Arbitrary-Order Derivatives of Quantum Chemical Methods via Automatic Differentiation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Calculating higher-order nuclear coordinate derivatives of electronic energies is crucial for understanding molecular properties and reaction dynamics.
• Traditional methods rely on numerical differentiation, which suffers from computational instability, or complex analytic derivative formulas that are difficult to derive for advanced quantum chemistry methods.

Purpose of the Study:

• To present a general and robust methodology for obtaining arbitrary-order nuclear coordinate derivatives of electronic energies.
• To bypass the limitations of numerical differentiation and the complexity of deriving analytic formulas for energy derivatives.

Main Methods:

• Leveraging modern automatic differentiation (AD) software to compute exact nuclear coordinate derivatives.
• Implementing the AD scheme in a freely available, open-source software package.
• Applying the methodology to various quantum chemistry methods, including Hartree-Fock, Møller-Plesset perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)].

Main Results:

• Demonstrated the ability to obtain exact arbitrary-order nuclear derivatives for electronic energies across different quantum chemistry methods.
• Successfully computed up to sextic derivatives for various test systems, showcasing the method's broad applicability.
• Achieved results that were previously unobtainable by exact means due to the lack of higher-order derivative formulas.

Conclusions:

• The developed automatic differentiation methodology provides a general, stable, and efficient approach for calculating high-order nuclear derivatives.
• This innovation significantly advances computational capabilities in quantum chemistry, enabling new avenues for theoretical studies.
• The open-source implementation facilitates wider adoption and further development of exact derivative calculations.