Space group additions: space_group_hall and space_group_it_number

[merkys]

Partially addresses #35 This PR introduces two symmetry space group notations, Hall symbol and IT number, closely following their usage in CIF. Both Hall symbol and IT number have their drawbacks: in some cases both need additional information to uniquely define symmetry space group of a crystal. To cover this drawback, a list of symmetry operations is needed, and its introduction is envisaged in #35. Nevertheless standardizing Hall symbol and IT number would facilitate searches on these widely used notations.

[rartino]

Correct me if I am wrong, but I have come to the conclusion that it is not 100% safe to assume there is a standard Hall symbol for all possibilities - in case a structure isn't placed with a "proper" origin. Is it absolutely safe to assume there is a non-standard Hall symbol that describes structures given with a completely arbitary origin?

Also, I think I'm for MAY support level on these. If you don't know the symmetry information it can be very expensive (arguably sometimes even impossible) to assign them.

[merkys]

Correct me if I am wrong, but I have come to the conclusion that it is not 100% safe to assume there is a standard Hall symbol for all possibilities - in case a structure isn't placed with a "proper" origin. Is it absolutely safe to assume there is a non-standard Hall symbol that describes structures given with a completely arbitary origin?

Right, but maybe we can say that only standard Hall symbols are supported, and they should be provided only for structures with "proper" origin? My point is that if we cannot use standard Hall symbol/IT number to unambiguously define symmetry, these fields should be null, and in future symmetry operator lists should be used to define such situations.

Also, I think I'm for MAY support level on these. If you don't know the symmetry information it can be very expensive (arguably sometimes even impossible) to assign them.

Sure, I am fine with OPTIONAL/MAY support level.

[rartino]

Based on a discussion with @BobHanson I now believe there exists a non-standard Hall symbol for every set of symmetry operators. So, I support this and we should not require the field to be a standard Hall symbol. (But is there also a redundancy in Hall symbols? Should we say that a standard Hall symbol SHOULD be given if it exists for the structure?)

(However, we also discussed that if the system has magnetism or other atomic-assigned properties that affects symmetry, then the Hall symbols are not sufficient to describe the symmetry.)

[rartino]

A few suggested changes

[ml-evs]

Suggested change

- If there exists a standard Hall symbol which represents the symmetry it SHOULD be used.

[BobHanson]

I see this thread now.

A list of Hall symbols and a bit about how they are constructed can be seen in https://sourceforge.net/p/jmol/code/HEAD/tree/trunk/Jmol/src/org/jmol/symmetry/SpaceGroup.java.

After thinking about what Giovanni said in the session, I agree completely that although the Hall symbol would, for example, allow a regression back to fractional coordinates from Cartesians, it's really not something that anyone would be interested in for any other reason. It's too specific for searching -- If I am interested in a space group, say ITA #40, I don't care how the originator set the origin. That's just a particular choice they happened to make for whatever reason. (The structure looked prettier that way?)

All of these are #40:

ITA#
       Schoenflies
                      Hermann-Mauguin
                                      Hall
"40: c2v^16;   a m a 2;   a 2 -2a",  
"40: c2v^16;   b b m 2;  b 2 -2b",  
"40: c2v^16;   b 2 m b;  b -2b 2",  
"40: c2v^16;   c 2 c m;   c -2c 2",  
"40: c2v^16;   c c 2 m;   c -2c -2c",  
"40: c2v^16;   a m 2 a;   a -2a -2a",  

In ITA#4, you can see the situation where different H-M notations refer to the same space group setting, and where the same H-M notation refers to two different Hall descriptions:

"4:b c2^2;   p 1 21 1;   p 2yb",   //full name
"4:b c2^2;   p 21;         p 2yb",  
"4:b c2^2;   p 1 21 1;   p 2y1",   //nonstandard
"4:c  c2^2;  p 1 1 21;   p 2c",  
"4:c  c2^2;  p 1 1 21;   p 21",   //nonstandard
"4:a  c2^2;  p 21 1 1;   p 2xa",  
"4:a  c2^2;  p 21 1 1;   p 2x1",   //nonstandard

"nonstandard" here refers to the setting, not the symbols.

Thus, the purpose of Hall notation is an unambiguous description of any setting of a space group. This is not relevant here.

Suggestion: Just give ITA space group number. I will always know that, and I can look it up easily enough at a service such as http://img.chem.ucl.ac.uk/sgp/large/sgp.htm in order to relate it to H-M notation.

[merkys]

A wish has been expressed to also include space group Hermann-Mauguin symbol. This might need more discussion, as given space-group type may be described by more than one Hermann-Mauguin symbol (citing CIF CORE dictionary).