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.     

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     

Nature of coordination bond in silatranes and its formation dynamics according to the ab initio calculations

Quantum-chemical calculations of 1-hydrosilatrane molecule with complete optimization of its geometry and at various fixed Si…N distances (2.0 to 3.7 Å) has been carried out at the MP2/6-31G(d) level. The silatranes coordination bond is formed of different atomic orbitals of Si and N atoms participating in a series of molecular orbitals. With the Si…N distance decreasing, contributions of the atomic orbitals in these molecular orbitals have been changed, number of the molecular orbitals has increased, and total energy of the molecule has decreased. At the coordination centers are getting closer, population of the nitrogen valence s and p _z orbitals have changed due to the corresponding bond angle change; the populations of Si and H orbitals are not significantly changed.     

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.     

Valence-bond studies of AH2 molecules

Minimal Slater basis set calculations are reported for H₂S. The calculations used both natural and hybrid atomic orbitals. The calculations were performed at H-S-H bond angles of 90 °, 92.2 ° and 95 °. The results are compared with similar calculations on H₂O and with calculations using the molecular orbital approximation. The only definite trend found in going from H₂O to H₂S is that the importance of the SH⁺H^– structure decreases. Changes in the relative importance of covalent and ionic structures depend upon which measure of importance is used. Calculations using a set of orthogonal hybrid orbitals again find the hybrid orbitals exhibiting non-perfect following behaviour with the hybrids remaining at about the equilibrium bond angle. Localized molecular orbitals were found to move in the opposite direction to the change in the H-S-H bond angle.     

Electron correlation effects on the shape of the Kohn–Sham molecular orbital

Even systems in which strong electron correlation effects are present, such as the large near-degeneracy correlation in a dissociating electron pair bond exemplified by stretched H₂, are represented in the Kohn–Sham (KS) model of non-interacting electrons by a determinantal wavefunction built from the KS molecular orbitals. As a contribution to the discussion on the status and meaning of the KS orbitals we investigate, for the prototype system of H₂ at large bond distance, and also for a one-dimensional molecular model, how the electron correlation effects show up in the shape of the KS σ _g orbital. KS orbitals φ^HL and φ^FCI obtained from the correlated Heitler-London and full configuration interaction wavefunctions are compared to the orbital φ^LCAO, the traditional linear combination of atomic orbitals (LCAO) form of the (approximate) Hartree-Fock orbital. Electron correlation manifests itself in an essentially non-LCAO structure of the KS orbitals φ^HL and φ^FCI around the bond midpoint, which shows up particularly clearly in the Laplacian of the KS orbital. There are corresponding features in the kinetic energy density t _s of the KS system (a well around the bond midpoint) and in the one-electron KS potential v _s (a peak). The KS features are lacking in the Hartree-Fock orbital, in a minimal LCAO approximation as well as in the exact one. Received: 11 December 1996 / Accepted: 10 January 1997     

Ab-Initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H₃C? NO₂ bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H₃C? NO₂ bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H₃C? NO₂ bond dissociation energies.     

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.     

Analysis of the space correlation factors in a MCSCF representation of LiH and Li2 molecules

The space correlation factor is studied in LiH and Li₂ molecules, using MCSCF wave-functions. The shape of the Fermi hole is related to the localization of molecular space orbitals, while the Coulomb hole study indicates the importance of symmetry properties of the molecular orbitals involved in excited configurations for the representation of the electronic correlation inside the chemical bond.     

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.     

An Insight of the Results Provided by Color‐Tuning Studies Made on Ir(III) Complexes: A pi‐Neutral CF3 Group Viewed by Adjusting Energies of pi‐type Molecular Orbitals

The pi‐nature of a CF₃ group can be understood through analysis of its bond orbitals (BOs) mixed into the pi‐type molecular orbitals of CF₃‐substituted Ir(ppy)₂MDPA⁺ complexes (ppy=2‐phenyl‐pyridine and MDPA=methylated 2,2′‐dipyridyl amine). It has been found that, through this natural bond orbital analysis, the parent’s molecular orbitals (MOs) can be stabilized by χρ^*_CF BO via negative hyperconjugation and, simultaneously, destabilized by electron lp(F) BO. Since these two competing pi‐effects are virtually counterbalanced as indicated by the vanishing values of crystal orbital overlap populations, the chemical substitution strategy originated from lowering of HOMO by using this electron‐withdrawing CF₃ group has been found effective in color‐tuning to blue region. Based on reduced shielding effect due to de‐ creased χρ‐electron density, the reported position dependent CF₃‐substitution effects on pi‐type MOs can also be understood through HOMO/LUMO wavefunction analysis.     

Interpreting the electronic structure of the hydrogen-bridge bond in B2H6 through a hypothetical reaction

In order to elucidate the electronic structure of the hydrogen-bridge bond in B₂H₆ molecule, the formation process of B₂H₆ had been created by a hypothetical reaction of “B₂H₄ ²⁻ + 2H⁺”, and the symmetry principles for reaction are applied in the process of creating new molecular orbitals through linear combination of the old orbitals. The orbital components of the hydrogen-bridge bond in B₂H₆ are obtained, and the electronic structure of the hydrogen-bridge bond is explained qualitatively. In addition, the idea that explains the structure of a molecule by creating a hypothetical reaction is proposed, which might make more application in other cases.     

On the determination of bond angles of triatomic radicals from electron spin resonance

The s and the p density of the sp hybrid orbital of the unpaired electron on the central nucleus of CO^?₂ and BF₂ are calculated as a function of the bond angle by the INDO molecular orbital method. The theory yields a dependence of the ratio of the p density to the s density on bond angle markedly different from a dependence derived from the orthogonality of sp hybrid orbitals and commonly used to determine the bond angle from ESR data.     

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.     

Variationally determined electronic states for the theoretical analysis of intramolecular interaction. II. Qualitative nature of the P?O bond in phosphine oxides

We have developed a space‐restricted wave function (SRW) method for the analysis of various types of intramolecular interactions. In this study, we demonstrate the applicability of our SRW method to the analysis of the nature of the P? O bond in phosphine oxide (R₃PO), one of the hypervalent molecules. An interesting character of this bond has been extensively studied by focusing on the negative hyperconjugation of the O lone pair (n_O) with the R₃P group. We reinvestigated the nature of the bond in terms of a change in total energy to produce evidence for the validity of our method. The electronic states without the interaction involving three n_O orbitals (R₃P⁺?O^?) produced by the method were used as reference states in the assessment of the effects of this n_O–R₃P interaction. The result confirms that this interaction plays an essential role in the nature of the bond and occurs between the n_O orbitals and the P? R antibonding orbitals, in agreement with previous studies. A molecular orbital (MO)‐pair analysis technique shows that the n_O–R₃P interaction is decomposed into the negative hyperconjugation and the Pauli repulsion. Considering a reference state where the P? O bond is completely broken (R₃P²⁺···O^2?) at an interacting distance, P? O bond formation is attributed to one σ bond plus two 0.5 π bonds. This is equivalent to three banana bonds highly polarized to the O atom. Consequently, the SRW method suggested improved explanations of the nature of the P? O bond. © 2012 Wiley Periodicals, Inc.     

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.     

A method for population and bonding analyses in calculations with extended basis sets

Summary A method for population and bonding analyses in the calculations with extended basis sets is proposed. The definition and evaluation method of the atomic orbitals in molecular environments (AOIMs) are described. It is shown that the AOIMs can be divided into two subsets, the strongly occupied minimal compact subset {AOIM}_B and the very weakly occupied “Rydberg” subset {AOIM}_R, according to the orbital population obtained from Mulliken analysis with AOIMs as basis sets. The viewpoint of “molecular orbitals consisting of minimal atomic orbital sets” can be optimally realized in terms of {AOIM}_B. The Mulliken population based on AOIMs is reasonable and fairly stable to changes of basis sets. The Mayer bond orders calculated based on {AOIM}_B are quite stable to the changes of basis sets; therefore they can be used to measure objectively the contribution of individual atomic orbitals to bonding.     

Coordination of neighboring C?H bond to transition metal center: III. Study on localized molecular orbitals of the binucleate ion [Fe2(CH3)(CO)(Ph2PCH2PPh2)Cp2]+

A localized INDO method was used to calculate the ion [Fe₂ (CH₃) (CO) (Ph₂PCH₂PPh₂)-Cp₂]⁺. Based on the analysis of the localized molecular orbitals (LMO), bond orders and contour maps, it was pointed out that the LMO no. 20 corresponds to the coordination of C(1)—H(1) σ bond to Fe(2) atom. Non occurrence of metal-metal bond between Fe(1) and Fe(2) atoms was found and the covalence of irons was numerated, which coincides with the value in ref 17.