Selected Configuration Interaction in a Basis of Cluster State Tensor Products

Automatic State Interaction with Large Localized Active Spaces for Multimetallic Systems

The localized active space self-consistent field method factorizes a complete active space wave function into an antisymmetrized product of localized active space wave function fragments. Correlation between fragments is then reintroduced through localized active space state interaction (LASSI), in which the Hamiltonian is diagonalized in a model space of LAS states. However, the optimal procedure for defining the LAS fragments and LASSI model space is unknown. We here present an automated framework to explore systematically convergent sets of model spaces, which we call LASSI[r, q]. This method requires the user to select only r, the number of electron hops from one fragment to another, and q, the number of fragment basis functions per Hilbert space, which converges to CASCI in the limit of r, q → ∞. Numerical tests of this method on the trimetal oxo-centered complexes [Fe(III)Al(III)Fe(II)(μ3-O)(HCOO)6] and [Fe(III)2Fe(II)(μ3-O)(HCOO)6] show efficient convergence to the CASCI limit with 4-10 orders of magnitude fewer states than CASCI.

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one- and two-dimensional J1 - J2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J2/J1 ≲ 0.6 regime of the J1 - J2 model─a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.

Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction Theory

Polariton chemistry has attracted great attention as a potential route to modify chemical structure, properties, and reactivity through strong interactions among molecular electronic, vibrational, or rovibrational degrees of freedom. A rigorous theoretical treatment of molecular polaritons requires the treatment of matter and photon degrees of freedom on equal quantum mechanical footing. In the limit of molecular electronic strong or ultrastrong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach we refer to as ab initio cavity quantum electrodynamics, where the photon degrees of freedom are treated at the level of cavity quantum electrodynamics. Here, we present an approach called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction theory to provide ground- and excited-state polaritonic surfaces with a balanced description of strong correlation effects among electronic and photonic degrees of freedom. This method provides a platform for ab initio cavity quantum electrodynamics when both strong electron correlation and strong light-matter coupling are important and is an important step toward computational approaches that yield multiple polaritonic potential energy surfaces and couplings that can be leveraged for ab initio molecular dynamics simulations of polariton chemistry.

Distributed Implementation of Full Configuration Interaction for One Trillion Determinants

Full configuration interaction (FCI) can provide an exact molecular ground-state energy within a given basis set and serve as a benchmark for approximate methods in quantum chemical calculations, including the emerging variational quantum eigensolver. However, its exponential computational and memory requirements easily exceed the capability of a single server and limit its applicability to large molecules. In this paper, we present a distributed FCI implementation employing a hybrid parallelization scheme with multithreading and multiprocessing to expand FCI's applicability. We optimize this scheme to minimize the bottlenecks arising from interprocess communications and interthread data management. Our implementation achieves higher scalability than the naive combination of prior works and successfully calculates the exact energy of C3H8/STO-3G with 1.31 trillion determinants, which is the largest FCI calculation to the best of our knowledge. Furthermore, we provide a comprehensive list of FCI results with 136 combinations of molecules and basis sets for future evaluation and development of approximate methods.

Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock

We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.

Machine Learning the Quantum Mechanical Wave Function

Strongly correlated systems have been challenging to computational chemists for a long time. To solve these systems, multireference methods have been developed over the years. Recently, with the fast development of machine learning and artificial intelligence methods, these methods have also influenced the quest for optimal wave function ansatz. Machine learning approaches have been used in many different flavors. From this perspective, we will discuss the different milestones achieved in the use of machine learning for solving the quantum many body problem.

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

In a recent paper [JCTC, 2020, 16, 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. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited-state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons with respect to the extrapolated result (i.e., near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.

Symmetry-projected cluster mean-field theory applied to spin systems

We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.

Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems

An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.

Machine-learning assisted scheduling optimization and its application in quantum chemical calculations

Easy and effective usage of computational resources is crucial for scientific calculations, both from the perspectives of timeliness and economic efficiency. This work proposes a bi-level optimization framework to optimize the computational sequences. Machine-learning (ML) assisted static load-balancing, and different dynamic load-balancing algorithms can be integrated. Consequently, the computational and scheduling engine of the ParaEngine is developed to invoke optimized quantum chemical (QC) calculations. Illustrated benchmark calculations include high-throughput drug suit, solvent model, P38 protein, and SARS-CoV-2 systems. The results show that the usage rate of given computational resources for high throughput and large-scale fragmentation QC calculations can primarily profit, and faster accomplishing computational tasks can be expected when employing high-performance computing (HPC) clusters.

Algorithm for analytic nuclear energy gradients of state averaged DMRG-CASSCF theory with newly derived coupled-perturbed equations

We present an algorithm for evaluating analytic nuclear energy gradients of the state-averaged density matrix renormalization group complete-active-space self-consistent field (SA-DMRG-CASSCF) theory based on the newly derived coupled-perturbed (CP) DMRG-CASSCF equations. The Lagrangian for the conventional SA-CASSCF analytic gradient theory is extended to the SA-DMRG-CASSCF variant that can fully consider a whole set of constraints on the parameters of multi-root canonical matrix product states formed at all the DMRG block configurations. An efficient algorithm to solve the CP-DMRG-CASSCF equations for determining the multipliers was developed. The complexity of the resultant analytic gradient algorithm is overall the same as that of the unperturbed SA-DMRG-CASSCF algorithm. In addition, a reduced-scaling approach was developed to directly compute the SA reduced density matrices (SA-RDMs) and their perturbed ones without calculating separate state-specific RDMs. As part of our implementation scheme, we neglect the term associated with the constraint on the active orbitals in terms of the active-active rotation in the Lagrangian. Thus, errors from the true analytic gradients may be caused in this scheme. The proposed gradient algorithm was tested with the spin-adapted implementation by checking how accurately the computed analytic energy gradients reproduce numerical gradients of the SA-DMRG-CASSCF energies using a common number of renormalized bases. The illustrative applications show that the errors are sufficiently small when using a typical number of the renormalized bases, which is required to attain adequate accuracy in DMRG's total energies.

Analytic Gradients for Selected Configuration Interaction

We develop analytic gradients for selected configuration interaction wave functions. Despite all pairs of molecular orbitals now potentially having to be considered for the coupled perturbed Hartree-Fock equations, we show that degenerate orbital pairs belonging to different irreducible representations in the largest abelian subgroup do not need to be included and instabilities due to degeneracies are avoided. We introduce seminumerical gradients and use them to validate the analytic approach even when near degeneracies are present due to high-symmetry geometries being slightly distorted to break symmetry. The method is applied to carbon monoxide, ammonia, square planar H₄, hexagonal planar H₆, and methane for a range of bond lengths where we demonstrate that analytic gradients for selected configuration interaction can approach the quality of full configuration interaction yet only use a very small fraction of its determinants.

Advances in Parallel Heat Bath Configuration Interaction

Heat-bath configuration interaction (HCI) is a deterministic method that approaches the full CI limit at greatly reduced computational cost. In this work, computational improvements to the HCI algorithm are introduced targeting speed, parallel efficiency, and memory requirements. The new implementation introduces a hash function to distribute determinants and takes advantage of MPI and OpenMP for parallelism allowing for a (22e,168o) active space to be studied, which explicitly includes 2.39 × 10⁷ variational determinants and 8.95 × 10¹⁰ perturbative determinants. Benchmarks show up to 86% parallel efficiency of the perturbative step on 32 nodes (4096 cores) and a total efficiency of 74%. The new HCI implementation is benchmarked for accuracy against prior results and applied to study the triplet-quintet gap in the challenging [FeO(NH₃)₅]²⁺ complex.

Localized Quantum Chemistry on Quantum Computers

Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here, we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground-state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with the system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H₂)₂ into two H₂ molecules and by breaking the two double bonds in trans-butadiene, and resource estimates are provided for linear chains of up to 20 H₂ molecules.

Localized Active Space-State Interaction: a Multireference Method for Chemical Insight

Multireference electronic structure methods, like the complete active space (CAS) self-consistent field model, have long been used to characterize chemically interesting processes. Important work has been done in recent years to develop modifications having a lower computational cost than CAS, but typically these methods offer no more chemical insight than that from the CAS solution being approximated. In this paper, we present the localized active space-state interaction (LASSI) method that can be used not only to lower the intrinsic cost of the multireference calculation but also to improve interpretability. The localized active space (LAS) approach utilizes the local nature of the electron-electron correlation to express a composite wave function as an antisymmetrized product of unentangled wave functions in local active subspaces. LASSI then uses these LAS states as a basis from which to express complete molecular wave functions. This not only makes the molecular wave function more compact but also permits flexibility in choosing those states to be included in the basis. Such selective inclusion of states translates to the selective inclusion of specific types of interactions, thereby allowing a quantitative analysis of these interactions. We demonstrate the use of LASSI to study charge migration and spin-flip excitations in multireference organic molecules. We also compute the J coupling parameter for a bimetallic compound using various LAS bases to construct the Hamiltonian to provide insights into the coupling mechanism.

Efficient Computation of Two-Electron Reduced Density Matrices via Selected Configuration Interaction

We create an approach to efficiently calculate two-electron reduced density matrices (2-RDMs) using selected configuration interaction wavefunctions. This is demonstrated using the specific example of Monte Carlo configuration interaction (MCCI). The computation of the 2-RDMs is accelerated by using ideas from fast implementations of full configuration interaction (FCI) and recent advances in implementing the Slater–Condon rules using hardware bitwise operations. This method enables a comparison of MCCI and truncated CI 2-RDMs with FCI values for a range of molecules, which includes stretched bonds and excited states. The accuracy in energies, wavefunctions, and 2-RDMs is seen to exhibit a similar behavior. We find that MCCI can reach sufficient accuracy of the 2-RDM using significantly fewer configurations than truncated CI, particularly for systems with strong multireference character.

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. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH₄ and F₂ where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems

We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J₁-J₂ Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.

Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N₂, F₂, C₂, CN⁺, CO, BN, BO⁺, and Cr₂) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

Active Learning Configuration Interaction for Excited-State Calculations of Polycyclic Aromatic Hydrocarbons

We present the active learning configuration interaction (ALCI) method for multiconfigurational calculations based on large active spaces. ALCI leverages the use of an active learning procedure to find important electronic configurations among the full configurational space generated within an active space. We tested it for the calculation of singlet-singlet excited states of acenes and pyrene using different machine learning algorithms. The ALCI method yields excitation energies within 0.2-0.3 eV from those obtained by traditional complete active-space configuration interaction (CASCI) calculations (affordable for active spaces up to 16 electrons in 16 orbitals) by including only a small fraction of the CASCI configuration space in the calculations. For larger active spaces (we tested up to 26 electrons in 26 orbitals), not affordable with traditional CI methods, ALCI captures the trends of experimental excitation energies. Overall, ALCI provides satisfactory approximations to large active-space wave functions with up to 10 orders of magnitude fewer determinants for the systems presented here. These ALCI wave functions are promising and affordable starting points for the subsequent second-order perturbation theory or pair-density functional theory calculations.

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 ¹(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 (K) between the triplets which leads to the spin splitting of the biexciton state into ¹(TT),³(TT) and ⁵(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state ¹(T···T). We develop a simple ab initio technique to compute both the biexciton exchange (K) and biexciton transfer coupling. Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene.

Reinforcement Learning Configuration Interaction

Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. We explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

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. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the MBE. This method, named cluster MBE (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from a RHF reference. We present numerical results for strongly correlated systems, such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended π space of several large π-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 10⁶⁶ determinants for the exact FCI solution.

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)₄S₄] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.

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 (J. Comput. Theor. Chem., 2014, 10, 3669). External relaxations are performed in the spin-flip calculations through a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals, and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.

Configuration interaction trained by neural networks: Application to model polyaromatic hydrocarbons

The main bottleneck of a stochastic or deterministic configuration interaction method is determining the relative weights or importance of each determinant or configuration, which requires large scale matrix diagonalization. Therefore, these methods can be improved significantly from a computational standpoint if the relative importance of each configuration in the ground and excited states of molecular/model systems can be learned using machine learning techniques such as artificial neural networks (ANNs). We have used neural networks to train the configuration interaction coefficients obtained from full configuration interaction and Monte Carlo configuration interaction methods and have tested different input descriptors and outputs to find the more efficient training techniques. These ANNs have been used to calculate the ground states of one- and two-dimensional Heisenberg spin chains along with Heisenberg ladder systems, which are good approximations of polyaromatic hydrocarbons. We find excellent efficiency of training and the model this trained was used to calculate the variational ground state energies of the systems.

Reduction of the molecular hamiltonian matrix using quantum community detection

Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree-Fock methods as future advances in quantum hardware become available.

The Shape of Full Configuration Interaction to Come

We present a Perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 2020 11, 8922]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years-the past decade, in particular-it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.