Potential surface calculations

A PM0-CND04 analysis6 of thiatriazole and several 5-substituted derivatives (R = Ph—, MeS—, NH2—, CH2=CH—) leads to the prediction that alkylation at position 4 is favored, the relative order being N-4 > N-2 > N-3 (see also Section III, B). Companion potential surface calculations suggest that both H+ and CHi prefer in-plane attack on the nitrogen a-lone pairs.2 Position 3 is again the least-favored attack site, in direct contradiction to experiment.6 Either the calculations are misleading or the complexity of thermodynamic versus kinetic control in the thiatriazole system has yet to be unraveled. 

Fig. 1. Schematic representation of the potential energy surface for the electronic (el) ground state of a molecule existing in two tautomeric forms, A and B. Superscripts exp, HF, CNDO/2, MINDO/3 indicate that energy differences 8 a,b calculated for potential energy surfaces determined either experimentally (exp) or calculated by means of ab initio method in the Hartree-Fock (HF) approximation or by semiempirical methods (CNDO/2, MINDO/3). The symbol eq stands for the geometrical equilibrium of both tautomers, while 2a and Qb indicate nonequilibrium geometries of tautomers A and B, respectively. Note that the theoretical potential surface calculated by sophisticated quantum-mechanical methods ( exact solution of electronic Schrbdinger equation includes electron correlation with geometry optimization) should be the same (or very similar) as that determined experimentally [in this case i>eor) ei

A theoretical study of the interaction of sulfur atoms with ethylene within the framework of the Extended Hiickel MO theory has been reported by HoflFmann and co-workers (19). Potential surface calculations revealed two minima for the 8( 02) + C2H4 system. The higher corresponds to vinyl mercaptan formation via C-H bond insertion, and the lower, lying about 20 kcal below the former, to the least-motion, symmetry-allowed addition of sulfur across the double bond. The two are viewed as competing concerted processes. Similar calculations for the... 

The H + H2 reaction has long served as a focal point for theoretical studies of gas phase chemical reaction dynamics. As the simplest of chemical reactions from the point of view of electronic structure, it has been the subject of numerous potential surface calculations (as reviewed in Ref. 1), and it is still the only reaction for which the potential surface is known to within a few tenths of a kcal/mol. From... 

In the following sections we will discuss some of the features mentioned above. The first (Section II) will address itself to the question of the overall accuracy that is generally achieved in excited-state potential surface calculations. The next (Section III) will present examples for species for which the theoretical predictions are sometimes the only data available challenging the experimentalists, or for which computed data have been around prior to measurements and are able to explain and predict general trends. Section IV will deal with the interaction of potential surfaces and the contribution of theoretical methods to this area. Section V will deal with the treatment of short-lived negative ions Section VI will show calculated fine-structure effects in the potential energy curves of simple systems and Section Vll will give a selected but representative set of examples from our own work carried out in conjunction with experiments or examples that have led to a re-evaluation of measured data. 

As a first step in extending the Stillinger-David approach to mineral systems, an Fe-O and Si-0 potential was introduced (Rustad et al. 1995 Rustad and Hay 1995). The basis for parameterization of the Fe-0 potential was the Fe -H20 potential surface calculated in Curtiss et al. (1987). The surface is given in Figure 3. 

This is an extremely troublesome problem. The standard way to deal with it is the counterpoise correction proposed by Boys Bernardi. The reference energy for A is calculated in the presence of the basis functions (but not the electrons or nuclei) of molecule B, and similarly the reference energy for B is calculated in the presence of the A basis functions. In this way, the variational improvement that arises from the presence of the foreign basis functions is included in the reference calculation as well as in the A B calculation. (The basis functions of the other molecule are sometimes called ghost orbitals when used like this.) An obvious problem is that if we change the relative positions of the two molecules in the A B complex, then we change the position of the B basis functions relative to A (and vice versa) so that the counterpoise-corrected calculation of the reference energies has to be repeated for every point on the surface. Clearly this increases the expense of the potential surface calculation by a factor of about 3. 

An approximate reaction surface for the thermal 1,3-sigmatropic rearrangement of bicyclo[3,2,0]hept-2-enes to norbornenes has been calculated using extended Huckel theory, The potential surfaces, calculated for bicyclo[3,2,0]heptene and 7-methylbicyclo[3,2,0]heptene, accommodate qualitatively the known experimental facts, but results of quantitative significance would require a dynamical approach. 

The MRCI method is shown to yield accurate potential surfaces for the systems studied here. The use of the externally contracted Cl method leads to relatively small errors( typically less than 1.0 kcal/mole) and this method is well suited to potential surface calculations. The neglect of correlation of the O 2s electrons (as in the H -f O2 calculations) leads to only small errors, but neglect of correlation of the N 2s electrons leads to larger errors for certain cases. 

At this level, then it cannot be assumed that the potential surface calculated in the usual way is an approximation to anything exact but it remains open to see whether it is possible to associate it with the exact solution when rotational motion is taken into account. 

The intrinsically relativistic nature of the electronic structure of the halogen monoxides is dictated by the presence of two spin-orbit components in the ground electronic state. Any accurate characterization of the XO Xj and X2 rii/2 potentials must therefore treat relativistic effects explicitly. However, diis requirement greatly increases the cost and complexity of the ab initio effort(26), resulting in few relativistic potential surface calculations such as the 10 study by Roszak et al.(21) One more frequently finds relativistic effects incorporated as corrections to non-relativistic energies or treated through the use of effective core potentials (23). 

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