Output File

The program generates two output files of extension .bsr and .fp. The first file contains the full information generated by BasIReps. The second file contains information in a format suitable to be pasted in the PCR file for FullProf program.


As stated above, the content of the output files is self-explanatory.


Sometimes, mostly when complex multidimensional representations are concerned, the number of calculated basis functions is greater than what is expected. That may be due to propagation errors in the calculation of the rank of a general complex matrix. If this situation appears for a particular case the user should inspect the obtained basis functions and try to extract the linear independent basis functions from the provided set.


From the version 3.0, a formal writing of the Fourier coefficients  Skj is output in the file of extension *.bsr. Symbols for the coefficients  Ca,m  are used in the following order:


       "u","v","w","p","q","r","a","b","c","d","e","f","g","l","m","n","s","t",

       "U","V","W","P","Q","R","A","B","C","D","E","F","G","L","M","N","S","T"


If particular real numbers appear in the components of the basis functions (this may be due, for instance, to incommensurate propagation vectors) the program tries to recognize them and in the writing of the Fourier coefficients these special numbers appear in symbolic form. The numbers are given the following names in the order of appearance:


"r0","r1","r2","r3","r4","r5","r6","r7","r8","r9",

"p0","p1","p2","p3","p4","p5","p6","p7","p8","p9",

"q0","q1","q2","q3","q4","q5","q6","q7","q8","q9",

"s0","s1","s2","s3","s4","s5","s6","s7","s8","s9",

"t0","t1","t2","t3","t4","t5","t6","t7","t8","t9"


The values of these numbers are given in separate lines with more precision than that used for writing the basis vectors

Va,m(k,v|j)  .


An example of output concerning this last point is given below. The calculation is performed for the following case:



TITLE Test Basireps

SPGR  P 4/n m m

KVEC   0.5000  0.2341  0.0000 X

BASIR AXIAL CEL

ATOM Mn   Mn    0.2500  0.2500  0.1320

.....



+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

=>Basis functions of Representation IRrep( 1) of dimension  2 contained 3 times in GAMMA

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


SYMM  x,y,z   -x+1,y+1/2,-z+1

Atoms:      Mn_1              Mn_2

  1:Re ( 1.00 0.00 0.00) ( 0.74 0.00 0.00)

    Im ( 0.00 0.00 0.00) (-0.67 0.00 0.00)

  2:Re ( 0.00 1.00 0.00) ( 0.00-0.74 0.00)

    Im ( 0.00 0.00 0.00) ( 0.00 0.67 0.00)

  3:Re ( 0.00 0.00 1.00) ( 0.00 0.00 0.74)

    Im ( 0.00 0.00 0.00) ( 0.00 0.00-0.67)

  4:Re (-0.74 0.00 0.00) ( 0.10 0.00 0.00)

    Im ( 0.67 0.00 0.00) (-1.00 0.00 0.00)

  5:Re ( 0.00 0.74 0.00) ( 0.00 0.10 0.00)

    Im ( 0.00-0.67 0.00) ( 0.00-1.00 0.00)

  6:Re ( 0.00 0.00 0.74) ( 0.00 0.00-0.10)

    Im ( 0.00 0.00-0.67) ( 0.00 0.00 1.00)



----- LINEAR COMBINATIONS of Basis Functions: coefficients u,v,w,p,q ....

       General expressions of the Fourier coefficients Sk(i) i=1,2,...nat


  SYMM x,y,z                                      Atom: Mn_1      0.2500  0.2500  0.1320

       Sk(1): (u-r0.p,v+r0.q,w+r0.r)+i.r1.(p,-q,-r)


  SYMM -x+1,y+1/2,-z+1                            Atom: Mn_2      0.7500  0.7500  0.8680

       Sk(2): (r0.u+r2.p,-r0.v+r2.q,r0.w-r2.r)+i.(-r1.u-r3.p,r1.v-r3.q,-r1.w+r3.r)



        Values of real constants r0,r1,...

              r0 =   0.741531    r1 =   0.670919    r2 =   0.099737    r3 =   0.995014


Check combinations of values by pairs: usually these real constants are related to k-vector. They can constitute real and/or imaginary parts of exp{2.pi.i.K.T }, being T a non-primitive translation of a symmetry operator. In many simple cases r0=cos(2.pi.k.t) and r1=sin(2.pi.k.t), etc ...


  .....



One can see that the constant r2 is written as "0.10" in the basis vectors and the constant r3 does not appear because it is approximated as "1.00" in the format used for writing the numerical vectors.


The meaning of these constants are related, as suggested in the comment of the output, to the propagation vector

k=(0.5000, 0.2341, 0.0000).


The complex numbers r0+i.r1 and r2+i.r3 are:


            r0+i.r1 = exp{pi.i.ky}   and    r2+i.r3 = exp{2.pi.i.ky}


This suggests a further simplification of the general Fourier coefficients that can be worked out by the user:


Sk(1)=(u-r0.p,v+r0.q,w+r0.r)+i.r1.(p,-q,-r)=(u,v,w)+r0.(-p,q,r)+i.r1.(p,-q,-r)

Sk(1) = (u,v,w) + r0.(-p,q,r)-i.r1.(-p,q,r) = (u,v,w) + (r0-ir1).(-p,q,r)

Sk(1) = (u,v,w) + (-p,q,r) .exp{-pi.i.ky}


Sk(2) = (r0.u+r2.p,-r0.v+r2.q,r0.w-r2.r)+i.(-r1.u-r3.p,r1.v-r3.q,-r1.w+r3.r)

Sk(2) = r0 (u,-v,w) + r2(p,q,-r) + i.r1.(-u,v,-w) +i.r3 (-p,-q,r)

Sk(2) = (r0-i.r1).(u,-v,w)+(r2-ir3).(p,q,-r)

Sk(2) = (u,-v,w).exp{-pi.i.ky}+(p,q,-r).exp{-2.pi.i.ky}

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