Estimation of N-H...O=C intramolecular hydrogen bond energy in polypeptides

Molecular Tailoring Approach for the Direct Estimation of Individual Noncovalent Interaction Energies in Molecular Systems

The noncovalent interactions (NCIs) are omnipresent in chemistry, physics, and biology. The study of such interactions offers insights into various physicochemical phenomena. Some indirect approaches proposed in the literature for exploring the NCIs are briefly reviewed in Section 1 of this Perspective. These include: (i) Shift in the stretching frequency of an X-Y bond involved in X-Y···Z interaction. (ii) Topological analysis of molecular electron density. (iii) Empirical equations derived employing experimental and theoretical quantities. However, a direct method for estimating individual intramolecular/intermolecular interaction energies has been conspicuous by its absence from the literature. We have developed a molecular tailoring approach (MTA)-based method enabling a direct and reliable estimation of the energy of intra- as well as intermolecular interactions. This method offers a direct and reliable estimation of these interactions, in particular of the hydrogen bonds (HB) in molecules/weakly bound clusters along with the respective cooperativity contribution. In Section 2, the basis of our method is discussed, along with some illustrative examples. The application of this method to a variety of molecules and clusters, with a special emphasis on estimating the HB energy along with the energy of other NCIs is presented in Section 3. Section 4 discusses some computational strategies for applying our method to large molecular clusters. The last Section provides a summary and a discussion on future developments.

Acyl Capping Group Identity Effects on α-Helicity: On the Importance of Amide·Water Hydrogen Bonds to α-Helix Stability

Acyl capping groups stabilize α-helices relative to free N-termini by providing one additional C═Oi···Hi+4-N hydrogen bond. The electronic properties of acyl capping groups might also directly modulate α-helix stability: electron-rich N-terminal acyl groups could stabilize the α-helix by strengthening both i/i + 4 hydrogen bonds and i/i + 1 n → π* interactions. This hypothesis was tested in peptides X-AKAAAAKAAAAKAAGY-NH2, where X = different acyl groups. Surprisingly, the most electron-rich acyl groups (pivaloyl and iso-butyryl) strongly destabilized the α-helix. Moreover, the formyl group induced nearly identical α-helicity to that of the acetyl group, despite being a weaker electron donor for hydrogen bonds and for n → π* interactions. Other acyl groups exhibited intermediate α-helicity. These results indicate that the electronic properties of the acyl carbonyl do not directly determine the α-helicity in peptides in water. In order to understand these effects, DFT calculations were conducted on α-helical peptides. Using implicit solvation, α-helix stability correlated with acyl group electronics, with the pivaloyl group exhibiting closer hydrogen bonds and n → π* interactions, in contrast to the experimental results. However, DFT and MD calculations with explicit water solvation revealed that hydrogen bonding to water was impacted by the sterics of the acyl capping group. Formyl capping groups exhibited the closest water-amide hydrogen bonds, while pivaloyl groups exhibited the longest. In α-helices in the PDB, the highest frequency of close amide-water hydrogen bonds is observed when the N-cap residue is Gly. The combination of experimental and computational results indicates that solvation (hydrogen bonding of water) to the N-terminal amide groups is a central determinant of α-helix stability.

Hydrogen bond energy estimation (H-BEE) in large molecular clusters: A Python program for quantum chemical investigations

A procedure, derived from the fragmentation-based molecular tailoring approach (MTA), has been proposed and extensively applied by Deshmukh and Gadre for directly estimating the individual hydrogen bond (HB) energies and cooperativity contributions in molecular clusters. However, the manual fragmentation and high computational cost of correlated quantum chemical methods make the application of this method to large molecular clusters quite formidable. In this article, we report an in-house developed software for automated hydrogen bond energy estimation (H-BEE) in large molecular clusters. This user-friendly software is essentially written in Python and executed on a Linux platform with the Gaussian package at the backend. Two approximations to the MTA-based procedure, viz. the first spherical shell (SS1) and the Fragments-in-Fragments (Frags-in-Frags), enabling cost-effective, automated evaluation of HB energies and cooperativity contributions, are also implemented in this software. The software has been extensively tested on a variety of molecular clusters and is expected to be of immense use, especially in conjunction with correlated methods such as MP2, CCSD(T), and so forth.

Interplay of Hydrogen, Pnicogen, and Chalcogen Bonding in X(H2O)n=1-5 (X = NO, NO+, and NO-) Complexes: Energetics Insights via a Molecular Tailoring Approach

Nitric oxide (NO) and its redox congeners (NO+ and NO-), designated as X, play vital roles in various atmospheric and biological events. Understanding the interaction between X and water is inevitable to explain the different reactions that occur during these events. The present study is a unified attempt to explore the noncovalent interactions in microhydrated networks of X using the MP2/aug-cc-pVTZ//MP2/6-311++G(d,p) level of theory. The interactions between X and water have been probed by the molecular electrostatic potential (MESP) by exploiting the features of the most positive (Vmax) and most negative potential (Vmin) sites. The individual energy and cooperativity contributions of various types of noncovalent interactions present in X(H2O)n=1-5 complexes are estimated with the help of a molecular tailoring-based approach (MTA-based). The MTA-based analysis reveals that among various possible interactions in NO(H2O)n complexes, the water···water hydrogen bonds (HBs) are the strongest. Neutral NO can form hydrogen and pnicogen bonds (PBs) with water depending on the orientation; however, such HBs and PBs are the weakest. On the other hand, in the NO+(H2O)n complexes, the NO+···water interactions that occur through PBs are the strongest; the next one is the chalcogen bonding (CB), and the water···water HBs are the weakest. In the case of the NO-(H2O)n complexes, the HB interactions via both N and O atoms of NO- and water molecules are the strongest ones. The strength of water···water HB interactions is also seen to increase with the increase in the number of water molecules in NO-(H2O)n. The present study exemplifies the applicability of MTA-based calculations for quantifying various types of individual noncovalent interactions and their interplay in microhydrated networks of NO and its related ions.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

Fragments-in-fragments method for efficient and reliable estimates of individual hydrogen bond energies in large molecular clusters

The knowledge of individual hydrogen bond (HB) strength in molecular clusters is indispensable to get insights into the bulk properties of condensed systems. Recently, we have developed the molecular tailoring approach based (MTA-based) method for the estimation of individual HB energy in molecular clusters. However, the direct use of this MTA-based method to large molecular clusters becomes progressively difficult with the increase in the size of a cluster. To overcome this caveat, herein, we propose the use of linear scaling method (such as the original MTA method) for the estimation of single-point (SP) energies of large-sized parent molecular cluster and their respective fragments. Because the fragments of the MTA-based method, for the estimation of HB energy, are further fragmented, this proposed strategy is called as Fragments-in-Fragments (Frags-in-Frags) method. The SP energies of fragments and parent cluster calculated by the Frags-in-Frags approach were utilized to estimate the individual HB energy. The estimated individual HB energies, in various molecular clusters, by Frags-in-Frags method are found to be in excellent linear agreement with their MTA-based counterparts (R²  = 0.9975 of 348 data points). The difference being less than 0.5 kcal/mol in most of the cases. Furthermore, RMSD is 0.43 kcal/mol, MAE is 0.33 kcal/mol, and the standard deviation is 0.44 kcal/mol. Importantly, the Frags-in-Frags method not only enables the reliable estimation of HB energy in large molecular clusters but also requires less computational time and can be possible even with off-the-shelf hardware.

On the Short-Range Nature of Cooperativity in Hydrogen-Bonded Large Molecular Clusters

The variation in the hydrogen bond (HB) strength has considerable consequences on the physicochemical properties of molecular clusters. Such a variation mainly arises due to the cooperative/anti-cooperative networking effect of neighboring molecules connected by HBs. In the present work, we systematically study the effect of neighboring molecules on the strength of an individual HB and the respective cooperativity contribution toward each of them in a variety of molecular clusters. For this purpose, we propose a use of a small model of a large molecular cluster called the spherical shell-1 (SS1) model. This SS1 model is constructed by placingg the spheres of an appropriate radius centered on X and Y atoms of the X-H···Y HB under consideration. The molecules falling within these spheres constitute the SS1 model. Utilizing this SS1 model, the individual HB energies are calculated within the molecular tailoring approach-based framework and the results are compared with their actual counterparts. It is found that the SS1 is a reasonably good model of large molecular clusters, providing 81-99% of the total HB energy estimated using the actual molecular clusters. This in turn suggests that the maximum cooperativity contribution toward a particular HB is due to the fewer number of molecules (in the SS1 model) directly interacting with two molecules involved in its formation. We further demonstrate that the remaining part of the energy or cooperativity (∼1 to 19%) is captured by the molecules falling in the second spherical shell (SS2) centered on the hetero-atom of the molecules in the SS1 model. The effect of increasing size of a cluster on the strength of a particular HB, calculated by the SS1 model, is also investigated. The calculated value of the HB energy remains unchanged with the increase in the size of a cluster, emphasizing the short-ranged nature of the HB cooperativity in neutral molecular clusters.

Two-Step ONIOM Method for the Accurate Estimation of Individual Hydrogen Bond Energy in Large Molecular Clusters

The study of molecular clusters to understand the properties of condensed systems has been the subject of immense interest. To get insight into these properties, the knowledge of various noncovalent interactions present in these molecular clusters is indispensable. Our recently developed molecular tailoring approach-based (MTA-based) method for the estimation of the individual hydrogen bond (HB) energy in molecular clusters is useful for this purpose. However, the direct application of this MTA-based method becomes progressively difficult with the increase in the size of the cluster. This is because of the difficulty in the evaluation of single-point energy at the correlated level of theory. To overcome this caveat, herein, we propose a two-step method within the our own N-layer integrated molecular orbital molecular mechanics (ONIOM) framework. In this method, the HB energy evaluated by the MTA-based method employing the actual molecular cluster at a low Hartree-Fock (HF) level of theory is added to the difference in the HB energies evaluated by the MTA-based method, employing an appropriate small model system, called the shell-1 model, calculated at high (MP2) and low (HF) levels of theory. The shell-1 model of a large molecular cluster is made up of only a few molecules that are in direct contact (by a single HB) with the two molecules involved in the formation of an HB under consideration. We tested this proposed two-step ONIOM method to estimate the individual HB energies in various molecular clusters, viz., water (W_n, n = 10-16, 18 and 20), (H₂O₂)₁₂, (H₂O₃)₈, (NH₃)_n and strongly interacting (HF)₁₅ and (HF)_m(W)_n clusters. Furthermore, these estimated individual HB energies by the ONIOM method are compared with those calculated by the MTA-based method using actual molecular clusters. The estimated individual HB energies by the ONIOM method, in all these clusters, are in excellent linear one-to-one agreement (R² = 0.9996) with those calculated by the MTA-based method using actual molecular clusters. Furthermore, the small values of root-mean-square deviation (0.06), mean absolute error (0.04), |ΔE_max| (0.21) and Sε (0.06) suggest that this two-step ONIOM method is a pragmatic approach to provide accurate estimates of individual HB energies in large molecular clusters.

Quantum chemical studies on hydrogen bonds in helical secondary structures

We present a brief review of our recent computational studies of hydrogen bonds (H-bonds) in helical secondary structures of proteins, α-helix and 3₁₀-helix, using a Negative Fragmentation Approach with density functional theory. We found that the depolarized electronic structures of the carbonyl oxygen of the ith residue and the amide hydrogen of the (i + 4)th residue cause weaker H-bond in an α-helix than in an isolated H-bond. Our calculations showed that the H-bond energies in the 3₁₀-helix were also weaker than those of the isolated H-bonds. In the 3₁₀-helices, the adjacent N-H group at the (i + 1)th residue was closer to the C=O group of the H-bond pair than the adjacent C=O group in the 3₁₀-helices, whereas the adjacent C=O group at the (i + 1)th residue was close to the H-bond acceptor in α-helices. Therefore, the destabilization of the H-bond is attributed to the depolarization caused by the adjacent residue of the helical backbone connecting the H-bond donor and acceptor. The differences in the change in electron density revealed that such depolarizations were caused by the local electronic interactions in their neighborhood inside the helical structure and redistributed the electron density. We also present the improvements in the force field of classical molecular simulation, based on our findings.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12551-022-01034-5.

Revealing the Reasons for Degeneration of Resonance-Assisted Hydrogen Bond on the Aromatic Platform: Calculations of Ortho-, Meta-, Para-Disubstituted Benzenes, and (Z)-(E)-Olefins

The energies of the O-H∙∙∙O=C intramolecular hydrogen bonds were compared quantitatively for the series of ortho-disubstituted benzenes and Z-isomers of olefins via a molecular tailoring approach. It was established that the hydrogen bond energy in the former series is significantly less than that in the latter one. The reason for lowering the hydrogen bond energy in the ortho-disubstituted benzenes compared to the Z-isomers of olefins is the decrease in the π-contribution to the total energy of the complex interaction, in which the hydrogen bond per se is enhanced by the resonance effect. By the example of the para- and meta-disubstituted benzenes, as well as E-isomers of olefins, it was explicitly shown that the aromatic ring is a much poorer conductor of the resonance effect compared to the double bond. The hydrogen bond in the ortho-disubstituted benzenes has a lower energy than a typical resonance-assisted hydrogen bond because the aromatic moiety cannot properly assist the hydrogen bond with a resonance effect. Thus, a hydrogen bond on an aromatic platform should fall into a special category, namely an aromaticity-assisted hydrogen bond, which is closer by nature to a simple hydrogen bond rather than to a resonance-assisted one.

Tuning the thermodynamic, optical, and rheological properties of thermoresponsive polymer solutions via silica nanoparticle shape and concentration

HYPOTHESIS

The shape and quantity of hydrophilic silica nanoparticles (NPs) can be used to tune the microstructure, rheology, and stability of phase-separating polymer solutions. In thermoresponsive polymer systems, silica nanospheres are well-studied whereas anisotropic NPs have little literature precedent. Here, we hypothesize that NP shape and concentration lower the onset of rheological and turbidimetric transitions of aqueous poly(N-isopropyl acrylamide) (PNIPAM) solutions.

EXPERIMENTS

Differential scanning calorimetry (DSC), Fourier-transform infrared spectroscopy (FTIR), turbidimetry, and oscillatory rheology are utilized to examine interactions between NPs, PNIPAM, and water and to track changes in phase separation and rheological properties due to NP concentration and shape.

FINDINGS

NP addition reduces phase separation enthalpy due to PNIPAM-NP hydrogen bonding interactions, the degree to which depends on polymer content. While NP addition minorly impacts thermodynamic and optical properties, rheological transitions and associated rheological properties are dramatically altered with increasing temperature, and depend on NP quantity, shape, and polymer molecular weight. Thus NP content and shape can be used to finely tune transition temperatures and mechanical properties for applications in stimuli-responsive materials.

A Tug of War between the Self- and Cross-associating Hydrogen Bonds in Neutral Ammonia-Water Clusters: Energetic Insights by Molecular Tailoring Approach

In the present work, the energies of various types of individual HBs observed in neutral (NH₃ )_m (H₂ O)_n , (m+n=2 to 7) clusters were estimated using the molecular tailoring approach (MTA)-based method. The calculated individual HB energies suggest that the O-H…N HBs are the strongest (1.21 to 12.49 kcal mol^-1 ). The next ones are the O-H…O (3.97 to 9.30 kcal mol^-1 ) HBs. The strengths of N-H…N (1.09 to 5.29 kcal mol^-1 ) and N-H…O (2.85 to 5.56 kcal mol^-1 ) HBs are the weakest. The HB energies in dimers also follow this rank ordering. However, the HB energies in dimers are much smaller than those obtained by the MTA-based method due to the loss in cooperativity contribution in the dimers. Thus, the calculated cooperativity contributions, for different types of HBs, fall in the range 0.64 to 5.73 kcal mol^-1 . We wish to emphasize based on the energetic rank ordering obtained by the MTA-based method that the O-H of water is a better HB donor than the N-H of ammonia. The reasons for the observed energetic rank ordering are two folds: (i) intrinsically stronger O-H…N HBs than the O-H…O ones as revealed by dimer energies and (ii) the higher cooperativity contribution in the former than the later ones. Indeed, the MTA-based method is useful in providing the missing energetic rank ordering of various type of HBs in neutral (NH₃ )_m (H₂ O)_n clusters, in the literature.

Depolarizing Effects in Hydrogen Bond Energy in 310-Helices Revealed by Quantum Chemical Analysis

Hydrogen-bond (H-bond) energies in 3₁₀-helices of short alanine peptides were systematically examined by precise DFT calculations with the negative fragmentation approach (NFA), a modified method based on the molecular tailoring approach. The contribution of each H-bond was evaluated in detail from the 3₁₀-helical conformation of total energies (whole helical model, WH_3-10 model), and the results were compared with the property of H-bond in α-helix from our previous study. The H-bond energies of the WH_3-10 model exhibited tendencies different from those exhibited by the α-helix in that they depended on the helical position of the relevant H-bond pair. H-bond pairs adjacent to the terminal H-bond pairs were observed to be strongly destabilized. The analysis of electronic structures indicated that structural characteristics cause the destabilization of the H-bond in 3₁₀-helices. We also found that the longer the helix length, the more stable the H-bond in the terminal pairs of the WH_3-10 model, suggesting the action of H-bond cooperativity.

Energetic Ordering of Hydrogen Bond Strengths in Methanol-Water Clusters: Insights via Molecular Tailoring Approach

In this work, we examine the strength of various types of individual hydrogen bond (HB) in mixed methanol-water M_n W_m , (n+m=2 to 7) clusters, with an aim to understand the relative order of their strength, using our recently proposed molecular tailoring-based approach (MTA). Among all the types of HB, it is observed that the O_M -H…O_W HBs are the strongest (6.9 to 12.4 kcal mol^-1 ). The next ones are O_M -H…O_M HBs (6.5 to 11.6 kcal mol^-1 ). The O_W -H…O_W (0.2 to 10.9 kcal mol^-1 ) and O_W -H…O_M HBs (0.3 to 10.3 kcal mol^-1 ) are the weakest ones. This energetic ordering of HBs is seen to be different from the respective HB energies in the dimer i. e., O_M -H…O_M (5.0 to 6.0 kcal mol^-1 )>O_W -H…O_M (1.5 to 6.0 kcal mol^-1 )>O_M -H…O_W (3.8 to 5.6 kcal mol^-1 )>O_W -H…O_W (1.2 to 5.0 kcal mol^-1 ). The plausible reason for the difference in the HB energy ordering may be attributed to the increase or decrease in HB strengths due to the formation of cooperative or anti-cooperative HB networks. For instance, the cooperativity contribution towards the different types of HB follows: O_M -H…O_W (2.4 to 8.6 kcal mol^-1 )>O_M -H…O_M (1.3 to 6.3 kcal mol^-1 )>O_W -H…O_W (-1.0 to 6.5 kcal mol^-1 )>O_W -H…O_M (-1.2 to 5.3 kcal mol^-1 ). This ordering of cooperativity contribution is similar to the HB energy ordering obtained by the MTA-based method. It is emphasized here that, the interplay between the cooperative and anti-cooperative contributions are indispensable for the correct energetic ordering of these HBs.

Guide to tuning the chalcone molecular properties based on the push-pull effect energy scale created via the molecular tailoring approach

Using the molecular tailoring approach, a total energy scale for the push-pull effect in the range from -40 to 100 kcal/mol is created for the wide series of neutral, charged and doubly charged compounds on the chalcone platform. Taking into account similar energy scale for hydrogen bonds, the strength of the push-pull effect is ranked in the seven categories, ranging from negative (anti-push-pull) to very weak and very strong push-pull effect. It is demonstrated that the molecular properties of chalcone can be tuned prior synthesis due to the created energy scale for the push-pull effect. The single bonds of the π-spacer in the chalcones are shortened, the double ones are lengthened, and the C=O bond vibrations are red shifted when the push-pull effect is enhanced along the energy scale. The HOMO and LUMO energies change systematically while the HOMO-LUMO energy gap narrows as the strength of the push-pull effect increases.

Hydration Shell Model for Expeditious and Reliable Individual Hydrogen Bond Energies in Large Water Clusters

Recently, we have developed and tested a method, based on the molecular tailoring approach (MTA-based) to directly estimate the individual hydrogen bond (HB) energies in molecular clusters. Application of this...

Assessment of hydrogen bond strengths and cooperativity in self- and cross-associating cyclic (HF)m(H2O)n (m + n = 2 to 8) clusters

In this work, we investigated the strengths of various self- and cross-associating hydrogen bonds (HBs) in mixed hydrogen fluoride–water cyclic (HF)m(H2O)n (m + n = 2 to 8) clusters, employing a molecular tailoring approach (MTA)-based method.

Unusually Large Hydrogen-Bond Cooperativity in Hydrogen Fluoride Clusters, (HF)n, n = 3 to 8, Revealed by the Molecular Tailoring Approach

In this work, our recently proposed molecular tailoring approach (MTA)-based method is employed for the evaluation of individual hydrogen-bond (HB) energies in linear (L) and cyclic (C) hydrogen fluoride clusters, (HF)_n (n = 3 to 8). The estimated individual HB energies calculated at the MP2(full)/aug-cc-pVTZ level for the L-(HF)_n are between 6.2 to 9.5 kcal/mol and those in the C-(HF)_n lie between 7.9 to 11.4 kcal/mol. The zero-point energy corrections and basis set superposition corrections are found to be very small (less than 0.6 and 1.2 kcal/mol, respectively). The cooperativity contribution toward individual HBs is seen to fall between 1.0 to 4.8 kcal/mol and 3.2 to 6.9 kcal/mol for linear and cyclic clusters, respectively. Interestingly, the HB energies in dimers, cleaved from these clusters, lie in a narrow range (4.4 to 5.2 kcal/mol) suggesting that the large HB strength in (HF)_n clusters is mainly due to the large cooperativity contribution, especially for n ≥ 5 (50 to 62% of the HBs energy). Furthermore, the HB energies in these clusters show a good qualitative correlation with geometrical parameters (H···F distance and F-H···F angles), stretching frequencies of F-H bonds, and electron density values at the (3, -1) bond critical points.

Appraisal of individual hydrogen bond strengths and cooperativity in ammonia clusters via a molecular tailoring approach

In this work, we propose and test a method, based on the molecular tailoring approach (MTA), for the evaluation of individual hydrogen bond (HB) energies in ammonia (NH₃)_n clusters. This methodology was tested, in our earlier work, on water clusters. Liquid ammonia being a universal, non-aqueous ionizing solvent, such information of individual HB strength is indispensable in many studies. The estimated HB energies by an MTA-based method, in (NH₃)_n for n = 3-8, were calculated to be in the range of 0.65 to 5.54 kcal mol^-1 with the cooperativity contribution falling between -0.54 and 1.88 kcal mol^-1 both calculated at the MP2(full)/aug-cc-pVTZ level of theory. It is seen that the strong HBs in (NH₃)_n clusters were additionally strengthened by the large contribution of HB cooperativity. The accuracy of these estimated HB energies was validated by approximately estimating the molecular energy of a given cluster by adding the sum of HB energies to the sum of monomer energies. This approximately estimated molecular energy of a given cluster was found to be in excellent agreement with the actual calculated values. The negligibly small difference (less than 5.6 kcal mol^-1) in these two values suggests that the estimated individual HB energies in ammonia clusters are quite reliable. Furthermore, these estimated HB energies by MTA are in excellent qualitative agreement with the other indirect measures of HB strength, such as HB bond distances and angles, N-H stretching frequency and the electron density values at the (3,-1) bond critical points.

Molecular Tailoring Approach for Estimating Individual Intermolecular Interaction Energies in Benzene Clusters

There is no general method available for the estimation of individual intermolecular interaction energies in weakly bound molecular clusters, and such studies are limited only to the dimer. Recently, we proposed a molecular tailoring approach-based method for the estimation of individual O-H···O hydrogen bond energies in water clusters. In the present work, we extend the applicability of this method for estimating the individual intermolecular interaction energies in benzene clusters, which are expected to be small. The basis set superposition error (BSSE)-corrected individual intermolecular interaction energies in linear (LN) benzene clusters, LN-(Bz)_n n = 3-7, were calculated to be in the range from -1.75 to -2.33 kcal/mol with the cooperativity contribution falling between 0.05 and 0.20 kcal/mol, calculated at the MP2.5/aug-cc-pVDZ level of theory. In the case of non-linear (NLN) benzene clusters, NLN-(Bz)_n n = 3-5, the BSSE-corrected individual intermolecular interaction energies exhibit a wider range from -1.16 to -2.55 kcal/mol with cooperativity contribution in the range from 0.02 to -0.61 kcal/mol. The accuracy of these estimated values was validated by adding the sum of interaction energies to the sum of monomer energies. These estimated molecular energies of clusters were compared with their actual calculated values. The small difference (<0.3 kcal/mol) in these two values suggests that our estimated individual intermolecular interaction energies in benzene clusters are quite reliable.

Interaction-Deletion: A Composite Energy Method for the Optimization of Molecular Systems Selectively Removing Specific Nonbonded Interactions

The complex interactions between different portions of a large molecule can be challenging to analyze through traditional electronic structure calculations. Moreover, standard methods cannot easily quantify the physical consequences of individual pairwise interactions inside a molecule. By creating a set of molecular fragments, we propose a composite energy method to explore changes in a molecule caused by removing selected nonbonded interactions between different molecular portions. Energies and forces are easily obtained with this composite approach, allowing geometry optimizations that lead to chemically meaningful structures that describe how the omitted interactions contribute to changes in the local geometrical minima. We illustrate the application of our new hybrid scheme by computing the influence of intramolecular hydrogen-bonding interactions in two small molecules: 1,6-(tG⁺G⁺TG⁺G⁺g^-)-hexanediol and a cyclic analogue, cis-1,4-cyclohexanediol. The resulting structural and energetic changes are interpreted to yield key physical insights and quantify concepts such as "preparation energy" or "reorganization energy". We demonstrate that the composite method can be extended to larger molecular systems by showing its application on a Si(100) surface model containing interactions between dissociated ammonia molecules on adjacent surface dimers. The scheme's efficacy is also tested by applying it to systems having multiple intramolecular interactions, viz., 3₁₀-polyglycine and H⁺GPGG. Furthermore, the cooperative nature of intramolecular hydrogen bonds is explored by using interaction-deletion in 2-nitrobenzene-1,3-diol.

Molecular Tailoring Approach for the Estimation of Intramolecular Hydrogen Bond Energy

Hydrogen bonds (HBs) play a crucial role in many physicochemical and biological processes. Theoretical methods can reliably estimate the intermolecular HB energies. However, the methods for the quantification of intramolecular HB (IHB) energy available in the literature are mostly empirical or indirect and limited only to evaluating the energy of a single HB. During the past decade, the authors have developed a direct procedure for the IHB energy estimation based on the molecular tailoring approach (MTA), a fragmentation method. This MTA-based method can yield a reliable estimate of individual IHB energy in a system containing multiple H-bonds. After explaining and illustrating the methodology of MTA, we present its use for the IHB energy estimation in molecules and clusters. We also discuss the use of this method by other researchers as a standard, state-of-the-art method for estimating IHB energy as well as those of other noncovalent interactions.

Strong intramolecular hydrogen bonding in confined amino acids

Intramolecular hydrogen bonding is evaluated in three different amino acids encapsulated in C₆₀ fullerene in the context of electron density analysis. While conventional intramolecular hydrogen bonding in isolated amino acids are dominated by electrostatic character, it is shown that strong intramolecular hydrogen bonding can be formed in confined amino acids so that in two cases covalent intramolecular hydrogen bonding is appeared in the confined species. Also, results show that zwitterionic amino acids are stable in confined state, where no implicit or explicit solvation is applied. Covalent character for intramolecular hydrogen bonding in amino acids have not yet been reported.

Direct and Reliable Method for Estimating the Hydrogen Bond Energies and Cooperativity in Water Clusters, Wn, n = 3 to 8

No direct method for estimating the individual O-H···O hydrogen bond (H-bond) energies in water clusters (W_n) exists in the literature. In this work, we propose such a direct method based on the molecular tailoring approach, which also enables the estimation of the cooperativity contributions. The calculated H-bond energies at MP2(full)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVDZ levels for W_n, n = 3 to 8, agree well with one another and fall between 0.3 and 11.6 kcal mol^-1 with the cooperativity contributions in the range of -1.2 and 7.0 kcal mol^-1. For gauging the accuracy of our H-bond energies for a cluster, the H-bond energy sum is added to the sum of monomer energies, and the results are compared with the respective total energy. These two values agree with each other to within 8.3 mH (∼5 kcal mol^-1), testifying the accuracy of our estimated H-bond energies. Further, these H-bond strengths show a good correlation with the respective O-H stretching frequencies and the molecular electron density values at the (3, -1) O-H···O H-bond critical point.

A molecular tailoring approach – a new guide to quantify the energy of push–pull effects: a case study on (E)-3-(1H-pyrrol-2-yl)prop-2-enones

We report a new approach to quantify the push–pull effect in molecules with internal charge transfer.

Fragmentation method reveals a wide spectrum of intramolecular hydrogen bond energies in antioxidant natural products

Very strong and weak IHBs in curcumin.

Hydrogen bond donors and acceptors are generally depolarized in α-helices as revealed by a molecular tailoring approach

Hydrogen-bond (H-bond) interaction energies in α-helices of short alanine peptides were systematically examined by precise density functional theory calculations, followed by a molecular tailoring approach. The contribution of each H-bond interaction in α-helices was estimated in detail from the entire conformation energies, and the results were compared with those in the minimal H-bond models, in which only H-bond donors and acceptors exist with the capping methyl groups. The former interaction energies were always significantly weaker than the latter energies, when the same geometries of the H-bond donors and acceptors were applied. The chemical origin of this phenomenon was investigated by analyzing the differences among the electronic structures of the local peptide backbones of the α-helices and those of the minimal H-bond models. Consequently, we found that the reduced H-bond energy originated from the depolarizations of both the H-bond donor and acceptor groups, due to the repulsive interactions with the neighboring polar peptide groups in the α-helix backbone. The classical force fields provide similar H-bond energies to those in the minimal H-bond models, which ignore the current depolarization effect, and thus they overestimate the actual H-bond energies in α-helices. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Molecular Hydration of Carbonic Acid: Ab Initio Quantum Chemical and Density Functional Theory Investigation

Molecular hydration of carbonic acid (H₂CO₃) is investigated in terms of bonding patterns in H₂CO₃···(H₂O) _n [ n = 1-4] hydrogen-bonded clusters within ab initio quantum chemical and density functional theory (DFT) frameworks. Successive addition of water molecules to H₂CO₃···H₂O entails elongation of O-H (hydroxyl) bond as well as contraction of specific intermolecular hydrogen bonds signifying hydration of carbonic acid; these structural features get markedly enhanced under the continuum solvation framework. A comparison between the structurally similar clusters H₂CO₃···(H₂O) _n and HCOOH···(H₂O) _n [ n = 1-3] brings out the structural stability of the former. The present investigation in conjunction with the binding energy behavior of approaching water molecule(s) should serve as a precursor for pathways exploring aqueous dissociation of H₂CO₃ for larger clusters, as well as development of force-field potentials for acid dissociation process.

Adsorption of phenolic compounds from water by a novel ethylenediamine rosin-based resin: Interaction models and adsorption mechanisms

This study describes the adsorption performance of a novel ethylenediamine rosin-based resin (EDAR) for several industrially-important phenolic compounds. Its removal of 4-nitrophenol (4-NP) from water was comparable to or better than many commercial resins, although it was less effective with other phenols (i. e., phenol, 2,4-dichlorophenol, 4-chlorophenol, and 4-methylphenol). Experimental conditions for batch adsorption of 4-NP by EDAR are evaluated, the adsorption kinetics is well described by the pseudo-second-order model (R² > 0.99) and isotherm follows the Langmuir isotherm model (R² > 0.99), with the maximum monolayer adsorption capacity of 82 mg g^-1 at pH 6.0 and 293 K. The thermodynamic parameters indicate that the adsorption is spontaneous and endothermic. Also, quantum chemistry calculations indicate involvement of hydrogen-bonding between 4-NP and amino groups of EDAR. 4-NP was efficiently desorbed from the loaded EDAR resin by 0.2 M HCl, and the resin could be recycled with only a small decrease in its initial adsorption capacities. Thus, EDAR is a promising adsorbent for the removal of 4-NP during water treatment.

Experimental and theoretical investigation of intramolecular cooperativity in cyclic benzene trimer motif

A series of new symmetrical tripodal molecules 1a–4b with a central benzene scaffold substituted with methyl/ethyl groups and three benzimidazolyl units having a bithiophene/biphenyl/5-alkylthiophene motif at the 2-position via a –CH₂– unit were synthesized and characterized by elemental analysis, HR-MS, and NMR spectroscopy. NMR spectral data reveal that all molecules adopt a cyclic benzene trimer (CBT) using three benzimidazolyl units. Intramolecular cooperative edge-to-face C–H⋯π interactions stabilize the CBT motif in solution and are strong in ethyl substituted molecules (1b–4b) compared to methyl substituted (1a–4a) ones. However, the strength of the CBT unit in the tripodal molecule is independent of the length of the substituent at the 2-position of the benzimidazolyl unit. The relative ¹H NMR chemical shift calculated at the MPW1PW91/6-311+G(d,p) level of theory corroborates the experimental values, and the calculations predict the distribution of the structures into syn isomers. The relative change in the NMR chemical shift is justified by the relative change in the magnitude of the (3,+3) critical point (CP) in the molecular electrostatic potential (MESP) topography. Also, a linear correlation of the intramolecular C–H⋯π interactions evaluated at M062X/6-311+G(d,p) with the relative NMR chemical shift suggest the latter as a measure of intramolecular cooperativity.

A family of biaryl/alkylthiophene (R–R) benzimidazolyl-based tripodal molecules with cyclic benzene trimer (CBT) motif was synthesized and studied by NMR spectroscopy and MPW1PW91/6-311+G(d,p) theory.

On the molecular origin of the cooperative coil-to-globule transition of poly(N-isopropylacrylamide) in water

The cooperativity of PNIPAM coil-to-globule transition in water arises from the structuring of solvent in proximity to hydrophobic groups.

By means of atomistic molecular dynamics simulations we investigate the behaviour of poly(N-isopropylacrylamide), PNIPAM, in water at temperatures below and above the lower critical solution temperature (LCST), including the undercooled regime. The transition between water soluble and insoluble states at the LCST is described as a cooperative process involving an intramolecular coil-to-globule transition preceding the aggregation of chains and the polymer precipitation. In this work we investigate the molecular origin of such cooperativity and the evolution of the hydration pattern in the undercooled polymer solution. The solution behaviour of an atactic 30-mer at high dilution is studied in the temperature interval from 243 to 323 K with a favourable comparison to available experimental data. In the water soluble states of PNIPAM we detect a correlation between polymer segmental dynamics and diffusion motion of bound water, occurring with the same activation energy. Simulation results show that below the coil-to-globule transition temperature PNIPAM is surrounded by a network of hydrogen bonded water molecules and that the cooperativity arises from the structuring of water clusters in proximity to hydrophobic groups. Differently, the perturbation of the hydrogen bond pattern involving water and amide groups occurs above the transition temperature. Altogether these findings reveal that even above the LCST PNIPAM remains largely hydrated and that the coil-to-globule transition is related with a significant rearrangement of the solvent in the proximity of the surface of the polymer. The comparison between the hydrogen bonding of water in the surrounding of PNIPAM isopropyl groups and in the bulk displays a decreased structuring of solvent at the hydrophobic polymer–water interface across the transition temperature, as expected because of the topological extension along the chain of such interface. No evidence of an upper critical solution temperature behaviour, postulated in theoretical and thermodynamics studies of PNIPAM aqueous solution, is observed in the low temperature domain.

A Critical Check for the Role of Resonance in Intramolecular Hydrogen Bonding

Although resonance-assisted H-bonds (RAHBs) are well recognized, the role of π resonance in RAHBs is controversial, as the seemingly enhanced H-bonds in unsaturated compounds may result from the constraints imposed by the σ skeleton. Herein the block-localized wave function (BLW) method, which can derive optimal yet resonance-quenched structures with related physiochemical properties, was employed to examine the correlation between π resonance and the strength of intramolecular RAHBs. Examination of a series of paradigmatic molecules with RAHBs and their saturated analogues showed that it is inappropriate to compare a conjugated system with its saturated counterpart, as they may have quite different σ frameworks. Nevertheless, comparison between a conjugated system and its resonance-quenched (i.e., electron-localized) state, which have identical σ skeletons, shows that in all studied cases, π resonance unanimously reduces the bonding distance by 0.111-0.477 Å, strengthens the bonding by 40-56 %, and redshifts the D-H vibrational frequency by 104-628 cm^-1 . Furthermore, there is an excellent correlation between hydrogen-bonding strength and the classical Coulomb attraction between the hydrogen-bond donor and the acceptor, which suggests that the dominant role of the electrostatic interaction in H-bonds and RAHBs originates from the charge flow from H-bond donors to acceptors through π conjugation.

The Origin of the Non-Additivity in Resonance-Assisted Hydrogen Bond Systems

The concept of resonance-assisted hydrogen bond (RAHB) has been widely accepted, and its impact on structures and energetics can be best studied computationally using the block-localized wave function (BLW) method, which is a variant of ab initio valence bond (VB) theory and able to derive strictly electron-localized structures self-consistently. In this work, we use the BLW method to examine a few molecules that result from the merging of two malonaldehyde molecules. As each of these molecules contains two hydrogen bonds, these intramolecular hydrogen bonds may be cooperative or anticooperative, depended on their relative orientations, and compared with the hydrogen bond in malonaldehyde. Apart from quantitatively confirming the concept of RAHB, the comparison of the computations with and without π resonance shows that both σ-framework and π-resonance contribute to the nonadditivity in these RAHB systems with multiple hydrogen bonds.

Linker-Mediated Self-Assembly Dynamics of Charged Nanoparticles

Using in situ liquid cell transmission electron microscopy (TEM), we visualized a stepwise self-assembly of surfactant-coated and hydrated gold nanoparticles (NPs) into linear chains or branched networks. The NP binding is facilitated by linker molecules, ethylenediammonium, which form hydrogen bonds with surfactant molecules of neighboring NPs. The observed spacing between bound neighboring NPs, ∼15 Å, matches the combined length of two surfactants and one linker molecule. Molecular dynamics simulations reveal that for lower concentrations of linkers, NPs with charged surfactants cannot be fully neutralized by strongly binding divalent linkers, so that NPs carry higher effective charges and tend to form chains, due to poor screening. The highly polar NP surfaces polarize and partly immobilize nearby water molecules, which promotes NPs binding. The presented experimental and theoretical approach allows for detail observation and explanation of self-assembly processes in colloidal nanosystems.

Structures, stability and hydrogen bonding in inositol conformers

Various ab initio calculations using the density-functional (DFT), the second order Möller-Plesset perturbation (MP2) and self-consistent reaction field (SCRF) theories were performed on thirteen theoretically possible inositol stereoisomers. Gas phase calculations reveal that the myo- and neo-isomers of inositol (bearing one and two axial hydroxyl groups, respectively) are marginally more stable (by 0.5 kcal mol(-1)) than the all equatorially substituted scyllo-inositol. The calculations when done in different polar solvents show that the scyllo-inositol becomes the most stable inositol isomer, a fact attributed to weaker intramolecular hydrogen bonds. The individual hydrogen bond energy in all the isomers of inositol was also estimated using the molecular tailoring approach (MTA). The calculated hydrogen bond energies in these isomers are in excellent agreement with reported O-H···O hydrogen bond distances and ν(O-H) stretching frequencies. The estimated H-bond energy values suggest that the order of the intramolecular hydrogen bond strength follows: axial-axial > equatorial-axial > axial-equatorial > equatorial-equatorial hydrogen bonds. The intramolecular hydrogen bonds in the scyllo isomer are much weaker than those in other conformers, thus making this isomer more stable in polar solvents.

Effects of Structure and Environment on the Spectroscopic Properties of (3-Amino-Substituted-Thieno[2,3-b] Pyridine-2-yl)Pyridine/Quinolin-2-yl)(Phenyl)Methanones: Experimental and Theoretical Study

The electronic absorption, excitation and fluorescence properties of two 3-amino-substituted-thieno[2,3-b]pyridine/quinolin-2-yl)(phenyl)methanones; (referred to as compounds 1-2: where 3-amino-4,5,6-trimethyl-thieno[2,3-b]pyridin-2-yl)(phenyl)methanone (1); and 3-amino-5,6,7,8-tetrahydro-thieno[2,3-b]quinolin-2-yl)(phenyl)methanone (2)) have been investigated in solvents of various polarity and hydrogen-bonding abilities. Results based on the electronic absorption, excitation and emission study of these compounds; indicated that singlets (S1 and S2) excited-states are populated in non-polar and polar protic/aprotic solvents giving dual fluorescence with weak charge transfer separation. The experimental results were interpreted with the aid of quantum chemistry calculations carried out with the DFT and TD-DFT/B3lyp/6-31 + G(d,p) methods. Based on these calculations, compounds 1-2 exist in two rotamers: anti and syn, separated by ca. 5-6 kcal mol(-1) energy barriers in favor of the anti-conformer. The anti-structure, was shown to be stabilized through existence of intramolecular NH…O hydrogen bond (H-b), which plays a dominant role in affecting the energy of the HOMO-1 molecular orbital. Further, methyl/alkyl substitution in the pyridyl-thiophene ring was shown to involve in σ-π hyper-conjugation and destabilization of the HOMO-1 MO's.

Stability of conformationally locked free fructose: theoretical and computational insights

Total stabilization is governed by three predominant factors viz. the sum of energy of all H-bonds, ring strain and anomeric stabilization.