1. The problem Experimentally available: nQ = eQVzz/h
generally with high accuracy, but
Product of nuclear and electronic quantity !
We need Vzz to calculate Q
Ratios of Q for isotopes accurate, however

2. Accuracy of nuclear quadrupole moments
Muonic x-rays (3-10%)
Atomic spectroscopy (3-20%)
Molecular spectroscopy (5-20%)
Solid state methods (10-30%)

3. Classical solid state methods
Nuclear Magnetic Resonance (NMR)
Nuclear Quadrupole Resonance (NQR)
Specific Heat (SH)
Require stable isotopes with I>1/2

4. Nuclear solid state methods
Moessbauer Spectroscopy (MS)
Perturbed Angular Correlation (PAC)
Perturbed Angular Distribution (PAD)
Nuclear Orientation (NO)
Beta NMR
Sometimes difficult to find the “missing link”

5. The problem cases: No I>1/2 stable isotope

6. The breakthrough in theory

7. APW method (1)

8. Kohn–Sham Hamiltonian
Full Hamiltonian
Kohn–Sham Hamiltonian

9. Density Functional Theory
The problem:
exc(ri) is not a simple function of
r(ri) but a functional depending on
all space r(r)

10. Local Density Approximation (LDA)
exc(r) = ex(r) + ec(r) both are simple functions of re(r)
Functions determined by fitting Monte Carlo for electron gas

11. Test case 1: 77Se (with P.Blaha)
At ISOLDE: 77Se in Se
nQ = 933 MHz, eta = .34
FLAPW (WIEN):
EFG = 50.9 *1021V/m2, eta = .33
Result: Q = .76 b
Check: MoSe2

12. Test case 2: 100Rh (with P. Blaha)
nQ (MHz)
EFG-the (1021V/m2)
Q (b)
Rh3Zr
15.7
4.32
.150
Rh3Nb
11.4
3.12
.152
Rh3Hf
14.6
3.81
.158

13. Generalized Gradient Approximation (GGA)
GGAexc(r) = LDAexc(re(r)) + f ( (re(r))
Gradient contributions determined by fitting “exact” quantum chemistry calculations for simple molecules (“training set”)
Most successful GGA: PBE (Perdew, Burke, Ernzerhof) D

14. Halogen Q (with H. Petrilli)

15. Quadrupole interaction frequencies nQ [MHz]

16. Electric field gradients [1021V/m2]

17. R-3 atomic values

18. Normalized EFG
Who can see what is wrong ?

19. Normalized EFG ratios
Who cannot see it ?

20. 121Sb Quadrupole moment 2000

21. 121Sb in molecules and solids

22. 121Sb Quadrupole moment 2010

23. 75As in molecules and solids

24. Revised normalized EFG ratios
We should be happy ! Or ?

25. 133Cs Quadrupole moment nQ (MHz) EFG (V/A2) Q-cal (b) Q-sta (b)
133CsC8
1.18
14.95
.00325
.00343
87RbC8
22.2
7.41
.1335
.124

26. Quadrupole moment of 111*Cd

27. New quadrupole moment of 111*Cd

28. History of 111*Cd quadrupole moment

29. Cd quadrupole moments

30. HFI2010: The quadrupole moments of Zn and Cd isotopes – an update
H. Haas and J.G. Correia
The nuclear quadrupole moments of 111*Cd (245 keV state) and 67Zn were determined from the quadrupole coupling constants and lattice parameters at low temperature. The required electric field gradients were obtained employing the WIEN2k code. The resultant numbers, 0.765(15) and 0.151(4) b, are in line with the previously used values but considerably more precise. Calculations for various other solids confirm the results, with less accuracy, however.

31. Widen your view !
Houston ! We have a problem !

32. 121Sb Quadrupole moment 2016 We have another problem !

33. EFG in Cu2O
All “standard” DFT calculations underestimate EFG by a factor of about 2 !
A BIG problem !

34. Results of GGA calculations
EFGth
EFGex
Cu2O Zn Ga Ge As Se Br2
(Ag) Cd In SnO Sb Te I2
EFGth
EFGex

35. LAPW / DFT problems
Highly correlated systems
Excited states (gaps in semiconductors)
Van-der-Waals interaction
The skeletons in the closet !

36. The structure of the solid halogens

38. Asymmetry parameter in solid halogens
What a mess !

39. Hybrid Calculations (Hyb)
Hybexc(r) = PBEec(r) + (1-a) PBEex(r) + a HFex(r)
Mixing Hartree-Fock (HF) exchange simulates
multi-electron effects
Most successful for molecules: PBE0 (a=.25)
Problem 1: a is apparently system dependent !
Problem 2: require 1000 times more computer time !

40. How to fix a ?

41. Optimized a by fitting energy gap for various insulators
JPCM 25 (2013)
David Koller1, Peter Blaha1 and Fabien Tran2

42. Results of Hybrid calculations
EFGth
EFGex
Cu2O Zn Ga Ge As Se Br2
(Ag) Cd In SnO Sb Te I2
EFGth
EFGex

43. Revised quadrupole moment of 111*Cd

44. New history of 111*Cd quadrupole moment

45. HFI2016: The quadrupole moments of Cd and Zn isotopes - an apology
HFI2010: The quadrupole moments of Zn and Cd isotopes – an update
H. Haas and J.G. Correia
The nuclear quadrupole moments of 111*Cd (245 keV state) and 67Zn were determined from the quadrupole coupling constants and lattice parameters at low temperature. The required electric field gradients were obtained employing the WIEN2k code. The resultant numbers, 0.765(15) and 0.151(4) b, are in line with the previously used values but considerably more precise. Calculations for various other solids confirm the results, with less accuracy, however.
HFI2016: The quadrupole moments of Cd and Zn isotopes - an apology
H. Haas1 and J. G. Correia2
Q(111Cd,5/2+)=.659(20)b, Q(67Zn,gs)=.130(6)b.

46. Cd quadrupole moments

47. Cd quadrupole moments

48. The case of 67Zn Old value: Q = .150(15) b PBE value: Q = .151(4) b
Hybrid value: Q = .130(6) b
Atomic calc: Q = .125 b
R-3 cor: Q = .120 b

49. Accuracy of nuclear quadrupole moments
Muonic X-rays (2-5%)
Atomic spectroscopy (3-10%) (1-3%)
Molecular spectroscopy (5-20%) (1-3%)
Solid state methods (10-30%) (2-5%)