Treatment Of Electron Correlation Research Articles

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group.

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

Experimental and Theoretical Insights on the Structural, Electronic, and Magnetic Properties of the Quaternary Selenides EuPrCuSe3 and EuNdCuSe3.

Magnetic semiconductors EuPrCuSe3 and EuNdCuSe3 were obtained by using the halide flux method. Their crystal structures and magnetic properties were studied and discussed. Optical properties of the obtained selenides were studied by the means of diffuse reflectance spectroscopy, which revealed the values of 1.92/1.97 and 0.90/0.94 eV for the direct and indirect band gaps of Ln = Nd/Pr, respectively. The structural, electronic, and magnetic properties of the obtained compounds were additionally studied with spin-polarized density functional theory calculations, wherein both systems were found to be two new examples of semiconducting quaternary selenides with disperse conduction bands of Nd/Pr 5d character. The modeling showed that various magnetic orderings in the systems have subtle influences on the alignments/overlaps between the Se/Cu, Eu, and Pr/Nd bands, and that the spin-state energetics are very dependent upon the treatment of electron correlation, but a distinguishing feature in the case of ferromagnetic coupling is that the spin density on the Se atoms is maximized. Overall, the calculations are in good agreement with the experimental characterization of ferromagnetism in the bulk crystals, wherein the ferromagnetic transition occurs at temperatures of about 2.5 K for EuPrCuSe3 and about 3 K for EuNdCuSe3.

Nonequilibrium Dynamics of the Hubbard Dimer

Electron dynamics in a two‐sites Hubbard model is studied using the nonequilibrium Green's function approach. The study is motivated by the empirical observation that a full solution of the integro‐differential Kadanoff–Baym equation (KBE) is more stable and often accompanied by artificial damping [Marc Puig von Friesen, C. Verdozzi, and C.‐O. Almbladh (2009)] than its time‐linear reformulations relying on the generalized Kadanoff–Baym ansatz (GKBA). Additionally, for conserving theories, numerical simulations suggest that KBE produces natural occupations bounded by one and zero in agreement with the Pauli exclusion principle, whereas, in some regimes, GKBA‐based theories violate this principle. As the first step for understanding these issues, the electron dynamics arising in the adiabatic switching scenario is studied. Many‐body approximations are classified according to the channel of the Bethe–Salpeter equation in which electronic correlations are explicitly treated. They give rise to the so‐called second Born, T‐matrix, and GW approximations. In each of these cases, the model is reduced to a system of ordinary differential equations, which resemble equations of motion for a driven harmonic oscillator with time‐dependent frequencies. A more complete treatment of electronic correlations is achieved by combining different correlation channels, with parquet theory serving as a starting point.

First-Principles Calculations on Diffusion and Association Behavior of Fluoride Ions in Ba-Doped LaF3 Solid Electrolyte

Fluoride ion batteries, which generate electrical energy through the fluorination/de-fluorination reaction of electrode active materials, are expected to be the next-generation storage batteries with high energy density. LaF3 with a tysonite-type structure is known as one of the representative solid-state fluoride ion conductors. Substitutional solid solution of divalent cations such as Ba or Sr ions at La sites forms fluoride ion vacancies as charge compensation, resulting in fluoride ion conductivity. The main objective of this study is to analyze the formation behavior of point defects in LaF3 through quantitative evaluation of their formation energies using first-principles calculations, and to elucidate the conduction mechanism of fluoride ions in LaF3.The plane-wave basis PAW method implemented in VASP code was used for the electronic structure calculations. The electron correlation treatment uses the PBEsol-type potential based on the generalized gradient approximation. Calculations for given point defects were performed. The cutoff energy of the plane wave basis sets was set to 420 eV, and the structure optimization calculations were performed until the Hellmann-Feynman force acting on each atom was less than 0.02 eV/Å.There are three fluoride ion sites (12g, 4d, and 2a) in the unit cell of LaF3. Using the supercell model, we calculated the defect formation energies of fluoride ion vacancies at each site. The formation energies at the 12g, 4d, and 2a sites are 0.17 eV, 0.52 eV, and 0.52 eV, respectively. According to the defect formation energies, fluoride ion vacancies are most likely to form at the 12g sites.To elucidate the elementary processes of fluoride ion transfer between 12g sites by the vacancy mechanism, we performed first-principles calculations and transition state search using the Nudged Elastic Band method. From symmetry, four different pathways exist in the lattice of undoped LaF3. The pathway with the highest energy barrier is shown to have very low transfer energies, 0.17 eV, and the energy barriers of the other pathways are less than 0.1 eV. These results suggest that LaF3 has a potential for very fast fluoride ionic conductivity by the vacancy mechanism. In the presentation, the mechanism of fluoride ion conduction in Ba-doped LaF3 will also be reported. This work was supported by the RISING2 (JPNP16001) and the RISING3 (JPNP21006) projects from the New Energy and Industrial Technology Development Organization (NEDO), Japan.

Introducing the embedded random phase approximation: H2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. We explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods.

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling.

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.

Theoretical molecular spectroscopy of actinide compounds: the ThO molecule

The tiny-core generalised (Gatchina) relativistic pseudopotential (GRPP) model provides an accurate approximation for many-electron Hamiltonians of molecules containing heavy atoms, ensuring a proper description of the effects of non-Coulombian electron-electron interactions, electronic self-energy and vacuum polarisation. Combining this model with electron correlation treatment in the frames of the intermediate Hamiltonian Fock space coupled cluster theory employing incomplete main model spaces, one obtains a reliable and economical tool for excited state modelling. The performance of this method is assessed in applications to ab initio modelling of excited electronic states of the thorium monoxide molecule with term energies below 20,000 cm. Radiative lifetimes of excited states are estimated using truncated expansions of effective and metric operators in powers of cluster amplitudes.

The multichannel i-propyl + O2 reaction system: A model of secondary alkyl radical oxidation.

The i-propyl + O2 reaction mechanism has been investigated by definitive quantum chemical methods to establish this system as a benchmark for the combustion of secondary alkyl radicals. Focal point analyses extrapolating to the abinitio limit were performed based on explicit computations with electron correlation treatments through coupled cluster single, double, triple, and quadruple excitations and basis sets up to cc-pV5Z. The rigorous coupled cluster single, double, and triple excitations/cc-pVTZ level of theory was used to fully optimize all reaction species and transition states, thus, removing some substantial flaws in reference geometries existing in the literature. The vital i-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1) were found 34.8 and 4.4kcal mol-1 below the reactants, respectively. Two β-hydrogen transfer transition states (TS2, TS2') lie above the reactants by (1.4, 2.5) kcal mol-1 and display large Born-Oppenheimer diagonal corrections indicative of nearby surface crossings. An α-hydrogen transfer transition state (TS5) is discovered 5.7kcal mol-1 above the reactants that bifurcates into equivalent α-peroxy radical hanging wells (MIN3) prior to a highly exothermic dissociation into acetone + OH. The reverse TS5 → MIN1 intrinsic reaction path also displays fascinating features, including another bifurcation and a conical intersection of potential energy surfaces. An exhaustive conformational search of two hydroperoxypropyl (QOOH) intermediates (MIN2 and MIN3) of the i-propyl + O2 system located nine rotamers within 0.9kcal mol-1 of the corresponding lowest-energy minima.

Improved semi-experimental equilibrium structure and high-level theoretical structures of ketene.

The millimeter-wave rotational spectrum of ketene (H2C=C=O) has been collected and analyzed from 130 to 750GHz, providing highly precise spectroscopic constants from a sextic, S-reduced Hamiltonian in the Ir representation. The chemical synthesis of deuteriated samples allowed spectroscopic measurements of five previously unstudied ketene isotopologues. Combined with previous work, these data provide a new, highly precise, and accurate semi-experimental (reSE) structure for ketene from 32 independent moments of inertia. This reSE structure was determined with the experimental rotational constants of each available isotopologue, together with computed vibration-rotation interaction and electron-mass distribution corrections from coupled-cluster calculations with single, double, and perturbative triple excitations [CCSD(T)/cc-pCVTZ]. The 2σ uncertainties of the reSE parameters are ≤0.0007 Å and 0.014° for the bond distances and angle, respectively. Only S-reduced spectroscopic constants were used in the structure determination due to a breakdown in the A-reduction of the Hamiltonian for the highly prolate ketene species. All four reSE structural parameters agree with the "best theoretical estimate" (BTE) values, which are derived from a high-level computed re structure [CCSD(T)/cc-pCV6Z] with corrections for the use of a finite basis set, the incomplete treatment of electron correlation, relativistic effects, and the diagonal Born-Oppenheimer breakdown. In each case, the computed value of the geometric parameter lies within the statistical experimental uncertainty (2σ) of the corresponding semi-experimental coordinate. The discrepancies between the BTE structure and the reSE structure are 0.0003, 0.0000, and 0.0004 Å for rC-C, rC-H, and rC-O, respectively, and 0.009° for θC-C-H.

Structure of the normal state and origin of the Schottky anomaly in the correlated heavy-fermion superconductor UTe2

The recently discovered $\mathrm{U}{\mathrm{Te}}_{2}$ superconductor is regarded as a heavy-fermion mixed-valence system with very peculiar properties within the normal and superconducting (SC) states. It shows no signs of magnetic order, but has a strong anisotropy of magnetic susceptibility and SC critical field. In addition to a heavy-fermion-like behavior in the normal state, it exhibits a distinctive Schottky-type anomaly at $\ensuremath{\sim}12$ K and a characteristic excitations gap $\ensuremath{\sim}35\ensuremath{-}40$ K. Here, we show, by virtue of dynamical mean-field theory calculations with a quasiatomic treatment of electron correlations, that ab initio-derived crystal-field splitting of the $5{f}^{2}$ ionic configuration yields agreement with these experimental observations. A close analogy of the normal paramagnetic state of $\mathrm{U}{\mathrm{Te}}_{2}$ to that of $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ in the Kondo arrest scenario is revealed. We consider the impact of anisotropic superexchange interactions within the U-U structural dimer on magnetization and development of strong orbital and magnetic moment fluctuations in $\mathrm{U}{\mathrm{Te}}_{2}$.

Periodic Bootstrap Embedding.

Bootstrap embedding (BE) is a recently developed electronic structure method that has shown great success at treating electron correlation in molecules. Here, we extend BE to treat surfaces and solids where the wave function is represented in periodic boundary conditions using reciprocal space sums (i.e., k-point sampling). The major benefit of this approach is that the resulting fragment Hamiltonians carry no explicit dependence on the reciprocal space sums, allowing one to apply traditional nonperiodic electronic structure codes to the fragments even though the entire system requires careful consideration of periodic boundary conditions. Using coupled cluster singles and doubles (CCSD) as an example method to solve the fragment Hamiltonians, we present minimal basis set CCSD-in-HF results on 1D conducting polymers. We show that periodic BE-CCSD can typically recover ∼99.9% of the electron correlation energy. We further demonstrate that periodic BE-CCSD is feasible even for complex donor-acceptor polymers of interest to organic solar cells─despite the fact that the monomers are sufficiently large that even a Γ-point periodic CCSD calculation is prohibitive. We conclude that BE is a promising new tool for applying molecular electronic structure tools to solids and interfaces.

Assessment of random phase approximation and second-order Møller-Plesset perturbation theory for many-body interactions in solid ethane, ethylene, and acetylene.

The relative energies of different phases or polymorphs of molecular solids can be small, less than a kilojoule/mol. A reliable description of such energy differences requires high-quality treatment of electron correlations, typically beyond that achievable by routinely applicable density functional theory (DFT) approximations. At the same time, high-level wave function theory is currently too computationally expensive. Methods employing an intermediate level of approximations, such as Møller-Plesset (MP) perturbation theory and the random phase approximation (RPA), are potentially useful. However, their development and application for molecular solids has been impeded by the scarcity of necessary benchmark data for these systems. In this work, we employ the coupled-cluster method with singles, doubles, and perturbative triples to obtain a reference-quality many-body expansion of the binding energy of four crystalline hydrocarbons with a varying π-electron character: ethane, ethene, and cubic and orthorhombic forms of acetylene. The binding energy is resolved into explicit dimer, trimer, and tetramer contributions, which facilitates the analysis of errors in the approximate approaches. With the newly generated benchmark data, we test the accuracy of MP2 and non-self-consistent RPA. We find that both of the methods poorly describe the non-additive many-body interactions in closely packed clusters. Using different DFT input states for RPA leads to similar total binding energies, but the many-body components strongly depend on the choice of the exchange-correlation functional.

Dihydropyrene/Cyclophanediene Photoswitching Mechanism Revisited with Spin-Flip Time-Dependent Density Functional Theory: Nature of the Photoisomerization Funnel at Stake!

The complex photoisomerization mechanism of the dihydropyrene (DHP) photochromic system is revisited using spin-flip time-dependent density functional theory (SF-TD-DFT). The photoinduced ring-opening reaction of DHP into its cyclophanediene isomer involves multiple coupled electronic states of different character. A balanced treatment of both static and dynamic electron correlations is required to determine both the photophysical and photochemical paths in this system. The present results provide a refinement of the mechanistic picture provided in a previous complete active space self-consistent field plus second-order perturbation theory (CASPT2//CASSCF) study based on geometry optimizations at the CASSCF level. In particular, the nature of the conical intersection playing the central role of the photochemical funnel is different. While at the CASSCF level, the crossing with the ground state involves a covalent doubly excited state leading to a three-electron/three-center bond conical intersection, SF-TD-DFT predicts a crossing between the ground state and a zwitterionic state. These results are supported by multi-state CASPT2 calculations. This study illustrates the importance of optimizing conical intersections at a sufficiently correlated level of theory to describe a photochemical path involving crossings between covalent and ionic states.

Epitaxially strained ultrathin LaNiO3/LaAlO3 and LaNiO3/SrTiO3 superlattices: A density functional theory + U study

By employing first-principles electronic structure calculations we investigate nickelate superlattices [LaNiO3]1/[LaAlO3]1 and [LaNiO3]1/[SrTiO3]1 with (001) orientation under epitaxial tensile strain. Within density functional theory augmented by mean-field treatment of on-site electronic correlations, the ground states show remarkable dependence on the correlation strength and the strain. In the weakly and intermediately correlated regimes with small epitaxial strain, the charge-disproportionated insulating states with antiferromagneitc order is favored over the other orbital and spin ordered phases. On the other hand, in the strongly correlated regime or under the large tensile strain, ferromagnetic spin states with Jahn-Teller orbital order become most stable. The effect from polar interfaces in LaNiO3]1/[SrTiO3]1 is found to be noticeable in our single-layered geometry. Detailed discussion is presented in comparison with previous experimental and theoretical studies.

Isolated-core quadrupole excitation of highly excited autoionizing Rydberg states

The structure and photoexcitation dynamics of high lying doubly excited states of the strontium atom with high angular momenta are studied in the vicinity of the Sr$^+(N=5)$ threshold. The spectra recorded using resonant multiphoton isolated core excitation are analyzed with calculations based on configuration interaction with exterior complex scaling, which treats the correlated motion of the two valence electrons of Sr from first principles. The results are rationalized with a model based on multichannel quantum-defect theory and transition dipole moments calculated with a perturbative treatment of electron correlations. Together, both approaches reveal that most of the lines observed in the spectra arise from the interaction of a single optically active state, coupled to the initial state by an electric-dipole transition, with entire doubly-excited Rydberg series. The long-range electron correlations responsible for this interaction unexpectedly vanish for identical values of the initial and final principal quantum numbers, a fact related to the quasi hydrogenic nature of the high-$l$ Rydberg electron. This special situation, and in particular the vanishing interaction, leads to the surprising observation of an electric \emph{quadrupole} isolated-core excitation with a similar intensity as the neighboring electric dipole transitions.

Perspective: Simultaneous treatment of relativity, correlation, and QED

AbstractElectronic structure calculations of many‐electron systems should in principle treat relativistic, correlation, and quantum electrodynamics (QED) effects simultaneously to a high precision, so as to match experimental measurements as close as possible. While both relativistic and QED effects can readily be built into the many‐electron Hamiltonian, electron correlation is more difficult to describe due to the exponential growth of the number of parameters in the wave function. Compared with the spin‐free case, spin–orbit interaction results in the loss of spin symmetry and concomitant complex algebra, thereby rendering the treatment of electron correlation even more difficult. Possible solutions to these issues are highlighted here.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

A comparison between the one- and two-step spin-orbit coupling approaches based on the ab initio density matrix renormalization group.

The efficient and reliable treatment of both spin-orbit coupling (SOC) and electron correlation is essential for understanding f-element chemistry. We analyze two approaches to the problem: the one-step approach, where both effects are treated simultaneously, and the two-step state interaction approach. We report an implementation of the ab initio density matrix renormalization group with a one-step treatment of the SOC effect, which can be compared to prior two-step treatments on an equal footing. Using a dysprosium octahedral complex and bridged dimer as benchmark systems, we identify characteristics of problems where the one-step approach is beneficial for obtaining the low-energy spectrum.

Route to Chemical Accuracy for Computational Uranium Thermochemistry.

Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO2) and for the bond dissociation energies of UO and UO2 are reported. The accuracy of these calculations in the treatments of relativistic, electron-correlation, and basis-set effects is analyzed. The intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).