Potential parameters atom/molecule

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. 

Fig. 3. Molecules used to fit potential parameters for Nb5+-02 interactions. Atoms are as in Figure 1, except that the small green atom is Nb5+. DFT calculations are compared with model predictions. Model predictions are given in parenthesis in blue text. Bond lengths are given in angstroms, and reaction energies are given in kcal/mol.

Bandyopadhyay and Yashonath (31), in an extension of their work on MD studies of noble gas diffusion, presented MD results for methane diffusion in NaY and NaCaA zeolites. The zeolite models were the same as those used in the noble gas simulations (13, 15, 17, 18, 20, 28, 29) and the zeolite lattice was held rigid. The methane molecule was approximated as a single interaction center and the guest-host potential parameters were calculated from data of Bezus et al. (49) (for the dispersive term) and by setting the force on a pair of atoms equal to zero at the sum of their van der Waals radii (for the repulsive term). Simulations were run for 600 ps with a time step of 10 fs. 

There are two parameters in the atomic coulomb functions, the effective nuclear charge and the quantum defect. The values of these were taken by Johnson and Rice from available spectral data. The effective atomic charge was adjusted to give the correct ionization potential of the molecule, 9.25 eV, requiring thereby z = 0.8243. The quantum defects of carbon were taken from the appropriate atomic series and were 1.04 for the 5-state and 0.73 for the p-states. It is interesting to compare the calculated molecular quantum defects (i.e., those corresponding to the Johnson-Rice LCAO function) with those which can be obtained from the various benzene Rydberg series.218 The asymptotic form of the elu orbital constructed from s atomic functions is... 

In the development of the set of intermolecular potentials for the nitramine crystals Sorescu, Rice, and Thompson [112-115] have considered as the starting point the general principles of atom-atom potentials, proven to be successful in modeling a large number of organic crystals [120,123]. Particularly, it was assumed that intermolecular interactions can be separated into dispersive-repulsive interactions of van der Waals and electrostatic interactions. An additional simplification has been made by assuming that the intermolecular interactions depend only on the interatomic distances and that the same type of van der Waals potential parameters can be used for the same type of atoms, independent of their valence state. The non-electric interactions between molecules have been represented by Buckingham exp-6 functions,... 

Other flexible molecular models of nitromethane were developed by Politzer et al. [131,132]. In these, parameters for classical force fields that describe intramolecular and intermolecular motion are adjusted at intervals during a condensed phase molecular dynamics simulation until experimental properties are reproduced. In their first study, these authors used quantum-mechanically calculated force constants for an isolated nitromethane molecule for the intramolecular interaction terms. Coulombic interactions were treated using partial charges centered on the nuclei of the atoms, and determined from fitting to the quantum mechanical electrostatic potential surrounding the molecule. After an equilibration trajectory in which the final temperature had been scaled to the desired value (300 K), a cluster of nine molecules was selected for a density function calculation from which... 

For the interaction of large molecules the angular expansions of the potential parameters, Eqs. (1-190) and (1-191), may be slowly convergent, and the calculation of the potential may become prohibitively time consuming. Therefore, in many applications the so-called atom-atom potentials are used. The functional form of an atom-atom potential partly follows from the distributed multipole analysis297,... 

The last term in the formula (1-196) describes electrostatic and Van der Waals interactions between atoms. In the Amber force field the Van der Waals interactions are approximated by the Lennard-Jones potential with appropriate Atj and force field parameters parametrized for monoatomic systems, i.e. i = j. Mixing rules are applied to obtain parameters for pairs of different atom types. Cornell et al.300 determined the parameters of various Lenard-Jones potentials by extensive Monte Carlo simulations for a number of simple liquids containing all necessary atom types in order to reproduce densities and enthalpies of vaporization of these liquids. Finally, the energy of electrostatic interactions between non-bonded atoms is calculated using a simple classical Coulomb potential with the partial atomic charges qt and q, obtained, e.g. by fitting them to reproduce the electrostatic potential around the molecule. 

Berend and Benson s classical treatment of V-V transfer [81] employs a two-dimensional collision model of a pair of diatomics with identical Morse interaction potentials between each pair of atoms. The Morse range parameter a was determined from experimental data for the N2-N2 T-V process. In-all, six functions are employed, one between each pair of atoms (Figure 3.5). Molecule CD, oriented at an angle / relative to its velocity vector, collides with molecule AB, with impact parameter b. Molecule AB is taken to be oriented parallel to the velocity vector of CD. The instantaneous angle between the molecular axis of AB and the line joining the centers of mass is denoted t). Cross sections for the reactions... 

The size-and-shape factor is of special importance with respect to electron confinement in atoms, molecules, crystals and interfaces. This confinement, empirically characterised by parameters such as electronegativity is the decisive fundamental factor that decides chemical reactivity. The demonstration that atomic electronegativity is equivalent to the chemical quantum potential of the valence state [108] holds the key to molecule formation by electron pairing and space-like delocalization. It opens a new angle on the nature of chemical binding, molecular structure, chemical equilibrium and surfaces. 

The energetic inhomogeneity of the surface along the x and y directions is not taken into account, but this is not expected to affect the results significantly at 308 and 333 K [39]. The cross interaction potential parameters between different sites were calculated according to the Lorentz-Berthelot rules Oap = aa + and eafi= ( The potential energy t/ due to the walls inside the slit pore model for each atom of the CO2 molecule is given by the expression C/ = + Uw(H-r where H is the distance between the carbon centers across... 

The most widely used model to date is the isotropic site-site model, in which the molecules interact at fixed sites on each molecule. The site-site interactions depend only on the distance rap between site a on molecule 1 and site P on molecule 2, and not on the orientations of the two molecules [52]. It is often assumed that such site interactions are transferable, i.e. the potential parameters are the same for different molecules having the same groups of atoms for which the site represents. An example of such a pair potential is... 

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