State-Specific Configuration Interaction for Excited States

Abstract

We introduce and benchmark a systematically improvable route for excited-state calculations, labeled state-specific configuration interaction (ΔCI), which is a particular realization of multiconfigurational self-consistent field and multireference configuration interaction. Starting with a reference built from optimized configuration state functions, separate CI calculations are performed for each targeted state (hence, state-specific orbitals and determinants). Accounting for single and double excitations produces the ΔCISD model, which can be improved with second-order Epstein−Nesbet perturbation theory (ΔCISD+EN2) or a posteriori Davidson corrections (ΔCISD+Q). These models were gauged against a vast and diverse set of 294 reference excitation energies. We have found that ΔCI is significantly more accurate than standard ground-statebased CI, whereas close performances were found between ΔCISD and EOM-CC2 and between ΔCISD+EN2 and EOM-CCSD. For larger systems, ΔCISD+Q delivers more accurate results than EOM-CC2 and EOM-CCSD. The ΔCI route can handle challenging multireference problems, singly and doubly excited states, from closed-and open-shell species, with overall comparable accuracy and thus represents a promising alternative to more established methodologies. In its current form, however, it is reliable only for relatively low-lying excited states.

Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following

“…In the cases of nitrobenzene and N -phenylpyrrole, the number of negative eigenvalues obtained this way is much larger than the saddle point order of the converged excited state. A much larger number of negative Hessian eigenvalues for the initial orbitals has also been recently observed in calculations based on the optimization of minimal configuration state functions . A constrained minimization of the energy, where the orbitals corresponding to the excited electron and the hole are frozen, is found to provide a better estimate of the saddle point order due to the partial inclusion of relaxation effects.…”

“…If the calculation involves orbital optimization, the Hessian eigenvalues are no longer proportional to the values of excitation energy, and the saddle point order does not necessarily increase monotonically with the energy of the excited state and depends on the level of theory. Excited states are nevertheless typically found to correspond to saddle points both at the correlated level of theory − as well as within mean-field approximations. ,,, …”

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

“…Practical solutions may rely on the identification of suitable initial guesses from more black-box techniques or by focusing on optimization algorithms that target desirable excited-state physical properties (e.g., dipole moments), such as the generalized variational principles developed by Hanscam and Neuscamman . Alternatively, more bespoke excited-state wave function ansätze , such as minimal configuration state functions or excited-state mean-field theory, ,, may remove unphysical solutions associated with redundant active orbitals and avoid the disappearance of solutions at pairwise coalescence points. Surmounting these issues will allow the benefits of state-specific calculations for computing excited states with bespoke orbitals and small active spaces to be fully realized.…”

“…The CASSCF wave function is a linear expansion of all the configurations that can be constructed from a set of partially occupied “active orbitals”, and the energy is optimized with respect to the configuration interaction (CI) and orbital coefficients simultaneously . It has long been known that higher-energy MCSCF solutions can represent electronic excited states − and that multiple symmetry-broken CASSCF solutions can occur for an inadequate active space. , More recently, MCSCF expansions truncated to single excitations have shown promise for singly excited charge transfer states, − while state-specific configuration interaction with higher degrees of truncation can handle challenging multireference problems and singly and doubly excited states . However, the strong coupling between the orbital and CI degrees of freedom makes the optimization challenging, and second-order optimization algorithms are generally required to reach convergence in practice. − …”

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory

“…Motivated in part by the limitations of linear response, there has been much recent work on excited-state-specific methods. Whether studying single-determinant wavefunctions, − configuration interaction (CI) wavefunctions, CC wavefunctions, − or DFT functionals, − the theme of locating higher energy, state-specific excited-state and open-shell roots is becoming increasingly prevalent across the field. Recognizing that, in the ground state, CCSD is a crucial stepping stone toward CCSD­(T) as well as a useful method in its own right, our focus here is to construct a CCSD-like excited-state-specific CC theory atop an excited-state mean field (ESMF) starting point − that, like HF in the ground state, has already taken care of state-specific orbital relaxations.…”