Explicitly correlated Gaussian basis approach to periodic systems

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Calculating the electronic structure of periodic solids is crucial for understanding material properties.
• Existing methods often involve complex approximations or computationally intensive calculations.

Purpose of the Study:

• To derive closed-form expressions for matrix elements in variational calculations of electronic structure for periodic solids.
• To develop a unified computational framework for these calculations.

Main Methods:

• Utilized a basis of explicitly correlated Gaussians.
• Constructed periodic basis functions by summing shifted correlated Gaussians over lattice translations.
• Applied a generalized unfolding theorem to simplify double lattice sums into single sums.
• Developed a unified framework for overlap, kinetic energy, and Coulomb potential operators.

Main Results:

• Derived closed-form expressions for all necessary matrix elements.
• Successfully applied the formalism to an infinite one-dimensional hydrogen chain.
• Computed ground-state energy per atom in the thermodynamic limit.

Conclusions:

• The new formalism provides an efficient and accurate method for electronic structure calculations in periodic solids.
• Results for the hydrogen chain model system show excellent agreement with extrapolated data from other many-body methods.
• This approach offers a promising avenue for advancing computational materials science.