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A *O(N*^{3}) scaling PNO-MP2 method using a hybrid OSV-PNO approach with an iterative direct generation of OSVs

Gunnar Schmitz^{1,a)}, Benjamin Helmich^{1,b)}, and Christof Hättig^{1,c)}

^{1}
*Lehrstuhl für Theoretische Chemie,
Ruhr-Universität Bochum,
D-44801 Bochum, Germany
*

*Mol. Phys.*

(Received 5th Febuary 2013; accepted 28th March 2013)

We present an implementation of pair natural orbital second-order Mølller-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, with an iterative block Davidson algorithm for solving
the equations for orbital-specific virtuals. We thereby avoid a complete diagonalization of amplitude matrices
and the explicit construction of the corresponding exchange integral matrices.
This reduces the cost-scaling for the generation of the orbital-specific virtuals and
of the pair natural orbitals to *O(N*^{3}) 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 (Gly)_{n} with n = 1, 2, 4, 8, 16, 32 in the aug-cc-pVTZ basis set reveal an early break even point between the *O(N*^{3})-scaling and the non-iterative *O(N*^{4})-scaling implementation that uses a full
diagonalization and with canonical RI-MP2.
We present applications to systems, which are of interest in the field of nano machines:
a C_{60} fullerene acceptor system with over 8000 basis functions and a foldamer
with nearly 8000 basis functions.

^{a)} Electronic mail: gunnar.schmitz@rub.de

^{b)} Electronic mail: benjamin.helmich@rub.de

^{c)} Electronic mail: christof.haettig@rub.de

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