Electronic structure computations rotational parameters

Abstract. Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TIE and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of the core properties (PNC effect, hyperfine structure etc., which are described by the operators heavily concentrated in atomic cores or on nuclei) usually require accurate accounting for both relativistic and correlation effects in heavy-atom systems. In this paper, some basic aspects of the experimental search for PNC effects in heavy-atom molecules and the computational methods used in their electronic structure calculations are discussed. The latter include the generalized relativistic effective core potential (GRECP) approach and the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component GRECP calculation of a molecule. Their efficiency is illustrated with calculations of parameters of the effective P,T-odd spin-rotational Hamiltonians in the molecules PbF, HgF, YbF, BaF, TIF, and PbO. 

Since the relevant dimensional parameter is 1/D, the pseudoclas-sical large-Z) limit is closer to D = 3 than is the hyperquantum low-D limit. As in Fig. 3, for D finite but very large, equivalent to a very heavy electronic mass, the electrons are confined to harmonic oscillations about the fixed positions attained in the D oo limit. We call these motions Langmuir vibrations, to acknowledge his prescient suggestion 70 years ago [89] that the electrons could...rotate, revolve, or oscillate about definite positions in the atom. In a dimensional perturbation expansion the first-order term, proportional to 1/D, corresponds to these harmonic vibrations, whereas higher-order terms correspond to anharmonic contributions. Standard methods for analysis of molecular vibrations [90] thus become directly applicable to electronic structure. These methods are semiclassical in form and far simpler, both conceptually and computationally, than the conventional orbital formulation. 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

It is not always necessary to detail the electronic behavior of materials an accurate understanding of the atomic interactions is often sufficient to describe the phenomenon of interest with reasonable accuracy. In contrast to ab initio methods, molecular mechanics is used to compute molecular properties, which do not depend on electronic effects. These include geometry, rotational barriers, vibrational spectra, heats of formation, and the relative stability of conformers. As the calculations are fast and efficient, molecular mechanics can be used to examine systems containing thousands of atoms. However, unlike ab initio methods, molecular mechanics relies on experimentally derived parameters so that calculations on new molecular structures may be misleading. 

The approach recentiy proposed by Pohmeno and Barone to simulate CW-ESR spectra [93] is composed of several steps. First, state-of-the-art QM calculations provide the structural and local magnetic properties of the investigated molecular system. Second, dissipative parameters such as rotational diffusion tensors are calculated by using stochastic Liouville equation. Third, in the case of multiple-label systems, electron exchange and dipolar interactions are computed. 

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