Half-Projected sigma Self-Consistent Field For Electronic Excited States

摘要

Fully self-consistent mean-field solutions of electronic excited states have been much less accessible compared to ground state solutions (e.g., Hartree-Fock). The main reason for this is that most excited states are energy saddle points, and hence energy-based optimization methods such as Delta-SCF often collapse to the ground state. Recently, our research group has developed a new method, sigma-SCF [J. Chem. Phys. 2017, 147, 214104], that successfully solves the "variational collapse" problem of energy-based methods. Despite the success, sigma-SCF solutions are often spin-contaminated for open-shell states due to the single-determinant nature; unphysical behaviors such as disappearing solutions and discontinuous first-order energy derivatives are also observed along with the spontaneous breaking of spin or spatial symmetries. In this work, we tackle these problems by partially restoring the broken spin-symmetry of a sigma-SCF solution through an approximate spin-projection scheme called half-projection. Orbitals of the projected wave function are optimized in a variation-after-projection (VAP) manner. The resulting theory, which we term half-projected (HP) sigma-SCF, brings substantial improvement to the description of singlet and triplet excitations of the original sigma-SCF method. Numerical simulations on small molecules suggest that HP sigma-SCF delivers high-quality excited-state solutions that exist in a wide range of geometries with smooth potential energy surfaces. We also show that local excitations in HP sigma-SCF can be size-intensive.