
















Germanium














Introduction














In
the Table that follows, RSD is the residual standard deviation of the
linear regression analysis of the calculated efg's versus the
experimental nqcc's for the molecules given on the previous
page.
This may be taken as a conservative estimate of the
uncertainty
in the calculated nqcc's. (Note: A RSD of 1.0 MHz is 1.1 % of
the
average absolute experimental nqcc for the molecules used for
calibration.) All three diagonal components of the efg
tensors
are plotted against the corresponding components of the experimental
nqcc tensors. This assures, because the tensors are traceless, that the
linear regression line pass through the origin. The slope of
this
line is eQ_{eff}/h from which the value
of Q_{eff} is extracted. Q_{eff}
is the model
dependent nuclear electric quadrupole moment effective
for calculation of the nqcc's. For comparison, the currently
recommended Q for ^{73}Ge
is 196 mb.
It is our goal to reproduce accurately as well as efficiently
the
experimental nqcc's  not Q. It is sufficient  indeed, all that can be
expected at the level of theory in this work  that Q_{eff}
and
Q agree to within a few percent. 













There
is a problem with molecules that contain tetrahedrally coordinated Ge,
such as GeH_{3}F and GeH_{3}Cl.
Certain
combinations of method and basis calculate components of the efg tensor
that are inconsistent with the symmetry of
the molecule. The diagonal components of the efg tensor
should
satisfy
the relationship X_{xx} = X_{yy}
= 1/2 X_{zz},
but
do not for some models. One example  the most egregious  is a
calculation
made on HCCGeH_{3} at the MP4(SDQ)/6311G(2d) level
of theory,
for
which the calculated efg's are 0.737463, 0.355524, and 0.381939 a.u.
Another, less troublesome, example is B3LYP/6311G(2d) for
both
GeH_{3}F
and GeH_{3}Cl. For the latter molecule, the
calculated efg's
are
2.013802, 1.006912, and 1.006890 a.u. Here the asymmetry is small, and
probably acceptable ... but results like these do not inspire
confidence.
The models listed in the following Table appear not to have
this
problem
(at least to the number of figures given in the Gaussian output). 













Polarization
and diffuse functions used with the Alhrichs TZV bases are those
developed for use with the Pople type bases. The 6311G(2d)
and
TZV(2d) bases, for example, contain the same polarization functions 
same exponents and coefficients. 













With
the MP2 method, FULL = all electron correlation.



















Table
1. ^{77}Ge. Calibration RSD (MHz) and
Q_{eff} (mb). 





Method/Basis

RSD

 Q_{eff}






B3P86/6311G(d) 
1.30 
193.9(5) 

B3P86/6311G(2d) 
0.95 
192.8(4) 

B3P86/6311G(3d) 
1.05 
191.8(4) 

B3P86/6311G(2df) 
1.26 
191.1(5) 

B3P86/TZV(2d) 
1.46 
197.8(6) 





B3PW91/6311G(d) 
1.33 
193.0(5) 

B3PW91/6311G(2d) 
0.96 
192.9(4) 

B3PW91/6311G(3d) 
1.12 
191.8(4) 





mPW1PW91/6311G(d) 
1.45 
191.7(6) 

mPW1PW91/6311G(2d) 
1.11 
190.6(4) 

mPW1PW91/6311G(3d) 
1.30 
189.6(5) 





PBE1PBE/6311G(d) 
1.56 
192.2(6) 

PBE1PBE/6311G(2d) 
1.20 
191.0(5) 

PBE1PBE/6311G(3d) 
1.38 
190.0(6) 





MP2(FULL)/6311G(2d) 
5.24 
202.8(22) 

MP2(FULL)/6311G(3d) 
5.16 
202.3(22) 

MP2(FULL)/6311G(3df) 
4.59 
199.3(19) 





MP4(SDQ)/6311G(d,p) 
5.26 
209.0(23) 


















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