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We introduce the fragment‐pairwise Local Energy Decomposition (fp‐LED) scheme for precise quantification of individual interactions contributing to the binding energy of arbitrary chemical entities, such as protein‐ligand binding energies, lattice energies of molecular crystals, or association energies of large biomolecular assemblies. Using fp‐LED, we can assess whether the contribution to the binding energy arising from noncovalent interactions between pairs of molecular fragments in any chemical system is attractive or repulsive, and accurately quantify its magnitude at the coupled cluster level ‐ commonly considered as the “gold standard” of computational chemistry. Such insights are crucial for advancing molecular and material design strategies in fields like catalysis and therapeutic development. Illustrative applications across diverse fields demonstrate the versatility and accuracy of this theoretical framework, promising profound implications for fundamental understanding and practical applications. [ABSTRACT FROM AUTHOR]

In this paper, based on [N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime, Commun. Math. Phys.374(3) (2020) 2097–2150; N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas, Invent. Math.225(3) (2021) 885–979; N. Benedikter, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas with large interaction potential, preprint (2021), arXiv:2106.13185], we present a recent estimate for the correlation energy of a Fermi gas in the so-called mean-field regime and we outline some of the main ideas of its proof. [ABSTRACT FROM AUTHOR]

In the present work, we present an investigation of Collins Conjecture, a hypothesis made by D. M. Collins in 1993 relating correlation energy and entanglement entropy, by calculating the ground state and singly‐excited triplet‐spin 1s2s 3S and 1s3s 3S state energies of the helium iso‐electronic sequence, with Z = 2–15. By using extensive orthonormal configuration interaction (CI) type wave functions with B‐Spline basis up to about 6000 terms, linear entropy and von Neumann entropy for the abovementioned atomic systems are determined. Together with the Hartree‐Fock energies obtained following a self‐consistent field theory, we have found that there exist linearly proportionalities between the renormalized correlation energies and entanglement entropies of both linear and von Neumann, showing a support for Collins Conjecture applicable to the ground and singly‐excited triplet‐spin states in the helium sequence, for a range of finite Z‐values. [ABSTRACT FROM AUTHOR]

Azoheteroarenes represent an attractive group of photochromes exhibiting a large structural variability and tunability of photoswitching characteristics. The thermal back‐isomerization can proceed via inversion or rotation mechanisms, depending on the functionalization and environment. However, the distinction between the two remains a challenge for both experiment and theory. Here, four experimentally fully characterized phenylazoindoles are studied to establish the mechanism of back‐reaction in solvent using density functional theory (DFT), spin‐flip time‐dependent (TD‐)DFT, mixed‐reference TD‐DFT, and restricted ensemble Kohn–Sham approaches as well as CASPT2 and CCSD(T). While the inversion is consistently described by all methods, the rotation mechanism requires multireference approaches including dynamic correlation. The balanced description of both pathways becomes even more important in solvent which apparently affects the mechanism. For the present set, the range‐separated functionals combined with continuum models appear to be the most consistent with experiment in terms of the substitutional and solvent effects on thermal halftimes. [ABSTRACT FROM AUTHOR]

Here, we demonstrate that the radial distribution function can be mapped into a radial density–energy space and the relationship between the radial density and radial energy is linear for the ground and excited states of helium-like systems; the gradient of the resulting straight line delivers the energy of the state considered. To utilize this finding, a simple analytical expression for the total energy in terms of the density at the most probable nucleus–electron distance of the systems considered is derived using a fitting procedure.

Although correlation energy in an atom can be decomposed into different components such as inter- and intra-orbital pair-correlation energies (PCE), it is generally believed that the PCEs in different atoms cannot be the same. In this work, we find that when the correlation energy is defined as the difference between the exact ground-state energy and the unrestricted Hartree–Fock energy, the PCEs associated with the valence electrons of the atoms in the same row of the periodic table have the same values. For two specific orbitals, the inter-orbital correlation energy is the same between two electrons of parallel or anti-parallel spins. • The inter- and intra-orbital pair-correlation energies (PCE) of the atoms are not entangled and their values depend only on the electron orbitals. • The PCEs associated with the valence electrons of the atoms in the same row of the periodic table have the same values. • For two specific orbitals, the inter-orbital correlation energy is the same between two electrons of parallel spins or anti-parallel spins. • The effects of orbital relaxation on the correlation energy are very small. [Display omitted] [ABSTRACT FROM AUTHOR]

We investigate the structural, surface and electronic properties of small silicon clusters Si n (for n = 2 to 15) using HF, DFT and FN-DMC calculations. We analyze the atomic configurations, surface properties and electronic structures and show that the radius and average surface area of the clusters can be modeled by a Jellium-type model. We found that the surface tension σ of the clusters decreases with increasing cluster size in the range of the clusters under investigation. An estimate of the surface tension for bulk silicon yields σ b u l k = 0. 88 (3) J/m2 in agreement with recent experiments. The average bond length of the clusters shows a non-monotonic behavior. Smaller clusters exhibit a high spin state influenced by electron correlation, especially during the 2D to 3D structural transition, which occurs at n = 4 to n = 5. We also find that the Si 4 , Si 10 and Si 12 clusters exhibit enhanced stability due to electron correlation. Our results are consistent with the experiments on bond length, binding energy and dissociation energy. [Display omitted] • Surface Tension Dynamics: Revealing how surface tension decreases with increasing cluster size. • Size-Dependent Bond Length: Identifying non-monotonic bond length changes and spin state influences during the 2D to 3D transition. • Enhanced Cluster Stability: Demonstrating the exceptional stability of Si 4 , Si 10 , and Si 12 clusters due to electron correlation. [ABSTRACT FROM AUTHOR]

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect. [ABSTRACT FROM AUTHOR]

Ab initio calculations were performed to investigate the structural and electronic properties of bulk CdTe using various exchange–correlation (XC) functionals available. Among the selected XC functionals include the local density approximation (LDA), generalized gradient approximation (GGA), meta-generalized gradient approximation (MGGA) (using the linear combination of atomic orbitals basis scheme) and Heyd–Scuseria–Ernzerhof-06 (HSE06) (using the plane-wave basis scheme). Further computational studies were performed based on the local density approximation-1/2 (LDA-1/2) and generalized gradient approximation-1/2 (GGA-1/2) self-energy correction schemes to verify their effect on the CdTe band gap in comparison to the other traditional XC functionals. The lattice parameter values obtained using different XC functionals (LDA, GGA and MGGA) were well in agreement with experimental value, with LDA predicting 6.548 Å. This is 1.02% greater than the experimental value of 6.482 Å. The electronic structure of CdTe was calculated for the fixed 6.482 Å lattice parameter of bulk CdTe and resulted in a band gap ranging between 0.68 and 1.56 eV for LDA, GGA, MGGA, and HSE06. The band gap values predicted by the LDA-1/2 and GGA-1/2 corrections were 1.47 eV and 1.50 eV, respectively, and are found to be in good agreement with experimental values. The influence of XC functionals and semi-empirical correction schemes are expected to have important implications on the prediction and understanding of bulk CdTe thin-films found in photovoltaic applications. [ABSTRACT FROM AUTHOR]

The use of simple q‐exponential functions, derived from Tsallis entropy distribution, as basis set of atomic orbitals, is explored within the non‐relativistic limit. As compared to Gaussian or to STO (Slater type orbitals) basis set, considering q as variational parameter, q‐exponentials functions lower considerably the energy of two electron systems, always respecting the Ritz variation principle, where E ≥ E0, with E0 being the true energy. The q parameter attains the highest value of 1.209 for Z = 1 (H−) slowly going down toward 1 as Z grows (for Z = 36 q = 1.005225, Kr+34). Interestingly, the correlation energy as determined considering the exact solution by the calculations of Pekeris with the current ones, shows a regular variation as a function of the q parameter. Moreover, the study confirms the link between correlation energy and Shannon information entropy. [ABSTRACT FROM AUTHOR]

In this study, phase transformation mechanisms in thin V2O3 and VO2 films are analysed based on experimental data and on the qualitative model for vanadium oxides proposed by the authors of the study. New features of semiconductor-metal phase transformation mechanism revealed in V2O3 are discussed. Characteristics of phase transition process in V2O3 is compared with the features of a similar phase transformation in thin VO2 in detail.

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect.

Accurate polarizabilities of atoms and molecules are critical in the treatment of optical and dielectric properties, in the modeling and interpretation of intermolecular interactions, in scattering processes, and in chemical reactivity. In this work we provide a systematic study of the atomic/ionic static dipole polarizabilities of the first‐row elements: B+, B, B−, C2+, C+, C, C−, N2+, N+, N, O2+, O+, O, O−, F2+, F+, F, and F−. We used the CCSD(T) method with a range of large correlation‐consistent basis sets augmented with a series of diffusion functions (x‐aug‐cc‐pVXZ). We discuss the trends in the dependence of dipole polarizability from the basis set size and/or number of diffuse functions and report the recommended values of average dipole polarizabilities for this series. The systematic survey of dipole polarizabilities for ions from boron to fluorine, including the extrapolation to complete basis set limit, is presented for the first time. [ABSTRACT FROM AUTHOR]

Local energy decomposition analysis provides a breakdown of the domain‐based local pair natural orbital CCSD(T) [DLPNO‐CCSD(T)] energy into additive contributions representing the interaction between pairs of user‐defined fragments. Each of these fragment‐pairwise components can be further decomposed into a sum of physically meaningful terms, such as electrostatics, dispersion, and exchange. In this study, the dependence of such energy terms on the basis set size, the approximations used for the two‐electron integrals, and the localization scheme used for the virtual orbitals have been carefully evaluated on the interaction energies of the S66 benchmark set. A comparison with the energy components obtained at the SAPT2 + (3)δMP2 level of Symmetry‐Adapted Perturbation Theory is also provided. [ABSTRACT FROM AUTHOR]

The possibilities of distributive bases from Gaussian sp-functions for calculating the correlation energy of molecules in the second order (Е(2)) of the Møller–Plesset perturbation theory (MPPT) have been investigated. The effectiveness of such bases has been demonstrated by comparing the Е(2) values obtained in distributive and standard atom-centered bases. Calculations have been performed for both the ground and excited states with ground symmetry. For this purpose, an analog of Møller–Plesset perturbation theory for excited states that preserves its advantages for the ground state has been developed. It has been shown that distributive sp-functions provide the accuracy of calculating Е(2) that is comparable to that of atom-centered bases including s-, p-, and d-functions. [ABSTRACT FROM AUTHOR]

Kohn-Sham density functional theory with the available exchange–correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated systems, and available functionals of the spin densities do not accurately predict energies for many strongly correlated systems when one uses multiconfigurational wave functions with spin symmetry. Furthermore, adding a correlation functional to a multiconfigurational reference energy can lead to double counting of electron correlation. Multiconfiguration pair-density functional theory (MC-PDFT) overcomes both obstacles, the second by calculating the quantum mechanical part of the electronic energy entirely by a functional, and the first by using a functional of the total density and the on-top pair density rather than the spin densities. This allows one to calculate the energy of strongly correlated systems efficiently with a pair-density functional and a suitable multiconfigurational reference function. This article reviews MC-PDFT and related background information. [ABSTRACT FROM AUTHOR]

Both [5]-circulene and [7]-circulene can be selected to design the molecular tweezers theoretically using the DFT method. Leaning on the cyclic polymerization mechanism, we obtain four new tweezer compounds. Theoretical results offer that tweezer compound (I) is additionally stable than other compounds because it has better energies than other compounds. The values were as follows: − 2606.83372937 a.u. for the total energy, − 5.39820 eV for (EHOMO), and 2.87407 eV for gap energy. The thermodynamic theoretical outcome showed that all reactions are exothermic and spontaneous, suggesting that tweezer compound (I) might correlate with several aromatic compounds, such as pyrene, benzo[ghi]perylene, ovalene, and hexabenzocoronene. The correlation energy results showed an increase as the aromatic compound becomes larger, while the correlation distance decreases. All correlation energy kinds are electrostatic. The value of the electrostatic correlation energy of tweezer compound (I)-ovalene is (− 6.4928615 kJ mol−1). The tweezer compound (I) has a spherical cavity equal to 3.73640 nm3, which adds an important application in the ability to capture chemicals, bacteria, or viruses that are close to the size of the cavity with ease. [ABSTRACT FROM AUTHOR]

Atoms under pressure undergo a number of modifications of their electronic structure. Good examples are the spontaneous ionization, stabilization of excited‐state configurations, and contraction of atomic‐shells. In this work, we study the effects of confinement with harmonic potentials on the electronic structure of atoms from H to Ne. Dynamic and static correlation is taken into account with coupled cluster with single and double excitations and CASSCF calculations. Because the strength of harmonic confinement cannot be translated into pressure, we envisioned a "calibration" method to transform confinement into pressure. We focused on the effect of confinement on: (a) changes of electron distribution and localization within the K and L shells, (b) confinement‐induced ionization pressure, (c) level crossing of electronic states, and (d) correlation energy. We found that contraction of valence and core‐shells are not negligible and that the use of standard pseudopotentials might be not adequate to study solids under extreme pressures. The critical pressure at which atoms ionize follows a periodic trend, and it ranges from 28 GPa for Li to 10.8 TPa for Ne. In Li and Be, pressure induces mixing of the ground state configuration with excited states. At high pressure, the ground states of Li and Be become a doublet and a triplet with configurations 1s22p and 1s22s2p, respectively, which could change the chemistry of Be. Finally, it is observed that atoms with fewer electrons correlation increases, but for atoms with more electrons, the increasing of kinetic energy dominates over electron correlation. [ABSTRACT FROM AUTHOR]

Using first-principles calculations, we investigate the ideal shear strengths σ max of L1 2 -Ni 3 Al crystals with various multiple additions of Re and W. A correlation energy function Δ E Re A + W B (d) is adopted to evaluate the interaction between point defects (i.e., Re A and W B ). The results indicate extra addition of Re or W does not change the site preference of Re and W at Al sites, and W in preference to Re occupies Al sites. In this preferred site, σ max of L1 2 -Ni 3 Al crystals with single Re addition is larger than that with single W addition, but the strengthening effect of double Re addition is weak compared with multiple addition of Re and W. Strong repulsion is found to be disadvantageous for the reinforcement of γ′-Ni 3 Al phases, and σ max in Re A + W B complexes decreases with increasing Δ E Re A + W B (d). The analysis of electronic and geometric structures reveals Re/W-addition-induced strengthening mainly originates from stronger Re/W Ni bonding than Al Ni bonding, but a significant increase of σ max in γ′-Ni 3 Al-Re W systems is attributed to a cooperative effect of electronic interaction and local elastic strain energy, and the local elastic strain energy is dominant. Image 1 • Interaction between Re and W does not change their site preferences in Al sublattices. • W in preference to Re occupies Al sites in the case of multiple addition of Re and W. • Extra addition of Re/W can increase σ max in ternary Ni 3 Al-Re/W crystals. • Strong repulsion between Re and W is harmful to the reinforcement of γ′-Ni 3 Al phases. • Local elastic strain energy plays a key role in the detrimental impact of Re W repulsion. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Analytic expressions for angular kinetic energy matrix elements for Hylleraas formalism. • We report angular correlation energies for the ground and excited states. • Trends are reported with varying atomic number. Abstract Partitioning of helium atom's correlation energy into radial and angular contributions, although of fundamental interest, has eluded critical scrutiny. Conventionally, radial and angular correlation energies of helium atom are defined for its ground state as deviations, from Hartree-Fock and exact values, of the energy obtained using a purely radial wavefunction devoid of any explicit dependence on the interelectronic distance. Here, we show this rationale to associate the contribution from radial-angular coupling entirely to the angular part underestimating the radial one, thereby also incorrectly predict non-vanishing residual radial probability densities. We derive analytic matrix elements for the high-precision Hylleraas basis set framework to seamlessly uncouple the angular correlation energy from its radial counterpart. The resulting formula agrees with numerical cubature yielding precise purely angular correlation energies for the ground as well as excited states. Our calculations indicate 60.2% of helium's correlation energy to arise from strictly radial interactions; when excluding the contribution from the radial-angular coupling, this value drops to 41.3%. [ABSTRACT FROM AUTHOR]

Abstract: Full configuration interaction calculations are performed for He2 using various orbital basis sets of the aug‐cc‐pVXZ type, with the correlation energies being extrapolated to the complete basis set (CBS) limit. A two‐point CBS extrapolation formula has been utilized for such a purpose. It is shown that the extrapolation formula with the offset parameter k(R) optimized for the equilibrium distance is not uniformly applicable to HeHe distances in the very short region of the potential energy curve. The offset parameter k(R) in the repulsive region of the potential energy curve can be largely different with the one in the long‐range distances especially in the cases of basis‐sets with large cardinality number. It is also noticed that the accuracy of this extrapolation scheme may not be improved with the increasing of the cardinality number. [ABSTRACT FROM AUTHOR]

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed. [ABSTRACT FROM AUTHOR]

We investigate the influence of oxygen doping on the structural and electronic properties of small lithium clusters using DFT, QMC and HF methods. The results show that substitution with oxygen shortens the bonds and reduces the coordination number of the clusters. The Li-O bonds are mainly polar covalent. Larger clusters exhibit greater stability due to oxygen. Electrostatic and exchange interactions strengthen the bonds, while electron correlation increases their stability. The results were compared with previously available theoretical and experimental work. [Display omitted] • Oxygen doping strengthens lithium cluster bonds, impacting structure and electron properties, aiding materials design. • Oxygen markedly enhances Li-O bonds, influencing electronic structure for potential material improvements. • Study offers guidance for developing novel materials by understanding the effects of oxygen doping in lithium clusters. [ABSTRACT FROM AUTHOR]

[Display omitted] • Correlation energy through Green function formalism. • Computing ionization energies and electron affinities of diatomic molecules. • Feynman diagrammatic expansion method for improving correlation energy estimation. • Partition energy procedure and the problem of particle number conservation. In this study, we revisit Green's function formalism in theoretical chemistry. Specifically, we investigate how it allows refining the Hartree-Fock model by introducing the self-energy's first and second-order corrections. Two distinct approaches are considered: the energy partition procedure and the Feynman diagrammatic expansion. These approaches are applied to the study of the π bond of ethylene, demonstrating that both provide better numerical results than those obtained using the Hartree-Fock model but worse than those obtained using the Configuration Interaction method. An optimization process of the energy partition procedure, capable of reproducing the results obtained by applying the Configuration Interaction method and solving the problem of the violation of particle number conservation, is also proposed. [ABSTRACT FROM AUTHOR]