arXiv subjects

Hugo Åström

Publications and source records attributed to Hugo Åström.

5 recordsLinked to original sources

arXiv2026

Real Quantum Chemistry With Complex Orbitals

We follow up our study of basis set truncation errors for atoms in magnetic fields [Åström 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.

physics.comp-ph↗

arXiv2025

Atomic Confinement Potentials and the Generation of Numerical Atomic Orbitals

We aim to develop novel reusable open source infrastructure [Lehtola, J. Chem. Phys. 159, 180901 (2023)] for numerical atomic orbitals (NAOs). Soft confinement potentials are typically used to force the NAO radial basis functions $ψ_{nl}(r)$ to vanish smoothly in increasing $r$ and to generate localized unoccupied states; we review such potentials and other commonly-used techniques in NAO generation as a follow-up to our recent study on atoms in hard-wall confinement [Åström and Lehtola, J. Phys. Chem. A 129, 2791 (2025)]. In addition to NAO generation, confinement potentials are also employed to simulate environmental effects in other research areas, such as studies of (i) atoms in solids, (ii) quantum dots, and (iii) high-pressure chemistry. As in our earlier work, we perform fully numerical density functional calculations with spherically averaged densities, as is usual in NAO studies. Our calculations employ the the finite element method (FEM) implemented in the HelFEM program, yielding variational energies and enabling the use of various boundary conditions. We consider four families of potentials to study the Mg and Ca atoms, which are textbook examples of extended electronic structures. We show that the resulting ground-state orbitals are surprisingly insensitive to the employed form of the confinement potential, and that the orbitals decay quickly under confinement. We study increasingly steep potentials and examine how they approach the hard-wall limit. Finally, we assess NAO basis set truncation errors for types of singular potentials that are now broadly used in the NAO literature.

physics.comp-ph↗

arXiv2024

Systematic study of confinement induced effects on atomic electronic structure

We point out that although a litany of studies have been published on atoms in hard-wall confinement, they have not been systematic or have not used robust numerical methods. We report a methodical study of atoms in hard-wall confinement employing a robust finite element method (FEM) in HelFEM that guarantees variational results and allows easily finding the numerically exact solution. Our fully numerical calculations are non-relativistic and are carried out at three levels of density functional theory with spherically averaged densities: the PW92, PBE, and r$^2$SCAN functionals. The three are in excellent agreement, confirming the physicality of our results. We systematically examine low lying configurations of the H-Xe atoms and their monocations, and investigate how the configurations - especially the ground state - behave as a function of the position of the hard-wall boundary. We consider both spin-polarized as well as spin-restricted densities, and demonstrate that spin-polarization effects are significant in open shell configurations, even though some previous studies have only considered the spin-restricted model. We demonstrate the importance of considering ground state changes for confined atoms by computing the ionization radii for the H-Xe atoms and observe significant differences to earlier studies. Confirming previous observations, we identify electron shifts on the outermost shells for a majority of the elements: valence $s$ electrons are highly unfavored under strong confinement, and the high-lying $3d$ and $4f$ orbitals become occupied in atoms of periods 2-3 and 3-4, respectively. We also comment on deficiencies of a commonly used density based estimate for the van der Waals (vdW) radius of atoms, and propose a better behaved variant in terms of the number of electrons outside the vdW radius that we expect will prove useful in future studies.

physics.atom-ph↗

arXiv2023

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA) as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles and perturbative triples [CCSD(T)]. Our study was later extended to local-hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density $(τ)$ in mGGA calculations by comparing the Maximoff--Scuseria formulation of $τ$ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH and scLH functionals outperform all the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors, while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character such as the ozone molecule, which is traditionally excluded from the statistical error evaluation due to its large errors with common density functionals.

physics.chem-ph↗

arXiv2023

Insight on Gaussian basis set truncation errors in weak to intermediate magnetic fields with an approximate Hamiltonian

Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structure of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with Gaussian basis sets designed for zero field, leading to large basis set truncation errors [Lehtola et al, Mol. Phys. 2020, 118, e1597989]. In this work, we aim to identify the failures of the Gaussian basis sets in atomic calculations to guide the design of new basis sets for strong magnetic fields. We achieve this by performing fully numerical electronic structure calculations at the complete basis set (CBS) limit for the ground state and low lying excited states of the atoms $1 \le Z \le 18$ in weak to intermediate magnetic fields. We also carry out finite-field calculations for a variety of Gaussian basis sets, introducing a real-orbital approximation for the magnetic-field Hamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has been used in many works in the literature. A study of the differences in total energies of the fully numerical CBS limit calculations and the approximate Gaussian basis calculations is carried out to provide insight into basis set truncation errors. Examining a variety of states over the range of magnetic field strengths from $B = 0$ to $B = 0.6 B_0$, we observe significant differences for the aug-cc-pVTZ basis set, while much smaller errors are afforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys. 2020, 152, 134108]. This suggests that there is considerable room to improve Gaussian basis sets for calculations at finite magnetic fields.

physics.chem-ph↗