[Jmol-users] jmol and space groups

[Bob H. <ha...@st...>]

In response to requests for Jmol to be able to visualize a wider range 
of crystallographic data sets, with the help of Peter and Judith 
Murray-Rust and Syd Hall, I've made a preliminary implementation of 
space group name analysis in Jmol 10.9.51. The basic idea is that Jmol 
is now able to generate symmetry operators without having them present 
in the file.

I think it's safe to say this is not the final word in this area. I'm 
getting it out there just so that those interested can take a look and 
comment and suggest.


For those who are interested, I have some comments and questions:

1) Reading and showing operator information based on Hall names is easy. 
For example, you can enter:

  show spacegroup "P 4n 2 -1n"

and see this on the console:

Hermann-Mauguin symbol: P 42/n n m:1
international table number: 134
Hall symbol: P 4n 2 -1n
primitive Hall symbol: P 4zn 2x -1n
lattice type: -P: centrosymmetric primitive

rotation term 1
input code: 4n; primitive code: 4zn
order: 4; axisType: z; translation: n
operator: -y+1/2,x+1/2,z+1/2
Seitz matrix(12ths): [
  [0.0	-1.0	0.0	6.0]
  [1.0	0.0	0.0	6.0]
  [0.0	0.0	1.0	6.0]
  [0.0	0.0	0.0	1.0] ]

rotation term 2
input code: 2; primitive code: 2x
order: 2; axisType: x
operator: x,-y,-z
Seitz matrix(12ths): [
  [1.0	0.0	0.0	0.0]
  [0.0	-1.0	0.0	0.0]
  [0.0	0.0	-1.0	0.0]
  [0.0	0.0	0.0	1.0] ]

rotation term 3
input code: -1n; primitive code: -1n
order: 1 (improper axis); translation: n
operator: -x+1/2,-y+1/2,-z+1/2
Seitz matrix(12ths): [
  [-1.0	0.0	0.0	6.0]
  [0.0	-1.0	0.0	6.0]
  [0.0	0.0	-1.0	6.0]
  [0.0	0.0	0.0	1.0] ]

Operators from Hall symbol (16):
x,y,z
-y+1/2,x+1/2,z+1/2
-x,-y,z
y+1/2,-x+1/2,z+1/2
y+1/2,x+1/2,-z-1/2
x,-y,-z
-y+1/2,-x+1/2,-z-1/2
-x,y,-z
-y,-x,z
-x+1/2,y+1/2,z+1/2
y,x,z
x+1/2,-y+1/2,z+1/2
-x+1/2,-y+1/2,-z+1/2
y,-x,-z
x+1/2,y+1/2,-z+1/2
-y,x,-z


Now, that's probably more than you want. Still, how does it look? Do you 
want more?
Note that double quotes are required in the command; to indicate a Hall 
symbol with ", use two single quotes:

  show spacegroup "P 32 2''"

2) Hermann-Mauguin symbols such as "P 42/n n m" or "Pmmn" can also be 
displayed:

  show spacegroup "Pmmm"

Hermann-Mauguin symbol: P m m m
international table number: 47
Hall symbol: -P 2 2
primitive Hall symbol: P 2z 2x -1
lattice type: P: primitive

rotation term 1
input code: 2; primitive code: 2z
order: 2; axisType: z
operator: -x,-y,z
Seitz matrix(12ths): [
  [-1.0	0.0	0.0	0.0]
  [0.0	-1.0	0.0	0.0]
  [0.0	0.0	1.0	0.0]
  [0.0	0.0	0.0	1.0] ]

rotation term 2
input code: 2; primitive code: 2x
order: 2; axisType: x
operator: x,-y,-z
Seitz matrix(12ths): [
  [1.0	0.0	0.0	0.0]
  [0.0	-1.0	0.0	0.0]
  [0.0	0.0	-1.0	0.0]
  [0.0	0.0	0.0	1.0] ]

rotation term 3
input code: -1; primitive code: -1
order: 1 (improper axis)
operator: -x,-y,-z
Seitz matrix(12ths): [
  [-1.0	0.0	0.0	0.0]
  [0.0	-1.0	0.0	0.0]
  [0.0	0.0	-1.0	0.0]
  [0.0	0.0	0.0	1.0] ]

Operators from Hall symbol (8):
x,y,z
-x,-y,z
-x,y,-z
x,-y,-z
x,-y,z
-x,y,z
-x,-y,-z
x,y,-z


3) Note that in this case some assumptions may be made, because the 
origin option was not specified. You can specify standard options after 
a colon ":":

  show spacegroup "P 2/m:b"

4) You can also substitute an international table number for the 
Hermann-Mauguin symbol:

  show spacegroup "227:1"

Right now I can't guarantee that this is all correct. I've put up the 
entire list of all of the operators generated by all of the space groups 
on the list that Syd sent me. This is accomplished by invoking

  show spacegroup "ALL"
 
See 
<http://www.stolaf.edu/academics/chemapps/jmol/docs/misc/showsymmetry.txt>

With this file, someone (not I!) should be able to verify that the 
algorithm is working or not.
Since I didn't edit that list, I take no credit for any errors there, 
but if the algorithm is not generating the correct operators, that would 
be good to know.

5) Finally, there is one more capability you can invoke. Any guesses as 
to what the following does?

  load "quartz.cif" {1 1 1} spacegroup "P 2/m"

Yup, now you can select the space group you want to apply to a model 
when it is loaded.

Check it out at 
http://www.stolaf.edu/academics/chemapps/jmol/docs/examples-11/new.htm

This should open up some interesting possibilities.

 

Volunteers? Suggestions? Any testing of this that anyone cares to do 
would be appreciated.



Bob Hanson