Actinium coordination chemistry: A density functional theory study with monodentate and bidentate ligands

In the current study, the coordination chemistry of nine-coordinate Ac(III) complexes with 35 monodentate and bidentate ligands was investigated using density functional theory (DFT) in terms of their geometries, charges, reaction energies, and bonding interactions. The energy decomposition analysis with naturals orbitals for chemical valence (EDA-NOCV) and the quantum theory of atoms in molecules (QTAIM) were employed as analysis methods. Trivalent Ac exhibits the highest affinities toward hard acids (such as charged oxophilic donors, fluoride), so its classification as a hard acid is justified. Natural population analysis quantified the involvement of 5f orbitals on Ac to be about 30% of total valence electron natural configuration indicating that Ac is a member of the actinide series. Pearson correlation coefficients were used to study the pairwise correlations among the bond lengths, ΔG reaction energies, charges on Ac and donor atoms, and data from EDA-NOCV and QTAIM. Strong correlations and anticorrelations were found between Voronoi charges on donor atoms with ΔG, EDA-NOCV interaction energies and QTAIM bond critical point densities.     

Localization of molecular orbitals on fragments

A non‐iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single‐determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments‐in‐molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree–Fock or Kohn–Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals. © 2012 Wiley Periodicals, Inc.     

Unusual Five-Center,Four-Electron Bonding in a Rhodium–Bismuth Complex with Pentagonal-Bipyramidal Geometry

A better understanding of the chemical bond in general is gained from the electronic structure of the molecular complex [{RhBi₇}Br₈]. The interactions in the central Bi₅ ring can be interpreted as an unusual five-center, four-electron bond based on ab initio calculations and group theory. Of the linear combinations of five Bi p orbitals two of the molecular orbitals are binding (depicted in the sketch).     

The Bonding Nature of the Canonical Molecular Orbitals in Simple Diatomic Molecules

The bonding nature of the canonical molecular orbitals 2σg, 2σu and 3σg in the molecules N₂,O₂, F₂ and the related analogous molecular orbitals in the molecules P₂ and CO, is analysed using Weinhold's natural bond orbital set. When the canonical molecular orbitals can be well localized into natural bond orbitals, the covalent bond can be completely attributed to the bonding type natural bond orbitals. The decomposition of canonical molecular orbitals into the natural bond orbital basis then gives the weighted bond order as the component of the bonding portion in the canonical molecular orbital. The weighted bond order results match the photoelectron spectroscopy assignment quite satisfactorily.     

Theoretical examination of covalency in berkelium(IV) carbonate complexes

Experimental studies on the speciation of berkelium in carbonate media have shown that complexation of berkelium(III) by carbonate results in spontaneous oxidation to berkelium(IV) and that multiple species can be present in solution. We studied two proposed structures present in solution based on theoretical comparisons with spectroscopic data previously reported for Bk(IV) carbonate solutions. The multiconfigurational character of the ground and low-lying excited states in both complexes is demonstrated to result from the strong spin-orbit coupling. Although bonding in Bk(IV) carbonate and carbonate-hydroxide complexes is dominated by strong Coulombic forces, the presence of non-negligible covalent character is supported by ligand-field theory, natural localized orbitals, topological studies of the electron density, and energy transition state natural orbitals for chemical valence. Bond orders based on natural localized molecular orbitals show that Bk OH bonds possess enhanced orbital overlap, which is reflected in the bond strength. This is also observed in the decomposition of the orbital interaction energy into individual deformation density pairs.     

Local orbital study of bonding in small rings: Cyclopropane,thiirane, oxirane,and aziridine

The nature of the bonding in the three-membered ring molecules cyclopropane, thiirane, oxirane, and aziridine has been investigated throughab initio FSGO calculations. The direct correspondence between floating spherical Gaussian orbitals and specific chemical bonds has been used to study the degree of “bond bending”. In accord with chemical intuition, it is demonstrated that the C-C ring bond becomes progressively more bent as the bond length is reduced. C-C bonds are found to be more flexible than C-N (O, S) bonds. The sizes and locations of carbon-heteroatom bond orbitals and C-H bond orbitals are also discussed.     

Analyzing Pt chemical shifts calculated from relativistic density functional theory using localized orbitals: the role of Pt 5d lone pairs

Pt chemical shifts were calculated from two-component relativistic density functional theory (DFT). The shielding tensors were analyzed by using a recently developed method to decompose the spin-orbit DFT results into contributions from spin-free localized orbitals (here: natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs)). Seven chemical shifts in six Pt complexes with Pt oxidation states II, III, and IV; and halide, amino, and amidate ligands were analyzed, with particular focus on the role of nonbonding Pt 5d orbitals. A simple d-orbital 'rotation' model has been used to rationalize some of the observed trends such as the main difference between Pt(II) and Pt(IV) chemical shifts. The localized orbital analysis data showed that most of this difference as well as trends among different Pt complexes with similar coordination can be rationalized by comparing properties of the nonbonding Pt 5d orbitals. We have also analyzed the spin-orbit effects on the chemical shifts of [PtCl4](2-) compared to [PtBr4](2-).     

Complexes of 4‐substituted phenolates with HF and HCN: Energy decomposition and electronic structure analyses of hydrogen bonding

We have computationally studied para‐X‐substituted phenols and phenolates (X = NO, NO₂, CHO, COMe, COOH, CONH₂, Cl, F, H, Me, OMe, and OH) and their hydrogen‐bonded complexes with B^? and HB (B = F and CN), respectively, at B3LYP/6‐311++G** and BLYP‐D/QZ4P levels of theory. Our purpose is to explore the structures and stabilities of these complexes. Moreover, to understand the emerging trends, we have analyzed the bonding mechanisms using the natural bond orbital scheme as well as Kohn–Sham molecular orbital (MO) theory in combination with quantitative energy decomposition analyses [energy decomposition analysis (EDA), extended transition state‐natural orbitals for chemical valence (ETS‐NOCV)]. These quantitative analyses allow for the construction of a simple physical model that explains all computational observations. © 2012 Wiley Periodicals, Inc.     

Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.     

Analysis of the putative Cr-Cr quintuple bond in Ar'CrCrAr' (Ar' = C6H3-2,6(C6H3-2,6-Pr(i)2)2 based on the combined natural orbitals for chemical valence and extended transition state method

The nature of the putative Cr-Cr quintuple bond in Ar'CrCrAr' (Ar' = C(6)H(3)-2,6(C(6)H(3)-2,6-Pr(i)(2))(2)) is investigated with the help of a newly developed energy and density decomposition scheme. The new approach combines the extended transition state (ETS) energy decomposition method with the natural orbitals for chemical valence (NOCV) density decomposition scheme within the same theoretical framework. The results show that in addition to the five bonding components (σ(2)π(2)π'(2)δ(2)δ'(2)) of the Cr-Cr bond, the quintuple bond is augmented by secondary Cr-C interactions involving the Cr-ipso-carbon of the flanking aryl rings. The presence of isopropyl groups (Pr(i)) is further shown to stabilize Ar'CrCrAr' by 20 kcal/mol compared to the two Ar'Cr monomers through stabilizing van der Waals dispersion interactions.     

Study on the maximum accuracy of the pseudopotential density functional method with localized atomic orbitals versus plane-wave basis sets

A detailed study on the accuracy attainable with numerical atomic orbitals in the context of pseudopotential first-principles density functional theory is presented. Dimers of first- and second-row elements are analyzed: bond lengths, atomization energies, and Kohn-Sham eigenvalue spectra obtained with localized orbitals and with plane-wave basis sets are compared. For each dimer, the cutoff radius, the shape, and the number of the atomic basis orbitals are varied in order to maximize the accuracy of the calculations. Optimized atomic orbitals are obtained following two routes: (i) maximization of the projection of plane wave results into atomic orbital basis sets and (ii) minimization of the total energy with respect to a set of primitive atomic orbitals as implemented in the OPENMX software package. It is found that by optimizing the numerical basis, chemical accuracy can be obtained even with a small set of orbitals.     

Improved chemical energy component analysis

An improved SCF energy decomposition scheme is proposed in which a special treatment is introduced for those "ionic" one-center electron-electron repulsion energy contributions which arise from the use of doubly filled bonding orbitals. These terms characterize the bonding pattern rather than the state of the atoms, therefore they are attributed to the bonds and are redistributed between them in accord with the bond orders. This permits one to solve the dilemma which we had with the previous decomposition schemes, and obtain very "chemical" one- and two-center energy components, characterizing well the bonding situation in different molecules.     

The nature of the chemical bond in UO2

The nature of the chemical bond in UO₂ was analyzed taking into account the X-ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO₈ (D_4h) cluster, reflecting uranium's close environment in UO₂, and the U₁₃O₅₆ and U₆₃O₂₁₆ clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO₂ single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO₂ are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO₂ was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO₈ and by 25% in U₆₃O₂₁₆.     

The Nature of Chemical Bonds from PNOF5 Calculations

Natural orbital functional theory (NOFT) is used for the first time in the analysis of different types of chemical bonds. Concretely, the Piris natural orbital functional PNOF5 is used. It provides a localization scheme that yields an orbital picture which agrees very well with the empirical valence shell electron pair repulsion theory (VSEPR) and Bent’s rule, as well as with other theoretical pictures provided by valence bond (VB) or linear combination of atomic orbitals–molecular orbital (LCAO‐MO) methods. In this context, PNOF5 provides a novel tool for chemical bond analysis. In this work, PNOF5 is applied to selected molecules that have ionic, polar covalent, covalent, multiple (σ and π), 3c–2e, and 3c–4e bonds.     

Agostic interaction in the methylidene metal dihydride complexes H2MCH2 (M=Y, Zr, Nb, Mo, Ru, Th, or U)

Multiconfigurational quantum chemical methods (complete active space self-consistent field (CASSCF)/second-order perturbation theory (CASPT2)) have been used to study the agostic interaction between the metal atom and H(C) in the methylidene metal dihydride complexes H2MCH2, where M is a second row transition metal or the actinide atoms Th or U. The geometry of some of these complexes is highly irregular due to the formation of a three center bond CH...M, where the electrons in the CH bond are delocalized onto empty or half empty orbitals of d- or f-type on the metal. No agostic interaction is expected when M=Y, where only a single bond with methylene can be formed, or when M=Ru, because of the lack of empty electron accepting metal valence orbitals. The largest agostic interaction is found in the Zr and U complexes.     

Two-dimensional Hückel molecular orbital theory

The simple Hückel molecular orbital theory is extended to include hydrocarbons with sp-hybridization in addition to the sp²-hybridization. Molecular orbitals are constructed as linear. combinations of 2p orbitals in two dimensions perpendicular to each other. Total π bond orders (P) are defined and cover the range up to P = 2 in the two-dimensional case. The relationship between bond orders and CC bond lengths is studied. The theory is applied to nine hydrocarbons, which include systems with conjugated and cumulated double bonds as well as triple bonds. Calculated bond lengths from the bond orders are found to agree within ±0.03 Å with experimental values.     

Importance of backdonation in [M-(CO)]p+ complexes isoelectronic to [Au-(CO)]+

In this contribution, we study several monocarbonyl-metal complexes in order to unravel the contribution of relativistic effects to the metal-ligand bond length and complexation energy. Using scalar density functional theory (DFT) constrained space orbital variation (CSOV) energy decomposition analysis supplemented by all-electron four-component DFT computations, we describe the dependency of relativistic effects on the orbitals involved in the complexation for the Au(+) isoelectronic series, namely, the fully occupied 5d orbitals and the empty 6s orbitals. We retrieve the well-known sensitivity of gold toward relativity. For platinum and gold, the four-component results illustrate the simultaneous relativistic expansion of the 5d orbitals and the contraction of the 6s orbitals. The consequences of such modifications are evidenced by CSOV computations, which show the importance of both donation and backdonation within such complexes. This peculiar synergy fades away with mercury and thallium for which coordination becomes driven by the accepting 6s orbitals only, which makes the corresponding complexes less sensitive toward the relativistic effects.