Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

Localized orbital calculations of the bonding in SO,SO2F2, ClO3F and SOCL2

Localized valence molecular orbitals have been obtained for SO, SO₂F₂, ClO₃F and SOCl₂ by the method due to Boys and Foster. The bonding in these molecules, in which the second row atom is exhibiting an excess valency, is discussed in terms of the form of these localized orbitals. The bonding of the second row atom to an oxygen atom is described by three bent bond orbitals, whilst bonding to a halogen atom is described by a single bond orbital. The participation of 3d functions in the various bonding and nonbonding orbitals is analysed in this localized orbital framework.     

The role of the sulfur 3d orbitals in bond formation in sulfur-containing compounds

The role of the sulfur 3d orbitals in bond formation is discussed by taking into account the influence of the environment on the orbitals of the sulfur atom in the molecules. The calculation results of a series of prototype molecules containing sulfur such as SF₂ SF₄, NSF₃, SF₀, H₂S are reported. It is convincingly shown that in highly electronegative environment the energy levels of the sulfur 3d orbitals are reduced to the vicinity of those of the ligand valence orbitals and their spatial distributions are contracted to the bonding area, and therefore they can participate in bond formation to a certain extent, which is enhanced by the formation of the d-p π back bonds. It seems that the result reported in this paper is helpful for the solution of the long-standing debate about the sulfur 3d orbital participation in bond formation.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

Weinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N₂ molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N₂ molecule. For example, the magnitude of F_ab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.     

Radial moment analysis of isovalent hybridization in N2

A radial moment analysis has been performed for the Hartree–Fock molecular orbitals of the nitrogen molecule. The objective of the analysis was to determine the extent of isovalent hybridization in even and odd sigma molecular orbitals. The radial moment analysis for the LC -SCF -AO fragments of the 2σ_g, 2σ_u, and 3σ_g molecular orbitals substantiates Mulliken's earlier conjecture concerning promotion into 3s atomic orbitals for the 3σ_g molecular orbital. The concept of free isovalent hybridization is discussed in terms of the atomic orbital shape defined by the extracted moments.     

Chemical Bonding in Silicon Carbonyl Complexes

Although silylene-carbonyl complexes are known for decades, only recently isolable examples have been accomplished. In this work, the bonding situation is re-evaluated to explain the origins of their remarkable stability within the Kohn-Sham molecular orbital theory framework. It is shown that the chemical bond can be understood as CO interaction with the silylene via a donor-acceptor interaction: a σ-donation from the σ_CO into the empty p-orbital of silicon, and a π-back donation from the sp² lone pair of silicon into the π*_CO antibonding orbitals. Notably, it was established that the driving force behind the surprisingly stable Si−CO compounds, however, is another π-back donation from a perpendicular bonding R−Si σ-orbital into the π*_CO antibonding orbitals. Consequently, the pyramidalization of the central silicon atom cannot be associated with the strength of the π-back donation, in sharp contrast to the established chemical bonding model. Considering this additional bonding interaction not only shed light on the bonding situation, but is also an indispensable key for broadening the scope of silylene-carbonyl chemistry.     

Pauli repulsion in the open shell species BeH and Co+

Using the natural bond orbital method, one may associate the valence bond configuration and Lewis structure concepts to wave functions consisting of molecular orbitals and thus gain intuitive insight into the molecular potential energy curves. Natural bond orbital analysis of the restricted open shell Hartree–Fock and unrestricted Hartree–Fock wave functions for the BeH ground state provides an intuitive model to help understand the nature of the bonding in this open shell species. The contrasting behavior of the bonding orbitals for different spins can be attributed to differences in the Pauli repulsive interactions with the lonepair orbitals. Such behavior occurs in BeH(²Σ) but does not in CO⁺(²Π) because the Pauli repulsion depends on the orbital overlap.     

The Pi‐Nature of Methyl Obtained by the Natural Bond Orbital Method: Orbital‐Based Rationalizations of Site‐Dependent Substitution Effects on Fine Color‐Tuning of Luminescence

Both C‐H bonding and antibonding (σ_CH and σ*_CH) of a methyl group would contribute to the highest occupied or lowest unoccupied molecular orbitals (HOMO or LUMO) in methylated derivatives of Ir(ppz)₂ 3 iq (ppz = 1‐phenylpyrazole and 3iq = isoquinoline‐3‐carboxylate). This is found by analysis of HOMO (or LUMO) formed by linear combination of bond orbitals using the natural bond orbital (NBO) method. The elevated level of HOMO (or LUMO) uniformly found for each methylated derivative, indicating the σ_CH‐destabilization outweighs the σ*_CH‐stabilization. To broaden the HOMO‐LUMO gap, methylation at a carbon having smaller contribution to HOMO and/or larger contribution to LUMO is suggested.     

Orbital Energy Order and the Through Bond Interaction in Homonuclear Diatomic Molecules

The homonuclear diatomic molecules are the simplest systems having both the σ framework and the lone pair orbitals n_a and _b for investigating their through space and through bond interaction. The striking orbital energy order n_g～ n_a+ n_b > n_n ～ n_a - n_b has been accounted for by the through bond interaction. However, when the p-content in the lone pair orbitals n_a and n_b decreases, one may have the reverse orbital energy order: n_g < n_g. A reverse orbital energy order has been found in F₂ and Cl₂, whose n_a and n_b are almost pure s-type atomic orbitals. The reverse order also occurs in molecule N₂ when the internuclear distance is larger man 1.5 Å. It is also found that the detail through space and through bond interaction and the eventual orbital energy order for n_g and n_u can be accounted for by the Fock operator within the localized molecular orbital space.     

Effect of bond orbital interactions on the conformational stabilities of 1,2-difluoroethane and 2,3-difluorobutanes

Several hypotheses have been proposed to explain the origin of the conformational stabilities of 1,2-difluoroalkanes, for which bond orbital interactions are an important factor. However, there is a limit to the effectiveness of the traditional approach focusing on only the antiperiplanar interactions between bonding and antibonding orbitals such as σ_C–H/σ_C–F*, σ_C–C/σ_C–F*, and σ_C–F/σ_C–F*, which cannot actually explain the conformational stabilities of 2,3-difuluorobutanes. In this study, to elucidate the effect of bond orbital interactions on the conformational stabilities of 1,2-difluoroethane, erythro-2,3-difluorobutane, and threo-2,3-difluorobutane, we extended the range of interactions considered to beyond these conventional interactions. The results showed that for 1,2-difluoroethane, the conformational stability can be understood by considering all antiperiplanar bond orbital interactions around the C1–C2 bond, and for 2,3-difluorobutanes, by considering all antiperiplanar bond orbital interactions around the C2–C3 bond in addition to bond orbital interactions between the methyl groups.     

Maximum bond order hybrid orbitals

Summary Based on the simplified calculation scheme of the maximum bond order principle and the basic idea of the maximum overlap symmetry orbital method, a simple procedure is suggested for constructing systematically the bonding hybrid orbitals, called maximum bond order hybrid orbitals, for a given molecule from the first-order density matrix obtained from a molecular orbital calculation. As an example, the proposed procedure is performed for some typical small molecules by use of the density matrix obtained from CNDO/2 calculation. It is shown that the bonding hybrid orbitals constructed by using the procedure are extremely close to those by using the natural hybrid orbital procedure and in good agreement with chemical intuition, and that the proposed procedure can be performed more easily than the natural hybrid orbital procedure and can given simultaneously the values of the maximum bond order for all bonds in molecules.The project was supported by National Natural Science Foundation of China and also supported partly by Foundation of Hubei Education Commission     

A Systemic DFT Study on Several 5<Emphasis Type="Italic">d</Emphasis>-Electron Element Dimers: Hf<Subscript>2</Subscript>, Ta<Subscript>2</Subscript>, Re<Subscript>2</Subscript>, W<Subscript>2</Subscript>, and Hg<Subscript>2</Subscript>

Eleven kinds of density functionals in conjunction with three different basis sets are employed to investigate the homonuclear 5d-electron dimers: Hf₂, Ta₂, Re₂, W₂ and Hg₂. The computed bond lengths, vibrational frequencies and dissociation energies of these molecules are used to compare with available experimental data to find the appropriate combination of functional and basis set. The different functionals and basis sets favor different ground electronic state for Hf₂ and Re₂ molecules, indicating that these two dimers are sensitive to the functionals used. The molecular properties of Hg₂ dimer depend strongly on both functionals and basis sets used. It is found that the BP86 and PBEPBE functionals are generally successful in describing the 5d-electron dimers. For the ground states of these dimers, the bonding patterns are determined by natural bond orbital (NBO) analysis. Natural electron configurations show that the 6s and 5d orbitals in the bonding atoms hybrid with each other for the studied dimers except for Hg₂.     

Bonding/antibonding character of “lone pair” molecular orbitals from their energy derivatives; consequences for experimental data

The derivative of molecular orbitals (MO) energies with respect to a bond length (dynamic orbital force [DOF]) is used to estimate the bonding/antibonding character of valence MOs along this bond, with a focus on lone pair MOs, in a series of small molecules: AH (A = F, Cl, Br), AH₂ (A = O, S, Se), AX₃ (A = N, P, As; X = H, F), and H₂CO. The HOMO DOF agrees with the calculated variation of bond length and force constant in the corresponding ground state cation, and of bond length variation by protonation. These results also agree with available experimental data. It is worthy to note that the p‐type HOMOs in AH and AH₂ are found bonding. The lone pair MO is bonding in NH₃, while it is antibonding in PH₃, AsH₃, and AF₃.     

Electronic charge density and mean kinetic energy of lithium orbitals in LiH,LiH+, Li2, Li2+, LiH2+, and Li2H+

The electron density near the lithium nucleus in the species LiH, LiH⁺, Li₂, Li₂⁺, LiH₂⁺, and Li₂H⁺ was analyzed by transforming the SCF molecular orbitals into a sum of atomic contribnutions, for both core and valence orbitals. These “hybrid-atomic” orbitals were used to compare: electron densities, orbital polarizations, and orbital mean kinetic energies with the corresponding lithium atom quantities. Core-orbital electron densities at the lithium nucleus were observed to increase by up to 0.5% relative to the lithium atom 1s orbital. Lithium cores also exhibited polarization but, surprisingly, in the direction away from the internuclear region. Similar dramatic changes were seen in the electron densities of the valence orbitals of lithium: The electron density at the nucleus for these orbitals increased two-fold for homonuclear species and twenty-fold for heteronuclear triatomic species relative to the electron density at the nucleus in lithium atom. The polarization of the valence orbital electronic charge, in the vicinity of the lithium nucleus, was also away from the internuclear region. The mean “hybrid-atomic” orbital kinetic energies associated with the lithium atom in the molecules also showed changes relative to the free lithium atom. Such changes, accompanying bond formation, were relatively small for the lithium core orbitals (within 0.2% of the value for lithium atom). The orbital kinetic energies for the lithium valence electrons, however, increased considerably relative to the lithium atom: By a factor of about 2 in homonuclear diatomics, by a factor of 7 in heteronuclear diatomics, and by a factor of 11 in the triatomic species. In summary, the total electronic density (core plus valence) at the lithium nucleus remained remarkably constant for all of the species studied, regardless of the effective charge on lithium. Thus, the drastic changes noted in the individual lithium orbitals occurred in a cooperative fashion so as to preserve a constant total electron density in the vicinity of the lithium nucleus. In all cases, bond formation was accompanied by an increase in the orbital kinetic energy of the lithium valence orbital. We suggest that these two observations represent important and significant features of chemical bonding which have not previously been emphasized.     

Valence bond studies of AH2 molecules

Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the³ B ₁ and¹ A ₁ states of CH₂. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the³ B ₁ state gave a geometry of R_C-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was ?38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH₂ as BeH₂. The nature of the lone-pair and bonding orbitals is found to be significantly different between the³ B ₁ and¹ A ₁ states. In the³ B ₁ state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the¹ A ₁ state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H₂O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.     

Balancing Donor-Acceptor and Dispersion Effects in Heavy Main Group Element π Interactions: Effect of Substituents on the Pnictogen⋅⋅⋅π Arene Interaction

High-level ab initio calculations using the DLPNO-CCSD(T) method in conjunction with the local energy decomposition (LED) were performed to investigate the nature of the intermolecular interaction in bismuth trichloride adducts with π arene systems. Special emphasis was put on the effect of substituents in the aromatic ring. For this purpose, benzene derivatives with one or three substituents (R=NO₂, CF₃, OCHO, OH, and NH₂) were chosen and their influence on donor-acceptor interaction as well as on the overall interaction strength was examined. Local energy decomposition was performed to gain deeper insight into the composition of the interaction. Additionally, the study was extended to the intermolecular adducts of arsenic and antimony trichloride with benzene derivatives having one substituent (R=NO₂ and NH₂) in order to rationalize trends in the periodic table. The analysis of natural charges and frontier molecular orbitals shows that donor-acceptor interactions are of π→σ* type and that their strength correlates with charge transfer and orbital energy differences. An analysis of different bonding motifs (Bi⋅⋅⋅π arene, Bi⋅⋅⋅R, and Cl⋅⋅⋅π arene) shows that if dispersion and donor-acceptor interaction coincide as the donor highest occupied molecular orbital (HOMO) of the arene is delocalized over the π system, the M⋅⋅⋅π arene motif is preferred. If the donor HOMO is localized on the substituent, R⋅⋅⋅π arene bonding motifs are preferred. The Cl⋅⋅⋅π arene bonding motif is the least favorable with the lowest overall interaction energy.     

Analysis of carbon-carbon bonding in small hydrocarbons and dicarbon using dynamic orbital forces: Bond energies and sigma/pi partition. Comparison with sila compounds

The CC bonding is analyzed using dynamic orbital forces (DOF) in the series cyclopropane-ethane- benzene-ethylene-acetylene. The sum Σ(DOF)_t of the DOF over occupied molecular orbitals (MOs) is found linearly correlated to bond energies and thus can be used as a tool for determination of CC bond strength. A partition of bonding into σ and π components indicates a weakening of the σ bonding along the series, mainly due to the decrease of the bonding character of the highest σ MO. For C₂ molecule, Σ(DOF) _t was computed taking into account the four dominant configurations. On the basis of the preceding correlation, the C₂ bond was found about 15 kcal/mol weaker than that of acetylene, with a 25% σ participation; the bond order of C₂ can be evaluated at about 2.8 if we assume bond orders of 3 for acetylene and 2 for ethylene. Some sila homologs of the preceding carbon compounds have been studied. They exhibit characteristics generally close to the carbon compounds. A quite good correlation between Σ(DOF)_t and bond energies is also observed.     

The Bond Order of C2 from a Strictly N‐Representable Natural Orbital Energy Functional Perspective

The bond order of the ground electronic state of the carbon dimer has been analyzed in the light of natural orbital functional theory calculations carried out with an approximate, albeit strictly N‐representable, energy functional. Three distinct solutions have been found from the Euler equations of the minimization of the energy functional with respect to the natural orbitals and their occupation numbers, which expand upon increasing values of the internuclear coordinate. In the close vicinity of the minimum energy region, two of the solutions compete around a discontinuity point. The former, corresponding to the absolute minimum energy, features two valence natural orbitals of each of the following symmetries, σ, σ*, π and π*, and has three bonding interactions and one antibonding interaction, which is very suggestive of a bond order large than two but smaller than three. The latter, features one σ–σ* linked pair of natural orbitals and three degenerate pseudo‐bonding like orbitals, paired each with one triply degenerate pseudo‐antibonding orbital, which points to a bond order larger than three. When correlation effects, other than Hartree–Fock for example, between the paired natural orbitals are accounted for, this second solution vanishes yielding a smooth continuous dissociation curve. Comparison of the vibrational energies and electron ionization energies, calculated on this curve, with their corresponding experimental marks, lend further support to a bond order for C ₂ intermediate between acetylene and ethylene.     

THE NATURE OF THE HOMONUCLEAR BOND IN ORGANIC AND INORGANIC DICHALCOGENIDES

Abstract

The electronic structures of a number of disulfide R₂S₂, and peroxide, R₂O₂, compounds are theoretically investigated or reinvestigated, and the results are compared and contrasted with each other as well as with experimental data. The results show that the enormous bond length variations in these compounds cannot be explained on the basis of the simple electronegativity difference model, but rather one must take into consideration terminal group atomic orbital contributions to the predominately homonuclear bonding molecular orbitals. The qualitative aspects of the bonding parameters of a large number of disulfide and peroxide compounds are explained.