A new efficient and fully symmetry‐adapted finite‐basis variational method for calculating the rovibrational eigenstates (J≥0) of any sequentially bonded four‐atom molecule is presented. The exact kinetic‐energy operator T̂VR in valence coordinates is used in a scheme of successive basis‐set contractions. The success of the method is demonstrated with new results for the molecules HCCH, HOOH, and HCNO, respectively linear, nonlinear, and quasilinear. The complexity of T̂VR contributes little to the computational cost, yielding a Hamiltonian matrix whose elements can all be cheaply calculated from products of arbitrarily accurate one‐dimensional integrals; the dominant cost is that of matrix diagonalization. Matrices of up to 6000×6000 are used to obtain low‐lying levels converged to small fractions of 1 cm−1, even for the difficult case of HOOH. The generalization to J≥0 allows the calculation of Π states for HCCH and HCNO and effective rotational constants for HCCH, all usefully converged. For the first time nine‐dimensional rovibrational wave functions for four‐atom systems are calculated without dynamical approximation and with basis sets well completed in all degrees of freedom. For HCCH it is straightforward to obtain hundreds of rovibrational (J=0,1,2) levels converged to better than 1.5 cm−1, opening up the possibility of the systematic refinement of the nuclear potential function V̂N.  

1.
G. D.
Carney
,
L. L.
Sprandel
, and
C. W.
Kern
,
Adv. Chem. Phys.
37
,
305
(
1978
).
2.
J.
Tennyson
,
Comput. Phys. Rep.
4
,
1
(
1986
).
3.
S.
Carter
and
N. C.
Handy
,
Comput. Phys. Rep.
5
,
115
(
1986
).
4.
Z.
Bačić
and
J. C.
Light
,
Annu. Rev. Phys. Chem.
40
,
469
(
1989
).
5.
J. K. L.
Macdonald
,
Phys. Rev.
43
,
830
(
1933
).
6.
J. K. G.
Watson
,
Mol. Phys.
15
,
479
(
1968
).
7.
J. K. G.
Watson
,
Mol. Phys.
19
,
465
(
1970
).
8.
R.
Bartholomae
,
D.
Martin
, and
B. T.
Sutcliffe
,
J. Mol. Spectrosc.
87
,
367
(
1981
).
9.
S.
Carter
and
N. C.
Handy
,
J. Mol. Spectrosc.
95
,
9
(
1982
).
10.
B. T. Sutcliffe, in Methods of Computational Chemistry, edited by S. Wilson (Plenum, New York, 1991).
11.
B. T.
Sutcliffe
and
J.
Tennyson
,
Mol. Phys.
58
,
1053
(
1986
).
12.
B. T.
Sutcliffe
and
J.
Tennyson
,
Int. J. Quantum Chem.
39
,
183
(
1991
).
13.
N. C.
Handy
,
Mol. Phys.
61
,
207
(
1987
).
14.
M. J.
Bramley
,
W. H.
Green
, and
N. C.
Handy
,
Mol. Phys.
73
,
1183
(
1991
).
15.
A.
Nauts
and
X.
Chapuisat
,
Mol. Phys.
55
,
1287
(
1985
).
16.
X.
Chapuisat
,
A.
Nauts
, and
J.-P.
Brunet
,
Mol. Phys.
72
,
1
(
1991
).
17.
X.
Chapuisat
,
Mol. Phys.
72
,
1233
(
1991
).
18.
X.
Chapuisat
,
A.
Belafhal
, and
A.
Nauts
,
J. Mol. Spectrosc.
149
,
274
(
1991
).
19.
X.
Chapuisat
and
C.
Iung
,
Phys. Rev. A
45
,
6217
(
1992
).
20.
S.
Carter
and
N. C.
Handy
,
Mol. Phys.
57
,
175
(
1986
).
21.
J.
Tennyson
and
B. T.
Sutcliffe
,
Mol. Phys.
58
,
1067
(
1986
).
22.
J. C.
Light
,
I. P.
Hamilton
, and
J. V.
Lill
,
J. Chem. Phys.
82
,
1400
(
1985
).
23.
Z.
Bačić
and
J. C.
Light
,
J. Chem. Phys.
86
,
3065
(
1987
).
24.
S.
Miller
and
J.
Tennyson
,
Chem. Phys. Lett.
145
,
117
(
1988
).
25.
J. A.
Bentley
,
J.-P.
Brunet
,
R. E.
Wyatt
,
R. A.
Friesner
, and
C.
Leforestier
,
Chem. Phys. Lett.
161
,
393
(
1989
).
26.
S.
Carter
,
N. C.
Handy
, and
I. M.
Mills
,
Philos. Trans. R. Soc. London, Sec. A
332
,
309
(
1990
).
27.
S.
Carter
and
W.
Meyer
,
J. Chem. Phys.
93
,
8902
(
1990
).
28.
J. R.
Henderson
and
J.
Tennyson
,
Chem. Phys. Lett.
173
,
133
(
1990
).
29.
M.
Mladenovic
and
Z.
Bačić
,
J. Chem. Phys.
93
,
3039
(
1990
).
30.
J. A.
Fernley
,
S.
Miller
, and
J.
Tennyson
,
J. Mol. Spectrosc.
150
,
597
(
1991
).
31.
N. C.
Handy
and
S.
Carter
,
Chem. Phys. Lett.
79
,
118
(
1981
).
32.
N. C.
Handy
and
S.
Carter
,
Chem. Phys. Lett.
83
,
216
(
1981
).
33.
B.
Maessen
and
M.
Wolfsberg
,
J. Chem. Phys.
80
,
4651
(
1984
).
34.
B.
Maessen
and
M.
Wolfsberg
,
J. Phys. Chem.
88
,
6420
(
1984
).
35.
B.
Maessen
and
M.
Wolfsberg
,
J. Phys. Chem.
89
,
3876
(
1985
).
36.
P.
Bopp
,
D. R.
McLaughlin
, and
M.
Wolfsberg
,
Z. Naturforsch.
37a
,
398
(
1982
).
37.
B.
Maessen
,
P.
Bopp
,
D. R.
McLaughlin
, and
M.
Wolfsberg
,
Z. Naturforsch.
39a
,
1005
(
1984
).
38.
H.
Romanowski
,
J. M.
Bowman
, and
L. B.
Harding
,
J. Chem. Phys.
82
,
4155
(
1985
).
39.
M.
Aoyagi
,
S. K.
Gray
, and
M. J.
Davis
,
J. Opt. Soc. Am. B
7
,
1859
(
1990
).
40.
M.
Aoyagi
and
S. K.
Gray
,
J. Chem. Phys.
94
,
195
(
1991
).
41.
S.
Carter
and
N. C.
Handy
,
Mol. Phys.
53
,
1033
(
1984
).
42.
S.
Carter
and
N. C.
Handy
,
Comput. Phys. Commun.
51
,
49
(
1988
).
43.
G.
Strey
and
I. M.
Mills
,
J. Mol. Spectrosc.
59
,
103
(
1976
).
44.
A.
Willetts
,
J. F.
Gaw
,
N. C.
Handy
, and
S.
Carter
,
J. Mol. Spectrosc.
135
,
370
(
1989
).
45.
M.-D.
Su
,
A.
Willetts
,
M. J.
Bramley
, and
N. C.
Handy
,
Mol. Phys.
73
,
1209
(
1991
).
46.
N. Pinnavaia, M. J. Bramley, M.-D. Su, W. H. Green, and N. C. Handy, Mol. Phys. (in press).
47.
M. J. Bramley, S. Carter, N. C. Handy, and I. M. Mills, J. Mol. Spectrosc. (in press).
48.
NAG Fortran Library Manual Mark 13, 1988.
49.
V. S.
Vasan
and
R. J.
Cross
,
J. Chem. Phys.
78
,
3869
(
1983
).
50.
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).
51.
S.
Carter
and
N. C.
Handy
,
J. Chem. Phys.
87
,
4294
(
1987
).
52.
J.
Tennyson
and
J. R.
Henderson
,
J. Chem. Phys.
91
,
3815
(
1989
).
53.
Quantities, Units and Symbols in Physical Chemistry, edited by I. M. Mills (Blackwell, Oxford, 1988).
54.
W. D.
Allen
,
Y.
Yamaguchi
,
A. G.
Császár
,
D. A.
Clabo
,
R. B.
Remington
, and
H. F.
Schaefer
,
Chem. Phys.
145
,
427
(
1990
).
55.
S. Carter (private communication).
56.
I. M. Mills (private communication).
57.
W. J.
Lafferty
and
A. S.
Pine
,
J. Mol. Spectrosc.
141
,
223
(
1990
).
58.
E.
Kostyk
and
H. L.
Welsh
,
Can. J. Phys.
58
,
912
(
1980
).
59.
J.
Hietanen
and
J.
Kaupinnen
,
Mol. Phys.
42
,
411
(
1981
).
60.
J.
Hietanen
,
Mol. Phys.
49
,
1029
(
1983
).
61.
K. F.
Palmer
,
M. E.
Mickelson
, and
K. N.
Rao
,
J. Mol. Spectrosc.
44
,
131
(
1972
).
62.
H. G. M.
Edwards
,
Spectrochim. Acta
46A
,
97
(
1990
).
63.
J.
Pliva
,
J. Mol. Spectrosc.
44
,
145
(
1972
).
64.
E. K.
Plyler
,
E. D.
Tidwell
, and
T. A.
Wiggins
,
J. Opt. Soc. Am.
53
,
589
(
1963
).
65.
H.
Finsterholzl
,
H. W.
Schrotter
, and
G.
Strey
,
J. Raman Spectrosc.
11
,
375
(
1981
).
66.
C. P.
Rinsland
,
A.
Baldacci
, and
K. N.
Rao
,
Astrophys. J. Suppl. Ser.
49
,
487
(
1982
).
67.
R.
D’Cunha
,
Y. A.
Sarma
,
G.
Guelachvili
,
R.
Farrenq
,
Q.
Kou
,
V.
Malathy Devi
,
D. C.
Benner
, and
K. N.
Rao
,
J. Mol. Spectrosc.
148
,
213
(
1991
).
68.
B. C.
Smith
and
J. S.
Winn
,
J. Chem. Phys.
89
,
4638
(
1988
).
69.
S.
Kinugawa
and
H.
Sasada
,
Jpn. J. Appl. Phys.
29
,
611
(
1990
).
70.
A.
Baldacci
,
S.
Ghersetti
, and
K. N.
Rao
,
J. Mol. Spectrosc.
68
,
183
(
1977
).
71.
T. R.
Huet
and
M.
Herman
,
J. Mol. Spectrosc.
132
,
361
(
1988
).
72.
M.
Huhanantti
,
J.
Hietanen
,
R.
Anttila
, and
J.
Kaupinnen
,
Mol. Phys.
37
,
905
(
1979
).
73.
R. M.
Talley
and
A. H.
Neilsen
,
J. Chem. Phys.
22
,
2030
(
1954
).
74.
S.
Ghersetti
,
J.
Pliva
, and
K. N.
Rao
,
J. Mol. Spectrosc.
38
,
53
(
1971
).
75.
S.
Alanko
,
R.
Paso
, and
R.
Anttila
,
Z. Naturforsch.
42a
,
1247
(
1987
).
76.
S. C.
Hurlock
,
S.
Ghersetti
, and
K. N.
Rao
,
Mem. Soc. R. Sci. Liege
1
,
87
(
1971
).
77.
A.
Baldacci
,
S.
Ghersetti
, and
S. C.
Hurlock
,
J. Mol. Spectrosc.
42
,
327
(
1972
).
78.
J.
Hietanen
,
R.
Anttila
, and
J.
Kaupinnen
,
Mol. Phys.
38
,
1367
(
1979
).
79.
R.
Anttila
,
J.
Hietanen
, and
J.
Kaupinnen
,
Mol. Phys.
37
,
925
(
1979
).
80.
A.
Baldacci
,
S.
Ghersetti
,
S. C.
Hurlock
, and
K. N.
Rao
,
J. Mol. Spectrosc.
59
,
116
(
1977
).
81.
T. R.
Huet
,
M.
Herman
, and
J. W. C.
Johns
,
J. Chem. Phys.
94
,
3407
(
1991
).
82.
G.
Wlodarczak
,
J.
Demaison
,
J.
Burie
, and
M. C.
Lasne
,
Mol. Phys.
66
,
669
(
1989
).
83.
A. Willetts (private communication).
84.
J. H.
Teles
,
G.
Maier
,
B. A.
Hess
,
L. J.
Schaad
,
M.
Winnewisser
, and
B. P.
Winnewisser
,
Chem. Ber.
122
,
753
(
1989
).
85.
J. H.
Teles
,
G.
Maier
,
B. A.
Hess
,
L. J.
Schaad
,
M.
Winnewisser
, and
B. P.
Winnewisser
,
Chem. Ber.
122
,
1219
(
1989
).
86.
B. P. Winnewisser, in Molecular Spectroscopy: Modern Research, Vol. III, edited by K. N. Rao (Academic, New York, 1985).
87.
K.
Yamada
and
M.
Winnewisser
,
Z. Naturforsch.
31a
,
139
(
1976
).
88.
B. P.
Winnewisser
,
M.
Winnewisser
, and
F.
Winther
,
J. Mol. Spectrosc.
51
,
65
(
1974
).
89.
E. L.
Ferretti
and
K. N.
Rao
,
J. Mol. Spectrosc.
51
,
97
(
1974
).
90.
M. T.
Nguyen
,
K.
Pierloot
, and
L. G.
Vanquickenborne
,
Chem. Phys. Lett.
181
,
83
(
1991
).
91.
A. P.
Rendell
,
T. J.
Lee
, and
R.
Lindh
,
Chem. Phys. Lett.
194
,
84
(
1992
).
92.
P. R.
Bunker
,
B. M.
Landsberg
, and
B. P.
Winnewisser
,
J. Mol. Spectrosc.
74
,
9
(
1979
).
93.
B. P.
Winnewisser
and
P.
Jensen
,
J. Mol. Spectrosc.
101
,
408
(
1983
).
94.
B. P.
Winnewisser
and
M.
Winnewisser
,
J. Mol. Spectrosc.
29
,
505
(
1969
).
95.
D. T.
Colbert
and
E. L.
Sibert
,
J. Chem. Phys.
94
,
6519
(
1991
).
This content is only available via PDF.
You do not currently have access to this content.