Z- matrix of Ethane, How to write a Z-Mtarix, and some examples Benzene, water,Acetylene, Ethylene

Z- matrix for Ethane


A sample Z-matrix for the staggered conformation of Ethane (see the fig 1.) as follows:

S.No. Atom B.L Atom No. Angle Atom No. Dihedral angle Atom no.



1 C

2 C 1.54 1

3 H 1.0 1 109.5 2

4 H 1.0 2 109.5 1 180.0 3

5 H 1.0 1 109.5 2 180.0 4

6 H 1.0 2 109.5 1 180.0 5

7 H 1.0 1 109.5 2 180.0 6

8 H 1.0 2 109.5 1 180.0 7



Fig. 1 Staggered conformation of ethane

In the first line of Z-matrix we define atom 1, which is a carbon atom.

Atom number 2 is also a carbon atom that is distance of 1.54 Ao from atom 1(column 3 and 4).

Atom 3 is a hydrogen atom that is bonded to atom 1with a bond length od 1 Ao. The angle formed by atoms 2-1-3 is 109.50, information that is specified in column 5 and 6.

Atom 4 is a hydrogen atom that is bonded to atom 2 with a bond length od 1 Ao. The angle formed by atoms 1-2-4 is 109.50, information that is specified in column 5 and 6. Etc…..

Z-Matrix of Benzene:


C



H 1 1.082


C 1 1.387 2 120.0


H 3 1.082 1 120.0 2 0.0


C 3 1.387 1 120.0 4 180.0


H 5 1.082 3 120.0 4 0.0


C 5 1.387 3 120.0 6 180.0


H 7 1.082 5 120.0 6 0.0


C 7 1.387 5 120.0 8 180.0


H 9 1.082 7 120.0 8 0.0


C 9 1.387 7 120.0 10 180.0


H 11 1.082 9 120.0 10 0.0


Z-matrix of Ethylene:

 H



C 1 HC


H 2 HC 1 A1


C 2 CC 3 A1 1 D1


H 4 HC 2 A1 1 D1


H 4 HC 2 A1 1 D2






HC = 1.08


CC = 1.4


A1 = 120.0


D1 = 180.0


D2 = 0.0

Z-Matrix Of Water

 
 
H



O 1 OH


H 2 OH 1 OHO






OH = 1.08


OHO = 107.5

Z-Matrix of Acetylene:
 

H



C 1 HC


X 2 XL 1 A1


C 2 CC 3 A1 1 D1


X 3 XL 2 A1 4 D2


H 4 HC 5 A1 2 D1






HC = 1.08


XL = 1.0


CC = 1.2


A1 = 90.0


D1 = 180.0


D2 = 0.0