Dynamical Correlation Effects Research Articles

Dynamic exchange correlation effects in the strongly coupled electron liquid

The first quasiexact path integral Monte Carlo (PIMC) investigation of the dynamic local field correction G̃(q,zl;rs,Θ) in the imaginary Matsubara frequency domain is reported, focusing on the unpolarized uniform electron gas in the warm dense matter and strongly coupled regimes. The impact of dynamic exchange–correlation effects on the static structure factor is investigated. A straightforward explanation is provided for previously reported spurious effects in the so-called [Dornheim , ], where the frequency dependence of the local field correction is neglected. The comprehensive analysis of the asymptotic Matsubara order behavior, the density dependence, and the temperature dependence hints at the intriguing possibility of constructing an analytical four-parameter representation of G̃(q,zl;rs,Θ) valid for a substantial part of the uniform electron gas phase diagram, which would constitute key input for thermal density functional theory simulations. Published by the American Physical Society 2024

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.

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.

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.

Tailored and Externally Corrected Coupled Cluster with Quantum Inputs.

We propose to use wave function overlaps obtained from a quantum computer as inputs for the classical split-amplitude techniques, tailored and externally corrected coupled cluster, to achieve balanced treatment of static and dynamic correlation effects in molecular electronic structure simulations. By combining insights from statistical properties of matchgate shadows, which are used to measure quantum trial state overlaps, with classical correlation diagnostics, we can provide quantum resource estimates well into the classically no longer exactly solvable regime. We find that rather imperfect wave functions and remarkably low shot counts are sufficient to cure qualitative failures of plain coupled cluster singles doubles and to obtain chemically precise dynamic correlation energy corrections. We provide insights into which wave function preparation schemes have a chance of yielding quantum advantage, and we test our proposed method using overlaps measured on Google's Sycamore device.

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.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12000 basis functions.

Variational Quantum Eigensolver Boosted by Adiabatic Connection.

In this work, we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital-optimized VQE methods are employed to capture the strong correlation within an active space, and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely, the dissociation of N2 and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can actually boost the VQE algorithms. Our work paves the way toward quantum simulations of real-life problems on near-term quantum computers.

A multidimensional appraisal of domestic investment, external debt and economic development nexus: evidence from SSA

PurposeThis study examines the effect of external debt and domestic capital formation on economic development in Sub-Saharan African (SSA) economies.Design/methodology/approachUsing the Dynamic Common Correlation Effects (DCCE) technique and the Driscoll and Kraay fixed-effect technique, this paper conducts a multidimensional assessment of external debt and domestic investment on economic development across a panel of 35 SSA countries from 1995 to 2018. The data utilized are sourced from the World Development Indicators (2021) and the United Nations Development Program (UNDP) database (2021).FindingsThe results reveal that domestic investment has a positive impact on economic development in SSA countries, consistent across all three dimensions of the human development index (income, education and life expectancy). However, external debt exhibits an adverse effect on economic development, consistently yielding negative outcomes for life expectancy, education and income.Practical implicationsBased on these findings, the authors recommend that SSA economies implement appropriate policies, such as reducing bureaucratic requirements and addressing corruption, to enhance domestic capital investment. Additionally, efforts should be directed toward channeling contracted debt into productive sectors like road construction and electricity provision.Originality/valueThis study is among the first to assess the impact of domestic investment and external debt on the three dimensions of human development outlined by the UNDP. Furthermore, it employs a robust econometric method that considers cross-sectional dependence (CD).

Towards structural optimization of gold nanoclusters with quantum Monte Carlo.

We study the prospects of using quantum Monte Carlo techniques (QMC) to optimize the electronic wavefunctions and atomic geometries of gold compounds. Complex gold nanoclusters are widely studied for diverse biochemical applications, but the dynamic correlation and relativistic effects in gold set the bar high for reliable, predictive simulation methods. Here we study selected ground state properties of few-atom gold clusters by using density functional theory (DFT) and various implementations of the variational Monte Carlo (VMC) and diffusion Monte Carlo. We show that the QMC methods mitigate the exchange-correlation (XC) approximation made in the DFT approach: the average QMC results are more accurate and significantly more consistent than corresponding DFT results based on different XC functionals. Furthermore, we use demonstrate structural optimization of selected thiolated gold clusters with between 1 and 3 gold atoms using VMC forces. The optimization workflow is demonstrably consistent, robust, and its computational cost scales with nb, where b < 3 and n is the system size. We discuss the implications of these results while laying out steps for further developments.

Larmor precession in strongly correlated itinerant electron systems

Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials.

Multivariate dynamics between emerging markets and digital asset markets: An application of the SNP-DCC model

As crypto markets become more integrated, measuring their spillovers with financial markets becomes fundamental for portfolio choice and risk management. We investigate high-order moment transmission between emerging/developed and digital asset markets through a flexible semi-nonparametric approach that accounts for dynamic conditional correlation and spillover effects, not only in conditional volatility but also in conditional skewness and kurtosis. The results show a (positive) transmission of volatility from emerging and developed markets to digital asset markets, as a signal of market integration, but also some positive/negative skewness and kurtosis spillovers (remarkably from Crypto and Blockchain indices to Emerging Asia and Latin America indices) detected at daily and weekly basis.

Reassessing the Composition of Hybrid Orbitals in Contemporary VB Calculations.

Large variations in the ratios between the p and s components of individual hybrid orbitals that have been observed in contemporary ab initio VB calculations are reassessed, and links are established to specific energy terms that drive bond formation. It is demonstrated that the ratios between the p and s components for individual hybrid orbitals are not indicative of the overall hybridization status of the relevant atom, which exhibits only relatively small variations with the level of theory, irrespective of whether or not non-dynamical and dynamical electron correlation effects are accounted for. An alternative orbital representation that turns out to be far more consistent with the overall hybridization of the relevant atom is examined. The chosen test cases, which can be compared with the classical sp3, sp2, and sp hybridization models for a central carbon atom, are CH4 (Td), trigonal CH3 (D3h), and triplet CH2 distorted from its ground state geometry so as to be linear (D∞h).

Unraveling effects of electron correlation in two-dimensional FenGeTe2 (n = 3, 4, 5) by dynamical mean field theory

The FenGeTe2 systems are recently discovered two-dimensional van-der-Waals materials, exhibiting magnetism at room temperature. The sub-systems belonging to FenGeTe2 class are special because they show site-dependent magnetic behavior. We focus on the critical evaluation of magnetic properties and electron correlation effects in FenGeTe2 (n = 3, 4, 5) (FGT) systems performing first-principles calculations. Three different ab initio approaches have been used primarily, viz., (i) standard density functional theory (GGA), (ii) incorporating static electron correlation (GGA + U) and (iii) inclusion of dynamic electron correlation effect (GGA + DMFT). Our results show that GGA + DMFT is the more accurate technique to correctly reproduce the magnetic interactions, experimentally observed transition temperatures and electronic properties. The inaccurate values of magnetic moments, exchange interactions obtained from GGA + U make this method inapplicable for the FGT family. Correct determination of magnetic properties for this class of materials is important since they are promising candidates for spin transport and spintronic applications at room temperature.

Dynamical response in strongly coupled uniform electron liquids: Observation of plasmon-roton coexistence using nine sum rules, Shannon information entropy, and path-integral Monte Carlo simulations

Dynamical properties of uniform electron fluids are studied within a nonperturbative approach consisting in the combination of the self-consistent version of the method of moments (SCMM) involving up to nine sum rules and other exact relations, the two-parameter Shannon information entropy maximization procedure, and the $\mathit{ab}\phantom{\rule{0.28em}{0ex}}\mathit{initio}$ path integral Monte Carlo (PIMC) simulations of the imaginary-time intermediate scattering function. The explicit dependence of the dynamic structure factor (DSF) on temperature and density is studied in a broad realm of variation of the dimensionless parameters ($2\ensuremath{\le}{r}_{s}\ensuremath{\le}36$ and $1\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}8$). When the coupling is strong (${r}_{s}\ensuremath{\ge}16$) we clearly observe a bimodal structure of the excitation spectrum with a lower-energy mode possessing a well pronounced rotonlike feature ($\ensuremath{\theta}\ensuremath{\le}2$) and an additional high-energy branch within the roton region which evolves into the strongly overdamped high-frequency shoulder when the coupling decreases (${r}_{s}\ensuremath{\le}10$). We are not aware of any reconstruction of the DSF at these conditions with the effects of dynamical correlations included here via the intermediate scattering and the dynamical Nevanlinna parameter functions. The standard static-local-field approach fails to reproduce this effect. The reliability of our method is confirmed by a detailed comparison with the recent $\mathit{ab}\phantom{\rule{0.28em}{0ex}}\mathit{initio}$ dynamic local field approach by T. Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)] available for high/moderate densities (${r}_{s}\ensuremath{\le}10$). Moreover, within the SCMM we are able to construct the modes' dispersion equation in a closed analytical form and find the decrements (lifetimes) of the quasiparticle excitations explicitly. The physical nature of the revealed modes is discussed. Mathematical details of the method are complemented in Appendix. The proposed approach, due to its rigorous mathematical foundation, can find numerous diverse applications in the physics of Fermi and Bose liquids.

Dynamic common correlation effects of financial development, foreign direct investment, market size and trade openness on domestic investment: an income-level prognosis

PurposeThe study examined the impact of financial development, foreign direct investment, market size and trade openness on domestic investment for 119 countries divided into four panels that are low-income countries (LIC), lower middle-income countries (LMIC), upper middle-income countries (UMIC) and high-income countries (HIC) between 1995 and 2019.Design/methodology/approachThe present study bases its empirical procedure on the bases of the data mix. To this end, based on the presence of cross-sectional dependence, covariate-augmented Dickey–Fuller unit root and Westerlund cointegration second-generation tests were employed to validate the stationarity and cointegration of the variables, respectively. The novel Dynamic Common Correlation Effects estimator was employed to estimate the heterogeneous parameters while the Dumitrescu and Hurlin test was used to test for causality direction of the highlighted variables.FindingsThe empirical results show that market size and trade openness had a positive and statistically significant effect on domestic investment for all the income groups. Results also show that financial development had a positive and statically significant effect on domestic investment only for LMIC and HIC economies, while a positive and statistically insignificant effect was obtained for LIC, UMIC and the global panel. The causality results revealed a bidirectional relationship between domestic investment and the exogenous variables – financial development, foreign direct investment, market size and trade openness.Research limitations/implicationsIt is therefore, recommended that LIC and LMIC need to consider harmonising the financial system to lower credit limitations and adopt business-friendly policies. HIC and UMIC should seek more outward FDI policies and harmonise their trade policy, to reap more benefits from FDI and international trade.Originality/valueOn novelty, previous studies have been criticised for the effect on technical innovation of bank financing and institutional quality. This research tackles the deficiency using systematic institutional quality indicators and by taking other variables into account.

Ecological footprint in a global perspective: the role of domestic investment, FDI, democracy and institutional quality

PurposeThe continuous increase in the negative gap between biocapacity and ecological footprint has remained globally persistent since early 1970. The purpose of this study is to examine the effect of foreign capital, domestic capital formation, institutional quality and democracy on ecological footprint within a global panel of 101 countries from 1995 to 2017.Design/methodology/approachThe empirical procedure is based on data mix. To this end, this study uses a battery of testing and estimation approaches both conventional (no cross-sectional dependence [CD]) and novel approaches (accounting for CD). Among the battery of estimation techniques used, there are the dynamic ordinary least square, the mean group, the common correlation effect mean group technique, the augmented mean group technique, the Pooled mean group and the dynamic common correlation effect technique with the desire to obtain outcomes robust to heteroskedasticity, endogeneity, cross-correlation and CD among others.FindingsThe estimated outcomes indicate that using different estimators’ domestic capital formation consistently degrades the environment through an increase in ecological footprint, while institutional quality consistently enhances the quality of the environment. Further, the outcome reveals that, though foreign capital inflow degrades the environment, the time period is essential, as it shows a short-run environmental improvement and a long-run environmental degradation. Democratic activities show a mixed outcome with short-run degrading effect and a long-run enhancement effect on environmental quality.Practical implicationsGreen investment should be the policy target of all economies, and these policies should be adopted to target both domestic capital and foreign capital alike. Second, the adoption of democratic practices will produce good leaders that will not just design short-term policies to blindfold the populace temporary but those that will produce long-term-oriented practices that will better and enhance the quality of the environment through the reduction of the global footprint. Equally, enhancing the institutional framework like respect for the rule of law in matters of abatement should be encouraged.Originality/valueAlthough much research on the role of macroeconomic indicators on environmental quality has been done this far, democratic practices, intuitional quality and domestic capital have been given little attention. This research fills this gap by considering robust empirical techniques.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy.

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.

Ab Initio Investigation of the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = Oxydiacetate) Series.

In this work, the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = oxydiacetate) series was analyzed with the ab initio ligand field theory (AILFT) module of the ORCA computational suite. The results were discussed within the framework of the angular overlap model (AOM) and compared to literature data. We find that the structural changes observed across the series exemplifies the effects of the lanthanide contraction also manifesting in the value of the AOM parameters. It is also shown that the complete active space self-consistent field (CASSCF) methodology is sufficient to describe the ligand field interactions in mononuclear lanthanide complexes, and the effects of dynamic correlation, through n-electron valence state perturbation theory (NEVPT2), are discussed. The calculated ligand field parameters of the present work are compared to the experimentally derived values from the literature.