Efficient analytical gradients of property-based diabatic states: Geometry optimizations for localized holes

15 March 2023, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


We present efficient analytical gradients of property-based diabatic states and couplings using a Lagrangian formalism. Unlike previous formulations, the method achieves a computational scaling that is independent of the number of adiabatic states used to construct the diabats. The approach is generalizable to other property-based diabatization schemes and electronic structure methods as long as analytical energy gradients are available and integral derivatives with the property operator can be formed. We also introduce a scheme to phase and reorder diabats to ensure their continuity between molecular configurations. We demonstrate this for the specific case of Boys diabatic states obtained from state-averaged complete active space self-consistent field electronic structure calculations with GPU acceleration in the TeraChem package. The method is used to test the Condon approximation for hole transfer in an explicitly solvated model DNA oligomer.


electron transfer
electronic structure
Marcus theory

Supplementary materials

Supporting Information
See the supplementary material for details of the integral derivatives; Boys SA-CASSCF coupled perturbed equations; effective diabatic OPDM, TPDM, and CI Lagrangian; test of analytical gradients against finite difference results; ethylene trimer geometries and energies; dependence of DNA hole states on basis set and an analysis of the wavefunctions and optimal geometries of DNA-localized hole states.


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