MP2/aug-cc-pVTZ(G03) Model for Calculation of Approximate Equilibrium Molecular Structures.
Accurate calculation of nuclear quadrupole coupling constants in gaseous state molecules requires, of course, accurate molecular structures on which to make the calculation.
Calculation of near equilibrium molecular structures requires a high level of ab initio theory - for example, CCSD(T) - in conjunction with large bases - for example, cc-pVTZ or larger; which in turn requires computer resources beyond those available for this work.
However, for calculation of approximate equilibrium structures, Demaison et al. have shown in a series of publications [1 - 8] that errors inherent in more modest quantum chemistry calculation of bond lengths are largely systematic and can be empirically corrected, and that accurate interatomic angles may be obtained at the MP2 level of theory in conjunction with fairly large triple-zeta bases.
Following the lead of Demaison et al., MP2/aug-cc-pVTZ(G03) optimization was made of a number of molecules containing CH, C-C, C=C, CC triple, CN triple, CF, CCl, and C=O for which equilibrium (re or rmrho) structures are known.  Linear regression analyses of the optimized bond lengths versus the equilibrium bond lengths yield regression equations that may be used for correction of the optimized bond lengths.  
Thus, the following equations have been derived.  Visit the links for more detail.
C-C ~ re(Å) = 0.95547 × ropt + 0.06568 RSD = 0.0012 Å
C=C ~ re(Å) = 0.98508 × ropt + 0.01614 RSD = 0.0021 Å
CC triple ~ re(Å) = 0.79708 × ropt + 0.23575 RSD = 0.0005 Å
CN triple ~ re(Å) = 0.69449 × ropt + 0.34294 RSD = 0.0006 Å
CF ~ re(Å) = 0.97993 × ropt + 0.02084 RSD = 0.0014 Å
CCl ~ re(Å) = 0.99872 × ropt - 0.00097 RSD = 0.0021 Å
CBr ~ re(Å) = 0.99078 × ropt + 0.02591 RSD = 0.0003 Å
C=O ~ re(Å) = 1.06234 × ropt - 0.08240 RSD = 0.0020 Å
The standard deviation of the the residuals (RSD) may be taken as a conservative estimate of the uncertainty in the approximate equilibrium bond length, ~ re.
CH Bond Length and Interatomic Angles
Figure 1 is a plot of optimized CH bond lengths versus equilibrium CH bond lengths.  Excluding the outliers (solid circles), the regression equation is
                               ~ re(Å) = 0.99945 × ropt + 0.00075 with RSD = 0.0008 Å,
which is near ~ re = ropt.  Without correction, the average and root mean square (RMS) differences between optimized and equilibrium bond lengths are respectively 0.0007 and 0.0008 Å.  With correction, the average and RMS differences are respectively 0.0006 and 0.0008 Å.  Correction seems to be unnecessary.
Figure 2 is a plot of optimized interatomic angles versus equilibrium interatomic angles.  With few exceptions the differences are all less than 0.5o.  The average difference (43 angles) is 0.17o, the RMS difference is 0.20o.
Calculations were made on a Mac G5 with the G03M quantum chemistry package of Gaussian Inc.  In this package, Dunning bases have been modified somewhat for efficiency.  That the bases used here are not the original is denoted by the appendage G03.
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Last modified: 29 Oct 2006