Electronic Structure Theory Research Articles

First-principles calculation of alloy scattering and n -type mobility in strained Ge−Sn

We use first-principles electronic-structure theory to determine the intra- and intervalley electron-alloy scattering parameters in -type Ge−Sn alloys. These parameters are used to determine the alloy scattering contributions to the -type electron mobility of Ge−Sn at 300 and 15K using a first iteration of the Boltzmann transport equation in the relaxation-time approximation. For unstrained Ge−Sn, we find that an Sn concentration of at least 13.5% is needed to achieve an electron mobility greater than that of Ge. Our results show that the mobility of Ge−Sn can be over 25 times that of Ge, or 105cm2/(Vs). At 15K, incorporation of less than 6% Sn into Ge quadruples its mobility, which suggests that Ge−Sn has potential applications as a high-mobility 2D electron gas. Applying biaxial tensile strain to Ge−Sn further increases the mobility and achieves this improvement at lower Sn content than in unstrained Ge−Sn. Published by the American Physical Society 2025

A Density Functional Valence Bond Study on the Excited States

The accurate description of excited states is crucial for the development of electronic structure theory. In addition to determining excitation energies, strong state interactions arise when electronic states with the same symmetry are degenerate or nearly degenerate, often requiring a multi-state treatment. These strong correlation effects and state interactions can be effectively handled by the Hamiltonian matrix correction-based density functional valence bond (hc-DFVB) method, a multi-reference density functional theory capable of accurately describing electronic state interactions. In this paper, we explore the low-lying excited states of four isoelectronic systems (C2H, CN, CO⁺, BO) using valence bond methods, including the valence bond self-consistent field (VBSCF) and hc-DFVB methods. Our results show that the hc-DFVB method provides significantly better excitation energies compared to VBSCF. Furthermore, hc-DFVB can reliably predict the correct ordering of excited states, whereas VBSCF shows some ordering inconsistencies. By categorizing the VB structures into groups based on point group symmetry, we can extract the key structural contributions and bonding pictures of each state from the weight distribution of these groups. Additionally, we study the potential energy curves for lithium fluoride (LiF) and a mixed-valence spiro cation, demonstrating the superior performance of hc-DFVB when applied to the study of near-degenerate excited states in the avoided crossing region.

Constrained Nuclear-Electronic Orbital Transition State Theory Using Energy Surfaces with Nuclear Quantum Effects.

Hydrogen-atom transfer is crucial in a myriad of chemical and biological processes, yet the accurate and efficient description of hydrogen-atom transfer reactions and kinetic isotope effects remains challenging due to significant quantum effects on hydrogenic motion, especially tunneling and zero-point energy. In this paper, we combine transition state theory (TST) with the recently developed constrained nuclear-electronic orbital (CNEO) theory to propose a new transition state theory denoted CNEO-TST. We use CNEO-TST with CNEO density functional theory (CNEO-DFT) to predict reaction rate constants for two prototypical gas-phase hydrogen-atom transfer reactions and their deuterated isotopologic reactions. CNEO-TST is similar to conventional TST except that it employs constrained minimized energy surfaces to include zero-point energy and shallow tunneling effects in the effective potential. We find that the new theory predicts reaction rates quite accurately at room temperature. The effective potential surface must be generated by CNEO theory rather than by ordinary electronic structure theory, but because of the favorable computational scaling of CNEO-DFT, the cost is economical even for large systems. Our results show that dynamics calculations with this approach achieve accuracy comparable to variational TST with a semiclassical multidimensional tunneling transmission coefficient at and above room temperature. Therefore, CNEO-TST can be a useful tool for rate prediction, even for reactions involving highly quantal motion, such as many chemical and biochemical reactions involving transfers of hydrogen atoms, protons, or hydride ions.

Data-efficient fine-tuning of foundational models for first-principles quality sublimation enthalpies.

Calculating sublimation enthalpies of molecular crystal polymorphs is relevant to a wide range of technological applications. However, predicting these quantities at first-principles accuracy - even with the aid of machine learning potentials - is a challenge that requires sub-kJ mol-1 accuracy in the potential energy surface and finite-temperature sampling. We present an accurate and data-efficient protocol for training machine learning interatomic potentials by fine-tuning the foundational MACE-MP-0 model and showcase its capabilities on sublimation enthalpies and physical properties of ice polymorphs. Our approach requires only a few tens of training structures to achieve sub-kJ mol-1 accuracy in the sublimation enthalpies and sub-1% error in densities at finite temperature and pressure. Exploiting this data efficiency, we perform preliminary NPT simulations of hexagonal ice at the random phase approximation level and demonstrate a good agreement with experiments. Our results show promise for finite-temperature modelling of molecular crystals with the accuracy of correlated electronic structure theory methods.

Design Criteria for Active and Selective Catalysts in the Nitrogen Oxidation Reaction.

The direct conversion of dinitrogen to nitrate is a dream reaction to combine the Haber-Bosch and Ostwald processes as well as steam reforming using electrochemistry in a single process. Regrettably, the corresponding nitrogen oxidation (NOR) reaction is hampered by a selectivity problem, since the oxygen evolution reaction (OER) is both thermodynamically and kinetically favored in the same potential range. This opens the search for the identification of active and selective NOR catalysts to enable nitrate production under anodic reaction conditions. While theoretical considerations using the computational hydrogen electrode approach have helped in identifying potential material motifs for electrocatalytic reactions over the last decades, the inherent complexity of the NOR, which consists of ten proton-coupled electron transfer steps and thus at least nine intermediate states, poses a challenge for electronic structure theory calculations in the realm of materials screening. To this end, we present a different strategy to capture the competing NOR and OER at the atomic scale. Using a data-driven method, we provide a framework to derive generalized design criteria for materials with selectivity toward NOR. This leads to a significant reduction of the computational costs, since only two free-energy changes need to be evaluated to draw a first conclusion on NOR selectivity.

A General and Transferable Local Hybrid Functional for Electronic Structure Theory and Many-Fermion Approaches.

Density functional theory has become the workhorse of quantum physics, chemistry, and materials science. Within these fields, a broad range of applications needs to be covered. These applications range from solids to molecular systems, from organic to inorganic chemistry, or even from electrons to other Fermions, such as protons or muons. This is emphasized by the plethora of density functional approximations that have been developed for various cases. In this work, two new local hybrid exchange-correlation density functionals are constructed from first-principles, promoting generality and transferability. We show that constraint satisfaction can be achieved even for admixtures with full exact exchange, without sacrificing accuracy. The performance of the new functionals CHYF-PBE and CHYF-B95 is assessed for thermochemical properties, excitation energies, Mössbauer isomer shifts, NMR spin-spin coupling constants, NMR shieldings and shifts, magnetizabilities, and EPR hyperfine coupling constants. Here, the new density functional shows excellent performance throughout all tests and is numerically robust only requiring small grids for converged results. Additionally, both functionals can easily be generalized to arbitrary Fermions as shown for electron-proton correlation energies. Therefore, we outline that density functionals generated in this way are general purpose tools for quantum mechanical studies.

Extended Active Space Ab Initio Ligand Field Theory: Applications to Transition-Metal Ions.

Ligand field theory (LFT) is one of the cornerstones of coordination chemistry since it provides a conceptual framework in which a great many properties of d- and f-element compounds can be discussed. While LFT serves as a powerful qualitative guide, it is not a tool for quantitative predictions on individual compounds since it incorporates semiempirical parameters that must be fitted to experiment. One way to connect the realms of first-principles electronic structure theory that has emerged as particularly powerful over the past decade is the ab initio ligand field theory (AILFT). The original formulation of this method involved the extraction of LFT parameters by fitting the ligand field Hamiltonian to a complete active space self-consistent field (CASSCF) Hamiltonian. The extraction was shown to be unique provided that the active space consists of 5/7 metal d/f-based molecular orbitals (MOs). Subsequent improvements have involved incorporating dynamical correlation using second-order N-electron valence state perturbation theory (NEVPT2) or second-order dynamical correlation dressed complete active space (DCDCAS). However, the limitation of past approaches is that the method requires a minimal space of 5/7 metal d- or f-based molecular orbitals. This leads to a number of limitations: (1) neglect of radial or semicore correlation would arise from the effect of a second d-shell or an sp-shell in the active space, (2) a more balanced description of metal-ligand bond covalency is lacking because the bonding ligand-based counterparts of the metal d/f orbitals are not in the active space. This usually leads to an exaggerated ionicity of the M-L bonds. In this work, we present an extended active space AILFT (esAILFT) that circumvents these limitations and is, in principle, applicable to arbitrary active spaces, as long as these contain the 5/7 metal d/f-based MOs as a subset. esAILFT was implemented in a development version of the ORCA software package. In order to help with the application of the new method, various criteria for active space extension were explored for 3d, 4d, and 5d transition-metal ions with varying charge. An interpretation of the trends in the Racah B parameter for these ions is also presented as a demonstration of the capabilities of esAILFT.

X2-GNN: A Physical Message Passing Neural Network with Natural Generalization Ability to Large and Complex Molecules.

Neural network models excel in molecular property predictions but often struggle with generalizing from smaller to larger molecules due to increased structural diversity and complex interactions. To address this, we introduce an E(3) invariant (and equivariant capable) message passing graph neural network (GNN), namely, X2-GNN, that integrates physical insights via atomic orbital overlap integrals and core Hamiltonians. These features provide essential information about bond strength, electron delocalization, and many-body interactions, enhanced by an attention mechanism for improved learning efficiency. Benchmarked against mainstream GNNs on diverse data sets, X2-GNN trained solely on the QM9 data set (up to nine heavy atoms) effectively generalizes to larger molecules with tens of heavy atoms, achieving credible per-atom error rates. It also excels in potential energy surface modeling and accurately predicts the bond dissociation energy within subseconds. These results highlight X2-GNN's scalability and broad applicability, emphasizing the importance of integrating data-driven approaches with basic knowledge from electronic structure theory.

Electronic Spectroscopy of the Halogenated Criegee Intermediate, ClCHOO: Experiment and Theory.

A chlorine-substituted Criegee intermediate, ClCHOO, is photolytically generated using a diiodo precursor, detected by VUV photoionization at 118 nm, and spectroscopically characterized via ultraviolet-visible (UV-vis)-induced depletion of m/z = 80 under jet cooled conditions. UV-vis excitation resonant with a π* ← π transition yields a significant ground state depletion, indicating a strong electronic transition and rapid photodissociation. The broad absorption spectrum peaks at 350 nm and is attributed to contributions from both syn (∼70%) and anti (∼30%) conformers of ClCHOO based on spectral simulations using a nuclear ensemble method. Electronic structure theory shows significant differences in the vertical excitation energies of the two conformers (330 and 371 nm, respectively) as well as their relative stabilities in the ground and excited electronic states associated with the π* ← π transition. Natural bond orbital analysis reveals significant and nonintuitive nonbonding contributions to the relative stabilities of the syn and anti conformers.

Enhancing Two-Photon Absorption of Green Fluorescent Protein by Quantum Entanglement.

Exploring the electronic states of molecules through excitation with entangled and classical photon pairs offers new insights into the nature of light-matter interactions and stimulates the development of quantum spectroscopy. Here, we address the importance of temporal entanglement of light in two-photon absorption (TPA) upon the S0 → S1 transition by the green fluorescent protein (GFP)─a key molecular unit in the bioimaging of living cells. By invoking a two-level model applicable when permanent dipole pathways dominate the two-photon transition, we derive a convenient closed-form analytical expression for the entangled TPA strength. For the first time, we disclose specific molecular properties that cause classical and entangled two-photon absorptions to be qualitatively different when exciting the same state. We reveal a new nonclassical contribution to the TPA strength, which is defined by the magnitude and directional alignment of permanent dipole moments in the initial and final states. Using high-level electronic structure theory, we show that the nonclassical contribution is intrinsically larger than the classical counterpart in GFP, leading to an enhancement of the TPA strength due to quantum entanglement by several orders of magnitude. We also present evidence that the classical and quantum TPA strengths can be modulated differently by the protein environment and demonstrate how to control the outcome by alterations in the local electric field of the protein caused by a single amino acid replacement. Our findings establish physical grounds for enhancing TPA in photoactive proteins by quantum entanglement, facilitating the rational design of high-efficiency biomarkers for future applications that utilize quantum light.

Many-body expansion based machine learning models for octahedral transition metal complexes

Abstract Graph-based machine learning (ML) models for material properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, a molecular graph featurization method, for predicting spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used ML methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary TMCs, the best MBE models achieve mean absolute errors (MAEs) of 2.75 kcal mol−1 on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30%–40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit MAEs of 4.00 kcal mol−1 (i.e. a 0.73 kcal mol−1 reduction) on the spin-splitting energies and 0.53 eV (i.e. a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

A detailed analysis of the key steps of the cyclopentene autoignition mechanism from calculated RRKM rate constants associated with ignition delay time simulations

Cyclopentene, a prototype for studying the combustion chemistry of cyclic olefins, appears in the oxidation of cyclic hydrocarbons and can provide key information in the understanding of the formation of polycyclic aromatic hydrocarbons. The ▪ addition to the double-bond is one of the main steps in low-temperature oxidation mechanisms of unsaturated organic compounds. In the case of cyclopentene, addition of ▪ yields a hydroxycyclopentyl radical, that can further react with O2. In this work, we studied the potential energy surface and reaction rates for the subsequent reactions of O2 with the hydroxycyclopentyl radical. The temperature and pressure dependence of the rate constants were determined using master equation simulations, with microcanonical rate coefficients calculated by RRKM theory. The potential energy surface was extracted from high-level electronic structure theory, based on geometries and frequencies obtained using density functional theory. Our results indicate that a Waddington-type mechanism, which produces glutaraldehyde and regenerates ▪ , is the dominant reaction pathway. However, at low-temperatures, a secondary pathway leading to the formation of epoxycyclopentanol and ▪ becomes equally significant. The thermochemistry of all ▪ radicals involved were also evaluated. The kinetic and thermodynamic data were incorporated into a comprehensive mechanism of cyclopentene autoignition, in order to simulate the associated ignition delays. The updated reaction mechanism resulted in shorter ignition delays compared to the non-updated mechanism. Sensitivity analysis was performed to identify the primary contributors.Novelty and Significance StatementCyclopentene is an important intermediate in the oxidation of cyclic olefins and serves as a precursor in the formation of polycyclic aromatic hydrocarbons. Kinetic modeling studies require detailed information on elementary reactions, much of which is typically unavailable from experiments. The novelty and significance of this study lie in the theoretical calculations of rate constants for key reactions in the oxidation of cyclopentene and their evaluation within the comprehensive mechanism proposed by Lokachari et al. The results demonstrate that the studied reactions significantly influence the ignition delays of cyclopentene at low temperatures. Furthermore, the data presented here can be applied in future studies focusing on the oxidation of cyclic olefins.

Analytical treatment of the Yukawa screened Coulomb interaction in a plane-wave basis

The calculation of the many-electron (screened) Coulomb and exchange integrals is a very common task to perform in modern electronic structure theory. While an analytical treatment of the complete integrals is too complicated to be attempted directly, essential insight can be gained by focusing on the most significant contributions, as determined by a physical criterion. The monopole term of the screened Coulomb interaction is particularly important, since it defines the Hubbard interaction U among a set of localized electrons, which is an essential parameter for effective models of strongly correlated systems. Here, we derive an analytical solution for the matrix elements of the screened Coulomb interaction on a plane-wave basis, which is routinely used in the most common methods for electronic structure calculations. Screening is treated using a Yukawa potential, which is suitable to describe the valence electrons in the Fermi level region. For the solution of the integrals, the plane waves and the Yukawa potential are first expanded in Bessel functions of first and second kind. Then, by means of the lower and upper incomplete gamma functions, we are able to obtain closed-form integrals of a series that remains convergent for realistic parameters. Our exact solution for the radial integrals of the monopole term can find usage in plane-wave codes for electronic structure calculations, both as an output tool as well as within the computational cycle, as e.g., for many-body extensions of density-functional theory. Considering the importance of Bessel functions in solid state physics and electronic structure theory, it is also easy to foresee that our solution to the various integrals across this work may become useful to several other problems in the field.

Non-adiabatic Couplings in Surface Hopping with Tight Binding Density Functional Theory: The Case of Molecular Motors.

Nonadiabatic molecular dynamics (NAMD) has become an essential computational technique for studying the photophysical relaxation of molecular systems after light absorption. These phenomena require approximations that go beyond the Born-Oppenheimer approximation, and the accuracy of the results heavily depends on the electronic structure theory employed. Sophisticated electronic methods, however, make these techniques computationally expensive, even for medium size systems. Consequently, simulations are often performed on simplified models to interpret the experimental results. In this context, a variety of techniques have been developed to perform NAMD using approximate methods, particularly density functional tight binding (DFTB). Despite the use of these techniques on large systems, where ab initio methods are computationally prohibitive, a comprehensive validation has been lacking. In this work, we present a new implementation of trajectory surface hopping combined with DFTB, utilizing nonadiabatic coupling vectors. We selected the methaniminium cation and furan systems for validation, providing an exhaustive comparison with the higher-level electronic structure methods. As a case study, we simulated a system from the class of molecular motors, which has been extensively studied experimentally but remains challenging to simulate with ab initio methods due to its inherent complexity. Our approach effectively captures the key photophysical mechanism of dihedral rotation after the absorption of light. Additionally, we successfully reproduced the transition from the bright to dark states observed in the time-dependent fluorescence experiments, providing valuable insights into this critical part of the photophysical behavior in molecular motors.

Creating Benchmarks for Lithium Clusters and Using Them for Testing and Validation.

Metal clusters often have a variety of possible structures, and they are calculated by a wide range of methods; however, fully converged benchmarks on the energy differences of structures and spin states that could be used to test or validate these methods are rare or nonexistent. Small lithium clusters are good candidates for such benchmarks to test different methods against well-converged relative energetics for qualitatively different structures because they have a small number of electrons. The present study provides fully converged benchmarks for Li4 and Li5 clusters and uses them to test a diverse group of approximation methods. To create a dataset of well-converged single-point energies for Li4 and Li5, stationary structures were optimized by Kohn-Sham density functional theory (KS-DFT) and then single-point energy calculations at these structures were carried out by two quite different beyond-CCSD(T) methods. To test other methods single-point energy calculations at these structures were carried out by KS-DFT, Mo̷ller-Plesset (MP) theory, coupled cluster (CC) theory, five composite methods (Gaussian-4, the Wuhan-Minnesota (WM) composite method, and the W2X, W3X, and W3X-L composite methods of Radom and co-workers), multiconfiguration pair-density functional theory (MC-PDFT), complete active space second-order perturbation theory (CASPT2), and n-electron valence state second-order perturbation theory (NEVPT2). Our results show that rhomboid and trigonal bipyramid (TBP) geometries are the most stable structures for Li4 and Li5, respectively. Using the W3X-L method to obtain our best estimates, the mean unsigned deviations were calculated for other methods for several structures and spin states of both Li4 and Li5. Binding energies and M diagnostics were calculated for all structures. The data in this paper are valuable for assessing the reliability of current electronic structure theories and also developing new density functionals and machine learned models.

From Gas to Solution: The Changing Neutral Structure of Proline upon Solvation.

Liquid-jet photoelectron spectroscopy (LJ-PES) and electronic-structure theory were employed to investigate the chemical and structural properties of the amino acid l-proline in aqueous solution for its three ionized states (protonated, zwitterionic, and deprotonated). This is the first PES study of this amino acid in its biologically relevant environment. Proline's structure in the aqueous phase under neutral conditions is zwitterionic, distinctly different from the nonionic neutral form in the gas phase. By analyzing the carbon 1s and nitrogen 1s core levels as well as the valence spectra of aqueous-phase proline, we found that the electronic structure is dominated by the protonation state of each constituent molecular site (the carboxyl and amine groups) with small yet noticeable interference across the molecule. The site-specific nature of the core-level spectra enables the probing of individual molecular constituents. The valence photoelectron spectra are more difficult to interpret because of the overlapping signals of proline with the solvent and pH-adjusting agents (HCl and NaOH). Yet, we are able to reveal subtle effects of specific (hydrogen-bonding) interaction with the solvent on the electronic structure. We also demonstrate that the relevant conformational space is much smaller for aqueous-phase proline than for its gas-phase analogue. This study suggests that caution must be taken when comparing photoelectron spectra for gaseous- and aqueous-phase molecules, particularly if those molecules are readily protonated/deprotonated in solution.

Comparing parameterized and self-consistent approaches to abinitio cavity quantum electrodynamics for electronic strong coupling.

Molecules under strong or ultra-strong light-matter coupling present an intriguing route to modify chemical structure, properties, and reactivity. A rigorous theoretical treatment of such systems requires handling matter and photon degrees of freedom on an equal quantum mechanical footing. In the regime of molecular electronic strong or ultra-strong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of abinitio quantum chemistry, yielding an approach referred to as abinitio cavity quantum electrodynamics (ai-QED), where the photon degrees of freedom are treated at the level of cavity QED. We analyze two complementary approaches to ai-QED: (1) a parameterized ai-QED, a two-step approach where the matter degrees of freedom are computed using existing electronic structure theories, enabling the construction of rigorous ai-QED Hamiltonians in a basis of many-electron eigenstates, and (2) self-consistent ai-QED, a one-step approach where electronic structure methods are generalized to include coupling between electronic and photon degrees of freedom. Although these approaches are equivalent in their exact limits, we identify a disparity between the projection of the two-body dipole self-energy operator that appears in the parameterized approach and its exact counterpart in the self-consistent approach. We provide a theoretical argument that this disparity resolves only under the limit of a complete orbital basis and a complete many-electron basis for the projection. We present numerical results highlighting this disparity and its resolution in a particularly simple molecular system of helium hydride cation, where it is possible to approach these two complete basis limits simultaneously. In this same helium hydride system, we examine and compare the practical issue of the computational cost required to converge each approach toward the complete orbital and many-electron bases limit. Finally, we assess the aspect of photonic convergence for polar and charged species, finding comparable behavior between parameterized and self-consistent approaches.

Convolutional network learning of self-consistent electron density via grid-projected atomic fingerprints

The self-consistent field (SCF) generation of the three-dimensional (3D) electron density distribution (ρ) represents a fundamental aspect of density functional theory (DFT) and related first-principles calculations, and how one can shorten or bypass the SCF loop represents a critical question in electronic structure theory from both practical and fundamental standpoints. Herein, a machine learning strategy, DeepSCF, is presented in which the map between the SCF ρ and the initial guess density (ρ0) constructed by the summation of neutral atomic densities is learned using 3D convolutional neural networks (CNNs). High accuracy and transferability of DeepSCF are achieved by first encoding ρ0 on a 3D grid and then expanding the input features to include atomic fingerprints beyond ρ0. The prediction of the residual density (δρ) rather than ρ itself is targeted, and given that δρ is indicative of chemical bonding information, a dataset of small-sized organic molecules featuring diverse bonding characters is adopted. The fidelity of DeepSCF is finally enhanced by subjecting the atomic geometries of the dataset to random rotations and strains. The effectiveness of DeepSCF is demonstrated using a complex carbon nanotube-based DNA sequencer model. This work evidences that the nearsightedness in electronic structure can be optimally represented via the spatial locality in CNNs, offering insight into the success of various machine learning-based atomistic materials simulations.

Ground and Excited Electronic Structure Analysis of FeH with Correlated Wave Function Theory and Density Functional Approximations.

FeH is one of the most challenging diatomic molecules to study under electronic structure theory. Here, we have successfully studied 22 electronic states of FeH using ab initio multireference configuration interaction (MRCI), Davidson-corrected MRCI (MRCI+Q), and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] levels of theory. We report their potential energy curves (PECs), excitation energies, dissociation energies, equilibrium electronic configurations, and a series of spectroscopic constants with the use of augmented triple-ζ, quadruple-ζ, and quintuple-ζ quality correlation consistent basis sets. The scalar relativistic effects and active space and core electron correlation contribution on the properties of FeH are also explored. The use of a large CASSCF active space that includes 4s, 4p, 3d, and 4d orbitals of Fe and the 1s of H is critical for producing accurate full PECs with proper dissociations and predicting the exact order of the electronic states. Our findings are in harmony with the experimental results available in the literature and will serve as reference values for future studies of FeH. Furthermore, with the use of PECs, the total internal partition function sum (TIPS) of FeH was calculated across a range of temperatures. Finally, we exploited the single-reference nature of the a6Δ of FeH and its ionized product FeH+ (X5Δ) to evaluate the associated density functional theory (DFT) errors on their dissociation energies and spectroscopic parameters.

Toward a resource-optimized dynamic quantum algorithm via non-iterative auxiliary subspace corrections.

Recent quantum algorithms pertaining to electronic structure theory primarily focus on the threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more accurate by tuning the threshold to include a greater number of operators into the ansatz. However, such improvements come at the cost of rapid proliferation of the circuit depth, especially for highly correlated molecular systems. In this work, we address this issue by the development of a novel theoretical framework that relies on the segregation of an ansatz into a dynamically selected core "principal" component, which is, by construction, adiabatically decoupled from the remaining operators. This enables us to perform computations involving the principal component using extremely shallow-depth circuits, whereas the effect of the remaining "auxiliary" component is folded into the energy function via a cost-efficient non-iterative correction, ensuring the requisite accuracy. We propose a formalism that analytically predicts the auxiliary parameters from the principal ones, followed by a suite of non-iterative auxiliary subspace correction techniques with different levels of sophistication. The auxiliary subspace corrections incur no additional quantum resources yet complement an inadequately expressive core of the ansatz to recover a significant amount of electronic correlations. We have numerically validated the resource efficiency and accuracy of our formalism with a number of strongly correlated molecular systems.