Stationary points, electronic structure calculations

Spectroscopic applications usually require us to go beyond single-point electronic energy calculations or structure optimizations. Scans of the potential energy hypersurface or at least Taylor expansions around stationary points are needed to extract nuclear dynamics information. If spectral intensity information is required, dipole moment or polarizability hypersurfaces [202] have to be developed as well. If multiple relevant minima exist on the potential energy hyper surface, efficient methods to explore them are needed [203, 204],... 

Rotational and vibrational partition functions can be computed from the geometry and vibrational frequencies that are calculated for a molecule or TS. The entropy can then be obtained from these partition functions. Thus, electronic structure calculations can be used to compute not only the enthalpy difference between two stationary points but also the entropy and free energy differences. 

In this section we report our experimental findings relatively to three different reactions of CN radicals with simple alkynes, namely acetylene, methyl-acetylene and dimethyl-acetylene. We have selected these reactive systems for different reasons the reactions with C2H2 is the prototype for the class of reactions CN +- alkynes/polyynes, thus is expected to reveal key concepts for reactions with the higher members of the same series the reactions with methylacetylene and dimethylacetylene were selected to observe the effect of the H substitution with one or two alkyl groups. In all cases, the experimental results are discussed in the light of the ab initio electronic structure calculations for the stationary points of the relevant potential energy surfaces. 

Using BOV A, one may calculate KIEs for any pair of reactant and TS structures. There is no requirement to use structures that are stationary points according to electronic structure calculations. One creates a vibrational model that treats the reactant and TS molecules as perfect harmonic oscillators with atoms (point masses) connected together with bonds (massless springs) with defined force constants. If the vibrational model and the structure of the reactant are accurate, then the TS model that gives calculated KIEs matching the experimental ones is considered the experimental transition state. 

The obvious ambiguity of the historical approach is eliminated by employing modern electronic structure calculations, which are capable of giving stationary points to chemical accuracy, and reliable vibrational frequencies and moments of inertia not only for the reactants, but also... 

If HL denotes the high level (e.g., QCISD(T)/aug-cc-pVTZ or QCIS(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ) and LL denotes the low level (e.g., NDDO-SRP or MP2/6-31G ), then the final result of these three steps is denoted HL///LL, which is a direct generalization of the // notation of electronic structure theory. In particular //LL means that stationary point geometries are calculated at level LL, whereas ///LL mans that the reaction path is calculated at level LL. 

One of the most important applications of electronic structure calculations is the exploration of PESs. In particular, the theoretical description of chemical transformations requires the knowledge of the main stationary points of the relevant PESs. 

The hrst step in theoretical predictions of pathway branching are electronic structure ab initio) calculations to define at least the lowest Born-Oppenheimer electronic potential energy surface for a system. For a system of N atoms, the PES has (iN — 6) dimensions, and is denoted V Ri,R2, - , RiN-6)- At a minimum, the energy, geometry, and vibrational frequencies of stationary points (i.e., asymptotes, wells, and saddle points where dV/dRi = 0) of the potential surface must be calculated. For the statistical methods described in Section IV.B, information on other areas of the potential are generally not needed. However, it must be stressed that failure to locate relevant stationary points may lead to omission of valid pathways. For this reason, as wide a search as practicable must be made through configuration space to ensure that the PES is sufficiently complete. Furthermore, a search only of stationary points will not treat pathways that avoid transition states. 

We discuss in this paper the unconstrained optimization of stationary points of a smooth function fix) in many variables. The emphasis is on methods useful for calculating molecular electronic energies and for determining molecular equilibrium and transition state structures. The discussion is general and practical aspects concerning computer implementations are not treated. 

---