Quantum chemical calculations coefficient

ACCURATE QUANTUM CHEMICAL CALCULATIONS coefficients to form a contribution to a. 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

Equations (9) and (11) indicate how the auxiliary radial function for the rotational factor becomes separable into contributions from atomic centres of types A and B. An analogous separation is practicable for both the vibrational g factor and the total adiabatic corrections for the latter quantity this separation is effected in the original quantum-chemical calculations. Accordingly we express these calculated values of rotational and vibrational g factors, presented in Table 1, and adiabatic corrections, presented in Table 3, of He H" to generate coefficients of radial functions for atomic centres of either type. He or H. The most useful variable for these functions is z, defined in terms of instantaneous R and equihbrium R internuclear distances as... 

In this connection a more detailed account will only be given of a method that permits calculation of HMO orbital energies of a model of a heterocycle without expanding the secular determinant from the knowledge of molecular orbital energies and expansion coefficients of the parent hydrocarbon.11-15 Now that automatic computing machines are commonly used for quantum-chemical calculations we see the chief merit of the method in that it permits one to study the effect of empirical parameters on energy characteristics in a clear-cut and concise manner. 

All pseudoazulenes possess an electronic transition in the visible spectral region (Table III). As can be derived from the extinction coefficient, as well as from investigations on solvent dependence, this electronic transition is a nn transition having a low negative solvatochromism that can be measured for some compounds.51 86 145 165 These spectral data correspond to the results of quantum chemical calculations (Section IV,B) and are analogous to those of azulenes. 

Octanol/Water Partition Coefficients by Quantum Chemical Calculations. 

These equations are used in semiempirical quantum chemical calculations of non-linear optical polarizabilities by applying perturbation theoretical expressions [the so-called sum-over-states (SOS) method]. Here we use them to derive some qualitative and very general trends in a few simple model systems. To this end we concentrate on the electronic structure, i.e. on the LCAO coefficients. We do not explicitly calculate the transition frequencies. This is justified for the qualitative discussion below since typical transition energies... 

In summary, the utility of quantum chemical calculations to elucidate the detailed mechanisms of OH radical reactions with oxygenated VOCs has been proven. The importance of including reactant complexes in such modeling, to obtain accurate values of the rate coefficients, has also been shown. The best results are those obtained when it is assumed that such complexes are in their vibrational ground state. The relative site reactivity of the studied compounds towards OH radicals has been shown to be strongly influenced by intramolecular hydrogen-bond-like interactions that arise in the transition states. 

The discussion above is intended to emphasize that a systematic selection of density basis functions can be accomplished by projection analysis. Also note that these x-ray population coefficients are not the elements of a density matrix from a quantum chemical calculation as has been suggested.23 To compare the x-ray results, one can project the theoretical one-electron density function by least squares into the same basis functions that were used in the x-ray analysis. 

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