Resolutions of the Coulomb operator: VI. Computation of auxiliary integrals

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb and long-range Ewald operators) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use

The two faces of static correlation

Restricted Hartree-Fock (RHF) and UHF wavefunctions for beryllium-like ions with nuclear charge 3 ≤ Z ≤ 5 are found using a near-complete Slater basis set. The triplet (RHF → UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z > 4.5. We reproduce this surprising behavior using a minimal-basis model and, by comparing with the stretched H(2) molecule, conclude that "static" (also known as nondynamical, near-degeneracy, first-order, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an "absolute near-degeneracy"; in the latter (Type B), there is a "relative near-degeneracy." This dichotomy clarifies discussions of static correlation effects.J.W.H. thanks P.-F. Loos for valuable discussions and the National Science and Engineering Research Council of Canada for funding. P.M.W.G. thanks the NCI National Facility for supercomputer time and the Australian Research Council (Grants Nos. DP0771978 and DP0984806)

The nature of electron correlation in a dissociating bond

We have constructed the unrestricted Hartree-Fock (UHF), restricted Hartree-Fock (RHF), and full configuration interaction (FCI) position and momentum intracules and holes for H···H at bond lengths R from 1 to 10 bohrs. We trace the recently discovered inversion of the UHF position hole at intermediate R to over-localization of the spin-orbitals, and support this by a correlation energy component analysis. The RHF and UHF momentum holes are found to be more complicated; however their features are explained through decomposition of electron correlation effects. The UHF momentum hole is also found to invert and exhibits interesting behavior at large R. The RHF (but not UHF) and FCI momentum intracules exhibit Young-type interference patterns related to recent double photoionization experiments. Our analyses yield the most comprehensive picture to date of the behavior of the electrons during homolytic bond fission.J. W. H. thanks the Natural Sciences and Engineering Research Council (NSERC) of Canada for funding. L.K.M. thanks the RSC for a Summer Research Scholarship. P.M.W.G. thanks the NCI National Facility for a generous grant of supercomputer time and the Australian Research Council (Grant Nos. DP0984806 and DP1094170)

Crystal structure and computational study of an oxo-bridged bis-titanium(III) complex

The solid-state structure of the new compound mu-oxido-bis[dichloridotris(tetrahydrofuran-kappa-O)titanium(III)], [Ti2Cl4O(C4H8O)6], at 150 K has been determined. The crystal has monoclinic (C2/c) symmetry and the complex features C2 symmetry about the bridging O atom. Positional disorder is evident in one of the three tetrahydrofuran environments. A post-Hartree–Fock computational analysis indicates that the complex has nearly degenerate triplet and singlet spin states, with the former favoured slightly by ca 2 kJ mol-1.Funding for this research was provided by: Natural Sciences and Engineering Research Council of Canada (grant No.RGPIN-2019-06725).https://doi.org/10.1107/S205322962100609

Effect of the tether length upon Truce‐Smiles rearrangement reactions

post-printThis report examines the effect of substrate design upon the Truce‐Smiles rearrangement, an intramolecular nucleophilic aromatic substitution reaction. The length of the molecular spacer that tethers the carbanion nucleophile to the substituted benzene ring was found to have a strong influence on the ability of the substrate to undergo the reaction successfully. Our experimental results show highest yield of desired aryl migration product for substrates designed with a 3‐atom tether, which proceed through a 5‐membered spirocyclic intermediate. The results are interpreted in comparison with a survey of Truce‐Smiles rearrangements described in the literature and found to be consistent. Computational studies support the observed reactivity trend and suggest an explanation of a favorable combination of ring strain and electrostatic repulsion leading to optimal reactivity of the substrate designed with a 3‐atom tether. Comparison of our results with trends for related ring‐closing reactions illustrate the unique electrostatic features of the system studied herein."Financial support for this work was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada (402608‐2011‐RGPIN, 435374‐2013‐RGPIN), the University of Winnipeg, and the Government of Manitoba Career Focus Program. We thank Westgrid and Compute Canada for supercomputing resources."https://onlinelibrary.wiley.com/doi/full/10.1002/poc.374

Spectroscopic characterization, DFT calculations, in vitro pharmacological potentials, and molecular docking studies of N, N, O-Schiff base and its trivalent metal complexes

In this study, trivalent metal complexes of the category: [M(L)(H2O)nCly] obtained from the interaction of metal3+ ion salts with organic N, N, O-Schiff base (HL) (where: HL = 4-{(Z)-((2-{(E)-((2-hydroxyphenyl)methylidene)amino}ethyl)imino)methyl}-2-methoxyphenol; n, y = 1 or 2 and M = Ti(III), Fe(III), Ru(III), Cr(III) and Al(III)) were synthesized and characterized viz molar conductance, FT-IR, and UV–Vis spectroscopies, elemental analyses, thermal analyses (TGA and DTA), and UV–Vis spectroscopy, theoretical calculations. A distorted octahedral structure around the metal ions was proposed based on the obtained experimental and calculated data. Thermal examination of the complexes signposts the step-by-step disintegration to give the final decomposition product as metal oxides. Moreover, DFT calculations were executed utilizing the B3LYP/LANL2DZ theory level, which revealed that the synthesized metal (III) complexes were more stable than the free ligand (HL). The value of ΔE for HL is 4.60 eV while the related values for the complexes of Cr(III) (C1), Ru(III) (C2), Fe(III) (C3), Al(III) (C4), and Ti(III) (C5) are respectively 2.59, 3.68, 3.15, 1.64, and 2.75 eV. Scavenging abilities of DPPH and ABTS radicals by the test compounds revealed promising antioxidant behavior. It was observed that the compounds are proficient DPPH radical scavengers in a dose-dependent configuration. Ru(III); IC50 = 1.69 ± 2.68 µM for DPPH and Ti(III); IC50 = 8.70 ± 2.78 µM for ABTS performed best. Similarly, the complexes demonstrated higher antimicrobial activities compared to HL against the designated strains, while ciprofloxacin acted as a standard antibiotic. Furthermore, the ligand and its most effective complexes C2 and C5 were docked against the targets S. aureus DNA gyrase (2XCT), S. pneumoniae DNA gyrase (5BOD), and E. coli DNA gyrase (5L3J). The binding sites were evaluated and the docking results showed that the studied molecules bind to the targets through classical O—H…O and/or N—H…O hydrogen bonds, as well as via hydrophobic contacts

Properties and applications of the average interparticle distance

The first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus. The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two electrons models the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule. -- The relationships discovered between the average interparticle distances and molecular energy components have led to the development of a new empirical approach to modelling the electronic structure of molecules. The general energy expression for a simulated electronic structure theory is defined, along with the functional form of the interatomic distance dependent energy functions. The theory is used to model the hydrogen molecule, the first-row hydrides, and ethane. The models, which have the correct RHF/6-31G(d) optimized geometries, also fit the RHF/6-31G(d) energy at equilibrium and the UHF/6-31G(d) energy at the bond dissociation limit, as well as some vibrational frequencies. -- Also directly related to the interelectronic distance, is the issue of electron correlation. Several new approaches to the electron correlation problem have emerged in recent years. Among the new methods is orbital functional theory, in which the correlation energy is a functional of the molecular orbitals. The correlation energy of different isoelectronic series as a function of nuclear charge is investigated in an effort to design a correlation operator. Insight is also gained by examining the explicit CISD energy expression

Capturing static and dynamic correlation with ΔNO\Delta \text{NO}-MP2 and ΔNO\Delta \text{NO}-CCSD

11 pages, 5 figuresInternational audienceThe $\Delta \text{NO}$ method for static correlation is combined with second-order M{\o}ller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results (exFCI), and on par with conventional multireference approaches

The Relative Alignment of Electron Momenta in Atoms and Molecules and the Effect of a Static Electric Field

The relative momentum of electron pairs in atoms and small molecules is examined through calculation of the <b><i>p</i></b>₁ · <b><i>p</i></b>₂ probability distribution. The likelihood of aligned or antialigned momenta between paired electrons is determined from the calculated distributions. Coulomb correlation aligns the momenta of electron pairs, and the amount of alignment varies when considering momenta in specific directions in three-dimensional space. A static electric field is found to have competing effects on momentum alignment parallel and perpendicular to the electric field. However, the net effect of the electric field on alignment is significantly smaller than the effect of Coulomb correlation. Recent experimental advances suggest that such a correlation of electron momenta can now be measured directly using attosecond spectroscopic tools