Effective basis set extrapolations for CCSDT, CCSDT(Q), and CCSDTQ correlation energies

Area of Science:

• Computational Quantum Chemistry
• Theoretical Chemistry
• Electronic Structure Theory

Background:

• Coupled-cluster single double triple [CCSD(T)] calculations are standard for high-accuracy electronic structure.
• Basis set convergence is crucial for accurate thermochemical predictions.
• Extrapolation methods are employed to approach the complete basis set (CBS) limit.

Purpose of the Study:

• To investigate the extrapolation of coupled-cluster expansion terms beyond CCSD(T) to the CBS limit.
• To determine optimal extrapolation exponents for various basis set pairs.
• To assess the accuracy of current post-CCSD(T) extrapolation schemes in composite thermochemical theories.

Main Methods:

• Calculated reference CCSDT-CCSD(T) [T3-(T)], CCSDT(Q)-CCSDT [(Q)], and CCSDTQ-CCSDT(Q) [T4-(Q)] contributions using cc-pV{5,6}Z extrapolations.
• Fitted extrapolation exponents using cc-pV{D,T}Z, cc-pV{T,Q}Z, and cc-pV{Q,5}Z basis set pairs.
• Investigated the effect of diffuse functions on extrapolation convergence.

Main Results:

• Optimal extrapolation exponents showed noticeable performance improvements, especially with the cc-pV{T,Q}Z basis set pair.
• The T3-(T) component converges more slowly to the CBS limit than (Q) and T4 terms.
• Diffuse functions systematically reduce T3-(T) but increase (Q) contributions, leading to error cancellation in cc-pVnZ basis sets.

Conclusions:

• Current post-CCSD(T) extrapolation methods in composite theories (e.g., W4, HEAT) are sufficiently accurate for sub-kJ/mole precision.
• Fitted exponents provide insights into the convergence behavior of different coupled-cluster terms.
• Understanding diffuse function effects is crucial for accurate high-level coupled-cluster calculations.