Valence-bond structures, linear

The separation of chemical species by size exclusion chromatography is more reproducible than any other type of chromatography. Once the SEC columns, the mobile phase (most often a pure solvent like THF or toluene), and the flow rate are selected, the retention volume (or retention time assuming the flow rate does not change) is primarily a function of linear molecular size, which can be obtained from the valence bond structure if the compound is known. Some of the chemical species can interact with the solvent forming complexes with an effective linear size greater than that of the molecule. This causes the expected retention volume, based on "free" molecular structure, to shift to a lower but very reproducible retention volume. Phenols in coal liquids form 1 1 complex with THF (9,10) and carry the effective linear molecular size to increase. As a result phenolic species elute sooner than expected from their... 

Trivalent ( classical ) carbenium ions contain an, vp2-hybridized electron-deficient carbon center that tends to be planar in the absence of constraining skeletal rigidity or steric interference. (It should be noted that ip-hybridized, linear acyl cations and vinyl cations also show substantial electron deficiency on carbon.) The carbenium carbon contains six valence electrons, and thus it is highly electron-deficient. The stmcture of trivalent carbocations can always be adequately described by using two-electron, two-center bonds (Lewis valence bond structures). 

N2O has a linear geometry with an N-O distance of 118.6 pm and an N-N distance of 112.6 pm. The N-N bond can be regarded to be between a double and triple bond, the N-O bond is between a single and a double bond. The extended valence bond structures in (142) describe the observed N-N and N-O bond lengths in N2O better. The right structure gives is the best representation of the actual bonding situation. ... 

The retention volume of several aliphatic, phenolic, heterocyclic, amine and aromatic compounds in THF and toluene have been reported elsewhere ( ). It is clear that aromatic compounds, as expected from their valence bond structures, have smaller linear molecular sizes compared to n-alkanes of similar molecular weight It is expected that most of the con-... 

In cis azobenzene, steric factors prevent the molecule being flat owing to the interference of the two hydrogen atoms in the ortho position, and the C—N—N system (the C being in a benzene ring) is not linear, with the result that a valence bond structure of the type VIII cannot contribute to the molecular resonance. The CN bond distance is found to be 1 46 A as in the single bond and the molecule is represented correctly by the formula IX. 

Although the bis(dithiocarbamate) complexes of Fe(II) are relatively unstable to air oxidation, early studies (12, 15) produced stable adducts of NO and CO. Both 5-coordinate [Fe(NO)(I dtc)2] and 6-coordinate [Fe(NO)2(R2dtc)2] complexes are known. There has been considerable interest in the mode of attachment of the NO molecule, as there are six possibilities (see Scheme 4). (A) and (B) represent valence-bond structures of the linear Fe-NO bond. Structure (C) involves a symmetric Fe-NO TT-bond. Structure D illustrates the bent mode of attachment, in which nitrosyl is coordinated to the metal through the nitrogen atom, but the Fe-NO bond-angle differs greatly from 180°. Structures (E) and (F) are valence-bond formalisms of an unsymmetrical, metal-NO 7r-bond. The structure of [Fe(NO)(R2dtc)2] (R = Me or Et) has been shown (230,231) to be square pyramidal, with four sulfur atoms in... 

The valency angles, in addition to the bond distances, may be determined from electron diffraction studies and the magnitude of the bond angle may be regarded as an indication of the extent of the contribution of various valence bond structures in which the angle is different. For example, methyl wocyanide is generally considered as being a linear mole. 

Alternatively, the valence bond (VB) theory provides an original basis for the definition of the resonance energy (RE) which is considered as the difference between the energy Esvb of a state described by a single valence bond structure and the energy mvb of the true state described by a linear combination of many valence bond structures. ... 

Li H" for LiH, or and for ) have configuration wave-functions (or structure wavefunctions or bond-eigenfunctions) designated as /i and Yj for their electrons, then the construction of linear combinations of these wave functions is equivalent to invoking resonance between the valence-bond structures. The valence-bond structmes are said to be stabilized by resonance if one of the linear combinations has a lower energy than has either... 

To improve further the molecular orbital wave-function, we may invoke configuration interaction (C.I.), i.e. linearly combine the bonding configuration Vab(l)Vab(2) with the antibonding configuration )/ (1) )/ (2). Covalent-ionic resonance improves the Heitler-London valence-bond function, This resonance involves linearly combining the covalent wave-function a(l)b(2) + b(l)a(2) with the wave-functions a(l)a(2) and b(l)b(2) for the ionic valence-bond structures A B" and A B . For Hj, the appropriate ionic wave-function is... 

If we choose the coefficients Q to Q so that the energy of T is minimized, we shall obtain six linear combinations, one of which we shall designate as T(best). Its energy is such that no other linear combination of Pi to can generate a lower energy. Alternatively, we may say that this energy is the lowest that can arise from resonance between the valence-bond structures (l)-(6). Each of these six structures is stabilized to a maximum extent by resonance with the other five structures. 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

Valence bond theory was initially the most widely accepted approach, probably because it depended on familiar concepts of mesomeric effects in conjugated systems. The theory assumed that the true wave function for the mesomeric state of a molecule is a linear sum of those of the contributing canonical forms. The technique was never successful for quantitative calculation of the absorption spectra of dyes, however, because of the difficulties encountered when introducing the numerous canonical structures necessary for computational precision. 

The first calculations on a two-electron bond was undertaken by Heitler and London for the H2 molecule and led to what is known as the valence bond approach. While the valence bond approach gained general acceptance in the chemical community, Robert S. Mulliken and others developed the molecular orbital approach for solving the electronic structure problem for molecules. The molecular orbital approach for molecules is the analogue of the atomic orbital approach for atoms. Each electron is subject to the electric field created by the nuclei plus that of the other electrons. Thus, one was led to a Hartree-Fock approach for molecules just as one had been for atoms. The molecular orbitals were written as linear combinations of atomic orbitals (i.e. hydrogen atom type atomic orbitals). The integrals that needed to be calculated presented great difficulty and the computations needed were... 

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