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 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.

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.

Quantum Information and Algorithms for Correlated Quantum Matter.

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

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.

Active-Space Pair Two-Electron Reduced Density Matrix Theory for Strong Correlation.

An active-space variational calculation of the two-electron reduced density matrix (2-RDM) is derived and implemented where the active orbitals are correlated within the pair approximation. The pair approximation considers only doubly occupied configurations of the wave function, which enables the calculation of the 2-RDM at a computational cost of [Formula: see text]. Calculations were performed both with the pair active-space configuration interaction (PASCI) method and the pair active-space self-consistent field (PASSCF) method. The latter includes a mixing of the active and inactive orbitals through unitary transformations. The active-space pair 2-RDM method is applied to the nitrogen molecule, the p-benzyne diradical, a newly synthesized biscobalt complex, and the nitrogenase cofactor FeMoco. The FeMoco molecule is treated in a [120,120] active space. Fractional occupations are recovered in each of these systems, indicating the presence of strong electron correlation.

Signature of van der Waals interactions in the cumulant density matrix.

Here we propose and implement a universal signature of the van der Waals interactions based on the cumulant part of the two-electron reduced density matrix (2-RDM). Due to the connected property of the cumulant, we can use it to detect the van der Waals interactions between two molecular moieties. In particular, we use the squared Frobenius norm of the cumulant of the 2-RDM, which has been previously shown to provide a size-extensive measure of the electron correlation. As two moieties are separated to infinity, the cumulant Frobenius norm exhibits an r-6 decay to its asymptotic limit, providing a density-based measure of the van der Waals interaction. We study this signature of van der Waals forces in a collection of small molecules of varying geometries. These computations agree with experimental trends of known literature values.

Satisfying fermionic statistics in the modeling of non-Markovian dynamics with one-electron reduced density matrices.

Treatment of Markovian, many-electron dynamics from the solution of the Lindblad equation for the 1-electron reduced density matrix requires additional constraints on the bath operators to maintain fermion statistics. Recently, we generalized Lindblad's formalism to non-Markovian dynamics through an ensemble of Lindbladian trajectories. Here we show that the fermion statistics of non-Markovian dynamics can be enforced through analogous constraints on the bath operators of each Lindbladian trajectory in the ensemble. To illustrate, we apply the non-Markovian method to three distinct systems of two fermions in three levels. While the electrons violate the fermion statistics without the constraints, correct fermion behavior is recovered with the constraints.

Pair 2-electron reduced density matrix theory using localized orbitals.

Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multi-reference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics.

Communication: satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices.

For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system's density matrix. While Lindblad's modification is correct for N-electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble N-electron density matrix (not ensemble N-representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F2, N2, CO, and BeH2 subject to environmental noise.