Assessing MP2 frozen natural orbitals for relativistic electronic structure

The O(N⁶) high computational cost is a bottleneck preventing performing Coupled-Cluster (CC) on large systems, particularly when employing 4-component based relativistic Hamiltonians, for which in practice one often uses uncontracted basis set generating large virtual molecular orbital (VMO) spaces.

The canonical Hartree-Fock (HF) orbitals are not the most compact representation for the post-HF method. Alternatively, using natural orbitals is an efficient way to reduce the orbital space while retaining accuracy. We, therefore, implemented the MP2 frozen natural orbital (FNO) method [1] in the Exacorr code [2], with the particularity that our implementation can generate both complex and quaternion FNOs, and also express these on AO basis. It also allows us to obtain CCSD natural orbitals on AO basis, which can be subsequently used in the analysis.

We have investigated the orbital truncation errors for both correlation energy (at CCSD(T) level) and molecular properties (at CCSD level) such as the electric field gradients at the nuclei (EFGs ), dipole and quadrupole moments for hydrogen halides HX (X=F, Cl, Br, I, At, Ts), and parity violation energy shift for the H₂X₂ systems (X= O, S, Se, Te, Po). We find that using FNOs accelerates the convergence of the correlation energy in a roughly uniform manner across the periodic table and that, with VMO spaces truncated to around half of the complete ones, we obtain reliable estimates for both energies and molecular properties in the complete VMO spaces.

 

[1] T. L. Barr, E. R. Davidson, Phys. Rev. A 1970, 1, 644; A. G. Taube, R. J. Bartlett, J. Chem. Phys. 2008, 128, 164101

[2] J. V. Pototschnig, A. Papadopoulos, D. I. Lyakh, M. Repisky, L. Halbert, A. S. P. Gomes, H- J Aa. Jensen, L. Visscher, J. Chem. Theory. Comput. 2021 (in press), arXiv:2013.08473