New estimate of the copper nuclear
quadrupole moment
Lan Cheng, Devin Matthews, Jürgen Gauss, and John
Stanton
Department of Chemistry, University of Texas at Austin
Institut für Physikalische Chemie, Universität Mainz
Copper nuclear quadrupole moment
• Research goal: Revision of the standard value, 220
(15) mb from muonic experiment, for the copper
Revision of the
nuclear quadrupole moment
quadrupole
moment value
Accurate experimental
quadrupole-coupling
parameters
Accurate computed
electric-field gradients
Value for the Nuclear Electric
Quadrupole Moment of Cu63
Muonic Experiment
Effenberger et. al., Z.
Phys. A 309, 77 (1982).
-220(15)
mb
Relativistic Density
Functional Theory
Thierfelder et al., Phys.
Rev. A 76, 034502 (2007).
-208 mb
Relativistic coupled
cluster theory
Santiago et al., Phys.
Chem. Chem. Phys. 16,
11590 (2014).
-198(10)
mb
General Consideration
Exp. Quadrupolecoupling constant
(in MHz)
“Exp.” Electric-field
gradient (in a.u.)
CuF
CuCl
21.956
16.169
-0.4247
-0.3128
To reduce the uncertainty of NQM to less than 3%, it
is necessary to compute EFG of CuF and CuCl to an
accuracy of 0.01 a.u.
• Electric-field gradient
• Local operator (
)
Electron density in the core region
Electron-correlation effects
Relativistic effects
Basis set effects
Relativistic effects on Cu electric-field
gradients
Cu efg in CuF
(in a.u.)
-0.6314
Cu efg in CuCl
(in a.u.)
-0.4086
One-electron scalarrelativistic effects
Two-electron scalar
relativistic effects
Spin-orbit effects
0.1901
0.1102
0.0025
0.0016
0.0008
-0.0002
Contribution of
Gaunt Term
-0.0087
-0.0048
Non-relativistic
value
CCSD(T)/cc-pVQZ-unc results
Electron-correlation effects
CuF
CuCl
SCF Contribution
HF-SCF
-1.1888
-0.8129
Singles and Doubles Contribution
CCSD
0.8320
0.5474
Triples Contribution
CCSD(T)
0.1406
0.0896
CCSD(T)Λ
0.2857
0.1546
CCSDT
0.2990
0.1722
Quadruples Contribution
CCSDTQ
~0.009
Uncontracted cc-pVDZ basis sets were used.
~0.0003
Basis-set effects
aug-cc-pwCV5Z-unc
It is necessary to augment regular basis sets with
additional steep functions systematically.
Design of the procedure
• Scalar-relativistic calculation with high-level
treatment of electron correlation
SFX2C-1e CCSD(T)Λ results with large basis sets
Higher excitations obtained via additivity schemes
• Small corrections
Spin orbit, Gaunt term, zero-point vibrational correction
A new value for Copper nuclear
quadrupole moment
NQM (in mb)
CuF
CuCl
CCSD(T)Λ
-209.9
-207.2
ΔT
-5.9
-8.6
ΔQ
-4.2
-0.2
Δ(2e p.c.)
-1.2
-1.1
Δ(SOC)
-0.4
0.2
Δ(Gaunt)
4.5
2.6
Δ(vib.)
-0.6
-0.2
Total
-217.7
-214.5
Mean Value
-216.1
Cheng, Matthews, Gauss, Stanton unpublished (2015).
A new estimate for Copper nuclear
quadrupole moment
NQM (in mb)
CuF
CuCl
CCSD(T)Λ
-209.9
-207.2
ΔT
-5.9
-8.6
ΔQ
-4.2 (?)
-0.2 (?)
Δ(2e p.c.)
-1.2
-1.1
Δ(SOC)
-0.4
0.2
Δ(Gaunt)
4.5 (?)
2.6 (?)
Δ(vib.)
-0.6
-0.2
Total
-217.7
-214.5
Mean Value
-216.1
Current standard value
-220(15)
Cheng, Matthews, Gauss, Stanton unpublished (2015).
Summary and Outlook
• A new estimate for the copper nuclear
quadrupole moment is being attempted via
systematic quantum-chemical calculations of
copper electric field gradients in CuF and CuCl.
• Accurate calculation of metal electric-field
gradients is a fair playground for
benchmarking quantum-chemical methods.