One of the most severe limitations of highly accurate wave function based methods (e.g. coupled cluster methods) is the steep scaling of computational resources with the system size. For example, the computational time of the coupled cluster model CCSD(T) , often referred to as „gold-standard“ for single reference systems, scales with N⁷, where N is a measure for the system size. On the other hand, local correlation methods aim at a reduction of this unphysical scaling of conventional wave function based methods by exploiting that electron correlation is a local phenomenon and its importance decays rapidly with the interelectronic distance.

In our group, we use the pair natural orbital (PNO) approximation to exploit the locality of electron correlation. The basis of this approximation is the truncation of the virtual orbital space by analyzing approximate model wave functions. This analysis then yields the most important orbitals which have to be included in the correlation treatment in order to obtain a certain accuracy.

The focus of our group within this field is to extend the applicability of the PNO approximation towards the calculation of excitation energies, molecular (response) properties and and to combine it with the enhanced basis set convergence of explicitly correlated F12 methods. For the development of the PNO-based methods, in particular the explicitly correlated F12 methods, we work closely together with David Tew from the MPI for Solid State Research in Stuttgar.

Publications related to our developments regarding the use and construction of excited state PNOs for excitations energies can be found here:

• Local pair natural orbitals for excited states

• A pair natural orbital implementation of the coupled cluster model CC2 for excitation energies

• A pair natural orbital based implementation of ADC(2)-x

• A pair natural orbital based implementation of CCSD excitation energies

Publications related to the incorporation of the PNO approximation in F12 theory can be found here:

• Local explicitly correlated second-order Møller-Plesset perturbation theory with pair natural orbitals

• Pair natural orbitals in explicitly-correlated second order Møller-Plesset theory

• Local explicitly correlated second- and third-order Møller-Plesset perturbation theory with pair natural orbitals

• Explicitly correlated PNO-MP2 and PNO-CCSD and its application to the S66 set and large molecular systems

• Perturbative triples correction for local pair natural orbital based explicitly correlated CCSD(F12*) using Laplace transformation techniques

And other related publications can be found here:

• A O(N³) scaling PNO-MP2 method using a hybrid OSV-PNO approach with an iterative direct generation of OSVs

• The PNO-MP2 gradient and its application to molecular geometry optimizations