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

Cluster-in-Cluster Approach for Computing MP2-Level Vibrational Infrared Spectra of Large Molecular Clusters

Constructing the Hessian matrix (HM) for large molecules demands huge computational resources. Here, we report a cluster-in-cluster (CIC) procedure for efficiently evaluating HM and dipole derivatives for large molecular clusters by employing the second-order Møller-Plesset perturbation (MP2) theory. The highlight of the proposal is the separation of the estimations of Hartree-Fock (HF) and post-HF components. The parent cluster with n molecules is divided (virtually) into n subclusters centering each monomer and accommodating its near neighbors decided by a distance cutoff. The HF-level HM is obtained by doing full calculation (FC), while the correlation part is approximated by the respective subclusters. A software automating the procedure [followed by calculating infrared (IR) frequencies and intensities] is applied to deduce the IR spectrum for a variety of molecular clusters, particularly water clusters of various sizes, containing up to ∼2000 basis functions. The accuracy of the IR spectrum constructed using CIC is remarkable, with a substantial time advantage (with respect to its FC counterpart). The reduced computational resources and the tractability of the computations are other major benefits of the procedure.

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.

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.

The catalytic activity and adsorption in faujasite and ZSM-5 zeolites: the role of differential stabilization and charge delocalization

Adsorption and chemical reactions occurring on industrially important ZSM-5 and faujasite zeolite catalysts are investigated with the quantum-mechanical fragment molecular orbital method combined with periodic boundary conditions. Suitable fragmentation patterns are devised and tested providing important case studies of computing real materials with fragmentation methods. A good accuracy is demonstrated in comparison to full calculations, and a good agreement with the available experimental data is obtained. The full production cycle of p-xylene on faujasite zeolite is mapped. The catalytic role of the zeolite in the dehydration reaction, analyzed with the partition analysis, is attributed to the delocalization of the negative charge over the zeolite. On the other hand, an increase of the barrier in the Diels-Alder reaction by the zeolite is attributed to the preferential stabilization of the reactants over the transition state as demonstrated by the guest-zeolite interaction energy.

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.

Analysis of Guest Adsorption on Crystal Surfaces Based on the Fragment Molecular Orbital Method

For gaining insights into interactions in periodic systems, an analysis is developed based on the fragment molecular orbital method combined with periodic boundary conditions. The adsorption energy is decomposed into guest and surface polarization and deformation energy, guest-surface and guest-guest interactions, and the vibrational free energy. The analysis is applied to the adsorption of guest molecules to Ih (001) ice surface. The cooperativity effects result in a non-linear change in the adsorption energy with coverage due to many-body effects. The role of dispersion is found to be dominant for guests with long hydrophobic tails. A rule is proposed relating the length of the alkyl tail with the formation of the guest layer. The computed binding enthalpies are in good agreement with experimental values. For high coverage, adsorbed molecules can form an ordered layer known as self-assembled monolayer.

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.