Electron pair-bond calculations

Why does an electron-pair bond calculated by the MO method not dissociate properly We have seen that half of the time both electrons in the low-energy molecular orbital are in the vicinity of just one of the nuclei. But as the nuclei move far apart, this corresponds to a far greater energy than having only one electron in the vicinity of each nucleus, as the VB method suggests. 

Data for which no reference is given are from the Slrukturbericht of P. P. Ewald and C. Hermann. 6 R. W. G. Wyckoff, Z. Krisl., 75,529 (1930). W. H. Zachariasen, ibid., 71, 501, 517 (1929). d The very small paramagnetic susceptibility of pyrite requires the presence of electron-pair bonds, eliminating an ionic structure Fe++S2. Angles are calculated for FeS2, for which the parameters have been most accurately determined. The parameter value (correct value = 0.371) and interatomic distances for molybdenite are incorrectly given in the Slrukturbericht. 

Here r is the radius vector from the origin to a point R in the crystal, t is the electron-pair-bond function in the region near R, Pfc is the momentum vector corresponding to the three quantum numbers k (the density of states being calculated in the usual way), h is Planck s constant, and G is the normalizing factor. 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

HMO calculations of the pi electronic energies of the radicals were done using the values of coulomb and bond integrals suggested by Streitwieser (5). The only exception to these integral values was for the case of a heteroatom (with lone electron pair) bonded to the radical center carbon. The bond integrals for this case were chosen to be one-half the values suggested by Streitwieser ... 

Point (3) above requires some amplification. At the quantitative level, the ultimate aim of either a VB or an MO calculation is to obtain the total molecular wave function. Such a function will lead to an electron density map for the molecule which should yield information about its bonding and insights into its reactivity. The function may also be manipulated in order to calculate various molecular constants whose theoretical values can be compared with experimental ones, if available. The kind of function we are talking about is a many-electron function it contains the coordinates of all the electrons in the molecule, and is usually expressed as a product of one-electron functions (i.e. orbitals). In MO theory, these are the MOs. The constraints of symmetry and orthogonality ensure that these MOs are amenable in themselves to quantum-mechanical manipulations. In VB theory, however, the one-electron functions are localised bond orbitals which are not quite respectable and are not immediately amenable to manipulation. The total molecular wave function obtained from a VB calculation is not necessarily inferior to its MO counterpart however, its factorisation into one-electron functions is designed to preserve the useful and successful notion of the localised electron-pair bond. This has the disadvantage that the one-electron functions are less useful for quantum-mechanical purposes. 

Is resonance a real phenomenon The answer is quite definitely no. We cannot say that the molecule has either one or the other structure or even that it oscillates between them. .. Putting it in mathematical terms, there is just one full, complete and proper solution of the Schrodinger wave equation which describes the motion of the electrons. Resonance is merely a way of dissecting this solution or, indeed, since the full solution is too complicated to work out in detail, resonance is one way - and then not the only way - of describing the approximate solution. It is a calculus , if by calculus we mean a method of calculation but it has no physical reality. It has grown up because chemists have become used to the idea of localized electron pair bonds that they are loath to abandon it, and prefer to speak of a superposition of definite structures, each of which contains familiar single or double bonds and can be easily visualizable. [30]... 

So far, OM1 is parameterized for C, H, N, O and F, and leads to a substantial improvement in the calculation of excitation energies OM2 is parameterized for C, H, N, and O, and provides a distinct improvement with regard to the stereochemical environment of electron pair bonds, which is important for modeling conformational properties (Thiel, 2000). Recent comparative analyses of the performance of various NDDO-based schemes include also results for OM1 and OM2 (Thiel, 1998 2000), and there are also other routes of improving the NDDO scheme (Repasky et al 2002a, 2002b). 

To compensate for experimental uncertainty it is assumed that the length of isolated electron-pair bonds are calculated from observed dissociation energies using r0 = 1.60 for carbon, and tabulated as d0 in Table 5.1. Differences in bond length, corresponding to the energy differences AE, are assumed given by... 

These predictions are borne out quantitatively in HL calculations of electron-pair bond energies and bond lengths for heteronuclear atomic pairs [114, 142]... 

Fg dissociation, for which the Hartree-Fock calculations favor two F atoms with respect to F by 130 kD/mole. Apparently in dissociations and potential curves involving the electron-pair bond rupture, the correlation energy is of crucial importance and use must be made of some approach which goes beyond the Hartree-Fock limit, A degree of success of some such treatments is discussed in Section 5,D. Sometimes one can arrive at the dissociation energy indirectly. For example, the reaction... 

Addresses all of the above shortcomings of VB theory Provides a deeper understanding of electron-pair bonds Accounts for the structure and properties of metals and semiconductors -> More facile for computer calculations than VB theory... 

The hydrogen molecule H2 is the simplest molecule which forms an electron-pair bond. Many calculations have been made for this molecule, which is a prototype for many other chemical bonds. One of the two basic quantum-mechanical treatments of the hydrogen molecule involves constructing a molecular orbital for the bond from a linear combination of atomic orbitals (LCAO method). The other involves constructing the molecular orbital as the product of wave functions for each of the two electrons forming the bond. Both of these methods will be outlined. 

Interesting criteria for the occurrence of a metal - metal bond can be obtained from a study of the electronic structure of the compound (molecular orbital and band structure calculations) and from the number of electrons available for metal - metal bonds, expressed by the so - called VEC (Valence Electron Concentration). In this counting of electrons, no attempt Is made to differentiate localized electron - pair bonds from bonding in terms of molecular orbitals delocalized over the entire cluster. 

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