Supplementary Material for
Second-order many-body perturbation study of Ice Ih
Xiao He,1,2 Olaseni Sode,1 Sotiris S. Xantheas,3 and So Hirata1*
1
Department of Chemistry, University of Illinois at Urbana-Champaign,
600 South Mathews Avenue, Urbana, Illinois 61801, U.S.A.
2
State Key Laboratory of Precision Spectroscopy and Department of Physics,
Institute of Theoretical and Computational Science,
East China Normal University, Shanghai, China 200062
3
Chemical Sciences Division, Pacific Northwest National Laboratory,
902 Battelle Boulevard, Richland, Washington 99352, U.S.A.
*
Corresponding author. E-mail: sohirata@illinois.edu
Table S1. The harmonic and anharmonic frequencies (in cm–1) of the fundamental vibrational transitions of water clusters in the pseudo-translational region. The equilibrium geometry and force constants were obtained at the MP2/aug-cc-pVnZ level (n = D, T, or Q) and the anharmonic vibrational analyses were based on the second-order vibrational perturbation theory.1,2 The infrared absorption intensities (in km/mol)
are given in brackets.
Cluster
(H2O)3
(H2O)4
(H2O)5
(H2O)6 (ring)
Theory
MP2/aug-cc-pVDZ
MP2/aug-cc-pVTZ
MP2/aug-cc-pVQZ
MP2/aug-cc-pVDZ
MP2/aug-cc-pVTZ
MP2/aug-cc-pVDZ
MP2/aug-cc-pVDZ
Lower-frequency mode
Harmonic
Anharmonic
184 [27]
154
188 [21]
148
191 [15]
165
79 [2]
70
81 [2]
72
241 [140]
204
216[21]
189
Higher-frequency mode
Harmonic
Anharmonic
217 [4]
187
219 [4]
180
221 [7]
190
209 [0], 259 [0]
183, 232
208 [0], 260 [0]
182, 232
300 [19]
255
299 [0], 332 [4]
267, 295
Table S2. The harmonic and anharmonic frequencies (in cm–1) of the fundamental vibrational transitions of water clusters in the O–H stretching
region. The equilibrium geometry and force constants were obtained at the MP2/aug-cc-pVnZ or CCSD(T)/aug-cc-pVnZ (n = D or Q) level. The
anharmonic vibrational analyses were based on the second-order vibrational perturbation theory1,2 using the MP2 force constants. The anharmonic frequencies at the CCSD(T) level are estimated as the sums of the anharmonic corrections obtained at the MP2 level and the CCSD(T)
harmonic frequencies for a given basis set. The deviations (in cm–1) from the experimental results3 are given in parentheses. Only the infrared-active modes are listed. For the monomer, the averages of symmetric and antisymmetric stretching frequencies are shown.
Cluster
H2O
(H2O)2
(H2O)3
(H2O)4
(H2O)5
(H2O)6 (S6)
MP2/aug-cc-pVDZ
Harmonic Anharmonic
3870
3682 (25)
3704
3553 (48)
3633
3464 (69)
3641
3475 (58)
3486
3316 (100)
3433
3275 (85)
3442
3282 (78)
3421
3271 (64)
MP2/aug-cc-pVQZ
Harmonic Anharmonic
3901
3722 (–15)
3733
3606 (–5)
3654
3497 (36)
3663
3507 (26)
3505
3335 (81)
3447
3288 (72)
3458
3297 (63)
3437
3288 (48)
CCSD(T)/aug-cc-pVDZ
Harmonic Anharmonic
3845
3657 (50)
3713
3563 (38)
3647
3478 (55)
3654
3488 (45)
3510
3339 (77)
3482
3324 (36)
3491
3331 (29)
···
···
CCSD(T)/aug-cc-pVQZ
Experiment3
Harmonic Anharmonic
3876
3697 (10)
3707
3743
3615 (–14)
3601
3668
3511 (22)
3533
3676
3520 (13)
3533
3529
3358 (58)
3416
3496
3337 (23)
3360
3507
3346 (14)
3360
···
···
3335
References.
1. Barone, V. Anharmonic vibrational properties by a fully automated second-order perturbative approach. J. Chem. Phys. 122, 014108 (2005).
2. Ruden, T. A., Taylor, P. R. & Helgaker, T. Automated calculation of fundamental frequencies: Application to AlH3 using the coupled-cluster
singles-and-doubles with perturbative triples method. J. Chem. Phys. 119, 1951–1960 (2003).
3. Burnham, C. J., Xantheas, S. S., Miller, M. A., Applegate, B. E. & Miller, R. E. The formation of cyclic water complexes by sequential ring
insertion: Experiment and theory. J. Chem. Phys. 117, 1109–1122 (2002).