Transformation-Free Generation of a Quasi-Diabatic Representation from the State-Average Orbital-Optimized Variational Quantum Eigensolver

In the present work, we examine how the recent quantum-computing algorithm known as the state-average orbital-optimized variational quantum eigensolver (SA-OO-VQE), viewed within the context of quantum chemistry as a type of multiconfiguration self-consistent field (MCSCF) electronic-structure approach, exhibits a propensity to produce an <i>ab initio</i> quasi-diabatic representation "for free" if considered as a least-transformed block-diagonalization procedure, as alluded to in our previous work (Yalouz, S. et al. <i>J. Chem. Theory Comput.</i> <b>2022</b>, <i>18</i>, 776-794) and thoroughly assessed herein. To this end, we introduce intrinsic and residual descriptors of diabaticity and re-explore the definition and linear-algebra properties, as well as their consequences on the vibronic nonadiabatic couplings, of an optimal diabatic representation within this context and how much one may deviate from it. Such considerations are illustrated numerically in the prototypical case of formaldimine, which presents a well-known conical intersection between its ground and first-excited singlet electronic states.