Quantum Wave Packet Dynamics Research Articles

Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: Momentum representation, coupled electron-nuclear dynamics, and external fields

We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al(27) - C(7) - Al(27) nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed.

Dynamics of quantum wave packets in complex molecules traced by 2D coherent electronic correlation spectroscopy

Electronic and nuclear molecular wavepackets are a clear manifestation of the wavelike properties of matter at the very heart of quantum mechanics. In this work we demonstrate how electronic two-dimensional spectroscopy (2D) serves as a highly evolved tool for the simultaneous investigation of both phenomena. In further analysis and theoretical treatments, 2D spectra form an ideal basis for the discussion of electronic decoherence, vibrational relaxation and electron-phonon coupling.

Trajectory approach to quantum wave packet dynamics: The correlated derivative propagation method

The correlated derivative propagation method is proposed for the time evolution of quantum wave packets. Without truncation of higher derivatives of hydrodynamic fields, the exact equations of motion derived in the derivative propagation method are solved through the Taylor series method by propagating correlated quantum trajectories. By mapping the physical grid to a uniform computational grid, the necessary higher derivatives of these fields are computed by the finite difference method, and the Jacobian terms of the transformation are determined by the moving least squares method. The Taylor coefficients for hydrodynamic fields and their derivatives are evaluated exactly using the automatic differentiation technique. Excellent results are obtained for barrier transmission problems.

A multistage ab initio quantum wavepacket dynamics formalism for electronic structure and dynamics in open systems

We propose a multistage quantum wavepacket dynamical treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. The full donor-bridge-acceptor system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. These facilitate a computationally efficient and potentially accurate treatment of the long-range coupling interactions between the bridge and donor/acceptor systems and the associated open system boundary conditions. Time-independent forms of the associated, partitioned equations are also derived. In the time-independent form corresponding to the bridge system, coupling to donor and acceptor, that is long-range interactions, is completely accounted. For the time-dependent study, the quantum dynamics of the electronic flux through the bridge-donor/acceptor interface is constructed using an accurate and efficient representation of the discretized quantum-mechanical free-propagator. A model for an electrode-molecular wire-electrode system is used to test the accuracy of the scheme proposed. Transmission probability is obtained directly from the probability density of the electronic flux in the acceptor region. Conductivity through the molecular wire is computed using a wavepacket flux correlation function.

Photochemical Ring-Opening of Cyclohexadiene: Quantum Wavepacket Dynamics on a Global Ab Initio Potential Energy Surface

We have assembled a global CASSCF potential energy surface for the excited 2A state of the cyclohexadiene -hexatriene system, in two degrees of freedom, with full relaxation in all other degrees of freedom. Quantum wavepacket dynamics on this surface yields simple interpretations of recent experimental data on the ultrafast photochemical ring-opening of cyclohexadiene as well as predictions on preferred product configurations. The feasibility of this system as a model for fulgide molecular switches is discussed.

Nonadiabatic quantum wave packet dynamics of the H + H2 reaction including the coriolis coupling

The effect of coriolis coupling on the dynamics of H + H2 reaction is examined by calculating the initial state-selected and energy resolved reaction probabilities on the coupled manifold of its degenerate 2p (E′) ground electronic state. H3 in this state is prone to the Jahn-Teller (JT) instability and consequently the degeneracy is split upon distortion from its D 3h equilibrium geometry. The orbital degeneracy is, however, restored along the D 3h symmetry configuration and it results into conical intersections of the two JT split component states. The energetically lower adiabatic component of latter is repulsive, and mainly (‘rather solely’) drive the H + H2 reaction dynamics. On the otherhand, the upper adiabatic component is of bound type and can only impart non-adiabaticity on the dynamics of lower state. Comparison calculations are therefore also carried out on the uncoupled lower adiabatic sheet to assess the nonadiabatic effect. Exact quantum scattering calculations are performed by a chebyshev polynomial propagator and employing the double many body expansion potential energy surface of the electronic ground state of H3. Reaction probabilities are reported up to a total energy of ∼ 3·0 eV, slightly above the energetic minimum of the seam of conical intersections at ∼ 2·74 eV. Reaction probabilities are calculated up to the total angular momentum, J = 20 and for each value of J, the projection quantum number K is varied from 0 to min (J, K max), with K max = 4. Probability results are compared and discussed with those obtained without the coriolis coupling.

Computing vibrational properties in hydrogen‐bonded systems using quantum wavepacket ab initio molecular dynamics

AbstractThe recently developed quantum wavepacket ab initio molecular dynamics method is discussed. The approach combines quantum wavepacket dynamics with ab initio molecular dynamics and is useful in studying problems where nuclear quantum effects play an important role. Computational bottlenecks and associated solutions are outlined. Chemical applications dealing with vibrational properties in hydrogen‐bonded clusters are discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Time-dependent quantum wave-packet description of H and D atom tunneling in N–H and N–D photodissociation of methylamine and methylamine-d2

The degree to which tunneling through a barrier in the N-H and N-D photodissociation channels of methylamine (CH3NH2) and its deuterated variant (CH3ND2), respectively, plays a role was investigated by time-dependent quantum wave-packet dynamics calculations. Two dimensional potential energy surfaces (PESs) of methylamine, presenting the N-H stretch and the HNC bend, were constructed employing multireference ab initio electronic-structure methods, allowing full description of the H motion on the HC-NH2 plane. The time-dependent Schrödinger equation was solved employing the Fourier method for calculating the Hamiltonian operation together with the Chebychev polynomial expansion of the evolution operator. The results show that tunneling and decay to vibrational resonant states on the first excited electronic PES are faster for the H atom than for the D. The decay into two of the resonant states found on the first PES strongly depends on the initially excited vibrational state on the ground electronic PES.

N-Inversion in 2-azabicyclopentane derivatives: model simulations for a laser controlled molecular switch

We report model quantum simulations for the nitrogen inversion in 2-azabicyclo[1.1.1]pentane derivates controlled by laser pulses proposing to use this class of molecules as molecular switches. The derivatives trans-5-fluoro-2-methyl-2-azabicyclo[1.1.1]pentane and cis-5-fluoro-2-methyl-2-azabicyclo[1.1.1]pentane are investigated by means of density functional theory and quantum wave packet dynamics. The molecules have two stable, i.e. energetically well-separated, conformers along the N-inversion coordinate. In 1D model simulations the transformation from one conformer to the other is accomplished in the electronic ground state by using two overlapping chirped linearly polarized IR laser pulses for the trans- and cis-isomer or alternatively via an electronic excited state employing a pump-dump sequence of ultrashort UV laser pulses.

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

We present an extension of our earlier work on adaptive quantum wavepacket dynamics [B. Hartke, Phys. Chem. Chem. Phys., 2006, 8, 3627]. In this dynamically pruned basis representation the wavepacket is only stored at places where it has non-negligible contributions. Here we enhance the former 1D proof-of-principle implementation to higher dimensions and optimize it by a new basis set, interpolating Gaussians with collocation. As a further improvement the Tnum approach from Lauvergnat and Nauts [J. Chem. Phys., 2002, 116, 8560] was implemented, which in combination with our adaptive representation offers the possibility of calculating the whole Hamiltonian on-the-fly. For a two-dimensional artificial benchmark and a three-dimensional real-life test case, we show that a sparse matrix implementation of this approach saves memory compared to traditional basis representations and comes even close to the efficiency of the fast Fourier transform method. Thus we arrive at a quantum wavepacket dynamics implementation featuring several important black-box characteristics: it can treat arbitrary systems without code changes, it calculates the kinetic and potential part of the Hamiltonian on-the-fly, and it employs a basis that is automatically optimized for the ongoing wavepacket dynamics.

Combining quantum wavepacket ab initio molecular dynamics with QM/MM and QM/QM techniques: Implementation blending ONIOM and empirical valence bond theory

We discuss hybrid quantum-mechanics/molecular-mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) generalizations to our recently developed quantum wavepacket ab initio molecular dynamics methodology for simultaneous dynamics of electrons and nuclei. The approach is a synergy between a quantum wavepacket dynamics, ab initio molecular dynamics, and the ONIOM scheme. We utilize this method to include nuclear quantum effects arising from a portion of the system along with a simultaneous description of the electronic structure. The generalizations provided here make the approach a potentially viable alternative for large systems. The quantum wavepacket dynamics is performed on a grid using a banded, sparse, and Toeplitz representation of the discrete free propagator, known as the "distributed approximating functional." Grid-based potential surfaces for wavepacket dynamics are constructed using an empirical valence bond generalization of ONIOM and further computational gains are achieved through the use of our recently introduced time-dependent deterministic sampling technique. The ab initio molecular dynamics is achieved using Born-Oppenheimer dynamics. All components of the methodology, namely, quantum dynamics and ONIOM molecular dynamics, are harnessed together using a time-dependent Hartree-like procedure. We benchmark the approach through the study of structural and vibrational properties of molecular, hydrogen bonded clusters inclusive of electronic, dynamical, temperature, and critical quantum nuclear effects. The vibrational properties are constructed through a velocity/flux correlation function formalism introduced by us in an earlier publication.

Hydrogen Tunneling in an Enzyme Active Site: A Quantum Wavepacket Dynamical Perspective

We study the hydrogen tunneling problem in a model system that represents the active site of the biological enzyme, soybean lipoxygenase-1. Toward this, we utilize quantum wavepacket dynamics performed on potential surfaces obtained by using hybrid density functional theory under the influence of a dynamical active site. The kinetic isotope effect is computed by using the transmission amplitude of the wavepacket, and the experimental value is reproduced. By computing the hydrogen nuclear orbitals (eigenstates) along the reaction coordinate, we note that tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical s-type proton wave functions and p-type polarized proton wave functions for transfer along the donor-acceptor axis. In addition, there is also a significant population transfer through distorted p-type proton wave functions directed perpendicular to the donor-acceptor axis (via intervening pi-type proton eigenstate interactions) which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor-acceptor axis and along directions perpendicular to the donor-acceptor axis. Furthermore, the tunneling process is facilitated by the occurrence of curve crossings and avoided crossings along the proton eigenstate adiabats.

Quantum wave packet dynamics of N(D2)+H2 reaction

The quantum wave packet dynamics of the title reaction within the coupled state approximation is examined here and initial state-selected reaction probabilities, integral reaction cross sections, and thermal rate constants are reported. The ab initio potential energy surface of the electronic ground state (1(2)A(")) of the system recently reported by Ho et al. [J. Chem. Phys., 119, 3063 (2003)] is employed in this investigation. All partial wave contributions up to the total angular momentum J=55 were necessary to obtain converged integral reaction cross sections up to a collision energy of 1.0 eV. Thermal rate constants are calculated from the reaction cross sections and compared with the available theoretical and experimental results. Typical resonances formed during the course of the reaction and elucidating the insertion type mechanism for the product formation are calculated. Vibrational energy levels supported by the deep well (approximately 5.5 eV) of the 1(2)A(") potential energy surface of NH(2) are also calculated for the total angular momentum J=0. A statistical analysis of the spacing between the adjacent levels of this energy spectrum is performed and the extent of irregularity in the spectral sequence is assessed.

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

Generalization of Classical Mechanics for Nuclear Motions on Nonadiabatically Coupled Potential Energy Surfaces in Chemical Reactions

Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.

Quantum wavepacket dynamics for time-resolved photoelectron spectroscopy of the NO 2 conical intersection

Quantum wavepacket dynamics at the X 2 A 1/ A 2 B 2 conical intersection of NO 2 molecule following a femtosecond pump pulse is computed, and subsequent probing of the dynamics with time-resolved femtosecond photoelectron spectroscopy is investigated theoretically. Diabatic representation of the ground and first excited state potential energy surfaces are constructed, and is used in time propagation of the vibrational wave function through pump and probe pulses in three dimensions. The Hamiltonian explicitly includes the pump interaction between the neutral states and probe interaction between the neutral and (discretized) ion continuum. Constant ionization matrix elements are used in this study. The computed photoelectron kinetic energy spectra are seen to reflect ultrafast wavepacket motion through the conical intersection region at early times.

Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.

On the calculation of circular dichroism spectra using quantum wave-packet dynamics with an application to molecular dimers

Circular dichroism (CD) spectra are calculated from the Fourier transform of a time-correlation function. The latter can efficiently be evaluated by wave-packet propagation methods. This approach is similar to the time-dependent evaluation of absorption or Raman spectra. As an application, correlation functions and CD spectra for a molecular dimer are determined and compared to the case of absorption.

Quantum wave packet dynamics on multidimensional adaptive grids: Applications of the moving boundary truncation method

AbstractRecently, we reported a novel method for integrating the time dependent Schrödinger equation which used hydrodynamic quantum trajectories to adapt the boundaries of a fixed spatial grid. The moving boundary truncation (MBT) method significantly reduced the number of grid points needed to perform accurate calculations while maintaining stability during the time propagation. In this work, the method is extended to multidimensional examples. The application of MBT to scattering on 2D and 3D potential energy surfaces shows a greater decrease in the number of grid points needed compared with full fixed grids while maintaining excellent accuracy and stability, even for very long propagation times. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

THE EFFECT OF THE COUPLING BETWEEN VALENCE STATE B2Π AND RYDBERG STATE C2Π ON THE ABSORPTION SPECTRUM OF THE NO MOLECULE

The effect of the coupling between the valence state B 2Π and the Rydberg state C 2Π on the absorption spectrum of the NO molecule is studied by using the quantum wave packet dynamics method. The results show that the coupling between the valence state B 2Π and the Rydberg state C 2Π affects the C 2Π ← X 2Π absorption spectrum both in the intensity and on the location of spectrum peaks. The dynamics of the wave packet of the excited states is also described. One part of the wave packet evolves on the Rydberg state C 2Π and the other is trapped in the valence state B 2Π.