Quantum theory of atoms in molecules (QTAIM) analysis
Quantum theory of atoms in molecules (QTAIM) analysis has been widely used to interpret any chemical bonds including the nature of H-bond interaction and confirmed to be a useful and successful tool for interpreting charge density. We carried out AIM study of electron density at the bond critical points (BCPs) by AIM2000 software to gain information on variation of the geometrical parameters and the H-bond strength in the conjugate bases of Deoxy-hexose sugars.
Topological parameters (calculated at the B3LYP/6-311++G(d,p) level) such as electron density,, and its Laplacian,, kinetic energy density, , potential energy density, , and H-bond energy,, at the BCPs for the conjugate bases of Deoxy-hexose sugars are listed in Tables 5 and 6.
According to Bader theory of atom in molecules [45], if hydrogen bond exists, the range of electron density is 0.002 to 0.035 (a.u,) and its Laplacian is 0.024-0.139 (e/au5). The value of electron density and its Laplacian at BCPs for the conjugate bases of CH3-pentose fall between 0.0233-0.0439 (a.u.) and 0.0877-0.1257 (e/au5), respectively (Table 5); and those for the conjugate bases of aldo-pentose fall between 0.0177-0.0752 (a.u.) and 0.0847-0.1380 (e/au5), respectively (Table 6). Based on these ranges, the characteristic values and at BCPs imply the presence of H-bond interaction in the conjugate bases of Deoxy-hexose sugars. Laplacian of electron density is related to the chemical bond interaction energy by a local expression of the virial theorem [38]. Based on QTAIM, a positive value of Laplacian of electron density at BCPs indicates closed-shell electrostatic interactions such as ionic bonds, hydrogen bonds, and van der Waals interactions; whereas a negative value of Laplacian of the electron density shows shared-shell electron covalent interaction [38]. Thus, a positive value of at BCPs of H-bonds in the conjugate bases of Deoxy-hexose sugars indicates that these H-bonds are mostly closed-shell electrostatic interactions.
The electronic energy densityat BCPs is defined as [47]; where refers to the electronic kinetic energy density, which is always positive, and refers to the electronic potential energy density and must be negative [46] . The sign of depends on which contribution, potential or kinetic, locally prevails at BCPs and it determines whether the accumulation of charge at a given point of r is stabilizing; or destabilizing. Popelier [39] proposed the following criteria of strength: for weak H-bond both and ; for medium H-bond and ; and for strong H-bond both and . This classification shows that weak H-bonds eventually merge with van der Waals interaction; whereas strong H-bonds merge with covalent and polar bonds.
Different types of H-bonds are seen in the conjugate bases of Deoxy-hexose sugars. For example, the O2…HO1-O1 and O2…HO3-O3 H-bonds (Figure 3h) in the conjugate base of L-xylose (formed from deprotonation of L-xylose at C2-HO2); and O3…HO1-O1 and O3…HO4-O4 H-bonds (Figure 3e) in the conjugate base of L-arabinose (formed from deprotonation of L-arabinose at C3-HO3) show one bifurcated H-bond. However, the O3…HO2-O2 and O3…HO4-O4 H-bonds in the conjugate base of D-ribose (formed from deprotonation of D-ribose at C3-HO3); and O4…HO2-O2 and O4…HO3-O3 H-bonds in this conjugate base (formed from deprotonation of D-ribose at C4-HO4) exhibit two bifurcated H-bonds (Figures 3m and 3n). Moreover, the conjugate bases of D-xylose and L-arabinose (formed from deprotonation at C1-HO1) do not indicate any H-bonds.
The conjugate bases of L-fucose formed from deprotonation of L-fucose at C2-HO2 and C4-HO4 show the O2….HO1-O1 and O4….HO3-O3hydrogen bonds, respectively (Figure 2b, 2d); and the conjugate base of L-rhamnose formed from deprotonation of L-rhamnose at C2-HO2 (Figure 2f ) indicates the O2….HO3-O3H-bond. These three H-bonds indicate medium and normal intramolecular H-bonds due to positive and negative . Thus, these O-H…O bonds are categorized as partially covalent-partially electrostatic (Pc-Pe ). Whereas, the conjugate bases of aldo-pentose sugars exhibit normal and bifurcated intramolecular O-H…O bonds. The normal intramolecular H-bonds in the conjugate base of D-xylose indicate van der Waals interaction due to > 0 and > 0. The bifurcated intramolecular H-bonds are identified in the conjugate base of D-ribose (formed from deprotonation of D-ribose at C3-HO3 and C4-HO4); and in the conjugate base of L-lyxose (formed from deprotonation of L-lyxose at C2-HO2); and in the conjugate base of L-arabinose (formed from deprotonation of L-arabinose at C3-HO3). These bifurcated intramolecular H-bonds are categorized as medium H-bonds and partially covalent-partially electrostatic (Pc-Pe ) interaction in nature due to and .
According to topological parameters discussed above and results given in Tables 5 and 6, the conjugate bases of L-fucose, L-rhamnose and L-D-xylose indicate conventional H-bonds; whereas conjugate bases of L- lyxose, L-arabinose, and L- arabinose show both conventional and unconventional H-bonds.