A Constraint-Based Orbital-Optimized Excited State Method (COOX)

In this work, we present a novel method to directly calculate
targeted
electronic excited states within a self-consistent field calculation
based on constrained density functional theory (cDFT). The constraint
is constructed from the static occupied-occupied and virtual-virtual
parts of the excited state difference density from (simplified) linear-response
time-dependent density functional theory calculations (LR-TDDFT).
Our new method shows a stable convergence behavior, provides an accurate
excited state density adhering to the Aufbau principle, and can be
solved within a restricted SCF for singlet excitations to avoid spin
contamination. This also allows the straightforward application of
post-SCF electron-correlation methods like MP2 or direct RPA methods.
We present the details of our constraint-based orbital-optimized excited
state method (COOX) and compare it to similar schemes. The accuracy
of excitation energies will be analyzed for a benchmark of systems,
while the quality of the resulting excited state densities is investigated
by evaluating excited state nuclear forces and excited state structure
optimizations. We also investigate the performance of the proposed
COOX method for long-range charge transfer excitations and conical
intersections with the ground-state.