Optimized nuclear configurations

Ab initio calculations using the CHF-GIAO approach on the optimized geometrical configurations of the compounds have also allowed to predict the 111, 13C, and 1SN nuclear magnetic resonance (NMR) spectra of the quinolizidine series. The calculated spectra fit fairly well the experimental data, with the exception of some signals... 

Theoretical studies of the properties of the individual components of nanocat-alytic systems (including metal nanoclusters, finite or extended supporting substrates, and molecular reactants and products), and of their assemblies (that is, a metal cluster anchored to the surface of a solid support material with molecular reactants adsorbed on either the cluster, the support surface, or both), employ an arsenal of diverse theoretical methodologies and techniques for a recent perspective article about computations in materials science and condensed matter studies [254], These theoretical tools include quantum mechanical electronic structure calculations coupled with structural optimizations (that is, determination of equilibrium, ground state nuclear configurations), searches for reaction pathways and microscopic reaction mechanisms, ab initio investigations of the dynamics of adsorption and reactive processes, statistical mechanical techniques (quantum, semiclassical, and classical) for determination of reaction rates, and evaluation of probabilities for reactive encounters between adsorbed reactants using kinetic equation for multiparticle adsorption, surface diffusion, and collisions between mobile adsorbed species, as well as explorations of spatiotemporal distributions of reactants and products. 

This procedure has been employed in the construction of the diabatic potential matrix for the l A and 2 A electronic states of H3 with conical intersection by Abrol and Kuppermann," in which the diabatization angle 7 (a function of internal nuclear coordinates) was calculated by solving the three-dimensional Poisson equation (with an optimal set of boundary conditions) for the entire U domain of nuclear configuration space bearing important significance for reactive scattering. The procedure was also employed by Mota and Varandas in their construction of the double many-body expansion (DMBE) diabatic potential matrix for the l A and 2 A states of the HN2 system, with a newly proposed diabatization scheme where the diabatization angle is represented by some specific functions. Earlier construction of the DK (Dobbyn and Knowles)... 

The electronic energy W in the Bom-Oppenlieimer approxunation can be written as W= fV(q, p), where q is the vector of nuclear coordinates and the vector p contains the parameters of the electronic wavefimction. The latter are usually orbital coefficients, configuration amplitudes and occasionally nonlinear basis fiinction parameters, e.g., atomic orbital positions and exponents. The electronic coordinates have been integrated out and do not appear in W. Optimizing the electronic parameters leaves a function depending on the nuclear coordinates only, E = (q). We will assume that both W q, p) and (q) and their first derivatives are continuous fimctions of the variables q- and py... 

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