Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory

Abstract

State-specific electronic structure theory provides a route toward balanced excited-state wave functions by exploiting higher-energy stationary points of the electronic energy. Multiconfigurational wave function approximations can describe both closed-and open-shell excited states and avoid the issues associated with state-averaged approaches. We investigate the existence of higher-energy solutions in complete active space self-consistent field (CASSCF) theory and characterize their topological properties. We demonstrate that state-specific approximations can provide accurate higherenergy excited states in H 2 (6-31G) with more compact active spaces than would be required in a state-averaged formalism. We then elucidate the unphysical stationary points, demonstrating that they arise from redundant orbitals when the active space is too large or symmetry breaking when the active space is too small. Furthermore, we investigate the singlet−triplet crossing in CH 2 (6-31G) and the avoided crossing in LiF (6-31G), revealing the severity of root flipping and demonstrating that state-specific solutions can behave quasi-diabatically or adiabatically. These results elucidate the complexity of the CASSCF energy landscape, highlighting the advantages and challenges of practical state-specific calculations.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

“…In state-specific electronic structure methods, ground and excited states can be found as stationary points on the electronic energy landscape, the surface described by the variation of the energy as a function of the electronic degrees of freedom . The ground state corresponds to a global minimum, while the excited states are typically saddle points. ,,,, Within the KS method, the excited stationary states correspond to higher-energy solutions of the KS equations and have nonaufbau orbital occupations. Therefore, they can be found by solving the KS equations through SCF algorithms based on sequential eigendecomposition of the KS Hamiltonian matrix if a given nonaufbau occupation of the orbitals can be preserved during the iterations.…”

“…Due to the nonlinearity of the orbital optimization, orbital-optimized calculations can be affected by the presence of stationary points on the electronic energy surface without a clear association with a particular electronic state. ,, In the context of intramolecular charge transfer excitations, it has been shown that orbital-optimized calculations can converge on solutions with significantly different degrees of charge transfer depending on the method used. This is exemplified by the A 1 LUMO + 1 ← HOMO charge transfer excitation in the twisted PP molecule .…”

Topology of Conical Intersection Seams and the Geometric Phase

“…The occurrence of discontinuities can be due to an unsuitable choice of the active space such that the global minimum of the CASSCF energy is obtained by a switch between active and doubly occupied or virtual orbitals. However, even when the active space is blameless, trapping in secondary minima may occur, depending on the convergence algorithm and on the choice of the initial guess orbitals. − As a result of such failures of computational methods, the predictions of the theory discussed in the previous sections may be occasionally contradicted by actual calculations.…”

Seniority and Hierarchy Configuration Interaction for Radicals and Excited States

“…Instead, one may optimize the orbitals for the excited state of interest (described with an appropriate reference), followed by a separate CI calculation, in a so-called state-specific approach (ΔCI). There has been a recent surge in the development of state-specific methods, covering single-reference and multiconfigurational self-consistent field, − density functional theory, − perturbation theory, − quantum Monte Carlo, − and coupled-cluster (CC) − methods. In particular, by employing a minimal configuration state function (CSF) reference, we have recently shown that excitation-based ΔCI models deliver far more accurate excitation energies than their ground-state-based analogs …”