Real-time time-dependent self-consistent field methods with dynamic magnetic fields

The first finite basis set implementation of the real-time time-dependent self-consistent field method in a dynamic (time-dependent) magnetic field using London atomic orbitals (LAOs) is presented. The accuracy of the finite basis approach using LAOs is benchmarked against numerical results from the literature for the hydrogen atom and H2 in the presence of rapidly oscillating magnetic fields. This comparison is used to inform the choice of appropriate basis sets for studies under such conditions. Remarkably, relatively modest compact LAO basis sets are sufficient to obtain accurate results. Analysis of electron dynamics in the hydrogen atom shows that LAO calculations correctly capture the time evolution of orbital occupations. The Fourier transformation of the autocorrelation function yields a power spectrum exhibiting harmonics associated with coherent emission, which closely matches the literature and further confirms the accuracy of this approach. The dynamical response of the electron density in H2 for a magnetic field parallel to the internuclear axis shows similar behavior to benchmark studies. The flexibility of this implementation is then demonstrated by considering how the dynamical response changes as a function of the orientation of the molecule relative to the applied field. At non-parallel orientations, the symmetry of the system is lowered and numerical benchmark data, which exploit cylindrical symmetry, are no-longer readily available. The present study demonstrates the utility of LAO-based calculations for extreme dynamic magnetic fields, providing a stress-test on the choice of basis. Future applications of this approach for less extreme dynamic magnetic fields are briefly discussed

Modeling Ultrafast Electron Dynamics in Strong Magnetic Fields Using Real-Time Time-Dependent Electronic Structure Methods

An implementation of real-time time-dependent Hartree-Fock (RT-TDHF) and current-density-functional theory (RT-TDCDFT) for molecules in strong uniform magnetic fields is presented. In contrast to earlier implementations, the present work enables the use of the RT-TDCDFT formalism, which explicitly includes field dependent terms in the exchange-correlation functional. A range of current dependent exchange-correlation functionals based on the TPSS functional are considered, including a range-separated variant, which is particularly suitable for application to excited state calculations. The performance of a wide range of propagator algorithms for real-time methods is investigated in this context. A recently proposed molecular orbital pair decomposition analysis allows for assignment of electronic transitions, providing detailed information about which molecular orbitals are involved in each excitation. 1 The application of these methods is demonstrated for the electronic absorption spectra of N 2 and H 2 O both in the absence and in the presence of a magnetic field. The dependence of electronic spectra on the magnetic field strength and its orientation relative to the molecule is studied. The complex evolution of the absorption spectra with magnetic field is rationalised using the molecular orbital pair decomposition analysis, which provides crucial insight in strong fields where the spectra are radically different from their zero-field counterparts

Understanding ground and excited-state molecular structure in strong magnetic fields using the maximum overlap method

The maximum overlap method (MOM) provides a simple but powerful approach for performing calculations on excited states by targeting solutions with non-Aufbau occupations from a reference set of molecular orbitals. In this work, the MOM is used to access excited states of (Formula presented.) and (Formula presented.) in strong magnetic fields. The lowest (Formula presented.), (Formula presented.) and (Formula presented.) states of (Formula presented.) in the absence of a field are compared with the corresponding states in strong magnetic fields. The changes in molecular structure in the presence of the field are examined by performing excited state geometry optimisations using the MOM. The (Formula presented.) state is significantly stabilised by the field, becoming the ground state in strong fields with a preferred orientation perpendicular to the applied field. Its potential energy surface evolves from being repulsive to bound, with an equilateral equilibrium geometry. In contrast, the (Formula presented.) state is destabilised and its structure distorts to an isosceles form with the longest H−H bond parallel to the applied field. Comparisons are made with the (Formula presented.) state of H3, which also becomes bound with an equilateral geometry at high fields. The structures of the high-spin ground states are rationalised by orbital correlation diagrams constructed using constrained geometry optimisations

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, nor are they able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym² that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly, and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym² is able to address all of these shortcomings. To illustrate these capabilities of QSym², four sets of case studies are examined in detail in this article: (i) high-symmetry C_{84}H_{64}, C_{60}, and B_9^– to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)_6^{3–} to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H_3^+ to demonstrate the analysis of density symmetries

Symmetry and reactivity of π-systems in electric and magnetic fields: a perspective from conceptual DFT

The extension of conceptual density-functional theory (conceptual DFT) to include external electromagnetic fields in chemical systems is utilised to investigate the effects of strong magnetic fields on the electronic charge distribution and its consequences on the reactivity of π-systems. Formaldehyde, H2CO, is considered as a prototypical example and current-density-functional theory (current-DFT) calculations are used to evaluate the electric dipole moment together with two principal local conceptual DFT descriptors, the electron density and the Fukui functions, which provide insight into how H2CO behaves chemically in a magnetic field. In particular, the symmetry properties of these quantities are analysed on the basis of group, representation, and corepresentation theories using a recently developed automatic program for symbolic symmetry analysis, QSym2. This allows us to leverage the simple symmetry constraints on the macroscopic electric dipole moment components to make profound predictions on the more nuanced symmetry transformation properties of the microscopic frontier molecular orbitals (MOs), electron densities, and Fukui functions. This is especially useful for complex-valued MOs in magnetic fields whose detailed symmetry analyses lead us to define the new concepts of modular and phasal symmetry breaking. Through these concepts, the deep connection between the vanishing constraints on the electric dipole moment components and the symmetry of electron densities and Fukui functions can be formalised, and the inability of the magnetic field in all three principal orientations considered to induce asymmetry with respect to the molecular plane of H2CO can be understood from a molecular perspective. Furthermore, the detailed forms of the Fukui functions reveal a remarkable reversal in the direction of the dipole moment along the C = O bond in the presence of a parallel or perpendicular magnetic field, the origin of which can be attributed to the mixing between the frontier MOs due to their subduced symmetries in magnetic fields. The findings in this work are also discussed in the wider context of a long-standing debate on the possibility to create enantioselectivity by external fields

An Embedded Fragment Method for Molecules in Strong Magnetic Fields

International audienceAn extension of the embedded fragment method for calculations on molecular clusters is presented, which includes strong external magnetic fields. The approach is flexible, allowing for calculations at the Hartree-Fock, current-density-functional theory, Møller-Plesset perturbation theory, and coupled-cluster levels using London atomic orbitals. For systems consisting of discrete molecular subunits, calculations using London atomic orbitals can be performed in a computationally tractable manner for systems beyond the reach of conventional calculations, even those accelerated by resolution-of-the-identity or Cholesky decomposition methods. To assess the applicability of the approach, applications to water clusters are presented, showing how strong magnetic fields enhance binding within the clusters. However, our calculations suggest that, contrary to previous suggestions in the literature, this enhanced binding may not be directly attributable to strengthening of hydrogen bonding. Instead, these results suggest that this arises for larger field strengths as a response of the system to the presence of the external field, which induces a charge density build up between the monomer units. The approach is embarrassingly parallel and its computational tractability is demonstrated for clusters of up to 103 water molecules in triple-ζ basis sets, which would correspond to conventional calculations with more than 12 000 basis functions

An Embedded Fragment Method for Molecules in Strong Magnetic Fields

An extension of the embedded fragment method for calculations on molecular clusters is presented, which includes strong external magnetic fields. The approach is flexible, allowing for calculations at the Hartree–Fock, current-density-functional theory, Møller–Plesset perturbation theory, and coupled-cluster levels using London atomic orbitals. For systems consisting of discrete molecular subunits, calculations using London atomic orbitals can be performed in a computationally tractable manner for systems beyond the reach of conventional calculations, even those accelerated by resolution-of-the-identity or Cholesky decomposition methods. To assess the applicability of the approach, applications to water clusters are presented, showing how strong magnetic fields enhance binding within the clusters. However, our calculations suggest that, contrary to previous suggestions in the literature, this enhanced binding may not be directly attributable to strengthening of hydrogen bonding. Instead, these results suggest that this arises for larger field strengths as a response of the system to the presence of the external field, which induces a charge density build up between the monomer units. The approach is embarrassingly parallel and its computational tractability is demonstrated for clusters of up to 103 water molecules in triple-ζ basis sets, which would correspond to conventional calculations with more than 12 000 basis functions