4. Bond Dissociation Energy

Starting from this lecture, we will introduce the applications of valence bond (VB) theory in computational chemistry. First, we will explain how to calculate the bond dissociation energy (BDE) of a molecule using VB calculations.

4.1. Definition of Bond Dissociation Energy

The bond dissociation energy (BDE) is, simply put, the energy released upon the formation of a chemical bond, or equivalently, the energy required for bond dissociation. Numerically, it is equal to the energy difference between the fully dissociated fragments and the equilibrium molecular structure:

\[BDE = E^\infty - E^{\textrm{eq}}\]

where \(E^\infty\) is the energy of the molecule at complete dissociation, and \(E^\textrm{eq}\) is the energy of the molecule at equilibrium.

4.2. How to Compute Bond Energy?

For diatomic molecules, we can simply increase the internuclear distance between the two atoms until it becomes sufficiently large. Generally, a separation larger than 10 Å can be considered as complete dissociation of the fragments. For example, for the HF molecule, the input file for its equilibrium geometry is:

 1$CTRL
 2VBSCF STR=FULL NAO=2 NAE=2
 3ORBTYP=HAO FRGTYP=SAO
 4INT=LIBCINT BASIS=6-31G*
 5$END
 6$FRAG
 71 1 1 1
 8spzdxxdyydzz 2
 9pxdxz 2
10pydyz 2
11s 1
12$END
13$ORB
141 1 1 1 1 1
151
161
172
183
191
204
21$END
22$GEO
23H 0.0 0.0 0.0
24F 0.0 0.0 1.0
25$END

To calculate the dissociation energy, we simply move the F atom along the Z-axis from 1.0 to 10.0 (keeping all else unchanged). This way, we can compute the energy of the fully dissociated HF molecule.

geometry, whereas in the radical form it is planar. If we simply stretch the distance between the two CH3 groups in ethane( C2 H6 ) until complete dissociation, the resulting energy will deviate considerably from the actual value. This deviation arises from the difference in geometry between the pyramidal CH3 group and the planar CH3 radical, and is referred to as the geometry relaxation energy. In bond dissociation energy calculations of polyatomic molecules, geometry relaxation energy must therefore be taken into account. In such cases, one cannot simply elongate the bond between the two fragments; instead, each dissociated fragment must be independently optimized to obtain its stable geometry, after which the optimized fragments are placed at a sufficiently large separation to represent complete dissociation, and the input file is constructed based on this geometry.