the van der Waals corrections, showing the importance of such interactions in the naphthalene crystal to reproduce the structural, dynamical, and spectroscopic properties.     

Mixed quantum-classical dynamics in the adiabatic representation to simulate molecules driven by strong laser pulses

The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynamics can be simulated quite accurately by a semiclassical surface-hopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na(2) using the surface-hopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.     

Applications of quantum-classical and quantum-stochastic molecular dynamics simulations for proton transfer processes

Quantum-classical and quantum-stochastic molecular dynamics models (QCMD/QSMD) are formulated and applied to describe proton transfer processes in three model systems - the proton bound ammonia-ammonia dimer in an external electrostatic field; malonaldehyde, which undergoes a quantum tautomeric rearrangement; and phospholipase A₂, an enzyme which induces a water dissociation process in its active site followed by proton hopping to a histidine imidazole ring. The proton dynamics are described by the time-dependent Schrödinger equation. The dynamics of the classical atoms are described using classical molecular dynamics. Coupling between the quantum proton (s) and the classical atoms is accomplished via conventional or extended Hellmann-Feynman forces, as well as the time-dependence of the potential energy function in the Schrödinger equation. The interaction of the system with its environment is described by stochastic forces. Possible extensions of the models as well as future applications in molecular structure and dynamics analysis will be briefly discussed.     

A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics

We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.