################################################################################# make polar plots of real combinations of spherical harmonics ## > gnuplot -persist orbitals.gnu ## I 2001, E. Koch, MPI-FKF ################################################################################## set term postscript portrait enh 'Helvetica' 21# set output 'tmp.ps'# set size 1.0, 0.7# set up coordinate system #####set view 60, 30scale=0.9set xrange [-scale:scale]set yrange [-scale:scale]set zrange [-scale:scale]set noborderset noxticsset noyticsset nozticsset nokey# coordinate axesset arrow 1 from -scale, 0, 0 to scale, 0, 0 lw 3 set arrow 2 from 0, -scale, 0 to 0, scale, 0 lw 3set arrow 3 from 0, 0, -scale to 0, 0, scale lw 3set label 'x' at scale,-.25*scale,0set label 'y' at 0,1.1*scale,-.15*scaleset label 'z' at 0.10*scale,0,scale# polar coordinates ####set parametricset urange [0:pi]set vrange [-pi:pi]x(u,v)=sin(u)*cos(v)y(u,v)=sin(u)*sin(v)z(u,v)=cos(u)set isosamples 22, 45set hidden3d# atomic orbitals ##### s orbitals(u,v)=sqrt(1.0/4.0/pi)# p orbitalspz(u,v)=sqrt(3.0/4.0/pi)*cos(u) # m =0px(u,v)=sqrt(3.0/4.0/pi)*sin(u)*cos(v) # |m|=1py(u,v)=sqrt(3.0/4.0/pi)*sin(u)*sin(v) # |m|=1# d orbitalsd3z2m1(u,v)=sqrt( 5.0/16.0/pi)*(3.0*cos(u)**2-1.0) # m =0dzx(u,v) =sqrt(15.0/16.0/pi)*sin(2.0*u)*cos(v) # |m|=1dyz(u,v) =sqrt(15.0/16.0/pi)*sin(2.0*u)*sin(v) # |m|=1dx2my2(u,v)=sqrt(15.0/16.0/pi)*sin(u)**2*cos(2.0*v) # |m|=2dxy(u,v) =sqrt(15.0/16.0/pi)*sin(u)**2*sin(2.0*v) # |m|=2# f orbitalsfz5z2m3 (u,v)=sqrt( 7.0/16.0/pi)*(5.0*cos(u)**2-3.0)*cos(u) # m =0fx5z2m1 (u,v)=sqrt( 21.0/32.0/pi)*(5.0*cos(u)**2-1.0)*sin(u)*cos(v) # |m|=1fy5z2m1 (u,v)=sqrt( 21.0/32.0/pi)*(5.0*cos(u)**2-1.0)*sin(u)*sin(v) # |m|=1fzx2my2 (u,v)=sqrt(105.0/16.0/pi)*cos(u)*sin(u)**2*cos(2.0*v) # |m|=2fxyz (u,v)=sqrt(105.0/16.0/pi)*cos(u)*sin(u)**2*sin(2.0*v) # |m|=2fxx2m3y2(u,v)=sqrt( 35.0/32.0/pi)*sin(u)**3*cos(3.0*v) # |m|=3fy3x2my2(u,v)=sqrt( 35.0/32.0/pi)*sin(u)**3*sin(3.0*v) # |m|=3# some hybrid orbitals # sp hybrids:\\sp_1(u,v)=sqrt(1.0/2.0)*(s(u,v)+pz(u,v))sp_2(u,v)=sqrt(1.0/2.0)*(s(u,v)-pz(u,v))# sp2 hybrids:sp2_1(u,v)=sqrt(1.0/3.0)*(s(u,v)+sqrt(2.0)*px(u,v))sp2_2(u,v)=sqrt(1.0/3.0)*(s(u,v)-sqrt(1.0/2.0)*px(u,v)+sqrt(3.0/2.0)*py(u,v))sp2_3(u,v)=sqrt(1.0/3.0)*(s(u,v)-sqrt(1.0/2.0)*px(u,v)-sqrt(3.0/2.0)*py(u,v))# sp3 hybrids:sp3_1(u,v)=0.5*(s(u,v)+px(u,v)+py(u,v)+pz(u,v))sp3_2(u,v)=0.5*(s(u,v)+px(u,v)-py(u,v)-pz(u,v))sp3_3(u,v)=0.5*(s(u,v)-px(u,v)+py(u,v)-pz(u,v))sp3_4(u,v)=0.5*(s(u,v)-px(u,v)-py(u,v)+pz(u,v))# >>> here you choose what orbital to plot