Real Quantum Chemistry With Complex Orbitals

Abstract

We follow up our study of basis set truncation errors for atoms in magnetic fields [{\AA}str\"om and Lehtola, J. Phys. Chem. A, 2023, 127, 10872]. Our previous study employed an approximate real-valued model. In this work, we implement a scheme to allow the use of complex basis functions and the true, complex Hamiltonian with linear molecules in a parallel magnetic field within the usual real-basis machinery of quantum chemistry. Our method performs additional unitary transformations before and after a conventional Fock build, thus allowing the reuse of existing software methods and algorithms. We apply our approach to calculations on low-lying configurations of the atoms $Z \leq 18$ in static magnetic fields up to 0.6 $B_0$. The calculations employ the uncontracted aug-cc-pVTZ and the benchmarking quality AHGBSP3-9 Gaussian-type orbital basis sets. We compare total energies obtained with real and complex orbitals using these basis sets to fully numerical ones at the complete basis set limit. We see that the states of the real-valued Hamiltonian are superpositions of the true eigenstates that are correctly captured by the complex calculations. Our results show that the complex basis machinery is necessary for targeting states with the correct symmetry for the studied range of magnetic field strengths. The novel tool is key for future work where we aim to optimize basis sets for finite-field calculations.