Structure of liquid water at ambient temperature from ab initio molecular dynamics performed in the complete basis set limit

Structural properties of liquid water at ambient temperature were studied using Car-Parrinello [Phys. Rev. Lett. 55, 2471 (1985)] ab initio molecular dynamics (CPAIMD) simulations combined with the Kohn-Sham (KS) density functional theory and the BLYP exchange-correlation functional for the electronic structure. Unlike other recent work on the same subject, where plane-wave (PW) or hybrid Gaussian/plane-wave basis sets were employed, in the present paper, a discrete variable representation (DVR) basis set is used to expand the KS orbitals, so that with the real-space grid adapted in the present work, the properties of liquid water could be obtained very near the complete basis set limit. Structural properties of liquid water were extracted from a 30 ps CPAIMD-BLYP/DVR trajectory at 300 K. The radial distribution functions (RDFs), spatial distribution functions, and hydrogen bond geometry obtained from the CPAIMD-BLYP/DVR simulation are generally in good agreement with the most up to date experimental measurements. Compared to recent ab initio MD simulations based on PW basis sets, less significant overstructuring was found in the RDFs and the distributions of hydrogen bond angles, suggesting that previous plane-wave and Gaussian basis set calculations have exaggerated the tendency toward overstructuring.     

Dynamical properties of hydrogen sulphide motion in its clathrate hydrate from ab initio and classical isobaric-isothermal molecular dynamics

Equilibrium ab initio (AI) and classical constant pressure-constant temperature molecular dynamics (MD) simulations have been performed to investigate the dynamical properties in (type I) hydrogen sulphide hydrate at 150 and 300 K and 1 bar, and also lower temperatures, with particular scrutiny of guest motion. The rattling motions of the guests in the large and small cavities were around 45 and 75-80 cm(-1), respectively, from AIMD, with the corresponding classical MD modes being 10-12 cm(-1) less at 150 K and around 5 cm(-1) lower at 300 K. The rattling motion in the small cavity overlapped somewhat with the translational motion of the host lattice (with modes at circa 85 and 110 cm(-1)), due in part to a smaller cage radius and more frequent occurrences of guest-host hydrogen bonding leading to greater coupling in the motion. The experimentally determined H-S stretch and H-S-H bending frequencies, in the vicinity of 2550-2620 and 1175 cm(-1) [H.R. Richardson et al., J. Chem. Phys.1985, 83, 4387] were reproduced successfully in the AIMD simulations. Consideration of Kubic harmonics for the guest molecules from AIMD revealed that a preferred orientation of the dipole-vector (or C(2)-axis) exists at 150 K vis--vis the [100] cube axis in both the small and large cavities, but is markedly more significant for the small cavity, while there is no preferred orientation at 300 K. In comparison, classical MD did not reveal any preferred orientation at either temperature, or at 75 K (closer to the AIMD simulation at 150 K vis-à-vis that approach's estimated melting point). Probing rotational dynamics of the guests reinforced this temperature effect, revealing more rapid rotational time scales at 300 K with faster decay times of dipole-vector (C(2)) and H-H-vector (C(2)(y)) being similar for each cage, at around 0.25 and 0.2 ps, respectively, versus approximately 0.45 and 0.5 ps (large) and 0.8 ps (small) at 150 K. It was found that the origin of the observed preferred orientations, especially in the small cages, at 150 K via AIMD was attributable to optimization of the dipolar interaction between the guest and outward-pointing water dipoles in the cavity, with guests "flitting" rotationally between various such configurations, forming occasionally hydrogen bonds with the host molecules.     

Ab initio molecular dynamics with discrete variable representation basis sets: techniques and application to liquid water

Finite temperature ab initio molecular dynamics (AIMD), in which forces are obtained from "on-the-fly" electronic structure calculations, is a widely used technique for studying structural and dynamical properties of chemically active systems. Recently, we introduced an AIMD scheme based on discrete variable representation (DVR) basis sets, which was shown to have improved convergence properties over the conventional plane wave (PW) basis set [Liu,Y.; et al. Phys. Rev. B 2003, 68, 125110]. In the present work, the numerical algorithms for the DVR based AIMD scheme (DVR/AIMD) are provided in detail, and the latest developments of the approach are presented. The accuracy and stability of the current implementation of the DVR/AIMD scheme are tested by performing a simulation of liquid water at ambient conditions. The structural information obtained from the present work is in good agreement with the result of recent AIMD simulations with a PW basis set (PW/AIMD). Advantages of using the DVR/AIMD scheme over the PW/AIMD method are discussed. In particular, it is shown that a DVR/AIMD simulation of liquid water in the complete basis set limit is possible with a relatively small number of grid points.     

聚N,N-二乙基丙烯酰胺低聚物水溶液的分子动力学研究

对50个单元构成的聚N,N-二乙基丙烯酰胺(PDEA)低聚物的水溶液体系进行了分子动力学的研究,分别模拟了300 K时的伸展链、310 K时的伸展链以及紧缩链与水构成的体系,对溶液中PDEA周围溶剂水分子的分布情况以及水分子形成氢键的情况进行了统计,结果表明在PDEA周围的水产生了比本体水更有序的结构,形成了更多的氢键,这种有序结构维持到第二水合层甚至更远.发生相分离后,PDEA与水分子形成的氢键大部分未被破坏,水合层中每个水分子形成的氢键数也没有明显变化,但水合层(形成有序结构的水分子)内水分子数目的减少使得总的氢键数目减少,从而造成体系能量增加及熵增加.同时还研究了聚合物及水分子的自扩散系数,表明PDEA影响周围水分子结构的同时,对水的动力学性质也产生了很大影响.     

Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe2+/Fe3+ Redox Reaction**

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe²⁺/Fe³⁺ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe²⁺/Fe³⁺ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe²⁺/Fe³⁺ system computed from these simulations are compared with the available experimental data for validation.     

eQE: An open‐source density functional embedding theory code for the condensed phase

In this work, we present the main features and algorithmic details of a novel implementation of the frozen density embedding (FDE) formulation of subsystem density functional theory (DFT) that is specifically designed to enable ab initio molecular dynamics (AIMD) simulations of large‐scale condensed‐phase systems containing 1000s of atoms. This code (available at http://eqe.rutgers.edu ) has been given the moniker of embedded Quantum ESPRESSO (eQE) as it is a generalization of the open‐source Quantum ESPRESSO (QE) suite of programs. The strengths of eQE reside in a hierarchical parallelization scheme that allows for an efficient and fully self‐consistent treatment of the electronic structure (via the addition of an additional DIIS extrapolation layer) while simultaneously exploiting the inherent symmetries and periodicities in the system (via sampling of subsystem‐specific first Brillouin zones and utilization of subsystem‐specific basis sets). While bulk liquids and molecular crystals are two classes of systems that exemplify the utility of the FDE approach (as these systems can be partitioned into weakly interacting subunits), we show that eQE has significantly extended this regime of applicability by outperforming standard semilocal Kohn–Sham DFT (KS‐DFT) for large‐scale heterogeneous catalysts with quite different layer‐specific electronic structure and intrinsic periodicities. eQE features very favorable strong parallel scaling for a model system of bulk liquid water composed of 256 water molecules, which allows for a significant decrease in the overall time to solution when compared to KS‐DFT. We show that eQE achieves speedups greater than one order of magnitude ( ) when performing AIMD simulations of such large‐scale condensed‐phase systems as: (1) molecular liquids via bulk liquid water represented by 1024 independent water molecules (3072 atoms with a 25.3× speedup over KS‐DFT), (2) polypeptide/biomolecule solvation via (gly )₆ solvated in (H₂O)₃₉₅ (1230 atoms with a 38.6× speedup over KS‐DFT), and (3) molecular crystals via a 3 × 3 × 3 periodic supercell of pentacene (1940 atoms with a 12.0× speedup over KS‐DFT). These results represent a significant improvement over the current state‐of‐the‐art and now enable subsystem DFT‐based AIMD simulations of realistically sized condensed‐phase systems of interest throughout chemistry, physics, and materials science.     

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.     

Evaluating rotational diffusion from protein MD simulations

It is now feasible to carry out molecular dynamics simulations of proteins in water that are long compared to the overall tumbling of the molecule. Here, we examine rotational diffusion in four small, globular proteins (ubiquitin, binase, lysozyme, and fragment B3 of protein G) with the TIP3P, TIP4P/EW, and SPC/E water models, in simulations that are 6 to 60 times as long as the mean rotational tumbling time. We describe a method for extracting diffusion tensors from such simulations and compare the results to experimental values extracted from NMR relaxation measurements. The simulation results accurately follow a diffusion equation, even for spherical harmonic correlation functions with l as large as 8. However, the best-fit tensors are significantly different from experiment, especially for the commonly used TIP3P water model. Simulations that are 20 to 100 times longer than the rotational tumbling times are needed for good statistics. A number of residues exhibit internal motions on the nanosecond time scale, but in all cases examined here, a product of internal and overall time-correlation functions matches the total time-correlation function well.     

Ab initio QM/MM molecular dynamics study on the excited-state hydrogen transfer of 7-azaindole in water solution

Ab initio molecular dynamics (AIMD) simulations for the excited-state hydrogen transfer (ESHT) reaction of 7-azaindole (7AI-(H2O)n; n = 1, 2) clusters in the gas phase and in water are presented. The effective fragment potential (EFP) is employed to model the surrounding water molecules. The AIMD simulations for 7AI-H2O and 7AI-(H2O)2 clusters show an asynchronous hydrogen transfer at t approximately 50 fs after the photoexcitation. While the ESHT mechanism for 7AI-H2O in water does not change appreciably compared with that in the gas phase, the AIMD simulations on 7AI-(H2O)2 in water solution exhibit two different mechanisms. Since the tautomer form is lower in energy compared to the normal form in the S1 state, 7AI and (H2O) n fragments separate from each other after the ESHT. With the use of the results of the AIMD trajectories, the minimum energy conical intersection point in the tautomer region has also been located.     

A molecular dynamics study of ethanol-water hydrogen bonding in binary structure I clathrate hydrate with CO2

Guest-host hydrogen bonding in clathrate hydrates occurs when in addition to the hydrophilic moiety which causes the molecule to form hydrates under high pressure-low temperature conditions, the guests contain a hydrophilic, hydrogen bonding functional group. In the presence of carbon dioxide, ethanol clathrate hydrate has been synthesized with 10% of large structure I (sI) cages occupied by ethanol. In this work, we use molecular dynamics simulations to study hydrogen bonding structure and dynamics in this binary sI clathrate hydrate in the temperature range of 100-250 K. We observe that ethanol forms long-lived (>500 ps) proton-donating and accepting hydrogen bonds with cage water molecules from both hexagonal and pentagonal faces of the large cages while maintaining the general cage integrity of the sI clathrate hydrate. The presence of the nondipolar CO(2) molecules stabilizes the hydrate phase, despite the strong and prevalent alcohol-water hydrogen bonding. The distortions of the large cages from the ideal form, the radial distribution functions of the guest-host interactions, and the ethanol guest dynamics are characterized in this study. In previous work through dielectric and NMR relaxation time studies, single crystal x-ray diffraction, and molecular dynamics simulations we have observed guest-water hydrogen bonding in structure II and structure H clathrate hydrates. The present work extends the observation of hydrogen bonding to structure I hydrates.     

Investigating the quartz (1010)/water interface using classical and ab initio molecular dynamics

Two different terminations of the (1010) surface of quartz (α and β) interacting with water are simulated by classical (CMD) (using two different force fields) and ab initio molecular dynamics (AIMD) and compared with previously published X-ray reflectivity (XR) experiments. Radial distribution functions between hydroxyl and water show good agreement between AIMD and CMD using the ClayFF force field for both terminations. The Lopes et al. (Lopes, P. E. M.; Murashov, V.; Tazi, M.; Demchuk, E.; MacKerell, A. D. J. Phys. Chem. B2006, 110, 2782-2792) force field (LFF), however, underestimates the extent of hydroxyl-water hydrogen bonding. The β termination is found to contain hydroxyl-hydroxyl hydrogen bonds; the quartz surface hydroxyl hydrogens and oxygens that hydrogen bond with each other exhibit greatly reduced hydrogen bonding to water. Conversely, the hydroxyl hydrogen and oxygens that are not hydrogen bonded to other surface hydroxyls but are connected to those that are show a considerable amount of hydrogen bonding to water. The electron density distribution of an annealed surface of quartz (1010) obtained by XR is in qualitative agreement with electron densities calculated by CMD and AIMD. In all simulation methods, the interfacial water peak appears farther from the surface than observed by XR. Agreement among AIMD, LFF, and XR is observed for the relaxation of the near-surface atoms; however, ClayFF shows a larger discrepancy. Overall, results show that for both terminations of (1010), LFF treats the near-surface structure more accurately whereas ClayFF treats the interfacial water structure more accurately. It is shown that the number of hydroxyl and water hydrogen bonds to the bridging Si-O-Si oxygens connecting the surface silica groups to the rest of the crystal is much greater for the α than the β termination. It is suggested that this may play a role in the greater resistance to dissolution of the β termination than that of the α termination.     

Insights into the structure and dynamics of a room-temperature ionic liquid: ab initio molecular dynamics simulation studies of 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) and the [bmim][PF6]-CO2 mixture

Ab initio molecular dynamics (AIMD) studies have been carried out on liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) and its mixture with CO2 using the Car-Parrinello molecular dynamics (CPMD) method. Results from AIMD and empirical potential molecular dynamics (MD) have been compared and were found to differ in some respects. With a strong resemblance to the crystal, the AIMD simulated neat liquid exhibits many cation-anion hydrogen bonds, a feature that is almost absent in the MD results. The anions were observed to be strongly polarized in the condensed phase. The addition of CO2 increased the probability of this hydrogen bond formation. CO2 molecules in the vicinity of the ions of [bmim][PF6] exhibit larger deviations from linearity in their instantaneous configurations. The polar environment of the liquid induces a dipole moment in CO2, lifting the degeneracy of its bending mode. The calculated splitting in the vibrational mode compares well with infrared spectroscopic data. The solvation of CO2 in [bmim][PF6] is primarily facilitated by the anion, as seen from the radial and spatial distribution functions. CO2 molecules were found to be aligned tangential to the PF6 spheres with their most probable location being the octahedral voids of the anion. The structural data obtained from AIMD simulations can serve as a benchmark to refine interaction potentials for this important room-temperature ionic liquid.     

Wavelet transform analysis of ab initio molecular dynamics simulation: application to core-excitation dynamics of BF3

We propose a novel analysis method of ab initio molecular dynamics (AIMD) simulation using a continuous wavelet transform (c-WT) technique. The c-WT technique, one of the time-frequency signal analysis methods, provides a clear view of the dynamical information in time developments. Combined with the auto-correlation function of velocity by AIMD simulation, c-WT analysis enables us to well understand dynamical distribution, such as the vibrational properties following a change of electronic structure in a molecular system. As a practical application, AIMD simulation of core-excited BF(3) (B1s --> 2a(2) (')) is illustrated. AIMD simulation leads to the change of vibrational motion as well as structural deformation by core-excitation. The c-WT analysis clarifies the relationship between structural deformation and the related significant vibrational modes in core-excitation within 50 fs.     

Embedded,graph-theoretically defined many-body approximations for wavefunction-in-DFT and DFT-in-DFT: Applications to gas- and condensed-phase ab initio molecular dynamics,and potential surfaces for quantum nuclear effects

We present a graph-theoretic approach to adaptively compute many-body approximations in an efficient manner to perform (a) accurate post-Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium- to large-sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed-phase simulations at the cost of pure density functionals, (c) reduced-cost on-the-fly basis extrapolation for gas-phase AIMD and condensed phase studies, and (d) accurate post-HF-level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM-like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many-body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph-theoretic methods. Specifically, a region of chemical interest is coarse-grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many-body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one-dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two-dimensional periodic boundary conditions.     

Description of collective effects in computer models of water

The dynamics of a system containing 3456 water molecules in a cubic cell with periodic boundary conditions at 297 K was simulated. The time dependence of distances between oxygen atoms was examined for many pairs of molecules. These distances often oscillate around a certain average value over long periods of time (10 ps and longer). These average values can be about 2.8 Å (hydrogen bond) or much larger, up to 12–13 Å and more. This suggests that big groups of molecules are involved in a concerted motion. Lists of hydrogen bonds in 50 configurations divided by an interval of about 1 ps are compared. The average lifetime of a hydrogen bond is about 7 ps. The network of hydrogen bonds is colored according to their lifetimes for one of the configurations. The bonds that live longer than 7 ps form an infinite cluster. The bonds that live longer than 8 ps join to form a great number of finite clusters including several hundreds of nodes (molecules). These clusters contain few closed cycles. Even the bonds that live longer than 20 ps are united into clusters each containing two or three nodes (molecules). The self-diffusion coefficient for molecules involved in long-lived bonds is likely to be slightly smaller than that for molecules which do not participate in these bonds.     

Correlations in liquid water for the TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP models

Water is one of the simplest molecules in existence, but also one of the most important in biological and engineered systems. However, understanding the structure and dynamics of liquid water remains a major scientific challenge. Molecular dynamics simulations of liquid water were performed using the water models TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP to calculate the radial distribution functions (RDFs), the relative angular distributions, and the excess enthalpies, entropies, and free energies. In addition, lower-order approximations to the entropy were considered, identifying the fourth-order approximation as an excellent estimate of the full entropy. The second-order and third-order approximations are ~20% larger and smaller than the true entropy, respectively. All four models perform very well in predicting the radial distribution functions, with the TIP5P-Ewald model providing the best match to the experimental data. The models also perform well in predicting the excess entropy, enthalpy, and free energy of liquid water. The TIP4P-2005 and SWM4-NDP models are more accurate than the TIP3P-Ewald and TIP5P-Ewald models in this respect. However, the relative angular distribution functions of the four water models reveal notable differences. The TIP5P-Ewald model demonstrates an increased preference for water molecules to act both as tetrahedral hydrogen bond donors and acceptors, whereas the SWM4-NDP model demonstrates an increased preference for water molecules to act as planar hydrogen bond acceptors. These differences are not uncovered by analysis of the RDFs or the commonly employed tetrahedral order parameter. However, they are expected to be very important when considering water molecules around solutes and are thus a key consideration in modelling solvent entropy.     

Dynamics of TIP5P and TIP4P/ice potentials

The dynamics of a thin film of ice Ih deposited on MgO (001) is studied through molecular dynamics simulations performed with two new potential models of ice. This system is chosen because it is possible to compare the results of the simulations to incoherent neutron quasielastic scattering experiments performed few years ago and to previous molecular dynamics simulations using the TIP4P potential model. The present simulations are performed to determine the evolution of the translational and orientational order parameters of the ice film upon temperature increase in the 250-280 K range. They are also used to calculate the translational and orientational diffusion coefficients of the water molecules in the supported film as a function of the temperature. When using the TIP5P potential, the present results show a better agreement with experimental data than those calculated with the TIP4P potential, especially regarding the temperature above which significant changes are obtained in the dynamics of the water film. Similar conclusions are obtained when using the TIP4P/ice potential, although this latter potential clearly underestimates the translational diffusion coefficients.     

Multiple time scales in solvation dynamics of DNA in aqueous solution: the role of water, counterions, and cross-correlations

Recent time domain experiments have explored solvation dynamics of a probe located inside a DNA duplex, in an effort to gain information, e.g., on the dynamics of water molecules in the DNA major and minor grooves and their environment. Multiple time constants in the range of a few picoseconds to several nanoseconds were obtained. We have carried out 15 ns long atomistic molecular dynamics simulations to study the solvation dynamics of bases of a 38 base-pair long DNA duplex in an aqueous solution containing counterions. We have computed the energy-energy time correlation function (TCF) of the four individual bases (A, T, G, and C) to characterize the solvation dynamics. All the TCFs display highly nonexponential decay with time. When the trajectories are analyzed with 100 fs time resolution, the TCF of each base shows initial ultrafast decay (with tau1 approximately equal 60-80 fs) followed by two intermediate components (tau2 approximately equal 1 ps, tau3 approximately equal 20-30 ps), in near complete agreement with a recent time domain experiment on DNA solvation. Interestingly, the solvation dynamics of each of the four different nucleotide bases exhibit rather similar time scales. To explore the existence of slow relaxation at longer times reported recently in a series of experiments, we also analyzed the solvation TCFs calculated with longer time trajectories and with a larger time resolution of 1 ps. In this case, an additional slow component with a time constant of the order of 250 ps is observed. Through an analysis of partial solvation TCFs, we find that the slow decay originates mainly from the interaction of the nucleotides with the dipolar water molecules and the counterions. An interesting negative cross-correlation between water and counterions is observed, which makes an important contribution to relaxation at intermediate to longer times.     

On the Problem of Criteria for Phase Transitions in Water Clusters (A Hexamer and Octamer Example)

The study concerns the dynamics of a network of hydrogen bonds in small water clusters (on the example of hexamer and octamer clusters). The numerical experiment is carried out with the molecular dynamics method using two analytical rigid potentials TIP4P and TIP5P. According to the obtained results, the criteria of phase transitions provided by the cluster theory are not reliable enough in the case of small water clusters. This is testified by the distributions of potential energies of individual molecules in the clusters. It is shown that the appearance of several peaks in these distributions reflects the number of hydrogen bonds between the molecule and other molecules of the cluster.