Theoretical indications on the relationship between pyrogallol [ 4 ] arenes dynamics of assembling and geometry short communication

Pyrogallol[4]arenes are macrocycles with high potential as building blocks for nanocapsules. We theoretically studied the dimeric precursors of 2,8,14,20-tetramethylpyrogallol[4]arene and 2,8,10,14-tetraphenylpyrogallol[4] arene to understand the dynamics of assembly of these compounds, and calculated the potential energy curves along the torsion angle of the (R-pyrogallol)CH–(R-pyrogallol) dimeric bond at the B3LYP/6-311G(d,p) level of theory. We found that the energy barriers for free rotation around the selected bond are 0.00133 Hartrees for the alkyl-substituted dimer and 0.77879 Hartrees for the aryl-substituted dimer. These values imply that the free rotation around the selected bond exists for the first dimer but not for the second one. Because the orientation of the substituent and the pyrogallol ring around this bond are likely to determine the geometry of the final structure, we propose that the alkyl-substituted compound will most likely adopt a crown-shaped geometry whereas the aryl-substituted compound will adopt a chair-shaped geometry. These predictions concur with experimental evidence, which shows that the geometry of pyrogallol[4]arenes depends on the substituents attached to them.


Theoretical indications on the relationship between pyrogallol[4]arenes dynamics of assembling and geometry
short communication Pyrogallol[4]arenes are obtained by the acidcatalyzed condensation of a pyrogallol and an aldehyde (Hoegberg 1980).Depending on the aldehyde used in the reaction, two stereoisomers are most commonly produced.A crown-shaped conformer, denoted as rccc, is obtained when alkyl aldehydes are utilized; and a chair-shaped conformer, denoted rctt, is obtained when aryl aldehydes are utilized, denoted rctt is obtained (Gerkensmeier et al. 2001, Zambrano et al. 2010).
In this work, we performed theoretical calculations (Jensen 2007) to obtain indications on the relationship between the dynamics of assembling of alkyl and aryl substituted pyrogallol[4]arenes and their final geometries (Weilnet & Schneider 1991, McKinlay et al. 2005).This information could be useful to project new, relevant applications of these compounds, such as their use as molecular hydrogen storage materials (Urbina et al. 2011, Gokel & Saeedeh 2013).

Materials and methods
We calculated the potential energy curves along the torsion angle of the (R-pyrogallol)CH-(R-pyrogallol) bond of the dimeric precursors of 2,8,14,20-tetramethylpyrogallol[4] arene and 2,8,14,20-tetramethylpyrogallol[4] arene using density functional theory (Koch & Holthausen 2001, Peverati & Baldridge 2008).A scheme of the dimers is shown in Figure 2; it highlights the bond that controls macrocycle assembly.We consider that the orientations adopted by the substituent and the pyrogallol ring with respect to such bond is likely to determine the geometry of the final product.
To generate the potential energy curves, we obtained the equilibrium geometries of the dimers at the B3LYP/6-311G(d,p) level of theory and used them as starting points of the curves.We then calculated the single-point energies of the structures; this was obtained by gradually increasing the torsion angle of the selected bond in increments of five degrees in the interval of zero to 180 degrees.The structure energy versus torsion angle increment data was plotted.All the calculations were performed using a Gaussian 09 software package (Frisch et al. 2009).

Results and discussion
The potential energy curve along the torsion angle of the selected bond for the precursor of the 2,8,14,20-tetramethylpyrogallol[4]arene is shown in Figure 3.This curve displays a minimum which corresponds to the starting structure, that is, the dimer equilibrium geometry and a maximum located at a torsion angle increment of 70 degrees.The energy difference between these two points provides the energy barrier for free rotation around the selected bond.This barrier is calculated to be 0.00133 Hartrees (8.3 kcal/mol).This value is low enough to suggest that, when R = methyl, the substituent and the pyrogallol ring can freely rotate around that bond and readily reorient from their initial positions with respect to the bond as the compound is assembled.That would lead to the formation of the crown-like conformer as the final product.
The potential energy curve along the torsion angle of the selected bond for the precursor of the 2,8,14,20-tetraphenylpyrogallol[4]arene is displayed in Figure 4.In this curve the minimum corresponds to the dimer equilibrium geometry and the maximum occurs at a torsion angle increment of 70 degrees.The energy barrier for free rotation around the selected bond is calculated to be 0.77879 Hartrees (488.7 kcal/mol).This high value implies that, when R = phenyl, the substituent and the pyrogallol ring may not rotate around that bond and remain in their original positions with respect to the bond as the compound is assembled.That would lead to the chair-like conformer as the final product.
These predictions concur with experimental evidence that has found that the most stable products for alkyl-and aryl-substituted pyrogallol[4]arenes adopt the rccc and rctt conformations, respectively (Barret et al. 2007, Thomas 2011).

Conclusion
We conducted a theoretical study of the dimers precursors of 2,8,14,20-tetra-methylpyrogallol[4] arene and 2,8,10,14-tetra-phenylpyrogallol[4]arene, and calculated the potential energy curves along the torsion angle of a selected bond of the dimers to get theoretical indications regarding the relationship

Fig. 1 .
Fig. 1.A scheme of the molecular structure of a pyrogallol[4]arene.The molecule is a macrocyclic oligomer containing four pyrogallol rings and four pendant substituents denoted by R. When R is an alkyl-substituent, the compound adopts a crown-shaped geometry whereas when R is an aryl-substituent the compound adopts a chair-like geometry.

Fig. 2 .
Fig. 2. A scheme of the dimer precursor of a pyrogallol[4]arene is shown.The C-C bond that controls the geometry of the final product is highlighted.The R-C-C-C torsion angle that is gradually increased in order to obtain the potential energy curves is indicated.

Fig. 3 .
Fig. 3.The potential energy curve along the selected torsion angle of the dimer precursor of the 2,8,14,20-tetramethylpyrogallol[4]arene.The curve displays a minimum which corresponds to the energy of the dimer equilibrium geometry, and a maximum located at a 65 degree torsion angle increment.The energy difference between the maximum and minimum provides the energy barrier for free rotation around the bond that controls the geometry of the final product.

Fig. 4 .
Fig. 4. The potential energy curve along the selected torsion angle of the dimer precursor of the 2,8,14,20-tetraphenylpyrogallol[4]arene.The curve displays a minimum which corresponds the energy of the dimer equilibrium geometry, and a maximum located at a 70 degree torsion angle increment.The energy difference between the maximum and minimum provides the energy barrier for free rotation around the bond that controls the geometry of the final product.