Aluminum






 






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 0.22 MHz is 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 eQeff/h from which the value of Qeff is extracted. Qeff is the model dependent nuclear electric quadrupole moment effective for calculation of the nqcc's.  For comparison, the currently recommended Q for 27Al is 146.6(10) 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 Qeff and Q agree to within a few percent.





 






For the Dunning correlation consistent basis sets, EMSL indicates that the source of the bases is the online EMSL basis set library.





 






Polarization and diffuse functions used with the Alhrichs TZV bases are those developed for use with the Pople type bases.  The 6-311G(2d) and TZV(2d) bases, for example, contain the same polarization functions - same exponents and coefficients.





 






With the MP2 method, FC = frozen core, and FULL = all electron correlation.






 






 





Table 1.  Calibration RSD (MHz) and Qeff (mb).





Method/aug-cc-pCVQZ(Al)/aug-cc-pVQZ (EMSL)






RSD
Qeff





HF
0.24
131.36(39)

B1LYP
0.39
135.90(65)

mPW1PW91
0.41
138.16(69)





Method/aug-cc-pCVTZ(Al)/aug-cc-pVTZ (EMSL)





HF
0.24
132.16(39)

MP2(FC)
0.38
142.47(67)

MP2(FULL)
0.38
142.46(66)

B1LYP
0.42
135.92(71)

B3LYP
0.46
136.46(77)

mPW1PW91
0.46
139.02(79)

PBE1PBE
0.48
139.32(82)

B98
0.47
138.72(80)





Method/aug-cc-pCVDZ(Al)/aug-cc-pVDZ (EMSL)





HF
0.13
138.71(23)

MP2(FULL)
0.51
153.15(97)

B1LYP
0.51
144.02(90)

mPW1PW91
0.51
144.79(91)





HF/aug-cc-pVDZ (EMSL) 0.35
168.70(73)

HF/cc-pCVDZ/cc-pVDZ (EMSL) 0.45
140.08(78)





Alhrichs' bases





HF/TZVP
0.25
127.90(40)

MP2(FULL)/TZVP
0.41
135.61(69)

B1LYP/TZVP
0.49
131.01(79)

mPW1PW91/TZVP
0.54
134.69(91)

HF/TZV(2d)
0.13
127.51(20)

MP2(FULL)/TZV(2d)
0.55
135.09(92)

B1LYP/TZV(2d)
0.56
130.09(91)

mPW1PW91/TZV(2d)
0.61
133.5(10)





Pople bases







HF/6-311G(2d)
0.22
131.96(35)

MP2(FULL)/6-311G(2d)
0.36
141.20(62)

B1LYP/6-311G(2d)
0.43
136.58(72)

mPW1PW91/6-311G(2d)
0.47
138.41(80)




 













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Last modified 14 Jan 2005