1 H and 13 C NMR Chemical shift assignments of a cyclopentane-fused cis -azetidinone ( cis -azabicyclo[3.2.0]heptan-7-one). A theoretical and experimental investigation

The 1 H and 13 C NMR chemical shifts of cyclopentane-fused cis -azetidinone ( cis - azabicyclo[3.2.0]heptan-7-one) were determined with the help of full spectral analysis. The geometry and electronic structure of the molecule were investigated at both the RHF and the B3LYP level with different basis sets. The NMR data were calculated by means of the GIAO, CSGT and IGAIM methods. All quantum-chemical calculations, including those of NMR data, were performed by ab initio level RHF and DFT methods. The geometry optimization resulted in an envelope-type conformation, while the four-membered heterocycle proved to be planar. Excellent agreement between the theoretical and experimental results was found for the RHF-level 1 H chemical shifts and for the B3LYP-type 13 C chemical shifts. The experimental spectra revealed equivalent methylene protons at position 5, indicating that the cyclopentane ring has a high degree of conformational freedom at this carbon


Introduction
The calculation of NMR parameters is a recent, but extremely rapidly progressing area of quantum chemistry.During the past decade numerous ab initio methods have been developed,

Results and Discussion
The numbering of the atoms is illustrated in Figure 1.The numbering of the atoms does not correspond to the IUPAC nomenclature.The geometrical parameters computed are listed in Table 1.A comparison of the C1 -H16 and C1 -H17, or C2 -H16 and C2 -H17 bond lengths demonstrates that the most favoured conformation is of envelope type, with conformational freedom only at C5.These results are in accordance with the experimental data obtained by X-ray crystallography. 5or comparison of the calculated and the experimental NMR data, the shielding tensors of the molecule in question were calculated with the standard Gaussian 94 program.The electronic structure of the molecule was treated by both RHF and B3LYP methods 1 , with four different basis sets [6-31G; 6-31G(d,p); 6-31 + G(d,p) and 6-311 + G(2d,2p)].
For both the RHF and the B3LYP method, with all basis sets, a geometry optimization was first performed for the molecule and for TMS.This means that we calculated eight geometries of the two molecules.To compare the ab initio methods, the NMR parameters were calculated by using the individual geometric parameters, despite these geometries being close to each other.The NMR shielding tensors were computed with three different methods: the GIAO (gaugeindependent atomic orbital), 6 CSGT (continuous set of gauge transformations) 7 and IGAIM (individual gauges for atoms in molecules) 8 methods.Table 2 gives 13 C and 1 H chemical shifts.RHF/GIAO denotes the following procedure: the geometry minimized the corresponding RHF energy and the wave function was calculated at the RHF level, presuming calculation of the optimum geometry.The NMR data were calculated by the GIAO method.The notations B3LYP/GIAO, RHF/IGAIM, B3LYP/IGAIM, etc. are similar.The results are presented in Tables 1 and 2. The energetically optimized ab initio structure of the compound in question is plotted in Figure 2.
Since these calculations are very computational time-consuming, the calculations on other cycloalkane-fused azetidinones will be performed on the basis of these results.The goal of this study is to find an appropriate theoretical method for the calculation of NMR parameters of small and medium-sized heterocycles.

Experimental Section
General procedures.The purity of the compound was checked by thin-layer chromatography, by melting point determination and via its NMR spectra.The synthetic route is described elsewhere. 9he 1 H, 13 C and 13 C JMOD NMR spectra, and the z-PFG 1 H, 13 C HMQC 2D spectra were recorded on a Bruker Avance DRX 500 NMR spectrometer equipped with an inverse detection 5 mm broad band probehead operating at 500.13 MHz for 1 H and at 125.77 MHz for 13 C in 0.05-0.1 M CDCl 3 solutions at 300 K.The 1 H and 13 C NMR chemical shifts were referenced to TMS: δ 1 H and 13 C (CH 3 ) 4 Si = 0.00 ppm.The   The data in Table 2 reveal that the RHF-based calculation results are in excellent agreement with the experimental 13 C chemical shift data.The B3LYP-based calculation demonstrates similar agreement for the 1 H chemical shifts.The results are based on fixed geometry and a rigid conformation.The high-amplitude conformational movement of C5 at the top of envelope causes the equivalency of the two methylene protons on this carbon (H16 and H17).
The vibrational correction of the computed data is in progress to take into account the conformational equilibrium so as to calculate NMR data on larger saturated cycloalkanecondensed azetidinones (C6, C7, C8 and C12).

Table 1 .
Calculated and X-Ray crystallographic 5 data on bond lengths (pm) and bond angles