Quantum Mechanical Calculations of Atomic Systems

Quantum mechanical calculations of atomic systems form the foundation of modern physical and chemical science. At their core lies the solution of the Schrödinger equation and, in more advanced treatments, the incorporation of electromagnetic interactions via quantum electrodynamics. These calculations enable the prediction of atomic energy levels, transition frequencies and response to external fields, underpinning applications from precision spectroscopy to materials design. Central developments include systematic approximations such as the Born–Oppenheimer scheme, methods for treating electron correlation beyond mean-field theories, and the deployment of variational, perturbative and stochastic algorithms to capture many-body effects. Recent advances have extended these approaches by integrating field-theoretic formalisms, machine-learning-driven sampling and high-precision correction schemes. As computational power and algorithmic sophistication continue to grow, quantum mechanical atomic calculations are poised to deliver ever more accurate benchmarks for experimental measurement, to guide the synthesis of novel materials and to deepen our understanding of fundamental interactions in the atomic regime.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Quantum Mechanical Calculations of Atomic Systems publication trend

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

Technical terms

Born–Oppenheimer approximation: A separation of electronic and nuclear motion that treats nuclei as fixed when solving the electronic Schrödinger equation.

Electron correlation: The interaction between electrons beyond the average field, requiring methods that go beyond mean-field approximations to capture instantaneous Coulomb effects.

Bethe–Salpeter equation: A field-theoretic wave equation for bound states in quantum electrodynamics, formulated in space-time coordinates to describe two-body interactions explicitly.

Potential energy surface: A multidimensional surface representing the energy of a system as a function of nuclear coordinates, central to understanding molecular dynamics and spectroscopy.

Wavefunction: A complex‐valued function that encodes the complete quantum state of a system, whose magnitude squared gives probability densities in configuration space.

References

1. Quantum Definition of Molecular Structure. Journal of the American Chemical Society (2024).
2. The Bethe–Salpeter QED Wave Equation for Bound-State Computations of Atoms and Molecules. ACS Physical Chemistry Au (2023).
3. Heavy-hole bilayer trions of transition metal dichalcogenides by analytical treatment to model He-isoelectronic ions upto dipole factor of Green’s function expansion of Coulomb interaction. Physics Open (2022).