Frank J. McLafferty

On classical paths and the Wigner path integral

We ask and answer the question: How do we derive the approximation of Heller (that the Wigner function propagates along classical paths) from the path integral formulation of the Wigner kernel of Kitahara?.

G2 ab initio calculations of the enthalpy of formation of hydrazoic acid, methyl azide, ethyl azide, methyl amine, and ethyl amine

G2 calculations on the title compounds yield total energies, E0=−164.560 33, −203.776 24, −243.004 79, −95.666 91, and −134.894 58 hartrees and ΔHf298=70.4, 71.0, 64.5, −5.9, and −12.4 kcal mol−1, respectively. Agreement with literature values for hydrazoic acid and both amines is good. We discuss the calculation for methyl and ethyl azide in relation to our recent experimental results from hydrogen calorimetry of a group of higher organic azides. While a substantial improvement over the existing literature value, the calculation yields an estimate for ΔHhyd298=−76.9 kcal mol−1, that is, 2.2 kcal mol−1 less exothermic than the lower limit of our estimated experimental uncertainty.

On nonadiabatic transitions and the Wigner path integral

We continue our study of dynamics in terms of the Wigner path integral. We investigate how nonadiabatic electronic transitions are described in the formalism. We find, using the approximation of Miller and George for the reduced propagator, and the classical path approximation for the nuclear degrees of freedom (i.e., assuming nuclear localization), that the Wigner path integral leads to a Tully–Preston surface hopping model. We discuss the relation of this result to general classically forbidden processes and to the dynamics of molecular systems in intense laser fields.

On quantum trajectories and an uncertainty relation

We discuss quantum trajectories from the point of view of Bohm and Wyatt. We find that the theory can be formally written in terms of a field (probability) [P(x,t)], a position [x], and an average momentum [〈p〉] in a density operator which is normalized and Hermitian, but not positive definite. One consequence of this is that the theory obeys, in a natural way, a formal relation ΔxΔp=0 for these averages. We interpret this as a consistency requirement for a trajectory in space–time with a position x and an average momentum which allows a space–time description. We show that a momentum space form can be written in terms of a field (probability) [P(p,t)], a momentum [p], and an average position [〈x〉]. We briefly discuss potential chemical applications of quantum trajectories in the theory of chemical dynamics, kinetics, and local field theory.

On quantum trajectories and an approximation to the Wigner path integral

In this paper we suggest an approximation to the Wigner Path integral using quantum trajectories. We discuss the results in terms of Bohm’s theory and Takabayasi’s study of the relation between Bohm and Wigner theory. We discuss how this new approach is an approximation to Bohm’s theory and discuss its validity. We also suggest a method of evaluation and where such an approach would be useful.

On bimolecular kinetics, the Bloch equation and Wigner path integrals

We continue our study of Wigner path integrals. We first define a Wigner path integral for the kernel of the Wigner–Bloch equation, solve it for the free particle and harmonic oscillator cases, discuss the physical interpretation which is new and then we apply it (along with the path integral representation of the Liouville equation) to obtain a path integral representation in phase space of the quantum transition state theory of Miller. We also obtain an expression involving products of Wigner kernels for the correlation function form of the exact bimolecular rate constant.