Faculté des sciences

Energy gradients with respect to atomic positions and cell parameters for the Kohn-Sham density-functional theory at the Γ point

Weber, Valéry ; Tymczak, Christopher J. ; Callacombe, Matt

In: The Journal of Chemical Physics, 2006, vol. 124, p. 224107

The application of theoretical methods based on density-functional theory is known to provide atomic and cell parameters in very good agreement with experimental values. Recently, construction of the exact Hartree-Fock exchange gradients with respect to atomic positions and cell parameters within the Γ-point approximation has been introduced [V. Weber et al., J. Chem. Phys. 124, 214105... Plus

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    Summary
    The application of theoretical methods based on density-functional theory is known to provide atomic and cell parameters in very good agreement with experimental values. Recently, construction of the exact Hartree-Fock exchange gradients with respect to atomic positions and cell parameters within the Γ-point approximation has been introduced [V. Weber et al., J. Chem. Phys. 124, 214105 (2006)]. In this article, the formalism is extended to the evaluation of analytical Γ-point density-functional atomic and cell gradients. The infinite Coulomb summation is solved with an effective periodic summation of multipole tensors [M. Challacombe et al., J. Chem. Phys. 107, 9708 (1997)]. While the evaluation of Coulomb and exchange-correlation gradients with respect to atomic positions are similar to those in the gas phase limit, the gradients with respect to cell parameters needs to be treated with some care. The derivative of the periodic multipole interaction tensor needs to be carefully handled in both direct and reciprocal space and the exchange-correlation energy derivative leads to a surface term that has its origin in derivatives of the integration limits that depend on the cell. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm [K. Németh and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] to optimize one-dimensional and three-dimensional periodic systems at the density-functional theory and hybrid Hartree-Fock/density-functional theory levels. We also report the full relaxation of forsterite supercells at the B3LYP level of theory.