Cauchy violation and charge transfer potentials

Sergey Sukhomlinov and Martin H. Müser, Forschungszentrum Jülich, Jülich, Germany

In a crystal where particles interact through central pair forces, the elastic tensor C_αβγξ possesses complete symmetry in its four indices, thus providing relations between components. These equalities are known as Cauchy relations. For a crystal of cubic symmetry only one equation remains C₁₂ = C₄₄

In the presence of many-body interactions Cauchy relation no longer holds, and violation C₄₄ - C₁₂ from it should be considered instead. As a consequence, Cauchy violation could be considered as an estimate of how well many-body effects are described by a potential.

Chemical potential equalization (CPE) models [1, 2, 3] provide a promising way ofconstructing force fields with environment-dependent parameters. Assuming the specific CPE model is appropriate and its parameters are reliable, the force field can then be used to study a system’s behaviour at the microscopic level. In such polarizable force fields, the atomic charges serve as a linkage between the electronic distribution in the system and itsinstantaneous structure at the atomic level. Present contribution addresses the question of how violation from Cauchy relation and its slope in the region of small temperatures and ambient pressures is reproduced by the CPE models in ionic compounds.

As a model system we considered rocksalt, which in many cases can be solved analytically. We analyzed how two different CPE models reproduce many-body effects in NaCl structure by considering Cauchy violation. Charge equilibration models that were used in this study include electronegativity equalization model (EEM) [2] and split-charge equilibration (SQE) [3] model. It was found that for rocksalt structure compounds the functional form of Cauchy violation and of its pressure derivative is the same for all CPE models considered given the fact that bond hardness κ_s, which is a parameter of SQE model, does not depend on the environment. Both Cauchy violation and its pressure derivative are predicted to have strictly positive values, which agrees with the results of density functional theory computations and available experimental data. Nevertheless, it should be noted that the value of Cauchy violation was found to depend crucially on screening effects.

[1] D. M. York, W. J. Yang J. Chem. Phys. 104, 159-172 (1996).
[2] W. Mortier, S. Ghosh, S. Shankar J. Am. Chem. Soc. 108, 4315-4320 (1986).
[3] R. A. Nistor, J. G. Polihronov, M. H. Müser, N. J. Mosey, J. Chem. Phys. 125, 094108 (2006).