Time-Sliced Thawed Gaussian Propagation Method for Simulations of Quantum Dynamics.

A rigorous method for simulations of quantum dynamics is introduced on the basis of concatenation of semiclassical thawed Gaussian propagation steps. The time-evolving state is represented as a linear superposition of closely overlapping Gaussians that evolve in time according to their characteristic equations of motion, integrated by fourth-order Runge-Kutta or velocity Verlet. The expansion coefficients of the initial superposition are updated after each semiclassical propagation period by implementing the Husimi Transform analytically in the basis of closely overlapping Gaussians. An advantage of the resulting time-sliced thawed Gaussian (TSTG) method is that it allows for full-quantum dynamics propagation without any kind of multidimensional integral calculation, or inversion of overlap matrices. The accuracy of the TSTG method is demonstrated as applied to simulations of quantum tunneling, showing quantitative agreement with benchmark calculations based on the split-operator Fourier transform method.

Toward adaptive control of coherent electron transport in semiconductors.

This work explores the feasibility of using shaped electrostatic potentials to achieve specified final scattering distributions of an electron wave packet in a two dimensional subsurface plane of a semiconductor. When electron transport takes place in the ballistic regime, and features of the scattering potentials are smaller than the wavelength of the incident electron then coherent quantum effects can arise. Simulations employing potential forms based on analogous optical principles demonstrate the ability to manipulate quantum interferences in two dimensions. Simulations are presented showing that suitably shaped electrostatic potentials may be used to separate an initially localized Gaussian wave packet into disjoint components or concomitantly to combine a highly dispersed packet into a compact form. The results also indicate that highly complex scattering objectives may be achieved by utilizing adaptive closed-loop optimal control in the laboratory to determine the potential forms needed to manipulate the scattering of an incoming wave packet. An adaptive feedback algorithm can be used to vary individual voltages of multipixel gates on the surface of a solid state structure to thereby find the potential features in the transport plane needed to produce a desired scattering objective. A proposed experimental design is described for testing the concept of adaptive control of coherent electron transport in semiconductors.

Classical Optimal Control for Energy Minimization Based On Diffeomorphic Modulation under Observable-Response-Preserving Homotopy.

We introduce the so-called "Classical Optimal Control Optimization" (COCO) method for global energy minimization based on the implementation of the diffeomorphic modulation under observable-response-preserving homotopy (DMORPH) gradient algorithm. A probe particle with time-dependent mass m( t;ß) and dipole µ( r, t;ß) is evolved classically on the potential energy surface V( r) coupled to an electric field E( t;ß), as described by the time-dependent density of states represented on a grid, or otherwise as a linear combination of Gaussians generated by the k-means clustering algorithm. Control parameters ß defining m( t;ß), µ( r, t;ß), and E( t;ß) are optimized by following the gradients of the energy with respect to ß, adapting them to steer the particle toward the global minimum energy configuration. We find that the resulting COCO algorithm is capable of resolving near-degenerate states separated by large energy barriers and successfully locates the global minima of golf potentials on flat and rugged surfaces, previously explored for testing quantum annealing methodologies and the quantum optimal control optimization (QuOCO) method. Preliminary results show successful energy minimization of multidimensional Lennard-Jones clusters. Beyond the analysis of energy minimization in the specific model systems investigated, we anticipate COCO should be valuable for solving minimization problems in general, including optimization of parameters in applications to machine learning and molecular structure determination.

Floquet Study of Quantum Control of the Cis-Trans Photoisomerization of Rhodopsin.

Understanding how to control reaction dynamics of polyatomic systems by using ultrafast laser technology is a fundamental challenge of great technological interest. Here, we report a Floquet theoretical study of the effect of light-induced potentials on the ultrafast cis-trans photoisomerization dynamics of rhodopsin. The Floquet Hamiltonian involves an empirical 3-state 25-mode model with frequencies and excited-state gradients parametrized to reproduce the rhodopsin electronic vertical excitation energy, the resonance Raman spectrum, and the photoisomerization time and efficiency as probed by ultrafast spectroscopy. We simulate the excited state relaxation dynamics using the time-dependent self-consistent field method, as described by a 3-state 2-mode nuclear wavepacket coupled to a Gaussian ansatz of 23 vibronic modes. We analyze the reaction time and product yield obtained with pulses of various widths and intensity profiles, defining 'dressed states' where the perturbational effect of the pulses is naturally decoupled along the different reaction channels. We find pulses that delay the excited-state photoisomerization for hundreds of femtoseconds, and we gain insights on the underlying control mechanisms. The reported findings provide understanding of quantum control, particularly valuable for the development of ultrafast optical switches based on visual pigments.

Photoinduced electron and proton transfer in the hydrogen-bonded pyridine-pyrrole system.

We present here a detailed analysis of the mechanism of photoinduced electron and proton transfer in the planar pyrrole-pyridine hydrogen-bonded system, a model for the photochemistry of hydrogen bonds in DNA base pairs. Two different crossings, an avoided crossing and a conical intersection, are the key steps for forward and backward electron and proton transfer providing to the system photostability against UV radiation by restoring the system in its initial electronic and geometric structure.

Steered quantum dynamics for energy minimization.

We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimized to find an effective Hamiltonian that steers the dynamics of the system into the global minimum without getting trapped into local minima. The algorithm is illustrated as applied to energy minimization on rugged surfaces and golf potentials comparable to those previously explored for testing quantum annealing methodologies.

Wave packet spreading and localization in electron-nuclear scattering.

The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schrödinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

Kepler Predictor-Corrector Algorithm: Scattering Dynamics with One-Over-R Singular Potentials.

An accurate and efficient algorithm for dynamics simulations of particles with attractive 1/r singular potentials is introduced. The method is applied to semiclassical dynamics simulations of electron-proton scattering processes in the Wigner-transform time-dependent picture, showing excellent agreement with full quantum dynamics calculations. Rather than avoiding the singularity problem by using a pseudopotential, the algorithm predicts the outcome of close-encounter two-body collisions for the true 1/r potential by solving the Kepler problem analytically and corrects the trajectory for multiscattering with other particles in the system by using standard numerical techniques (e.g., velocity Verlet, or Gear Predictor corrector algorithms). The resulting integration is time-reversal symmetric and can be applied to the general multibody dynamics problem featuring close encounters as occur in electron-ion scattering events, in particle-antiparticle dynamics, as well as in classical simulations of charged interstellar gas dynamics and gravitational celestial mechanics.

Chemisorption of HCl to the MgO(001) surface: a DFT study.

We use plane wave and embedded cluster ab initio density functional calculations to study adsorption, dissociation and diffusion of the HCl molecule on the MgO(001) surface. The two methods yield comparable results for adsorption of an isolated HCl molecule and complement each other when considering charged species and coverage effects. We find dissociative chemisorption at a coverage smaller than 0.5 monolayer with a Cl(-) ion electrostatically coupled to the OH(-) ion at the surface oxygen site. The adsorption energy of the Cl(-)[dot dot dot](OH)(-) complex is 1.5 eV and the activation energy of Cl(-) diffusion away from OH(-) is 0.6 eV. There is no significant activation energy for rotation of Cl(-) around the adsorption site. At rising coverage, an increase in dipole-dipole repulsion between HCl molecules leads to a lowering of the adsorption energy per HCl and a change of binding towards hydrogen-bridge type as well as a lowering of the activation energy for Cl(-) diffusion. OH(-) formed in the surface due to HCl adsorption has a stretch frequency of 3,083 cm(-1) with Cl(-) associated and 3,648 cm(-1) with Cl(-) removed.

Allene and pentatetraene cations as models for intramolecular charge transfer: vibronic coupling Hamiltonian and conical intersections.

We consider the vibronic coupling effects involving cationic states with degenerate components that can be represented as charge localized at either end of the short cumulene molecules allene and pentatetraene. Our aim is to simulate dynamically the charge transfer process when one component is artificially depopulated. We model the Jahn-Teller vibronic interaction within these states as well as their pseudo-Jahn-Teller coupling with some neighboring states. For the manifold of these states, we have calculated cross sections of the ab initio adiabatic potential energy surfaces along all nuclear degrees of freedom, including points at large distances from the equilibrium to increase the physical significance of our model. Ab initio calculations for the cationic states of allene and pentatetraene were based on the fourth-order Møller-Plesset method and the outer valence Green's function method. In some cases we had to go beyond this method and use the more involved third-order algebraic diagrammatic construction method to include intersections with satellite states. The parameters for a five-state, all-mode diabatic vibronic coupling model Hamiltonian were least-square fitted to these potentials. The coupling parameters for the diabatic model Hamiltonian are such that, in comparison to allene, an enhanced preference for indirect charge transfer is predicted for pentatetraene.

Simulation of a complex spectrum: interplay of five electronic states and 21 vibrational degrees of freedom in C5H4 +.

Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B (2)E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum.