Rydberg and charge-transfer excited states calculated using saddle point search methods and neural-network accelerated configuration interaction

Calculations of Rydberg and charge-transfer excited states based on variational optimisation of orbitals in state specific density functional calculations of molecules and defects in solids are presented. The method is based on the generalised mode following (GMF) saddle point search algorithm [1] and direct optimisation as implemented in the GPAW software for condensed matter simulations where the orbitals are represented with plane waves or on a real space grid. The GMF method is used to converge on a saddle point of a given order on the electronic energy surface representing an excited state. The calculated excitation energy obtained using generalised gradient and meta-generalised gradient functionals is found to be in remarkably good agreement with experimental estimates [2] and defect states in solids [3]. Even better results are obtained by applying scaled Perdew-Zunger self-interaction correction to the energy functionals [3]. Alternatively, reference values are obtained using selective configuration interaction (CI) calculations where a convolutional neural-network is used to identify the important Slater determinants [4] with orbitals optimised for the state of interest. As an example, previously published results of full CI calculations of propane, N₂, H₂O and NH₃ molecules are reproduced with several orders of magnitude fewer Slater determinants selected by the neural network.

References:

1. Schmerwitz, Y. L. A. ; Levi, G.; Jónsson, H. J. Chem. Theory Comput. 19, 3634 (2023).

2. Sigurdarson, A. E.; Schmerwitz, Y. L. A.; Tveiten, D. K. V.; Levi, G.; Jónsson, H. J. Chem. Phys. 159, 214109 (2023).

3. Ivanov, A. V.; Schmerwitz,Y. L. A.; Levi, G.; Jónsson, H. SciPost Physics 15, 009 (2023); L. Sun et al. (arXiv:2510.24144).

4. Schmerwitz,Y. L. A. et al. J. Chem. Theory Comput. 21, 2301 (2025); Levi et al. (arXiv:2510.26751)