the effective magnetic moment is directly related to what
the spin and orbital quantum number
S+L = root 4s(s+1) + L(L+1)
to get the L(L+1) thing what needs to occur
electrons need to move between orbitals
when do we expect first order orbital contribution
when the orbitals the e- are travelling between are degenerate and have the shape shape.
an example of orbitals of tha swme energy and shape can be the
the t2g orbitals
aka e- can move begeeen them and generate magnetic moment
can d1 give first order orbital contribution in Oh
yess
the electron can move between the degenerate and same shape t2g orbitals
t2g
can d2 give first order orbital contribution
yes
(t1g)
can d3 Oh give a first order orbital contribution
nope bc they can’t move anywhere (A2g)
can d4 high spin give rise to first order orbital contribution
nope
bc t2g and eg are different in energy!! they’re not degenerate or the same shape
Eg term
are dx2-dy2 and dz2 the same shape
nope!!
does d4 low spin give FOOC
yes
e- can move to any of the t2g orbitals
T1g
does high spin d5 give FOOC
nope
bc the dx2-y2 and dz2 are diff shapes
is low spin d5 giving us Fooc
yes bc the e- can go into any t2g orbital
does d1 Td give us FOOC
nope
remember dz2 and dx2y2 are diff shapes
E
is d2 Td giving FOOC
nope
diff shapes
is d3 Td high spin giving FOOC
yesss
e- can go in any t2 orbital
T term issss
temp dependent
has FOOC
their magnetic moment will be temp dependent
do ground terms with A or E terms have a FOOC
nope!!
they have a second order orbital contribution but it’s independent of temp.
the gs and es mix
what’s up with the magnetic moment formula for T terms
it has the spin and orbital quantum numbers
what’s up with the magnetic moment for E and A terms
it has the spin quantum number only
no orbital bc the orbitals aren’t the same for e- to be moving between them
what’s the spin only magnetic moment equation
root 4s(s+1) capital
root(n(n+2)
in A and E terms what can’t occur
first order orbital coupling can’t occur
although FOOC can’t occur for A and E terms what can
there can be mixing with the orbital contribution from high T terms of the same multiplicity as the ground term ( same spin)