The electrostatic potential (ESP) stands an effective descriptor for determining

preferential sites for electrophilic or nucleophilic attack. It helps to identify HB in organic compounds [29] [30] [31]. Equation (2-2) suggests that this statistic concern the interaction energy V, on the one hand, between a proton and those of the nucleus and, on the other hand, with the electrons of a molecule:

V ( r ) = ∑ A Nucleus Z A | R A − r | − ∫ ​ ρ ( r ′ ) d r ′ | r ′ − r | (2-2)

Z A is the charge of the nuclei A. R A − r and r ′ − r are corresponding to the proton-nucleus and proton-electron distances respectively. ρ ( r ′ ) is the electronic density. The first term represents the repulsion energy between nuclei and protons. The second reflects that relating to the attraction between them and the electrons. Furthermore, in regions where the influence of the latter dominates, the sign of V(r) becomes negative. These sites are around free pairs of heteroatoms. An HB donor will be attracted to the point where V(r) has its lowest V_s,max value on the molecular surface. This latter corresponds to a surface of electronic “isodensity” [32].

Furthermore, the potential V(r) becomes positive if the influence of the nucleus goes greater. It’s also observed around atoms that behave like Lewis’s acids. This study exploits the potential V_s,max to identify sites favourable to oryzenin HB. These can have their geometric parameters.

HB stands an attractive interaction. The latter arise between the hydrogen of X-H within a molecule with one or more of their nucleophilic atoms. These are at the distance d [33] from the hydrogen. The first atom losses associated with oxygen or nitrogen of the molecule.

Here, it arises from the approach between the hydrogen of oryzenin with the osidic bridge’s oxygen of amylose. Before the optimization of the complexes, the linearity angle α goes set to 180˚. The hybridization state of the last two atoms finds sp³; β reports 109.5˚ (Figure 2). The distance d from oxygen to hydrogen remains identical to 2 Å. It corresponds to the minimum approach length of the two.

According to [34], an HB can exist if d appears smaller than the sum of the Van der Waals radii of oxygen (1.52 Å) and hydrogen (1.1 Å) [35]. In other words, if d ≤ 2.62 Å [36] [37], HB becomes strong if d decreases and if the angles α and β don’t deviate too much from their ideal values. Moreover, its characterization attends clarified by the energy parameters.

HB formation brings about a change in enthalpy, free enthalpy, and entropy. These quantities correspond to the differences obtained between the complex form and the monomer of a molecular entity. For a reaction at 298.15 K, with the contributions of the translational, rotational, and vibrational entropy, the variation of these can be determined using Equations (2-3):

Δ S 298   K = ∑ S Complex − ∑ S Monomers (2-3)

Similarly, the free enthalpy or energy of the Gibbs reaction at 298.15 K is obtained from Equations (2-4). More, the present work uses spectroscopic descriptors to characterize HB.

Δ G 298   K = Δ H 298   K − T Δ S 298   K (2-4)

where:

Δ H 298   K = Δ E 298   K + Δ n R T (2-5)

The formation of HB leads to a weakening of the X-H bond, it appears associated with its elongation and the simultaneous decrease of its stretching frequency. However, for many examples, this frequency increases with the contraction of the bond during the formation of the HB [38] [39]; spectroscopic descriptors represent an interesting tool to determine the strength of the HB. The relative displacement of H about X can be calculated using the following relationship:

υ = υ free − υ complex (2-6)

In practice, the higher the ∆υ variation, the more HB formation is enabled. Moreover, NBO analysis permits verifying the formation process of HB.

NBO analysis appears a method to study donor-acceptor exchanges for intra- and intermolecular HB. It also permits the evaluation of charge transfer and conjugate interactions in chemical systems [40] [41]. It considers the important role of atoms free pairs in chemical processes. It allows accessing to the intermolecular energy of HB associated with the X-H…Y type. It evaluates the stabilization energy E⁽²⁾ between the free doublet σ(Y) of the electron donor and the anti-bonding orbital σ*(X-H) of the proton (electron acceptor) using the second-order perturbation theory. For each donor (i) and acceptor (j), the stabilization energy E⁽²⁾ connected with the delocalization (i)→(j) is estimated as follows:

E ( 2 ) = Δ E i j = q i F ( i , j ) ε i ε j (2-7)

where F(i, j) stands a non-diagonal element of the Fock matrix, q_i represents the electron density in the donor orbital. ε_i and ε_j find the energies of the occupied (i) and vacant (j) NBO orbitals. The stabilization origin of a molecule comes from E⁽²⁾. The higher this latter, the stronger the interaction is. However, this study only considers exchanges with an E⁽²⁾ value above 1.5 kcal∙mol⁻¹. The present work reveals the results of the calculations and discusses them.

Table 1 presents the V_s,max of all hydrogen atoms in oryzenin. Figure 3 shows the map of its electrostatic potential. The values of V_s,max varies from −2.9 × 10³ kJ∙mol⁻¹ to −2.5 × 10³ kJ∙mol⁻¹. The largest appears those of H₁₀ and H₃₀ linked

N₉-H₁₀ and O₂₉-H₃₀ bonds respectively. Their V_s,max reports −2.5 × 10³ kJ∙mol⁻¹ and −2.6 × 10³ kJ∙mol⁻¹ in increasing order. These atoms find the potential HB donor sites. In other words, HB with oryzenin protons is preferably carried out in the order: H₁₀ then H₃₀. The following sections discuss the interactions of AM2G-oryzenin complexes.

Figure 4 illustrate the spatial structure of the complexes after optimization. They show oryzenin interactions with the proton acceptor site of amylose. More, this work discusses the geometrical parameters.

Geometric Parameters

Table 2 shows the geometrical parameters of the AM2G-Oryzenin interaction. These are the distance d (Å), the linearity angles α and directional angle β. The approach distances of HB to the osidic bridge are between 1.88 Å and 2.48 Å. These hydrogen bond lengths are less than 2.62 Å as recommended by [36] and [37]. Generally, the hydrogen bond length between two neutral fragments is about1.5 Å to 2.2 Å [43]. The O₂₉-H₃₀…O₄₆ interaction satisfies this constraint. It suggests O₂₉-H₃₀…O₄₆ is much stronger than N₉H₁₀…O₄₆. The angle α of O₂₉-H₃₀…O₄₆ is the highest (159.8˚). Its relative proximity to 180˚ corroborates the thick interaction O₂₉-H₃₀…O₄₆. The β angle of 102.9˚ confirms this result; it remains close to 90˚. These geometrical features suggest the strength of HB with the osidic bridge is preferentially realized with O₂₉-H₃₀…O₄₆. A greater length than 2.2 Å indicates a weak hydrogen bond. It’s with a direction angle that deviates from linearity. This is the case for the N₉-H₁₀…O₄₆ interaction. The research also goes interested in the energy parameters.

Energy parameters

Table 3 shows the enthalpies, entropy, and free enthalpies of reaction. These energy parameters aren’t revised by the basis set superposition error. The enthalpies indicated that the O₂₉-H₃₀…O₄₆ HB appears the most stable. Its enthalpy

(−23.160 kcal∙mol⁻¹) is about that of strong HB. It’s lower than the HB enthalpies of trichloroacetic acid and triphenylphosphine oxide. These are almost −16 kcal∙mol⁻¹ [44]. Its free enthalpy of reaction (∆_rG = −10.156 kcal∙mol⁻¹) proves that this interaction occurs normally; the HB establishment goes spontaneously. The negative value of its entropy reflects the transition from two to a single entity in the gaseous state. They suggest that they not find natural. The N₉-H₁₀…O₄₆ interaction is comparable to the hydrogen bond in the phenol-triethylamine interaction (−8.85 kcal∙mol⁻¹) [45]. Spectroscopic descriptors can also characterize HB.

Spectroscopic parameters

Table 4 shows the O-H and N-H elongation frequencies of non-complexes and complex oryzenin. ∆υ indicate their difference. The vibrational frequencies of O-H (3839 cm⁻¹) and N-H (3591 cm⁻¹) of oryzenin are comparable to those calculated for uracil. In principle, their HB are of the same nature. The O-H elongation frequencies of this compound vary from 3901 cm⁻¹ to 3882 cm⁻¹ while those of N-H are between 3585 cm⁻¹ and 3631 cm⁻¹. The O-H stretches of oryzenin differ by 62 cm⁻¹ to 43 cm⁻¹ from those of uracil. Those of N-H move from −6 cm⁻¹ to 40 cm⁻¹. The υ (OH) and υ (NH) of oryzenin are overestimated on average compared to the experimental υ (OH) and υ (NH) of free uracil. These quantities equal 3727 cm⁻¹ and 3343 cm⁻¹. The complexation lowers vibrational frequencies. The variation depends on the strength of the HB. The variation of ∆υ = 232 cm⁻¹ in the O₂₉-H₃₀…O₄₆ interaction exceeds that of N₉H₁₀…O₄₆ (∆υ = 65 cm⁻¹). It reflects the relatively strong attraction exerted by the oxygen of the saccharide bridge (O₄₆ acceptor) on the hydrogen of the probe. Under these conditions, O₂₉-H₃₀…O₄₆ HB becomes stronger than N₉H₁₀…O₄₆ one.

For AM2G, the breakdown of amyloidosis takes place mainly through HB O₂₉-H₃₀…O₄₆. In other words, it occurs at the level of the osidic oxygen at the end of the amyloidosis chain. It promotes the presence of monosaccharides in the amylose’s degradation products. This research is also interested in the AM3G-oryzenin interaction.

Figure 5 shows the optimized structures of the AM3G-oryzenin complex. They show the main interactions between these two molecules. This work details their geometrical parameters.

Geometrical Parameters

The geometric analysis of HB associated with the interaction of AM3G with the oryzenin molecule is based on the recommendations of [37]. Table 5 shows the HB lengths (d), their linearity (α) and directional angle (β) established with osidic bridge. The HB lengths d of O₂₉-H₃₀…O₄₆ and N₉-H₁₀…O₄₆ find 1.93 Å and 2.19 Å respectively.

They suggest that the first interaction appear the thickest. Moreover, its parameters reveal its stability. The linearity α = 179.3˚ and the angle β = 102.2˚ sit close to the ideal values (α = 180˚ and β = 90˚). These parameters indicate that the O₂₉-H₃₀…O₄₆ HB reports stronger than those of N₉-H₁₀…O₄₆. The energy factors help to classify the HB of this complex.

Energy parameters

Table 6 shows the enthalpies, entropy, and free enthalpies of reaction O₂₉-H₃₀…O₄₆, and N₉-H₁₀…O₄₆. The first quantities reach ∆_rH = −21.037 kcal∙mol⁻¹ and ∆_rH = −2.309 kcal∙mol⁻¹ respectively. These data prove that the O₂₉-H₃₀…O₄₆ HB represents more stable of the two. This enthalpy is slightly higher than its correspondent in AM2G. The negative evolution of the free enthalpy during the O₂₉-H₃₀…O₄₆ approach (∆_rG = −7.143 kcal∙mol⁻¹) indicates that this is achieved suddenly in contrast to its counterpart (∆_rG = 8.600 kcal∙mol⁻¹). The energy characteristics reflect a stronger interaction of O₂₉-H₃₀…O₄₆. Spectroscopic parameters explain the elongation of HB.

Spectroscopic Parameters

Table 7 shows the elongation frequencies υ_(O-H) and υ_(N-H) of free and complex oryzenin when OH or NH approaches the osidic bridge. Its last column displays the frequency gap. This stands strong for the O₂₉-H₃₀…O₄₆ interaction. Its relative value ∆υ =161 cm⁻¹ becomes higher than the second interaction one (N₉-H₁₀…O₄₆: ∆υ = 107 cm⁻¹). The spectroscopic parameters confirm the greater stability of the O₂₉-H₃₀…O₄₆ HB. However, this variation in elongation frequency is small compared to that of AM2G. It reflects the fact that the dominant interaction of oryzenin with AM3G is weaker than that with AM2G.

For AM3G, the degradation is mainly related to the formation of HB O₂₉-H₃₀…O₄₆. It involves the atom of the osidic bridge at the end of the AM3G chain. It promotes the presence of monosaccharides in the amylose’s degradation products. Moreover, this result indicates that the elongation of a unit doesn’t modify the mechanism of its degradation. This research also focuses on the AM4G-oryzenin complex.

The molecular structure of AM4G has three saccharide bridges. Their interaction with the two HB sites of oryzenin leads to four cases. Figure 6 shows the geometries of the AM4G-oryzenin complex. The osidic oxygen at the end of the chain is called O (1) and that of the middle O (2). The geometric parameters make it possible to identify these interactions.

Geometrical Parameters

The geometry optimization is performed at the DFT/B3LYP/6 - 31 + G(d, p) level of theory. It provides access to the structural features of the AM4G-oryzenin complex.

Table 8 presents its HB lengths (d) and its α linearity and β-directional angles. The strongest HB corresponds to the O₂₉-H₃₀…O (1) interaction. Its HB length (d =1.88 Å) remains the smallest. Its angle α = 164˚ and β = 106.4˚ finds closest to their ideal values. The geometrical parameters indicate that HB O₂₉-H₃₀…O (1) stays the most probable. They provide evidence that under the action of

oryzenin the degradation of amylose starts at the end of the chain. The distance d = 1.91 Å proves that this process continues in the middle. The products of amylose degradation represent mainly monosaccharides and secondary disaccharides. The latter also deteriorate as AM2G-oryzenin. This result agrees with the observation of [46]. These authors mention that the rice degradation is materialized by a decrease in disaccharides and an increase in monosaccharides. The following section focuses on the energy parameters of these interactions.

Energy Parameters

Table 9 shows the enthalpy, entropy and free enthalpy of reaction variations related to AM4G-oryzenin interaction. The first (∆_rH = −35.413 kcal∙mol⁻¹) establishes that O₂₉-H₃₀…O (2) HB stands the most stable. Moreover, its formation lives natural; its free enthalpy goes negative (∆_rG = −18.291 kcal∙mol⁻¹) like other interactions. The entropy varies only slightly.

The energy parameters suggest that this bond appear the most favoured. Otherwise, the dissociation of this amylose starts in the middle of its chain. It continues at its end; the HB (O₂₉-H₃₀…O (1)) is the second most stable (∆_rH = −26.410 kcal∙mol⁻¹). The spectroscopic parameters allow dealing with this contradiction. In this case, the geometrical and energetic characteristics lead to a controversial conclusion. The former assert that AM4G degradation starts at the end of the chain as a matter of priority, while the latter considers it to be in the middle at the start. Spectroscopic parameters could help to resolve this contradiction.

Spectroscopic parameters

Table 10 contains the elongation frequencies υ(O-H) and υ(N-H) of free and complex oryzenin when the OH or NH hydrogen approaches the osidic bridge. Its last column shows their variations.

There is a decrease in the elongation frequencies of O-H and N-H when oryzenin sits complex. HB leads to an elongation of the O-H and N-H lengths. This represents the effect of charge transfer, which causes a drop in vibrational frequencies.

This decrease is observed in the AM4G-Oryzenin complex. Besides, it’s 287 cm⁻¹ for the strongest O₂₉-H₃₀…O (1) interaction. This result goes compatible with the one generated by the geometrical parameters. It establishes that this HB predominates for the AM4G-oryzenin complex.

For AM4G, the degradation is based on the probable formation of O₂₉-H₃₀…O (1). It continues with that of O₂₉-H₃₀…O (2). This result provides evidence that under the action of oryzenin, the alteration of amylose starts at the end of the chain’s amylose. It lives secondary to its middle. Besides, the AM2G elongation of two units modifies the mechanism of amylose’s transformation. AM4G degrades it at its extremities and its middle. More, NBO analysis offers another way to understand the oryzenin’s action of amylose.

Lone pairs of electrons play an important role in chemical processes. NBO analysis provides access to the HB intermolecular energy of X-H…Y type. It proceeds by evaluating the stabilization energy E⁽²⁾ as illustrated in materials and calculation methods section. Tables 11-13 collect the stabilization energies E⁽²⁾, the energy differences of NBO electron donors (i) and acceptor one (j) and the Fock matrix elements F_i,j.

The NBO analysis data show a strong stabilization of the delocalization energy related to the interactions for the single pairs of the chloride ion Cl₃₆. Specifically, the dominant interactions in the complexes report HB linked to the n Cl 36 ( 4 ) → σ O 48 -H 49 * transition (E⁽²⁾ = 35.76 kcal∙mol⁻¹), for AM2G-Oryzenin complex, n Cl 36 ( 4 ) → σ O 92 -H 93 * (E⁽²⁾ = 25.58 kcal∙mol⁻¹) for AM3G-Oryzenin complex, and n Cl 36 ( 4 ) → σ O 120 -H 121 * (E⁽²⁾ = 33.02 kcal∙mol⁻¹) for the AM4G-Oryzenin complex. After these, follow the interactions established with O₂₉-H₃₀. Their

stabilization energies correspond to 7.84 kcal∙mol⁻¹ for the n O 46 ( 1 ) → σ O 29 -H 30 * transition in AM2G-Oryzenin complex, 5.87 kcal∙mol⁻¹ in AM3G-Oryzenin complex and 9.32 kcal∙mol⁻¹ for the AM4G-Oryzenin complex.

The NBO analysis corroborates that the main HB of the amylose-oryzenin complexes results from the interaction between O₂₉-H₃₀ and the oxygen of the osidic bridge. Furthermore, for AM4G-oryzenin complex, the strongest HB is established with this latter at the end of the chain. This result confirms that the products of amylose degradation find predominately monosaccharides; it substantiates the experimental observation of [46]. This last discussion leads us to conclude this work.