Elsevier

Journal of Molecular Liquids

Volume 285, 1 July 2019, Pages 171-177
Journal of Molecular Liquids

Two- and three-body, and relaxation energy terms in water clusters: Application of the hierarchical BSSE corrected decomposition scheme

https://doi.org/10.1016/j.molliq.2019.04.088Get rights and content

Highlights

  • The two- and three-body interaction energy terms are about 80 and 25.

  • The deformation energy of water molecules depends on their H-bonded environment.

  • We analyzed the three-body interaction energy terms.

Abstract

A detailed analysis of the two- and three-body interaction energy components in water clusters containing up to 30 water molecules is performed at the M05-2X/6-311G** level of theory, using the “hierarchical” basis set superposition error (BSSE)-corrected energy decomposition scheme, VMFC(3), of Valiron and Mayer. We showed that the average BSSE-corrected two- and three-body interaction energy terms are about 74 to 80 and 20 to 26%, respectively, of the total BSSE-corrected interaction energy for all investigated clusters. It was observed that the three-body interaction energy component is significantly negative/positive if there are two H-bonds and one attraction/repulsion interaction energy in the corresponding trimer, respectively. Our calculations also revealed that the deformation energy of water molecules is dependent on their H-bonded environment. To assess the accuracy of the calculations presented here, benchmark calculations were carried out at the high, LNO-CCSD(T)/CBS, level of theory.

Introduction

There has been a general consensus that the unique physical, chemical and structural properties of liquid water are originated from the existence of a complex and dynamic three-dimensional hydrogen bonded network [[1], [2], [3], [4], [5], [6]]. There is a series of hypotheses which suggest that the cooperativity of hydrogen bonds has an important role in determining the anomalous properties of water [[7], [8], [9], [10], [11], [12]]. The collective interactions between the water molecules strongly influence a variety of important chemical and physical processes in liquid and solid states, as well. Water clusters [[13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]] can serve as model systems for the precise investigation of H-bonding in condensed phase, thus providing a quantitative estimation of the cooperative effects that determine the structure of aqueous environments such as in liquid water and ice. There are several investigations in the literature in which the authors assessed the influence of cooperativity in water clusters [[29], [30], [31], [32], [33], [34], [35]].

A typical manifestation of the cooperativity is the large proportion of many-body interactions in the clusters. Higher order (three-body and above) non-additive energy terms have been shown to contribute significantly to the energetics of water clusters, up to about 30% of the total interaction energy [[36], [37], [38], [39], [40], [41], [42]]. However, a major problem emerges from many-body energy decompositions schemes when basis set superposition error (BSSE) [[43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]] corrections are also to be computed. BSSE arises as a consequence of using incomplete basis sets for the individual subsystems (“monomers”). There are at least two different approaches for taking into account the BSSE in supramolecular (water cluster) calculations. The “hierarchical” BSSE-corrected energy decomposition scheme named as VMFC(m) (Valiron and Mayer) [[44], [45], [46], [47]] is based on the assumption that for every k-body subcluster [[50], [51], [52], [53], [54], [55]] one can perform an energy decomposition by calculating each 1, 2, …, k-body energy component by using its own k-body basis set (more detailed discussions are given later). The second scheme can be regarded as a direct generalization of the most conventional interpretation of the Boys−Bernardi counterpoise (CP) [43] method, in which every interaction energy term is calculated within the full basis set of the system.

Here we applied the VMFC(m) method for water clusters in the size range of 3 to 30. We systematically assessed the accuracy of our calculations by comparing to high level LNO-CCSD(T)/CBS results [58,59]. We also investigated the contributions of various terms (relaxation energy, two-, three- and many-body terms) in these clusters. In addition, we investigated the relationship between the relaxation energy term and the structure of the H-bonded environment around a central molecule.

Section snippets

Many body energy decomposition scheme

It is widely accepted [46] that one of the main problems when calculating weak intermolecular interactions is the proper consideration of the basis set superposition error (BSSE). The BSSE is an artificial “mathematical effect” which is related to the incomplete and unbalanced quantum chemical description of the monomers in clusters. Valiron and Mayer introduced a generalized method (VMFC(m), where “m” is the last term in the hierarchical scheme) for a consistent treatment of BSSE [44,45] as

Computational details

The geometries of water clusters consisting of 3 to 30, 35, 42, 50(a, b, c, d), 54, 55, 80 and 81 monomers were optimized at the M05-2X/6-311G** level of theory, which method is suitable for such calculations [64]. The initial cluster geometries were taken from the literature [[13], [14], [15],19,20]. These geometries are one of the typical low energy conformers of these water clusters.

In order to assess the accuracy of the correction scheme applied, two different reference calculations were

Hydrogen bond properties of water clusters at their global minima

The structures investigated consist of 3 to 30, 35, 42, 50(a, b, c, d), 54, 55, 80 and 81 water molecules and are denoted as “wan” throughout this article. Cartesian coordinates of the optimized geometries are collected in the Supplementary material. The structures of some representative clusters investigated are shown in Fig. 1. The properties of hydrogen-bonded network topologies have already been studied by several authors [[13], [14], [15],19,20]. It is known that hydrogen bonding

Conclusions

In this study, detailed analyses are presented for the two- and three-body water-water interactions in water clusters of 3 to 30 water molecules, as evaluated at the M05-2X/6-311G** level of theory, by using the hierarchical BSSE-corrected energy decomposition scheme VMFC(3) of Valiron and Mayer [[41], [42], [43]]. At this level of theory, the classical CP, two-body and three-body correction terms are 39%, 5% and 2% of total BSSE-corrected interaction energy, respectively. The accuracy of

Acknowledgements

The authors are grateful to the National Research Development and Innovation Office (NRDIO, NKFIH) for financial support K 124885 K128136. We would like to express appreciation to NIIF for the provided computational resources.

References (64)

  • F. Sciortiono et al.

    Hydrogen bond cooperativity in simulated water: time dependence analysis of pair interactions

    J. Chem. Phys.

    (1989)
  • D.A. Schmidt et al.

    Defective continuous hydrogen-bond networks: an alternative interpretation of IR spectroscopy

    ChemPhysChem

    (2008)
  • A. Luzar

    Extent of inter-hydrogen bond correlations in water. Temperature effect

    Chem. Phys.

    (2000)
  • A. Luzar et al.

    Hydrogen-bond kinetics in liquid water

    Nature

    (1996)
  • J.R. Errington et al.

    Relationship between structural order and the anomalies of liquid water

    Nature

    (2001)
  • J.R. Erringtoni et al.

    Cooperative origin of low-density domains in liquid water

    Phys. Rev. Lett.

    (2002)
  • A. Lenz et al.

    A theoretical study of water equilibria: the cluster distribution versus temperature and pressure for (H2O)n, n = 1–60, and ice

    J. Chem. Phys.

    (2009)
  • A. Lenz et al.

    Theoretical IR spectra for water clusters (H2O)n (n = 6–22, 28, 30) and identification of spectral contributions from different H-bond conformations in gaseous and liquid water

    J. Phys. Chem. A

    (2006)
  • A. Lenz et al.

    Computational studies of the stability of the (H2O)100 nanodrop

    J. Mol. Struct. THEOCHEM

    (2010)
  • K. Hermannson

    Many-body effects in tetrahedral water clusters

    J. Chem. Phys.

    (1988)
  • J. Del bene et al.

    Theory of molecular interactions. I. Molecular orbital studies of water polymers using a minimal slater-type basis

    J. Chem. Phys.

    (1970)
  • L. Ojamaee et al.

    Ab initio study of cooperativity in water chains: binding energies and anharmonic frequencies

    J. Phys. Chem.

    (1994)
  • Y. Tao et al.

    Different ways of hydrogen bonding in water - why does warm water freeze faster than cold water?

    J. Chem. Theory Comput.

    (2017)
  • P. Qian et al.

    Ab initio investigation of water clusters (H2O)n (n = 2–34)

    Int. J. Quantum Chem.

    (2010)
  • T. Anacker et al.

    New accurate benchmark energies for large water clusters: DFT is better than expected

    J. Comput. Chem.

    (2014)
  • P.D. Mezei et al.

    Application of a dual-hybrid direct random phase approximation to water clusters

    J. Chem. Theory Comput.

    (2016)
  • M.J. Gillan et al.

    Energy benchmarks for water clusters and ice structures from an embedded many body expansion

    J. Chem. Phys.

    (2013)
  • J.C. Howard et al.

    Wavefunction methods for the accurate characterization of water clusters

    WIREs Comput. Mol. Sci.

    (2014)
  • K. Kumar et al.

    Conventional and explicitly correlated ab initio benchmark study on water clusters: revision of the BEGDB and WATER27 datasets

    J. Chem. Theory Comput.

    (2017)
  • D. Yuan et al.

    Benchmark relative energies for large water clusters with the generalized energy-based fragmentation method

    J. Chem. Theory Comput.

    (2017)
  • D. Yuan et al.

    Are fragment-based quantum chemistry methods applicable to medium-sized water clusters?

    Phys. Chem. Chem. Phys.

    (2016)
  • S. Iwata et al.

    Cooperative roles of charge transfer and dispersion terms in hydrogen-bonded networks of (H2O)n, n = 6, 11, 16

    J. Phys. Chem. A

    (2013)
  • Cited by (10)

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

      2022, Journal of Molecular Graphics and Modelling
      Citation Excerpt :

      For MP2/aug-cc-pVDZ used for optimization and relative energies as well as DFT functionals associated with aug-cc-pVTZ, BSSE can affect the reported results. Generally, the BSSE correction lower the absolute value of binding energies of the clusters (see for example Bako et al. [95]). Thus, consideration of the BSSE corrections could decrease the binding energies of the clusters.

    View all citing articles on Scopus
    View full text