Electron Correlation Contributions Research Articles

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

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

Robust room temperature perpendicular magnetic anisotropy and anomalous Hall effect of sputtered NiCo2O4 film

Inverse spinel ferrimagnetic NiCo2O4 (NCO) exhibits volatile physical properties due to the complex ion/valence occupation, which complicates the study its intrinsic properties. In this work, robust room temperature perpendicular magnetic anisotropy (PMA) is distinctly observed in high-quality RF-sputtered NCO film down to 3 uc (2.4 nm), confirmed by the room temperature anomalous Hall effect. The NCO films show a good metallic conductivity with a dimensional driven metal-insulator transition. The scaling relation between anomalous Hall conductivity ( σxy ) and the longitudinal conductivity ( σxx ) reveals the dirty metal behavior in conjunction with the contribution of intrinsic Berry phase or disorder-enhanced electron correlation contribute to the anomalous Hall effect for thick films while the dirty scaling law dominates for the thin films. This work introduces an oxide candidate with robust room temperature PMA as well as massive production ability for the functional spintronic applications.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations.

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Ab initio calculations of the 2p3/2→2s transition in He-, Li-, and Be-like uranium

The bound-state QED approach is applied to calculations of the $2p_{3/2} \rightarrow 2s$ transition energies in He-, Li-, and Be-like uranium. For U$^{90+}$ and U$^{89+}$, standard perturbation theory for a single level is employed, while the calculations of U$^{88+}$ have required its counterpart for quasidegenerate levels. The utilized approach merges the rigorous QED treatment up to the second order of perturbation theory with the higher-order electron-correlation contributions evaluated within the Breit approximation. The higher-order screened QED effects are estimated by means of the model-QED operator. The nuclear recoil, nuclear polarization, and nuclear deformation effects are taken into account as well. Along with the transition energies, their pairwise differences are calculated. The comprehensive analysis of the uncertainties due to uncalculated effects is carried out, and the most accurate theoretical predictions, which are in perfect agreement with available experimental data, are obtained.

Electron correlation effects on the g factor of lithiumlike ions

We present the systematic QED treatment of the electron correlation effects on the $g$ factor of lithiumlike ions for the wide range of nuclear charge number $Z=14$--82. The one- and two-photon exchange corrections are evaluated rigorously within the QED formalism. The electron-correlation contributions of the third and higher orders are accounted for within the Breit approximation employing the recursive perturbation theory. The calculations are performed in the framework of the extended Furry picture, i.e., with inclusion of the effective local screening potential in the zeroth-order approximation. In comparison to the previous theoretical calculations, the accuracy of the interelectronic-interaction contributions to the bound electron $g$ factor in lithiumlike ions is substantially improved.

Scale-free-modeling (harmonic) vibrational frequencies: Assessing accuracy and cost-effectiveness by CBS extrapolation.

Empirical scaling of calculated vibrational harmonic frequencies is a popular approach used in the field of molecular sciences. A nonempirical scheme that aims at reducing their basis set error is suggested here. Nearly as cost-effective as the scaled Kohn-Sham density functional theory (KS DFT), it consists of splitting the frequencies into Hartree-Fock and electron correlation contributions, followed by their extrapolation to the complete basis set (CBS) limit. Since the former converges exponentially, the overall cost may actually equal that of CBS extrapolation of the correlation part. Despite shifts in the molecular geometry during vibration, reasons are advanced to justify the approach, with extrapolation from the first two steps of the basis set ladder being effective in accelerating convergence. As benchmark data, a set of harmonic frequencies and zero-point energies for 15 molecules is employed at the second-order Moller-Plesset and coupled-cluster single double triple [CCSD(T)] levels of theory. The results outperform the optimized KS DFT scaled values. As a second test set, equilibrium structures and harmonic frequencies were computed for H2O2, CH2NH, C2H2O, and the trans-isomer of 1,2-C2H2F2. The results are also encouraging, particularly when improved for excess correlation at the CCSD(T)/VDZ level via the focal-point approach. In extreme cases, CBS extrapolation is done from two double-ζ calculations: one canonical and the other using explicit correlation theory. As a further case study, benzene is considered. While the CCSD(T) results show the smallest deviation from the best estimates, the MP2 results also attain good quality: When improved for excess correlation, they show 6-10cm-1 errors relative to the best data, only slightly outperformed at the CCSD(T)/CBS level. Tentative results for the fundamental frequencies are also presented.

Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning.

This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree-Fock computations. A MOB pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of MOs. The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant derivative kernel for Gaussian process regression (GPR) is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly accurate models for both dipole moments and energies on water and 14 small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering GPR scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with the literature results, MOB-ML provides the best test mean absolute errors of 4.21 mD and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110 000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.

Formation and relaxation of K-2 and K-2V double-core-hole states in n-butane.

Using a magnetic bottle multi-electron time-of-flight spectrometer in combination with synchrotron radiation, double-core-hole pre-edge and continuum states involving the K-shell of the carbon atoms in n-butane (n-C4H10) have been identified, where the ejected core electron(s) and the emitted Auger electrons from the decay of such states have been detected in coincidence. An assignment of the main observed spectral features is based on the results of multi-configurational self-consistent field (MCSCF) calculations for the excitation energies and static exchange (STEX) calculations for energies and intensities. MCSCF results have been analyzed in terms of static and dynamic electron relaxation as well as electron correlation contributions to double-core-hole state ionization potentials. The analysis of applicability of the STEX method, which implements the one-particle picture toward the complete basis set limit, is motivated by the fact that it scales well toward large species. We find that combining the MCSCF and STEX techniques is a viable approach to analyze double-core-hole spectra.

Electronic correlation contribution to the intermolecular interaction energy from symmetrized systematic molecular fragmentation model

The applicability of the systematic molecular fragmentation (SMF) model to reproduce the correlation part of intermolecular interaction energies has been studied for a new variant of the SMF, denoted by us as symmetrized SMF (SSMF). At third level of fragmentation (SSMF3) this contribution is reproduced with a small error of a few per cent in comparison to the accurate value. We have also examined the Hartree-Fock part of the interaction energy and found that for large intermolecular distances it is only qualitatively correct. However, the calculation of the Hartree-Fock interaction energies can be easily performed even for large molecules, while the correlated part of the interaction energy can be obtained with a much higher computational effort. Therefore, we propose to evaluate the interaction energy with a hybrid method, where the uncorrelated part is obtained in a classical way, while for the expensive electron-correlated part the SSMF approach is applied.

Probing the ground-state structural transition in small lithium clusters by quantum Monte Carlo simulations.

The ground-state structural transition in small lithium clusters Lin (n = 4 - 6) is analyzed based on the many-body expansion of the interaction energy using the total energy calculated by the fixed-node diffusion Monte Carlo (FN-DMC) simulations. The results show that the transition from 2D to 3D structure occurs through an intricate competition of attractive and repulsive interaction energies. As the structure dimensionality increases from 2D to 3D, the electron-correlation contribution to the interaction energy in the isomer of the ground-state structure is always the largest.

Concentration-dependent adsorption of organic contaminants by graphene nanosheets: quantum-mechanical models.

Adsorption is the key process in the expression of environmentally relevant physicochemical and toxicological properties of carbon nanomaterials. However, the adsorption of organic contaminants on to nanomaterials is a highly complex phenomenon, owing to the heterogeneity of adsorption sites, for example, on graphene surface as well as due to multiple factors operative during the adsorption, particularly, at the quantum-mechanical level. For predicting the concentration-dependent adsorption coefficients of organic contaminants by carbon nanomaterials, one option has been to rely on the existing linear-solvation energy relationship (LSER) models. The present work on the adsorption of aromatic and aliphatic organic contaminants by graphene nanosheets reveals that the existing LSER models are prone to failure when tested for internal and external validation using an external prediction set of compounds unknown to the model. As an alternative to the LSERs, the present work reports pure quantum-mechanical models developed using computational only quantum-mechanical descriptors. The reliability of the quantum-mechanical models was tested using state-of-the-art validation procedures employing an external prediction set of compounds. The proposed quantum-mechanical models reveal mean polarizability, zero-point vibrational energy, and its electron-correlation contribution to be the key descriptors in the prediction of adsorption coefficients of organic contaminants by graphene nanosheets.

The Many-Body Expansion for Aqueous Systems Revisited: I. Water-Water Interactions.

We revisit the many-body expansion (MBE) for water-water interactions by examining the effects of the basis set, including those resulting from the basis set superposition error (BSSE) correction, and electron correlation on the various terms for selected sizes of water clusters up to n = 21. The analysis is performed at the second-order Møller-Plesset (MP2) perturbation theory with the family of augmented correlation consistent basis sets up to five zeta quality (aug-cc-pVxZ, x = D, T, Q, 5) for the (H2O)n, n = 7, 10, 13, 16, and 21, clusters for which we report either the complete MBE (for n = 7, 10) or the ones through the 6-body (for n = 13) and the 5-body terms (for n = 16, 21). For the n = 3 and 7 clusters, we also report the analysis at the coupled cluster with single, double, and perturbative triple replacements in order to assess the effects of a higher correlation on the magnitude and percentage of the various MBE terms. Our results suggest that the oscillatory behavior around zero found for the 5-body and larger terms is solely an artifact of the (small) size of the basis set. Indeed, all terms above the 4-body converge monotonically to practically zero upon increasing the size of the basis set toward the complete basis set (CBS) limit. In that respect, the BSSE-corrected 5-body and above terms do not exhibit the oscillatory behavior on either side of zero with the basis set observed for the BSSE-uncorrected terms. In addition, the magnitudes of the 5-body and above terms are accurately reproduced even with the smaller basis set of the series (aug-cc-pVDZ) once the BSSE correction is taken into account. The same level of theory (MP2/aug-cc-pVDZ, BSSE-corrected) also accurately reproduces the MP2/CBS values of the 3- and 4-body terms. The contribution of electron correlation to the 3- and 4-body terms is quite small so that neglecting the correlation contribution in all terms above the 3-body results in an error of the order of 0.1%. The BSSE correction to the largest 2-body term in the MBE was accurately estimated from the function a[1 + erf( - b·R)], which is proportional to the common (overlapping) area between two Gaussian distributions whose centers are separated by R with the constants a and b fitted to the calculated BSSE corrections for the individual 2-body terms of the clusters with each basis set and R is the distance between oxygen atoms. Our results demonstrate that the MBE for water-water interactions converges by the 4-body term since any finite terms above the 4-body are artifacts of the size of the basis set. The MBE can thus be safely truncated at the 4-body term when either a very large basis set is used or BSSE corrections are taken into account even with the smaller aug-cc-pVDZ basis set. We expect these findings to have important consequences in the pursuit of accurate ab initio based many-body molecular dynamics simulations for aqueous systems.

Important components for accurate hyperfine coupling constants: electron correlation, dynamic contributions, and solvation effects

ABSTRACT The calculation of hyperfine coupling constants is a challenging task in balancing accuracy and computational effort. While previous work has shown the importance of electron correlation and molecular dynamic contributions, we present a systematic study simultaneously analyzing the influence of both effects on hyperfine coupling constants. To this end, we thoroughly study two organic radicals, namely the dimethylamino radical and ethanal radical cation, proving the need to account for conformational flexibility as well as the large influence of electron correlation. Based on these results, we analyse the effect of electron correlation and dynamic simulations on a set of 12 organic radicals, illustrating that both effects are vital for an accurate in silico description on the same scale. Furthermore, we study the influence of solvation using the efficient nuclei-selected algorithm to obtain hyperfine coupling constants with electron correlation for large systems, indicating the necessity to include explicit solvent molecules. Finally, we introduce a composite approach to incorporate all contributions for hyperfine coupling of radicals in solution at comparatively low computational cost. This is successfully tested on the hydroxylated TEMPO radical in aqueous solution, where we are able to compute a 14 N-HFCC of 44.4 MHz compared to the experimentally measured 47.6 MHz.

Excluded-volume descriptors for dipole-bound anions: Amine N-oxides as a test case.

Dipole-bound anions can be theoretically characterized at three fundamentally different levels. The highest are ab initio calculations, which themselves range from fairly approximate, say, Koopmans's Theorem (KT) or second-order Møller-Plesset perturbation theory, to highly sophisticated, say, the electron affinity equation-of-motion couple-cluster with single, double, and perturbative triple substitutions, which rivals experiments in reliability. The next level down is represented by one-electron model Hamiltonians. Again, one-electron model Hamiltonians can be fairly approximate, especially if the molecular system is modeled by a simple point-dipole and point-polarizable site; however, very reliable models have been developed for specific systems, for example, water clusters. At the lowest level, one can qualitatively explain trends in classes of dipole-bound anions in terms of the dipole moment, μ, the polarizability, α, and the so-called excluded volume, Vx. This project aims at the qualitative level. While the dipole moment and the polarizability possess clear-cut definitions, the excluded volume must-similar to all molecular volumes-remain a rather vaguely defined term, and so far, we are unaware of any quantitative definition in the literature. Here, we introduce and investigate three descriptors for Vx. To this end, we first establish a dataset with consistent ab initio results for 25 amine N-oxides structures. Then, we demonstrate that the descriptors are indeed able to explain trends for sets of isomers and conformers and investigate to what extent the descriptors are able to predict electron binding energy of dipole-bound states using simple quantitative structure-property relationship-like models. It turns out that μ and Vx provide a reasonably accurate prediction of the electrostatic part of the electron bind energy (the KT value) and that the polarizability α provides an acceptable prediction of the electron correlation contribution.

Calculations of Relativistic, Correlation, Nuclear, and Quantum-Electrodynamics Corrections to Energy and Ionization Potential of the Ground State of Helium-Like Ions

Nonrelativistic and relativistic variational calculations of energies and ionization potentials of the ground state of helium-like ions with nuclear number Z = 2−20 have been performed. All leading corrections to the total energy have been calculated, including the contribution of electron correlations, relativistic and quantum-electrodynamics corrections, and contributions due to the finite nuclear size (field shift) and finite nuclear mass (nuclear recoil) effects. Relativistic wave functions were calculated using the Dirac–Coulomb–Breit Hamiltonian.

Formation of Al + (C 6 H 6 ) 13 : The Origin of Magic Number in Metal–Benzene Clusters Determined by the Nature of the Core

The identification of highly abundant, “magic” species in the mass spectra of clusters have proven to be valuable in nanoscience, leading to the discovery of new stable species such as fullerenes a...

Intermolecular interaction energies from fourth order many-body perturbation theory. Impact of individual electron correlation contributions.

The performance of Møller-Plesset perturbation theory methods for describing intermolecular interaction energies has been investigated with the focus on illuminating the impact of individual electron correlation energy contributions in fourth order. It is shown that a physically meaningful decomposition of the fourth order correlation energy can be obtained by grouping individual correlation energy terms that share the same diagrammatic loop structure. This decomposition of the fourth order singles (S), doubles (D), triples (T), and quadruples (Q) terms revealed that individual terms from each excitation class can have a huge impact on the energy that is much larger than the total fourth order correlation contribution. A partial summation of S, D, and Q terms has been derived that can reproduce the full fourth order interaction energies with a good accuracy and which does not include the computationally expensive triples energy term.

An ab initio study of the O1s and Mg1s, Mg2s, Mg2p core electron binding energies in bulk MgO

Embedded cluster models combined with wavefunction based quantum chemical ab initio methods were used to calculate the O1s and Mg1s, Mg2s, Mg2p core electron binding energies (CEBEs) of bulk MgO. The calculations were performed at three levels of theory: Koopmans' theorem (KT, initial state effects), ΔSCF (relaxation of the electronic wavefunction after core ionization, final state effects, with inclusion of scalar relativistic effects), and approximate coupled cluster (CC) approach to account for electron correlation. Several basis sets as well as MgO clusters of various design and size were employed to study their influence on the CEBEs. The contribution of electron correlation being in the order of 1 eV, but very much different for the different core levels, was analyzed in detail. Our final results are 529.5 eV for the O1s CEBE and 1303.5, 87.7 and 48.8 eV for Mg1s, Mg2s, Mg2p, respectively (all relative to the Fermi level). They agree with recent experimental XPS data within about 0.5 eV.

Modeling the Solubility of C70 Fullerenes in Diverse Solvents: Role of Quantum-mechanical Descriptors.

Solubility of fullerenes in diverse solvents is difficult to model owing to the involvement of inherent quantum-mechanical interactions. This work proposes pure quantum mechanical models for predicting the solubility of C70 fullerenes. The models are developed using single-molecule quantum mechanical properties of solvents,which includes electron-correlation based descriptors accounting for the instantaneous inter-electronic interactions responsible for the origin of these properties. The external predictivity of the models was validated using an external prediction set of compounds not exposed to the model during its development. The most influential factor affecting the solubility was found to be electron-correlation contribution to the energy of highest occupied molecular orbital of solvents, which in fact, has been analyzed to suppress the solubility of fullerenes. However, the polarizability of the solvents, particularly that due to the quantum-mechanical exchange interactions between the electrons, is observed to drive the solubility of C70 fullerenes. The present work also found several other quantum mechanical properties affecting the solubility of fullerenes, which pay valuable insights towards the origin of the solubility of carbon-based nano-materials.

Optical Stark and Zeeman Spectroscopy of Thorium Fluoride (ThF) and Thorium Chloride (ThCl).

Experimentally and theoretically determined magnetic and electric dipole moments, bond distances, and vibrational spacings are used for a comparative study of the bonding in ThF and ThCl. Numerous bands in the visible electronic spectra between 16 400 and 18 800 cm-1 of supersonically cooled molecular beam samples have been detected using medium-resolution (Δν ≈ 0.1 cm-1) 2D spectroscopy. High-resolution (Δν < 20 MHz) field-free, Stark, and Zeeman spectroscopy of the detected [18.6]Ω = 3/2 - X2Δ3/2 band of ThF near 538.4 nm and the [18.2]Ω = 3/2 - X2Δ3/2 band of ThCl near 551.0 nm have been recorded and analyzed. Stark shifts and splitting were analyzed to produce | μ⃗el| values of 1.453(7) D and 0.588(9) D for the X2Δ3/2 and [18.6]Ω = 3/2 states of ThF, respectively, and 2.022(35) D and 3.020(55) D for the X2Δ3/2 and [18.2]Ω = 3/2 states of ThCl. Zeeman splittings and shifts were analyzed to produce ge values of 1.038(4) and 1.079(4) for the X2Δ3/2 and [18.6]Ω = 3/2 states of ThF and 1.130(4) and 1.638(4) for the X2Δ3/2and [18.2]Ω = 3/2 states of ThCl. Analysis of ge values demonstrates that the X2Δ3/2 and [18.6]Ω = 3/2 states of ThF and the X2Δ3/2 state of ThCl are predominately 2Δ3/2 spin-orbit components, whereas the [18.2]Ω = 3/2 state of ThCl is an admixture of 2Δ3/2 and 2Π3/2 spin-orbit components. A molecular orbital description of the ground states is used to rationalize the observed | μ⃗el|values for the ThX (X = F, Cl, O, and S) series and garner insight into the bonding mechanism. The dipole moments in the ground state of ThF and ThCl have been calculated using relativistic coupled-cluster methods. It is demonstrated that the systematic inclusion of electron-correlation contributions plays an essential role in obtaining accurate predictions for the dipole-moment values in ThF and ThCl.