# Half-Projected σ Self-Consistent Field For Electronic Excited States

journal contribution

posted on 17.04.2019, 00:00 by Hong-Zhou Ye, Troy Van VoorhisFully
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 Δ-SCF often collapse to the ground state. Recently,
our research group has developed a new method, σ-SCF [J. Chem. Phys. 2017, 147, 214104], that successfully solves the
“variational collapse” problem of energy-based methods.
Despite the success, σ-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 σ-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)
σ-SCF, brings substantial improvement to the description of
singlet and triplet excitations of the original σ-SCF method.
Numerical simulations on small molecules suggest that HP σ-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 σ-SCF can be size-intensive.