Internal coordinate z matrix computational

z matrix

1. Representing Molecules
Water
H
2
O
H‐O‐H
H
H
O
O 0.0 0.0 0.0
H -0.76 0.0 0.54
H 0.76 0.0 0.54
Cartesian coordinates
Z-matrix
O
H 1 1.0
H 1 1.0 2 104.5
simplified molecular-input line-entry
system(SMILES)
O , [OH2], [H]O[H]

2. Z‐matrix
Z‐matrix is a molecule representation method widely used in com putational 
chemistry programs.
Each atom is identified by its  internal coordinates, ie. bond length, bond 
angle and dihedral angle in relation to other atoms in the mole cule.
Element‐label, atom1, bond‐length, atom2, bond‐angle, atom3, dihedral‐angle The format for each line is
atom1, atom2, atom3 are the labels for previously‐specified atoms and are 
used to define the current atoms' position.
Items within a line can be separated by comma or space
Element‐labelis the chemical symbol for the atom  or the symbol with 
an identifying integer: C1, H2, etc.

3. Z‐matrix
Variables may be used to specify some or all of the values with in the Z‐matrix.
bond angles must be in the range 0 °< angle< 180°.
Dihedral angles may take on any value including negative.
Z‐matrix is also called  internal coordinate representation.
The name  z‐matrix arises because it assigns the second atom al ong the Z 
axis from the first atom, which is at the origin.
Bond length is in Angstrom
All the three internal coordinates need to be specified from th e fourth 
atom onwards
For the same molecule different Z‐matrices may be written depen ding on 
numbering order

4. Z‐matrix
4
2.  Diatomic molecule first line:
H
second line:connectivitylength10.8
Draw the structure
eg. H
2
H 2
nd
atom symbol
first atom symbol
H --- H
12
number the atoms in any order
2 lines in Z-matrix
.8 A
0
1. Single atom‐eg. C  only one line in the z‐matrix, only element symbol is needed
C 

5. Z‐matrix
5
O
HH
third line: symbol connectivitylength connectivityangle
second line: element symbol connectivitylength
first line: element symbol
3. triatomic molecule
Eg. H
2
O
1
2
3
H 10.8
H 1 0.8 2107.5
O
number the atoms
H 1roh
H 1roh 2107.5
O
roh=0.8
Use of variable names to enforce symmetry
one blank line
2-1 length .8
3-1 length .8
3-1-2 angle 107.5
107.5
0.8
0.8
2
3
1

6. Z‐matrix
6
third line: symbol connectivitylength connectivityangle
second line: element symbol connectivitylength
first line: element symbol
4. tetratomic molecule
Eg.Formaldehyde HCHO
O 11.2
H 1 1.1 2120.0
C
draw structure
2
3
1
C
HH
O
1
2
3
4
120
1.1
1.1
1.2
H 1 1.1 2120.0
Fourth line: symbol connectivitylength connectivityangle connectivitydihedral angle
Dihedral angle is the angle 
between two planes
4
180.0
angle between 4-1-2 and 1-2-3 planes
3 180.0
number the atoms

7. Z‐matrix
3. Polyatomic molecule
Eg. H
2
O
2
OO
H
H
O 11.3
H 11.0 2100.0
O
H 21.0 1100.0
Fourth line: symbol connectivitylength connectivityangle connectivitydihedral angle
110.0
7
4-2 length 1.0
4-2-1 angle 100.0
0
4-2-1-3 dihedral angle 110.0
0
or 4-2-1 plane and 2-1-3 plane angle is 110.0
0
4
1.3
3110.0
draw the structure. number the atoms
1
3
2
4
Dihedral angle is the angle between two planes

8. Z‐matrix
Linear polyatomic molecule
H
1
C
2
N
4
X
3
C 11.0
X 21.0 190.0
H
N 21.4 390.0
180.0
Eg. H----C----N
Z-matrix bond angles should be less than 180
0
Use dummy atom, X
1 180.0
8

9. Z‐matrix
4. polyatomic  molecule
9
third line: symbol connectivitylength connectivityangle
first line: symbol
second line: element symbol connectivitylength
fourth line: symbol connectivitylength
connectivityangle connectivitydihedral angle
H
Eg. CH
4
C
H 10.8
H 10.8 2109.5
H 10.8 2109.5 3 120.0
H 10.8 2109.5 3 -120.0
number the atoms
1
2
C
H
H
H
5
3
4
fifth line: symbol connectivitylength
connectivityangle connectivitydihedral angle
C
1
H
3
H
5
H
4
-120
0
120
0
angle between 4-1-2 plane
and 1-2-3 plane

10. Z‐matrix
10
Staggered Ethane
C
C   1    1.5 
h   1    1.0     2    109.
h   1   1.0     2     109.      3      120. 
h    1   1.0     2     109.     3    ‐120. 
h    2   1.0     1    109.      4       60. 
h    2   1.0     1    109.      6     120. 
h    2    1.0    1    109.      6    ‐120. 

11. Z‐matrix
11
Eclipsed Ethane
C
C   1    1.5 
h   1    1.0     2    109.
h   1   1.0     2     109.      3      120. 
h    1   1.0     2     109.     3    ‐120. 
h    2   1.0     1    109.      4       0. 
h    2   1.0     1    109.      6     120. 
h    2    1.0    1    109.      6    ‐120.