Abstract
Due to their improved accuracy, double-hybrid density functionals emerged as an important method for molecular electronic-structure calculations. The high computational costs of double-hybrid calculations in the condensed phase and the lack of efficient gradient implementations thereof inhibit a wide applicability for periodic systems. We present an implementation of forces and stress tensors for double-hybrid density functionals within the Gaussian and plane-waves electronic structure framework. The auxiliary density matrix method is used to reduce the overhead of the Hartree-Fock kernel providing an efficient and accurate methodology to tackle condensed phase systems. First applications to water systems of different densities and molecular crystals show the efficiency of the implementation and pave the way for advanced studies. Finally, we present large benchmark systems to discuss the performance of our implementation on modern large-scale computers.
Highlights
Because the calculation of the HF kernel still consumes a significant amount of computation time of the DH gradient calculation, a reduction of its costs is of general interest
We find that Auxiliary Density Matrix Method (ADMM) provides a significant reduction of the total computational time of DH gradient calculations with TZ primary basis set (PBS)
Besides the size of the ADMM basis, the most important parameter determining the performance of HF calculations is the Schwarz screening threshold
Summary
Most applications of electronic structure methods are currently based on Density Functional Theory (DFT).[1,2] DFT methods are widely available in standard quantum chemical software, are computationally efficient and a range of low scaling approaches was developed.[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] The different density functionals are often classified within a hierarchical scheme (Jacob’s ladder analogy) with respect to their explicit dependence on information of the electronic density.[20]. The total number of electron repulsion integrals of atom centered basis functions increases at most quartically with respect to system size. This scaling can be reduced by different techniques up to linear scaling.[75–82]. HF implementations for periodic systems need special care due to the singularity at the Gamma point and the slow decay of the Coulomb operator These problems are addressed by the use of short-ranged operators or by direct summation approaches.[91–97]. HF and hybrid functional calculations with augmented basis sets for weakly interacting systems are computationally demanding because of the large extent of the additional diffuse basis functions and the resulting larger number of significant integrals.[98–102].
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