22
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
E(A−B) = E(AB) − {E(A) + E(B)}
(2.4)
where E(X) designates the energy of the molecule or its fragment X after the zeropoint energy correction. Note that in this definition the bond energy is normally
obtained as a negative value signifying energetical stabilization due to the bond
formation. All these E(X) values can be replaced with enthalpies at certain temperature and pressure with the thermochemistry subroutine normally attached to the
usual MO calculation softwares.
2.2.4 Bond Orders
Bond order is another theoretical measure for the bond strength from rather early time.
This quantity is expressed by a numerical value and hence comparatively quantitative.
However, one should note that there has been no decisive way of definition for the
bond order. Originally, this quantity b is intuitively defined by
b =
1
2
n − n
∗
(2.5)
where n and n* designate the electron number occupying the bonding orbital and the
antibonding orbital, respectively, in the sense of the LMO’s. Thus the LMO’s purely
representing a single and a double bonds give the values of b as 1 and 2, respectively.
In a simple MO theory (Hückel MO theory) dealing with only π electrons this
quantity between the sites (that is, atoms) r and s, that is, the π-AO components at r
and s, is called π bond order and is defined by
p rs =
occ
i
ν i c ir c is
(2.6)
where c ir the i-th MO coefficient of the r-th π AO with ν i being the occupation
number of the i-th MO. Generally, p rs becomes the total electron density between
the r-th and the s-th AO’s.
By inclusion of the overlap S rs between the r-th and the s-th AO’s the bond order
p rs changes into n rs as
n rs =
occ
i
ν i c ir c is S rs
(2.7)
which is called AO bond population (Mulliken 1955). Collection of n rs in the atoms
A and B
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
E(A−B) = E(AB) − {E(A) + E(B)}
(2.4)
where E(X) designates the energy of the molecule or its fragment X after the zeropoint energy correction. Note that in this definition the bond energy is normally
obtained as a negative value signifying energetical stabilization due to the bond
formation. All these E(X) values can be replaced with enthalpies at certain temperature and pressure with the thermochemistry subroutine normally attached to the
usual MO calculation softwares.
2.2.4 Bond Orders
Bond order is another theoretical measure for the bond strength from rather early time.
This quantity is expressed by a numerical value and hence comparatively quantitative.
However, one should note that there has been no decisive way of definition for the
bond order. Originally, this quantity b is intuitively defined by
b =
1
2
n − n
∗
(2.5)
where n and n* designate the electron number occupying the bonding orbital and the
antibonding orbital, respectively, in the sense of the LMO’s. Thus the LMO’s purely
representing a single and a double bonds give the values of b as 1 and 2, respectively.
In a simple MO theory (Hückel MO theory) dealing with only π electrons this
quantity between the sites (that is, atoms) r and s, that is, the π-AO components at r
and s, is called π bond order and is defined by
p rs =
occ
i
ν i c ir c is
(2.6)
where c ir the i-th MO coefficient of the r-th π AO with ν i being the occupation
number of the i-th MO. Generally, p rs becomes the total electron density between
the r-th and the s-th AO’s.
By inclusion of the overlap S rs between the r-th and the s-th AO’s the bond order
p rs changes into n rs as
n rs =
occ
i
ν i c ir c is S rs
(2.7)
which is called AO bond population (Mulliken 1955). Collection of n rs in the atoms
A and B