Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Exploring the importance of quantum effects in nucleation: the archetypical Ne(n) case

The effect of quantum mechanics (QM) on the details of the nucleation process is explored employing Ne clusters as test cases due to their semi-quantal nature. In particular, we investigate the impact of quantum mechanics on both condensation and dissociation rates in the framework of the microcanonical ensemble. Using both classical trajectories and two semi-quantal approaches (zero point averaged dynamics, ZPAD, and Gaussian-based time dependent Hartree, G-TDH) to model cluster and collision dynamics, we simulate the dissociation and monomer capture for Ne(8) as a function of the cluster internal energy, impact parameter and collision speed. The results for the capture probability P(s)(b) as a function of the impact parameter suggest that classical trajectories always underestimate capture probabilities with respect to ZPAD, albeit at most by 15%-20% in the cases we studied. They also do so in some important situations when using G-TDH. More interestingly, dissociation rates k(diss) are grossly overestimated by classical mechanics, at least by one order of magnitude. We interpret both behaviours as mainly due to the reduced amount of kinetic energy available to a quantum cluster for a chosen total internal energy. We also find that the decrease in monomer dissociation energy due to zero point energy effects plays a key role in defining dissociation rates. In fact, semi-quantal and classical results for k(diss) seem to follow a common "corresponding states" behaviour when the proper definition of internal and dissociation energies are used in a transition state model estimation of the evaporation rate constants.     

Quasiclassical trajectory study of reactive and dissociative processes in H2+H2: comparison with quantum-mechanical calculations

Quasiclassical trajectory calculations have been carried out for H(2)(v(1)=high)+H(2)(v(2)=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v(1)'s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H(2)(v(1)=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined.     

Measures of stochasticity for nonstationary initial preparations of coupled oscillators

The contributions of different eigenstates of a nonlinearly coupled oscillator system to the expansion of a local wave packet are analyzed from an information theoretical point of view. Such a wave packet can be considered as a nonstationary vibrational state of an electronically excited manifold of a molecule after Franck–Condon type initial preparation. The distributions of these contributions are compared to their individual stochastic ideals using Ruch's concept of “mixing distances.” The stochastic ideals are constructed via a probability diffusion process between neighboring states of the original distributions, representing an initial preparation corresponding to a Hamiltonian with only irregular eigenstates. Gaussian minimum uncertainty wave packets as initial states in a two-dimensional nonlinear oscillator system with classically regular and chaotic energy ranges are studied numerically. It is found that distance measures, partly reflecting the “mixing distance” of a distribution from its stochastic ideal, show a large fluctuation in the classical regular energy range and a small fluctuation in the range where most of the classical trajectories move chaotically. This indicates that for this type of initial preparation process the actual location of the initial state in space plays the dominant role for the dynamics in the low-energy range while for wave packets starting near the dissociation energy of the model system this location becomes unimportant.     

Quantum dynamics study on multichannel dissociation and isomerization reactions of formaldehyde

We study quantum dynamics of the multichannel reactions of H(2)CO including the molecular and radical dissociation channels as well as the isomerization ones, H(2)CO-->trans-HCOH and trans-HCOH-->cis-HCOH. For this purpose, the previously developed potential energy function [T. Yonehara and S. Kato, J. Chem. Phys. 117, 11131 (2002)] is refined to give accurate transition state energies and to describe the radical dissociation channel. The cumulative reaction probabilities for the molecular dissociation and two isomerization channels are calculated by using the full Watson Hamiltonian. We also carry out wave packet dynamics calculations starting from the transition state region for the molecular dissociation. A contracted basis set for the angular coordinates is constructed to reduce the size of dynamics calculations. The intramolecular vibrational relaxation dynamics is found to be fast and almost complete within 300 fs. Using the energy filtered wave functions, the time propagation of HCOH population is obtained in the energy range from 81 to 94 kcal/mol. The branching ratio of the radical product is estimated by calculating the time dependent reactive fluxes to the molecular and radical dissociation products.     

基于量子波包方法的态-态分辨反应散射动力学计算

本文回顾了最近十几年利用量子波包方法研究气相分子反应散射动力学的工作进展,特别是在态-态分辨水平上的工作进展。比较详细地讨论了目前存在的利用量子波包方法计算态-态微分截面的几种方法。目前态-态分辨的波包动力学计算可以精确地预测三原子和四原子分子反应散射的各种信息,文章最后对几个典型的利用波包方法在态-态分辨水平上研究过的三原子和四原子反应散射体系做了讨论。     

Femtosecond study of Cu(H(2)O) dynamics

The short-time nuclear dynamics of Cu(H(2)O) is investigated using femtosecond photodetachment-photoionization spectroscopy and time-dependent quantum wave packet calculations. The Cu(H(2)O) dynamics is initiated in the electronic ground state of the complex by electron photodetachment from the Cu(-)(H(2)O) complex, where hydrogen atoms are oriented toward Cu. Several time-resolved resonant multiphoton ionization schemes are used to probe the ensuing reorientation and dissociation. Immediately following photodetachment, the neutral complex is far from its minimum energy geometry and possesses an internal energy comparable to the Cu-H(2)O dissociation energy and undergoes both large-amplitude H(2)O motion and dissociation. Dissociation is observed to occur on three distinct time scales: 0.6, 8, and 100 ps. These results are compared to the results of time-dependent J=0 wave packet calculations, propagating the initial anion vibrational wave functions on the ground-state potential of the neutral complex. An excellent agreement is obtained between the experimental results and the ionization signals derived from the calculated probability amplitudes. Related experiments and calculations are carried out on the Cu(D(2)O) complex, with results very similar to those of Cu(H(2)O).     

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies.     

Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: Br2 in Ar matrix

The intramolecular wave packet dynamics on the electronic B (3pi0) potential of Br2 in solid argon is induced and interrogated by femtosecond pump-probe spectroscopy. An effective potential of the chromophore in the solid is derived from the wave packet period for different excitation photon energies. Deep in the potential well, it is consistent with vibrational energies from wavelength-resolved spectra. It extends to higher energies, where the vibrational bands merge to a continuum, and even beyond the dissociation limit, thus quantifying the cage effect of the argon matrix. This advantage of pump-probe spectroscopy is related to a reduced contribution of homogeneous and inhomogeneous line broadenings. The vibrational energy relaxation rates are determined by a variation of the probe window spatial position via the probe quantum energy. A very large energy loss in the first excursion of the wave packet is observed near the dissociation limit. This strong interaction with the argon matrix is directly displayed in an experimental trajectory.     

A semiclassical study of wave packet dynamics in anharmonic potentials

Classical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pump-probe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of first-order canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a final-value representation semiclassical method, specifically designed for the purpose of computing pump-probe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of one-color pump probe, a simple phase-space quantization scheme is devised to reproduce the temporal profile at the left-turning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pump-probe signal.     

Dissociation, solvation, and dynamics of HBr in small water clusters

The dissociation of hydrogen bromide in a small water cluster (H₂O)_n (n=3–5) has been studied with quantum chemical methods. The dynamics of dissociation was followed by classical molecular dynamics, and stationary points were studied in order to compute the free energy change associated with the ionization process. The nudged elastic band method was used to map out the energy profile of the reaction paths. The results show that HBr can dissociate in the presence of just four water molecules if they are in the correct configuration.The relation of our results to recent experiments is discussed.     

Moving boundary truncated grid method: Multidimensional quantum dynamics

The moving boundary truncated grid (TG) method is used to study wave packet dynamics of multidimensional quantum systems. As time evolves, appropriate Eulerian grid points required for propagating a wave packet are activated and deactivated with no advance information about the dynamics. This method is applied to the Henon-Heiles potential and wave packet barrier scattering in two, three, and four dimensions. Computational results demonstrate that the TG method not only leads to a great reduction in the number of grid points needed to perform accurate calculations but also is computationally more efficient than the full grid calculations.     

Quantum theory for transition state absorption

A time-dependent quantum model involving two wave packets on two excited-state surfaces is presented to describe absorption (or emission) from the transition state of a chemical reaction. The connection between the quantum result and existing classical theories is shown. The model ia applied to the direct dissociation of ICN* and gives results in good agreement with experiment. The dissociation time - the time to half-maximal absorption - is almost invariant with the pulse width but is dependent on the probe wavelength. A lower absorption plateau and a longer dissociation time is predicted for probe energies above the asymptotic resonance energy.     

Control of nonadiabatic dissociation dynamics with the use of laser-induced wave packet interferences

Based on wave packet interferences induced by a stationary laser field, a simple way of controlling nonadiabatic dissociation dynamics is proposed. We treat a simple two-state model of diatomic molecules. In this model, there exist two dissociative potential energy curves which cross and are strongly coupled at an internuclear distance, and thus dissociations into one channel are predominant. We propose a control scheme to selectively dissociate a molecule into any favorite channel by choosing the laser frequency and intensity appropriately. The semiclassical estimation of desirable laser parameters can be performed easily by regarding the dissociation processes as nonadiabatic transitions between the Floquet states. The agreement between the semiclassical estimation and the quantum wave packet calculation is found to be satisfactory in the high frequency region (> or =1000 cm(-1)) where the Floquet state picture is valid. In the low frequency region (<1000 cm(-1)), on the other hand, there are discrepancies between them due to the invalidity of the Floquet picture and the dissociation probability is sensitive to the laser phase. This control scheme is applied to the predissociation dynamics of NaI, NaI-->Na+I.     

A six-dimensional wave packet study of the vibrational overtone induced decomposition of hydrogen peroxide

A converged quantum wave packet study is presented for the unimolecular reaction HOOH → OH+OH induced by the fifth OH-overtone excitation employing an ab initio potential energy surface. All six internal vibrational degrees of freedom are explicitly represented in this simulation for total angular momentum zero. It is found that the decay of the survival probability and of the autocorrelation function is non-exponential and that the long time dynamics is likely due to the superposition of a number of resonance states. The simulated overtone spectrum and rotational product distribution is in good agreement with experimental measurements. It is concluded that: (1) the reaction dynamics is non-statistical on a 30 ps timescale, (2) the observed line width is roughly a factor of 1.7 larger than implied by the reactive lifetimes suggesting that a significant portion of the linewidth is due to intramolecular vibrational energy relaxation, and (3) the quantum reaction rate is suppressed by about a factor of two relative to its classical counterpart.     

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.     

State-to-state dynamics of H + O2 reaction, evidence for nonstatistical behavior

Converged differential and integral cross sections are reported for the H + O2 --> OH + O reaction on an improved potential energy surface of HO2(X2A') using a dynamically exact quantum wave packet method and Gaussian weighted quasi-classical trajectory method. The complex-forming mechanism is confirmed by strong forward and backward scattering peaks and by highly inverted OH rotational state distributions. Both the quantum and classical results provide strong evidence for nonstatistical behavior in this important reaction.     

D_2在Ni(100)表面离解吸附的量子动力学研究

用量子含时波包法研究了Ｄ２在镍表面顶－桥位上离解吸附量子动力学．计算了不同入射动能及初始振转态的离解几率．讨论了分子的同核对称性、转动取向和振动激发对离解几率的影响，并与其他理论计算结果做了比较．