Higher-order Correlation Effects Research Articles

Cumulant Green's function methods for molecules.

The cumulant expansion of the Green's function is a computationally efficient beyond-GW approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous GW approximation of many-body perturbation theory, ab initio cumulant expansions performed on top of GW (GW + C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of GW + C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (Ne, HF, H2O, NH3, and CH4) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available.

Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory.

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter (α) was set to recover the exact dissociation limit of H2 in a minimal basis set. Alternatively α can be viewed as a regularization parameter, where each value of α represents a valid variant of BW-s2, which we denote as BW-s2(α). In this work, we semi-empirically optimize α for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the abinitio parameterization of BW-s2 and MP2. We demonstrate that the optimal α parameter (α = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2(α) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2(α) is iterative O(N5), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

Ab initio potential energy surface and vibration-rotation energy levels of magnesium monohydroxide revisited

The accurate potential energy surface of magnesium monohydroxide, MgOH, in its ground electronic state X˜2Σ+ has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. The core-electron correlation, higher-order electron correlation, scalar relativistic, and adiabatic effects were taken into account. The equilibrium configuration of the MgOH molecule was confirmed to be linear, although with the bending potential energy function being very flat near the minimum. The vibration–rotation-spin energy levels of the MgOH, MgOD, 25MgOH, and 26MgOH isotopologues were predicted using a variational approach. The spectroscopic constants of these isotopologues were determined to high accuracy.

Complex-scaled ab initio QED approach to autoionizing states

Ab initio method based on a complex-scaling approach and aimed at a rigorous QED description of autoionizing states is worked out. The autoionizing-state binding energies are treated nonperturbatively in $\alpha Z$ and include all the many-electron QED contributions up to the second order. The higher-order electron correlation, nuclear recoil, and nuclear polarization effects are taken into account as well. The developed formalism is demonstrated on the $LL$ resonances in heliumlike argon and uranium. The most accurate theoretical predictions for the binding energies are obtained.

Regularized Second-Order Møller-Plesset Theory: A More Accurate Alternative to Conventional MP2 for Noncovalent Interactions and Transition Metal Thermochemistry for the Same Computational Cost.

Second-order Møller-Plesset theory (MP2) notoriously breaks down for π-driven dispersion interactions and dative bonds in transition metal complexes. Herein, we investigate three physically justified forms of single-parameter, energy-gap dependent regularization which can yield high and transferable accuracy for a variety of noncovalent interactions (including S22, S66, and L7 test sets) and (mostly closed shell) transition metal thermochemistry. Regularization serves to damp overestimated pairwise additive contributions, renormalizing first-order amplitudes such that the effects of higher-order correlations are incorporated. The optimal parameter values for the noncovalent and transition metal sets are 1.1, 0.7, and 0.4 for κ, σ, and σ2 regularizers, respectively. However, such regularization slightly degrades the accuracy of conventional MP2 for some small-molecule test sets, most of which have relatively large average frontier energy gaps. Our results suggest that appropriately regularized MP2 models may improve double hybrid density functionals, at no additional cost over conventional MP2.

The role of QED effects in transition energies of heavy-atom alkaline earth monofluoride molecules: A theoretical study of Ba+, BaF, RaF, and E120F.

Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. A comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects' contribution into characteristics of these neutral heavy-atom molecules have been performed. Recently, we have formulated and implemented such an approach to calculate QED contributions to transition energies of molecules [L. V. Skripnikov, J. Chem. Phys. 154, 201101 (2021)]. In this paper, we perform a benchmark theoretical study of the transition energies in the Ba+ cation and BaF molecule. The deviation of the calculated values from the experimental ones is of the order 10 cm-1 and is more than an order of magnitude better than the "chemical accuracy," 350 cm-1. The achievement of such an agreement has been provided, in particular, by the inclusion of the QED effects. The latter appeared to be not less important than the high-order correlation effects beyond the coupled cluster with single, double, and perturbative triple cluster amplitude level. We compare the role of QED effects for transition energies with heavier molecules-RaF and E120F, where E120 is the superheavy Z = 120 homologof Ra.

Signatures of moiré trions in WSe2/MoSe2 heterobilayers.

Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators1-4, superconductors5-10 and generalized Wigner crystals2. When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects11-16. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. Here we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.

Энергия связи основного состояния бериллиеподобного молибдена: корреляционные и квантово-электродинамические эффекты

High-precision calculations of the ground-state binding energy of berylliumlike molybdenum ($Z=42$) are performed. The applied approach merges rigorous quantum-electrodynamics (QED) treatment up to the second order of perturbation theory in the framework of the Furry picture and the third- and higher-order correlation effects evaluated within the Breit approximation. The mixing of the close configurations of the same symmetry due to the electron--electron interaction is considered by employing the QED perturbation theory for quasi-degenerate levels. The most accurate up-to-date theoretical predictions for the binding energy are obtained.

Zero-temperature phases of the two-dimensional Hubbard-Holstein model: A non-Gaussian exact diagonalization study

We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wavefunction that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wavefunction exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.

The structure of ScC2 (X̃2A1): A combined Fourier transform microwave/millimeter-wave spectroscopic and computational study.

Pure rotational spectra of Sc13C2 (X̃2A1) and Sc12C13C (X̃2A') have been measured using Fourier transform microwave/millimeter-wave methods. These molecules were synthesized in a DC discharge from the reaction of scandium vapor, produced via laser ablation, with 13CH4 or 13CH4/12CH4, diluted in argon. The NKa,Kc = 10,1 → 00,0, 20,2 → 10,1, 30,3 → 20,2, and 40,4 → 30,3 transitions in the frequency range of 14 GHz-61 GHz were observed for both species, each exhibiting hyperfine splittings due to the nuclear spins of 13C (I = 1/2) and/or Sc (I = 7/2). These data have been analyzed with an asymmetric top Hamiltonian, and rotational, spin-rotation, and hyperfine parameters have been determined for Sc13C2 and Sc12C13C. In addition, a quartic force field was calculated for ScC2 and its isotopologues using a highly accurate coupled cluster-based composite method, incorporating complete basis set extrapolation, scalar relativistic corrections, outer core and inner core electron correlation, and higher-order valence correlation effects. The agreement between experimental and computed rotational constants, including the effective constant (B + C), is ∼0.5% for all three isotopologues. This remarkable agreement suggests promise in predicting rotational spectra of new transition metal-carbon bearing molecules. In combination with previous work on Sc12C2, an accurate structure for ScC2 has been established using combined experimental (B, C) and theoretical (A) rotational constants. The radical is cyclic (or T-shaped) with r(Sc-C) = 2.048(2) Å, r(C-C) = 1.272(2) Å, and ∠(C-Sc-C) = 36.2(1)°. The experimental and theoretical results also suggest that ScC2 contains a C2 - moiety and is largely ionic.

Exciton-Scattering-Induced Dephasing in Two-Dimensional Semiconductors.

Enhanced Coulomb interactions in monolayer transition metal dichalcogenides cause tightly bound electron-hole pairs (excitons) that dominate their linear and nonlinear optical response. The latter includes bleaching, energy renormalizations, and higher-order Coulomb correlation effects like biexcitons and excitation-induced dephasing. While the first three are extensively studied, no theoretical footing for excitation-induced dephasing in exciton-dominated semiconductors is available so far. In this Letter, we present microscopic calculations based on excitonic Heisenberg equations of motion and identify the coupling of optically pumped excitons to exciton-exciton scattering continua as the leading mechanism responsible for an optical-power-dependent linewidth broadening (excitation-induced dephasing) and sideband formation. Performing time-, momentum-, and energy-resolved simulations, we quantitatively evaluate the exciton-induced dephasing for the most common monolayer transition metal dichalcogenides and find an excellent agreement with recent experiments.

Prediction of a Non-Valence Temporary Anion State of (NaCl)2.

The equation-of-motion coupled cluster method is used to characterize the low-lying anion states of (NaCl)2 in its rhombic structure. This species is known to possess a non-valence bound anion of Ag symmetry. Our calculations also demonstrate that it has a non-valence temporary anion of B2u symmetry, about 14 meV above threshold. The potential energy curves of the two anion states and of the ground state of the neutral molecule are reported as a function of distortion along the symmetric stretch normal coordinate. Implications for experimental detection of the temporary anion state are discussed. The sensitivity of the results to the inclusion of high-order correlation effects and of core correlation is examined.

High-precision determination of Lorentz-symmetry-violating parameters in Ca+

We present high-precision calculations of local Lorentz invariance (LLI) violating parameters of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2;5/2}$ states in ${\mathrm{Ca}}^{+}$. We have employed three variants of the relativistic coupled-cluster (RCC) theory to determine these coefficients by gradually including electron correlation effects through the single, double, and triple excitation determinants from the Dirac-Hartree-Fock wave function. A precise estimate of the energy shift due to LLI violation depends on accurate evaluations of the expectation values of the square of the momentum operator ($\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$) and a second rank tensor ($\ensuremath{\langle}{T}_{0}^{(2)}\ensuremath{\rangle}$). It is found that the $\ensuremath{\langle}{T}_{0}^{(2)}\ensuremath{\rangle}$ values converge smoothly with the systematic inclusion of higher-order correlation effects in an expectation value evaluation approach, however, that is not the case for $\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$. Similar trends were also observed in the finite-field approach. To circumvent these problems, we determine $\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$ values very precisely by developing and applying an analytic gradient approach in the RCC framework. Corrections due to the Breit and quantum electrodynamics interactions are also estimated. Further, these calculations are validated by evaluating the energies and the quadrupole moments of the above states at different levels of approximations.

Ab initio structure and vibration-rotation dynamics of germylene, GeH2.

Accurate structure and potential energy surface of germylene, GeH2 , in its ground electronic state 1 A1 were determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to sextuple-zeta quality. The Born-Oppenheimer equilibrium structural parameters for the 1 A1 state are estimated to be re (GeH) = 1.5793 Å and ∠e (HGeH) = 91.19∘ . The term value Te for the lowest excited electronic state ã3 B1 of GeH2 is predicted to be 9140 cm-1 . The vibration-rotation energy levels for the 1 A1 state of the 74 GeH2 , 74 GeD2 , 72 GeH2 , and 70 GeH2 isotopologues were determined using a variational approach and compared with the experimental data. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, spin-orbit, and adiabatic effects for prediction of the structure and vibration-rotation dynamics of the GeH2 molecule is discussed. © 2019 Wiley Periodicals, Inc.

Ab initio structure and vibration-rotation dynamics of the formyl and isoformyl cations, HCO+/HOC.

Accurate structure and potential energy surface of the formyl and isoformyl cation system, HCO+/HOC+, in its ground electronic state X̃ 1Σ+ have been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. Both the isomers are confirmed to be linear at equilibrium, with the total energy minimum of HOC+ lying 14 120 cm-1 above that of HCO+ and the HCO+ → HOC+ isomerization energy barrier being 26 870 cm-1 (in the Born-Oppenheimer approximation). The equilibrium structural parameters for HCO+ are estimated to be re(HC) = 1.0919 Å and re(CO) = 1.1058 Å, whereas those for HOC+ are estimated to be re(HO) = 0.9899 Å and re(CO) = 1.1544 Å. The vibration-rotation energy levels were predicted for various isotopologues using a variational approach and compared with the experimental data. For the spectroscopically well characterized formyl cation, the observed vibration-rotation energies and the effective rotational constants are reproduced to within about 2.3 cm-1 and 1.7 MHz, respectively. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, and adiabatic effects in determining the structure and vibration-rotation dynamics of both the isomers is discussed.

QED calculations of the n=2 to n=1 x-ray transition energies in middle- Z heliumlike ions

Ab initio QED calculations of the four x-ray transitions from the $L$ to $K$ shell in heliumlike argon, titanium, iron, copper, and krypton are performed. The binding energies for all the $n=1$ and $n=2$ states are evaluated as well. The calculation approach combines the rigorous QED treatment in the first two orders of the perturbation theory constructed within the extended Furry picture with the third- and higher-order correlation effects evaluated in the Breit approximation. The obtained results are compared with the previous evaluations and available experimental data.

Application of the finite-field coupled-cluster method to calculate molecular properties relevant to electron electric-dipole-moment searches

Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron (eEDM), in order to explore physics beyond the Standard Model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite field coupled cluster approach (FFCC). This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of eEDM searches. We used the relativistic FFCC to calculate molecular properties of interest to eEDM experiments, that is, the effective electric field (Eeff), and the permanent electric dipole moment (PDM). We theoretically determine these quantities for the alkaline earth monofluorides (AEMs), the mercury monohalides (HgX), and PbF. The latter two systems, as well as BaF from the AEMs, are of interest to eEDM searches. We also report the calculations of the properties using a relativistic coupled cluster approach with single, double, and partial triples' excitations, which is considered to be the gold standard of electronic structure calculations. We also present a detailed error estimate, including errors that stem from the choice of basis sets, and higher order correlation effects.

Diverse trends of electron correlation effects for properties with different radial and angular factors in an atomic system: a case study in Ca+

Dependencies of electron correlation effects with the rank and radial behavior of spectroscopic properties are analyzed in the singly charged calcium ion (Ca+). To demonstrate these trends, we have determined field shift constants, magnetic dipole and electric quadrupole hyperfine structure constants, Landé gJ factors, and electric quadrupole moments that are described by electronic operators with different radial and angular factors. Radial dependencies are investigated by comparing correlation trends among the properties that have similar angular factors and vice versa. To highlight these observations, we present results from the mean-field approach to all-orders along with intermediate contributions. Contributions from higher relativistic corrections are also given. These findings suggest that sometime lower-order approximations can give results agreeing with the experimental results, but inclusion of some of higher-order correlation effects can cause large disagreement with the experimental values. Therefore, validity of a method for accurate evaluation of atomic properties can be tested by performing calculations of several properties simultaneously that have diverse dependencies on the angular and radial factors and comparing with the available experimental results. Nevertheless, it is imperative to include full triple and quadrupole excitations in the all-order many-body methods for high-precision calculations that are yet to be developed adopting spherical coordinate system for atomic studies.

Atomic properties of actinide ions with particle-hole configurations

We study the effects of higher-order electronic correlations in the systems with particle-hole excited states using a relativistic hybrid method that combines configuration interaction and linearized coupled-cluster approaches. We find the configuration interaction part of the calculation sufficiently complete for eight electrons while maintaining good quality of the effective coupled-cluster potential for the core. Excellent agreement with experiment was demonstrated for a test case of La$^{3+}$. We apply our method for homologue actinide ions Th$^{4+}$ and U$^{6+}$ which are of experimental interest due to a puzzle associated with the resonant excitation Stark ionization spectroscopy (RESIS) method. These ions are also of interest to actinide chemistry and this is the first precision calculation of their atomic properties.

DFT study of benzyl alcohol/TiO2 interfacial surface complex: reaction pathway and mechanism of visible light absorption.

We propose a new pathway for the adsorption of benzyl alcohol on the surface of TiO2 and the formation of interfacial surface complex (ISC). The reaction free energies and reaction kinetics were thoroughly investigated by density functional calculations. The TiO2 surfaces were modeled by clusters consisting of 4 Ti atoms and 18 O atoms passivated by H, OH group and H2O molecules. Compared with solid-state calculations utilizing the periodicity of the materials, such cluster modeling allows inclusion of the high-order correlation effects that seem to be essential for the adsorption of organic molecules onto solid surfaces. The effects of both acidity and solvation are included in our calculations, which demonstrate that the new pathway is competitive with a previous pathway. The electronic structure calculations based on the relaxed ISC structures reveal that the chemisorption of benzyl alcohol on the TiO2 surface greatly alters the nature of the frontier molecular orbitals. The resulted reduced energy gap in ISC matches the energy of visible light, showing how the adsorption of benzyl alcohol sensitizes the TiO2 surface. Graphical Abstract The chemisorption of benzyl alcohol on TiO2 surface greatly alters the nature of the frontier molecular orbitals and the formed interfacial surface complex can be sensitized by visible light.