Study of the electronic structure of molecules. XV. Comments on the molecular orbital valency state and on the molecular orbital energies

The valency state (vs) concept is analyzed in the Hartree–Fock approximation. A valency state “standard” is defined for atoms at infinite separation. A molecular orbital valency state (Movs) is defined from a partitioning technique (bond energy analysis) previously introduced for the Hartree–Fock molecular wave functions. The Movs for a given atom in a molecule is much higher in energy than the vs and its energy varies from molecule to molecule depending on the exact field of the surrounding atoms. The examples selected in the discussion are the CH₄ CH₃F, CH₂F₂, CHF₃ and CF₄ molecules. An analysis of the orbital energies is then given in terms of the bond energy. The importance of the rearrangement effects following ionization of inner shell electrons (simulation of ESCA type experiments) is illustrated with computations of the positive ion for methane and its fluoroderivatives. It is concluded that rearrangement following ionization from inner shells is as important as rearrangements following ionization from valency electrons. A direct consequence is that the orbital energies should not be equated to the inner shell ionization potentials. The computation of such ionization potentials agrees to about 99.5% with ESCA data, when the energy of both the neutral and ionic species are computed; the use of the orbital energies limits this agreement to about 95%.     

Classical chemical concepts from ab initio SCF calculations

Alternative definitions of bond order, valency, gross orbital populations and total atomic charge for SCF wavefunctions are compared. It is found that there are sound theoretical and numerical reasons for preferring definitions based on the Löwdin density matrix.     

Polycyclic aromatic hydrocarbons with five-membered rings: Modeling of experimental X-ray and neutron-diffraction structures

Several of the readily available theoretical programs are evaluated as tools for modeling the structures of polycyclic aromatic hydrocarbons with five-membered rings (CPAHs). The experimentally determined bond lengths and angles are compared to calculated values. Experimental bond lengths are also compared to Pauling and Huckel molecular orbital (HMO) bond orders. Previously published experimental X-ray and neutron-diffraction structures of acenaphthene, acenaphthylene, fluoranthene, cyclopent[o,p,q,r]benz[c]phenanthrene, and corannulene are modeled by the programs MMX, AM1, MNDO, and PM3, and previously reported STO-3G and 6-31G * data are also evaluated. In general, the error differences between the experimental and calculated results for all of the semiempirical programs were small. However, PM3 performed slightly better than AM1 and MMX, while MNDO generated structures which exhibited the largest deviation from experiment. Although the standard deviations for all programs are shown to be of comparable magnitude, a particular bond length or bond angle in any given theoretical calculation can exhibit significant error from the experimental data. The scatter in the bond order data computed from Huckel molecular orbital theory and valence bond theory is contrary to results obtained with alternant systems. It appears that these approaches are less successful at modeling accurately the nonalternant hydrocarbon systems described in this paper.     

Molecular mechanics force-field parameterization procedures

A set of procedures and guidelines are presented for the estimation of bond length, bond angle, and torsional potential constants for molecular mechanics force fields. The force field constants are ultimately derived by “subtracting” nonbonded molecular mechanics energies from corresponding molecular orbital energies using a model compound containing the chemical structure to be parameterized. Case study examples of bond length, bond angle, and torsional rotation force field parameterizations are presented. A general discussion of molecular mechanics force field parameterization strategy is included for reference and completeness. Finally, a curve-fitting program to generate force field parameters from raw data is given in Appendix I.     

Standard bond lengths for use in ab initio molecular orbital calculations

Standard bond lengths are proposed for a wide variety of bond lengths involving first row elements. These were obtained as average values from a large number of calculations made at the ab initio molecular orbital 4-31G level with geometry optimization. It is shown that these are generally in good agreement with accurate experimental values, where available.     

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.     

元素最高价态无机含氧酸氧化能力次周期性讨论

从原子轨道能量差异对杂化轨道成键后强度影响的角度对元素最高价态无机含氧酸氧化能力次周期性现象进行了讨论，提出了一些新的看法，半定量地解释了这一现象。     

Orbital Interaction and the Mulliken-Walsh Diagram for AH2 Systems

We define θ- (or R-) bonding (or antibonding) character of the molecular orbitals according to the slopes of the orbital energy curves when the internuclear angle (or internuclear distance) is varied. So far the slope of the orbital curve has only been accounted for by the qualitative argument based on two factors: the orbital overlap and the s-p mixing. We employ the bond orbitals instead of the usual atomic orbitals as the basis set to analysis the character of the molecular orbitals. The Fock matrix in the bond orbital basis can then quantitatively account for the effects of both the overlap and s-p mixing factors. Our analysis also show that a third factor, the orbital interaction, is essential to account for both the “typical” and “abnormal” behavior of the slopes.     

About counterintuitive orbital mixing and bond populations

It is shown that negative bond and orbital populations may be avoided by the introduction of a weight factor in a bond index definition, together with a suitable parameterization. The negative bond populations found for first-row metal complexes need not be ascribed to counterintuitive orbital mixing but rather, essentially, to the equipartition of the charge distribution. Different definitions of the bond population are compared for ferrocene and the effects of some parameterizations are discussed.     

Evolution of defect states in doped polythiophene: A study based on the method of simulated annealing

A modified Su–Schrieffer–Heeger Hamiltonian‐based model is used to compute the electronic and geometric structures of fairly long polythiophene (PT) chains, neutral as well as doped. The geometry optimization is carried out by the simulated annealing method. Both Metropolis and Glauber functions are used for sampling. It is shown that a bipolaron can be structurally represented by a fragment of the PT chain containing 14 thiophene units. As a series of bipolaronic defects are introduced in a long PT chain (50–100 rings), the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap energy (Δ) becomes vanishingly small, a feature not present in the PT chains of similar sizes containing polaronic defects. The Fermi energy level (E_F) also moves into the valency band and nonzero density of states at ? = E_F are created. Once again, this feature is shown to be missing in PT chains containing polaronic defects. Implications of these findings are analyzed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

MNDO MO theoretical study of electronic structure and homolytic dissociation of perfluoroalkanoyl peroxides

The MNDO molecular orbital method was applied to alkanoyl peroxides and the effect of fluorination on the electronic structure and the rate of the homolytic 0-0 cleavage of alkanoyl peroxides were analyzed. The fluorine atom introduced at the carbon atom makes the peroxy 0-0 bond long and the dihedral angle between two COO planes large. The analysis of two-atom energy and its components energies has shown that the rate of the 0-0 cleavage correlates well with the destabilization of the resonance energy of the 0-0 bond and not with the electrostatic energy. The effect of elongation of the perfluoroalkyl group is also well elucidated by the two-atom energy. The perfluoroalkyl group lowers the σ*(0-0) anti-bonding orbital considerably, and this fully explains the observed rate of induced decomposition of perfluoroalkanoyl peroxides with benzene.     

Explaining the effects of T-O-T bond angles on NMR chemical shifts in aluminosilicates: A natural bonding orbital (NBO) and natural chemical shielding (NCS) analysis

It has long been recognized that the 29Si and 27Al NMR chemical shifts for aluminosilicate crystals and glasses correlate to some extent with the T-O-T bond angle (where T is the tetrahedral atom Si or Al). With increasing T-O-T bond angle, the 29Si and 27Al NMR shieldings increase and the shifts thus become more negative. This result has been demonstrated both experimentally and through quantum computations. However, no simple qualitative explanation has ever been given for what appears to be a simple qualitative trend. We here provide such an explanation based upon quantum calculations. We have used high level ab initio NMR shielding calculations, natural bonding orbital (NBO) analysis, and natural chemical shielding (NCS) analysis, performed on model clusters with different T-O-T angles, to obtain an explanation for this trend from an electronic structure point of view. On the basis of both NBO populations and the NCS analysis, the following factors account for the correlation of shift with T-O-T angle: (1) a slight increase in population of the Al-O and Si-O bond orbital electrons and a dramatic change in bond orbital shapes and hybridization (with more s character and less bond bending as the T-O-T angle increases), (2) a movement of one of the lone pairs on O toward the vicinity of the Si or Al as the T-O-T angle increases, and (3) a change in the shielding contribution from the core 2p electrons of Al or Si. The changes in the 17O NMR shift with T-O-T angle are more complex, and the shifts are also more strongly influenced by distant atoms, but some systematic changes in O lone pair contributions can be identified.     

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.     

一维〔M（tmp）〕_2ReO_4（M＝Ni、Cu、Pd）聚合物的能带结构

用紧束缚ＥＨＴ晶体轨道方法对一维〔Ｍ（ｔｍｐ）〕_２ＲｅＯ_４（Ｍ＝Ｎｉ、Ｃｕ、Ｐｄ）聚合物进行了能带计算，利用键向量近似方法对能带的结构及组成进行了讨论。结果表明，该类型聚合物具有不同的导电机理，并进一步研究了环平面间的成键性质及转角改变对聚合物导电性能的影响。     

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     

An ICSCF investigation of Walsh's rules

The ICSCF method is applied to the calculation of orbital energies as a function of bond angle for several AH₂ molecules. The resulting orbital energy diagrams are quite similar in appearance to the canonical SCF results even though the sum of the ICSCF energies is the SCF energy. The method is also applied to Li₂O, CO₂, HCN and a few AH₃ molecules with similar results. The sum of the ICSCF valence orbital energies generally correlates better with the equilibrium bond angle than does the similar sum of canonical orbital energies.     

Computation of pressure components due to Class II force fields

It has been shown that purely angle dependent terms in a force field do not contribute to the total pressure in a molecular simulation. However, this is not the case for the individual components of the pressure tensor, and is also untrue for crossterms in the force field including bond stretch. In this article, we show that virial contributions to the pressure tensor are easily computed in terms of bond distance vectors and atom forces for the bond topologies present in a Class II force field. Results from a simulation of a phospholipid biomembrane using the cff97 force field show that angle and torsional crossterms make a significant contribution to the pressure tensor.     

A density functional study on magnetic exchange interaction between Mn(II) ion and nitronyl nitroxide radical in trans- and cis-metal-radical complexes

In the recent few years, transition metal complexeswith radical ligands have received much attentionaiming at a so-called metal-radical approach for novelmolecular magnet design[1]. One of the more popularfamilies is concerned in nitronyl nitroxide radica…     

The rotational barrier in ethane: a molecular orbital study

The energy change on each Occupied Molecular Orbital as a function of rotation about the C-C bond in ethane was studied using the B3LYP, mPWB95 functional and MP2 methods with different basis sets. Also, the effect of the ZPE on rotational barrier was analyzed. We have found that σ and π energies contribution stabilize a staggered conformation. The σ(s) molecular orbital stabilizes the staggered conformation while the stabilizes the eclipsed conformation and destabilize the staggered conformation. The π(z) and molecular orbitals stabilize both the eclipsed and staggered conformations, which are destabilized by the π(v) and molecular orbitals. The results show that the method of calculation has the effect of changing the behavior of the energy change in each Occupied Molecular Orbital energy as a function of the angle of rotation about the C-C bond in ethane. Finally, we found that if the molecular orbital energy contribution is deleted from the rotational energy, an inversion in conformational preference occurs.