Molecular-orbital-free algorithm for the excited-state force in time-dependent density functional theory.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical chemistry

Background:

• Time-dependent density functional theory (TD-DFT) is crucial for studying excited states.
• Calculating excited-state properties often involves computationally intensive methods.
• Existing methods typically use a molecular orbital (MO) basis, requiring basis transformations.

Purpose of the Study:

• To reformulate the analytical gradient of excited-state energy within TD-DFT.
• To develop a method using a nonorthogonal Gaussian atom-centered orbital (AO) basis.
• To improve computational efficiency by avoiding AO-MO transformations.

Main Methods:

• Derivation of a Z-vector equation in the AO basis for the reduced one-electronic density matrix.
• Implementation of the AO-based energy gradient expression.
• Application to excited-state geometry optimization and adiabatic excitation energy calculations.

Main Results:

• The study successfully derived and implemented an AO-based analytical energy gradient for TD-DFT excited states.
• Numerical tests on small molecules demonstrated the method's effectiveness.
• The AO-based approach showed comparable accuracy to the traditional MO-based scheme.

Conclusions:

• The developed AO-based TD-DFT energy gradient offers a computationally efficient alternative.
• This method facilitates exploiting quantum locality of the density matrix.
• It provides a valuable tool for excited-state calculations in computational chemistry.