quadrupole interaction in the solid halogens – a new (not final) look h. haas
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Quadrupole interaction in the solid halogens – a new (not final) look
H. Haas
Instituto Tecnológico e Nuclear, Estrada Nacional 10, P-2685 Sacavém, Portugal, and CERN/EP-SC, CH-1211 Geneve-23, Switzerland,
e-mail: heinz.haas@cern.ch
Experimentalists credo (old):If theory and experiment do not agree, theory must be wrong
Quadrupole interaction in the solid halogens – a new (not final) look
H. Haas
Instituto Tecnológico e Nuclear, Estrada Nacional 10, P-2685 Sacavém, Portugal, and CERN/EP-SC, CH-1211 Geneve-23, Switzerland,
e-mail: heinz.haas@cern.ch
Experimentalists credo (old):If theory and experiment do not agree, theory must be wrong
Theorists credo (new):If theory and experiment do not agree, experiment must be wrong
Quadrupole interaction in the solid halogens – a new (not final) look
H. Haas
Instituto Tecnológico e Nuclear, Estrada Nacional 10, P-2685 Sacavém, Portugal, and CERN/EP-SC, CH-1211 Geneve-23, Switzerland,
e-mail: heinz.haas@cern.ch
Experimentalists credo (old):If theory and experiment do not agree, theory must be wrong
Theorists credo (new):If theory and experiment do not agree, experiment must be wrong
I will try to convince you:If theory and experiment do agree, they may both be wrong !
The structure of the solid halogens
The experimental situation
0
0.1
0.2
0.3
0.4
0.5
0.6h
Cl2 Br2 I2
The experimental situation
0
0.1
0.2
0.3
0.4
0.5
0.6h
Cl2 Br2 I2
A mess !
The advent of theory
0
0.1
0.2
0.3
0.4
0.5
0.6h
Cl2 Br2 I2
Blaha. (92)
More new theories
0
0.1
0.2
0.3
0.4
0.5
0.6h
Cl2 Br2 I2
Alonso.. (04)
Blaha. (92)
Aryal.. (07)
More new theories
0
0.1
0.2
0.3
0.4
0.5
0.6h
Cl2 Br2 I2
Alonso.. (04)
Blaha. (92)
Aryal.. (07)
A mess !
Structural parameters as function of temperature
8.1
8.3
8.5
8.7
8.9
9.1
9.3
9.5
9.7
9.9
0 0.2 0.4 0.6 0.8 1
c (A)
4.3
4.4
4.5
4.6
4.7
4.8
4.9
0 0.2 0.4 0.6 0.8 1
b (A)
6.1
6.3
6.5
6.7
6.9
7.1
7.3
7.5
0 0.2 0.4 0.6 0.8 1
a (A)
T/Tm
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
7.1
0 0.2 0.4 0.6 0.8 1
V1/3 (A)
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
0 0.2 0.4 0.6 0.8 1
R (A)
56.0
56.2
56.4
56.6
56.8
57.0
57.2
57.4
57.6
57.8
58.0
0 0.2 0.4 0.6 0.8 1
q (°)
Structural data extrapolated to T = 0
Cl2 Br2 I2
Rmol (A) 1.9881 2.2809 2.6660
Rsol (A) 1.9950 2.3006 2.7124
q (o) 57.093 57.339 57.863
a (A) 6.1360 6.5672 7.1191
b (A) 4.3889 4.4678 4.6600
c (A) 8.1492 8.6938 9.7962
Experimental frequencies (MHz) extrapolated to T = 0
Cl2 Br2 I2
Q (mol) 111.79 810.0 2452.6
Q (sol) 108.97 763.1 2156.2
Q0 (sol) 109.79 768.2 2160.0
Temperature dependence Cl2 (Nakamura 67)
53.0
53.5
54.0
54.5
55.0
55.5
56.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
NQR frequency (MHz)
Corrected
Molecule
Halogen Q (with H. Petrilli)
0
400
800
1200
1600
0 400 800 1200 1600
Br
0
200
400
600
800
0 200 400 600 800
Cl
F
ClBr
I
H
0
600
1200
1800
2400
0 600 1200 1800 2400
IEFG-the
EFG-exp
0
50
100
150
200
250
300
0 50 100 150 200 250 300
Ga
0
20
40
60
80
100
120
0 20 40 60 80 100 120
Al
F
ClBr
I
0
100
200
300
400
0 100 200 300 400
In
WIEN2k results (1021 V/m2)
Cl2 Br2 I2
EFG(mol) 57.27 112.99 152.88
EFG(sol) 54.11 97.86 119.75
/0(cal) 0.055 0.134 0.217
/0(exp) 0.018 0.052 0.119
WIEN2k results (1021 V/m2)
Cl2 Br2 I2
EFG(mol) 57.27 112.99 152.88
EFG(sol) 54.11 97.86 119.75
/0(cal) 0.055 0.134 0.217
/0(exp) 0.018 0.052 0.119
Conclusion:Present DFT overestimates the frequency shift due to the
intermolecular interaction by a factor 2 to 2.5
WIEN2k results (1021 V/m2)
Cl2 Br2 I2
EFG(mol) 57.27 112.99 152.88
EFG(sol) 54.11 97.86 119.75
/0(cal) 0.055 0.134 0.217
/0(exp) 0.018 0.052 0.119
Conclusion:Present DFT overestimates the frequency shift due to the
intermolecular interaction by a factor 2 to 2.5
Assumption:The calculated intermolecular interaction overestimates h by a
similar factor
Final results
Cl2 Br2 I2
EFG(mol) 57.27 112.99 152.88
EFG(sol) 54.11 97.86 119.75
/0(cal) 0.055 0.134 0.217
/0(exp) 0.018 0.052 0.119
h(cal) 0.071 0.183 0.320
h(cor) 0.023 0.071 0.176
Comparison with experimentsCl2 Br2 I2
EFG(mol) 57.27 112.99 152.88
EFG(sol) 54.11 97.86 119.75
/0(cal) 0.055 0.134 0.217
/0(exp) 0.018 0.052 0.119
h(cal) 0.071 0.183 0.320
h(cor) 0.023 0.071 0.176
h(pub) 0.0-0.2 0.200 0.175
Conclusions:Experiment for Br2 must be grossly wrongThe low value of h (>.3) for Cl2 is favored
Expanded lattice calculations
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
h/0
/0
Expanded lattice calculations
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
h/0
/0
Conclusion:With proper choice of the degree of expansion, fixed to the
result at T=0, one can compute the EFG also for high T
Temperature dependence Cl2 (Nakamura 67)
53.0
53.5
54.0
54.5
55.0
55.5
56.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
NQR frequency (MHz)
Corrected
Molecule
Temperature dependence Cl2 (new)
53.0
53.5
54.0
54.5
55.0
55.5
56.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Temperature dependence Br2
376
378
380
382
384
386
388
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
NQR frequency (MHz)
Temperature dependence I2
2140
2150
2160
2170
2180
2190
2200
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Q (MHz)
General conclusions
• We need a proper theory for treatment of the intermolecular interaction !
• For better calculations one would require more accurate crystal structure data
• A remeasurement of h for solid Br2 is highly recommended
• Interesting effects are predicted for the temperature dependence of the NQR frequency for Br2 and I2
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