Theoretical Study of Hydrogen Bond Formation in Four Rare Sugars: Gulose, Allose, Altrose, and Talose

Rare sugars are monosaccharides with tremendous potential for applications in pharmaceutical, cosmetics, nutraceutical, and flavors industries. The four rare sugars, including; gulose, allose, altrose and talose are stereoisomers that are different in the hydroxyl group orientation (axial or equatorial) on the C 2-4 atoms. The DFT, AIM, and, NBO calculations were used to probe the probability of formation of internal H-bonds in four rare sugars. The AIM analysis identified that altrose and talose can form three predominantly intramolecular H-bonds, whereas gulose and allose revealed one and two H-bonds, respectively and these normal intramolecular H-bonds are mostly closed-shell interactions. The theoretical calculated O-H stretching FT-IR vibrational frequencies confirmed that the intramolecular H-bonds shifted toward low frequencies in comparison to the free hydroxyl group, which caused the red-shift. Also, the lowest IR frequency in each sugar was related to the structure with the highest stabilization energy and the most strongest intramolecular H-bonds.


Introduction
Rare sugars are monosaccharides with various known biological functions and tremendous potential for applications in pharmaceutical, cosmetics, nutraceuticals, and flavors industries [1][2][3][4][5]. Some rare sugars are used as building blocks for synthesizing nucleotide analogs, which are important as antiviral and anticancer agents. Moreover, due to their immunosuppressive properties, they are used as anti-inflammatory agents [6]. Among different monosaccharides, glucose, galactose, and mannose are abundant in Nature, while gulose, allose, altrose, and talose existing in very small amounts in Nature [7]. Rare sugars have exciting characteristics. They have lower calories than traditional sugars such as sucrose, fructose, glucose, or lactose. The small amount of these sugars makes their separation from the primary sources economically unprofitable. Therefore, inevitable biological processes such as fermentation or enzyme conversion are used to produce these compounds. The studies of rare sugars were limited due to the lack of methods to produce these sugars on a bulk scale until Izumori's group have developed a new methodology for rare sugars productions [8].
Allose occurs as a 6-O-cinnamyl glycoside in the leaves of the African shrub Protea rubropilosa and also in tissues of some plants such as rice [9]. It is soluble in water but practically insoluble in methanol [10].
Gulose is another rare monosaccharide in Nature. It has been found in archaebacteria and eukaryotes [13].
Rare sugars such as; ß-D/ gulose, allose, altrose, and talose contain multiple chiral carbons, and their hydroxyl groups orientations are different (axial/equatorial). These sugars are isomeric molecules having the same molecular formula and sequence of bonded atoms but differ in spatial orientations. Although their only difference is in the hydroxyl groups orientation (axial or equatorial) on the C2, C3, and C4, this small difference has caused many different physico-chemical properties such as different melting and boiling points [14]. Figure 1 shows the orientation (axial and equatorial) of different hydroxyl groups on C2, C3, and C4 atoms in several rare sugars, including gulose, allose, altrose, and, talose which are β-D-anomer. It is worth mentioning that these sugars are stereoisomers, which are epimers to each other.
The hydrogen bond (H-bond) is defined as X-H…Y interaction, where X-H is the typical covalent bond being the proton donating moiety and Y is a proton accepting center. The X and Y are electronegative atoms such as O, N, and F. The H-bond is a weak attraction with a binding strength less than one-tenth that of a regular covalent bond [16]. Generally, the H-bond energy value for weak H-bond is as low as 0.24 to 0.28 kcal.mol -1 , although it could reach a maximum of 38 kcal.mol -1 . On average, the H-bonds are fall in the range of 1.2 to 7.2 kcal.mol -1 [17][18][19]. In the context of the sugar groups, the water-carbohydrate bond energies are in the range of approximately 3.34-6.45 kcal.mol -1 . The H-bonds, specifically intramolecular H-bonds have a strong effect on the physico-chemical properties and self-assembly behavior of the biomolecules. They could participate in the essential vital phenomena either singly or as intricate networks conveying structural and thermodynamic cooperativity [20]. In biology, H-bond is responsible for the formation and functionality of the cell membranes to help the proteins and nucleic acids form and maintain specific shapes [21,22]. According to Lipinski's rule [23], five of the majority of orally active drugs tend to have about five H-bond as donors and ten H-bonds as acceptors to the design of drugs.
Several theoretical methods have been used to investigate the structural and electronic properties of carbohydrate sugars to understand the nature of H-bonds interactions [24][25][26][27][28]. The present study aims to investigate the H-bonds formation and the orientation effects of five hydroxyl groups in the four rare sugars theoretically. To achieve this goal, density functional theory (DFT) was used for optimizing the equilibrium geometry of the above-mentioned sugars. The atoms in molecules (AIM) approach [29]  strength [30]. The natural bond orbital [31,32] analysis of the H-bond was applied to analyze the charge transfer energy during the H-bonds interaction in these rare sugars. Furthermore, the H-bond effects on the OH stretching frequency of these rare sugars were calculated.

Computational details
Three methods of DFT, AIM, and NBO have been used to investigate the role of the intra-molecular Hbond interactions in four rare sugars, including gulose, allose, altrose, and talose. The lowest-energy conformers of each sugar were explored at the relative energy range of 0-10 (kcal.mol -1 ) using the Merck Molecular Force Field (MMFF) in SPARTAN 14 software [33]. Afterward, the most stable conformers were optimized based on Backe's three-parameter hybrid functional [34], together with Lee-Yang-Parr correlation functional (B3LYP) of the density functional theory (DFT) with 6-31G* basis set in Gaussian 09 [35] package. As the energy ordering changes between MMFF and DFT, the lowest energy of MMFF conformers at the relative energy range of 1-3 (kcal.mol -1 ) were selected for DFT optimization. For instance, from 75 gulose conformers obtained at the relative energy from 0 to 10 (kcal.mol -1 ) using MMFF, just five gulose conformers were in the energy range of 1-3 (kcal.mol -1 ), and these five conformers of gulose has been selected for the DFT optimization. The excellent performance of the B3LYP method for describing sugar isomers has been discussed in previous publications [36,37]. It has been extensively used to study carbohydrate systems. Momany et.al calculated the geometry optimization of carbohydrates such as α-/ß-D-glucopyranose [38], α-/ß-D-mannopyranose [36] and, α-/ß-D-galactopyranose [39] using the B3LYP method. The absence of negative frequency in normal mode analysis proved each of the optimized structures is located at a stable minimum point of the potential energy surface (PES).
The structural and electronic properties such as electron density and Laplacian of the electron density at the bond critical point (BCP) of the formed H-bond were calculated using the theory of atoms in molecules (AIM) proposed by Bader [40,41] with the AIM 2000 software [42]. The natural bond orbital (NBO) analysis was performed using NBO 3.1 package [43] as implemented in the Gaussian 09 software at the same method and basis set in order to investigate the nature of intramolecular interactions of these four rare sugars. Furthermore, the OH stretching frequencies (FT-IR spectra) were calculated for these rare sugars.

Results and Discussions
Energies and geometry optimization Table 1 summarizes the bond length, bond angle, and relative energy for gulose, allose, altrose, and talose criteria for H-bond is the distance of less than 3.2 (Å) between donor and acceptor [16]. On the other hand, the bond lengths in carbohydrates are in the range of 1.8-2.6 (Å) [44], which specifically are 1. (kcal.mol -1 ), -431051 (kcal.mol -1 ) and -431056 (kcal.mol -1 ), respectively. It was found that talose with three intramolecular H-bonds is the most stable in the last three rare sugars. In comparison between talose and gulose, gulose with one intramolecular H-bond is more stable. This can be related to the free rotation of the HO6 group on C6 which leads to the formation of the more stable (O6...HO4) intramolecular H-bond. Whilst, the HO1, HO2, HO3 and, HO4 groups in talose are connected to the C atom of the sugar ring. These dependencies will be confirmed by AIM, NBO, and FT-IR results in the next sections.
where EHB is the energy of interatomic interaction. , and H-bond energy (EHB) for the selected rare sugars at the bond critical points at the B3LYP/6-31G* level of theory. Sugars Topological parameters and AIM molecular graphs for considered sugars are represented in Table 2 and Ellipticity,(ε), is another interesting parameter which is defined as: Where as 1  and 2  are the curvatures of the density with respect to the two principal axes of X' and Y'.
Ellipticity is a measure of bond stability, i.e., a high ellipticity value indicates the instability of the bond [51].

Figure.2
The optimized structure and AIM molecular graphs of gulose, allose, altrose, and talose sugars. Large circles correspond to attractors attributed to atomic positions: gray, hydrogen; black, carbon; and red, oxygen. Small circles are attributed to critical points: red, bond critical point (BCP (kcal.mol -1 ). These values are in good agreement with our previous results for glucose and idose sugars [25].

Natural Bond Orbital (NBO) analysis
The NBO [32] analysis interpreted the electronic wave functions in terms of a set of occupied Lewis and a set of unoccupied non-Lewis localized orbitals. Delocalization effects can be identified from the presence of off-diagonal elements of the Fock matrix. The strengths of these delocalization interactions are estimated by the second-order perturbation theory ( ) 2 ( E ). Besides, the stabilization energy ( ) 2 ( E ) is associated with j i  delocalization, and is explicitly estimated by the following equation: Where qi is the i th donor orbital occupancy, i  and j  are diagonal elements (orbital energies), and F (i, j) is the off-diagonal element. Therefore, there is a direct relationship between the off-diagonal elements and the orbitals overlap. The formation of H-bonds in the selected rare sugars implies that certain amounts of electronic charges are transferred from the lone pair of the oxygen atom to the anti-bonding orbital. Table 3  (kcal.mol -1 ), respectively. The highest stabilization energy and strongest H-bond were identified for O4…HO6 bond in talose since it has the highest H-bond energy, the smallest bond length, and the highest bond angle. As a result, altrose with three low H-bonds energies and low ellipticities is less stable than talose. The highest stabilization energy, the smallest bond length, and the highest bond angle were identified for O4…HO6 bond in talose. In summary, the stabilization energies values clearly indicate the charge transfer takes place between the donor and acceptor atoms. Accordingly, the favorable intramolecular Hbonds will construct in four investigated rare sugars.

Infrared spectroscopy
The structural and analytical properties of carbohydrates are difficult to investigate since the physical and chemical properties of the basic units in these polymeric systems are very similar. Infrared spectroscopy is a powerful tool to monitor the presence and nature of the H-bonds; inter-or intra-molecular H-bond [52].
The existence of the H-bond leads to significant changes in infrared spectroscopy which resulted in the stiffness bond and altered the frequency of O-H stretching and produces broadband that occurs in the 3700-3600 cm-1 range [53]. The probability of the formation of intramolecular (internal) H-bond increased If the hydroxy group bands do not change dramatically with concentration [54]. The OH group vibrations are very sensitive to the environment, therefore, there are pronounced shifts in the spectra of the H-bond towards the low frequency and red-shift occurs. As such, the H-bonded OH stretching (H-O…H) shifts toward 3500 to 2500 cm -1 [53]. The formed intramolecular H-bonds cause their vibrational modes to be vibrated at a lower frequency than the normal vibration frequency in all known molecular systems including; amines, O-H groups, and halogen-H interactions [55,56]. The lowering of the frequency appears to be a function of the degree and strength of the H-bond [57]. However, it is not well established experimental IR spectroscopy to determine intra-molecular H-bond. In this study, we used the theoretical IR spectroscopy method at the B3LYP/6-31G* level to study the presence of H-bond in the selected rare sugars. We have used the scaling factor value of 0.9614 [58] for the B3LYP/6-31G* method since the DFT method systematically overestimates the vibrational wavenumbers [59]. We carried out the scaling factor only for allose and talose because we had not found any experimental FT-IR results for gulose and altrose.
The calculated and scaled OH-stretching vibrations in H-bonded and intramolecular H-bond frequencies of four rare sugars are listed in Table 4 and the corresponded IR spectrum is presented in Figure 3. According to Table 4, the calculated frequencies of O-H stretching for free hydroxyl groups are in the region of 3670-3600 cm -1 for four rare sugars. It was found that the vibration frequency of the HO6 group in gulose was shifted to 3465 cm -1 , whilst the calculated vibration frequencies of the HO2 and HO6 groups in allose were shifted to 3585, and 3565 cm-1, respectively (see Figure 3). On the other hand, the lowest frequency was associated with the HO2, HO4, and HO6 groups at 3590, 3591, and 3568 cm -1 for altrose. However, the calculated frequencies of HO2, HO4 and HO6 groups at 3593, 3360, and 3495 cm -1 for talose (see in Figure   3) revealed these hydroxyl groups are capable of forming the intramolecular H-bonds. Accordingly, the intramolecular H-bonds strength was reflected in lowering of the O-H…O stretching frequencies in selected rare sugars which exhibited the red-shift.  [60].
Furthermore, gulose, altrose, and talose have two (OH) groups in the axial orientation, whilst allose has two (OH) groups in the equatorial orientation, therefore, slight differences have been found between their OH stretching frequencies. It seems that the hydroxyl groups in axial orientation are shown the lowest stretching frequency due to the formation of intramolecular H-bond. As an example, the values of 3593 cm -1 and 3360 cm -1 are assigned to the HO2 and HO4 groups in the axial orientation for talose, respectively (see Figure 1). Therefore, according to the orientation of the OH groups (axial/equatorial) on the C atoms, these rare sugars could have different H-bonds with different strengths and energies. Our scaled vibrational frequency results are in good agreement with the experimental values [60] and other calculated frequencies by B3LYP and HF methods and various basis sets [59] and also other available literatures [61][62][63]. As can be seen from IR spectra in Figure 3, the (OH) vibration frequency for selected rare sugars confirmed the existence of two types of H-bonds, one is related to the free hydroxyl groups and the other one belongs to the intramolecular H-bonds.
It is clear that the O2…HO4-O4 bond in talose with the energy of EHB=11.73 kcal.mol -1 has the lowest frequency of 3360 cm -1 (see Table 2,4) which is comparable with the previous resul of Desiraju et al [55] and is in excellent agreement with our previous study for glucose and idose sugars [25]. The change of the

Figure.3
Theoretical FT-IR spectra by B3LYP/6-31G* method for gulose, allose, altrose, and talose. Free hydroxyl groups illustrated with black color whereas blue colors are intramolecular H-bonds that were shifted to low frequencies.

Conclusions
Three methods , namely DFT, AIM, and NBO were used to investigate the existence, nature, and strength of the H-bonds formed in the four rare sugars including; gulose, allose, altrose, and talose. It was found that

Declarations;
Funding: The authors did not receive support from any organization for the submitted work.

Conflicts of interest/Competing interests:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Figure 1 Schematic view of molecular structures of gulose, allose, altrose, and talose sugars. aThe IUPAC naming convention for carbohydrates has been used for labeling the atoms [15].

Figure 2
The optimized structure and AIM molecular graphs of gulose, allose, altrose, and talose sugars. Large circles correspond to attractors attributed to atomic positions: gray, hydrogen; black, carbon; and red, oxygen. Small circles are attributed to critical points: red, bond critical point (BCP).

Figure 3
Theoretical FT-IR spectra by B3LYP/6-31G* method for gulose, allose, altrose, and talose. Free hydroxyl groups illustrated with black color whereas blue colors are intramolecular H-bonds that were shifted to low frequencies.