Rapid calculation of the hydrogen bonding energies in waterclusters#HAO Jiaojiao, JIANG Xiaonan, WANG Changsheng*510152025303540(School of Chemistry and Chemical Engineering, Liaoning Normal University)Abstract: In this paper the hydrogen binding energies in water clusters (H2O)n (n=3-20) are estimatedwith a polarizable two-dipole model. In this polarizable two-dipole model we regard the two O-Hbonds of a water molecule as two dipoles. The magnitude of the O-H bond dipole moment can bevaried by the presence of a second water molecule. An analytic potential energy function eq. (9), whichexplicitly contains the permanent dipole-dipole interactions, the polarization interactions, the van derWaals interactions and the covalent interactions, is therefore established. The hydrogen bondingenergies in water clusters (H2O)n (n=3-20) are then evaluated by using eq. (9) and compared withthose obtained from MP2/aug-cc-pVTZ calculations including BSSE corrections and with thoseobtained from AMBER99, CHARMM19 and OPLSAA/L force fields. The results show that thehydrogen bonding energies produced by eq. (9) are as accurate as those produced byMP2/aug-cc-pVTZ calculations with BSSE corrections, much better than those produced by the threeforce fields. Calculation results also show that the permanent dipole-dipole interaction is the mostimportant part in hydrogen bonding interaction.Key words: hydrogen bonding energies; polarization; water clusters; dipole-dipole interaction1. IntroductionWater is the most abundant liquid on earth and the most common solvent in chemistry. Theproperties of ice, liquid water and water vapor are truly remarkable and of the utmost importancein a host of chemical and biological processes.1,2 Because the hydrogen bond governs thecharacteristic nature of water, the hydrogen bond network structure of water has been of broadinterest. To understand the network structure of water at the molecular level, water clusters,(H2O)n, have been extensively studied both experimentally and theoretically.A water dimer forms a linear structure,3,4 and a ring structure starts to be formed at trimer.5,6Mandziuk7 have presented a simple perturbation model for the cyclic water trimer whichcorrectly reproduces the experimentally observed low energy vibrational levels. Werner et al8used local electron correlation methods to study the structures and stabilities of water clusters(H2O)n (n=2-4). Balasubramanian9 studied nonrigid group theory, tunneling splittings and nuclearspin statistics of water pentamer. Shields10 predicted accurate anharmonic experimentalvibrational frequencies for water clusters (H2O)n (n=2-5) on the basis of comparing differentmethods with MP2/aug-cc-pVTZ calculated and experimental anharmonic frequencies. Truhlar etal11 evaluated the accuracy of density functionals for prediction of relative energies andgeometries of low-lying isomers of water hexamers. Tschumper and Bates12 presented the MP2and CCSD(T) complete basis set (CBS) limit relative energies for eight low-lying structures of thewater hexamer. Shields et al13 used a scheme combining molecular dynamics (MD) samplingwith MP2 calculations to locate the global and many low lying local minima for water clusters(H2O)n (n=2-10). Sadlej14 theoretically studied structure and spectra of cage clusters (H2O)n(n=7-10). Yoo et al15 found the lowest-energy structures of water (H2O)16 and (H2O)17 at the MP2Foundations: Work supported by the National Natural Science Foundation of China (21133005), the SpecializedResearch Fund for the Doctoral Program of Higher Education of China (20102136110001) and the Program forLiaoning Excellent Talents in University (LR2012037).Brief author introduction:Hao Jiaojiao (1983),female, Doctor Degree Candidate, theoretical and computationalchemistryCorrespondance author: Wang Changsheng (1963), male, professor of Liaoning Normal University, doctor, doctorsupervisor, theoretical and computational chemistry. chwangcslnnu.edu.cn-1-BE 32 cos cos sin sin cos Evdwand CCSD(T) levels of theory.Although ab initio methods such as MP2 and CCSD(T) can produce accurate hydrogenbonding energies for hydrogen-bonded complexes, they are limited when applied to large systems455055such as proteins, nucleic acids, liquid water and ice. In this paper we propose a polarizabletwo-dipole model for water molecule. The parameters needed are derived from fitting to theresults of MP2/aug-cc-pVTZ calculations with the basis set superposition error (BSSE) correctionsof linear water chains containing from five to seven monomeric units. This polarizable two-dipolemodel is then used to evaluate the hydrogen bonding energies in water clusters (H2O)n (n=3-20).The results are compared with those obtained from MP2/aug-cc-pVTZ calculations includingBSSE corrections, and form AMBER99, CHARMM19 and OPLSAA/L calculations. Thecomparisons indicate that the hydrogen bonding energies obtained from this polarizabletw