Complex ground-state and excitation energies in coupled-cluster theory

Theory of electronic resonances: fundamental aspects and recent advances

“…Complex energies were considered to be an exotic phenomenon and were discussed mostly as an unwanted byproduct of some electronic-structure models, notably truncated coupled-cluster methods. 3–6 However, driven by the growing relevance of processes involving unbound electrons, the importance of electronic decay for chemistry has increased in recent years and is expected to continue increasing. State-of-the-art experimental techniques make it possible to create, in a controlled manner, environments where selected electrons are no longer bound to the nuclei.…”

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

“…Some of the other advantages associated with the EOM-CC formalism are its theoretical rigour, the accuracy and correct scaling behavior of energy differences computed, and the ability to systematically improve the results. However, standard quantum chemistry methods like EOM-CC sometimes face challenges in a quantitative determination of excited states and their properties, notably for same-symmetry conical intersections [41][42][43][44] and when the ground state has a prominent multi-reference character [45][46][47][48]. Since VQE algorithms are expected to provide accurate ground-state wavefunctions, even in the case of strongly correlated systems, NISQ era devices can help address these challenging problems with practical computational expenses.…”

Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version

“…On the other hand, the non-Hermiticity of CC theory introduces nontrivial fundamental problems. CCSD calculations in combination with complex-valued Hamiltonians, e.g., Hamiltonians in the presence of a finite external magnetic field − or with spin–orbit coupling, ,,, produce complex ground-state energies in general . While real parts of CCSD energies in these calculations may practically serve as good approximations to corresponding full configuration interaction energies, the emergence of complex energies is still a nontrivial formal problem of CC theory.…”

“…While real parts of CCSD energies in these calculations may practically serve as good approximations to corresponding full configuration interaction energies, the emergence of complex energies is still a nontrivial formal problem of CC theory. Furthermore, the non-Hermiticity of the CC transformed Hamiltonian gives rise to incorrect crossing conditions in EOM-CCSD calculations of intersections between electronic states of the same symmetry (“same-symmetry conical intersections”). − Calculations of same-symmetry conical intersections with CC accuracy is of significant interest to study of molecular spectroscopy and photochemistry. One promising route toward achieving this is to modify EOM-CCSD to rectify the crossing conditions.…”

“…CCSD calculations in combination with complex-valued Hamiltonians, e.g., Hamiltonians in the presence of a finite external magnetic field 84−87 or with spin−orbit coupling, 71,74,76,83 produce complex ground-state energies in general. 88 While real parts of CCSD energies in these calculations may practically serve as good approximations to corresponding full configuration interaction energies, the emergence of complex energies is still a nontrivial formal problem of CC theory. Furthermore, the non-Hermiticity of the CC transformed Hamiltonian gives rise to incorrect crossing conditions in EOM-CCSD calculations of intersections between electronic states of the same symmetry ("same-symmetry conical intersections").…”