Potential Energy Surfaces

The concept of Potential Energy Surface (PES) is of paramount importance in the field of chemical physics. Usually, the dynamics of very complex systems such as atoms and molecules is accurately described in terms of motion of nuclei subject to electrostatic interactions among them and with instantaneous electron clouds, i.e. the system's PES for the given electronic state. Thus, a chemical reaction becomes a 'simple' rolling-ball motion in a multidimensional space and the reaction rate is determined by the PES features, like mountain-passes, sinks and valleys. Actual motion is quantum mechanical (i.e. true dynamics allows for motion in classically forbidden regions, it allows superposition of states and it must account for the uncertainty principle effects -e.g. Zero-Point-Energy effects-) but usually this classical picture is quite realistic.

A pictorial view of possible reactions in the ground and in the first excited electronic states of the LiH₂⁺ system. Accurate Potential Energy Surfaces for this system have been computed and analytically fitted to a simple functional form. Fortran77 routines that generate the above PESs are available; they are GROUND.F and EXCITED.F, for the ground and the first excited electronic state, respectively.

Even when a simple adiabatic picture of the dynamics is not possible only a few number of Potential Energy Surfaces (and possibly their 'interaction terms') is needed in order to accurately describe the system dynamics. In this case, intersections between surfaces are key-features of any dynamical event since non-adiabatic transitions are likely to occur in such regions and they are very fast, much faster than e.g. radiative transitions.

The ²A₁/²B₂ conical intersection in the CH₂⁺ system. On the left the ²A₁ (white) and the ²B₂ (green) PESs in C_2v configuration. They have been recently computed with MRCI wavefunctions which used state-averaged CASSCF-optimized molecular orbitals and a large basis-set of aug-cc-pVQZ quality. On the right the ground-state PES on the same axes.

The ²A₁/²B₁ Renner-Teller intersection in the CH₂⁺ system, shown in the C_2v configuration. The ²A₁ (white) and the ²B₁ (blue) PESs are computed as in the above figures.

In gas-surface collision problems the use of a unique Potential Energy Surface is often questionable, because of the large number of involved electronic states, e.g. in collisions with metal substrates. Nevertheless, it remains an useful tool to model the system dynamics, which often should only be 'slightly' corrected for the 'electron friction'.

The semiemipirical Embedded-Diatomic-In-Molecule (EDIM) potential for an Hydrogen atom interacting with a H atom adsorbed on a Ni(100) surface. A few number of isosurfaces is plotted as a function of the projectile coordinates, the other coordinates being held fixed.