Tuning the Electronic Properties of the Dative N−B Bond with Associated O−B Interaction: Electron Localizability Indicator from X‐Ray Wavefunction Refinement

Despite the immense growth in interest in difluoroborate dyes, the nature of the interactions of the boron atom within the N‐BF₂‐O kernel is not yet fully understood. Herein, a set of real‐space bonding indicators is used to quantify the electronic characteristics of the dative N?B bond in difluoroborate derivatives. The atoms‐in‐molecules (AIM) partitioning scheme is complemented by the electron localizability indicator (ELI‐D) approach, and both were applied to experimental and theoretical electron‐density distributions (X‐ray constrained wavefunction fitting vs. DFT calculations). Additionally, Fermi orbital analysis was introduced for small DFT models to support and extend the findings for structures that contain BF₂.     

Theoretical study of Pu and Am tetracarbide molecules

The electronic structure and ground‐state molecular properties of Pu and Am tetracarbides have been investigated by relativistic multireference calculations using CASSCF/CASPT2 theory as well as by density functional theory in conjunction with relativistic pseudopotentials. The CASSCF/CASPT2 treatment has been extended by spin–orbit coupling effects for selected species using the CAS state‐interaction method. The five atoms can form various structural isomers, from which 12 ones have been identified in our study. The electronic ground state in both molecules corresponds to a planar fan‐type structure of C_2v symmetry, in which the actinide atom is connected to a bent C₄ moiety. The other structures are much higher in energy, the ones computed in this study appear between 250 and 1050 kJ/mol. The bonding characteristics in the most relevant structures have been analyzed on the basis of the valence molecular orbitals and natural bond orbital analysis. The most stable structures have been characterized by their spectroscopic (vibrational and electron) properties. © 2014 Wiley Periodicals, Inc.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Basis set selections for relativistic self-consistent field calculations

Practical methods of generating reliable and economic basis sets for relativistic self-consistent fields (RSCF) calculations are developed. Large component basis sets are generated from constrained optimizations of exponents in the nonrelativistic atomic calculations for light atoms. For heavy atoms, large component basis sets for inner core orbitals are generated by fitting numerical atomic spinors of Dirac-Hartree-Fock calculations with appropriate number of Slater-type functions. Small component basis sets are obtained by using the kinetic balance condition and other computational criteria. With judicious selections of the basis sets, virtual orbitals in RSCF calculations become very similar to those in nonrelativistic calculations, implying that relativistic virtual orbitals can be used in electron correlation calculations in the same manner as the conventional nonrelativistic virtual orbitals. It is also evident that the Koopmans' theorem is also valid in RSCF results.     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. II. N2, O2, F2, and Ne2

Electron localizability indicators based on the electron pair density ELI–D and ELIA Electron localizability indicators ELI‐D and ELIA based on the electron pair density are studied for the correlated ground‐state wavefunctions of N₂, O₂, F₂, and Ne₂ diatomics. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two indicators. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for O₂ and F₂, the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Atomic and Ionic Radii of Elements 1–96

Atomic and cationic radii have been calculated for the first 96 elements, together with selected anionic radii. The metric adopted is the average distance from the nucleus where the electron density falls to 0.001 electrons per bohr³, following earlier work by Boyd. Our radii are derived using relativistic all‐electron density functional theory calculations, close to the basis set limit. They offer a systematic quantitative measure of the sizes of non‐interacting atoms, commonly invoked in the rationalization of chemical bonding, structure, and different properties. Remarkably, the atomic radii as defined in this way correlate well with van der Waals radii derived from crystal structures. A rationalization for trends and exceptions in those correlations is provided.     

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

A recently developed Thouless‐expansion‐based diagonalization‐free approach for improving the efficiency of self‐consistent field (SCF) methods (Noga and ?imunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four‐component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four‐component diagonalization‐free SCF calculations on several heavy‐metal complexes, the largest of which contains more than 80 atoms (about 6000 4‐spinor basis functions). The diagonalization‐free procedure is about twice as fast as the corresponding diagonalization. © 2014 Wiley Periodicals, Inc.     

New relativistic ANO basis sets for transition metal atoms

New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.     

ChemInform Abstract: Atomic and Ionic Radii of Elements 1—96.

The atomic radii obtained by relativistic all‐electron DFT calculations correlate remarkably well with van der Waals radii derived from crystal structures.     

Relativistic calculations for highly correlated atomic and highly charged ionic systems

The effect of electron correlations in many electron atoms or many electron atomic ions are discussed extensively based on the MultiConfiguration Dirac Fock (MCDF) calculations. In a precision atomic physics the relativistic treatment of the system is indispensable. The correlation effects and the relativistic effects are no more additive if one want to treat the many electron systems accurately. In the excited states, the single electron orbitals are modified in accordance with the vacancies near the atomic center. The electron correlations may be evaluated from the non-orthogonality of the single electron orbitals. Several examples have been given. The electronic configurations with the same total parities may interact each other even in the cases the constituent single electron orbitals have opposite parities. Such the configuration interactions may provide us with characteristic interference structures in the optical emission or absorption spectra. The anormally of the extreme ultra-violet optical emission spectra of highly charged tin ions has been illustrated as an example.     

Molecular structures of the 1,6-disubstituted triptycenes Sb2(C6F4)3 and Bi2(C6F4)3 using gas-phase electron diffraction and ab initio and DFT calculations

The structures of the D(3h)-symmetric molecules dodecafluoro-1,6-distibatriptycene and dodecafluoro-1,6-dibismatriptycene [Z2(C6F4)3 (Z = Sb, Bi)] have been determined in the gas phase by electron diffraction, using the SARACEN method, with restraints obtained from quantum chemical calculations. Several methods of ab initio and density functional theory geometry calculations have been performed and recommendations made as to their relative suitabilities for determining the structures of such species. Calculations using the MP2 method with a small-core pseudopotential (aug-cc-pVQZ-PP) on the Sb and Bi atoms and the 6-311G* basis set on the light atoms were found to give the closest correlation with the experimental results for both molecules. Differences in structure were found depending on whether a large-core or small-core pseudopotential was used on the heavy atoms.     

The bonding picture in hypervalent XF3 (X = Cl,Br, I,At) fluorides revisited with quantum chemical topology

Hypervalent XF₃ (X = Cl, Br, I, At) fluorides exhibit T‐shaped C_2V equilibrium structures with the heavier of them, AtF₃, also revealing an almost isoenergetic planar D_3h structure. Factors explaining this behavior based on simple “chemical intuition” are currently missing. In this work, we combine non‐relativistic (ClF₃), scalar‐relativistic and two‐component (X = Br − At) density functional theory calculations, and bonding analyses based on the electron localization function and the quantum theory of atoms in molecules. Typical signatures of charge‐shift bonding have been identified at the bent T‐shaped structures of ClF₃ and BrF₃, while the bonds of the other structures exhibit a dominant ionic character. With the aim of explaining the D_3h structure of AtF₃, we extend the multipole expansion analysis to the framework of two‐component single‐reference calculations. This methodological advance enables us to rationalize the relative stability of the T‐shaped C_2v and the planar D_3h structures: the Coulomb repulsions between the two lone‐pairs of the central atom and between each lone‐pair and each fluorine ligand are found significantly larger at the D_3h structures than at the C_2v ones for X = Cl − I, but not with X = At. This comes with the increasing stabilization, along the XF₃ series, of the planar D_3h structure with respect to the global T‐shaped C_2v minima. Hence, we show that the careful use of principles that are at the heart of the valence shell electron pair repulsion model provides reasonable justifications for stable planar D_3h structures in AX₃E₂ systems. © 2017 Wiley Periodicals, Inc.     

Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

We test the performance of four‐component relativistic density functional theory by calculating the static and frequency‐dependent electric dipole–dipole polarizabilities of all (ground‐state) closed‐shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape‐corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient‐regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple‐zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite‐field calculations using the coupled‐cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape‐corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare‐gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.     

Relativistic effects on inversion barriers of pyramidal group 15 hydrides

Quantum chemistry is an important tool for determining general molecular properties, although relativistic corrections are usually required for systems containing heavy and super heavy elements. Non‐relativistic along with relativistic two‐ and four‐component electronic structure calculations done with the CCSD‐T method and the new RPF‐4Z basis set have therefore been applied for determining inversion barriers, corresponding to the change from a pyramidal (C_3v) ground‐state structure to the trigonal planar (D_3h) transition state, TS, of group 15 hydrides, XH₃ (X= N, P, As, Sb, and Bi). The ground‐state structure of the McH₃ molecule, which contains the super heavy element Moscovium, is also predicted as pyramidal (C_3v), with an atomization energy of 90.8 kcal mol⁻¹. However, although non‐relativistic calculations still provided a D_3h planar TS for McH₃, four‐component relativistic calculations based on single‐reference wave functions are unable to elucidate the definitive TS geometry in this case. Hence, the results show that relativistic effects are crucial for this barrier determination in those hydrides containing Bi and Mc. Moreover, while the scalar relativistic effects predominate, increasing barrier heights by as much as 17.6 kcal mol⁻¹ (32%) in BiH₃, the spin‐orbit coupling cannot be disregarded in those hydrides containing the heaviest group 15 elements, decreasing the barrier by 2.5 kcal mol⁻¹ (4.5%) in this same molecule.     

Relativistic all-electron molecular Hartree-Fock-Dirac-(Breit) calculations on CH4, SiH4, GeH4, SnH4, PbH4

Summary Results and details of molecular Fock-Dirac-(Breit) calculations on CH₄, SiH₄, GeH₄, SnH₄, and PbH₄ obtained with the MOLFDIR© program package are presented and compared with other calculations and experimental results. The relativistic ground state energies (including the Breit interaction) of the atoms C, Si, Ge, Sn, and Pb, necessary for reference purposes, have been calculated using a small relativistic CI. One of our findings is that for the heavier systems perturbation theory over-estimates the relativistic bond length contraction. The Breit interaction has only a small effect on the bond lengths.     

Spodium Bonds: Noncovalent Interactions Involving Group 12 Elements

The term spodium (Sp) bond is proposed to refer to a net attractive interaction between any element of Group 12 and electron‐rich atoms (Lewis bases or anions). These noncovalent interactions are markedly different from coordination bonds (antibonding Sp–ligand orbital involved). Evidence is provided for the existence of this interaction by calculations at the RI‐MP2/aug‐cc‐pVTZ level of theory, atoms‐in‐molecules, and natural bond orbital analyses and by examining solid‐state structures in the Cambridge Structure Database.