• Energy Research

We present a kinetic energy operator and inner product that can be used to solve the Schroedinger equation in redundant coordinates. The goal is to develop equations and a computational procedure that can be used with N coordinates for a system with M degrees of freedom, where N > M. In chemical physics, this might be useful for exploiting symmetry or exploiting certain representations of potentials. Calculations demonstrate that the ideas work.

Now that we have presented some symmetry-adapted perturbation schemes, we would like to understand the reasons that suggest or motivate their introduction for the ab-initio prediction of the interaction energy ΔE = E(ABC…) – (EA + EB + EC + ….) between a number of atomic or molecular partners A, B, C, …, in a given configuration.

The inversion potentials of R2CO (R=H, F, Cl) molecules in the lowest excited electronic states were determined from experimental data using various model potential functions and approximations for the kinetic energy operator of inversion motion. The estimates of the heights of the barriers to inversion and the equilibrium values of the inversion coordinate for the H2CO molecule in the S1 and T1 states are fairly stable. The results for the F2CO and Cl2CO molecules are strongly dependent on the approximation used; for these molecules, the most reliable parameters of the potential functions were chosen. The problem of qualitative characteristics of the shape of inversion potentials is discussed using the results ofab initio quantum-chemical calculations of the molecules under study.

Ever since Lowdin /1/ in 1959 wrote his monumental survey of the correlation problem it has been recognized that this problem is one of the central issues in many-electron quantum mechanics. A clear insight into the problem is needed not only when wavefunctions of high accuracy are calculated but also when assessing the possibility of using a relatively poor wavefunction to predict experimental quantities. Although the form of the wavefunction changes greatly in its details from the He atom through molecules to solids and plasma there is a common problem of understanding how the electrons are correlated and how this correlation can be incorporated into the wavefunction.

It is shown that quantum chemical calculations are able to calculate lifetimes of small molecules in electronically excited states with an accuracy which is comparable to that of experimental determination. The advantage of the calculations is, that they can treat processes from the nanosec scale up to lifetimes of minutes in principle by the same procedure, and that this is possible for radiative and radiation less transitions. Calculations are furthermore able to give insight into the mechanism of the various processes.

Recent work on quantum coupled oscillators and the collinear dynamics of three bodies, as models for unimolecular and bimolecular reactions, is reviewed with special reference to the role of resonances. The approach, semiclassical in spirit, exploits the approximate separability of the radius of hyperspherical formulations and allows to localize the breakdown of adiabaticity at “ridges in the potential”, where transitions between modes occur.