








MP2/augccpVTZ(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,
ccpVTZ 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 triplezeta bases. 






Following the lead of Demaison et
al., MP2/augccpVTZ(G03) optimization was made of a number of
molecules containing CH, CC, C=C, CC triple, CN triple, CF, CCl, and C=O for which equilibrium (r_{e} or r_{m}^{rho})
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. 







CC 
~ r_{e}(Å) = 0.95547 × r_{opt} + 0.06568 
RSD = 0.0012 Å 





C=C 
~ r_{e}(Å) = 0.98508 × r_{opt} + 0.01614 
RSD = 0.0021 Å 





CC triple 
~ r_{e}(Å) = 0.79708 × r_{opt} + 0.23575 
RSD = 0.0005 Å 





CN triple 
~ r_{e}(Å) = 0.69449 × r_{opt} + 0.34294 
RSD = 0.0006 Å 





CF 
~ r_{e}(Å) = 0.97993 × r_{opt} + 0.02084 
RSD = 0.0014 Å 





CCl 
~ r_{e}(Å) = 0.99872 × r_{opt}  0.00097 
RSD = 0.0021 Å 





CBr 
~ r_{e}(Å) = 0.99078 × r_{opt} + 0.02591 
RSD = 0.0003 Å 





C=O 
~ r_{e}(Å) = 1.06234 × r_{opt}  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, ~ r_{e}. 










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 






~ r_{e}(Å) = 0.99945 × r_{opt} + 0.00075 with RSD = 0.0008 Å, 






which is near ~ r_{e} = r_{opt}.
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 0.5^{o}. The average difference (43 angles) is 0.17^{o}, the RMS difference is 0.20^{o}. 










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. 










[1] J.M.Colmont, D.Priem, P.Dréan, J.Demaison, and J.E.Boggs, J.Mol. Spectrosc. 191,158(1998). 


[2] J.Demaison, G.Wlodarczak, H.Rück, K.H.Wiedenmann, and H.D.Rudolph, J.Mol.Struct. 376,399(1996). 


[3] I.Merke, L.Poteau, G.Wlodarczak, A.Bouddou, and J.Demaison, J.Mol.Spectrosc. 177,232(1996). 


[4] R.M.Villamañan, W.D.Chen,
G.Wlodarczak, J.Demaison, A.G.Lesarri, J.C.López, and
J.L.Alonso, J.Mol.Spectrosc. 171,223(1995). 


[5] J.Demaison, J.Cosléou, R.Bocquet, and A.G.Lesarri, J.Mol.Spectrosc. 167,400(1994). 


[6] J.Demaison and G.Wlodarczak, Struct.Chem. 5,57(1994). 


[7] M.LeGuennec, J.Demaison, G.Wlodarczak, and C.J.Marsden, J.Mol.Spectrosc. 160,471(1993). 


[8] M.LeGuennec, G.Wlodarczak, J.Burie, and J.Demaison, J.Mol. Spectrosc. 154,305(1992). 











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Last modified: 29 Oct 2006 




