Orbitals bonding and antibonding

Addition of orbitals builds up electron density in overlap r ion 

In addition, two types of antibonding orbitals may also be involved in the transition  

Note r -orbitals do not exist because the electrons present in a q atomic orbital do not form bonds. 

Subtraction results in low electron density in overlap region 

Note It is possible for an electron to occupy the antibonding molecular orbital this is known as the excited state. 

With respect to which wave function corresponds to the most stable state, we shall be helped by considering the electron distribution that corresponds to each. For i jx = (1/n/2)(Xi + X2) the wave functions centered on nuclei 1 and 2 have the same sign, and their cross sections can be represented graphically as follows  

The square of the sum of (1/n/2)(Xj + X2) is a measure of the total electron probability (not the radial probability used on p. 2 ) and is here represented schematically both in cross section and from above with contour lines connected between points of equal probability as shown on the next page. It will be seen that the electron will have a considerable probability between the nuclei and will act to overcome the internuclear repulsion. While we cannot be sure without more detailed calculation whether or not the overall result will be net binding, at least the orbital might be classed as a bonding orbital because of the character of its electron distribution. On this basis, p must be a negative number. 

For the orbital = (l/ 2)(Xi X2) a similar treatmer gives the following cross section and electron probability curves  

Here we see that the electron probability is zero midway between the nuclei. As a result the electron i s not on the average well-positioned to pull the nuclei together, and we call this molecular orbital an antibonding molecular orbital. 

Although we have only concluded that and are bonding and antibonding relative to one another, it turns out 

Do we know what phase a Is orbital has In an atom, any property we want to calculate, such as the energy or the electron distribution, involves the electron density, the square of the wavefunction, and this tells us nothing about the sign of the wavefunction. So no observable property of an isolated atom will tell us the phase of the Is orbital. When we want to combine two Is orbitals, however, it matters very much whether the two have the same sign or not. In the previous Section we took two Is orbitals with the same sign, but suppose we took two Is orbitals of opposite sign. 

Midway between the nuclei, there is no chance of finding the electron because there is a nodal plane at right-angles to the molecular axis, where the electron density is zero. 

Is orbitals with (a) positive phase and (b) negative phase. 

We shall label this second orbital (lsA - lsB). (It does not matter whether we take the combination (lsA - I sB) or the combination (lsB - lsA) both will have the same observable properties.) 

An electron in an (lsA - lsB) orbital has even less chance of being attracted to both nuclei than one in a Is orbital on one of the atoms. This orbital is therefore of higher energy than the Is atomic orbital. 

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What is the energy separation E2 — E of the bonding and antibonding orbitals in ethylene, assuming that the overlap integral S is 0.27 ... 

The O atom uses one of its sp or sp hybrids to form the CO a bond and antibond. When sp hybrids are used in conceptualizing the bonding, the other sp hybrid forms a lone pair orbital directed away from the CO bond axis one of the atomic p orbitals is involved in the CO n and 71 orbitals, while the other forms an in-plane non-bonding orbital. Alternatively, when sp hybrids are used, the two sp hybrids that do not interact with the C-atom sp2 orbital form the two non-bonding orbitals. Hence, the final picture of bonding, non-bonding, and antibonding orbitals does not depend on which hybrids one uses as intermediates. 

It is well known that bonding and antibonding orbitals are formed when a pair of atomie orbitals from neighboring atoms interaet. The energy splitting between the bonding... 

In the H2 molecule, there are two Is electrons. They fill the crls orbital giving a single bond. In the He2 molecule, there would be four electrons, two from each atom. These would fill the bonding and antibonding orbitals. As a result, the number of bonds (the bond order) in He2 is zero. The general relation is... 

The notation is the same as in Exercise 3.45.) Confirm that the bonding and antibonding orbitals are mutually orthogonal— that is, that the integral over the product of the two wavefunctions is zero. 

For nonaltemant hydrocarbons the energies of the bonding and antibonding orbitals are not equal and opposite and charge distributions are not the same in... 

Butadiene has two n bonds. The interaction between the two n bonds is one of the simplest models to derive molecular orbitals from bond orbitals. A n bond in butadiene is similar to that in ethylene. The n bond is represented by the bonding and antibonding orbitals. The interactions occur between the n bonds in butadiene. The bond interactions are represented by the bond orbital interactions. 

Non-cyclic interactions of two and three orbitals are described in the preceding chapters of this volume. We describe here cyclic interactions of three or more orbitals (Scheme 1). In 1982, cyclic orbital interaction was found in non-cyclic conjugation [15]. Interactions of bonds in molecules contain cyclic interactions of bond (bonding and antibonding) orbitals even if the molecular geometry is non-cyclic. The cyclic... 

Bonds interact with one another in molecules. The bond interactions are accompanied by the delocahzation of electrons from bond to bond and the polarization of bonds. In this section, bond orbitals (bonding and antibonding orbitals of bonds) including non-bonding orbitals for lone pairs are shown to interact in a cychc manner even in non-cychc conjugation. Conditions are derived for effective cychc orbital interactions or for a continuous orbital phase. 

The history of orbital phase can be traced back to the theory of chemical bond or bonding and antibonding orbitals by Lennard-Jones in 1929. The second milestone was the discovery of the importance of orbital symmetry in chemical reactions, pointed ont by Fnkni in 1964 (Scheme 3) and established by Woodward and... 

Additive and subtractive combinations of p orbitals lead to bonding and antibonding orbitals, (a) End-on overlap gives a orbitals, (b) Side-by-side overlap gives orbitals. 

The wave function for the bonding and antibonding orbitals can be written as... 

Figure 6.22. Adsorption of an atom on a d metal. The valence electron of the adsorbate, initially at 12 eV above the bottom of the metal band, interacts both weakly with a broad sp band and strongly with a narrow d band located between 9 and 12 eV. Note the significant splitting of the adsorbate density of states into bonding and antibonding orbitals of Ha( ) due to the interaction with the d band.

Finally we look at the chemisorption of a molecule with a pair of bonding and antibonding orbitals on a transition metal (Fig. 6.25). This situation can be simply visualized with FI2, for which the bonding orbital contains two electrons and the antibonding orbital is empty, but other molecules can also be examined. In principle, we simply apply Section 6.4.2.2 twice, once to the bonding orbital, and once to the antibonding orbital of the molecule. This has been done in Fig. 6.25. 

Figure 6.32 Self-consistent calculation of the electronic structure of CO adsorbed on Al and Pt. The sharp 5

FIGU RE 3.3 Combination of two s orbitals to produce bonding and antibonding orbitals. 

The combination of fully occupied bonding and antibonding orbitals does not lead to bonding between A and B (In chemisorption theory it is sometimes said that the interaction between A and B is repulsive). 

Dimeric Cr(II) and Mo(II) carboxylate complexes, investigated by Green et al (119,120) show low-energy multiple ionization patterns of the [d4]2 system, assigned to metal-metal a, n and 8 bonding and antibonding orbitals. 

Thus in ethylene the combination of two p orbitals gives a n bonding orbital and a n antibonding orbital. An important difference between the bonding and antibonding orbitals is their symmetry. 

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