A general, recursive, and open-ended response code.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Response theory is crucial for understanding molecular properties.
• Previous methods for time- and perturbation-dependent basis sets were limited.
• Efficient computation of high-order derivatives is computationally intensive.

Purpose of the Study:

• To implement a new formulation of open-ended response theory.
• To develop a novel recursive programming technique for analytic response property calculations.
• To demonstrate the code's capability with high-order derivative calculations.

Main Methods:

• Implementation of open-ended response theory for time- and perturbation-dependent basis sets.
• Utilized recursive programming for compact and efficient code development.
• Calculations performed at Hartree-Fock and density functional theory levels.

Main Results:

• Developed a novel, compact code for analytic response property calculations.
• The recursive scheme is applicable to linear-scaling formulations and relativistic wave functions.
• Successfully computed third geometrical derivatives of frequency-dependent second hyperpolarizability for HSOH.

Conclusions:

• The new implementation provides an efficient and versatile tool for response theory calculations.
• Recursive programming significantly simplifies the calculation of complex response properties.
• The method is suitable for advanced computational chemistry applications.