Analytical Gradients for the MSINDO-sCIS and MSINDO-UCIS Method: Theory, Implementation, Benchmarks, and Examples

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of excited states is crucial for understanding photochemical reactions.
• Semiempirical methods offer a computationally efficient alternative to ab initio methods for electronic structure calculations.
• Analytical gradients are essential for geometry optimization and exploring reaction pathways.

Purpose of the Study:

• To derive and implement analytical expressions for sCIS and UCIS energy gradients within the MSINDO semiempirical method.
• To enhance the computational efficiency of gradient calculations using the transpose-free quasiminimal residual (TFQMR) algorithm.
• To evaluate the accuracy and applicability of the developed method for excited-state geometry optimizations and periodic systems.

Main Methods:

• Derivation of analytical energy gradients for sCIS and UCIS.
• Implementation of the gradients into the MSINDO program package.
• Optimization of the Z-vector method using the TFQMR algorithm for enhanced computational efficiency.
• Benchmark timing tests comparing MSINDO with TD-B3LYP.
• Geometry optimizations of organic molecules in excited states.
• Calculations on periodic systems using the cyclic cluster model.

Main Results:

• Analytical expressions for sCIS and UCIS energy gradients in MSINDO were successfully derived and implemented.
• The TFQMR algorithm significantly improved the computational efficiency of the Z-vector method.
• Benchmark tests showed competitive performance compared to TD-B3LYP.
• Geometry optimizations of excited states in organic molecules demonstrated good agreement with CASPT2 and TD-B3LYP/TZVP.
• First calculations of excited-state structures for ethyne adsorbed on NaCl (100) surface were performed, showcasing applicability to periodic systems.

Conclusions:

• The developed MSINDO-based analytical gradients provide an efficient and accurate approach for excited-state geometry optimizations.
• The method is applicable to both molecular and periodic systems, expanding its utility in computational chemistry.
• This work lays the foundation for further studies on excited-state properties using semiempirical methods.