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.

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.

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.

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 (Wn, 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), |ΔEmax| (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.

One-pot C-C, C-N, and C-S bond construction for synthesis of 3-sulfenylindoles directly from unactivated anilines involving dual palladium catalysis and mechanistic insights from DFT.

An efficient dual Pd-catalytic system was developed for one-pot synthesis of 3-sulfenylindoles via C-C, C-N and C-S bond construction directly from unactivated 2-iodo(NH)anilines under mild reaction conditions. Furthermore, 3-selenyl/halo/carbon-functionalized indoles were synthesized in good yields and a short reaction time. The synthetic utility of 3-sulfenylindole was also demonstrated. The key role of solvent in palladium catalysis was unravelled by DFT.

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 MTA-based method to large molecular clusters is prohibitively difficult due to the evaluation of the energy of large-sized fragments. We propose here a smaller model system called the shell model, to overcome this difficulty. The shell model represents the first hydration shell of water molecules involved in the formation of HB under consideration. Utilizing the shell model as a parent system, fragmentation is carried out, in a fashion similar to the actual MTA-based method, to estimate individual HB energies in large water clusters (Wn, n = 10-16, 18 and 20). The estimated individual HB energies in these Wn clusters, employing the shell model, fall between 0.2 and 12.5 kcal mol-1 at the MP2/aug-cc-pVTZ level, with no net loss in the cooperativity contribution. We have also applied this shell model-based approach to estimate individual HB energies in the two lowest energy conformers of ammonia octamers (NH3)8 and mixed hydrogen fluoride-water clusters. The estimated individual HB energies employing the shell model, in all these molecular clusters studied in this work, are in good agreement with their actual MTA-based counterparts. The typical difference is less than 1 kcal mol-1. Importantly, the shell model has a huge computational time advantage over the actual MTA-based method and it requires only modest hardware.

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 Mn Wm , (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 OM -H…OW HBs are the strongest (6.9 to 12.4 kcal mol-1 ). The next ones are OM -H…OM HBs (6.5 to 11.6 kcal mol-1 ). The OW -H…OW (0.2 to 10.9 kcal mol-1 ) and OW -H…OM 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., OM -H…OM (5.0 to 6.0 kcal mol-1 )>OW -H…OM (1.5 to 6.0 kcal mol-1 )>OM -H…OW (3.8 to 5.6 kcal mol-1 )>OW -H…OW (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: OM -H…OW (2.4 to 8.6 kcal mol-1 )>OM -H…OM (1.3 to 6.3 kcal mol-1 )>OW -H…OW (-1.0 to 6.5 kcal mol-1 )>OW -H…OM (-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.

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.

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 (Wn) 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 Wn, 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.