Quantum chemical investigations on molecular clusters

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.

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.

Spectroscopic and Theoretical Identifications of Two Structural Motifs of (H2O)10 Cluster

Precise characterization of archetypal systems of aqueous hydrogen-bonding networks is essential for developing accurate potential functions and universal models of water. The structures of water clusters (H2O)n (n = 2-9) have been verified recently through size-specific infrared spectroscopy with a vacuum ultraviolet free electron laser (VUV-FEL) and quantum chemical studies. For (H2O)10, the pentagonal prism and butterfly motifs were proposed to be important building blocks and were observed in previous experiments. Here we report the size-specific infrared spectra of (H2O)10 via a joint experimental and theoretical study. Well-resolved spectra provide a unique signature for the coexistence of pentagonal prism and butterfly motifs. These (H2O)10 motifs develop from the dominant structures of (H2O)n (n = 8, 9) clusters. This work provides an intriguing prelude to the diverse structure of liquid water and opens avenues for size-dependent measurement of larger systems to understand the stepwise formation mechanism of hydrogen-bonding networks.

Correlation of the Charge Resonance Interaction with Cluster Conformations Probed by Electronic Spectroscopy of Dimer Radical Cations of CO2 and CS2 in a Cryogenic Ion Trap

Radical cations of dimeric clusters of carbon dioxide/disulfide, [(CX2)2]+• (X = O and S), form strong intracluster bonds through charge resonance (CR) interactions. We herein performed electronic photodissociation spectroscopy of [(CX2)2]+• while regulating the temperature under ambient and cryogenic conditions using a quadrupole ion trap. Both ions exhibited broad band absorption in the near-infrared-visible light region; it is called the "CR band", as a measure of the strength of the CR interaction. Strikingly, this band underwent a noticeable blue shift upon cryogenic cooling for [(CS2)2]+• while not for [(CO2)2]+•. On the basis of quantum chemical calculations with a coupled cluster method, the band shift was attributed to the variations in the relative population of two energetically close conformers found for [(CS2)2]+•. This study highlights a strong correlation between CR interactions and conformation of the radical dimer cations, demonstrating the exceptional significance of cryogenic cooling in the chemistry of ionic molecular clusters.

Hydration of [Formula: see text]aminobenzoic acid: structures and non-covalent bondings of aminobenzoic acid-water clusters

CONTEXT

Micro-hydration of the aminobenzoic acid is essential to understand its interaction with surrounding water molecules. Understanding the micro-hydration of the aminobenzoic acid is also essential to study its remediation from wastewater. Therefore, we explored the potential energy surfaces (PESs) of the para-aminobenzoic acid-water clusters, ABW[Formula: see text], [Formula: see text], to study the microsolvation of the aminobenzoic acid in water. In addition, we performed a quantum theory of atoms in molecules (QTAIM) analysis to identify the nature of non-covalent bondings in the aminobenzoic acid-water clusters. Furthermore, temperature effects on the stability of the located isomers have been examined. The located structures have been used to calculate the hydration free energy and the hydration enthalpy of the aminobenzoic acid using the cluster continuum solvation model. The hydration free energy and the hydration enthalpy of the aminobenzoic acid at room temperature are evaluated to be -7.0 kcal/mol and -18.1 kcal/mol, respectively. The hydration enthalpy is in perfect agreement with a previous experimental estimate. Besides, temperature effects on the calculated hydration enthalpy and free energy are reported. Finally, we calculated the gas phase binding energies of the most stable structures of the ABW[Formula: see text] clusters using twelve functionals of density functional theory (DFT), including empirical dispersion. The DFT functionals are benchmarked against the DLPNO-CCSD(T)/CBS. We have found that the three most suitable DFT functionals are classified in the following order: PW6B95D3 > MN15 > [Formula: see text]B97XD. Therefore, the PW6B95D3 functional is recommended for further study of the aminobenzoic acid-water clusters and similar systems.

METHODS

The exploration started with classical molecular dynamics simulations followed by complete optimization at the PW6B95D3/def2-TZVP level of theory. Optimizations are performed using Gaussian 16 suite of codes. QTAIM analysis is performed using the AIMAll program.

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.

REAlgo: Rapid and efficient algorithm for estimating MP2/CCSD energy gradients for large molecular clusters

This work reports the development of an algorithm for rapid and efficient evaluation of energy gradients for large molecular clusters employing correlated methods viz. second-order Møller-Plesset perturbation theory (MP2) theory and couple cluster singles and doubles (CCSD). The procedure segregates the estimation of Hartree-Fock (HF) and correlation components. The HF energy and gradients are obtained by performing a full calculation. The correlation energy is approximated as the corresponding two-body interaction energy. Correlation gradients for each monomer are approximated from the respective monomer-centric fragments comprising its immediate neighbours. The programmed algorithm is explored for the geometry optimization of large molecular clusters using the BERNY optimizer as implemented in the Gaussian suite of software. The accuracy and efficacy of the method are critically probed for a variety of large molecular clusters containing up to 3000 basis functions, in particular large water clusters. The CCSD level geometry optimization of molecular clusters containing ∼800 basis functions employing a modest hardware is also reported.

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.

Polymer Dynamics in Glycerol-Water Mixtures

Velocity correlation spectra (VAS) in binary mixtures of water and glycerol (G/W), obtained by measurements using the modulated gradient spin echo (MGSE) NMR method, were explained by the interactions of water molecules with clusters formed around the hydrophilic glycerol molecule, which drastically change the molecular dynamics and rheology of the mixture. It indicates a thickening of the shear viscosity, which could affect the dynamics of submerged macromolecules. The calculation of the polymer dynamics with the Langevin equations according to the Rouse model, where the friction was replaced by the memory function of the retarded friction, gave the dependence of the dynamics of the polymer on the rate of shear viscous properties of the solvent. The obtained formula was used to calculate the segmental VAS of the polymer when immersed in pure water and in a G/W mixture with 33 vol% glycerol content, taking into account the inverse proportionality between the solvent VAS and friction. The spectrum shows that in the G/W mixture, the fast movements of the polymer segments are strongly inhibited, which creates the conditions for slow processes caused by the internal interaction between the polymer segments, such as interactions that cause disordered polypeptides to spontaneously fold into biologically active protein molecules when immersed in such a solvent.

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.

A scheme for rapid evaluation of the intermolecular three-body polarization effect in water clusters

The ability to accurately and rapidly evaluate the intermolecular many-body polarization effect of the water system is very important for computer simulations of biomolecule in aqueous. In this paper, a scheme is proposed based on the polarizable dipole-dipole interaction model and used to rapidly estimate the intermolecular many-body polarization effect in water clusters. We use a bond-dipole-based polarization function to evaluate the polarization energy. We regard two OH bonds of a water molecule as two bond-dipoles and set the permanent OH bond-dipole moment of a water molecule to be 1.51 Debye. We estimate the induced OH bond-dipole moment via a simple formula in which only one correction factor is needed. This scheme is then applied to tens of water clusters to calculate the three- and four-body interaction energies. The three-body interaction energies of 93 water clusters produced by our scheme are compared with those produced by the counterpoise-corrected CCSD(T)/aug-cc-pVDZ, MP2/aug-cc-pVDZ, M06-2X/jul-cc-pVTZ methods, by the AMOEBApro13, iAMOEBA, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The four-body interaction energies of 47 water clusters yielded by our scheme are compared with those yielded by the counterpoise-corrected MP2/aug-cc-pVDZ and M06-2X/ jul-cc-pVTZ methods, by the AMOEBApro13, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The comparison results show that the scheme proposed in this paper can reproduce the counterpoise-corrected CCSD(T)/aug-cc-pVDZ three-body interaction energies and reproduce the counterpoise-corrected MP2/aug-cc-pVDZ four-body interaction energies both accurately and efficiently. We anticipate the scheme proposed here can be useful for computer simulations of liquid water and aqueous solutions.

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.

Constructing Potential Energy Surface with Correlated Theory for Dipeptides Using Molecular Tailoring Approach

We demonstrate a cost-effective alternative employing the fragment-based molecular tailoring approach (MTA) for building the potential energy surface (PES) for two dipeptides viz. alanine-alanine and alanine-proline employing correlated theory, with augmented Dunning basis sets. About 1369 geometries are generated for each test dipeptide by systematically varying the dihedral angles Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . These conformational geometries are partially optimized by relaxing all the other Z-matrix parameters, fixing the values of Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . The MP2 level PES is constructed from the MTA-energies of chemically intact geometries using minimal hardware. The fidelity of MP2/aug-cc-pVDZ level PES is brought out by comparing it with its full calculation counterpart. Further, we bring out the power of the method by reporting the MTA-based CCSD/aug-cc-pVDZ level PES for these two dipeptides containing 498 and 562 basis functions respectively.

Development and testing of an algorithm for efficient MP2/CCSD(T) energy estimation of molecular clusters with the 2-body approach

This work reports the development and testing of an automated algorithm for estimating the energies of weakly bound molecular clusters employing correlated theory. Firstly, the monomers and dimers of (homo/hetero) clusters are identified, and the sum of one-body and two-body contributions to correlation energy is calculated. The addition of this contribution to the Hartree-Fock full calculation (FC) energies provides a good estimate of the total energies at Møller-Plesset second-order perturbation theory (MP2)/coupled-cluster method with singles and doubles (CCSD) (T)-level theory using augmented Dunning basis sets. The estimated energies for several test clusters show an excellent agreement with their FC counterparts, with a substantial wall-clock time saving employing off-the-shelf hardware. Furthermore, the complete basis set (CBS) limit for MP2 energy computed using the two-body approach also agrees with its CBS energy with its FC counterpart.

Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems

Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.

Characterization of non-covalent contacts in mono- and di-halo substituted acetaldehydes: probing the substitution effects of electron donating and withdrawing groups

In the current work, a systematic evaluation of the different types of non-covalent interactions (NCIs) in acetaldehyde dimers, including dimers of mono-halo (XCH₂CHO)₂, di-halo (X₂CHCHO)₂ and tri-halo substituted (X₃CCHO)₂ acetaldehydes via the associated stabilization energy of these dimers has been performed. Furthermore, a topological analysis of the electron density based on the quantum theory of atoms in molecules (QTAIM) and non-covalent interaction reduced density gradient (NCI-RDG) isosurfaces has also been performed to evaluate the nature of these NCIs. The geometrical and electronic characteristics have been evaluated via the presence of different electron-donating groups (EDGs) and electron-withdrawing groups (EWGs) or substituents in dimers of these molecules, namely, XCH(Y)CHO and X₂C(Y)CHO (wherein X = -F, -Cl, and -Br and Y = -SO₃H, -CN, -NO₂, -NH₂, -CH₃, -OCH₃, and -SMe₃). The C-H⋯O, C-H⋯X, X⋯X, X⋯O and C⋯O tetrel bonded contacts have been recognized to play an important role in the stabilization of the formed dimers. This study also establishes the fact that the overall stability of the dimeric assemblies is governed by the contributions from the mutual and complex interplay of a variety of interactions in the investigated dimers. Hence considerations based on strong H-bond donor-acceptor characteristics hold relevance for simple systems only, but slight alteration in the electronic environment can affect the overall stabilization energies of the system being investigated and the nature of the interactions that contribute towards the same.

Spectroscopic snapshot for neutral water nonamer (H2O)9: Adding a H2O onto a hydrogen bond-unbroken edge of (H2O)8

Structural characterization of neutral water clusters is crucial to understanding the structures and properties of water, but it has been proven to be a challenging experimental target due to the difficulty in size selection. Here, we report the size-specific infrared spectra of confinement-free neutral water nonamer (H₂O)₉ based on threshold photoionization, using a tunable vacuum ultraviolet free-electron laser. Distinct OH stretch vibrational fundamentals in the 3200-3350 cm^-1 region are observed, providing unique spectral signatures for the formation of an unprecedented (H₂O)₉ structure evolved by adding a ninth water molecule onto a hydrogen bond-unbroken edge of the (H₂O)₈ octamer with D_2d symmetry. This nonamer structure coexists with the five previously identified structures that can be viewed as derived by inserting a ninth water molecule into a hydrogen bond-broken edge of the D_2d/S₄ octamer. These findings provide key microscopic information for systematic understanding of the formation and growth mechanism of dynamical hydrogen-bonding networks that are responsible for the structure and properties of condensed-phase water.

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.

Are cyclic plant and animal behaviours driven by gravimetric mechanical forces?

The celestial mechanics of the Sun, Moon, and Earth dominate the variations in gravitational force that all matter, live or inert, experiences on Earth. Expressed as gravimetric tides, these variations are pervasive and have forever been part of the physical ecology with which organisms evolved. Here, we first offer a brief review of previously proposed explanations that gravimetric tides constitute a tangible and potent force shaping the rhythmic activities of organisms. Through meta-analysis, we then interrogate data from three study cases and show the close association between the omnipresent gravimetric tides and cyclic activity. As exemplified by free-running cyclic locomotor activity in isopods, reproductive effort in coral, and modulation of growth in seedlings, biological rhythms coincide with temporal patterns of the local gravimetric tide. These data reveal that, in the presumed absence of rhythmic cues such as light and temperature, local gravimetric tide is sufficient to entrain cyclic behaviour. The present evidence thus questions the phenomenological significance of so-called free-run experiments.

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...

Capturing the potential energy landscape of large size molecular clusters from atomic interactions up to a 4-body system using deep learning

We propose a new method that utilizes the database of stable conformers and borrow the fragmentation concept of many-body-expansion (MBE) methods in ab initio methods to train a deep-learning machine learning (ML) model using SchNet.

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.

Effect of confinement on the dynamics of 1-propanol and other monohydroxy alcohols

We report the effect of confinement on the dynamics of three monohydroxy alcohols (1-propanol, 2-ethyl-1-hexanol, and 4-methyl-3-heptanol) differing in their chemical structure and, consequently, in the dielectric strength of the "Debye" process. Density functional theory calculations in bulk 1-propanol identified both linear and ring-like associations composed of up to five repeat units. The simulation results revealed that the ring structures, with a low dipole moment (∼2 D), are energetically preferred over the linear assemblies with a dipole moment of 2.18 D per repeat unit. Under confinement in nanoporous alumina (in templates with pore diameters ranging from 400 to 20 nm), all dynamic processes were found to speed up irrespective of the molecular architecture. The characteristic freezing temperatures of the α and the Debye-like processes followed the pore size dependence: T_a,D=T_a,D ^bulk-A/d^1/2, where d is the pore diameter. The characteristic "freezing" temperatures for the Debye-like (the slow process for confined 1-propanol is non-Debye) and the α-processes decrease, respectively, by 6.5 and 13 K in confined 1-propanol, by 9.5 and 19 K in confined 2-ethyl-1-hexanol, and by 9 and 23 K in confined 4-methyl-3-heptanol within the same 25 nm pores. In 2-ethyl-1-hexanol, confinement reduced the number of linearly associated repeats from approximately heptamers in the bulk to dimers within 25 pores. In addition, the slower process in bulk 2-ethyl-1-hexanol and 4-methyl-3-heptanol, where the signal is dominated by ring-like supramolecular assemblies, is clearly non-Debye. The results suggest that the effect of confinement is dominant in the latter assemblies.

A unified and flexible formulation of molecular fragmentation schemes

We present a flexible formulation for energy-based molecular fragmentation schemes. This framework does not only incorporate the majority of existing fragmentation expansions but also allows for flexible formulation of novel schemes. We further illustrate its application in multi-level approaches and for electronic interaction energies. For the examples of small water clusters, a small protein, and protein-protein interaction energies, we show how this flexible setup can be exploited to generate a well-suited multi-level fragmentation expansion for the given case. With such a setup, we reproduce the electronic protein-protein interaction energy of ten different structures of a neurotensin and an extracellular loop of its receptor with a mean absolute deviation to the respective super-system calculations below 1 kJ/mol.

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.

iOI: An Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem

An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is distinctive in that (1) it divides and conquers not only the energy but also the wave function and that (2) the subsystem sizes are automatically determined by successively merging neighboring small subsystems until they are just enough for converging the wave function to a given accuracy. Orthonormal occupied and virtual localized molecular orbitals are obtained in a natural manner, which can be used for all post-SCF purposes.

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.

Density-Based Many-Body Expansion as an Efficient and Accurate Quantum-Chemical Fragmentation Method: Application to Water Clusters

Fragmentation methods based on the many-body expansion offer an attractive approach for the quantum-chemical treatment of large molecular systems, such as molecular clusters and crystals. Conventionally, the many-body expansion is performed for the total energy, but such an energy-based many-body expansion often suffers from a slow convergence with respect to the expansion order. For systems that show strong polarization effects such as water clusters, this can render the energy-based many-body expansion infeasible. Here, we establish a density-based many-body expansion as a promising alternative approach. By performing the many-body expansion for the electron density instead of the total energy and inserting the resulting total electron density into the total energy functional of density functional theory, one can derive a density-based energy correction, which in principle accounts for all higher-order polarization effects. Here, we systematically assess the accuracy of such a density-based many-body expansion for test sets of water clusters. We show that already a density-based two-body expansion is able to reproduce interaction energies per fragment within chemical accuracy and is able to accurately predict the energetic ordering as well as the relative interaction energies of different isomers of water clusters.

Quantifying Frustrations for Molecular Complexes with Noncovalent Interactions

Molecular systems bound together through noncovalent interactions are involved in a lot of life-essential processes such as molecular recognition, signal transduction, and allosteric regulation. While cooperation as an important effect discovered in these systems focuses on the behavior of system's entirety, we need also examine the behavior of individual parts. In this work, using the distortion energy as the descriptor, we quantify frustration as the energetic loss of individual parts due to the formation of nonadditive molecular complexes. The applicability of our approach has been illustrated by a few simple clusters. Our results show that the frustration effect is smaller than the cooperation effect, but same as cooperativity, it can be both positive and negative. The ultimate benefit of a system made of multiple parts is dictated by the balance between the cooperative behavior among parts and the sacrifice from its individuals. This conflicting yet complementary conceptual pair of cooperation and frustration provides us with a different perspective from the systems' viewpoint for molecular complexes. This new angle of appreciating molecular complexes can be applied in conformational changes, enzymatic catalysis, and many more.

Mechanisms of a Cyclobutane-Fused Lactone Hydrolysis in Alkaline and Acidic Conditions

Searching for functional polyesters with stability and degradability is important due to their potential applications in biomedical supplies, biomass fuel, and environmental protection. Recently, a cyclobutane-fused lactone (CBL) polymer was experimentally found to have superior stability and controllable degradability through hydrolysis reactions after activation by mechanical force. In order to provide a theoretical basis for developing new functional degradable polyesters, in this work, we performed a detailed quantum chemical study of the alkaline and acidic hydrolysis of CBL using dispersion-corrected density functional theory (DFT-D3) and mixed implicit/explicit solvent models. Various possible hydrolysis mechanisms were found: B_AC2 and B_AL2 in the alkaline condition and A_AC2, A_AL2, and A_AL1 in the acidic condition. Our calculations indicated that CBL favors the B_AC2 and A_AC2 mechanisms in alkaline and acidic conditions, respectively. In addition, we found that incorporating explicit water solvent molecules is highly necessary because of their strong hydrogen-bonding with reactant/intermediate/product molecules.

Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F−, Cl−, Br−, and I− on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal (H2O)nX clusters, with X = Cl−, Br−, and I−, exhibit surface hydration structures. Computed free energies, based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (ab initio molecular dynamics) simulation stream. This rough-landscape procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect addressed. Nevertheless, this procedure can break down when n≳4, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of (H2O)nX clusters, including ramified structures natural in physical cluster theories. With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

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.

Formation of covalently bound C4H4 + upon electron-impact ionization of acetylene dimer

We investigate the formation mechanisms of covalently bound C₄H₄ ⁺ cations from direct ionization of hydrogen bonded dimers of acetylene molecules through fragment ion and electron coincident momentum spectroscopy and quantum chemistry calculations. The measurements of momenta and energies of two outgoing electrons and one ion in triple-coincidence allow us to assign the ionization channels associated with different ionic fragments. The measured binding energy spectra show that the formation of C₄H₄ ⁺ can be attributed to the ionization of the outermost 1π_u orbital of acetylene. The kinetic energy distributions of the ionic fragments indicate that the C₄H₄ ⁺ ions originate from direct ionization of acetylene dimers while ions resulting from the fragmentation of larger clusters would obtain significantly larger momenta. The formation of C₄H₄ ⁺ through the evaporation mechanism in larger clusters is not identified in the present experiments. The calculated potential energy curves show a potential well for the electronic ground state of (C₂H₂)2⁺, supporting that the ionization of (C₂H₂)₂ dimers can form stable C₂H₂⋅C₂H₂ ⁺(1π_u ^-1) cations. Further transition state analysis and ab initio molecular dynamics simulations reveal a detailed picture of the formation dynamics. After ionization of (C₂H₂)₂, the system undergoes a significant rearrangement of the structure involving, in particular, C-C bond formation and hydrogen migrations, leading to different C₄4⁺ isomers.

Directional Proton Transfer in the Reaction of the Simplest Criegee Intermediate with Water Involving the Formation of Transient H3O. J Phys Chem Lett 2021;12:3379-3386. [PMID: 33784110 DOI: 10.1021/acs.jpclett.1c00448]

The reaction of Criegee intermediates with water vapor has been widely known as a key Criegee reaction in the troposphere. Herein, we investigated the reaction of the smallest Criegee intermediate, CH₂OO, with a water cluster through fragment-based ab initio molecular dynamics simulations at the MP2/aug-cc-pVDZ level. Our results show that the CH₂OO-water reaction could occur not only at the air/water interface but also inside the water cluster. Moreover, more than one reactive water molecules are required for the CH₂OO-water reaction, which is always initiated from the Criegee carbon atom and ends at the terminal Criegee oxygen atom via a directional proton transfer process. The observed reaction pathways include the loop-structure-mediated and stepwise mechanisms, and the latter involves the formation of transient H₃O⁺. The lifetime of transient H₃O⁺ is on the order of a few picoseconds, which may impact the atmospheric budget of the other trace gases in the actual atmosphere.

Role of the Environment in Quenching the Production of H_{3}^{+} from Dicationic Clusters of Methanol

Ionization and subsequent isomerization of organic molecules has been suggested as an important source of trihydrogen H_{3}^{+} cations in outer space. The high interest in such reactions has initiated many experimental and theoretical studies for various molecules. Here, we report measurements as well as ab initio molecular dynamics simulations on the fragmentation of dicationic methanol monomers and clusters ionized by low-energy (90 eV) electrons. Experimentally, for dicationic monomers, a fragmentation channel for the formation of H_{3}^{+} in coincidence with a COH^{+} cation is observed. The simulations show that an intermediate neutral H_{2} is formed in the first step, and its roaming around the dication ends in the formation of H_{3}^{+}. The entire reaction takes about 100-500 fs. The calculated kinetic energy release for the H_{3}^{+}+COH^{+} ion pair is in excellent agreement with the experimental result. In contrast, for the dicationic clusters, due to the possibility of distributing the two charges onto different molecules, several fast dissociation channels occur and suppress the roaming of H_{2} and formation of H_{3}^{+}. The present Letter suggests that the quenching of H_{3}^{+} formation by the chemical environment is a general phenomenon in dicationic clusters of organic molecules.

Isomeric Scandium-Organic Frameworks with High Hydrolytic Stability and Selective Adsorption of Acetylene

Two solvent-controlled topological isomers of scandium-organic frameworks [Sc(Hpzc)(pzc)]·DMF·2H₂O (1·DMF·2H₂O) and [Sc(Hpzc)(pzc)]·DMA·4H₂O (2·DMA·4H₂O) were synthesized using 2,5-pyrazinedicarboxylate (pzc^2-) (DMF = dimethylformamide; DMA = dimethylacetamide). Despite the isomeric nature of the obtained metal-organic frameworks (MOFs), they possess different structural features and unique adsorption properties toward gases and iodine. The compound 1 has widely spread among MOF structures a dia topology with ultranarrow channels, which together with inner surface functionalization leads to enhanced CO₂ adsorption and high selectivity factors in CO₂/CH₄ and CO₂/N₂ gas mixtures (25.9 and 35.6, respectively, 1/1 v/v). Moreover, a rare preferable adsorption of CO₂ over C₂H₂ was demonstrated. The biporous isomeric framework 2 has a crb topology inherent in zeolites. A remarkable adsorption affinity to C₂H₂ with the ideal adsorbed solution theory selectivity factor of 127.1 for a C₂H₂/C₂H₄ mixture (1/99 v/v) was achieved for 2. Both compounds have exceptional chemical stability in a wide range of pH from acidic to basic media.

Temperature-dependent oxidation of BSCAPE molecule in methanol medium

Temperature-dependent solvation free energy and oxidation by free energy of ionization of 2-Phenylethyl (2E)-3-(1-benzenesulfonyl-4,5-dihydroxyphenyl) acrylate (BSCAPE) in methanol medium are the concerns of the present work. This molecule is a relevant phenolic acid enclosing multiple bioactivities. The explicit, implicit and discrete-continuum models of solvation were used. The methanol molecules were coordinated to this acid to form cluster complexes. The dual method M06-2X/6-31++G(d,p)//B3LYP/6-31G(d) was employed along with basis set superposition error correction. The results show that, the free energy of coordination and solvation are distant. Both quantities increase with temperature. From discrete-continuum treatment, there is non-spontaneity of solvation process, while coordination yielded spontaneity and non-spontaneity at cold and hot room temperatures, respectively. The ionization potential in gas phase, decreases with temperature. All the solvation models yielded lower ionization potential than that of gas phase. Thus, it follows that, the increase of temperature and methanol medium favours the oxidation of BSCAPE. Consequently, this favours its metabolism processes.