Excited states, symmetry breaking, and unphysical solutions in state-specific CASSCF theory

Abstract

State-specific electronic structure theory provides a route towards 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 characterise their topological properties. We demonstrate that state-specific approximations can provide accurate higher-energy excited states in ${\mathrm{H}}_2$ (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 conical intersection in ${\mathrm{CH}}_2$ (6-31G) and the avoided crossing in $\mathrm{LiF}$ (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.

14 pages, 8 figures

References in corpus (11)

• Time-dependent density functional theory: Past, present, and future
• Excited States From State Specific Orbital Optimized Pair Coupled Cluster
• Distinguishing Artificial and Essential Symmetry Breaking in a Single Determinant: Approach and Application to the C${}_{60}$, C${}_{36}$, and C${}_{20}$ Fullerenes
• Variational coupled cluster for ground and excited states
• Unrestricted Hartree-Fock theory of Wigner crystals
• Steering Orbital Optimization out of Local Minima and Saddle Points Toward Lower Energy
• Reaching Full Correlation through Nonorthogonal Configuration Interaction: A Second-Order Perturbative Approach
• Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems
• Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms
• Generalized nonorthogonal matrix elements for arbitrary excitations
• A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions

Cited by in corpus (11)

• Orbital-optimized versus time-dependent density functional calculations of intramolecular charge transfer excited states
• State-Specific Coupled-Cluster Methods for Excited States
• Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
• Weighted Active Space Protocol for Multireference Machine-Learned Potentials
• ExROPPP: Fast, Accurate and Spin-Pure Calculation of the Electronically Excited States of Organic Hydrocarbon Radicals
• Double Configuration Interaction Singles: Scalable and size-intensive approach for orbital relaxation in excited states and bond-dissociation
• Freeze-and-release direct optimization method for variational calculations of excited electronic states
• Numerically Stable Resonating Hartree-Fock
• Two Determinant Distinguishable Cluster
• Critical point search and linear response theory for computing electronic excitation energies of molecular systems. Part I: General framework, application to Hartree-Fock and DFT
• Orthogonally Constrained CASSCF Framework: Newton-Raphson Orbital Optimization and Nuclear Gradients