TLS matrices

giulioisacco

Hi everybody,

I have been trying to insert the TLS matrices for molecular motion in my refinement with no success.
I wrote a macro taking the equations that I found in the TLSview manual:
http://pymmlib.sourceforge.net/tlsview/tlsview.html

Here are the lines I wrote in my local.inc:

macro TLS_adps(T11, vT11, T12, vT12, T13, vT13, T22, vT22, T23, vT23, T33, vT33, L11, vL11, L12, vL12, L13, vL13, L22, vL22, L23, vL23, L33, vL33, S11, vS11, S12, vS12, S13, vS13, S21, vS21, S22, vS22, S23, vS23, S31, vS31, S32, vS32, S33, vS33)
{
#m_argu T11
#m_argu T12
#m_argu T13
#m_argu T22
#m_argu T23
#m_argu T33
#m_argu L11
#m_argu L12
#m_argu L13
#m_argu L22
#m_argu L23
#m_argu L33
#m_argu S11
#m_argu S12
#m_argu S13
#m_argu S21
#m_argu S22
#m_argu S23
#m_argu S31
#m_argu S32
#m_argu S33

u11 = CeV(L22, vL22) * uz ^ 2 + CeV(L33, vL33) * uy ^ 2 - 2 * CeV(L23, vL23) * uy * uz + 2 * CeV(S21, vS21) * uz - 2 * CeV(S31, vS31) * uy + CeV(T11, vT11);
u22 = CeV(L11, vL11) * uz ^ 2 + CeV(L33, vL33) * ux ^ 2 - 2 * CeV(L13, vL13) * ux * uz - 2 * CeV(S12, vS12) * uz + 2 * CeV(S31, vS32) * ux + CeV(T22, vT22);
u33 = CeV(L11, vL11) * uy ^ 2 + CeV(L22, vL22) * ux ^ 2 - 2 * CeV(L12, vL12) * ux * uy - 2 * CeV(S23, vS23) * ux + 2 * CeV(S13, vS13) * uy + CeV(T33, vT33);
u12 = - CeV(L33, vL33) * ux * uy + CeV(L23, vL23) * uy * ux * uz - CeV(L13, vL13) * uy * uz - CeV(L12, vL12) * uz ^ 2 - CeV(S11, vS11) * uz + CeV(S22, vS22) * uz + CeV(S31, vS31) * ux - CeV(S32, vS32) * uy + CeV(T12, vT12);
u13 = - CeV(L22, vL22) * ux * uz + CeV(L23, vL23) * uy * ux - CeV(L13, vL13) * uy ^ 2 + CeV(L12, vL12) * uy * uz + CeV(S11, vS11) * uy - CeV(S33, vS33) * uy + CeV(S23, vS23) * uz - CeV(S21, vS21) * ux + CeV(T13, vT13);
u23 = - CeV(L11, vL11) * uy * uz - CeV(L23, vL23) * ux ^ 2 + CeV(L13, vL13) * ux * uy + CeV(L12, vL12) * ux * uz - CeV(S22, vS22) * ux + CeV(S33, vS33) * ux + CeV(S12, vS12) * uy - CeV(S13, vS13) * uz + CeV(T23, vT23);
}

Consider that I am describing my rigid body using point_for_site with Cartesian coordinates.
This is the line I added in my input file:

TLS_adps(T11, 1, T12, 0, T13, 0, T22, 1, T23, , T33, 1, L11, 10, L12, 0, L13, 0, L22, 10, L23, 0, L33, 10, S11, 0, S12, 0, S13, 0, S21, 0, S22, 0, S23, 0, S31, 0, S32, 0, S33, 0)

If I run Topas with this line AFTER the atom list I get an abnormal program termination and Topas says “Uninitialized_Variable in equation: L22”.

If I run Topas with this line BEFORE the atom list, Topas performs the refinement but does not use my macro at all. I tried to activate the adps before inserting the macro, but it did not help.

Can anybody help me?

Ciao!

Giulio

alancoelho

Hi Giulio

See below where I have inserted If_Prm_Eqn_Rpt(,,) etc...

I also separated the parameter definitions from the equations.

macro TLS_adps_eqn(T11,T12,T13,T22,T23,T33,L11,L12,L13,L22,L23,L33,S11,S12,S13,S21,S22,S23,S31,S32,S33)
{
u11 = L22 uz ^ 2 + L33 uy ^ 2 - 2 L23 uy uz + 2 S21 uz - 2 S31 uy + T11;
u22 = L11 uz ^ 2 + L33 ux ^ 2 - 2 L13 ux uz - 2 S12 uz + 2 S31 ux + T22;
u33 = L11 uy ^ 2 + L22 ux ^ 2 - 2 L12 ux uy - 2 S23 ux + 2 S13 uy + T33;
u12 = - L33 ux uy + L23 uy ux uz - L13 uy uz - L12 uz ^ 2 - S11 uz + S22 uz + S31 ux - S32 uy + T12;
u13 = - L22 ux uz + L23 uy ux - L13 uy ^ 2 + L12 uy uz + S11 uy - S33 uy + S23 uz - S21 ux + T13;
u23 = - L11 uy uz - L23 ux ^ 2 + L13 ux uy + L12 ux uz - S22 ux + S33 ux + S12 uy - S13 uz + T23;
}
macro TLS_adps(T11, vT11, T12, vT12, T13, vT13, T22, vT22, T23, vT23, T33, vT33, L11, vL11, L12, vL12, L13, vL13, L22, vL22, L23, vL23, L33, vL33, S11, vS11, S12, vS12, S13, vS13, S21, vS21, S22, vS22, S23, vS23, S31, vS31, S32, vS32, S33, vS33)
{
#m_argu T11 If_Prm_Eqn_Rpt(T11,vT11,)
#m_argu T12 If_Prm_Eqn_Rpt(T12,vT12,)
#m_argu T13 If_Prm_Eqn_Rpt(T13,vT13,)
#m_argu T22 If_Prm_Eqn_Rpt(T22,vT22,)
#m_argu T23 If_Prm_Eqn_Rpt(T23,vT23,)
#m_argu T33 If_Prm_Eqn_Rpt(T33,vT33,)
#m_argu L11 If_Prm_Eqn_Rpt(L11,vL11,)
#m_argu L12 If_Prm_Eqn_Rpt(L12,vL12,)
#m_argu L13 If_Prm_Eqn_Rpt(L13,vL13,)
#m_argu L22 If_Prm_Eqn_Rpt(L22,vL22,)
#m_argu L23 If_Prm_Eqn_Rpt(L23,vL23,)
#m_argu L33 If_Prm_Eqn_Rpt(L33,vL33,)
#m_argu S11 If_Prm_Eqn_Rpt(S11,vS11,)
#m_argu S12 If_Prm_Eqn_Rpt(S12,vS12,)
#m_argu S13 If_Prm_Eqn_Rpt(S13,vS13,)
#m_argu S21 If_Prm_Eqn_Rpt(S21,vS21,)
#m_argu S22 If_Prm_Eqn_Rpt(S22,vS22,)
#m_argu S23 If_Prm_Eqn_Rpt(S23,vS23,)
#m_argu S31 If_Prm_Eqn_Rpt(S31,vS31,)
#m_argu S32 If_Prm_Eqn_Rpt(S32,vS32,)
#m_argu S33 If_Prm_Eqn_Rpt(S33,vS33,)

TLS_adps_eqn(
CeV(T11,vT11),
CeV(T12,vT12),
CeV(T13,vT13),
CeV(T22,vT22),
CeV(T23,vT23),
CeV(T33,vT33),
CeV(L11,vL11),
CeV(L12,vL12),
CeV(L13,vL13),
CeV(L22,vL22),
CeV(L23,vL23),
CeV(L33,vL33),
CeV(S11,vS11),
CeV(S12,vS12),
CeV(S13,vS13),
CeV(S21,vS21),
CeV(S22,vS22),
CeV(S23,vS23),
CeV(S31,vS31),
CeV(S32,vS32),
CeV(S33,vS33)
)
}

cheers
alan

giulioisacco

Dear Alan,

Thank you for your help.
I copied your macros in the place of mine. Now when I run it it Topas gives me another error: "Uninitialized_Variable in equation: uz", or "uy", depending on where I write the command line in the the input file, before or after the atom list.
That surprised me. Aren't ux, uy and uz given a value for each atom of the rigid body with the point_for_site command? Why are they not recognized then? Maybe I musunderstood something...
Could you please fix this problem too?

Best regards,

Giulio

simonparsons

Dear Giulio-
I got TLS to work for a refinement of pyridine. I'd paste the file in but it's > 10000 characters. Happy to send it by email though. Drop me a line at S.Parsons@ed.ac.uk
All best wishes, Simon

giulioisacco

This is how far I have got. Here is an example with a one dummy atom + one real atom rigid body.

rigid
point_for_site Cd1
point_for_site N1 ux 0.0012 uy 1.1298 uz 0.0000
Rotate_about_axies(xrota -62.90335 , yrota -5.59696, zrota -234.16765 )
translate tx @ 19.06296 ty @ 6.65451 tz @ 7.51142

prm !uxN1 0.0012
prm !uyN1 1.1298
prm !uzN1 0.0000

prm L11 -0.03990`
prm L22 0.01772`
prm L33 0.00562`
prm L12 -0.00118`
prm L13 0.02093`
prm L23 0.00078`
prm T11 0.06174`
prm T22 0.23035`
prm T33 0.10519`
prm T12 0.03880`
prm T13 0.02714`
prm T23 -0.01338`
prm S11 0
prm S22 0
prm S33 0
prm S12 0
prm S13 0
prm S21 0
prm S23 0
prm S31 0
prm S32 0

prm u11N1 = L22 uzN1 ^ 2 + L33 uyN1 ^ 2 - 2 L23 uyN1 uzN1 + 2 S21 uzN1 - 2 S31 uyN1 + T11;
prm u22N1 = L11 uzN1 ^ 2 + L33 uxN1 ^ 2 - 2 L13 uxN1 uzN1 - 2 S12 uzN1 + 2 S31 uxN1 + T22;
prm u33N1 = L11 uyN1 ^ 2 + L22 uxN1 ^ 2 - 2 L12 uxN1 uyN1 - 2 S23 uxN1 + 2 S13 uyN1 + T33;
prm u12N1 = - L33 uxN1 uyN1 + L23 uyN1 uxN1 uzN1 - L13 uyN1 uzN1 - L12 uzN1 ^ 2 - S11 uzN1 + S22 uzN1 + S31 uxN1 - S32 uyN1 + T12;
prm u13N1 = - L22 uxN1 uzN1 + L23 uyN1 uxN1 - L13 uyN1 ^ 2 + L12 uyN1 uzN1 + S11 uyN1 - S33 uyN1 + S23 uzN1 - S21 uxN1 + T13;
prm u23N1 = - L11 uyN1 uzN1 - L23 uxN1 ^ 2 + L13 uxN1 uyN1 + L12 uxN1 uzN1 - S22 uxN1 + S33 uxN1 + S12 uyN1 - S13 uzN1 + T23;

site N1 x 0.97176 y 0.32248 z 0.41615 occ N 1 u11 =u11N1; u22 =u22N1; u33 =u33N1; u12=u12N1; u13 =u13N1; u23 =u23N1;

The equations for u11N1, u22N1 etc. must be rewritten for each atom of the rigid body. The rules about TLS matrix elements can be found in the 1968 paper "On the rigid-body motion of molecules in crystals" by Shomaker and Trueblood.
I hope I didn't make any mistake.
There are still a few things I don't get. One is how to write these things as a macro. Another one is the best min and max values for the TLS matrix elements to be inserted in the code.

Hope this helps.
Ciao!

Giulio

alancoelho

Hi Giulio

Are you saying that the program is now finding your ux, uy and uz parameters.

Also, if you want to use the fractional coordinates in the unn parameters you could use:

site x # y # z # occ O # u11 = Get(x); u22 = Get(y); etc...

The Get command will get the x frcational and y coordinates from the u11 and u22 parameters. This is because the unn parameters are dependents of site; thus Get(x) will Get the nearest x fractional coordinate parameter.

cheers
alan