**6. Applications to Biomolecules**

We now discuss the application of the MTA-based method for the energy estimation of the N–H···O=C, N–H···N, N–H···S, N–H···O, C–H···N, and resonance-assisted O–H···O=C HBs in biomolecules. Quantitative estimates of the strengths of such individual HB interactions are scarcely available, although they play a vital role in the determination of the structure of biomolecules such as polypeptides/proteins. In order to gauge the strengths of the N–H···O=C HBs, a model tetrapeptide was taken as a test case [89]. It has two different N–H···O=C HBs, the fragmentation scheme being similar to that discussed earlier. In the present case, we remove a –(H)N–(O=C)- functional group of amino acids, involved in the formation of N–H···O=C HB to generate the primary fragments (see Ref. [89]). The MTA-based methodology is applied for the estimation of these IHB energies in five different substituted tetrapeptides of polyglycine abbreviated as GGGGG apart from the capped acetyl and NH2 groups. The five substituted tetrapeptides (viz., GAGGG, GVGGG, GLGGG, and GIGGG) in which the second amino acid residue is replaced by alanine (A), valine (V), leucine (L), and isoleucine (I), respectively, were considered (see Figure 5). The corresponding completely substituted tetrapeptides, AAAAA, VVVVV, LLLLL, and IIIII, were also employed with a view to addressing the effect of substituents on the strengths of the different types of N–H···O=C HBs (Chain 1 and Chain 2 in Figure 5). The estimated HB energies at B3LYP/D95(d,p) level were in the range of 4 to 6 kcal/mol in the partially and fully substituted polypeptides. These values were in concurrence with the geometric parameters and reflected the subtle substituents effects for the substituted polypeptides. The MTA-based procedure was thus considered to be applicable for the IHB energy estimation in polypeptides and it would be fascinating to apply it to an actual protein.

**Figure 5.** Hydrogen-bonded chains in the helical peptide structures. "X" represents the substituent at the second position. A, B, C and D are four hydrogen bonds. See text for details. Reprinted from Ref. [89] with permission from American Chemical Society. *Copyright (2009) The American Chemical Society.*

Recently, the MTA-based procedure was applied to another biologically important class of molecules, viz., porphyrin analogs called meta-benziporphodimethenes (**1**) and Nconfused isomers containing γ-lactam ring (**2** and **3**) [90,91]. In γ-lactam-containing isomers **3** (not shown in Figure 6) the ring O-atom of lactam ring is down, whereas, in isomer **2**, Oatom is up (see Figure 6). The substitution at meso *sp<sup>3</sup>* (R) and on the benzene at *sp<sup>2</sup>* carbons (R1 to R5) may affect the strengths of N–H···N, N–H···S, N-H···O, C-H···N HBs, which, in

turn, decide the stability of these conformers. Hence, the IHB strengths in substituted **1**, **2**, and **3** were determined by the MTA-based methodology. The estimated N–H···N HB energies were between 11.0 to 15.6 kcal/mol at B3LYP/6-311+G(d,p) level, the individual bifurcated N–H···N interactions being ~6.0 kcal/mol. The N-H···O (~10.0 kcal/mol) and N–H···S (11.2 kcal/mol) HBs were found to be weaker than the N–H···N HBs, with the C-H···N HBs being the weakest (0.1 to 4.4 kcal/mol) [90]. The substituent effect on IHB strength was also investigated [90,91].

**Figure 6.** Structures of meta-benziporphodimethene **1** and N-confused meta-benziporphodimethene containing γ-lactam ring isomer (O-up, **2**). See text for details.

It has been suggested that intramolecular O–H···O and resonance-assisted (RA) O– H···O=C HBs may have a pronounced effect on the antioxidant activity of the natural products [104–107]. Hence, an attempt was made to obtain reliable estimates of IHB energies in these molecules [92]. The presence of an RA IHB was seen in all the antioxidant molecules studied. In some molecules, this type of HB was found to be in the nature of two bifurcated HBs along with IHBs such as O–H···OCH3, O–H···OH, and O–H···O(ring) also being present. The energies of O–H···OCH3 HBs were found to lie between 2.2 to 2.4 kcal/mol, with the O–H···O (ring) HB energies being much smaller (~0.5 to 0.6 kcal/mol) at the MP2/6-311G(d,p) level. The energy of RA O–H···O=C IHB being largest (10.0 to 17.9 kcal/mol.) Recently, Restropo et al. [108] suggested that the weak HBs are directly related to the antioxidant properties of these molecules. The reliable estimates of the strengths of these weak HBs by the MTA-based method could be useful for quantitative structure–activity relationship (QSAR) studies on a larger set of antioxidant molecules.

#### **7. Use of the MTA-Based Method by Other Researchers**

We summarize here the use of our MTA-based method for the estimation of IHB energy by other researchers [109–117]. In an early use of the method, Lopes Jesus et al. [109] studied the 65 local minima conformers of 1,4-butanediol molecule. The H···O IHB energies in the two lowest energy conformers (c1, c2) were estimated using the MTA method to be 5.5 and 4.1 kcal/mol, respectively. The IHB energies were also obtained by two other methods, viz., conformational analysis (CA) [33,41,42] and use of the empirical Iogansen equation (IE) to spectroscopic data [110]. The IHB energy values turned out to be CA: (4.5 and 3.1 kcal/mol) and IE: (4.1 and 2.2 kcal/mol), in good qualitative agreemen<sup>t</sup> with their MTA counterparts.

Rusinska-Roszak et al. extensively used the MTA-based method [111–113]. In an early work [111], they estimated the O–H···O=C IHB energies in several aliphatic systems. However, their fragmentation scheme consisted of two appropriately made primary fragments and an overlapping fragment. The IHB energy was estimated, by using the energies of these three fragments and the actual energy of the parent system, ignoring the ternary and quaternary overlap fragments. The estimated IHB energies at MP2/6-311++(2d,2p) level in the saturated hydroxyl compounds were between 1.4 to 7.0 kcal/mol and 13.7 kcal/mol in the unsaturated ones [111].

In another work [112], they estimated the O − H···O=C IHB energies in 299 structures of hydroxycarbonyl aliphatic compounds involving resonance-assisted HB. The estimated IHB energies showed a wide range, from 8.2 to 26.3 kcal/mol. The HB energies showed a good qualitative correlation with other indirect measures of HB strength, viz., geometrical parameters, the O–H stretching frequencies, and the MED values at the BCP [112].

These authors [113] also applied the MTA-based method for the estimation of Ar–O– H···O=C HBs in mono-, di-, and triphenols substituted (by electron-donating/withdrawing groups) at the ortho- position by carbonyl-containing functional groups. The estimated HB energies for phenolic O–H···O=C (six-membered ring) fall in the range of 5.4 to 15.4 kcal/mol at MP2/6-311++G(2d,2p) level. These HBs energies are smaller (4.6 to 9.6 kcal/mol) when the O=C group is a part of seven or eight-membered rings. These HBs' energy range is similar to corresponding HBs involving saturated carbonyl substituted alcohols.

Very recently, Afonin et al. [114] applied our method for estimating the energy of push– pull effect in *β*-diketones. In this push–pull system, the intramolecular charge transfer (ICT) occurs as a result of interaction between the π-donor and -acceptor parts, joined by a π linker. Further, the IHB is also present in the *Z*-conformation of *β*-diketones. Here, basic idea is to estimate the π component of conjugation energy in these systems. For this purpose, an *E* conformation of the parent *β*-diketones was considered wherein this HB is not present. The molecule in this configuration was fragmented using the MTA-based method. The donor and acceptor groups involved in ICT interaction were separated into two primary fragments, F1 and F2, and the overlapping fragment, F3, is the conjugation unit connecting these groups. The energy expression for the π conjugation energy is similar to that discussed in Section 3, viz., E*π*(MTA) = [(EF1 + EF2 − EF3) − EM], E M being the energy of the parent molecule in *E* configuration. The effect of electron-donating and -withdrawing groups on the π component of conjugation energy was also estimated. The authors stated [114] that "although the choice of the fragmentation scheme and the computational protocol used did not play a decisive role in estimating the energies of the same IMHB, this issue also needs to be investigated when estimating the conjugation energy."

Afonin et al. [115] applied the methodology for the quantitative decomposition of RAHB energy in β-diketones into resonance and hydrogen bonding components. They also compared the estimated HB energy by the MTA method with that obtained by the functional-based approach (FBA). In FBA, the HB energy is written as an empirical function of HB descriptors, EHB = f(D), the parameter D is one of the H-bond descriptors (i.e., geometrical, topological, and/or spectral characteristics of the H-bond). For details of these empirical FBA equations, see Ref. [115]. It has been shown by these authors that the FBA method evaluates "the component of RAHB interaction corresponding to the energy of the pure H-bond without resonance component." However, the MTA method implicitly takes into account the π component in the RAHB interaction and hence "the difference in the energy of the IMHB as evaluated by means of the MTA and FBA yields a quantitative estimate of the resonance component in the case of the resonance-assisted hydrogen bonds" [115]. The resonance component energy was reported to be 6 to 7 kcal/mol for the weak to strong RAHB, respectively. The HB component varied in the wide range from 2 to 20 kcal/mol in a series of the β-diketone molecules [115]. In summary, the energy of IHB by the MTA-based method provides reliable values for the RAHB, including both the resonance and HB components.

Recently the IHB energies estimated by the MTA-based method were compared with those obtained by other indirect HB descriptors for the wide range of malonaldehyde derivatives by Nowroozi et al. [116]. The latter included structural, spectroscopic, topological, and molecular orbital parameters in the intramolecular RAHBs. The substituent effect of electron-donating and -accepting groups on the HB energy was also estimated by the MTA-based method [116]. Further, the significance of π-electron delocalization (π-ED) of RAHB rings was evaluated by the geometrical factor and the harmonic oscillator model of aromaticity (HOMA). The authors [116] stated that "the excellent linear correlations with MTA energies, which may be implied on the validity of RAHB theory". Further, it was emphasized by authors that "On the basis of these results, one can claim that the MTA method is reliable for estimation of IMHB energies of RAHB systems."

A significant application of our MTA-method was in the determination of the push– pull π+/π<sup>−</sup> (PPππ) effect in the Henry reaction [117], an organocatalytic reaction catalyzed by squaramide [118]. In this reaction, several noncovalent interactions such as HBs, <sup>π</sup>···H, <sup>π</sup>···O, etc. were observed between the squaramide and benzaldehyde. It was suggested that the reaction proceeds via an unprecedented mode of activation, modulated by π···H (<sup>π</sup>···δ+) and <sup>π</sup>···O (<sup>π</sup>···δ−) interactions formed with the two rings of a naphthyl group and benzaldehyde. These authors employed the MTA-based approach for determining the energies of these two π interactions [118]. Here, the naphthyl group involved in the PPππ interactions, observed in the intermediates (INTs) and transition state (TS) structures, along the most favorable pathway (P1), was replaced with an H atom. Thus, generated INTs and TS structures along the modeled pathway (P1–H) have the same noncovalent interactions as P1, except the two π interactions whose energy is to be determined. The interaction energy of these two π interactions in the INTs and TS structures were estimated as the energy difference in the total interaction energies between the catalyst and the substrates in P1 and that in modeled P1−H pathways. The estimated sum of two π interactions in INTs and TS were found to be between 2.7 to 4.7 kcal/mol at the ωB97X-D level of theory. In summary, the MTA-based method proposed by us has been successfully employed by several other active research groups for exploring the strengths of IHBs and other intramolecular noncovalent interactions in a variety of systems.

## **8. Summary and Concluding Remarks**

This review article has summarized a direct and simple procedure for the estimation of X–H···Y IHB energy employing a fragmentation method, viz., the molecular tailoring approach (MTA). It has been applied to a variety of systems having multiple HBs over the last one and half decades. A plus point of the method is that it provides the reliable energy of every individual HB and can also estimate the corresponding cooperativity contribution as a result of interconnected networks of HBs. In this present review article, we have discussed the application of the MTA-based method for the estimation of X–H···Y (X–H = O–H, N–H, C–H, etc. and Y = N, O, S, OH, OCH3, O=C, etc.) HB energies in a variety of systems. The systems covered ranged from small alkanediols to large systems such as cyclodextrins and biomolecules such as polypeptides, meta-benzoporphodimethenes, and antioxidant molecules. Further, being of general nature, our method has been utilized as a standard method for a reliable estimation of HB energies by other research groups. It may be emphasized here that the MTA-based method is applicable for the estimation of other noncovalent interactions as well. In recent years, this approach has been applied for the estimation of O–H···O HB energies in water clusters, the π component of the conjugation energy in resonance-assisted, hydrogen-bonded push–pull systems, etc. In a recent impressive application, the method is employed for determining the favorable organocatalytic reaction pathways [118].

It may be noted that the present method can, in principle, be applied to the estimation of IHB energy in larger molecular systems. However, with the increase in the size of a molecule, the size of the fragments would also increase, making the evaluation of HB energies computationally rather demanding. This difficulty can, in principle, be

overcome by the use of the MTA methodology discussed in Section 2. For instance, the energy of the parent and fragment molecules can be reliably calculated using MTA at a correlated level of theory which may be further used for estimating the HB energies in larger molecular systems.

Being general in nature, the MTA-based method can be employed for exploring other intramolecular interactions such as π··· π [119], C-H··· π [120], the so-called halogen bonds [121], dihydrogen bonds [122], sulfur bonds [123], metal-H···S and metal-H···Se bonds [124], etc. Although identified in the recent literature by these labels, they are cut from the same cloth called the *non-covalent interactions*. The prowess of the MTA-based method is that it can be applied to all such inter- and intramolecular interactions.

**Author Contributions:** M.M.D. and S.R.G. contribute equally to this article, conceptualization, methodology, writing and review. All authors have read and agreed to the published version of the manuscript.

**Funding:** The publication of this research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding authors.

**Acknowledgments:** M.M.D. thanks the University Grant Commission (UGC), New Delhi, for the Start-up gran<sup>t</sup> (F.30-56/2014/BSR). S.R.G. is thankful to the National Supercomputing Mission (NSM) for support under the project [CORP: DG:3187], which enabled the use of computational resources at the PARAM Shivay facility at IIT, BHU.

**Conflicts of Interest:** The authors declare no conflict of interest.
