Restricted Open-Shell Cluster Mean-Field theory for Strongly Correlated Systems.

The cluster-based Mean Field method (cMF) and it is second order perturbative correction was introduced by Jiménez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated by allowing the α and β orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wave function was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods.

Accurate and interpretable representation of correlated electronic structure Tensor Product Selected CI.

The task of computing wavefunctions that are accurate, yet simple enough mathematical objects to use for reasoning, has long been a challenge in quantum chemistry. The difficulty in drawing physical conclusions from a wavefunction is often related to the generally large number of configurations with similar weights. In Tensor Product Selected Configuration Interaction (TPSCI), we use a locally correlated tensor product state basis, which has the effect of concentrating the weight of a state onto a smaller number of physically interpretable degrees of freedom.

Physically Motivated Improvements of Variational Quantum Eigensolvers.

The adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from the electronic structure theory, we concentrate on optimizing state preparation without added computational burden and guiding ansatz expansion to yield more concise wave functions with expedited convergence toward exact solutions.

Quantum Simulation of Molecular Response Properties in the NISQ Era.

Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements.

Generalization of the Tensor Product Selected CI Method for Molecular Excited States.

In a recent paper [, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space.

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

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing.

New Local Explorations of the Unitary Coupled Cluster Energy Landscape.

The recent quantum information boom has effected a resurgence of interest in the unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ansätze prompted us to investigate the approach of truncating the Taylor series expansion (instead of a perturbative expansion) of the UCC with singles and doubles (UCCSD) energy at the second order. This amounts to an approach where the electron correlation energy is estimated by taking a single Newton-Raphson step from Hartree-Fock toward UCCSD.

Symmetry Breaking Slows Convergence of the ADAPT Variational Quantum Eigensolver.

Because quantum simulation of molecular systems is expected to provide the strongest advantage over classical computing methods for systems exhibiting strong electron correlation, it is critical that the performance of VQEs be assessed for strongly correlated systems. For classical simulation, strong correlation often results in symmetry breaking of the Hartree-Fock reference, leading to Löwdin's well-known "symmetry dilemma", whereby accuracy in the energy can be increased by breaking spin or spatial symmetries. Here, we explore the impact of symmetry breaking on the performance of ADAPT-VQE using two strongly correlated systems: (i) the "fermionized" anisotropic Heisenberg model, where the anisotropy parameter controls the correlation in the system, and (ii) symmetrically stretched linear H, where correlation increases with increasing H-H separation.

ONIOM Method with Charge Transfer Corrections (ONIOM-CT): Analytic Gradients and Benchmarking.

Hybrid methods such as ONIOM that treat different regions of a large molecule using different methods are widely used to investigate chemical reactions in a variety of materials and biological systems. However, there are inherent sources of significant errors due to the standard treatment of the boundary between the regions using hydrogen link atoms. In particular, an unbalanced charge distribution in the chemically important model region is a potential source of such problems.

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions.

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity.

Revealing the Contest between Triplet-Triplet Exchange and Triplet-Triplet Energy Transfer Coupling in Correlated Triplet Pair States in Singlet Fission.

Understanding the separation of the correlated triplet pair state (TT) intermediate is critical for leveraging singlet fission to improve solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction () between the triplets which leads to the spin splitting of the biexciton state into (TT),(TT) and (TT) states, and (ii) the triplet-triplet energy transfer integral () which enables the formation of the spatially separated (but still spin entangled) state (T···T). We develop a simple ab initio technique to compute both the biexciton exchange () and biexciton transfer coupling.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods.

Cluster many-body expansion: A many-body expansion of the electron correlation energy about a cluster mean field reference.

The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized nth order Bethe-Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction.

Spin-Flip Pair-Density Functional Theory: A Practical Approach To Treat Static and Dynamical Correlations in Large Molecules.

We present a practical approach to treat static and dynamical correlation accurately in large multiconfigurational systems. The static correlation is taken into account by using the spin-flip approach, which is well-known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (, , , 3669).

Selected Configuration Interaction in a Basis of Cluster State Tensor Products.

Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation.

Spin-Orbit Matrix Elements for a Combined Spin-Flip and IP/EA approach.

We present a practical approach for computing the Breit-Pauli spin-orbit matrix elements of multiconfigurational systems with both spin and spatial degeneracies based on our recently developed RAS-SF-IP/EA method (Houck, S. E.; et al.

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators.

Simple and Efficient Truncation of Virtual Spaces in Embedded Wave Functions via Concentric Localization.

We present a strategy to generate "concentrically local orbitals" for the purpose of decreasing the computational cost of wave function-in-density functional theory (WF-in-DFT) embedding. The concentric localization is performed for the virtual orbitals by first projecting the virtual space onto atomic orbitals centered on the embedded atoms. Using a one-particle operator, these projected orbitals are then taken as a starting point to iteratively span the virtual space, recursively creating virtual orbital "shells" with consecutively decreasing correlation energy recovery at each iteration.

Multireference Ab Initio Studies of Magnetic Properties of Terbium-Based Single-Molecule Magnets.

We investigate how different chemical environments influence magnetic properties of terbium(III) (Tb)-based single-molecule magnets (SMMs), using first-principles relativistic multireference methods. Recent experiments showed that Tb-based SMMs can have exceptionally large magnetic anisotropy and that they can be used for experimental realization of quantum information applications, with a judicious choice of chemical environment. Here, we perform complete active space self-consistent field calculations including relativistic spin-orbit interaction for representative Tb-based SMMs such as TbPc and TbPcNc in three charge states.

An adaptive variational algorithm for exact molecular simulations on a quantum computer.

Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated.

A Combined Spin-Flip and IP/EA Approach for Handling Spin and Spatial Degeneracies: Application to Double Exchange Systems.

Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip ionization potential/electron affinity ( nSF-IP or nSF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly correlated N, as well as several double exchange systems.

Automatic Partition of Orbital Spaces Based on Singular Value Decomposition in the Context of Embedding Theories.

We present a simple approach for orbital space partitioning to be employed in the projection-based embedding theory developed by Goodpaster and co-workers [ Manby et al. J. Chem.

Simple Rule To Predict Boundedness of Multiexciton States in Covalently Linked Singlet-Fission Dimers.

Because of the potential for increasing solar cell efficiencies, significant effort has been spent understanding the mechanism of singlet fission. We provide a simple connectivity rule to predict whether the through-bond coupling will be stabilizing or destabilizing for the (TT) state in covalently linked singlet-fission chromophores. By drawing an analogy between the chemical system and a simple spin-lattice, one is able to determine the ordering of the multiexciton spin state via a generalized usage of Ovchinnikov's rule.