Robert E. Wyatt

Bio: Robert E. Wyatt is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Wave function & Wave packet. The author has an hindex of 44, co-authored 260 publications receiving 7213 citations.

Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics

Abstract: to Quantum Trajectories.- The Bohmian Route to the Hydrodynamic Equations.- The Phase Space Route to the Hydrodynamic Equations.- The Dynamics and Properties of Quantum Trajectories.- Function and Derivative Approximation on Unstructured Grids.- Applications of the Quantum Trajectory Method.- Adaptive Methods for Trajectory Dynamics.- Quantum Trajectories for Multidimensional Dynamics.- Approximations to the Quantum Force.- Derivative Propagation Along Quantum Trajectories.- Quantum Trajectories in Phase Space.- Mixed Quantum-Classical Dynamics.- Topics in Quantum Hydrodynamics: The Stress Tensor and Vorticity.- Quantum Trajectories for Stationary States.- Challenges and Opportunities.

Corresponding Orbitals and the Nonorthogonality Problem in Molecular Quantum Mechanics

Abstract: Given any two sets of spin orbitals ai and bj, there exist equivalent sets âi and bj such that their overlap matrix is diagonal, i.e., 〈âi | bj〉=diiδij. This is the basis of the corresponding orbital transformation of Amos and Hall. Their transformation is shown to have widespread application to quantum chemistry. It leads to a simple generalization of the Slater—Condon rules for the expectation value of an operator between two determinantal wavefunctions when the spin orbitals of one function have no simple orthogonality relationship to those of the other function. In the case of single‐determinantal wavefunctions, use of the corresponding orbital transformation and the integral Hellmann—Feynman formula leads to a very simple expression for the energy difference associated with two similar configurations of a molecular system. Extensions to limited configuration interaction expansions are discussed. Given single‐determinantal wavefunctions for two related molecular systems, it is shown that the corres...

Dynamics of the Collinear H+H2 Reaction. I. Probability Density and Flux

Abstract: The time evolution of the collinear H+H2 reaction as given by classical mechanics and by time‐dependent quantum mechanics has been studied. The calculations employed the Porter–Karplus potential surface. The relevant equations of motion were solved to high accuracy by direct numerical integration. The evolution of the quantal probability density in the interaction region of the potential surface is shown in a series of perspective plots. Classical mechanics gives an amazingly good description of the probability density and flux patterns during most of the reaction; however, the classical and quantal descriptions begin to diverge near the end of the reaction. Essentially, the classical reaction terminates before the quantal reaction. The dynamic behavior of the reaction is hydrodynamically turbulent, as shown by transient whirlpool formation on the inside of the reaction path. All results reported in this paper are for one average system energy, namely, 0.65 eV (initial average translational energy = 0.38 eV).

Optical potential for laser induced dissociation

Abstract: A new computational approach to molecular multiphoton dissociation is presented. Use of an optical potential allows the continuum channels to be represented as a set of pseudobound states coupled to the actual bound states of the molecule. The evolution of the system is thus amenable to the standard problem of laser induced transitions between bounds states. The long time behavior is then efficiently computed by using Floquet analysis. Results for a nonrotating diatomic are discussed.

General atomic and molecular electronic structure system

Abstract: A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.

A complete basis set model chemistry. II. Open‐shell systems and the total energies of the first‐row atoms

Abstract: The major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. An open‐shell complete basis set (CBS) model chemistry, based on the unrestricted Hartree–Fock (UHF) zero‐order wave function, is defined to include corrections for basis set truncation errors. The total correlation energy for the first‐row atoms is calculated using the unrestricted Mo/ller–Plesset perturbation theory, the quadratic configuration interaction (QCI) method, and the CBS extrapolation. The correlation energies of the atoms He, Li, Be, B, C, N, O, F, and Ne, calculated using atomic pair natural orbital (APNO) basis sets, vary from 85.1% to 95.5% of the experimental correlation energies. However, extrapolation using the asymptotic convergence of the pair natural orbital expansions retrieves from 99.3% to 100.6% of the experimental correlation energies for these atoms. The total extrapolated energies (ESCF+Ecorrelation) are then in agreement with experiment to within ±0...

The Quantum Theory of Light

Abstract: (b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method

Abstract: A novel discrete variable representation (DVR) is introduced for use as the L2 basis of the S‐matrix version of the Kohn variational method [Zhang, Chu, and Miller, J. Chem. Phys. 88, 6233 (1988)] for quantum reactive scattering. (It can also be readily used for quantum eigenvalue problems.) The primary novel feature is that this DVR gives an extremely simple kinetic energy matrix (the potential energy matrix is diagonal, as in all DVRs) which is in a sense ‘‘universal,’’ i.e., independent of any explicit reference to an underlying set of basis functions; it can, in fact, be derived as an infinite limit using different basis functions. An energy truncation procedure allows the DVR grid points to be adapted naturally to the shape of any given potential energy surface. Application to the benchmark collinear H+H2→H2+H reaction shows that convergence in the reaction probabilities is achieved with only about 15% more DVR grid points than the number of conventional basis functions used in previous S‐matrix Kohn...