What is the Best Density Functional to Describe Water Clusters: Evaluation of Widely Used Density Functionals with Various Basis Sets for (H2O)n (n=110)

Fengyu Li, Lu Wang, and Jijun Zhao[*]

School of Physics and Optoelectronic Technology, andCollege of Advanced Science and Technology,Dalian University of Technology, Dalian 116024, China

John Rui-Hua Xie

Department of Applied Physics, Xi’an Jiaotong University, Xi’an 710049, China

Fengyu Li

Department of Physics, University of Puerto Rico, San Juan, PR 00923, USA

Kevin E. Riley, Zhongfang Chen[†]

Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, San Juan, PR 00923, USA

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Table S1 Geometry parameters (RO-H,θH-O-H, RO-O), dipole moments (μ), stabilization energies (SE), and vibration frequencies (υ) of water monomer and dimer from X3LYP calculations with split-valence basis sets of different sizes as implemented in Gaussian 09 program.

monomer / dimer
RO-H (Å) / θH-O-H(°) / μ (Debye) / υ (cm-1) / RO-O (Å) / μ (Debye) / υ (cm-1) / SE (kcal/mol)
Expt. / 0.958a / 104.52a / 1.854b / 1648
3832
3943 a / 2.976c / 2.60d / 3718
3797
3881
3899 e / 2.72 ± 0.35f
6-311+G(2df,2p) / 0.960 / 105.20 / 1.966 / 1632
3826
3929 / 2.905 / 2.69 / 3713
3820
3902
3920 / 2.68
6-31+G(2df,2p) / 0.961 / 105.28 / 1.982 / 1616
3825
3935 / 2.901 / 2.77 / 3700
3821
3906
3927 / 2.67
6-31+G(2d,2p) / 0.960 / 104.27 / 2.085 / 1647
3847
3981 / 2.903 / 2.81 / 3737
3838
3946
3966 / 2.69
6-31+G(2d,p) / 0.963 / 105.33 / 2.013 / 1636
3817
3929 / 2.901 / 2.56 / 3690
3810
3899
3918 / 2.76
6-31+G(d,p) / 0.965 / 105.79 / 2.198 / 1605
3816
3938 / 2.875 / 3.07 / 3700
3817
3907
3933 / 3.23
6-31+G(d) / 0.969 / 105.53 / 2.251 / 1664
3745
3868 / 2.866 / 2.89 / 3635
3747
3834
3863 / 3.44

aBenedict WS, Gailar N, Plyler EK (1956) J Chem Phys 24: 1139-1165

bDyke TR (1973) J Chem Phys 59: 3125-3127

cDyke TR, Mack KM, Muetner JS (1977) J Chem Phys 66: 498-510

dDyke TR (1977) J Chem Phys 66: 492-497

eFredin L, Nelander B, Ribbegard G (1977) J Chem Phys 66: 4065-4072; B.Nelander (1978) J Chem Phys 69: 3870-3871

fCurtiss LA, Frurip DJ, Blander M (1979) J Chem Phys 71: 2703-2711

Table S2.Geometry parameters, dipole moments (μ), stabilization energies (SE), and vibration frequencies (υ) of water monomer and dimer using PBE/TNP method with different cutoff parameters as implemented in DMol3 program.

Expt. / Cutoff (Å)
3.0 / 4.0 / 5.0 / 6.0 / 7.0
(H2O) / RO-H (Å) / 0.958 a / 0.968 / 0.969 / 0.970 / 0.970 / 0.970
θH-O-H(°) / 104.52a / 103.91 / 104.17 / 104.18 / 104.22 / 104.24
μ (Debye) / 1.855b / 1.79 / 1.79 / 1.79 / 1.78 / 1.78
υ(cm-1) / 1648 a
3832, 3943 / 1606,
3703, 3807 / 1591,
3710, 3815 / 1587,
3690, 3796 / 1588,
3691, 3798 / 1592,
3709, 3815
(H2O)2 / RO-O (Å) / 2.976 c / 2.889 / 2.890 / 2.887 / 2.888 / 2.888
μ (Debye) / 2.60 d / 2.67 / 2.65 / 2.65 / 2.65 / 2.64
υ(cm-1) / 3718, 3797
3881, 3899e / 3566, 3722
3788, 3814 / 3551, 3716
3788, 3820 / 3536, 3697
3771, 3801 / 3522, 3691
3763, 3795 / 3535, 3689
3775, 3792
SE (kcal/mol) / 2.7 ± 0.35f / 3.49 / 2.68 / 2.65 / 2.70 / 2.69

aBenedict WS, Gailar N, Plyler EK (1956) J Chem Phys 24: 1139-1165

bDyke TR (1973) J Chem Phys 59: 3125-3127

cDyke TR, Mack KM, Muetner JS (1977) J Chem Phys 66: 498-510

dDyke TR (1977) J Chem Phys 66: 492-497

eFredin L, Nelander B, Ribbegard G (1977) J Chem Phys 66: 4065-8; B.Nelander (1978) J Chem Phys 69: 3870-3871

fCurtiss LA, Frurip DJ, Blander M (1979) J Chem Phys 71: 2703-2711

Table S3.Average adjacent O-O distances (Å) of ground state of (H2O)n (n = 210) from PBE/TNP geometry optimization with different cutoff parameters as implemented in DMol3 program.

PBE/TNP
Cutoff (Å) / 3.0 / 4.0 / 5.0 / 6.0 / 7.0
w2 / 2.889 / 2.890 / 2.887 / 2.888 / 2.888
w3 / 2.766 / 2.768 / 2.767 / 2.767 / 2.767
w4-0 / 2.694 / 2.703 / 2.702 / 2.702 / 2.702
w5-0 / 2.679 / 2.680 / 2.679 / 2.680 / 2.680
w6-0 / 2.816 / 2.818 / 2.816 / 2.816 / 2.817
w7-0 / 2.763 / 2.787 / 2.784 / 2.784 / 2.784
w8-0 / 2.763 / 2.767 / 2.765 / 2.765 / 2.765
w9-0 / 2.729 / 2.751 / 2.750 / 2.750 / 2.751
w10-0 / 2.757 / 2.758 / 2.757 / 2.757 / 2.758

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Reference 95. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, J. A. Montgomery Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Revision A.02 Gaussian, Inc., Wallingford CT

Reference 109.Werner H-L,Knowles PJ, Amos RD, Bernhardsson A, Berning A, Celani P, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Hampel C, Hetzer G, Korona T, Lindh R, Lloyd AW, McNicholas SJ, Manby FR, Meyer W, Mura ME, Nicklass A, Palmieri P, Pitzer R, Rauhut G, Schütz M, Schumann U, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T (2002) MOLPRO, 2002.6 ed. Univ of Birmingham, Birmingham, U.K.

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