Orbital entanglement and the double d-shell effect in binary transition metal molecules.

Accurate modeling of transition metal-containing compounds is of great interest due to their wide-ranging and significant applications. These systems present several challenges from an electronic structure perspective, including significant multi-reference characters and many chemically relevant orbitals. A further complication arises from the so-called double d-shell effect, which is known to cause a myriad of issues in the treatment of first-row transition metals with both single- and multi-reference methods. While this effect has been well documented for several decades, a comprehensive understanding of its consequences and underlying causes is still evolving. Here, we characterize the second d-shell effect by analyzing the information entropy of correlated wavefunctions in a periodic series of 3d and 4d transition metal molecular hydrides and oxides. These quantum information techniques provide unique insight into the nuanced electronic structure of these species and are powerful tools for the study of weak and strong correlations in the transition metal d manifold.

The overlooked role of excited anion states in NiO2- photodetachment.

Photodetachment spectra of anionic species provide significant insights into the energies and nature of ground and excited states of both the anion and resultant neutral molecules. Direct detachment of the excess electron to the continuum may occur via formally allowed or forbidden transitions (perhaps as the result of intensity borrowing through vibronic coupling). However, alternate indirect pathways are also possible and often overlooked. Here, we report a two-dimensional photoelectron spectral study, combined with correlated electronic structure calculations, to elucidate the nature of photodetachment from NiO2-. The spectra are comprised of allowed and forbidden transitions, in excellent agreement with previously reported slow electron velocity mapped imaging spectra of the same system, which were interpreted in terms of direct detachment. In the current work, the contributions of indirect processes are revealed. Measured oscillations in the branching ratios of the spectral channels clearly indicate non-direct detachment processes, and the electronic structure calculations suggest that excited states of the appropriate symmetry and degeneracy lie slightly above the neutral ground state. Taken together, the results suggest that the origin of the observed forbidden transitions is the result of anion excited states mediating the electron detachment process.

Characterizing Excited States of a Copper-Based Molecular Qubit Candidate with Correlated Electronic Structure Methods.

Molecular spins have a variety of potential advantages as qubits for quantum computation, such as tunability and well-understood design pathways through organometallic synthesis. Organometallic and heavy-metal-based molecular spin qubits can also exhibit rich electronic structures due to ligand field interactions and electron correlation. These features make consistent and reliable modeling of these species a considerable challenge for contemporary electronic structure techniques. Here, we elucidate the electronic structure of a Cu(II) complex analogous to a recently proposed room-temperature molecular spin qubit. Using active space methods to describe the electron correlation, we show the nuanced interaction between the metal d orbitals and ligand σ and π orbitals makes these systems challenging to model, both in terms of the delocalized spin density and the excited state ordering. We show that predicting the correct spin delocalization requires special consideration of the Cu d orbitals and that the excited state spectrum for the Cu(III) complex also requires the explicit inclusion of the π orbitals in the active space. These interactions are rather common in molecular spin qubit motifs and may play an important role in spin-decoherence processes. Our results may lend insight into future studies of the orbital interactions and electron delocalization of similar complexes.

Characterizing the origin band spectrum of isoquinoline with resonance enhanced multiphoton ionization and electronic structure calculations.

We report the experimental resonance enhanced multiphoton ionization spectrum of isoquinoline between 315 and 310 nm, along with correlated electronic structure calculations on the ground and excited states of this species. This spectral region spans the origin transitions to a π-π* excited state, which previous work has suggested to be vibronically coupled with a lower lying singlet n-π* state. Our computational results corroborate previous density functional theory calculations that predict the vertical excitation energy for the n-π* state to be higher than the π-π* state; however, we find an increase in the C-N-C angle brings the n-π* state below the energy of the π-π* state. The calculations find two out-of-plane vibrational modes of the n-π* state, which may be brought into near resonance with the π-π* state as the C-N-C bond angle increases. Therefore, the C-N-C bond angle may be important in activating vibronic coupling between the states. We fit the experimental rotational contour with a genetic algorithm to determine the excited state rotational constants and orientation of the transition dipole moment. The fits show a mostly in-plane polarized transition, and the projection of the transition dipole moment in the a-b plane is about 84° away from the a axis. These results are consistent with the prediction of our electronic structure calculations for the transition dipole moment of the π-π* excited state.

Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators.

Electron transport in realistic physical and chemical systems often involves the nontrivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a nonunitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here, we present a general algorithm for implementing the action of any nonunitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating nonunitary operations on intermediate-term and future quantum devices.

Structural and Spectroscopic Comparison of Soft-Se vs. Hard-O Donor Bonding in Trivalent Americium/Neodymium Molecules.

Covalency is often considered to be an influential factor in driving An3+ vs. Ln3+ selectivity invoked by soft donor ligands. This is intensely debated, particularly the extent to which An3+ /Ln3+ covalency differences prevail and manifest as the f-block is traversed, and the effects of periodic breaks beyond Pu. Herein, two Am complexes, [Am{N(E=PPh2 )2 }3 ] (1-Am, E=Se; 2-Am, E=O) are compared to isoradial [Nd{N(E=PPh2 )2 }3 ] (1-Nd, 2-Nd) complexes. Covalent contributions are assessed and compared to U/La and Pu/Ce analogues. Through ab initio calculations grounded in UV-vis-NIR spectroscopy and single-crystal X-ray structures, we observe differences in f orbital involvement between Am-Se and Nd-Se bonds, which are not present in O-donor congeners.

Analytical gradients of variational reduced-density-matrix and wavefunction-based methods from an overlap-reweighted semidefinite program.

Analytical gradients of variational two-electron reduced-density matrix (2-RDM) methods are derived by transforming the atomic-orbital reduced-density matrices to remove the dependence of the N-representability conditions on the orbital-overlap matrix. The transformation, performed through a Cholesky decomposition of the geminal-overlap matrix, generates a Hellmann-Feynman-like expression for the gradient that only depends on the derivative of the transformed reduced Hamiltonian matrix. The formulation is applicable not only to the variational 2-RDM method but also to variational wavefunction methods like the full configuration interaction and complete active-space self-consistent-field. To illustrate, we apply the analytical gradients to perform geometry optimizations on several transition metal complexes, octahedral and trigonal prismatic CrF6 as well as the (ethylene-1,2-dithiolato)nickel, or Ni(edt)2, complex.

Static and Dynamic Electron Correlation in the Ligand Noninnocent Oxidation of Nickel Dithiolates.

Metal dithiolates have a wide range of applications from catalysis to molecular conductors with the ligands being the source of electrons during electrochemical oxidation in an effect known as ligand noninnocence. Recent large-scale variational two-electron reduced-density matrix (2-RDM) calculations of the vanadium oxo complex and manganese superoxide dismutase show that quantum entanglement stabilizes the addition of an electron to the ligands, providing a quantum mechanical explanation for ligand noninnocence. In this paper, we confirm and explore the ligand noninnocence in the electron oxidation series of bis(ethylene-1,2-dithiolato)nickel or [Ni(edt2)](-2,-1,0) with variational 2-RDM calculations. While previous wave function calculations of this series have selected only the ligand π orbitals as the critical (active) orbitals to be correlated, we find that both ligand π and nickel d orbitals must be correlated to generate a realistic picture of the electron-transfer process. Using the computed 2-RDM to seed a solution of the anti-Hermitian contracted Schrödinger equation, we predict that the singlet state is lower in energy than the triplet state, which is consistent with experimental observations.

Singular Value Decomposition Quantum Algorithm for Quantum Biology.

There has been a recent interest in quantum algorithms for the modeling and prediction of nonunitary quantum dynamics using current quantum computers. The field of quantum biology is one area where these algorithms could prove to be useful as biological systems are generally intractable to treat in their complete form but amenable to an open quantum systems approach. Here, we present the application of a recently developed singular value decomposition (SVD) algorithm to two systems in quantum biology: excitonic energy transport through the Fenna-Matthews-Olson complex and the radical pair mechanism for avian navigation. We demonstrate that the SVD algorithm is capable of capturing accurate short- and long-time dynamics for these systems through implementation on a quantum simulator and conclude that while the implementation of this algorithm is beyond the reach of current quantum computers, it has the potential to be an effective tool for the future study of systems relevant to quantum biology.

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

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.