Entangled Electrons Foil Synthesis of Elusive Low-Valent Vanadium Oxo Complex

Abstract

We examine the recently reported first synthesis of the elusive low-valent vanadium(III) in a vanadium oxo complex with a computation representing 10(21) quantum degrees of freedom. While this computation is intractable with a conventionally constructed wave function, it is performed here by a direct calculation of the system's two-electron reduced density matrix (2-RDM), where the 2-RDM is constrained by nontrivial conditions, known as N-representability conditions, that restrict the 2-RDM to represent an N electron quantum system. We show that the added (reducing) electron becomes entangled among the five pyridine ligands. While smaller calculations predict a metal-centered addition, large-scale 2-RDM calculations show that quantum entanglement redirects the electron transfer to the pyridine ligands, resulting in a ligand-centered addition. Beyond its implications for the synthesis of low-valent vanadium oxo complexes, the result suggests new possibilities for using quantum entanglement to predict and control electron transfer in chemical and biological materials.

Strong Electron Correlation in Nitrogenase Cofactor, FeMoco

“…[19][20][21] Recent studies involving ligand non-innocence in manganese porphyrins and vanadium oxo complexes have shown that methods that fail to capture multireference electron correlation can mistakenly attribute a redox event to being metal-centered. [22][23][24] In separate studies on polyaromatic hydrocarbons, multireference correlation was found to give rise to increasing polyradical character with increasing size for both linear chains and two-dimensional geometries. 25 In this work, we study strong electron correlation in FeMoco using two multireference methods: the configuration interaction complete-active-space self-consistent-field (CI-CASSCF) method 26,27 and the variational two-electron reduced density matrix (V2RDM) method.…”

Efficient algorithm for multiconfiguration pair-density functional theory with application to the heterolytic dissociation energy of ferrocene

“…Standard CASSCF techniques are limited by computational costs to modest-sized systems, for example, for closed-shell singlets, to the treatment of no more than approximately 18 electrons in 18 active orbitals, but the treatment of larger active spaces is possible through the use of GASSCF or other MCSCF methods, including restricted active space self-consistent field (RASSCF), 15 occupation-restricted multiple active space (ORMAS), 16 splitGAS, 17,18 stochastic CASSCF approaches, 19 density matrix renormalization group (DMRG), [20][21][22] and the variational 2-RDM method. [23][24][25] One kind of post-SCF correction (step (ii)) is multireference second-order perturbation theory (MR-PT2), which can be used with a number of reference wave functions including CASSCF, which yields CASPT2, 26 RASSCF, which yields RASPT2, 27 and GASSCF, which yields GASPT2. 28 Another kind of post-SCF treatment, which is the main subject of the present paper, is MC-PDFT.…”

Quantum signature of exciton condensation

“…The quantum signature developed here, the large eigenvalue of the (modified) particle-hole matrix [25][26][27][28][29] , is present if and only if the fermion system exhibits condensation of particle-hole pairs (excitons) into a global state-exciton condensation. It allows us to predict the existence and extent of exciton condensation in any quantum system from only an electronic structure calculation of the two-electron reduced density matrix (2-RDM) [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] . While this definition includes various phase transitions involving condensates of soft phonons that are not conventionally viewed in these terms, such disruptive transitions, as explained by Kohn and Sherrington 45 , can be relevantly viewed in the context of exciton condensation.…”

“…Non-trivial direct calculations of the two-electron reduced density matrix (2-RDM) capture strong electron correlation including the long-range order of the exciton condensation. Such calculations, cited by the National Research Council in 1995 as one of the top outstanding problems in physical science, have only become possible recently [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and correspond to wavefunction calculations where the wavefunction, if constructible as a combination of determinants, would require a billion times the degrees of freedom treatable today by stateof-the-art supercomputers. Molecular-scale condensates, screened by electronic structure calculations, may be useful for the development of dissipationless molecular circuits and devices, especially in the context of molecular electronics.…”

“…For each system the 2-RDM was directly determined without computation of the many-electron wave function. The energy was computed as a variational functional of the 2-RDM [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]60 which was constrained by N -representability conditions 32,41,44,61 that are necessary for it to represent an N -electron quantum system. Because the N -representability conditions are non-perturbative with polynomial computational scaling, the variational 2-RDM method is able to catpture strong correlation in molecules that are too correlated to treat by density functional theory or single-reference ab initio methods and yet too large to treat by either full or partial configuration-interaction calculations.…”