A discrete-variable-representation-based symmetry adaptation algorithm is presented and implemented in the fourth-age quantum-chemical rotational-vibrational code GENIUSH. The utility of the symmetry-adapted version of GENIUSH is demonstrated by the computation of seven-dimensional bend-only vibrational and rovibrational eigenstates of the highly fluxionally symmetric C H 5 + molecular ion, a prototypical astructural system. While the numerical results obtained and the symmetry labels of the computed rovibrational states of C H 5 + are of considerable utility by themselves, it must also be noted that the present study confirms that the nearly unconstrained motion of the five hydrogen atoms orbiting around the central carbon atom results in highly complex rotational-vibrational quantum dynamics and renders the understanding of the high-resolution spectra of C H 5 + extremely challenging.

1.
M.
Quack
,
Handbook of High-Resolution Spectroscopy
(
Wiley
,
New York
,
2011
), Vol. 1, pp.
659
722
.
2.
Symmetrie und Asymmetrie in Wissenschaft und Kunst
, Nova Acta Leopoldina NF Vol. 412, edited by
M.
Quack
and
J.
Hacker
(
Wissenschaftliche Verlagsgesellschaft
,
Stuttgart
,
2016
), pp.
7
275
, with 14 articles from various authors.
3.
C.
Lanczos
,
J. Res. Natl. Bur. Stand.
45
,
255
(
1950
).
4.
H. C.
Longuet-Higgins
,
Mol. Phys.
6
,
445
(
1963
).
5.
M.
Quack
,
Mol. Phys.
34
,
477
(
1977
).
6.
P. R.
Bunker
and
P.
Jensen
,
Molecular Symmetry and Spectroscopy
, 2nd ed. (
NRC Research Press
,
Ottawa
,
1998
).
7.
I. M.
Mills
and
M.
Quack
,
Mol. Phys.
100
,
9
(
2002
).
8.
M.
Schnell
,
Handbook of High-Resolution Spectroscopy
(
Wiley
,
New York
,
2011
), Vol. 1, pp.
607
632
.
9.
T.
Oka
,
Handbook of High-Resolution Spectroscopy
(
Wiley
,
New York
,
2011
), Vol. 1, pp.
633
658
.
10.
R. M.
Whitnell
and
J. C.
Light
,
J. Chem. Phys.
89
,
3674
(
1988
).
11.
H.
Wei
and
T.
Carrington
,
J. Chem. Phys.
101
,
1343
(
1994
).
12.
A.
McNichols
and
T.
Carrington
,
Chem. Phys. Lett.
202
,
464
(
1993
).
13.
H.-S.
Lee
,
H.
Chen
, and
J. C.
Light
,
J. Chem. Phys.
119
,
4187
(
2003
).
14.
H.-G.
Yu
,
J. Chem. Phys.
117
,
2030
(
2002
).
15.
D. O.
Harris
,
G. G.
Engerholm
, and
W. D.
Gwinn
,
J. Chem. Phys.
43
,
1515
(
1965
).
16.
J. C.
Light
and
T.
Carrington
,
Adv. Chem. Phys.
114
,
263
(
2000
).
17.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
114
,
1473
(
2001
).
18.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
118
,
6946
(
2003
).
19.
B.
Poirier
,
J. Chem. Phys.
119
,
90
(
2003
).
20.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
119
,
94
(
2003
).
21.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
119
,
101
(
2003
).
22.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
121
,
2937
(
2004
).
23.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
123
,
154303
(
2005
).
24.
R.
Marquardt
and
M.
Quack
,
J. Chem. Phys.
109
,
10628
(
1998
).
25.
B. J.
Braams
and
J. M.
Bowman
,
Int. Rev. Phys. Chem.
28
,
577
(
2009
).
26.
S. N.
Yurchenko
,
A.
Yachmenev
, and
R. I.
Ovsyannikov
,
J. Chem. Theory Comput.
13
,
4368
(
2017
).
27.
NITROGEN, Numerical and Iterative Techniques for Rovibronic Energies with General Internal Coordinates, a program by
P. B.
Changala
, http://www.colorado.edu/nitrogen.
28.
V. L.
Tal’roze
and
A. K.
Lyubimova
,
Dokl. Akad. Nauk SSSR
86
,
909
(
1952
).
29.
G. A.
Olah
,
My Search for Carbocations and Their Role in Chemistry
, Les Prix Nobel en 1994 (
The Nobel Foundation
,
Stockholm
,
1994
), pp.
149
176
, Nobel Lecture, 8 December 1994.
30.
G. A.
Olah
,
J. Am. Chem. Soc.
94
,
808
(
1972
).
31.
Carbonium Ions
, edited by
G. A.
Olah
and
P. v. R.
Schleyer
(
Wiley
,
New York
,
1968−1976
), Vols. 1–5.
32.
G. A.
Olah
,
Carbocations and Electrophilic Reactions
(
VCH-Wiley Publishers
,
Weinheim
,
1974
).
33.
G. A.
Olah
,
G. K. S.
Prakash
,
K.
Wade
,
Á.
Molnár
, and
R. E.
Williams
,
Hypercarbon Chemistry
, 2nd ed. (
Wiley
,
Hoboken, NJ
,
2011
).
34.
G. A.
Olah
and
G. R. H.
Schlosberg
,
J. Am. Chem. Soc.
90
,
2726
(
1968
).
35.
G. A.
Olah
,
G.
Klopman
, and
R. H.
Schlosberg
,
J. Am. Chem. Soc.
91
,
3261
(
1969
).
36.
G.
Rasul
,
G. K. S.
Prakash
, and
G. A.
Olah
,
Chem. Phys. Lett.
517
,
1
(
2011
).
37.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
129
,
234102
(
2008
).
38.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
144
,
204304
(
2016
).
39.
R.
Wodraszka
and
U.
Manthe
,
J. Phys. Chem. Lett.
6
,
4229
(
2015
).
40.
I. M.
Mills
and
H. W.
Thompson
,
Proc. R. Soc. London, Ser. A
226
,
306
(
1954
).
41.
P. R.
Bunker
and
H. C.
Longuet-Higgins
,
Proc. R. Soc. London, Ser. A
280
,
340
(
1964
).
42.
C.
Fábri
,
J.
Sarka
, and
A. G.
Császár
,
J. Chem. Phys.
140
,
051101
(
2014
).
43.
J.
Sarka
,
C.
Fábri
,
T.
Szidarovszky
,
A. G.
Császár
,
Z.
Lin
, and
A. B.
McCoy
,
Mol. Phys.
113
,
1873
(
2015
).
44.
J.
Sarka
and
A. G.
Császár
,
J. Chem. Phys.
144
,
154309
(
2016
).
45.
J.
Sarka
,
A. G.
Császár
,
S. C.
Althorpe
,
D. J.
Wales
, and
E.
Mátyus
,
Phys. Chem. Chem. Phys.
18
,
22816
(
2016
).
46.
J.
Sarka
,
A. G.
Császár
, and
E.
Mátyus
,
Phys. Chem. Chem. Phys.
19
,
15335
(
2017
).
47.
T.
Oka
, in
Proceedings of 17th Colloquium on High Resolution Molecular Spectroscopy, Nijmegen
,
2001
(Infrared Spectroscopy of H 3 + , with discussion of C H 5 + spectra and a bet with M. Quack), p.
290
.
48.
E. T.
White
,
J.
Tang
, and
T.
Oka
,
Science
284
,
135
(
1999
).
49.
O.
Asvany
,
P.
Kumar
,
P. B.
Redlich
,
I.
Hegemann
,
S.
Schlemmer
, and
D.
Marx
,
Science
309
,
1219
(
2005
).
50.
S. D.
Ivanov
,
O.
Asvany
,
A.
Witt
,
E.
Hugo
,
G.
Mathias
,
B.
Redlich
,
D.
Marx
, and
S.
Schlemmer
,
Nat. Chem.
2
,
298
(
2010
).
51.
O.
Asvany
,
K. M. T.
Yamada
,
S.
Brünken
,
A.
Potapov
, and
S.
Schlemmer
,
Science
347
,
1346
(
2015
).
52.
S.
Brackertz
,
S.
Schlemmer
, and
O.
Asvany
, “
Searching for new symmetry species of C H 5 + − From lines to states without a model
,”
J. Mol. Spectrosc.
(to be published).
53.
P. R.
Schreiner
,
S.-J.
Kim
,
H. F.
Schaefer
 III
, and
P. v. R.
Schleyer
,
J. Chem. Phys.
99
,
3716
(
1993
).
54.
H.
Müller
,
W.
Kutzelnigg
,
J.
Noga
, and
W.
Klopper
,
J. Chem. Phys.
106
,
1863
(
1997
).
55.
A.
Brown
,
A. B.
McCoy
,
B. J.
Braams
,
Z.
Jin
, and
J. M.
Bowman
,
J. Chem. Phys.
121
,
4105
(
2004
).
56.
Z.
Jin
,
B. J.
Braams
, and
J. M.
Bowman
,
J. Phys. Chem. A
110
,
1569
(
2006
).
57.
P. R.
Bunker
,
J. Mol. Spectrosc.
176
,
297
(
1996
).
58.
M.
Kolbuszewski
and
P. R.
Bunker
,
J. Chem. Phys.
105
,
3649
(
1996
).
59.
A. L. L.
East
and
P. R.
Bunker
,
J. Mol. Spectrosc.
183
,
157
(
1997
).
60.
A. L. L.
East
,
M.
Kolbuszewski
, and
P. R.
Bunker
,
J. Phys. Chem. A
101
,
6746
(
1997
).
61.
P. R.
Bunker
,
B.
Ostojić
, and
S.
Yurchenko
,
J. Mol. Struct.
695-696
,
253
(
2004
).
62.
D.
Marx
and
M.
Parrinello
,
Nature
375
,
216
(
1995
).
63.
X.
Huang
,
A. B.
McCoy
,
J. M.
Bowman
,
L. M.
Johnson
,
C.
Savage
,
F.
Dong
, and
D. J.
Nesbitt
,
Science
311
,
60
(
2006
).
64.
G. A.
Natanson
,
G. S.
Ezra
,
G.
Delgado-Barrio
, and
R. S.
Berry
,
J. Chem. Phys.
81
,
3400
(
1984
).
65.
G. A.
Natanson
,
G. S.
Ezra
,
G.
Delgado-Barrio
, and
R. S.
Berry
,
J. Chem. Phys.
84
,
2035
(
1986
).
66.
D. M.
Leitner
,
G. A.
Natanson
,
R. S.
Berry
,
P.
Villareal
, and
G.
Delgado-Barrio
,
Comput. Phys. Commun.
51
,
207
(
1988
).
67.
J. E.
Hunter
 III
,
D. M.
Leitner
,
G. A.
Natanson
, and
R. S.
Berry
,
Chem. Phys. Lett.
144
,
145
(
1988
).
68.
M. P.
Deskevich
and
D. J.
Nesbitt
,
J. Chem. Phys.
123
,
084304
(
2005
).
69.
M. P.
Deskevich
,
A. B.
McCoy
,
J. M.
Hutson
, and
D. J.
Nesbitt
,
J. Chem. Phys.
128
,
094306
(
2008
).
70.
F.
Uhl
,
Ł.
Walewski
,
H.
Forbert
, and
D.
Marx
,
J. Chem. Phys.
141
,
104110
(
2014
).
71.
L. M.
Johnson
and
A. B.
McCoy
,
J. Phys. Chem. A
110
,
8213
(
2006
).
72.
C. E.
Hinkle
and
A. B.
McCoy
,
J. Phys. Chem. A
112
,
2058
(
2008
).
73.
C. E.
Hinkle
and
A. B.
McCoy
,
J. Phys. Chem. A
113
,
4587
(
2009
).
74.
C. E.
Hinkle
and
A. B.
McCoy
,
J. Phys. Chem. Lett.
1
,
562
(
2010
).
75.
C. E.
Hinkle
and
A. B.
McCoy
,
J. Phys. Chem. A
116
,
4687
(
2012
).
76.
A. S.
Petit
,
J. E.
Ford
, and
A. B.
McCoy
,
J. Phys. Chem. A
118
,
7206
(
2014
).
77.
H.
Schmiedt
,
S.
Schlemmer
, and
P.
Jensen
,
J. Chem. Phys.
143
,
154302
(
2015
).
78.
H.
Schmiedt
,
P.
Jensen
, and
S.
Schlemmer
,
Phys. Rev. Lett.
117
,
223002
(
2016
).
79.
H.
Schmiedt
,
P.
Jensen
, and
S.
Schlemmer
,
Chem. Phys. Lett.
672
,
34
(
2017
).
80.
A. G.
Császár
,
C.
Fábri
,
T.
Szidarovszky
,
E.
Mátyus
,
T.
Furtenbacher
, and
G.
Czakó
,
Phys. Chem. Chem. Phys.
14
,
1085
(
2012
).
81.
E.
Mátyus
,
G.
Czakó
, and
A. G.
Császár
,
J. Chem. Phys.
130
,
134112
(
2009
).
82.
C.
Fábri
,
E.
Mátyus
, and
A. G.
Császár
,
J. Chem. Phys.
134
,
074105
(
2011
).
83.
C.
Fábri
,
E.
Mátyus
,
T.
Furtenbacher
,
L.
Nemes
,
B.
Mihályi
,
T.
Zoltáni
, and
A. G.
Császár
,
J. Chem. Phys.
135
,
094307
(
2011
).
84.
S. N.
Yurchenko
,
R. J.
Barber
,
A.
Yachmenev
,
W.
Thiel
,
P.
Jensen
, and
J.
Tennyson
,
J. Phys. Chem. A
113
,
11845
(
2009
).
85.
X.-G.
Wang
and
T.
Carrington
,
J. Chem. Phys.
138
,
104106
(
2013
).
86.
B. T.
Sutcliffe
and
J.
Tennyson
,
Int. J. Quantum Chem.
39
,
183
(
1991
).
87.
R.
Wodraszka
and
U.
Manthe
,
J. Phys. Chem. A
117
,
7246
(
2013
).
88.
M.
Rey
,
A. V.
Nikitin
, and
V. G.
Tyuterev
,
Phys. Chem. Chem. Phys.
15
,
10049
(
2013
).
89.
M.
Rey
,
A. V.
Nikitin
, and
V. G.
Tyuterev
,
J. Chem. Phys.
141
,
044316
(
2014
).
90.
M.
Rey
,
A. V.
Nikitin
, and
V. G.
Tyuterev
,
J. Phys. Chem. A
119
,
4763
(
2015
).
91.
E.
Mátyus
,
C.
Fábri
,
T.
Szidarovszky
,
G.
Czakó
,
W. D.
Allen
, and
A. G.
Császár
,
J. Chem. Phys.
133
,
034113
(
2010
).
92.
C.
Eckart
,
Phys. Rev.
47
,
552
(
1935
).
93.
T.
Szidarovszky
,
C.
Fábri
, and
A. G.
Császár
,
J. Chem. Phys.
136
,
174112
(
2012
).
94.
C.
Fábri
,
E.
Mátyus
, and
A. G.
Császár
,
Spectrochim. Acta, Part A
119
,
84
(
2014
).
95.
S. V.
Krasnoshchekov
,
E. V.
Isayeva
, and
N. F.
Stepanov
,
J. Chem. Phys.
140
,
154104
(
2014
).
96.
K.
Sadri
,
D.
Lauvergnat
,
F.
Gatti
, and
H.-D.
Meyer
,
J. Chem. Phys.
141
,
114101
(
2014
).
97.
J.
Pesonen
,
J. Chem. Phys.
140
,
074101
(
2014
).
98.
V.
Szalay
,
J. Chem. Phys.
140
,
234107
(
2014
).
99.
V.
Szalay
,
J. Chem. Phys.
142
,
174107
(
2015
).
100.
V.
Szalay
,
J. Chem. Phys.
143
,
064104
(
2015
).
101.
A.
Yachmenev
and
S.
Yurchenko
,
J. Chem. Phys.
143
,
014105
(
2015
).
102.
E. P.
Wigner
,
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra
(
Academic Press
,
New York
,
1959
).
103.
C.
Leforestier
,
L. B.
Braly
,
K.
Liu
,
M. J.
Elrod
, and
R. J.
Saykally
,
J. Chem. Phys.
106
,
8527
(
1997
).
104.
F. T.
Smith
,
Phys. Rev. Lett.
45
,
1157
(
1980
).
105.
J.
Echave
and
D. C.
Clary
,
Chem. Phys. Lett.
190
,
225
(
1992
).
106.
H.
Wei
and
T.
Carrington
,
J. Chem. Phys.
97
,
3029
(
1992
).
107.
V.
Szalay
,
G.
Czakó
,
Á.
Nagy
,
T.
Furtenbacher
, and
A. G.
Császár
,
J. Chem. Phys.
119
,
10512
(
2003
).
108.
R.
Meyer
,
J. Chem. Phys.
52
,
2053
(
1970
).
109.
J.
Dai
and
J. C.
Light
,
J. Chem. Phys.
107
,
8432
(
1997
).
110.
E. R.
Cohen
,
T.
Cvitas
,
J. G.
Frey
,
B.
Holmström
,
K.
Kuchitsu
,
R.
Marquardt
,
I.
Mills
,
F.
Pavese
,
M.
Quack
,
J.
Stohner
,
H. L.
Strauss
,
M.
Takami
, and
A.
Thor
, , 3rd ed. (Royal Society of Chemistry,
2007
).
111.
B. J.
Dalton
,
Mol. Phys.
11
,
265
(
1966
).
112.
B. J.
Dalton
,
J. Chem. Phys.
54
,
4745
(
1971
).
113.
The GAP Group, GAP–Groups, Algorithms, and Programming, version 4.8.7, 2017, http://www.gap-system.org.

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