Long time wave packet dynamics from energy eigenfunctions: nonuniform energy resolution via adaptive bisection fast Fourier transformation

This article presents a new approach to long time wave packet propagation. The methodology relies on energy domain calculations and an on-the-surface straightforward energy to time transformation to provide wave packet time evolution. The adaptive bisection fast Fourier transform method employs selective bisection to create a multiresolution energy grid, dense near resonances. To implement fast Fourier transforms on the nonuniform grid, the uniform grid corresponding to the finest resolution is reconstructed using an iterative interpolation process. By proper choice of the energy grid points, we are able to produce results equivalent to grids of the finest resolution, with far fewer grid points. We have seen savings 20-fold in the number of eigenfunction calculations. Since the method requires computation of energy eigenfunctions, it is best suited for situations where many wave packet propagations are of interest at a fixed small set of points--as in time dependent flux computations. The fast Fourier transform (FFT) algorithm used is an adaptation of the Danielson-Lanczos FFT algorithm to sparse input data. A specific advantage of the adaptive bisection FFT is the possibility of long time wave packet propagations showing slow resonant decay. A method is discussed for obtaining resonance parameters by least squares fitting of energy domain data. The key innovation presented is the means of separating out the smooth background from the sharp resonance structure.     

Time‐dependent schrödinger equation with Markovian outgoing wave boundary conditions: Applications to quantum tunneling dynamics and photoionization

Markovian outgoing wave boundary conditions are introduced as an approximate method to reduce the size of the computational grid for time integration of the time‐dependent Schrödinger equation. The ratio and polynomial methods developed as open boundary conditions are applied to the wave function at the boundaries of the computational grid. This computational method is used to study the wave packet dynamics for a metastable well, a double well, and strong‐field ionization of a model atom. Accurate results demonstrate that this method can significantly reduce the number of grid points required in a dynamical calculation for quantum dynamical problems. © 2012 Wiley Periodicals, Inc.     

Quantum dynamics of inelastic scattering with a moving grid

The time‐dependent discrete variable representation (TDDVR) of a wave function with grid points defined by the Hermite part of the Gauss–Hermite (G‐H) basis set introduces quantum corrections to classical mechanics. The grid points in this method follow classical trajectory and the approach converges to the exact quantum formulation with sufficient trajectories (TDDVR points) but just with a single grid point; only classical mechanics performs the dynamics. This newly formulated approach (developed for handling time‐dependent molecular quantum dynamics) has been explored to calculate vibrational transitions in the inelastic scattering processes. Traditional quantum mechanical results exhibit an excellent agreement with TDDVR profiles during the entire propagation when enough grid points are included in the quantum‐classical dynamics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Scattered wave packet formalism for the energy-resolved reaction probability

The scattered wave packet formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is utilized to calculate the energy-resolved transmission probability. The total wave function is split into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by the polynomial method. The wave packet correlation function approach is employed to compute the energy-resolved transmission probability for a one-dimensional potential barrier and a one-dimensional model chemical reaction exhibiting a quantum resonance. Accurate results demonstrate that this formalism can significantly reduce the number of grid points required in a dynamical calculation for the reaction probability.     

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.     

Higher-order split operator schemes for solving the Schrödinger equation in the time-dependent wave packet method: applications to triatomic reactive scattering calculations

The efficiency of the numerical propagators for solving the time-dependent Schr?dinger equation in the wave packet approach to reactive scattering is of vital importance. In this Perspective, we first briefly review the propagators used in quantum reactive scattering calculations and their applications to triatomic reactions. Then we present a detailed comparison of about thirty higher-order split operator propagators for solving the Schr?dinger equation with their applications to the wave packet evolution within a one-dimensional Morse potential, and the total reaction probability calculations for the H + HD, H + NH, H + O(2), and F + HD reactions. These four triatomic reactions have quite different dynamic characteristics and thus provide a comprehensive picture of the relative advantages of these higher-order propagation methods for describing reactive scattering dynamics. Our calculations reveal that the most often used second-order split operator method is typically more efficient for a direct reaction, particularly for those involving flat potential energy surfaces. However, the optimal higher-order split operator methods are more suitable for a reaction with resonances and intermediate complexes or a reaction experiencing potential energy surface with fluctuations of considerable amplitude. Three 4th-order and one 6th-order split operator methods, which are most efficient for solving reactive scattering in various conditions among the tested ones, are recommended for general applications. In addition, a brief discussion on the relative performance between the Chebyshev real wave packet method and the split operator method is given. The results in this Perspective are expected to stimulate more applications of (high-order) split operators to the quantum reactive scattering calculation and other related problems.     

Multidimensional quantum dynamical study of beta-hydrogen transfer in a cationic rhodium complex

The dynamics of migratory insertion and beta-hydrogen elimination in the cationic complex [CpRh(PH3)H(C2H4)]+ is studied from a quantal point of view. On the basis of DFT results for the relevant stationary points of the potential energy surface, three coordinates are identified that vary strongly during the reaction. A suitable three-dimensional grid, along with an appropriate kinetic energy operator, are constructed that are employed in the subsequent wave packet propagations. The latter are performed in the spirit of transition state spectroscopy and start from the various saddle points of the potential energy surface. Vibrational periods and lifetimes for these elementary processes, relevant to homogeneous catalysis, are obtained in this way for the first time. This work is considered to provide the basis for a subsequent treatment of equilibrium rate constants and to shed new light on the electronic factors governing these prototypical reaction steps.     

Construction of an accurate quartic force field by using generalised least-squares fitting and experimental design

In this work we present an attractive least-squares fitting procedure which allows for the calculation of a quartic force field by jointly using energy, gradient, and Hessian data, obtained from electronic wave function calculations on a suitably chosen grid of points. We use the experimental design to select the grid points: a “simplex-sum” of Box and Behnken grid was chosen for its efficiency and accuracy. We illustrate the numerical implementations of the method by using the energy and gradient data for H₂O and H₂CO. The B3LYP/cc-pVTZ quartic force field performed from 11 and 44 simplex-sum configurations shows excellent agreement in comparison to the classical 44 and 168 energy calculations.     

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。     

Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations.     

Accurate potential energy surface and quantum reaction rate calculations for the H+CH4-->H2+CH3 reaction

Calculations for the cumulative reaction probability N(E) (for J=0) and the thermal rate constant k(T) of the H+CH(4)-->H(2)+CH(3) reaction are presented. Accurate electronic structure calculations and a converged Shepard-interpolation approach are used to construct a potential energy surface which is specifically designed to allow the precise calculation of k(T) and N(E). Accurate quantum dynamics calculations employing flux correlation functions and multiconfigurational time-dependent Hartree wave packet propagation compute N(E) and k(T) based on this potential energy surface. The present work describes in detail the various convergence test performed to investigate the accuracy of the calculations at each step. These tests demonstrate the predictive power of the present calculations. In addition, approximate approaches for reaction rate calculations are discussed. A quite accurate approximation can be obtained from a potential energy surface which includes only interpolation points on the minimum energy path.     

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).     

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface(PES)for the dissociative chemisorption of HCl on Au(111)using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory(DFT)calculations.The resulting PES is accurate and smooth,based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations.Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points,as well as to the fitting process.The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite diferent from the four-dimensional fixed-site calculations,indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.     

Photoionization-induced dynamics of ammonia: ab initio potential energy surfaces and time-dependent wave packet calculations for the ammonia cation

An analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation has been developed which is tailored to model the ultrafast photoinduced dynamics. Selected ab initio cuts, obtained by multireference configuration interaction calculations, have been used to determine the parameters of a diabatic representation for this Jahn-Teller and pseudo-Jahn-Teller system. The model includes higher-order coupling terms both for the Jahn-Teller and for the pseudo-Jahn-Teller matrix elements. The relaxation to the ground state is possible via dynamical pseudo-Jahn-Teller couplings involving the asymmetric bending and stretching coordinates. The photoelectron spectrum of NH3 and the internal conversion dynamics of NH3+ have been determined by wave packet propagation calculations employing the multiconfigurational time-dependent Hartree method. Three different time scales are found in the dynamics calculations for the second absorption band. The ultrafast Jahn-Teller dynamics of the two excited states occurs on a 5 fs time scale. The major part of the internal conversion to the ground state takes place within a short time scale of 20 fs. This fast internal conversion is, however, incomplete and the remaining excited state population does not decay completely even within 100 fs.     

Direct dynamics study of ultrafast vibrational energy relaxation in ice Ih

Car-Parrinello molecular dynamics (CPMD) and a previously developed wave packet model are used to study ultrafast relaxation in water clusters. Water clusters of 15 water molecules are used to represent ice Ih. The relaxation is studied by exciting a symmetric or an asymmetric stretch mode of the central water molecule. The CPMD results suggest that relaxation occurs within 100 fs. This is in agreement with experimental work by Woutersen and Bakker and the earlier wave packet calculations. The CPMD results further indicate that the excitation energy is transferred both intramolecularly and intermolecularly on roughly the same time scale. The intramolecular energy transfer occurs predominantly between the symmetric and asymmetric modes while the bend mode is largely left unexcited on the short time scale studied here.     

Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions

Dynamics of molecules in an intense laser field is studied in terms of the quantum electronic wave packet coupled with classical nuclear motions. The equations of motion are derived taking a proper account of molecular interactions with the vector potential of a classical electromagnetic field, along with the nonadiabatic interaction due to the breakdown of the Born-Oppenheimer approximation. With the aid of electronic structure calculations, the present method enables us to track, in an ab initio manner, the dynamics of polyatomic molecules in an intense field. Preliminary calculations are carried out for the vibrational state of LiF and a collision of Li+F under an intense laser pulse, which are limited to the domain of no ionization.     

Limits of the creation of electronic wave packets using time-dependent density functional theory

Explicitly time-dependent density functional theory (TDDFT) has often been suggested as the method of choice for controlling the correlated dynamics of many electron systems. However, it is not yet clear which control tasks can be achieved reliably and how this depends on the functionals used. In this article, we show that the control task of creating a simple wave packet, having a population of 50% in the excited state, can indeed be achieved if a certain condition is fulfilled. This result is in contrast to the observation that a full population inversion is extremely difficult to achieve. In addition, we identify a rule to predict when TDDFT produces the correct wave packet. To illustrate our findings, we study the molecules Li(2)C(2), Li(7)OH, and B(2)N(2)CO using two different functionals as well as time-dependent Hartree-Fock (TDHF). To assess the performance of TDDFT and TDHF, we compare with time-dependent configuration interaction calculations.