Volume 2: Chapters 11-14 by Brilliant Light Power

Volume 2: Chapters 11-14

Chapter 13

554

( Z  n)e 2  1 1       13.60580 eV  0.30647  2   8.33948 eV 8 0  r5 r6  n4 4

ET  CN , C 2 p   

(13.831)

The radius r7 of the nitrogen atom before bonding is given by Eq. (10.142): r7  0.93084a0

(13.832)

Using the initial radius r7 of the N atom and the final radius r6 of the N 2 p shell of CN (Eq. (13.829)) and by considering that

the central Coulombic field decreases by an integer for each successive electron of the shell, the sum ET  CN , N 2 p  of the

Coulombic energy change of the N 2 p electron is determined using Eq. (10.102): ( Z  n)e 2  1 1       13.60580 eV  0.23518  2  3  15.99929 eV 8 0  r6 r7  n4 5

ET  CN , N 2 p   

(13.833)

FORCE BALANCE OF THE  MO OF THE CARBON NITRIDE RADICAL

The diamagnetic force FdiamagneticMO1 for the  -MO of the CN molecule due to the two paired electrons in the N 2 p shell given by Eq. (13.633) with ne  2 is: 2 (13.834) Di 2me a 2b 2 The force FdiamagneticMO 2 is given by Eq. (13.634) except that the force is summed over the individual diamagnetic-force terms due

FdiamagneticMO1 

to each component of angular momentum Li acting on the electrons of the  -MO from each atom having a nucleus of charge Z j at one of the foci of the  -MO:

FdiamagneticMO 2  

Li 

Di (13.835) Z j 2me a 2b 2 Using Eqs. (11.200), (13.633-13.634), and (13.834-13.835), the force balance for the  -MO of the carbon nitride radical 3 comprising carbon with charge Z1  6 and L1   and L2   and nitrogen with Z 2  7 and L3   is 4 i, j

  3 2   1 e   4 1    1      D D D D  Z 8 0 ab 2 2me a 2b 2 me a 2b 2 Z1 Z 2  2me a 2b 2 1  2

  3  1 1  2 e2 2 4   D D    D 2 2 8 0 ab 2 me a 2b 2  Z1 Z1 Z 2  2me a b   3   2 1 1 e2 2  4    D D  8 0 ab 2 Z1 Z1 Z 2  2me a 2b 2    3  1 1  4 a   2     a0 Z1 Z1 Z 2  

(13.836)

(13.837)

(13.838)

(13.839)

Substitution of Z1  6 and Z 2  7 into Eq. (13.839) gives a  2.45386a0  1.29853 X 1010 m

(13.840)

Substitution of Eq. (13.840) into Eq. (11.79) is c  1.10767a0  5.86153 X 1011 m

(13.841)

The internuclear distance given by multiplying Eq. (13.841) by two is 2c  2.21534a0  1.17231 X 1010 m

(13.842)

The experimental bond distance from Ref. [28] is 2c  1.17181 X 1010 m Substitution of Eqs. (13.840-13.841) into Eq. (11.80) is

(13.843)