Natural polyelectron population analysis

A method to perform a polyelectron population analysis of correlated molecular orbital wave functions on the basis of natural atomic orbitals (NAO s), as given by Weinhold, is presented. The method allows calculations of the probabilities of finding various types of electronic events occuring in some target AO positions, including the contributions of ionic and covalent resonance structures. This method is general and neither the theory nor the developed algorithm limit the number of electrons and holes that can be considered. Thus, the analyzed MO wave function can be a usual CI or a MCSCF one, and apart from Weinhold's NAO s. any other type of orthogonal AO s can be used as analyzers, provided that these AO s are linear combinations of the SCF-AO s. Numerical applications are given for ethylene, formaldehyde, butadiene, and acroleine, by adopting various AO basis-set levels (STO ?4G , 4–31G , and 6–31G ) and by analyzing correlated wave functions (CISD ). Improvements in the polyelectron populations when increasing the quality of AO basis sets and the corresponding valence NAO s are revealed by several examples. Furthermore, it is shown that the electroegativity of oxygen in acroleine only has an effect on contributions of ionic and covalent resonance structures, but not on delocalization of the double bonds. 1993 John Wiley & Sons, Inc.     

A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.     

[La(CCl_3COO)_3·dipy·H_2O]_2配合物的电子结构和化学键

作者曾系统研究[Ln(CCl_3COO)_3·dipy·H_2O]2配合物的合成和性质,并测定了[La(CCl_3COO)_3·dipy·H_2O]_2的晶体结构(待发表)。本文用量子化学INDO方法探讨镧配合物的电子结构和化学键。程序和参数见文献[1]。分子结构采用晶体结构数据。计算模型取配合物的一半,用HCOO~-代CCl_3COO~-,这样的近似对结果可能有影响,但在讨论羧基与La配位以及双聚机理时使图象更为简明清晰。分子骨架结构见图1,其中HCO_1O_5~-的一个氧     

INDO STUDIES ON THE ELECTRONIC STRUCTURE OF[Ln(CCl_3COO)_3·phen·C_2H_5OH]_2(Ln=Pr,Sm)

The electronic structure and chemical bonding of the title comp-lexes have been studied by an unrestricted INDO program made applicable forthe lanthanoid compounds.The results indicated:(1)In coordinated bonds O-Lnand N-Ln,5d orbitals of Ln have large contribution in all valence orbitalsof Ln and 4f orbitals have very small contribution.(2)The covalent chara-cter and ionic character are almost equal in the chemical bond which iscomparatively weak between phen,C_2H_5OH and Ln are mainly ionic with somecovalent character.     

Metal-thiolate bonds in bioinorganic chemistry

Metal-thiolate active sites play major roles in bioinorganic chemistry. The M--S(thiolate) bonds can be very covalent, and involve different orbital interactions. Spectroscopic features of these active sites (intense, low-energy charge transfer transitions) reflect the high covalency of the M--S(thiolate) bonds. The energy of the metal-thiolate bond is fairly insensitive to its ionic/covalent and pi/sigma nature as increasing M--S covalency reduces the charge distribution, hence the ionic term, and these contributions can compensate. Thus, trends observed in stability constants (i.e., the Irving-Williams series) mostly reflect the dominantly ionic contribution to bonding of the innocent ligand being replaced by the thiolate. Due to high effective nuclear charges of the Cu(II) and Fe(III) ions, the cupric- and ferric-thiolate bonds are very covalent, with the former having strong pi and the latter having more sigma character. For the blue copper site, the high pi covalency couples the metal ion into the protein for rapid directional long range electron transfer. For rubredoxins, because the redox active molecular orbital is pi in nature, electron transfer tends to be more localized in the vicinity of the active site. Although the energy of hydrogen bonding of the protein environment to the thiolate ligands tends to be fairly small, H-bonding can significantly affect the covalency of the metal-thiolate bond and contribute to redox tuning by the protein environment.     

[La(CCl3COO)3·dipy·H2O]2配合物的电子结构和化学键

作者曾系统研究[Ln(CCl₃COO)₃·dipy·H₂O]₂配合物的合成和性质,并测定了[La(CCl₃COO)₃·dipy·H₂O]₂的晶体结构(待发表)。     

Identification of hydrogen bonds using quantum electrodynamics

A method for the identification of hydrogen bonds was investigated from the viewpoint of the stress tensor density proposed by Tachibana and following other works in this field. Hydrogen bonds are known to exhibit common features with ionic and covalent bonds. In quantum electrodynamics, the covalent bond has been demonstrated to display a spindle structure of the stress tensor density. Importantly, this spindle structure is also seen in the hydrogen bond, although the covalency is considerably weaker than in a typical covalent bond. Distinguishing it from the ionic bond is most imperative for the identification of the hydrogen bond. In the present study, the directionality of the hydrogen bond is investigated as the ionic bond is nearly isotropic, while the hydrogen bond exhibits the directionality. It was demonstrated that the hydrogen bond can be distinguished from the ionic bond using the angle dependence of the largest eigenvalue of the stress tensor density.     

Chemical bonding in the oxides of the elements: A new appraisal

The role of electronegativity in the bonding of binary compounds is discussed and it is concluded that the usual electronegativity criteria for ionic, covalent, and metallic bonding do not apply to the oxides of the elements. One of the reasons for this is the wide variation observed in the electronegativity value of oxygen; for example, it is 3.5 in SiO₂ but 2.5 in Na₂O. It is argued that the electronegativity of oxygen is a better indication of ionicity (falling with decreasing covalency) than the electronegativity difference. Metallic bonding in oxides is treated from the point of view of polarization, and it is shown how experimental parameters of polarization and of band theory are closely related. These parameters are used for charting the proximity of oxides to the onset of metallization, while, simultaneously, the oxygen electronegativity is used for charting ionic/covalent bonding.     

Iron–sulfur bond covalency from electronic structure calculations for classical iron–sulfur clusters

The covalent character of iron–sulfur bonds is a fundamental electronic structural feature for understanding the electronic and magnetic properties and the reactivity of biological and biomimetic iron–sulfur clusters. Conceptually, bond covalency obtained from X‐ray absorption spectroscopy (XAS) can be directly related to orbital compositions from electronic structure calculations, providing a standard for evaluation of density functional theoretical methods. Typically, a combination of functional and basis set that optimally reproduces experimental bond covalency is chosen, but its dependence on the population analysis method is often neglected, despite its important role in deriving theoretical bond covalency. In this study of iron tetrathiolates, and classical [2Fe? 2S] and [4Fe? 4S] clusters with only thiolate ligands, we find that orbital compositions can vary significantly depending on whether they are derived from frontier orbitals, spin densities, or electron sharing indexes from “Átoms in Molecules” (ÁIM) theory. The benefits and limitations of Mulliken, Minimum Basis Set Mulliken, Natural, Coefficients‐Squared, Hirshfeld, and AIM population analyses are described using ab initio wave function‐based (QCISD) and experimental (S K‐edge XAS) bond covalency. We find that the AIM theory coupled with a triple‐ζ basis set and the hybrid functional B(5%HF)P86 gives the most reasonable electronic structure for the studied Fe? S clusters. 2014 Wiley Periodicals, Inc.     

Experimental and theoretical comparison of actinide and lanthanide bonding in M[N(EPR(2))(2)](3) complexes (M = U, Pu, La, Ce; E = S, Se, Te; R = Ph, iPr, H)

Treatment of M[N(SiMe3)2]3 (M = U, Pu (An); La, Ce (Ln)) with NH(EPPh2)2 and NH(EPiPr2)2 (E = S, Se), afforded the neutral complexes M[N(EPR2)2]3 (R = Ph, iPr). Tellurium donor complexes were synthesized by treatment of MI3(sol)4 (M = U, Pu; sol = py and M = La, Ce; sol = thf) with Na(tmeda)[N(TePiPr2)2]. The complexes have been structurally and spectroscopically characterized with concomitant computational modeling through density functional theory (DFT) calculations. The An-E bond lengths are shorter than the Ln-E bond lengths for metal ions of similar ionic radii, consistent with an increase in covalent interactions in the actinide bonding relative to the lanthanide bonding. In addition, the magnitude of the differences in the bonding is slightly greater with increasing softness of the chalcogen donor atom. The DFT calculations for the model systems correlate well with experimentally determined metrical parameters. They indicate that the enhanced covalency in the M-E bond as group 16 is descended arises mostly from increased metal d-orbital participation. Conversely, an increase in f-orbital participation is responsible for the enhancement of covalency in An-E bonds compared to Ln-E bonds. The fundamental and practical importance of such studies of the role of the valence d and f orbitals in the bonding of the f elements is emphasized.     

A variational biorthogonal valence bond method

The details of a simple and efficient scheme for performing variational biorthogonal valence bond calculations are presented. A variational bound on the energy functional is obtained through the use of a complete configuration expansion in a well-chosen subset of orbitals. The resultant wave functions are clearly dominated by the covalent (spin-coupled) structures, with a negligible contribution from ionic structures. The orbitals obtained compare favorably with overlap enhanced atomic orbitals obtained by other valence bond approaches. The method is illustrated by calculations on water and dioxygen difluoride. © 1994 by John Wiley & Sons, Inc.     

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.     

Avoided crossing of molecular excited states and photochemistry: Butadiene and unprotonated Schiff base

Consequences of the twisting motion around the C?C bond of butadiene and around C?C, C?N, and C? C bonds of the small unprotonated Schiff base (allylideneimine) on low-lying singlet and triplet states have been investigated employing large scale CI treatments. Characterization of the important features of the electronic wave functions in terms of VB-like ionic and covalent contributions in different twist intervals has been carried out. Importance of the zwitterionic singlet states with large charge separation in two different parts of molecule attached to the relaxed bond versus low-lying covalent excited state has been discussed. Photochemical implications of different minima on the energy hypersurfaces of the excited states with different features of electronic wave functions have been proposed.     

Ab initio study on the structural and electronic properties of Li3GaP2 compared with Li3GaN2

Structural and electronic properties of Li₃GaP₂ and Li₃GaN₂ have been investigated by the first-principles calculations within the density functional theory. The calculated lattice parameters of the two compounds are in excellent agreement with the available experimental data. Both Li₃GaP₂ and Li₃GaN₂ are direct band gap semiconductors with the band gaps of 1.26 eV and 2.37 eV, respectively. The Ga–P (Ga–N) and Li–P bonds consist of a mixture of ionic character and covalent nature, while the Li–N bond exhibits almost ionic. The bonds in the Li₃GaP₂ are shown to have stronger covalency and weaker ionicity as compared to the corresponding ones in the Li₃GaN₂.     

Valence Bond Study of Dissociation Behavior and Spectroscopic Constants for the Ground States of LiF and NaF

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On the "yl" bond weakening in uranyl(VI) coordination complexes

The U-O(yl) triple bonds in the UO(2)(2+) aquo ion are known to be weakened by replacing the first shell water with organic or inorganic ligands. Weakening of the U-O(yl) bond may enhance the reactivity of "yl" oxygens and uranyl(VI) cation-cation interactions. Density functional theory calculations as well as previously published vibrational spectroscopic data have been used to study the origin of the U-O(yl) bond weakening in uranyl(VI) coordination complexes. Natural population analyses (NPA) revealed that the electron localization on the O(yl) 2p orbital is a direct measure of the U-O(yl) bond weakening, indicating that the bond weakening is correlated to the weakening of the U-O(yl) covalent bond and not that of the ionic bond. The Mulliken analysis gives poor results for uranium to ligand electron partitioning and is thus unreliable. Further analyses of molecular orbitals near the highest occupied molecular orbital (HOMO) show that both the σ and π donating abilities of the ligands may account for the U-O(yl) bond weakening. The mechanism of the bond weakening varies with coordinating ligand so that each case needs to be examined independently.     

Orbital overlap and chemical bonding

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).     

How Chemical Bonding Impacts Halide Perovskite Nanocrystals Growth to Bulk Films: Implication of Pb−X Bond on Growth Kinetics

Lead halide perovskites nanocrystals have emerged as a leading candidate in perovskite solar cells and light-emitting diodes. Given their favorable, tunable optoelectronic properties through modifying the size of nanocrystals, it is imperative to understand and control the growth of lead halide perovskite nanocrystals. However, during the nanocrystal growth into bulk films, the effect of halide bonding on growth kinetics remains elusive. To understand how a chemical bonding of Pb−X (covalency and ionicity) impact on growth of nanocrystals, we have examined two different halide perovskite nanocrystals of CsPbCl₃ (more ionic) and CsPbI₃ (more covalent) derived from the same parent CsPbBr₃ nanocrystals. Tracking the growth of nanocrystals by monitoring the spectral features of bulk peaks (at 445 nm for Cl and at 650 nm for I) enables us to determine the growth activation energy to be 92 kJ/mol (for CsPbCl₃) versus 71 kJ/mol (for CsPbI₃). The electronegativity of halides in Pb−X bonds governs the bond strength (150–240 kJ/mol), characteristics of bonding (ionic versus covalent), and growth kinetics and resulting activation energies. A fundamental understanding of Pb−X bonding provides a significant insight into controlling the size of the perovskite nanocrystals with more desired optoelectronic properties.