What are the set of d orbitals involved in forming capped octahedral geometry?
1 Answer
OR
To visualize this geometry more clearly, go here and play around with the animation GUI.
A capped octahedral geometry is basically octahedral with an extra ligand in between the equatorial ligands, above the equatorial plane:
The principal axis of rotation here is a
Since the
Therefore, one option I would guess is
If you're into group theory, the character table for
The reducible representation is gotten by operating with
This turns out to be:
#" "" "hatE" "2hatC_3" "3hatsigma_v#
#Gamma_(sigma) = 7" "1" "" "3#
and this reduces down to:
#Gamma_(sigma)^(red) = 3A_1 + 2E#
On the character table,
#s harr x^2 + y^2# #p_x harr x# #p_y harr y# #p_z harr z# #d_(z^2) harr z^2# #d_(x^2-y^2) harr x^2-y^2# #d_(xy) harr xy# #d_(xz) harr xz# #d_(yz) harr yz#
Therefore, this can correspond to the linear combination:
#overbrace(s)^(A_1) + overbrace(p_z)^(A_1) + overbrace(d_(z^2))^(A_1) + overbrace((p_x", "p_y))^(E) + overbrace((d_(x^2-y^2)", "d_(xy)))^(E)#
#ul("orbital"" "" "" ""IRREP")#
#s" "" "" "" "" "" "A_1#
#p_z" "" "" "" "" "color(white)(.)A_1#
#(p_x,p_y)" "" "" "color(white)(.)E#
#d_(z^2)" "" "" "" "color(white)(....)A_1#
#(d_(x^2-y^2), d_(xy))" "color(white)(.)E#
The other choice, though not as easy to see, is:
#overbrace(s)^(A_1) + overbrace(p_z)^(A_1) + overbrace(d_(z^2))^(A_1) + overbrace((p_x", "p_y))^(E) + overbrace((d_(xz)", "d_(yz)))^(E)#
#ul("orbital"" "" "" ""IRREP")#
#s" "" "" "" "" "" "A_1#
#p_z" "" "" "" "" "color(white)(.)A_1#
#(p_x,p_y)" "" "" "color(white)(.)E#
#d_(z^2)" "" "" "" "color(white)(....)A_1#
#(d_(xz), d_(yz))" "" "color(white)(..)E#