The problem Experimentally available: nQ = eQVzz/h

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Presentation transcript:

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

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

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

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”

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

The breakthrough in theory

APW method (1)

Kohn–Sham Hamiltonian Full Hamiltonian Kohn–Sham Hamiltonian

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

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

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

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

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

Halogen Q (with H. Petrilli)

Quadrupole interaction frequencies nQ [MHz]

Electric field gradients [1021V/m2]

R-3 atomic values

Normalized EFG Who can see what is wrong ?

Normalized EFG ratios Who cannot see it ?

121Sb Quadrupole moment 2000

121Sb in molecules and solids

121Sb Quadrupole moment 2010

75As in molecules and solids

Revised normalized EFG ratios We should be happy ! Or ?

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

Quadrupole moment of 111*Cd

New quadrupole moment of 111*Cd

History of 111*Cd quadrupole moment

Cd quadrupole moments

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.

Widen your view ! Houston ! We have a problem !

121Sb Quadrupole moment 2016 We have another problem !

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

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

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

The structure of the solid halogens

Asymmetry parameter in solid halogens What a mess !

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 !

How to fix a ?

Optimized a by fitting energy gap for various insulators JPCM 25 (2013) 435503 David Koller1, Peter Blaha1 and Fabien Tran2

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

Revised quadrupole moment of 111*Cd

New history of 111*Cd quadrupole moment

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.

Cd quadrupole moments

Cd quadrupole moments

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

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%)