Control of ab initio calculation correctness of the electron distribution in chlorine-containing molecules using 35 Cl NQR data

Ab initio calculations of 2-chlorodioxene and 1-chloro-1-methoxycyclohexane were performed with total optimization of their geometry using the Hartree-Fock theory and the split valence basis set 6-31G(d). The 35 Cl frequencies at 77K for these compounds were obtained as well. These frequencies were compared with those resulting from ab initio calculations. This comparison allows controlling the correctness of ab initio calculations of electron distribution in chloro-containing molecules using 35 Cl NQR data.


Introduction
Our investigations have shown that the atomic orbital coefficients in different molecular orbitals, Mulliken's populations of atomic orbitals, etc. may be obtained incorrectly from the analysis of the electron distribution in molecules using quantum mechanical calculations, for instance at the RHF/6-31G(d) level.This incorrectness may result from coordinate origin displacement and molecule rotation in the process of the calculation.The authenticity of calculations carried out on chlorine-containing molecules may be controlled using 35 Cl nuclear quadrupole resonance (NQR) data.Recently we have established that the 35 Cl NQR frequencies (ν) and asymmetry parameters (η) of the electric field gradient (EFG) at 35 Cl nuclei as calculated using equations 1 and 2, [1][2][3] and populations of the less diffuse 3p-components of the chlorine atom valence porbitals in chlorine-containing molecules calculated with the Hartree-Fock method RHF/6-31G(d), satisfactorily conform to the corresponding experimental 35 Cl NQR data (e.g.refs [3][4][5] ).
Q is the atomic quadrupole moment, eq аt is the electric field gradient of the free atom, h is Planck's constant, Np x , Np y and Np z are the populations of the indicator atom valence p-orbitals along the X-, Y-and Z-axes, respectively.
For a large number of organic and organometallic compounds the correlation between 35 Cl NQR parameters estimated in this manner and those experimentally determined has been established.For instance, the correlation between the calculated (ν c ) and experimental (ν e ) 35 Cl NQR frequencies has been observed for 42 compounds (equation 3). 5 ν c = 1.001(±0.030)νe -0.147(±0.989),r = 0.996 Eq 3 The conformity between estimated and experimental 35 Cl NQR parameters proves the correctness of the ab initio calculations on electron distribution in a molecule, and consequently, any substantial difference between these data indicates an erroneous calculation.

Results and Discussion
In this communication we provide the results of ab initio calculations on 2-chlorodioxene (1) and 1-chloro-1-methoxycyclohexane (2) as examples, using the Hartree-Fock theory, the split and polarized valence basis set 6-31G(d), and the Gaussian 94W program. 6These calculations were performed with total optimization of the molecular geometry.The coordinate origin is chosen to be at the Cl nucleus, the Z-axis coincides with the Cl-C bond.

2
The geometrical characteristics of compounds 1 and 2 are given in Table 1, the atomic charges in Table 2; the populations of the valence p-orbitals of the chlorine atoms and the carbon atoms attached to them (Np), as well the populations of components of these orbitals are listed in Table 3.
The atoms O 1 ClC 2 =C 3 HO 4 in molecule 1 are practically in one plane (the dihedral angles are close to 0° or 180°).The O 4 -C 5 and O 1 -C 6 bonds deviate from this plane by more than 40° (Table 1).Molecule 2 assumes the chair conformation.The angle C 1 OC 7 is substantially greater than the COC angles in 1 (Table 1).In both molecules the charges at the oxygen atoms are practically the same (Table 2).Table 1.Bond lengths (d), internal (α) and dihedral angles (β) of 1 and 2 obtained from RHF/6-31G(d) calculations  The 35 Cl NQR frequencies and the asymmetry parameters of the electric field gradient at the 35 Cl nuclei were estimated using the populations of 3p-components of the chlorine atom valence p-orbitals in molecules 1 and 2 and equations 1 and 2. For comparison, the experimental 35 Cl NQR frequencies at 77K have been measured for these compounds.The 35 Cl NQR spectra exhibit one line each at the frequency 35.814MHz and 28.984 MHz, respectively (the signal to noise ratio for both lines is 10).The calculated NQR frequency for 1 (28.062MHz) turned out to be considerably lower, and the asymmetry parameter (32.8%) is considerably higher than the experimental ones for the chlorine atoms bonded to the sp 2 -hybridized carbon atom in unsaturated molecules; the majority of the latter is in the range of ~5-15% (see, e.g. 3,7 .The 35 Cl NQR frequency calculated for molecule 2 (24.385MHz) turned out considerably lower than the experimental value, and the estimated asymmetry parameter (14.4%) is considerably higher than the experimental values measured for saturated chlorine-containing organic compounds, usually being close to zero. 3,7 le 3. Populations (Np, e) valence p-orbitals of the chlorine atom and the attached carbon atom in 1 and 2 as well as their (3p-and 4p-) and (2p-and 3p-) components, respectively, resulting from incorrect (1a and 2a) and correct (  35 Cl NQR parameters with those resulting from RHF/6-31G(d) calculations of the investigated molecules shows that the calculations of the populations of the chlorine atom valence p-orbitals are incorrect.The incorrectness may be caused by the displacement of the coordinate origin and by the deviation of the symmetry axes of the chlorine atom valence p-orbitals from the directions of the coordinate axes during the calculation process.The reason for this may be the long calculation time.The displacement of the coordinate origin can be seen from the output file.At the end of the calculation process the coordinates of the chlorine atom in 1 became -0.051, 1.128 and 0.439Å, in 2 -0.801, 0.359 and -0.417Å.Ab initio calculations of 1 and 2 at the RHF/6-31G(d) level have been repeated with the estimated geometrical characteristics as in the parameters.As a consequence, the coordinates of the chlorine atoms in 1 and 2 remained unchanged (0.000, 0.000 and 0.000 Å) or close to these values.The recalculated geometrical characteristics of these molecules (Table 1) and the atomic charges (Table 2) remained the same within the limits of calculation errors.The total energies for each of the molecules 1 and 2 in both calculations coincide as well.However, the coefficients at the atomic orbitals in different molecular orbitals, the populations of the atomic valence porbitals, as well as their components have substantially changed (Table 3).The recalculated 35 Cl NQR frequencies obtained when using the populations of 3p-components of the chlorine atom valence p-orbitals in 1 and 2 (35.64 MHz and 28.301 MHz, respectively) are close to the experimental values (see above).The asymmetry parameter of the EFG at the 35 Cl nuclei in 1 estimated using the recalculated populations of 3p-components of the chlorine atom valence porbitals in this molecule (2.0%) is close to the η-value for the trans chlorine atoms in molecules of the type Cl 2 C=CHOR. 3For the recalculated molecule 2, the asymmetry parameter is close to zero too (2.1%).This is characteristic for chlorine atoms bonded to a sp 3 -hybridized carbon atom. 3,7 he estimated 35 Cl NQR frequencies and asymmetry parameters of the EFG at the 35 Cl nuclei for the recalculated molecules 1 and 2 allow the conclusion that the estimation of the electron density distribution is correct.
Thus, the correctness of ab initio calculations at the RHF/6-31G(d) level of electron distribution in chlorine-containing molecules may be proven using 35 Cl NQR data and does not require experimental NQR data.At present, a large number of chlorine-containing organic, inorganic and organometallic compounds is studied by this method (e.g.refs 3,[8][9][10] ).Therefore the range of frequencies and of asymmetry parameters in which these NQR parameters for the molecule calculated should be easily estimated using available 35 Cl NQR data.The comparison with those estimated using the populations of 3p-components of the given chlorine atom valence p-orbitals allows to judge the correctness of the calculations of electron distribution in these molecules.