Capped Bonds

Sometimes the system being studied is too large to be calculated using MOPAC. When only a part of the system is of interest, a mechanism exists to allow only that part to be calculated, and to ignore or not consider the rest of the system. Capped bonds are used to satisfy valency requirements.

The procedure for using capped bonds (Cb) is as follows:

1.: Identify all atoms which are important to the calculation. For an enzyme, this would be the residues of the active site, for example.

2.: Identify bonds which would be broken in order to isolate the atoms of interest. Make sure these are single bonds, and try to ensure that there is not more than one broken bond on any atom. Examples of "good" broken bonds are: CH₂-CH₂, CH₂-NH, NH-NH.

3.: Attach a Cb to each atom which has a broken bond. The Cb should be positioned in the direction of the atom which has deleted, and should have a bond-length of 1.7Å, exactly. Do not mark the Cb bond length for optimization. If two broken bonds exist on an atom, use two Cb, but make the Cb-atom-Cb angle 109.471221 $^\circ$ , exactly, and do not let it optimize.

A Cb behaves like a monovalent atom, but always has a zero charge. In other words, a Cb has a core charge of +1, and always has an electron population of 1.0. Cbs have one orbital, and so can be regarded as being hydrogen-like.

Capped bonds are different from hydrogen atoms, however, in that they have a large β-value. The β value is used in the calculation of the one-electron two-center integral. Because the β value is so large, the difference in electronegativity of the Cb and the atom it is attached to, A, becomes negligible. Therefore the bonding M.O. consists of (1/2)^1/2(Cb+A). From this, it follows that the bonding M.O. contributes 1.0 electrons to the Cb.

In addition to the bonding M.O., there is an antibonding M.O. This M.O. is of form (1/2)^1/2(Cb-A), and is of very high energy.

To prevent capped bonds from forming bonds to all nearby atoms, overlaps from capped bonds to all atoms further away than 1.8Å are set to zero. Because of this, the coupling between capped bonds and all atoms, other than A, is zero. Of course, A can interact with other atoms, once it has satisfied the demands of the attached capped bond.

Because of the huge β-value, the energy of a Cb-atom bond is very large. To prevent this interfering with the calculation, when the electronic energy is calculated, contributions from Cb are ignored. For this reason it is important that the bond-length for the Cb should not be optimized.

The M.O. energy levels due to Cb-type bonds are also enormous. Before the M.O. energy levels are printed in the normal output, energy levels arising from Cb-atom bonds are first set to zero.

The electronic behavior of capped bonds can easily be studied by use of 1SCF DENSITY VECTORS.