Hydrogen bond energies and cooperativity in substituted calix[n]arenes (n = 4, 5)

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.

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.

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.

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.

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.

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.

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.

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.

On single-electron magnesium bonding formation and the effect of methyl substitution

The complexes formed between MgX₂ (X = F, H) molecules and alkyl radicals Y [Y = CH₃, CH₂CH₃, CH(CH₃)₂, and C(CH₃)₃] have been characterized by using quantum chemical methods. The binding distance in all cases is less than the sum of vdW radii of Mg and C, indicating the formation of a non-covalent interaction, namely single-electron magnesium bond. Energy decomposition analysis reveals that electrostatic and polarization contributions are the major components responsible for the stability of the studied complexes. According to interaction energy, atoms in molecules, and independent gradient model analyses, methyl substitution on electron donor Y imposes a positive effect on its complexation with MgX₂. When compared with other nonbonded interactions, the single-electron magnesium bond is found to have strength comparable to those of the single-electron beryllium bond and π-magnesium bond.

The complexes formed between MgX₂ (X = F, H) molecules and alkyl radicals Y [Y = CH₃, CH₂CH₃, CH(CH₃)₂, and C(CH₃)₃] have been characterized by using quantum chemical methods.

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.

Microhydration of a Carbonyl Group: How does the Molecular Electrostatic Potential (MESP) Impact the Formation of (H2O)n:(R2C═O)Complexes?

The presence of a carbonyl group in a molecule usually leads to the identification of a π-hole on the molecular electrostatic potential (MESP) of the species. How does this electrophilic site influence the formation of microhydrated complexes? To address this point, a panel of R₂CO solutes with various MESPs was selected, and we identified the structures and properties of several complexes containing one, two, three and six water molecules. The following solutes were considered in the present study: H₂CO, F₂CO, Cl₂CO,(NC)₂CO and H₂C═CO. Geometry optimizations and frequency calculations were carried out at the LC-ωPBE/6-311++G(d,p) level, with the GD3BJ empirical correction for dispersion. For a number of n water molecules around the R₂CO solute, the structure and the features of the most stable (H₂O)_n:(R₂CO) complexes are highly dependent on the MESP of the isolated R₂CO solute. The formation of pi-hole bondings appears to play a decisive role in the initiation of a three-dimensional organization of water molecules around the solute.

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

Very strong and weak IHBs in curcumin.

Inter-molecular inter-actions in a phenol-substituted benzimidazole

Hydrogen bonding plays an important role in the design of solid-state structures and gels with desirable properties. 1-(4-Hydroxybenzyl)-2-(4-hydroxyphenyl)-5,6-dimethyl-1H-benzimidazole was isolated as the acetone disolvate, C22H20N2O2·2C3H6O. O-H⋯N hydrogen bonding between benz-imidazole mol-ecules results in chains parallel to [010]. One of the acetone solvate mol-ecules participates in O-H⋯O hydrogen bonding with the benzimidazole derivative. C-H⋯π inter-actions are observed in the extended structure. Hirshfeld surface analysis was used to explore the inter-molecular inter-actions and density functional theory was used to estimate the strength of the hydrogen bonds.

The effects of the heteroatom and position on excited-state intramolecular proton transfer of new hydroxyphenyl benzoxazole derivatives: a time-dependent density functional theory study

The effects of the heteroatom and position on excited-state intramolecular proton transfer (ESIPT) of 2-[4′-(N-4,6-dichloro-1,3,5-triazi-n-2-yl)2′hydroxyphenyl]benzoxazole (4THBO) have been investigated via time-dependent density functional theory studies.

Exploring the ESIPT dynamical processes of two novel chromophores: symmetrical structure CHC and asymmetric structure CHN

The detailed ESIPT dynamical processes of CHC (symmetrical structure) and CHN (asymmetric structure) chromophores were revealed and compared using the TDDFT method at the B3LYP/6-31+G(d,p) level.

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.

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.