The water trimer, as the smallest water cluster in which the three-body interactions can manifest, is arguably the most important hydrogen-bonded trimer. Accurate, fully coupled quantum treatment of its excited intermolecular vibrations has long been an elusive goal. Here, we present the methodology that for the first time allows rigorous twelve-dimensional (12D) quantum calculation of the intermolecular vibration-tunneling eigenstates of the water trimer, with the monomers treated as rigid. These 12D eigenstates are used to simulate the low-frequency absorption spectrum of the trimer for direct comparison with the measured far-infrared (FIR) spectrum of the water trimer in helium nanodroplets. The 12D calculations reveal weak coupling between the large-amplitude torsional and intermolecular stretching vibrations. The calculated torsional tunneling splittings are in excellent agreement with spectroscopic results. There are visible differences between the spectrum simulated using the 12D eigenstates and that based on our earlier 9D calculations where the stretching vibrations are not included. The peaks in the 12D spectrum are generally shifted to slightly lower energies relative to those in the 9D spectrum, as well as the measured FIR spectrum, and are often split by intermolecular stretch–bend Fermi resonances that the 9D treatment cannot capture.

1.
S. S.
Xantheas
,
J. Chem. Phys.
100
,
7523
(
1994
).
2.
M. P.
Hodges
,
A. J.
Stone
, and
S. S.
Xantheas
,
J. Phys. Chem. A
101
,
9163
(
1997
).
3.
Z.
Bačić
and
R. E.
Miller
,
J. Phys. Chem.
100
,
12945
(
1996
).
4.
Y.
Wang
,
X.
Huang
,
B. C.
Shepler
,
B. J.
Braams
, and
J. M.
Bowman
,
J. Chem. Phys.
134
,
094509
(
2011
).
5.
V.
Babin
,
G. R.
Medders
, and
F.
Paesani
,
J. Chem. Theory Comput.
10
,
1599
(
2014
).
6.
U.
Gora
,
W.
Cencek
,
R.
Podeszwa
,
A.
van der Avoird
, and
K.
Szalewicz
,
J. Chem. Phys.
140
,
194101
(
2014
).
7.
Y. C.
Zhu
,
S.
Yang
,
J. X.
Zeng
,
W.
Fang
,
L.
Jiang
,
D. H.
Zhang
, and
X. Z.
Li
,
J. Am. Chem. Soc.
144
,
21356
(
2022
).
8.
W.
Cencek
,
K.
Szalewicz
,
C.
Leforestier
,
R.
van Harrevelt
, and
A.
van der Avoird
,
Phys. Chem. Chem. Phys.
10
,
4716
(
2008
).
9.
C.
Leforestier
,
K.
Szalewicz
, and
A.
van der Avoird
,
J. Chem. Phys.
137
,
014305
(
2012
).
10.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
148
,
074108
(
2018
).
11.
R.
Schwan
,
C.
Qu
,
D.
Mani
,
N.
Pal
,
L.
van der Meer
,
B.
Redlich
,
C.
Leforestier
,
J. M.
Bowman
,
G.
Schwaab
, and
M.
Havenith
,
Angew. Chem., Int. Ed.
58
,
13119
(
2019
).
12.
E.
Vogt
and
H. G.
Kjaergaard
,
Annu. Rev. Phys. Chem.
73
,
209
(
2022
).
13.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
158
,
084107
(
2023
).
14.
N.
Pugliano
and
R. J.
Saykally
,
Science
257
,
1937
(
1992
).
15.
K.
Liu
,
J. G.
Loeser
,
M. J.
Elrod
,
B. C.
Host
,
J. A.
Rzepiela
,
N.
Pugliano
, and
R. J.
Saykally
,
J. Am. Chem. Soc.
116
,
3507
(
1994
).
16.
S.
Suzuki
and
G. A.
Blake
,
Chem. Phys. Lett.
229
,
499
(
1994
).
17.
M. R.
Viant
,
J. D.
Cruzan
,
D. D.
Lucas
,
M. G.
Brown
,
K.
Liu
, and
R. J.
Saykally
,
J. Phys. Chem. A
101
,
9032
(
1997
).
18.
F. N.
Keutsch
and
R. J.
Saykally
,
Proc. Natl. Acad. Sci. U.S.A.
98
,
10533
(
2001
).
19.
F. N.
Keutsch
,
R. S.
Fellers
,
M. G.
Brown
,
M. R.
Viant
,
P. B.
Petersen
, and
R. J.
Saykally
,
J. Am. Chem. Soc.
123
,
5938
(
2001
).
20.
F. N.
Keutsch
,
J. D.
Cruzan
, and
R. J.
Saykally
,
Chem. Rev.
103
,
2533
(
2003
).
21.
M.
Schütz
,
T.
Bürgi
,
S.
Leutwyler
, and
H. B.
Bürgi
,
J. Chem. Phys.
99
,
5228
(
1993
).
22.
D. J.
Wales
,
J. Am. Chem. Soc.
115
,
11180
(
1993
).
23.
T. R.
Walsh
and
D. J.
Wales
,
J. Chem. Soc., Faraday Trans.
92
,
2505
(
1996
).
24.
D.
Sabo
,
Z.
Bačić
,
T.
Bürgi
, and
S.
Leutwyler
,
Chem. Phys. Lett.
244
,
283
(
1995
).
25.
A.
van der Avoird
,
E. H. T.
Olthof
, and
P. E. S.
Wormer
,
J. Chem. Phys.
105
,
8034
(
1996
).
26.
P. M.
Felker
and
Z.
Bačić
,
J. Chem. Phys.
158
,
234109
(
2023
).
27.
I.
Simkó
,
P. M.
Felker
, and
Z.
Bačić
,
J. Chem. Phys.
160
,
164304
(
2024
).
28.
J.
Li
,
P.
Vindel-Zandbergen
,
J.
Li
,
P. M.
Felker
, and
Z.
Bačić
,
J. Phys. Chem. A
128
,
9707
(
2024
).
29.
D.
Sabo
,
Z.
Bačić
,
S.
Graf
, and
S.
Leutwyler
,
Chem. Phys. Lett.
261
,
318
(
1996
).
30.
Z.
Bačić
,
Comput. Phys. Commun.
145
,
184
(
2002
).
31.
E. H. T.
Olthof
,
A.
van der Avoird
,
P. E. S.
Wormer
,
K.
Liu
, and
R. J.
Saykally
,
J. Chem. Phys.
105
,
8051
(
1996
).
32.
M.
Geleijns
and
A.
van der Avoird
,
J. Chem. Phys.
110
,
823
(
1999
).
33.
J. K.
Gregory
and
D. C.
Clary
,
J. Chem. Phys.
102
,
7817
(
1995
).
34.
D.
Blume
and
K. B.
Whaley
,
J. Chem. Phys.
112
,
2218
(
2000
).
35.
R.
Schwan
,
C.
Qu
,
D.
Mani
,
N.
Pal
,
G.
Schwaab
,
J. M.
Bowman
,
G.
Tschumper
, and
M.
Havenith
,
Angew. Chem., Int. Ed.
59
,
11399
(
2020
).
36.
J. O.
Richardson
,
S. C.
Althorpe
, and
D. J.
Wales
,
J. Chem. Phys.
135
,
124109
(
2011
).
37.
M.
Eraković
,
C. L.
Vaillant
, and
M. T.
Cvitaš
,
J. Chem. Phys.
152
,
084111
(
2020
).
38.
C. L.
Vaillant
,
D. J.
Wales
, and
S. C.
Althorpe
,
J. Phys. Chem. Lett.
10
,
7300
(
2019
).
39.
P. M.
Felker
and
Z.
Bačić
,
J. Chem. Phys.
157
,
194103
(
2022
).
40.
T.
Carrington
, Jr.
and
X.-G.
Wang
,
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
1
,
952
(
2011
).
41.
A.
van der Avoird
, “
Vibration-rotation-tunneling levels and spectra of van der Waals molecules
,” in
Vibrational Dynamics of Molecules
, edited by
J. M.
Bowman
(
World Scientific
,
Singapore
,
2022
), p.
194
.
42.
E.
Mátyus
,
A.
Martín Santa Daria
, and
G.
Avila
,
Chem. Commun.
59
,
366
(
2023
).
43.
P. M.
Felker
,
I.
Simkó
, and
Z.
Bačić
,
J. Phys. Chem. A
128
,
8170
(
2024
).
44.
X.-G.
Wang
and
T.
Carrington
, Jr.
,
Can. J. Phys.
79
,
623
(
2001
).
45.
G.
Czakó
,
E.
Mátyus
, and
A. G.
Császár
,
J. Phys. Chem. A
113
,
11665
(
2009
).
46.
H.
Wei
and
T.
Carrington
, Jr.
,
J. Chem. Phys.
97
,
3029
(
1992
).
47.
J.
Echave
and
D. C.
Clary
,
Chem. Phys. Lett.
190
,
225
(
1992
).
48.
P. R.
Bunker
and
P.
Jensen
,
Molecular Symmetry and Spectroscopy
(
NRC Research Press
,
Ottawa, ON
,
1998
).
49.
M. G.
Brown
,
M. R.
Viant
,
R. P.
McLaughlin
,
C. J.
Keoshian
,
E.
Michael
,
J. D.
Cruzan
,
R. J.
Saykally
, and
A.
van der Avoird
,
J. Chem. Phys.
111
,
7789
(
1999
).
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