A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs^†

Abstract

We present an implementation of pair natural orbital second-order Møller–Plesset perturbation theory with computational costs that scale only cubically with the system size. The low cost-scaling is achieved by combining a hybrid approach, where the pair natural orbitals are build from orbital-specific virtuals OSVs, with an iterative block Davidson algorithm for solving the equations for OSVs. We thereby avoid a complete diagonalisation of amplitude matrices and the explicit construction of the corresponding exchange integral matrices. This reduces the cost-scaling for the generation of the OSVs and of the pair natural orbitals to without a priori assumptions about locality. The costs can be further reduced by combining the approach with a local resolution-of-the-identity approximation for the exchange integrals. The errors introduced by these approximations are negligible and do not affect the final accuracy of the correlation energy. Test calculations on a set of organic and inorganic molecules demonstrate that the additional errors are at least one order of magnitude smaller than the truncation error for the pair natural orbital space and that the accuracies for all steps can be controlled by a single threshold parameter. Calculations on glycine chains with n = 1, 2, 4, 8, 16, 32 in the aug-cc-pVTZ basis set reveal an early break even point between the -scaling and the non-iterative -scaling implementation that uses a full diagonalisation and with canonical RI-MP2. We present applications to systems, which are of interest in the field of nano machines: a fullerene acceptor system with over 8000 basis functions and a foldamer with nearly 8000 basis functions.

Keywords:

• local MP2
• hybrid OSV–PNO approach
• iterative OSV generation
• local RI

Acknowledgements

We thank R. Schmid for providing the structure of the fullerene acceptor system and M. Böckmann for the structures of the foldamer. Financial support by the Deutsche Forschungsgemeinschaft through grant no. HA/2588/7 and the TURBOMOLE GmbH is gratefully acknowledged. C.H. thanks D.P. Tew for helpful discussions about the local RI approximations.

Dedicated to Prof. Dr. Werner Kutzelnigg on the occasion of his 80th birthday

Notes

The evaluation of the 3-index integrals was parallelised over 10 cores. Therefore we extrapolated for better comparison the time for this step on a single core.