Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections

Photoelectron Spectroscopy and Computational Study on Microsolvated [B10H10]2- Clusters and Comparisons to Their [B12H12]2- Analogues

Microhydrated closo-boranes have attracted great interest due to their superchaotropic activity related to the well-known Hofmeister effect and important applications in biomedical and battery fields. In this work, we report a combined negative ion photoelectron spectroscopy and quantum chemical investigation on hydrated closo-decaborate clusters [B10H10]2-·nH2O (n = 1-7) with a direct comparison to their analogues [B12H12]2-·nH2O and free water clusters. A single H2O molecule is found to be sufficient to stabilize the intrinsically unstable [B10H10]2- dianion. The first two water molecules strongly interact with the solute forming B-H···H-O dihydrogen bonds while additional water molecules show substantially reduced binding energies. Unlike [B12H12]2-·nH2O possessing a highly structured water network with the attached H2O molecules arranged in a unified pattern by maximizing B-H···H-O dihydrogen bonding, distinct structural arrangements of the water clusters within [B10H10]2-·nH2O are achieved with the water cluster networks from trimer to heptamer resembling free water clusters. Such a distinct difference arises from the variations in size, symmetry, and charge distributions between these two dianions. The present finding again confirms the structural diversity of hydrogen-bonding networks in microhydrated closo-boranes and enriches our understanding of aqueous borate chemistry.

Tailored carbon dioxide capacity in carboxylate-based ionic liquids

We have used a library of thermally stable tetraalkylphosphonium carboxylate ionic liquids that were easily prepared from available carboxylic acids. Depending on the pKa in water of the precursor acids, the resulting ionic liquids either dissolve or reversibly chemically absorb CO2, with some exhibiting notable gas capacities, reaching a CO2 mole fraction of 0.2 at 1 bar and 343 K. While equilibrium constants and ionic liquid capacities generally correlate with the pKa of the acids, certain exceptions underscore the influence of liquid structure and physical properties of the ionic liquids, elucidated through molecular dynamics simulations and density functional theory calculations. Unlike the trends observed in other CO2-absorbing ILs, phosphonium carboxylates do not experience increased viscosity upon gas absorption; instead, enhanced diffusivities are observed, facilitating efficient gas-liquid transfer.

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.

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [Kanungo, B. J. Phys. Chem. Lett. 2024, 15, 323-328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN 50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree-Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

Why do dipole moments of HCl-water clusters fail to determine acid dissociation?

This paper quantitatively examines why dipole moments of HCl(H2O)n=1-8 cannot serve as the dissociation criterion for acid molecules using the Hirshfeld-I approach. Also, we propose the possible experimental parameter 〈P(HCl)〉, whose statistical average enables the assessment of acid dissociation in mixed clusters. Furthermore, our calculations reveal that a minimum of four water molecules are necessary to dissociate an HCl molecule.

Toward Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo

We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N2 dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.

A reactive neural network framework for water-loaded acidic zeolites

Under operating conditions, the dynamics of water and ions confined within protonic aluminosilicate zeolite micropores are responsible for many of their properties, including hydrothermal stability, acidity and catalytic activity. However, due to high computational cost, operando studies of acidic zeolites are currently rare and limited to specific cases and simplified models. In this work, we have developed a reactive neural network potential (NNP) attempting to cover the entire class of acidic zeolites, including the full range of experimentally relevant water concentrations and Si/Al ratios. This NNP has the potential to dramatically improve sampling, retaining the (meta)GGA DFT level accuracy, with the capacity for discovery of new chemistry, such as collective defect formation mechanisms at the zeolite surface. Furthermore, we exemplify how the NNP can be used as a basis for further extensions/improvements which include data-efficient adoption of higher-level (hybrid) references via Δ-learning and the acceleration of rare event sampling via automatic construction of collective variables. These developments represent a significant step towards accurate simulations of realistic catalysts under operando conditions.

Solvate Suite: A Command-Line Interface for Molecular Simulations and Multiscale Microsolvation Modeling

In this work, we introduce the Solvate Suite, a comprehensive and modular command-line interface designed for molecular simulation and microsolvation modeling. The suite interfaces with widely used scientific software, streamlining computational experiments for liquid systems through the automated creation of simulation boxes and topology with adjustable simulation parameters. Furthermore, it has features for graphical and statistical analysis of simulated properties and extraction of trajectory configurations with various filters. Additionally, it introduces innovative strategies for microsolvation modeling with a multiscale approach, employing equilibrated dynamics to identify favorable solute-solvent interactions and enabling full cluster optimization for free-energy calculations without imaginary frequency contamination.

A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

Water Arrangements upon Interaction with a Rigid Solute: Multiconfigurational Fenchone-(H2O)4-7 Hydrates

Insight into the arrangements of water molecules around solutes is important to understand how solvation proceeds and to build reliable models to describe water-solute interactions. We report the stepwise solvation of fenchone, a biogenic ketone, with 4-7 water molecules. Multiple hydrates were observed using broadband rotational spectroscopy, and the configurations of four fenchone-(H2O)4, three fenchone-(H2O)5, two fenchone-(H2O)6, and one fenchone-(H2O)7 complexes were characterized from the analysis of their rotational spectra in combination with quantum-chemical calculations. Interactions with fenchone deeply perturb water configurations compared with the pure water tetramer and pentamer. In two fenchone-(H2O)4 complexes, the water tetramer adopts completely new arrangements, and in fenchone-(H2O)5, the water pentamer is no longer close to being planar. The water hexamer interacts with fenchone as the least abundant book isomer, while the water heptamer adopts a distorted prism structure, which forms a water cube when including the fenchone oxygen in the hydrogen bonding network. Differences in hydrogen bonding networks compared with those of pure water clusters show the influence of fenchone's topology. Specifically, all observed hydrates except one show two water molecules binding to fenchone through each oxygen lone pair. The observation of several water arrangements for fenchone-(H2O)4-7 complexes highlights water adaptability and provides insight into the solvation process.

The strength of the OH-bend/OH-stretch Fermi resonance in small water clusters

A novel Raman jet-spectrometer is used to study the Fermi resonance between the OH bending overtone and OH stretching fundamental in small cyclic water clusters (H2O)n with n = 3, 4, 5. The new setup features a recirculating vacuum system which reduces the gas consumption by 2 to 3 orders of magnitude and enables long-term measurements of very weak Raman signals. Raman spectra measured from highly diluted expansions with unprecedented signal-to-noise ratio are presented and cluster-specific intensity ratios and effective coupling constants are derived using Markov-Chain Monte-Carlo methods, yielding a high probability for an almost "perfect" resonance for the tetramer and pentamer, i.e. a close frequency match of bend overtone and stretch fundamental with intensity ratios close to 1, but a larger coupling constant for the trimer, with best estimates close to W5 ≲ 50 cm-1 < W4 ≲ 60 cm-1 < W3 ≈ 65 cm-1.

A computational study of H-bonded networks in cyclic water clusters, (H2O)n (n = 3-12)

CONTEXT

We have performed a detailed MM and DFT investigation of neutral water clusters (H2O)n (n = 3-12). Our results show the trend of interaction energies in these clusters as a function of the size of the cluster. They show that the H-bond strength increases with cluster size and that the model of water is better described if two different partial charges are used on the hydrogen, depending on whether hydrogen is H-bonded or not. The average binding enthalpy change due to the formation of H-bonds between water molecules is found to be - 25.9 kJ mol-1 at B3LYP/aug-cc-pVDZ level of theory. We observe the formation of cyclic H-bonded networks through the analysis of frontier orbitals and IR vibrational frequencies spectra. For the water cluster with n = 11, we observe an unusual reduction of the bandgap indicative of a cyclic H-bonded network.

METHODS

Calculations were performed with the MMFF94 force field and the B3LYP method using various large basis sets. Molecular orbital diagrams and population analysis were done using standard tools in Gaussian.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory

This work systematically examines the interactions between a single argon atom and the edges and faces of cyclic H2O clusters containing three-five water molecules (Ar(H2O)n=3-5). Full geometry optimizations and subsequent harmonic vibrational frequency computations were performed using MP2 with a triple-ζ correlation consistent basis set augmented with diffuse functions on the heavy atoms (cc-pVTZ for H and aug-cc-pVTZ for O and Ar; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the two-body-many-body (2b:Mb) and three-body-many-body (3b:Mb) techniques; here, high-level CCSD(T) computations capture up through the two-body or three-body contributions from the many-body expansion, respectively, while less demanding MP2 computations recover all higher-order contributions. Five unique stationary points have been identified in which Ar binds to the cyclic water trimer, along with four for (H2O)4 and three for (H2O)5. To the best of our knowledge, eleven of these twelve structures have been characterized here for the first time. Ar consistently binds more strongly to the faces than the edges of the cyclic (H2O)n clusters, by as much as a factor of two. The 3b:Mb electronic energies computed with the haTZ basis set indicate that Ar binds to the faces of the water clusters by at least 3 kJ mol-1 and by nearly 6 kJ mol-1 for one Ar(H2O)5 complex. An analysis of the interaction energies for the different binding motifs based on symmetry-adapted perturbation theory (SAPT) indicates that dispersion interactions are primarily responsible for the observed trends. The binding of a single Ar atom to a face of these cyclic water clusters can induce perturbations to the harmonic vibrational frequencies on the order of 5 cm-1 for some hydrogen-bonded OH stretching frequencies.

Prebiotic dimer and trimer peptide formation in gas-phase atmospheric nanoclusters of water

Insight into the origin of prebiotic molecules is key to our understanding of how living systems evolved into the complex network of biological processes on Earth. By modelling diglycine and triglycine peptide formation in the prebiotic atmosphere, we provide a plausible pathway for peptide growth. By examining different transition states (TSs), we conclude that the formation of diglycine and triglycine in atmospheric nanoclusters of water in the prebiotic atmosphere kinetically favors peptide growth by an N-to-C synthesis of glycines through a trans conformation. Addition of water stabilizes the TS structures and lowers the Gibbs free activation energies. At temperatures that model the prebiotic atmosphere, the free energies of activation with a six water nanocluster as part of the TS are predicted to be 16 kcal mol-1 relative to the prereactive complex. Examination of the trans vs. cis six water transition states reveals that a homodromic water network that maximizes the acceptor/donor nature of the six waters is responsible for enhanced kinetic favorability of the trans N-to-C pathway. Compared to the non-hydrated trans TS, the trans six-water TS accelerates the reaction of diglycine and glycine to form triglycine by 13 orders of magnitude at 217 K. Nature uses the trans N-to-C pathway to synthesize proteins in the ribosome, and we note the similarities in hydrogen bond stabilization between the transition state for peptide synthesis in the ribosome and the transition states formed in nanoclusters of water in the same pathway. These results support the hypothesis that small oligomers formed in the prebiotic atmosphere and rained onto earth's surface.

Chitosan Polysaccharides from a Polarizable Multiscale Approach

We report simulations of chitosan polysaccharides in the aqueous phase, at infinite dilute conditions and zero ionic strength. Those simulations are performed by means of a polarizable multiscale modeling scheme that relies on a polarizable all atom force field to model solutes and on a polarizable solvent coarse grained approach. Force field parameters are assigned only from quantum chemistry ab initio data. We simulate chitosan monomer units, dimers and 50-long chains. Regarding the 50-long chains we simulate three sets of ten randomly built chain replica at three different pH conditions (corresponding to different chain protonation states, the chain degree of deacetylation is 85%). Our simulations show the persistence length of 50-long chitosan chains at strong acidic conditions (pH <5) to be 24 ± 2 nm (at weak/negligible ionic strength conditions), and to be 1 order of magnitude shorter at usual pH conditions. Our simulation data support the most recent simulation and experimental studies devoted to chitosan polysaccharides in the aqueous phase.

Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules

We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO2, and O2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (D_e's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (D_e's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

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.

A specific MNDO parameterization for water

A modified neglect of differential overlap has been parameterized specifically for water and its oligomers with the addition of polarization functions on both hydrogen and oxygen, Feynman dispersion, and a slight modification of the treatment of the hydrogen nucleus. The results show that it is possible to easily obtain good geometries and energies for hydrogen-bonded water aggregates. Data from the Benchmark Energy and Geometry Database water-cluster database were used to parameterize the new Hamiltonian for water clusters from the dimer to the decamer using MP2/aug-cc-pVDZ optimized geometries and CCSD(T)/CBS oligomerization energies. Seventy five oligomerization and rearrangement energies derived from the parameterization data are reproduced with a root mean-square error (RMSE) of 0.79 kcal mol^-1 and the geometries of 38 oligomers with an RMSE of 0.17 Å. Interestingly, the Feynman dispersion term adopts a role different from that intended and tunes the atomic polarizability. The implications of these results in terms of future dedicated neglect of diatomic differential overlap Hamiltonians and those that use force-field-like atom types are discussed.

Hydrogen bond networks of dimethylsulfoxide (DMSO) pentamer

Understanding of clusters of dimethylsulfoxide (DMSO) is important in several applications in Chemistry. Despite its importance, very few studies of DMSO clusters, (DMSO)_n, have been reported in comparison to systems such as water clusters or methanol clusters. In order to provide further understanding of DMSO clusters, we investigated the structures and non-covalent interactions of the (DMSO)_n, n=5. Therefore, the potential energy surface (PES) of the DMSO pentamer has been examined using classical molecular dynamics. The structures generated using classical molecular dynamics are further optimized at the PW6B95D3/aug-cc-pVDZ level of theory. To comprehend the non-covalent bondings in the DMSO pentamer, we carried out a quantum theory of atoms in molecule (QTAIM) analysis. In addition, the effects of temperature on the structural stability is investigated between 20 and 500K. It comes out that seven different kind of non-covalent bondings can be found in DMSO pentamers.

Adsorption free energy of phenol onto coronene: Solvent and temperature effects

Molecular modeling can considerably speed up the discovery of materials with high adsorption capacity for wastewater treatment. Despite considerable efforts in computational studies, the molecular modeling of adsorption processes has several limitations in reproducing experimental conditions. Handling the environmental effects (solvent effects) and the temperature effects are part of the important limitations in the literature. In this work, we address these two limitations using the adsorption of phenol onto coronene as case study. In the proposed model, for the solvent effects, we used a hybrid solvation model, with n explicit water molecules and implicit solvation. We increasingly used n=1 to n=12 explicit water molecules. To account for the temperature effects, we evaluated the adsorption efficiency using the adsorption free energy for temperatures varying from 200 to 400K. We generated initial configurations using classical molecular dynamics, before further optimisation at the ωB97XD/aug-cc-pVDZ level of theory. Polarisable continuum solvation model (PCM) is used for the implicit solvation. The adsorption free energy is evaluated to be -1.3kcal/mol at room temperature. It has been found that the adsorption free energy is more negative at low temperatures. Above 360K, the adsorption free energy is found to be positive.

Transferable Potential Function for Flexible H2O Molecules Based on the Single-Center Multipole Expansion

A potential function is presented for describing a system of flexible H₂O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H₂O)_n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Probing the Free Energy of Small Water Clusters: Revisiting Classical Nucleation Theory

By addressing the defects in classical nucleation theory (CNT), we develop an approach for extracting the free energy of small water clusters from nucleation rate experiments without any assumptions about the form of the cluster free energy. For temperatures higher than ∼250 K, the extracted free energies from experimental data points indicate that their ratio to the free energies predicted by CNT exhibits nonmonotonic behavior as the cluster size changes. We show that this ratio increases from almost zero for monomers and passes through (at least) one maximum before approaching one for large clusters. For temperatures lower than ∼250 K, the behavior of the ratio between extracted energies and CNT's prediction changes; it increases with cluster size, but it remains below one for almost all of the experimental data points. We also applied a state-of-the-art quantum mechanics model to calculate free energies of water clusters (2-14 molecules); the results support the observed change in behavior based on temperature, albeit for temperatures above and below ∼298 K. We compared two different model chemistries, DLPNO-CCSD(T)/CBS//ωB97xD/6-31++G** and G3, against each other and the experimental value for formation of the water dimer.

Amino Acids Compete with Ammonia in Sulfuric Acid-Based Atmospheric Aerosol Prenucleation: The Case of Glycine and Serine

We present a computational investigation of the sulfuric acid, glycine, serine, ammonia, and water system to understand if this system can form prenucleation clusters, which are precursors to larger aerosols in the atmosphere. We have performed a comprehensive configurational search of all possible clusters in this system, starting with the four different monomers and zero to five waters. Accurate Gibbs free energies of formation have been calculated with the DLPNO-CCSD(T)/complete basis set (CBS) method on ωb97xd/6-31++G** geometries. For the dry dimers of sulfuric acid, the weakest base, serine, is found to form the most stable complex, which is a consequence of the strong di-ionic complex formed between the bisulfate ion and the protonated serine cation. For the dry dimers without sulfuric acid, the glycine-serine complex is more stable than the glycine-ammonia or serine-ammonia complexes, stemming from the detailed structure and not related to base strength. For the larger complexes, sulfuric acid deprotonates and the proton is shifted to glycine, serine, or ammonia. The two amino acids and ammonia are almost interchangeable and there is no easy way to predict which molecule will be protonated without the calculated results. Assuming reasonable starting concentrations and a closed system of sulfuric acid, glycine, serine, ammonia, and five waters, we predict the concentrations of all possible complexes at two temperatures spanning the troposphere. The most negative ΔG° values are a function of the detailed molecular interactions of these clusters. These details are more important than the base strength of ammonia, glycine, and serine.

Attosecond spectroscopy of size-resolved water clusters

Electron dynamics in water are of fundamental importance for a broad range of phenomena^1-3, but their real-time study faces numerous conceptual and methodological challenges^4-6. Here, we introduce attosecond size-resolved cluster spectroscopy and build up a molecular-level understanding of the attosecond electron dynamics in water. We measure the effect that the addition of single water molecules has on the photoionization time delays^7-9 of water clusters. We find a continuous increase of the delay for clusters containing up to 4-5 molecules and little change towards larger clusters. We show that these delays are proportional to the spatial extension of the created electron hole, which first increases with cluster size and then partially localizes through the onset of structural disorder that is characteristic of large clusters and bulk liquid water. These results suggest a previously unknown sensitivity of photoionization delays to electron-hole delocalization and indicate a direct link between electronic structure and attosecond photoionization dynamics. Our results offer novel perspectives for studying electron/hole delocalization and its attosecond dynamics.

How Good Is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What Is So Right about the Hartree-Fock Density?

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H^*, covalently bound to the donor oxygen atom) from the acceptor (O_A) and donor (O_D) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

A double exponential coupled cluster theory in the fragment molecular orbital framework

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

Putting together the puzzle of ion transfer in single-digit carbon nanotubes: mean-field meets ab initio

Nature employs channel proteins to selectively pass water across cell membranes, which inspires the search for bio-mimetic analogues. Carbon nanotube porins (CNTPs) are intriguing mimics of water channels, yet ion transport in CNTPs still poses questions. As an alternative to continuum models, here we present a molecular mean-field model that transparently describes ion coupling, yet unlike continuum models, computes ab initio all required thermodynamic quantities for the KCl salt and H⁺ and OH^- ions present in water. Starting from water transfer, the model considers the transfer of free ions, along with ion-pair formation as a proxy of non-mean-field ion-ion interactions. High affinity to hydroxide, suggested by experiments, making it a dominant charge carrier in CNTPs, is revealed as an exceptionally favorable transfer of KOH pairs. Nevertheless, free ions, coexisting with less mobile ion-pairs, apparently control ion transport. The model well explains the observed effects of salt concentration and pH on conductivity, transport numbers, anion permeation and its activation energies, and current rectification. The proposed approach is extendable to other sub-nanochannels and helps design novel osmotic materials and devices.

Finding critical points and reconstruction of electron densities on grids

The quantum theory of atoms in molecules (QTAIM), developed by Bader and co-workers, is one of the most popular ways of extracting chemical insight from the results of quantum mechanical calculations. One of the basic tasks in QTAIM is to locate the critical points of the electron density and calculate various quantities (density, Laplacian, etc.) on them since these have been found to correlate with molecular properties of interest. If the electron density is given analytically, this process is relatively straightforward. However, locating the critical points is more challenging if the density is known only on a three-dimensional uniform grid. A density grid is common in periodic solids because it is the natural expression for the electron density in plane-wave calculations. In this article, we explore the reconstruction of the electron density from a grid and its use in critical point localization. The proposed reconstruction method employs polyharmonic spline interpolation combined with a smoothing function based on the promolecular density. The critical point search based on this reconstruction is accurate, trivially parallelizable, works for periodic and non-periodic systems, does not present directional lattice bias when the grid is non-orthogonal, and locates all critical points of the underlying electron density in all tests studied. The proposed method also provides an accurate reconstruction of the electron density over the space spanned by the grid, which may be useful in other contexts besides critical point localization.

Solvation stabilizes intercarbonyl n→π* interactions and polyproline II helix

n→π* interactions between consecutive carbonyls stabilize the α-helix and polyproline II helix (PPII) conformations in proteins. n→π* interactions have been suggested to provide significant conformational biases to the disordered states of proteins. To understand the roles of solvation on the strength of n→π* interactions, computational investigations were conducted on a model n→π* interaction, the twisted-parallel-offset formaldehyde dimer, as a function of explicit solvation of the donor and acceptor carbonyls, using water and HF. In addition, the effects of urea, thiourea, guanidinium, and monovalent cations on n→π* interaction strength were examined. Solvation of the acceptor carbonyl significantly strengthens the n→π* interaction, while solvation of the donor carbonyl only modestly weakens the n→π* interaction. The n→π* interaction strength was maximized with two solvent molecules on the acceptor carbonyl. Urea stabilized the n→π* interaction via simultaneous engagement of both oxygen lone pairs on the acceptor carbonyl. Solvent effects were further investigated in the model peptides Ac-Pro-NMe₂, Ac-Ala-NMe₂, and Ac-Pro₂-NMe₂. Solvent effects in peptides were similar to those in the formaldehyde dimer, with solvation of the acceptor carbonyl increasing n→π* interaction strength and resulting in more compact conformations, in both the proline endo and exo ring puckers, as well as a reduction in the energy difference between these ring puckers. Carbonyl solvation leads to an energetic preference for PPII over both the α-helix and β/extended conformations, consistent with experimental data that protic solvents and protein denaturants both promote PPII. Solvation of the acceptor carbonyl weakens the intraresidue C5 hydrogen bond that stabilizes the β conformation.

Assessing the Interplay between Functional-Driven and Density-Driven Errors in DFT Models of Water

We investigate the interplay between functional-driven and density-driven errors in different density functional approximations within density functional theory (DFT) and the implications of these errors for simulations of water with DFT-based data-driven potentials. Specifically, we quantify density-driven errors in two widely used dispersion-corrected functionals derived within the generalized gradient approximation (GGA), namely BLYP-D3 and revPBE-D3, and two modern meta-GGA functionals, namely strongly constrained and appropriately normed (SCAN) and B97M-rV. The effects of functional-driven and density-driven errors on the interaction energies are first assessed for the water clusters of the BEGDB dataset. Further insights into the nature of functional-driven errors are gained from applying the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) to the interaction energies, which demonstrates that functional-driven errors are strongly correlated with the nature of the interactions. We discuss cases where density-corrected DFT (DC-DFT) models display higher accuracy than the original DFT models and cases where reducing the density-driven errors leads to larger deviations from the reference energies due to the presence of large functional-driven errors. Finally, molecular dynamics simulations are performed with data-driven many-body potentials derived from DFT and DC-DFT data to determine the effect that minimizing density-driven errors has on the description of liquid water. Besides rationalizing the performance of widely used DFT models of water, we believe that our findings unveil fundamental relations between the shortcomings of some common DFT approximations and the requirements for accurate descriptions of molecular interactions, which will aid the development of a consistent, DFT-based framework for the development of data-driven and machine-learned potentials for simulations of condensed-phase systems.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Density Functional Theory of Water with the Machine-Learned DM21 Functional

The delicate interplay between functional-driven and density-driven errors in density functional theory (DFT) has hindered traditional density functional approximations (DFAs) from providing an accurate description of water for over 30 years. Recently, the deep-learned DeepMind 21 (DM21) functional has been shown to overcome the limitations of traditional DFAs as it is free of delocalization error. To determine if DM21 can enable a molecular-level description of the physical properties of aqueous systems within Kohn-Sham DFT, we assess the accuracy of the DM21 functional for neutral, protonated, and deprotonated water clusters. We find that the ability of DM21 to accurately predict the energetics of aqueous clusters varies significantly with cluster size. Additionally, we introduce the many-body MB-DM21 potential derived from DM21 data within the many-body expansion of the energy and use it in simulations of liquid water as a function of temperature at ambient pressure. We find that size-dependent functional-driven errors identified in the analysis of the energetics of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength and, consequently, predicting a more ice-like local structure of water at room temperature.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Hydrogen-Bond Topology Is More Important Than Acid/Base Strength in Atmospheric Prenucleation Clusters

We explored the hypothesis that on the nanoscale level, acids and bases might exhibit different behavior than in bulk solution. Our study system consisted of sulfuric acid, formic acid, ammonia, and water. We calculated highly accurate Domain-based Local pair-Natural Orbital- Coupled-Cluster/Complete Basis Set (DLPNO-CCSD(T)/CBS) energies on DFT geometries and used the resulting Gibbs free energies for cluster formation to compute the overall equilibrium constants for every possible cluster. The equilibrium constants combined with the initial monomer concentrations were used to predict the formation of clusters at the top and the bottom of the troposphere. Our results show that formic acid is as effective as ammonia at forming clusters with sulfuric acid and water. The structure of formic acid is uniquely suited to form hydrogen bonds with sulfuric acid. Additionally, it can partner with water to form bridges from one side of sulfuric acid to the other, hence demonstrating that hydrogen bonding topology is more important than acid/base strength in these atmospheric prenucleation clusters.

Low-energy electron distributions from the photoionization of liquid water: a sensitive test of electron mean free paths

The availability of accurate mean free paths for slow electrons (<50 eV) in water is central to the understanding of many electron-driven processes in aqueous solutions, but their determination poses major challenges to experiment and theory alike. Here, we describe a joint experimental and theoretical study demonstrating a novel approach for testing, and, in the future, refining such mean free paths. We report the development of Monte-Carlo electron-trajectory simulations including elastic and inelastic electron scattering, as well as energy loss and secondary-electron production to predict complete photoelectron spectra of liquid water. These simulations are compared to a new set of photoelectron spectra of a liquid-water microjet recorded over a broad range of photon energies in the extreme ultraviolet (20-57 eV). Several previously published sets of scattering parameters are investigated, providing direct and intuitive insights on how they influence the shape of the low-energy electron spectra. A pronounced sensitivity to the escape barrier is also demonstrated. These simulations considerably advance our understanding of the origin of the prominent low-energy electron distributions in photoelectron spectra of liquid water and clarify the influence of scattering parameters and the escape barrier on their shape. They moreover describe the reshaping and displacement of low-energy photoelectron bands caused by vibrationally inelastic scattering. Our work provides a quantitative basis for the interpretation of the complete photoelectron spectra of liquids and opens the path to fully predictive simulations of low-energy scattering in liquid water.

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...

Coupled Anharmonic Thermochemistry from Stratified Monte Carlo Integration

This study presents configuration integral Monte Carlo integration (CIMCI), a new semiclassical method for handling fully coupled anharmonicity in gas-phase thermodynamics that promises to be black boxable, to be applicable to all kinds of anharmonicity, and to scale better at higher dimensionality than other methods for handling gas-phase molecular anharmonicity. The method does so using automatically and recursively stratified, simultaneous Monte Carlo (MC) integration of multiple functions, following a modified version of the standard MISER scheme that converges at a rate of about the square of naïve MC integration. For the small systems analyzed by this study where proper reference data is available (H₂O and H₂O₂), the method's anharmonic entropy corrections match reference data better than those of other black box anharmonic methods, e.g., vibrational perturbation theory (VPT2) and the McClurg hindered rotor model used with automatic detection of rotors; for H₂O₂ and NH₂OH, the method is also in general agreement with one-dimensional hindered rotor treatments at low temperatures. This holds even when sampling with CIMCI is done with primitive force fields, e.g., UFF, while the competing methods are used with proper, comprehensive potentials, e.g., the M06-2X metahybrid density-functional theory (DFT) functional.

Regularized Second-Order Møller-Plesset Theory: A More Accurate Alternative to Conventional MP2 for Noncovalent Interactions and Transition Metal Thermochemistry for the Same Computational Cost

Second-order Møller-Plesset theory (MP2) notoriously breaks down for π-driven dispersion interactions and dative bonds in transition metal complexes. Herein, we investigate three physically justified forms of single-parameter, energy-gap dependent regularization which can yield high and transferable accuracy for a variety of noncovalent interactions (including S22, S66, and L7 test sets) and (mostly closed shell) transition metal thermochemistry. Regularization serves to damp overestimated pairwise additive contributions, renormalizing first-order amplitudes such that the effects of higher-order correlations are incorporated. The optimal parameter values for the noncovalent and transition metal sets are 1.1, 0.7, and 0.4 for κ, σ, and σ² regularizers, respectively. However, such regularization slightly degrades the accuracy of conventional MP2 for some small-molecule test sets, most of which have relatively large average frontier energy gaps. Our results suggest that appropriately regularized MP2 models may improve double hybrid density functionals, at no additional cost over conventional MP2.

Theoretical Aspects of Nonconventional Hydrogen Bonds in the Complexes of Aldehydes and Hydrogen Chalcogenides

Hydrogen bonds (H-bonds) in the complexes between aldehydes and hydrogen chalcogenides, XCHO...nH₂Z with X = H, F, Cl, Br, and CH₃, Z = O, S, Se, and Te, and n = 1,2, were investigated using high-level ab initio calculations. The C_sp2-H...O H-bonds are found to be about twice as strong as the C_sp2-H...S/Se/Te counterparts. Remarkably, the S/Se/Te-H...S/Se/Te H-bonds are 4.5 times as weak as the O-H...O ones. The addition of the second H₂Z molecule into binary systems induces stronger complexes and causes a positive cooperative effect in ternary complexes. The blue shift of C_sp2-H stretching frequency involving the C_sp2-H...Z H-bond sharply increases when replacing one H atom in HCHO by a CH₃ group. In contrast, when one H atom in HCHO is substituted with a halogen, the magnitude of blue-shifting of the C_sp2-H...Z H-bond becomes smaller. The largest blue shift up to 92 cm^-1 of C_sp2-H stretching frequency in C_sp2-H...O H-bond in CH₃CHO...2H₂O has rarely been observed and is much greater than that in the cases of the C_sp2-H...S/Se/Te ones. The C_sp2-H blue shift of C_sp2-H...Z bonds in the halogenated aldehydes is converted into a red shift when H₂O is replaced by a heavier analogue, such as H₂S, H₂Se, or H₂Te. The stability and classification of nonconventional H-bonds including C_sp2-H...Se/Te, Te-H...Te, and Se/Te-H...O have been established for the first time.

Structures, binding energies and non-covalent interactions of furan clusters

Understanding of the furan solvent is subjected to the knowledge of the structures of the furan clusters and interactions taking place therein. Although, furan clusters can be very important to determine the dynamics and the properties of the furan solvent, there has been only a few investigations reported on furan dimer. In this work, we have explored the potential energy surfaces (PESs) of the furan clusters using two incremental levels of theory. Structures have been initially generated using classical molecular dynamics followed by full optimization at the MP2/aug-cc-pVDZ level of theory. The results show that the most stable structure of the furan dimer has a stacking configuration while that of the trimer has a cyclic configuration. We have noted that the structures of the furan tetramer have no definite configurations. In addition, we have performed a quantum theory of atoms in molecule (QTAIM) analysis to identify all possible non-covalent interactions of the furan clusters. The results show that six different types of non-covalent interactions can be identified in furan clusters. We have noted that the CH⋯C and CH⋯O hydrogen bondings are the strongest non-covalent interactions while the H⋯H bonding interaction is found to be the weakest. Furthermore, we have assessed the performance of ten DFT functionals in calculating the binding energies of the furan clusters. The ten DFT functionals (M05, M05-2X, M06, M06-2X, M08HX, PBE0, ωB97XD, PW6B95D3, APFD and MN15) have been benchmarked to DLPNO-CCSD(T)/CBS. The functionals M05-2X and M06 are recommended for further affordable investigations of the furan clusters.