Complete Basis Set Extrapolation of Electronic Correlation Energies Using the Riemann Zeta Function

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Complete basis set (CBS) extrapolation is crucial for accurate quantum chemical calculations.
• Traditional CBS methods often rely on empirical fitting schemes.
• Missing contributions from higher angular momenta (l) in basis sets pose a challenge.

Purpose of the Study:

• To develop and validate a novel CBS extrapolation method based on the Riemann zeta function.
• To analytically resummate missing correlation energy contributions.
• To provide an 'empirical' parameter-free extrapolation scheme.

Main Methods:

• Applied the Riemann zeta function to extrapolate correlation energies.
• Analytically resummated contributions from higher angular momenta (l).
• Assessed the asymptotic behavior of these contributions as an inverse power of l.

Main Results:

• Developed a zeta-function-based expression for the CBS limit.
• The proposed method is easy to use and requires no empirical parameter optimization.
• Zeta-function extrapolation errors were several times smaller than conventional schemes on average.

Conclusions:

• The Riemann zeta function provides an effective and accurate approach for CBS extrapolation of correlation energies.
• This method offers a significant improvement over standard extrapolation schemes.
• A recipe for estimating residual extrapolation error is also presented.