
















Sulfur














Introduction














In
the Tables that follow, 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 an estimate of the
uncertainty
in the calculated nqcc's. (Note: A RSD of 0.46 MHz is 2.0 %
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 ^{33}S
is 67.8(13) 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. 













For
the Dunning correlation consistent basis sets, G03 and EMSL indicate
the source of the bases used for the calculation. G03 is
Gaussian
03, which contains these bases somewhat modified to increase
computational efficiency. EMSL is the online EMSL Basis Set
Library. ccpCVTZ/ccpVTZ is ccpVTZ with extra functions 
on
only the sulfur atom  that are designed for corevalence correlation. 













Polarization
and diffuse functions used with the Alhrichs TZV bases are those
developed for use with the Pople type bases. The
6311++G(3df,3p)
and
TZV++(3df,3p)) bases, for example, contain the same polarization and
diffuse functions 
same exponents and coefficients. 













Alhrichs' QZVP bases are available at http://www.ipc.unikarlsruhe.de/tch/tch1/index.de.html. 


















Table
1. Calibration of
HFDFT/6311G(3df,3p). RSD (MHz) and
Q_{eff} (mb). 





Method

RSD

Q_{eff}






B1B95

0.56

66.27(26)


B1LYP

0.50

65.78(23)


B3LYP

0.39

66.00(18)






B3P86

0.43

66.70(20)


B3PW91

0.46

66.88(22)


mPW1PW91

0.61

66.80(29)


PBE1PBE

0.66

67.40(31)






B98

0.61

66.97(29)


B971

0.59

67.33(28)


B972

0.60

67.27(28)
























Table
2. Calibration of
HFDFT/TZV+(3df,3p). RSD (MHz) and
Q_{eff} (mb). 





Method

RSD

Q_{eff}






B1B95

0.49

68.47(24)


B1LYP

0.41

68.26(20)


B3LYP

0.35

68.49(17)






B3P86

0.37

69.21(18)


B3PW91

0.40

69.59(20)


mPW1PW91

0.53

69.48(26)


PBE1PBE

0.57

69.88(28)






B98

0.56

69.67(27)


B971

0.54

69.94(27)


B972

0.53

70.08(26)
























Table
3. Calibration of B1LYP/Basis. RSD (MHz) and
Q_{eff} (mb). 





B1LYP/Basis

RSD

Q_{eff}






6311G(3df,3p)

0.50

65.78(23)


6311+G(3df,3p)

0.45

65.72(21)


6311++G(3df,3p)

0.45

65.72(21)






TZV(3df,3p) 
0.43

67.32(20)


TZV+(3df,3p) 
0.41

68.26(20)


TZV++(3df,3p)

0.42

68.27(20)






QZVP 
0.46 
65.83(21) 





ccpVTZ (G03)

0.49

69.33(24)


augccpVTZ
(G03)

0.53

71.07(26)


ccpCVTZ/ccpVTZ
(EMSL)

0.43

65.73(20)


augccpCVTZ/augccpVTZ
(EMSL) 
0.46

66.71(22)
























Table
4. Calibration of B3LYP/Basis. RSD (MHz) and
Q_{eff} (mb). 





B3LYP/Basis

RSD

Q_{eff}






6311G(3df,3p)

0.39

66.00(18)


6311+G(3df,3p)

0.39

65.94(18)


6311++G(3df,3p)

0.39

65.93(18)






TZV(3df,3p) 
0.39

67.56(19)


TZV+(3df,3p)

0.35

68.49(17)


TZV++(3df,3p)

0.35

68.50(17)






QZVP 
0.37 
66.04(17) 





ccpVTZ (G03)

0.40

69.63(19)


ccpVTZ (EMSL)

0.40

69.63(19)


augccpVTZ
(G03)

0.46

71.38(23)


ccpCVTZ/ccpVTZ
(EMSL) 
0.40

65.96(18)


augccpCVTZ/augccpVTZ
(EMSL)

0.41

66.92(19)
























Table
5. Calibration of B3P86/Basis. RSD (MHz) and
Q_{eff} (mb). 





B3P86/Basis

RSD

Q_{eff}






6311G(3df,3p) 
0.43

66.70(20)


6311+G(3df,3p)

0.42

66.63(20)


6311++G(3df,3p)

0.42

66.63(20)






TZV(3df,3p) 
0.40

68.16(19)


TZV+(3df,3p) 
0.37

69.21(18)


TZV++(3df,3p) 
0.38

69.22(18)






QZVP 
0.46 
66.79(22) 





ccpVTZ (G03)

0.48

70.72(24)


augccpVTZ
(G03) 
0.55

72.07(28)


ccpCVTZ/ccpVTZ
(EMSL) 
0.39

67.00(18)


augccpCVTZ/augccpVTZ
(EMSL)

0.40

67.72(19)
























Table
6. Calibration of B3PW91/Basis. RSD (MHz) and
Q_{eff} (mb). 





B3PW91/Basis

RSD

Q_{eff}






6311G(3df,3p) 
0.46

66.88(22)


6311+G(3df,3p)

0.45

66.83(21)


6311++G(3df,3p)

0.45

66.83(21)






TZV(3df,3p) 
0.43

68.82(21)


TZV+(3df,3p) 
0.40

69.59(20)


TZV++(3df,3p) 
0.40

69.54(20)






QZVP 
0.49 
66.99(23) 





ccpVTZ (G03)

0.51

71.05(25)


augccpVTZ
(G03) 
0.59

72.45(30)


ccpCVTZ/ccpVTZ
(EMSL) 
0.42

67.16(20)


augccpCVTZ/augccpVTZ
(EMSL)

0.43

67.91(21)



















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Sulfur Molecules

















