Atom-diatom potential energy surfaces

If the electrons occupy orbitals different from the most stable (ground) electronic state, the bonding between the atoms also changes. Therefore, an entirely different potential energy surface is produced for each new electronic configuration. This is illustrated in Figure 6.6 for a diatomic molecule. 

Potential energy surface (PES) can be understood by making a plot of energy as a function of various interatomic distances in the complex that is formed during the reaction. For simplicity, let us consider a simplet chemical reaction between an atom A and a diatomic molecule BC to yield another atom C and a diatomic molecule AB as... 

By the introduction of the (x, y) coordinate system, one has reduced the problem to the motion of a particle of mass (i in a two-dimensional rectilinear space (x, y). Thus, the problem of the collision between an atom and a diatomic molecule in a collinear geometry has been converted into a problem of a single particle on the potential energy surface expressed in terms of the coordinates x and y rather than the coordinates rAB and rBc The coordinates x and y which transform the kinetic energy to diagonal form in such way that the kinetic energy contains only one (effective) mass are referred to as mass scaled Jacobi coordinates. 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

Second, most of the articles cited and the calculations presented are for collisions of diatomic molecules with atoms. The effects of external fields have been studied only for three molecule-molecule collision systems O2-O2 in a magnetic field, NH-NH in a magnetic field, and OH-OH in an electric field. In each case, the calculations are based on significant simplifications of the interaction potential operator. Most of the NH-NH calculations and the O2-O2 studies assume that the collision dynamics occurs on the maximal spin adiabatic potential energy surface of the two-molecule complex. There is only one study that considers the dynamics of NH-NH collisions in a magnetic field with account of transitions to lower spin surfaces [48]. 

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

A brief comment on the accuracy of current approaches seems in order. For atomic systems in the first or second row of the periodic table, quantitative ( 0.01eV) studies have been carried out. For diatomic systems, constructed from these atoms, an accuracy of 1 kcal in the potential curves can be realized. For polyatomic systems the situation is less clear because of the great increase in computational difficulty. Accuracy of 5 to 10 kcal can probably be achieved for simple potential-energy surfaces, although very few surfaces have been examined in detail. 

In reactions involving electronically excited states, the interaction of two potential energy surfaces is likely to be involved. This interaction is reasonably well understood and easy to visualize in the case of potential curves for diatomic systems, but for systems containing more than two atoms, the situation is considerably less tractable. One tries to develop a description, starting from the observed kinetics of a reaction and using whatever spectroscopic data may be available. 

The one-dimensional potential curves depicted in Figures 1.1-1.3 represent the dissociation of diatomic molecules for which the potential V(Rab) depends only on the internuclear distance between atoms A and B. However, if one or both constituents are molecules, V is a multidimensional object, a so-called potential energy surface which depends on several (at least three) nuclear coordinates denoted by the vector Q = (Ql,Q2,Q3,---) (Margenau and Kestner 1969 Balint-Kurti 1974 Kuntz 1976 Schaefer III 1979 Kuntz 1979 Truhlar 1981 Salem 1982 Murrell et al. 1984 Hirst 1985 Levine and Bernstein 1987 ch.4 Hirst 1990 ch.3). The intramolecular and intermolecular forces, defined by... 

This list, which is by no means complete, clearly demonstrates that the generic type of final state distribution is not only observed for atom-diatom systems but also if the recoiling partner is a large polyatomic molecule. In contrast to the many experimental examples, there are only a few systems for which rotational excitation has been analyzed by means of ab initio potential energy surfaces and exact quantum mechanical or classical calculations. In the following we discuss two of them. 

Figure 1 The ubiquitous elbow potential energy surface showing for the dissociation of a diatomic molecule on a surface. This is a function of die molecular bond length and the molecule-surface distance. The reactants are intact molecules, while die products are the atoms chemisorbed separately on the surface. The two extreme cases are shown, an early barrier for which the initial vibration of the molecule is ineffective in overcoming the barrier, and a late barrier for which vibration assists in the dissociation process.

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