!-------------------------------------------------------------------------------- ! Copyright (c) 2016 Peter Grünberg Institut, Forschungszentrum Jülich, Germany ! This file is part of FLEUR and available as free software under the conditions ! of the MIT license as expressed in the LICENSE file in more detail. !-------------------------------------------------------------------------------- MODULE m_loccoeff ! coefficients used in locrectify: COMPLEX coeffi(1:28,1:28,0:13) LOGICAL coffkind(1:28,0:13) COMPLEX, PARAMETER :: one = ( 1.0, 0.0) COMPLEX, PARAMETER :: mone = (-1.0, 0.0) COMPLEX, PARAMETER :: zro = ( 0.0, 0.0) COMPLEX, PARAMETER :: ci = ( 0.0, 1.0) COMPLEX, PARAMETER :: mci = ( 0.0,-1.0) !*************************************************************************** !*************************************************************************** !*************************************************************************** ! ANGULAR MOMENTUM: 0 !*************************************************************************** !*************************************************************************** !*************************************************************************** !*************************************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=0 (two atoms NOT in xy-plane) !*************************************************************************** ! even parity => leave as is ! z-refl: even DATA coffkind(1,0) /.true./ DATA coeffi(1:2,1,0) /one,one/ ! odd parity => multiply with i ! z-refl: odd DATA coffkind(2,0) /.false./ DATA coeffi(1:2,2,0) /ci,mci/ !*************************************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=0 (four atoms) !*************************************************************************** ! even parity => leave as is ! z-refl: even DATA coffkind(1,6) /.true./ DATA coeffi(1:4,1,6) /one,one,one,one/ ! even parity => leave as is ! z-refl: odd DATA coffkind(2,6) /.false./ DATA coeffi(1:4,2,6) /one,one,mone,mone/ ! odd parity => multiply with i ! z-refl: even DATA coffkind(3,6) /.true./ DATA coeffi(1:4,3,6) /ci,mci,ci,mci/ ! odd parity => multiply with i ! z-refl: odd DATA coffkind(4,6) /.false./ DATA coeffi(1:4,4,6) /ci,mci,mci,ci/ !*************************************************************************** !*************************************************************************** !*************************************************************************** ! ANGULAR MOMENTUM: 1 !*************************************************************************** !*************************************************************************** !*************************************************************************** !******************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=1 (single atom) !******************************************************** !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//odd parity => multiply with i !z-refl: even DATA coffkind(1,1) /.true./ DATA coeffi(1:3,1,1) /one,zro,one/ !cos(theta) <==> Y10// odd parity => multiply with i !z-refl: odd DATA coffkind(2,1) /.false./ DATA coeffi(1:3,2,1) /zro,ci,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// odd parity => multiply with i !z-refl: even DATA coffkind(3,1) /.true./ DATA coeffi(1:3,3,1) /ci,zro,mci/ !******************************************************** ! linear combinations of locs for l=1 (two atoms; both atoms in xy-plane) !******************************************************** !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//even parity => leave as is !z-refl: even DATA coffkind(1,3) /.true./ DATA coeffi(1:6,1,3) /ci,zro,ci,mci,zro,mci/ !cos(theta) <==> Y10//odd parity => multiply with i !z-refl: odd DATA coffkind(2,3) /.false./ DATA coeffi(1:6,2,3) /zro,ci,zro,zro,ci,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// odd parity => multiply with i !z-refl: even DATA coffkind(3,3) /.true./ DATA coeffi(1:6,3,3) /ci,zro,mci,ci,zro,mci/ !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//odd parity => multiply with i !z-refl: even DATA coffkind(4,3) /.true./ DATA coeffi(1:6,4,3) /one,zro,one,one,zro,one/ !cos(theta) <==> Y10//even parity => leave as is !z-refl: odd DATA coffkind(5,3) /.false./ DATA coeffi(1:6,5,3) /zro,one,zro,zro,mone,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// even parity => leave as is !z-refl: even DATA coffkind(6,3) /.true./ DATA coeffi(1:6,6,3) /one,zro,mone,mone,zro,one/ !******************************************************** ! linear combinations of locs for l=1 (two atoms; atoms NOT in xy-plane) !******************************************************** !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//even parity => leave as is !z-refl: odd DATA coffkind(1,4) /.false./ DATA coeffi(1:6,1,4) /ci,zro,ci,mci,zro,mci/ !cos(theta) <==> Y10//odd parity => multiply with i !z-refl: odd DATA coffkind(2,4) /.false./ DATA coeffi(1:6,2,4) /zro,ci,zro,zro,ci,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// odd parity => multiply with i !z-refl: even DATA coffkind(3,4) /.true./ DATA coeffi(1:6,3,4) /ci,zro,mci,ci,zro,mci/ !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//odd parity => multiply with i !z-refl: even DATA coffkind(4,4) /.true./ DATA coeffi(1:6,4,4) /one,zro,one,one,zro,one/ !cos(theta) <==> Y10//even parity => leave as is !z-refl: even DATA coffkind(5,4) /.true./ DATA coeffi(1:6,5,4) /zro,one,zro,zro,mone,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// even parity => leave as is !z-refl: odd DATA coffkind(6,4) /.false./ DATA coeffi(1:6,6,4) /one,zro,mone,mone,zro,one/ !******************************************************** ! linear combinations of locs for l=1 (four atoms) !******************************************************** !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//even parity => leave as is !z-refl: even DATA coffkind(1,7) /.false./ DATA coeffi(1:12,1,7) /ci,zro,ci,mci,zro,mci, ci,zro,ci,mci,zro,mci/ !cos(theta) <==> Y10//odd parity => multiply with i !z-refl: odd DATA coffkind(2,7) /.false./ DATA coeffi(1:12,2,7) /zro,ci,zro,zro,ci,zro, zro,ci,zro,zro,ci,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// odd parity => multiply with i !z-refl: even DATA coffkind(3,7) /.true./ DATA coeffi(1:12,3,7) /ci,zro,mci,ci,zro,mci, ci,zro,mci,ci,zro,mci/ !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//odd parity => multiply with i !z-refl: odd DATA coffkind(4,7) /.false./ DATA coeffi(1:12,4,7) / one,zro, one, one,zro, one, mone,zro,mone,mone,zro,mone/ !cos(theta) <==> Y10//even parity => leave as is !z-refl: odd DATA coffkind(5,7) /.false./ DATA coeffi(1:12,5,7) /zro, one,zro,zro,mone,zro, zro, one,zro,zro,mone,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// even parity => leave as is !z-refl: even DATA coffkind(6,7) /.true./ DATA coeffi(1:12,6,7) /one,zro,mone,mone,zro,one, one,zro,mone,mone,zro,one/ !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//even parity => leave as is !z-refl: odd DATA coffkind(7,7) /.false./ DATA coeffi(1:12,7,7) / ci,zro, ci,mci,zro,mci, mci,zro,mci, ci,zro, ci/ !cos(theta) <==> Y10//odd parity => multiply with i !z-refl: even DATA coffkind(8,7) /.true./ DATA coeffi(1:12,8,7) /zro, ci,zro,zro, ci,zro, zro,mci,zro,zro,mci,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// odd parity => multiply with i !z-refl: odd DATA coffkind(9,7) /.false./ DATA coeffi(1:12,9,7) / ci,zro,mci, ci,zro,mci, mci,zro, ci,mci,zro, ci/ !sin(phi)sin(theta) <==> i(Y11 + Y1-1)//odd parity => multiply with i !z-refl: true DATA coffkind(10,7) /.true./ DATA coeffi(1:12,10,7) /one,zro,one,one,zro,one, one,zro,one,one,zro,one/ !cos(theta) <==> Y10//even parity => leave as is !z-refl: even DATA coffkind(11,7) /.true./ DATA coeffi(1:12,11,7) /zro, one,zro,zro,mone,zro, zro,mone,zro,zro, one,zro/ !cos(phi)sin(theta) <==> (Y11 - Y1-1)// even parity => leave as is !z-refl: odd DATA coffkind(12,7) /.false./ DATA coeffi(1:12,12,7) / one,zro,mone,mone,zro, one, mone,zro, one, one,zro,mone/ !*************************************************************************** !*************************************************************************** !*************************************************************************** ! ANGULAR MOMENTUM: 2 !*************************************************************************** !*************************************************************************** !*************************************************************************** !******************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=2 (single atom) !******************************************************** !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)// even parity => take as is !z-refl: even DATA coffkind(1,2) /.true./ DATA coeffi(1:5,1,2) /one,zro,zro,zro,one/ !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(2,2) /.false./ DATA coeffi(1:5,2,2) / zro ,one ,zro ,mone ,zro/ !(3*cos^2(theta)-1) <==> Y20// even parity => take as is !z-refl: even DATA coffkind(3,2) /.true./ DATA coeffi(1:5,3,2) / zro ,zro ,one ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(4,2) /.false./ DATA coeffi(1:5,4,2) / zro , ci ,zro , ci ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// even parity => take as is !z-refl: even DATA coffkind(5,2) /.true./ DATA coeffi(1:5,5,2) / ci ,zro ,zro ,zro ,mci / !****************************************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=2; two atoms NOT in xy-plane !****************************************************************************** !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)// even parity => take as is !z-refl: even DATA coffkind(1,8) /.true./ DATA coeffi(1:10,1,8) / one ,zro ,zro ,zro ,one ,one ,zro ,zro ,zro ,one / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(2,8) /.false./ DATA coeffi(1:10,2,8) / zro ,one ,zro ,mone ,zro ,zro ,one ,zro ,mone ,zro / !(3*cos^2(theta)-1) <==> Y20// even parity => take as is !z-refl: even DATA coffkind(3,8) /.true./ DATA coeffi(1:10,3,8) / zro ,zro ,one ,zro ,zro ,zro ,zro ,one ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(4,8) /.false./ DATA coeffi(1:10,4,8) / zro , ci ,zro , ci ,zro ,zro , ci ,zro , ci ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// even parity => take as is !z-refl: even DATA coffkind(5,8) /.true./ DATA coeffi(1:10,5,8) / ci ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,mci / !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)//odd parity => factor i !z-refl: odd DATA coffkind(6,8) /.false./ DATA coeffi(1:10,6,8) / ci ,zro ,zro ,zro , ci ,mci ,zro ,zro ,zro ,mci / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// odd parity => factor i !z-refl: even DATA coffkind(7,8) /.true./ DATA coeffi(1:10,7,8) / zro , ci ,zro ,mci ,zro ,zro ,mci ,zro , ci ,zro / !(3*cos^2(theta)-1) <==> Y20// odd parity => factor i !z-refl: odd DATA coffkind(8,8) /.false./ DATA coeffi(1:10,8,8) / zro ,zro , ci ,zro ,zro ,zro ,zro ,mci ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// odd parity => factor i !z-refl: even DATA coffkind(9,8) /.true./ DATA coeffi(1:10,9,8) / zro ,one ,zro ,one ,zro ,zro ,mone ,zro ,mone ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// odd parity => factor i !z-refl: odd DATA coffkind(10,8) /.false./ DATA coeffi(1:10,10,8) / one ,zro ,zro ,zro ,mone ,mone ,zro ,zro ,zro ,one / !****************************************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=2; two atoms IN xy-plane !****************************************************************************** !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)// odd parity => factor i !z-refl: even DATA coffkind(1,9) /.true./ DATA coeffi(1:10,1,9) / ci ,zro ,zro ,zro , ci ,mci ,zro ,zro ,zro ,mci / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(2,9) /.false./ DATA coeffi(1:10,2,9) / zro ,one ,zro ,mone ,zro ,zro ,one ,zro ,mone ,zro / !(3*cos^2(theta)-1) <==> Y20// even parity => take as is !z-refl: even DATA coffkind(3,9) /.true./ DATA coeffi(1:10,3,9) / zro ,zro ,one ,zro ,zro ,zro ,zro ,one ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(4,9) /.false./ DATA coeffi(1:10,4,9) / zro , ci ,zro , ci ,zro ,zro , ci ,zro , ci ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// even parity => take as is !z-refl: even DATA coffkind(5,9) /.true./ DATA coeffi(1:10,5,9) / ci ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,mci / !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)//even parity => leave as is !z-refl: even DATA coffkind(6,9) /.true./ DATA coeffi(1:10,6,9) / one ,zro ,zro ,zro ,one ,one ,zro ,zro ,zro ,one / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// odd parity => factor i !z-refl: odd DATA coffkind(7,9) /.false./ DATA coeffi(1:10,7,9) / zro , ci ,zro ,mci ,zro ,zro ,mci ,zro , ci ,zro / !(3*cos^2(theta)-1) <==> Y20// odd parity => factor i !z-refl: even DATA coffkind(8,9) /.true./ DATA coeffi(1:10,8,9) / zro ,zro , ci ,zro ,zro ,zro ,zro ,mci ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// odd parity => factor i !z-refl: odd DATA coffkind(9,9) /.false./ DATA coeffi(1:10,9,9) / zro ,one ,zro ,one ,zro ,zro ,mone ,zro ,mone ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// odd parity => factor i !z-refl: even DATA coffkind(10,9) /.true./ DATA coeffi(1:10,10,9) / one ,zro ,zro ,zro ,mone ,mone ,zro ,zro ,zro ,one / !****************************************************************************** ! linear combinations of locs that are eigenfunctions ! of z-reflection operation for l=2; four entangled atoms !****************************************************************************** !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)// even parity => take as is !z-refl: even DATA coffkind(1,10) /.true./ DATA coeffi(1:20,1,10) / one ,zro ,zro ,zro ,one ,one ,zro ,zro ,zro ,one& ,one ,zro ,zro ,zro ,one ,one ,zro ,zro ,zro ,one / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(2,10) /.false./ DATA coeffi(1:20,2,10) / zro ,one ,zro ,mone ,zro ,zro ,one ,zro ,mone ,zro& ,zro ,one ,zro ,mone ,zro ,zro ,one ,zro ,mone ,zro / !(3*cos^2(theta)-1) <==> Y20// even parity => take as is !z-refl: even DATA coffkind(3,10) /.true./ DATA coeffi(1:20,3,10) / zro ,zro ,one ,zro ,zro ,zro ,zro ,one ,zro ,zro& ,zro ,zro ,one ,zro ,zro ,zro ,zro ,one ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// even parity => take as is !z-refl: odd DATA coffkind(4,10) /.false./ DATA coeffi(1:20,4,10) / zro , ci ,zro , ci ,zro ,zro , ci ,zro , ci ,zro& ,zro , ci ,zro , ci ,zro ,zro , ci ,zro , ci ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// even parity => take as is !z-refl: even DATA coffkind(5,10) /.true./ DATA coeffi(1:20,5,10) / ci ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,mci& , ci ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,mci / !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)//odd parity => factor i !z-refl: odd DATA coffkind(6,10) /.false./ DATA coeffi(1:20,6,10) / ci ,zro ,zro ,zro , ci ,mci ,zro ,zro ,zro ,mci& ,mci ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro , ci / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// odd parity => factor i !z-refl: odd DATA coffkind(7,10) /.false./ DATA coeffi(1:20,7,10) / zro , ci ,zro ,mci ,zro ,zro ,mci ,zro , ci ,zro& ,zro , ci ,zro ,mci ,zro ,zro ,mci ,zro , ci ,zro / !(3*cos^2(theta)-1) <==> Y20// odd parity => factor i !z-refl: odd DATA coffkind(8,10) /.false./ DATA coeffi(1:20,8,10) / zro ,zro , ci ,zro ,zro ,zro ,zro ,mci ,zro ,zro& ,zro ,zro ,mci ,zro ,zro ,zro ,zro , ci ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// odd parity => factor i !z-refl: even DATA coffkind(9,10) /.true./ DATA coeffi(1:20,9,10) / zro ,one ,zro ,one ,zro ,zro ,mone ,zro ,mone ,zro& ,zro ,mone ,zro ,mone ,zro ,zro ,one ,zro ,one ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// odd parity => factor i !z-refl: odd DATA coffkind(10,10) /.false./ DATA coeffi(1:20,10,10) / one ,zro ,zro ,zro ,mone ,mone ,zro ,zro ,zro ,one& ,mone ,zro ,zro ,zro ,one ,one ,zro ,zro ,zro ,mone / !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)// even parity => take as is !z-refl: odd DATA coffkind(11,10) /.false./ DATA coeffi(1:20,11,10) / one ,zro ,zro ,zro ,one ,one ,zro ,zro ,zro ,one& ,mone ,zro ,zro ,zro ,mone ,mone ,zro ,zro ,zro ,mone / !sin^2(theta)cos(2*phi) <==> (Y22 + Y2-2)//odd parity => factor i !z-refl: odd DATA coffkind(12,10) /.false./ DATA coeffi(1:20,12,10) / ci ,zro ,zro ,zro , ci ,mci ,zro ,zro ,zro ,mci& , ci ,zro ,zro ,zro , ci ,mci ,zro ,zro ,zro ,mci / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// even parity => take as is !z-refl: even DATA coffkind(13,10) /.true./ DATA coeffi(1:20,13,10) / zro ,one ,zro ,mone ,zro ,zro ,one ,zro ,mone ,zro& ,zro ,mone ,zro ,one ,zro ,zro ,mone ,zro ,one ,zro / !sin(theta)cos(theta)cos(phi) <==> (Y21 - Y2-1)// odd parity => factor i !z-refl: even DATA coffkind(14,10) /.true./ DATA coeffi(1:20,14,10) / zro , ci ,zro ,mci ,zro ,zro ,mci ,zro , ci ,zro& ,zro ,mci ,zro , ci ,zro ,zro , ci ,zro ,mci ,zro / !(3*cos^2(theta)-1) <==> Y20// even parity => take as is !z-refl: odd DATA coffkind(15,10) /.false./ DATA coeffi(1:20,15,10) / zro ,zro ,one ,zro ,zro ,zro ,zro ,one ,zro ,zro& ,zro ,zro ,mone ,zro ,zro ,zro ,zro ,mone ,zro ,zro / !(3*cos^2(theta)-1) <==> Y20// odd parity => factor i !z-refl: even DATA coffkind(16,10) /.true./ DATA coeffi(1:20,16,10) / zro ,zro , ci ,zro ,zro ,zro ,zro ,mci ,zro ,zro& ,zro ,zro , ci ,zro ,zro ,zro ,zro ,mci ,zro ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// even parity => take as is !z-refl: even DATA coffkind(17,10) /.true./ DATA coeffi(1:20,17,10) / zro , ci ,zro , ci ,zro ,zro , ci ,zro , ci ,zro& ,zro ,mci ,zro ,mci ,zro ,zro ,mci ,zro ,mci ,zro / !sin(theta)cos(theta)sin(phi) <==> i(Y21 + Y2-1)// odd parity => factor i !z-refl: odd DATA coffkind(18,10) /.false./ DATA coeffi(1:20,18,10) / zro ,one ,zro ,one ,zro ,zro ,mone ,zro ,mone ,zro& ,zro ,one ,zro ,one ,zro ,zro ,mone ,zro ,mone ,zro / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// even parity => take as is !z-refl: odd DATA coffkind(19,10) /.false./ DATA coeffi(1:20,19,10) / ci ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,mci& ,mci ,zro ,zro ,zro , ci ,mci ,zro ,zro ,zro , ci / !sin^2(theta)sin(2*phi) <==> i(Y22 - Y2-2)// odd parity => factor i !z-refl: even DATA coffkind(20,10) /.true./ DATA coeffi(1:20,20,10) / one ,zro ,zro ,zro ,mone ,mone ,zro ,zro ,zro ,one& ,one ,zro ,zro ,zro ,mone ,mone ,zro ,zro ,zro ,one / !*************************************************************************** !*************************************************************************** !*************************************************************************** ! ANGULAR MOMENTUM: 3 !*************************************************************************** !*************************************************************************** !*************************************************************************** !************************************************************* ! linear combinations of locs that are eigenfunctions of ! z-reflection operation for l=3 (single locs) !************************************************************* !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(1,5) /.true./ DATA coeffi(1:7,1,5) / one ,zro ,zro ,zro ,zro ,zro ,one / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(2,5) /.false./ DATA coeffi(1:7,2,5) / zro , ci ,zro ,zro ,zro , ci ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(3,5) /.true./ DATA coeffi(1:7,3,5) / zro ,zro ,one ,zro ,one ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//odd parity=>multiply by i !z-refl: odd DATA coffkind(4,5) /.false./ DATA coeffi(1:7,4,5) / zro ,zro ,zro , ci ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(5,5) /.true./ DATA coeffi(1:7,5,5) / zro ,zro , ci ,zro ,mci ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(6,5) /.false./ DATA coeffi(1:7,6,5) / zro ,one ,zro ,zro ,zro ,mone ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(7,5) /.true./ DATA coeffi(1:7,7,5) / ci ,zro ,zro ,zro ,zro ,zro ,mci / !*************************************************************************** ! linear combinations of locs that are eigenfunctions of ! z-reflection operation for l=3; two locs NOT in xy-plane (double locs) !*************************************************************************** !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(1,11) /.true./ DATA coeffi(1:14,1,11) / one ,zro ,zro ,zro ,zro ,zro ,one , one ,zro ,zro ,zro ,zro ,zro ,one / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(2,11) /.false./ DATA coeffi(1:14,2,11) / zro , ci ,zro ,zro ,zro , ci ,zro , zro , ci ,zro ,zro ,zro , ci ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(3,11) /.true./ DATA coeffi(1:14,3,11) / zro ,zro ,one ,zro ,one ,zro ,zro , zro ,zro ,one ,zro ,one ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//odd parity=>multiply by i !z-refl: odd DATA coffkind(4,11) /.false./ DATA coeffi(1:14,4,11) / zro ,zro ,zro , ci ,zro ,zro ,zro , zro ,zro ,zro , ci ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(5,11) /.true./ DATA coeffi(1:14,5,11) / zro ,zro , ci ,zro ,mci ,zro ,zro , zro ,zro , ci ,zro ,mci ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(6,11) /.false./ DATA coeffi(1:14,6,11) / zro ,one ,zro ,zro ,zro ,mone ,zro , zro ,one ,zro ,zro ,zro ,mone ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(7,11) /.true./ DATA coeffi(1:14,7,11) / ci ,zro ,zro ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,zro ,zro ,mci / !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)//even parity => leave as is !z-refl: odd DATA coffkind(8,11) /.false./ DATA coeffi(1:14,8,11) / ci ,zro ,zro ,zro ,zro ,zro , ci , mci ,zro ,zro ,zro ,zro ,zro ,mci / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)//even parity => leave as is !z-refl: even DATA coffkind(9,11) /.true./ DATA coeffi(1:14,9,11) / zro ,one ,zro ,zro ,zro ,one ,zro , zro ,mone ,zro ,zro ,zro ,mone ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//even parity => leave as is !z-refl: odd DATA coffkind(10,11) /.false./ DATA coeffi(1:14,10,11) / zro ,zro , ci ,zro , ci ,zro ,zro , zro ,zro ,mci ,zro ,mci ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//even parity => leave as is !z-refl: even DATA coffkind(11,11) /.true./ DATA coeffi(1:14,11,11) / zro ,zro ,zro ,one ,zro ,zro ,zro , zro ,zro ,zro ,mone ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//even parity => leave as is !z-refl: odd DATA coffkind(12,11) /.false./ DATA coeffi(1:14,12,11) / zro ,zro ,one ,zro ,mone ,zro ,zro , zro ,zro ,mone ,zro ,one ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)//even parity => leave as is !z-refl: true DATA coffkind(13,11) /.true./ DATA coeffi(1:14,13,11) / zro , ci ,zro ,zro ,zro ,mci ,zro , zro ,mci ,zro ,zro ,zro , ci ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)//even parity => leave as is !z-refl: odd DATA coffkind(14,11) /.false./ DATA coeffi(1:14,14,11) / one ,zro ,zro ,zro ,zro ,zro ,mone , mone ,zro ,zro ,zro ,zro ,zro ,one / !*************************************************************************** ! linear combinations of locs that are eigenfunctions of ! z-reflection operation for l=3; two locs IN xy-plane (double locs) !*************************************************************************** !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(1,12) /.true./ DATA coeffi(1:14,1,12) / one ,zro ,zro ,zro ,zro ,zro ,one , one ,zro ,zro ,zro ,zro ,zro ,one / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(2,12) /.false./ DATA coeffi(1:14,2,12) / zro , ci ,zro ,zro ,zro , ci ,zro , zro , ci ,zro ,zro ,zro , ci ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(3,12) /.true./ DATA coeffi(1:14,3,12) / zro ,zro ,one ,zro ,one ,zro ,zro , zro ,zro ,one ,zro ,one ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//odd parity=>multiply by i !z-refl: odd DATA coffkind(4,12) /.false./ DATA coeffi(1:14,4,12) / zro ,zro ,zro , ci ,zro ,zro ,zro , zro ,zro ,zro , ci ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(5,12) /.true./ DATA coeffi(1:14,5,12) / zro ,zro , ci ,zro ,mci ,zro ,zro , zro ,zro , ci ,zro ,mci ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(6,12) /.false./ DATA coeffi(1:14,6,12) / zro ,one ,zro ,zro ,zro ,mone ,zro , zro ,one ,zro ,zro ,zro ,mone ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(7,12) /.true./ DATA coeffi(1:14,7,12) / ci ,zro ,zro ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,zro ,zro ,mci / !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)//even parity => leave as is !z-refl: even DATA coffkind(8,12) /.true./ DATA coeffi(1:14,8,12) / ci ,zro ,zro ,zro ,zro ,zro , ci , mci ,zro ,zro ,zro ,zro ,zro ,mci / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)//even parity => leave as is !z-refl: odd DATA coffkind(9,12) /.false./ DATA coeffi(1:14,9,12) / zro ,one ,zro ,zro ,zro ,one ,zro , zro ,mone ,zro ,zro ,zro ,mone ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//even parity => leave as is !z-refl: even DATA coffkind(10,12) /.true./ DATA coeffi(1:14,10,12) / zro ,zro , ci ,zro , ci ,zro ,zro , zro ,zro ,mci ,zro ,mci ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//even parity => leave as is !z-refl: odd DATA coffkind(11,12) /.false./ DATA coeffi(1:14,11,12) / zro ,zro ,zro ,one ,zro ,zro ,zro , zro ,zro ,zro ,mone ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//even parity => leave as is !z-refl: even DATA coffkind(12,12) /.true./ DATA coeffi(1:14,12,12) / zro ,zro ,one ,zro ,mone ,zro ,zro , zro ,zro ,mone ,zro ,one ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)//even parity => leave as is !z-refl: odd DATA coffkind(13,12) /.false./ DATA coeffi(1:14,13,12) / zro , ci ,zro ,zro ,zro ,mci ,zro , zro ,mci ,zro ,zro ,zro , ci ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)//even parity => leave as is !z-refl: even DATA coffkind(14,12) /.true./ DATA coeffi(1:14,14,12) / one ,zro ,zro ,zro ,zro ,zro ,mone , mone ,zro ,zro ,zro ,zro ,zro ,one / !*************************************************************************** ! linear combinations of locs that are eigenfunctions of ! z-reflection operation for l=3; four entangled atoms !*************************************************************************** !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(1,13) /.true./ DATA coeffi(1:28,1,13) / one ,zro ,zro ,zro ,zro ,zro ,one , one ,zro ,zro ,zro ,zro ,zro ,one& , one ,zro ,zro ,zro ,zro ,zro ,one , one ,zro ,zro ,zro ,zro ,zro ,one / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(2,13) /.false./ DATA coeffi(1:28,2,13) / zro , ci ,zro ,zro ,zro , ci ,zro , zro , ci ,zro ,zro ,zro , ci ,zro& , zro , ci ,zro ,zro ,zro , ci ,zro , zro , ci ,zro ,zro ,zro , ci ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(3,13) /.true./ DATA coeffi(1:28,3,13) / zro ,zro ,one ,zro ,one ,zro ,zro , zro ,zro ,one ,zro ,one ,zro ,zro& , zro ,zro ,one ,zro ,one ,zro ,zro , zro ,zro ,one ,zro ,one ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//odd parity=>multiply by i !z-refl: odd DATA coffkind(4,13) /.false./ DATA coeffi(1:28,4,13) / zro ,zro ,zro , ci ,zro ,zro ,zro , zro ,zro ,zro , ci ,zro ,zro ,zro& , zro ,zro ,zro , ci ,zro ,zro ,zro , zro ,zro ,zro , ci ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//odd parity=>multiply by i !z-refl: even DATA coffkind(5,13) /.true./ DATA coeffi(1:28,5,13) / zro ,zro , ci ,zro ,mci ,zro ,zro , zro ,zro , ci ,zro ,mci ,zro ,zro& , zro ,zro , ci ,zro ,mci ,zro ,zro , zro ,zro , ci ,zro ,mci ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)// odd parity => multiply by i !z-refl: odd DATA coffkind(6,13) /.false./ DATA coeffi(1:28,6,13) / zro ,one ,zro ,zro ,zro ,mone ,zro , zro ,one ,zro ,zro ,zro ,mone ,zro& , zro ,one ,zro ,zro ,zro ,mone ,zro , zro ,one ,zro ,zro ,zro ,mone ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)// odd parity => multiply by i !z-refl: even DATA coffkind(7,13) /.true./ DATA coeffi(1:28,7,13) / ci ,zro ,zro ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,zro ,zro ,mci& , ci ,zro ,zro ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,zro ,zro ,mci / !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)//even parity => leave as is !z-refl: even DATA coffkind(8,13) /.true./ DATA coeffi(1:28,8,13) / ci ,zro ,zro ,zro ,zro ,zro , ci , mci ,zro ,zro ,zro ,zro ,zro ,mci& , ci ,zro ,zro ,zro ,zro ,zro , ci , mci ,zro ,zro ,zro ,zro ,zro ,mci / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)//even parity => leave as is !z-refl: odd DATA coffkind(9,13) /.false./ DATA coeffi(1:28,9,13) / zro ,one ,zro ,zro ,zro ,one ,zro , zro ,mone ,zro ,zro ,zro ,mone ,zro& , zro ,one ,zro ,zro ,zro ,one ,zro , zro ,mone ,zro ,zro ,zro ,mone ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//even parity => leave as is !z-refl: even DATA coffkind(10,13) /.true./ DATA coeffi(1:28,10,13) / zro ,zro , ci ,zro , ci ,zro ,zro , zro ,zro ,mci ,zro ,mci ,zro ,zro& , zro ,zro , ci ,zro , ci ,zro ,zro , zro ,zro ,mci ,zro ,mci ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//even parity => leave as is !z-refl: odd DATA coffkind(11,13) /.false./ DATA coeffi(1:28,11,13) / zro ,zro ,zro ,one ,zro ,zro ,zro , zro ,zro ,zro ,mone ,zro ,zro ,zro& , zro ,zro ,zro ,one ,zro ,zro ,zro , zro ,zro ,zro ,mone ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//even parity => leave as is !z-refl: even DATA coffkind(12,13) /.true./ DATA coeffi(1:28,12,13) / zro ,zro ,one ,zro ,mone ,zro ,zro , zro ,zro ,mone ,zro ,one ,zro ,zro& , zro ,zro ,one ,zro ,mone ,zro ,zro , zro ,zro ,mone ,zro ,one ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)//even parity => leave as is !z-refl: odd DATA coffkind(13,13) /.false./ DATA coeffi(1:28,13,13) / zro , ci ,zro ,zro ,zro ,mci ,zro , zro ,mci ,zro ,zro ,zro , ci ,zro& , zro , ci ,zro ,zro ,zro ,mci ,zro , zro ,mci ,zro ,zro ,zro , ci ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)//even parity => leave as is !z-refl: even DATA coffkind(14,13) /.true./ DATA coeffi(1:28,14,13) / one ,zro ,zro ,zro ,zro ,zro ,mone , mone ,zro ,zro ,zro ,zro ,zro ,one& , one ,zro ,zro ,zro ,zro ,zro ,mone , mone ,zro ,zro ,zro ,zro ,zro ,one / !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)// odd parity => multiply by i !z-refl: odd DATA coffkind(15,13) /.false./ DATA coeffi(1:28,15,13) / one ,zro ,zro ,zro ,zro ,zro ,one , one ,zro ,zro ,zro ,zro ,zro ,one& , mone ,zro ,zro ,zro ,zro ,zro ,mone , mone ,zro ,zro ,zro ,zro ,zro ,mone / !sin^3(theta)sin(3*phi) <==> i(Y33+Y3-3)//even parity => leave as is !z-refl: odd DATA coffkind(16,13) /.false./ DATA coeffi(1:28,16,13) / ci ,zro ,zro ,zro ,zro ,zro , ci , mci ,zro ,zro ,zro ,zro ,zro ,mci& , mci ,zro ,zro ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,zro ,zro , ci / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)// odd parity => multiply by i !z-refl: even DATA coffkind(17,13) /.true./ DATA coeffi(1:28,17,13) / zro , ci ,zro ,zro ,zro , ci ,zro , zro , ci ,zro ,zro ,zro , ci ,zro& , zro ,mci ,zro ,zro ,zro ,mci ,zro , zro ,mci ,zro ,zro ,zro ,mci ,zro / !sin^2(theta)cos(theta)cos(2*phi)<==>(Y32+Y3-2)//even parity => leave as is !z-refl: even DATA coffkind(18,13) /.true./ DATA coeffi(1:28,18,13) / zro ,one ,zro ,zro ,zro ,one ,zro , zro ,mone ,zro ,zro ,zro ,mone ,zro& , zro ,mone ,zro ,zro ,zro ,mone ,zro , zro ,one ,zro ,zro ,zro ,one ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//odd parity=>multiply by i !z-refl: odd DATA coffkind(19,13) /.false./ DATA coeffi(1:28,19,13) / zro ,zro ,one ,zro ,one ,zro ,zro , zro ,zro ,one ,zro ,one ,zro ,zro& , zro ,zro ,mone ,zro ,mone ,zro ,zro , zro ,zro ,mone ,zro ,mone ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]sin(phi)<==>i(Y31+Y3-1)//even parity => leave as is !z-refl: odd DATA coffkind(20,13) /.false./ DATA coeffi(1:28,20,13) / zro ,zro , ci ,zro , ci ,zro ,zro , zro ,zro ,mci ,zro ,mci ,zro ,zro& , zro ,zro ,mci ,zro ,mci ,zro ,zro , zro ,zro , ci ,zro , ci ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//odd parity=>multiply by i !z-refl: even DATA coffkind(21,13) /.true./ DATA coeffi(1:28,21,13) / zro ,zro ,zro , ci ,zro ,zro ,zro , zro ,zro ,zro , ci ,zro ,zro ,zro& , zro ,zro ,zro ,mci ,zro ,zro ,zro , zro ,zro ,zro ,mci ,zro ,zro ,zro / ![5*cos^3(theta)-3*cos(theta)]<==>Y30//even parity => leave as is !z-refl: even DATA coffkind(22,13) /.true./ DATA coeffi(1:28,22,13) / zro ,zro ,zro ,one ,zro ,zro ,zro , zro ,zro ,zro ,mone ,zro ,zro ,zro& , zro ,zro ,zro ,mone ,zro ,zro ,zro , zro ,zro ,zro ,one ,zro ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//odd parity=>multiply by i !z-refl: odd DATA coffkind(23,13) /.false./ DATA coeffi(1:28,23,13) / zro ,zro , ci ,zro ,mci ,zro ,zro , zro ,zro , ci ,zro ,mci ,zro ,zro& , zro ,zro ,mci ,zro , ci ,zro ,zro , zro ,zro ,mci ,zro , ci ,zro ,zro / !sin(theta)[5*cos^2(theta)-1]cos(phi)<==>(Y31-Y3-1)//even parity => leave as is !z-refl: odd DATA coffkind(24,13) /.false./ DATA coeffi(1:28,24,13) / zro ,zro ,one ,zro ,mone ,zro ,zro , zro ,zro ,mone ,zro ,one ,zro ,zro& , zro ,zro ,mone ,zro ,one ,zro ,zro , zro ,zro ,one ,zro ,mone ,zro ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)// odd parity => multiply by i !z-refl: even DATA coffkind(25,13) /.true./ DATA coeffi(1:28,25,13) / zro ,one ,zro ,zro ,zro ,mone ,zro , zro ,one ,zro ,zro ,zro ,mone ,zro& , zro ,mone ,zro ,zro ,zro ,one ,zro , zro ,mone ,zro ,zro ,zro ,one ,zro / !sin^2(theta)cos(theta)sin(2*phi)<==>i(Y32-Y3-2)//even parity => leave as is !z-refl: even DATA coffkind(26,13) /.true./ DATA coeffi(1:28,26,13) / zro , ci ,zro ,zro ,zro ,mci ,zro , zro ,mci ,zro ,zro ,zro , ci ,zro& , zro ,mci ,zro ,zro ,zro , ci ,zro , zro , ci ,zro ,zro ,zro ,mci ,zro / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)// odd parity => multiply by i !z-refl: odd DATA coffkind(27,13) /.false./ DATA coeffi(1:28,27,13) / ci ,zro ,zro ,zro ,zro ,zro ,mci , ci ,zro ,zro ,zro ,zro ,zro ,mci& , mci ,zro ,zro ,zro ,zro ,zro , ci , mci ,zro ,zro ,zro ,zro ,zro , ci / !sin^3(theta)cos(3*phi) <==> (Y33 - Y3-3)//even parity => leave as is !z-refl: odd DATA coffkind(28,13) /.false./ DATA coeffi(1:28,28,13) / one ,zro ,zro ,zro ,zro ,zro ,mone , mone ,zro ,zro ,zro ,zro ,zro ,one& , mone ,zro ,zro ,zro ,zro ,zro ,one , one ,zro ,zro ,zro ,zro ,zro ,mone / END MODULE m_loccoeff