[Related articles/posters: 015 097 117 ]

Ring Conformation in 3,4-Dihydropyrimidine-2-ones: An Ab Initio and Density Functional Theory Study

C. Oliver Kappe* and Walter M. F. Fabian

Introduction

Dihydropyrimidines of type 1 (DHPMs, Biginelli compounds) [1] represent a long-known class of heterocycles that show a diverse range of biological activities [2]. Most notable is the recently discovered cardiovascular (i.e. antihypertensive) activity exhibited by certain functionalized derivatives, e.g. 2, that compares very favorable with the activity displayed by the structurally related antihypertensive dihydropyridine drugs (DHPs) amlodipine and nicardipine (e.g. 3) [3,4]. Although several questions about the exact stereochemical and conformational requirements for activity remain, a reasonable pharmacophore model for DHP/DHPM calcium channel modulators has been proposed recently [5]. The main features of this model include: (i) a boat-like conformation of the DHP/DHPM ring; (ii) an axially positioned substituted aryl ring and (iii) an ester group at C5 oriented cis with respect to the C5=C6 double bond [5].  

In a recent experimental (X-ray) and low-level computational (AM1, PM3, ab initio HF/3-21G) study [6] on conformational properties of several 4-aryl-dihydropyrimidines 1 (R = Ar) we have obtained reasonable overall agreement between calculated and experimental structures. Nevertheless, in order to get further insight into the preferred conformation of the C5 ester substituent and the inherent ring pucker of such DHPM derivatives we have now performed detailed ab initio (RHF and MP2) and density functional (B3LYP) calculations on two rotamers of the C4 unsubstituted DHPM derivative 4 (cis-4a, trans-4b). These calculations were performed at significantly higher levels of theory and with larger basis sets than any previous study on DHP/DHPM calcium channel modulators. Of particular interest to us was a systematical analysis of the basis set effects on (i) the ring conformation of the dihydropyrimidine ring, and (ii) the energy gap between the cis and trans esters. These computations were complemented by an X-ray structure determination of the benzyl ester analog 5.

Results and Discussion

Relative energies and the torsional angle j (C6-C5-C9-O10), characterizing the ester conformation (cis ca. 0°, trans ca. 180°) for the two main rotamers of 4a,b are summarized in Table 1. Independent of the basis set as well as the computational level (RHF vs. B3LYP vs. MP2) invariably a slight preference for the cis rotamer 4a is predicted by the calculations, indicating an intrinsic greater stability of this isomer. The energy difference, however, is quite small (ca. 1 kcal/mol) and is decreasing with an increasing level of theory (B3LYP yield nearly identical E values as RHF, those obtained by MP2 are slightly smaller). It is, therefore, not surprising that one can observe experimentally a rather subtle dependence of the preferred conformation of such DHPMs (i.e. 1, R = Ar) on structural modifications of the parent molecule [6]. The benzyl ester derivative 5 adopts the cis conformation in the solid state (Figure 1). Intermolecular interactions, e.g. hydrogen bonding of the ester carbonyl CO to the N1-H of a second DHPM molecule in the solid state [6], may preferentially stabilize the trans rotamer, overriding the inherent preference for the cis ester orientation. In both conformations, the ester group is nearly coplanar to the C5=C6 double bond with the largest twist angles (< 12°) obtained at the MP2 level and the smallest one (< 5°) with B3LYP. In the solid state, for benzyl ester 5, the corresponding value is -2.3°. For the 4-aryl derivatives 1 (R = Ar) ester torsions of 1.3° and 12.6° for cis, and -165.4° and -166.4° for trans isomers, respectively, are found by X-ray structure determination [6]. Calculated bond lenghths for DHPMs 4a,b have been compared with the distances obtained by X-ray crystallographic analysis of 5. There is a reasonable good agreement between the calculated and experimental values.

Figure 1. Solid-state structure of dihydropyrimidine 5.AcOH (click here to view the ORTEP Plot). Click on the above image to manipulate the structure (.pdb file) live on your screen. You will need to install the MDL Chemscape Chime plug-in to do this.

The results of the ring puckering analysis are summarized in Table 2. Here a rather drastic dependence on the computational procedure is found. With all basis sets used, the largest deviations from planarity inevitably are predicted by MP2 calculations. Specifically, the MP2 S t values (> 150°) obtained for 4a,b represent strongly puckered geometries (Figure 2) which deviate considerably from the almost planar structures delivered by X-ray crystallography [7]. Furthermore, they are even larger than the experimental S t values of the 4-aryl substituted derivatives 1 (S t  = 90^o - 140°), which are known to exist in a puckered boat conformation [6]. Considerably less puckered structures are obtained by the RHF method and B3LYP yields somewhat stronger distortions than RHF. With respect to basis set dependence the following conclusions emerge: except for the triply split 6-311G basis, those without polarization functions lead to planar ring structures. Inclusion of polarization functions on heavy atoms invariably yields non planar geometries. Adding polarization functions on hydrogens or diffuse functions has only little effect. Structures with a trans ester orientation (4b) are consistently stronger puckered than those with a cis ester orientation (4a). This finding is also evident from the calculated puckering amplitudes Q (Table 2), which generally are larger for 4b. In agreement with interring torsions (not shown) puckering amplitudes increase in the order Q(RHF) < Q(B3LYP) < Q(MP2). The MP2 puckering amplitudes ( > 0.4 Å) are similar to that for e.g. cyclopentane (Q = 0.43 Å) [8], indicating unexpected strong puckering for 4a,b.

 

Figure 2. HF/6-31G (left) and MP2/6-31G* (right) optimized geometries of 4a (side view). Click on the images to manipulate the structures (.pdb files) live on your screen. You will need to install the MDL Chemscape Chime plug-in to do this..

To address the question what energetical cost is necessary to transform the puckered ring conformations predicted by the MP2 calculations (and to a lesser extent by B3LYP and RHF) to the almost completely planar ones found by X-ray crystallography in the solid state, calculations on 4a with enforced planarity of the dihydropyrimidine ring have been performed. The results (energy difference DE = E(opt) - E(planar)) obtained at several levels of theory are collected in Table 3. Generally, at the RHF or B3LYP level these energy differences are almost negligible indicating a highly flexible ring structure. MP2 calculations, in contrast, yield a substantially larger energetical preference for the puckered geometries. Inclusion of diffuse functions has a significant effect (ca. 100% increase in DE). These planar ring geometries are, however, not minima but rather transition states with one, albeit very small imaginary frequency.

Summary and Conclusion

In the present poster we have presented a detailed ring conformational analysis of dihydropyrimidine 4 based on ab initio and density functional calculations at various levels of theory. While all experimental data - at least in the solid state - indicate an almost completely planar six-membered ring in C4-unsubstituted DHPMs [7], the computations suggest significant puckering (Figure 2). However, we find a strong dependence of the amount of puckering on both the basis set (inclusion of polarization functions inevitably leads to puckered structures) as well as the computational method (increasing deviation from planarity in the order RHF < B3LYP < MP2). An analogous sensitivity on the employed computational procedure had been observed previously in amides and ureas [9-16]. While in simple amides and ureas such an effect is reflected in differences of amide bond planarity, in cyclic derivatives like 4, puckering of the six-membered ring will be observed. Whether the nonplanarity of the dihydropyrimidine ring in 4 is an intrinsic property of the molecule itself or an artefact of the calculation cannot be decided with certainty at this point: the computed energy differences between planar and puckered ring geometries are rather small (Table 3). Therefore, intermolecular forces (crystal packing) might lead to at least some flattening. On the other hand, difficulties of MP2 calculations in the correct treatment of conformational properties of amino acids [17] and amides (overestimation of the deviation of the heavy atom skeleton from planarity) [18] are known. Pending gas phase structure and puckering potential measurements at present no definitive conclusions concerning the intrinsic ring conformation of dihydropyrimidines are possible.
 

Acknowledgements
This work was supported by the Austrian Academy of Sciences and the Austrian Science Fund. We thank Dr. Marcus A. Semones for obtaining X-ray data of compound 5.

References

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