Bonding orbitals wave function

For the standard valence-bond resonance of Section 23-3, we have used two types of wave-functions for the electron-pair bonds, namely the Heitler-London and the bond-orbital functions. We may do the same for the increased-valence functions of this section ". If we assume that electrons which occupy spatially adjacent orbitals have opposite spins, we may write down the following Heitler-London and bond-orbital wave-functions for the resonance between the increased-valence stmctures of (11) and (12). 

Molecular orbital (MO) theory describes covalent bond formation as arising from a mathematical combination of atomic orbitals (wave functions) on different atoms to form molecular orbitals, so called because they belong to the entire molecule rather than to an individual atom. Just as an atomic orbital, whether un hybridized or hybridized, describes a region of space around an atom where an electron is likely to be found, so a molecular orbital describes a region of space in a molecule where electrons are most likely to be found. 

Molecular orbital (MO) theory (Section 1.11) A description of covalent bond formation as resulting from a mathematical combination of atomic orbitals (wave functions) to form molecular orbitals. 

The equations for the bonding and anti-bonding molecular orbital wave functions for the linear combinations of the two Is atomic orbitals of the two hydrogen atoms may now be written in the forms ... 

The relationship between p or s character and bond angle will also be discussed in Chapter 6. For now we need only consider the possibility of s-p hybridization other than sp, sp2, and sp3. If we take the ratio of (he s contribution to the total orbital complement in these hybrids, we obtain 50%, 33%, and 25% s character, respectively, for these hybrids. A pure s orbital would be 100% 5, and a p orbital would have 0%r character. Since hybrid orbitals are constructed as linear combinations of s and p orbital wave functions,... 

Consider each boron atom to be ip3 hybridized.123 The two terminal B—H bonds on each boron atom presumably are simple a bonds involving a pair of electrons each. This accounts for eight of the total of twelve electrons available for bonding. Each of the bridging B—H—B linkages then involves a delocalized or three-center bond as follows. The appropriate combinations of the three orbital wave functions. B. d>D, (approximately spi hybrids), and (an s orbital) result in three molecular orbitals ... 

The obvious deduction from these observations is that the orbital energy splitting is not primarily of a simple electrostatic nature, but reflects rather the much shorter range effects to be expected of covalence in chemical bonding to the immediate donor atoms. The conclusion is reinforced by the fact that when the known interionic separations are used together with free ion 3d-orbital wave functions to evaluate Dq for first transition series ions in an MF2 lattice, values too small by an order of magnitude are obtained.6 20-22... 

P. C. Hiberty, C. Leforestier, J. Am. Chem. Soc. 100, 2012 (1978). Expansion of Molecular Orbital Wave Functions into Valence Bond Wave Functions. A Simplified Procedure. 

It will be recalled that the transformation to localized orbitals leaves the molecular orbital wave function, charge density and all other ground state properties completely unchanged. The relationship between LMOs, which are convenient for describing bonding and the CMOs, which give a zeroth order description of the one-electron ion states, was described in the last section. 

It follows, therefore, that there is only one state of the hydrogen molecule with a symmetric orbital wave function, which as we have seen leads to bond formation. On the other hand there are three states with antisymmetric orbit wave functions, which lead to repulsion. The stable form is termed a singlet and the repulsion form a triplet state. On a collision between two atoms of hydrogen, the probability that a molecule will result is therefore i 4. 

These are called sp hybrid atomic orbitais because they are formed from one s and two p orbitals. The formation, shape, and orientation of the sp hybrids are shown in Figure 6.42. They lie in the x-y plane with an angle of 120 between them. After hybridization, the electron configuration of the atom is B (1s) ( i) ( 2) (A3) Each of the sp hybrids can overlap with a H(ls) orbital to produce a a bond. The wave functions for all bonding pairs would be the same, and they will have the same form as those in Equations 6.34a and 6.34b. The third column of Eigure 6.42 shows the traditional qualitative sketches of the orbital overlap leading to a bonds in BH3, and the fourth column shows the electron density in these bonds as calculated by GVB. Experimentally, BH3 molecules turn out to be unstable and react rapidly to form or other higher com-... 

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