Quantum Chemical Modeling of Atomic Systems

Quantum chemical modelling of atomic systems encompasses a suite of computational techniques that approximate the behaviour of electrons and nuclei under the laws of quantum mechanics. At its core, this discipline seeks to solve the Schrödinger or Dirac equations for many‐electron atoms, employing methods ranging from self-consistent field approaches to advanced correlation treatments. Central strategies include the Hartree–Fock method, which provides a mean-field description of electron–electron repulsion, and post-Hartree–Fock schemes such as configuration interaction, coupled cluster and many-body perturbation theory to capture dynamic and static correlations. Density functional theory offers an alternative by recasting the problem in terms of electron density, while relativistic corrections and effective core potentials become essential for heavy elements. The accuracy of any calculation depends critically on the choice of basis set—collections of functions that describe atomic orbitals—and their associated exponents and contraction schemes. Recent progress has focused on reducing computational cost without sacrificing precision, enabling the modelling of complex atoms, ions and clusters. These models provide insight into fundamental properties such as ionisation potentials, excitation energies, magnetic shielding and chemical shifts, and underpin applications in materials design, spectroscopy, catalysis and quantum information science. By bridging detailed electronic structure with observable physical quantities, quantum chemical modelling of atomic systems continues to drive innovation across the physical and chemical sciences.

Research from Nature Portfolio

Recent studies have elucidated the interplay between electronic structure and solvation dynamics by simulating the 129Xe chemical shift in aqueous environments. Molecular dynamics trajectories coupled with quantum‐chemical calculations reproduced the non-monotonic temperature dependence of the shift and demonstrated how local water density and Xe–H2O collision energetics determine the chemical shift extremum. In parallel, advanced many-body computations on hexaboride clusters have revealed strong p-electron correlations within B6 octahedra. By computing excitation energies that align with resonant inelastic X-ray scattering data, these investigations have characterised hexaborides as atypical p-electron correlated systems, motivating further many-body studies across the alkaline and rare-earth series.

Quantum Chemical Modeling of Atomic Systems publication trend

The graph below shows the total number of articles in quantum chemical modeling of atomic systems across all publications each year (not limited to Nature Index journals).

Technical terms

Hartree–Fock method: A self-consistent field approach that approximates the many-electron wavefunction as a single determinant of one-electron orbitals.

Electron correlation: The interaction between electrons beyond the average potential captured in mean-field theories, requiring post-Hartree–Fock or density-functional treatments.

Basis set: A predefined collection of mathematical functions used to expand atomic orbitals in quantum-chemical calculations.

Orbital exponent: A parameter that governs the radial decay rate of basis functions, critical for the flexibility and accuracy of expansions.

Fock expansion: A series representation of the two-electron wavefunction near coalescence points, expressed in angular and logarithmic terms.

Chemical shift: The variation in nuclear magnetic resonance frequency caused by the electronic environment surrounding a nucleus.

References

1. Chemical shift extremum of 129Xe(aq) reveals details of hydrophobic solvation. Scientific Reports (2018).
2. Quantum chemical insights into hexaboride electronic structures: correlations within the boron p-orbital subsystem. Communications Physics (2022).
3. Accurate Exponential Representations for the Ground State Wave Functions of the Collinear Two-Electron Atomic Systems. Atoms (2021).
4. Fock Expansion for Two-Electron Atoms: High-Order Angular Coefficients. Atoms (2022).
5. Moseley Law for Atomic Orbital Exponents. Russian Journal of Physical Chemistry A (2024).