In this section local correlation methods that use pair natural orbitals (PNOs) are described. This program is entirely distinct from the older PAO-based methods that were described in the previous section. It is designed for parallel execution, and disk I/O is avoided as much as possible. This means that more memory is required than in other programs. However, the data are distributed over all computing cores, and the memory requirement per core is inversely linear in the number of cores used. Therefore, it is normally not recommended to use these programs on a single core. Depending on the molecular size, parallelization works well up to 100-200 cores using multiple nodes, provided a fast network (Infiniband or similar) is available.
Appropriate default values are set which normally yield results that are close to the canonical ones. In particular, sub-kJ/mol accuracy of relative energies is usually achieved with PNO-LMP2-F12 (relative to MP2-F12).
Currently the PNO program of MOLPRO can perform closed-shell PNO-LMP2 and PNO-LMP2-F12 calculations. We strongly recommend that the user reads the following references for the concepts and local approximations used in the PNO program.
H.-J. Werner, G. Knizia, C. Krause, and M. Schwilk, Scalable Electron Correlation Methods. I.: PNO-LMP2 with Linear Scaling in the Molecular Size and Near-Inverse-Linear Scaling in the Number of Processors, J. Chem. Theory Comput., 11, 484 (2015).
Q. Ma and H.-J. Werner, Scalable Electron Correlation Methods. 2. Parallel PNO-LMP2-F12 with Near Linear Scaling in the Molecular Size, J. Chem. Theory Comput.,
DOI: 10.1021/acs.jctc.5b00843 (2015).
M. Schwilk, D. Usvyat, and H.-J. Werner, Communication: Improved pair approximations in local coupled-cluster methods, J. Chem. Phys., 142, 121102 (2015).
The point group symmetry support of the PNO-LMP2 method is described in
C. Köppl and H.-J. Werner, On the use of Abelian point group symmetry in density-fitted local MP2 using various types of virtual orbitals, J. Chem. Phys., 142, 164108 (2015).
More references on the correlation methods, including some reviews suitable for an introduction, are listed in Sec. 32.
The PNO program is currently under active development. More features, including a PNO-LCCSD method, and performance improvements, will be available in future releases.