Transcript 11ColNiCl.ppt

An approximate Heff formalism
for treating electronic and rotational
energy levels in the 3d9 manifold
of nickel halide molecules
Jon T. Hougen
NIST
Molecules considered:
NiX = NiF, NiCl, NiBr, and NiI (No NiH)
Ni+X has one “d hole”
has 3d9 manifold of electronic states
Related molecules: PdX and PtX
Configuration:
4d9
5d9
Topics considered:
Position of all 3d9 spin-orbit components
Large -type doubling in  = ½ states
Effective Hamiltonian = Hnon-rot + Hrot
Helectronic = HCrystal-Field + HSpin-Orbit
HSO = A L·S (familiar) 
= ALzSz + ½ A(L+S + LS+)
HCF = C0 + C2Y20() + C4Y40()
= (unfamiliar)
Helectronic-rotational = HCF + HSO + Hrot
All 10 electronic basis set functions
|, with L=2 and S=½
2
2
5/2
3/2
2
3/2
2
1/2
2
1/2
|2, ½
|2, ½
|1, ½
|1, ½
|0, ½
 =  5/2
 =  3/2
 =  3/2
 =  1/2
 =  1/2
NiF 3d9 Electronic Energy Levels
3/2
2
D3/2
2000
1/2

cm
-1
2
2
1000
D

2
2
D
5/2

2
A=0
mol.
0
2
D5/2
A
1/2
3/2
=0
AL·S
Ni+
obs
9
NiCl 3d Electronic Energy Levels
2000
1/2
2
cm
-1
3/2
D3/2

2
1000
2
D
2

2

2
A=0
mol.
0
A
1/2
5/2
3/2
=0
2
obs
D5/2
AL·S
atom
D
Fit the observed electronic levels
(= 5 spin-orbit components) to determine
Two crystal-field splitting parameters =
C2 and C4 and
One spin-orbit splitting parameter = A and
One “orbital impurity factor”   0.9
Turn these four parameters into one
=0 mixing coefficient parameter 
Define: rcos2 = (A + C2  5C4)/4
rsin2 = +A(3/2)
L=2,=1|L+|L=2,=0 = [L(L+1)]1/2
The two  = ½ wave functions become
|, 
|, 
upper = +cos |1,½ + sin |0,+½
lower = sin |1,½ + cos |0,+½
Hrot = B(JLS)2
= B[(J2Jz2)+(L2Lz2)+(S2Sz2)]
 2B[(JxSx+JySy)+(JxLx+JyLy)]
+ 2B(LxSx+LySy)
Taking red terms into account
Erot(=½) = BJ(J+1)  ½p(J+½)
(p/2B)upper = ½ + ½cos2  6 sin2
(p/2B)lower = ½  ½cos2 + 6 sin2
p/2B for upper and lower  =1/2 states of NiF
with empirical correction factor =0.875 in =1|L+|=0
2
obs
p/2B (unitless)
1
0
-1
-2
obs
-3
0
1
2
3
2 in radians
4
2 5
calc
6
p/2B for upper and lower  =1/2 states of NiCl
with empirical correction factor  =0.89 in  =1|L +| =0 
2
p/2B (unitless)
obs
1
0
-1
-2
obs
-3
0
1
2
3
2 in radians
4
2
calc
5
6
What questions have been raised by this theory?
Main questions concern parity assignments (+ or -)
of the rotational levels, which affect sign of p.
NiF
Relative parities
(p/2B)theoretical = -2.51 +1.51 (signs different)
(p/2B)experimental = -2.23 -1.19 (signs the same)
Can be decided by experiment.
An experimental test of this theory would be
to analyze an appropriate pair of NiF transitions
to determine the relative signs of p for the two
 = 1/2 states in the 3d9 manifold
NiF Electronic states
Rotationally analyzed
Not rotationally analyzed
J. Mol. Spectrosc. 214
(2002) 152-174
Krouti, Hirao, Dufour,
Boulezhar, Pinchemel,
Bernath
3d9 manifold 
 = 1/2
 = 1/2
NiCl
Absolute parities
(p/2B)theoretical = -2.46 +1.46 (signs – and +)
(p/2B)experimental =+2.32 -1.32 (signs + and –)
Can only be decided by theory.
There are two theoretical results asking for
this absolute parity sign change
1. The present work wants signs of p changed.
2. Ab initio work wants a 2+ state at 12,300 cm-1
to be reassigned as 2
W.-L. Zou & W.-J. Liu, J. Chem. Phys.124 (2002) 154312
New experimental work to which this theory should
be applicable
NiI (3d9):
Electronic spectroscopy:
V.L. Ayles, L.G. Muzangwa, S.A. Reid
Chem. Phys. Lett. 497 (2010) 168-171
PdX (4d9):
Microwave spectroscopy
T. Okabayashi’s group
Possible new theoretical work
Formulas for splitting  (J+1/2)3
in the two  = 3/2 states of the d9 manifold
(probably quite easy with this model)
Look at d8s manifold
(maybe not doable with this model)
Note that to treat all  = ½ states
on an equal footing, it is most convenient
to use the case (a) splitting expression
Erot(=½) = BJ(J+1)  ½p(J+½)
It is much less convenient
to use the case (b) splitting expression
Erot(2) = BN(N+1) + ½N
Erot(2) = BN(N+1) - ½(N+1)
for J=N+1/2
for J=N-1/2
HCF = C0 + C2Y20() + C4Y40()
= unfamiliar
Yl,m>0(,) do not occur in electric field for
a cylindrical symmetric charge.
Yl >4,0() do not have non-zero matrix
elements within L = 2 manifold.
Yodd,0() do not have non-zero matrix
elements within 3d manifold.
C0Y00
is a constant energy shift
C2Y20() is interaction of charge of d-hole
with electric quadrupole moment
of the molecule
C4Y40() is interaction of charge of d-hole
with electric hexadecapole
moment of the molecule
Operator equivalents
Greatly simplify calculations
Good for L = 0 matrix elements
 Good within d9 manifold
C2Y20()  (1/6)C2[3Lz2 – L2]
C4Y40()  (1/48)C4[35Lz4 – 30L2Lz2 + 3L4
+ 25Lz2 – 6L2]
We use 3 crystal-field parameters C0,C2,C4
for 3 electronic states 2,2,2 !
Why not just use T0 for each state???
3 T0’s are used in the paper
The electronic structure of NiH:
The {Ni+ 3d9 2D} supermultiplet.
by J.A. Gray, M. Li, T. Nelis, R.W. Field,
J. Chem. Phys. 95 (1991) 7164-7178
I hope that variation of the C0,C2,C4 crystal-field
parameters with halogen (F, Cl, Br, I) and
with metal (Ni, Pd, Pt) will be more chemically
meaningful than changes in energy positions.
Strengths of present electronic model:
We can visualize “2” limiting cases:
A = 0 (no spin orbit interaction) or
C2=C4=0 (only spin-orbit interaction)
Errors  4% of total 3d9 manifold spread
Predict 2 missing levels from 3 obs ??
Errors  0.4% with correction factor 0.9
L=2,=+2|L+|L=2, =+1 = [(L-1)(L+2)]1/2
L=2,=+1|L+|L=2, =0 = [L(L+1)]1/2
Weakness of present electronic model =
too many adjustable parameters
Even with A = 603 cm-1 = fixed, we have
3 parameters (C0, C1, C2) for 5 levels or
4 parameters (C0, C1, C2, ) for 5 levels