Dynamic Electron Correlation Research Articles

An “ultimate” coupled cluster method based entirely on T2

Electronic structure methods built around double-electron excitations have a rich history in quantum chemistry. However, it seems to be the case that such methods are only suitable in particular situations and are not naturally equipped to simultaneously handle the variety of electron correlations that might be present in chemical systems. To this end, the current work seeks a computationally efficient, low-rank, “ultimate” coupled cluster method based exclusively on T2 and its products that can effectively emulate more “complete” methods that explicitly consider higher-rank, T2m, operators. We introduce a hierarchy of methods designed to systematically account for higher, even order cluster operators, such as T4, T6, …, T2m, by invoking tenets of the factorization theorem of many-body perturbation theory (MBPT) and expectation-value coupled cluster theory. It is shown that each member within this methodological hierarchy is defined such that both the wavefunction and energy are correct through some order in MBPT and can be extended up to arbitrarily high orders in T2. The efficacy of such approximations are determined by studying the potential energy surface of several closed and open-shell molecules. We find that the proposed hierarchy of augmented T2 methods essentially reduces to standard CCD for problems where dynamic electron correlations dominate but offer improvements in situations where non-dynamic and static correlations become relevant. A notable highlight of this work is that the cheapest methods in this hierarchy—which are correct through fifth-order in MBPT—consistently emulate the behavior of the O(N10) CCDQ method, yet only require a O(N6) algorithm by virtue of factorized intermediates.

Time Delays as Attosecond Probe of Interelectronic Coherence and Entanglement.

Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.

Computational Modeling of the Conformation-Dependent Atmospheric Reactivity of Criegee Intermediates.

The impacts of Criegee intermediates (CIs) on atmospheric chemistry depend significantly on the CI conformation. In this Perspective, I highlight examples of how electronic structure and statistical rate theory calculations, in conjunction with experiment, have revealed conformation-dependent details of both CI ground-state reactivity and electronic excitation. Calculations using single-reference electronic structure methods and conventional transition state theory have predicted that CIs with syn-alkyl or syn-vinyl substituents isomerize rapidly to vinyl hydroperoxides (VHPs) or dioxoles, both of which can decompose rapidly under atmospheric conditions. Ongoing computational research on hydroxyl radical (OH) roaming initiated by VHP dissociation requires the application of multireference electronic structure methods and variational transition state theory. CIs that lack both syn-alkyl and syn-vinyl substituents undergo either bimolecular reaction or π* ← π electronic excitation in the atmosphere. Accurate predictions of CI ultraviolet-visible spectra require multireference calculations with large active spaces and at least a second-order perturbative treatment of dynamic electron correlation. The extent to which electronic spectra can be diagnostic of the presence of specific CI conformers varies significantly with CI chemical identity.

Nonsequential double ionization of Ar in two-color inhomogeneous laser fields

With the classical ensemble method, we investigate the correlated electron dynamics in nonsequential double ionization (NSDI) of Ar in parallel two-color inhomogeneous laser fields with different inhomogeneity parameter ϵ. Numerical results show that at low laser intensities, the probability of NSDI is higher for two-color laser fields with a higher inhomogeneity parameter ϵ. At high laser intensities, however, the probability of NSDI decreases as ϵ increases. It is also shown that under low laser intensities, the two-color inhomogeneous laser fields drives the NSDI predominantly dominated by the RII channel, and the ratio of the RII channel increases as ϵ increases. More interestingly, an arc-like structure is found in the correlated electron momentum distributions for the two-color inhomogeneous laser fields. The underlying dynamics are revealed by tracing back to classical trajectories.

Ab initio extended Hubbard model of short polyenes for efficient quantum computing.

We propose introducing an extended Hubbard Hamiltonian derived via the abinitio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-normof the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional abinitio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the abinitio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.

Simulation of Vibrational Circular Dichroism Spectra Using Second-Order Møller-Plesset Perturbation Theory and Configuration Interaction Doubles.

We present the first single-reference calculations of the atomic axial tensors (AATs) with wave function-based methods including dynamic electron correlation effects using second-order Møller-Plesset perturbation theory (MP2) and configuration interaction doubles (CID). Our implementation involves computing the overlap of numerical derivatives of the correlated wave functions with respect to both nuclear displacement coordinates and the external magnetic field. Out test set included three small molecules, including the axially chiral hydrogen molecule dimer and (P)-hydrogen peroxide, and the achiral H2O. For our molecular test set, we observed deviations of the AATs for MP2 and CID from that of the Hartree-Fock (HF) method upward of 49%, varying with the choice of basis set. For (P)-hydrogen peroxide, electron correlation effects on the vibrational circular dichroism (VCD) rotatory strengths and corresponding spectra were particularly significant, with maximum deviations of the rotatory strengths of 62 and 49% for MP2 and CID, respectively, using our largest basis set. The inclusion of dynamic electron correlation to the computation of the AATs can have a significant impact on the resulting rotatory strengths and VCD spectra.

Coherent Charge Hopping Suppresses Photoexcited Polarons in ErFeO3

We measure how coherent charge hopping competes with and slows small polaron formation. The coupling of photoexcited charge carriers with phonons in the crystal lattice that results in polaron formation causes carrier localization and limits transport to site-to-site hopping. ErFeO3, a rare-earth orthoferrite, is designed where the large rare earth atom frustrates the FeO6 octahedra, reducing the energetic favorability of polaron formation. We compare transient extreme ultraviolet (XUV) measurements with ab initio theory and transport measurements to quantify the polaron formation rate and mobility. Polaron formation occurs within several picoseconds following multiple coherent charge hopping events between neighboring Fe3+–Fe2+ sites. This timescale is more than an order of magnitude longer compared to previously studied materials. The delay in polaron formation is notable because the photoexcited carriers shed excess thermal energy before forming the polaron. To date, polarons have been measured to form instantaneously with the first electron-phonon scattering event. The measured interplay between optical phonons, electron coupling, and on-site lattice deformation emphasizes the importance of dynamic electron correlations for tuning polaron formation in photocatalysts.

Dynamical Electron Correlation and the Chemical Bond. IV. Covalent Bonds in A2 Molecules (A = N-As and F-Br).

In a series of recent papers, we investigated the effect of dynamical electron correlation on the potential energy curves and spectroscopic constants of several diatomic molecules, including the simple diatomic hydrides (AH) and the more complex diatomic fluorides (AF) and homonuclear diatomic molecules (A2) with A = B-F (AF) or A = C-F (A2), respectively. Our goal was to understand the dependence of the dynamical electron correlation energy, EDEC, on the internuclear distance, R, and quantify how dynamical electron correlation influences the spectroscopic constants (De, Re, and ωe) of these molecules. At large R, we found that the magnitude of EDEC(R) had a simple dependence on R, with EDEC(R) increasing nearly exponentially with decreasing R. However, as R continued to decrease, there were significant variations in EDEC(R). These variations led to differing changes in the predicted spectroscopic constants of the molecules. In many molecules, the changes in EDEC(R) could be correlated with changes in the underlying spin-coupled generalized valence bond wave function, either in the orbitals or the spin-coupling coefficients. In the current paper, we extend these studies to higher main group elements, comparing the effects of EDEC(R) on P2 and As2 versus N2, and on Cl2 and Br2 versus F2. We find that there are significant differences between the effects of dynamical electron correlation on the molecules in the first and subsequent rows of the periodic table.

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory.

Coupled cluster methods based exclusively on double excitations are comparatively "cheap" and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

A new parameterization of the DFT/CIS method with applications to core-level spectroscopy.

Time-dependent density functional theory (TD-DFT) within a restricted excitation space is an efficient means to compute core-level excitation energies using only a small subset of the occupied orbitals. However, core-to-valence excitation energies are significantly underestimated when standard exchange-correlation functionals are used, which is partly traceable to systemic issues with TD-DFT's description of Rydberg and charge-transfer excited states. To mitigate this, we have implemented an empirically modified combination of configuration interaction with single substitutions (CIS) based on Kohn-Sham orbitals, which is known as "DFT/CIS." This semi-empirical approach is well-suited for simulating x-ray near-edge spectra, as it contains sufficient exact exchange to model charge-transfer excitations yet retains DFT's low-cost description of dynamical electron correlation. Empirical corrections to the matrix elements enable semi-quantitative simulation of near-edge x-ray spectra without the need for significant a posteriori shifts; this should be useful in complex molecules and materials with multiple overlapping x-ray edges. Parameter optimization for use with a specific range-separated hybrid functional makes this a black-box method intended for both core and valence spectroscopy. Results herein demonstrate that realistic K-edge absorption and emission spectra can be obtained for second- and third-row elements and 3d transition metals, with promising results for L-edge spectra as well. DFT/CIS calculations require absolute shifts that are considerably smaller than what is typical in TD-DFT.

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin–orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac–Hartree–Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO−D). Employing additional sets of diffuse and core–valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO−D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.

Structural distortion and dynamical electron correlation driven enhanced ferromagnetism in Ni-doped two-dimensional Fe5GeTe2 beyond room temperature

Achieving beyond room-temperature ferromagnetism in two-dimensional (2D) magnets is immensely desirable for spintronic applications. Fe5GeTe2 is an exceptional van der Waals metallic ferromagnet due to its tunable physical properties and relatively higher Curie temperature ( TC ) than other 2D magnets. Using density functional theory combined with dynamical electron correlation and Monte Carlo simulations, we find the TC of (Fe 1−δ Ni δ)5 GeTe2 monolayer can increase up to ∼400 K at δ∼0.20 (δ: fractional occupation). Two specific Fe sublattices are identified to be the most energetically preferred sites to host Ni. Exchange interactions between particular Fe pairs play a dominating role in controlling TC , influenced by the dopant-induced structural distortions. Dynamical electron correlation induces site- and orbital-specific quasi-particle mass of Fe-d states with varying Ni concentrations. This work provides fundamental insights into 2D magnetism as an interplay of structural and electronic aspects and would guide to tailoring exciting magnetic phenomena in similar systems.

Potential-Energy Curves for the Ground and Several Electronic States of NdO and NdS.

Potential energy curves (PECs) were calculated for 21 and 18 electronic states of NdO and NdS molecules, respectively. In each case, static electron correlation effects were described by incomplete model space multiconfiguration self-consistent field wave functions based on an active space that included the most important valence orbitals. Dynamic electron correlation was included by the multireference second-order generalized Van Vleck perturbation theory method. Scalar-relativistic contributions were included by the effective core potential approach, using def2-TZVPP basis sets. Spin-dependent relativistic corrections were determined to be small and negligible for the Nd atom and so were not included in the calculations. The 21 and 18 electronic states of NdO and NdS were predicted to be in the excitation energy range of ∼3.2 and ∼2.7 eV, respectively. The ground electronic states of NdO and NdS were determined as 15H (6s4fσ4fϕ4fδ) and 15H (4fϕ4fπ4fπ6s), with spectroscopic constants: bond length Re = 1.780 and 2.325 Å, and harmonic frequency ωe = 891 and 538 cm-1, respectively.

Unravelling the Highest Magnetic Anisotropy Among all the nd-Shells in [WCp2]0 Metallocene.

Single-molecule magnets (SMMs) with a large magnetization reversal barrier are predominated by the lanthanide systems due to their strong spin-orbit coupling (SOC). However, the transition metals have also emerged as potential contenders and the largest magnetic anisotropy has been identified for a cobalt system among any d-series-based SMMs (Bunting et al. Science 2018, 362, eaat7319). In this work, we have explored the magnetic anisotropy in highly axial ligand field systems of metallocene, having different d-subshell (3d4, 4d4, and 5d4). The wave function-based multireference methods including static and dynamic electron correlations have been employed to investigate the zero-field splitting (ZFS) parameters. Here, we report exceptionally large magnetic anisotropy for a 5d complex of [WCp2]0 with the highest energy barrier that is nearly twice as high as the previous record value for the Co complex. We have also observed that the axial ZFS parameter (D) is increasing down the group in the order of 3d < 4d < 5d, pertaining to a large SOC.

Superconducting transition temperatures of pure vanadium and vanadium-titanium alloys in the presence of dynamical electronic correlations

Superconducting transition temperatures of pure vanadium and vanadium-titanium alloys in the presence of dynamical electronic correlations

Dynamic and relativistic effects on Pt-Pt indirect spin-spin coupling in aqueous solution studied by abinitio molecular dynamics and two- vs four-component density functional NMR calculations.

Treating 195Pt nuclear magnetic resonance parameters in solution remains a considerable challenge from a quantum chemistry point of view, requiring a high level of theory that simultaneously takes into account the relativistic effects, the dynamic treatment of the solvent-solute system, and the dynamic electron correlation. A combination of Car-Parrinello molecular dynamics (CPMD) and relativistic calculations based on two-component zeroth order regular approximation spin-orbit Kohn-Sham (2c-ZKS) and four-component Dirac-Kohn-Sham (4c-DKS) Hamiltonians is performed to address the solvent effect (water) on the conformational changes and JPtPt1 coupling. A series of bridged PtIII dinuclear complexes [L1-Pt2(NH3)4(Am)2-L2]n+ (Am = α-pyrrolidonate and pivalamidate; L = H2O, Cl-, and Br-) are studied. The computed Pt-Pt coupling is strongly dependent on the conformational dynamics of the complexes, which, in turn, is correlated with the trans influence among axial ligands and with the angle N-C-O from the bridging ligands. The J-coupling is decomposed in terms of dynamic contributions. The decomposition reveals that the vibrational and explicit solvation contributions reduce JPtPt1 of diaquo complexes (L1 = L2 = H2O) in comparison to the static gas-phase magnitude, whereas the implicit solvation and bulk contributions correspond to an increase in JPtPt1 in dihalo (L1 = L2 = X-) and aquahalo (L1 = H2O; L2 = X-) complexes. Relativistic treatment combined with CPMD shows that the 2c-ZKS Hamiltonian performs as well as 4c-DKS for the JPtPt1 coupling.

On‐Surface Synthesis and Determination of the Open‐Shell Singlet Ground State of Tridecacene**

AbstractThe character of the electronic structure of acenes has been the subject of longstanding discussion. However, convincing experimental evidence of their open‐shell character has so far been missing. Here, we present the on‐surface synthesis of tridecacene molecules by thermal annealing of octahydrotridecacene on a Au(111) surface. We characterized the electronic structure of the tridecacene by scanning probe microscopy, which reveals the presence of an inelastic signal at 126 meV. We attribute the inelastic signal to spin excitation from the singlet diradical ground state to the triplet excited state. To rationalize the experimental findings, we carried out many‐body ab initio calculations as well as model Hamiltonians to take into account the effect of the metallic substrate. Moreover, we provide a detailed analysis of how the dynamic electron correlation and virtual charge fluctuation between the molecule and metallic surface reduces the singlet‐triplet band gap. Thus, this work provides the first experimental confirmation of the magnetic character of tridecacene.

Dynamical electron correlation and the chemical bond. III. Covalent bonds in the A2 molecules (A = C–F)

The behavior of the dynamical electron correlation energy is remarkably complex at short internuclear distances: ΔEDEC(ΔR) = EDEC(ΔR) − EDEC(R = ∞) with ΔR = R − Re.

Striking the right balance of encoding electron correlation in the Hamiltonian and the wavefunction ansatz.

Multi-configurational electronic structure theory delivers the most versatile approximations to many-electron wavefunctions, flexible enough to deal with all sorts of transformations, ranging from electronic excitations, to open-shell molecules and chemical reactions. Multi-configurational models are therefore essential to establish universally applicable, predictive ab initio methods for chemistry. Here, we present a discussion of explicit correlation approaches which address the nagging problem of dealing with static and dynamic electron correlation in multi-configurational active-space approaches. We review the latest developments and then point to their key obstacles. Our discussion is supported by new data obtained with tensor network methods. We argue in favor of simple electron-only correlator expressions that may allow one to define transcorrelated models in which the correlator does not bear a dependence on molecular structure.

Ab initio calculation of magnetic anisotropy and thermal spin transition in the variable temperature crystal conformations of [Co(terpy)2]2.

The structure-property correlation of [Co(terpy)2]2+, which shows a spin crossover at 270 K, has been computationally investigated based on its variable temperature crystal structures. Among the employed DFT functionals, only the re-parametrized hybrid B3LYP* functional could describe the correct spin transition temperature. Explicit consideration of metal-ligand sigma bonding with dynamic electron correlation is found to be necessary for an accurate determination of the SCO temperature with multi-reference calculations. The metal-ligand axial bond distances are found to be the most significant internal coordinates in deciding SCO. A small structural change along the axial distance causes a change in the t2g orbital splitting pattern and a reorientation of the magnetization axes at the SCO temperature. The complex shows an unusual triaxial magnetic anisotropy, with an easy axis of magnetization developing at higher temperatures. The strong coupling of low-frequency wagging motion of the two terpyridine ligands with the spin states of the complex provides an effective pathway for the relaxation of magnetization, resulting in a small magnetic anisotropy barrier.