Exploitation of complex Abelian point groups in quantum-chemical calculations

TL;DR

The paper addresses the limitation of symmetry exploitation to real Abelian point groups in quantum-chemical calculations by developing and implementing a framework for complex Abelian PGs, which frequently arise in finite magnetic fields. It establishes a theoretical basis via double-coset decomposition, SAOs, and second-quantization selection rules, and encodes these into HF and post-HF workflows with a block-tensor approach. The authors implement complex PG handling in cfour and qcumbre, validating the approach with four small hydrocarbons under magnetic fields and demonstrating substantial speedups, particularly in SCF and CCSD steps, though integral evaluation shows system-dependent gains. The work demonstrates that complex Abelian PGs can significantly reduce computational cost in magnetic-field simulations, enabling efficient, symmetry-aware quantum chemistry and richer state-targeting capabilities. Practical impact includes enabling more scalable simulations in magnetic fields and related contexts where complex wavefunctions are essential.

Abstract

Quantum-chemical calculations often make use of point-group theory to exploit molecular symmetry, resulting in a reduction of the computational cost and in insights into the electronic structure. This exploitation is often limited to subgroups of $D_{2h}$ which are Abelian with real characters. Here, we extend the symmetry exploitation to Abelian point groups with complex characters. Such point groups are often encountered in calculations that involve finite magnetic fields, though their occurrence is not limited to these cases alone. We present the evaluation of integrals over symmetry-adapted orbitals using the double-coset decomposition, as well as the use of these symmetries in the contractions needed within post Hartree Fock calculations in the context of block tensors. Efficiency gains are discussed for four simple hydrocarbons that exhibit a complex Abelian point group in the presence of a magnetic field.