Total energy and derivatives

The evaluation to the desired numerical accuracy of the density functional total energy has been a major obstacle to such calculations for many years. Part of the difficulty can be related to truncation errors in the orbital representation, or equivalently to basis set limitations, in variational calculations. Another part of the difficulty can be related to inaccuracies in the solution of Poisson s equation. The problem of maximizing the computational accuracy of the Coulomb self-interaction term in the context of least-squares-fitted auxiliary densities has been addressed in [39]. A third part of the difficulty may arise from the numerical integration, which is unavoidable in calculating the exchange and correlation contributions to the total energy in the density functional framework. 

Et equals the self-consistent KS total energy Et. Here t (r) are the self-consistent KS orbitals for the fixed basis set. For other input densities Et differs by 0((p — p)2) 

The energy derivatives have been implemented in DMol in such a way that the calculation of all derivatives scales, to leading order, with the cube of the molecule size, as 

Based on the analysis of correlation energy in the He atom by Colie and Salvetti [68], Lee, Yang and Parr derived a density functional for correlation. Since the He atom, as a two electron system, only has a/3 correlation in its ground state, also the functional derived from it lacks aa correlation. It may seem surprising then that this functioned is applicable to systems with more than two electrons, in fact it is among the most successful correlation functionals. 

The revised generalized gradient approximation by Perdew and Wang [77,78] for both the exchange (PW91) and the correlation functional satisfies various sum rules, scaling 

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Once the self-consistent electron density is obtained for the molecule or cluster, it may be used to calculate the total energy and derived properties, such as dissociation energies,... 

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