A singular value decomposition based harmonic inversion signal processing scheme is applied to the semiclassical initial value representation (IVR) calculation of molecular vibrational states. Relative to usual IVR procedure of Fourier analysis of a signal made from the Monte Carlo evaluation of the phase space integral in which many trajectories are needed, the new procedure obtains acceptable results with many fewer trajectories. Calculations are carried out for vibrational energy levels of H2O to illustrate the overall procedure.

1.
W. H.
Miller
,
J. Phys. Chem. A
105
,
2942
(
2001
).
2.
K. G.
Kay
,
J. Phys. Chem. A
105
,
2535
(
2001
).
3.
D. J.
Tannor
and
S.
Garashchuk
,
Annu. Rev. Phys. Chem.
51
,
553
(
2000
).
4.
Y.
Zhao
and
N.
Makri
,
Chem. Phys.
280
,
135
(
2002
).
5.
M. F.
Herman
and
E.
Kluk
,
Chem. Phys.
91
,
27
(
1984
).
6.
E. J.
Heller
,
J. Chem. Phys.
62
,
1544
(
1975
).
7.
E. J.
Heller
,
Acc. Chem. Res.
14
,
368
(
1981
).
8.
J. H. V.
Vleck
,
Proc. Natl. Acad. Sci. U.S.A.
14
,
178
(
1928
).
9.
S.
Tomsovic
and
E. J.
Heller
,
Phys. Rev. Lett.
67
,
664
(
1991
).
10.
X.
Sun
and
W. H.
Miller
,
J. Chem. Phys.
108
,
8870
(
1998
).
11.
M. L.
Brewer
,
J. S.
Hulme
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
106
,
4832
(
1997
).
12.
V. S.
Batista
and
W. H.
Miller
,
J. Chem. Phys.
108
,
498
(
1998
).
13.
E. A.
Coronado
,
V. S.
Batista
, and
W. H.
Miller
,
J. Chem. Phys.
112
,
5566
(
2000
).
14.
M.
Thoss
,
W. H.
Miller
, and
G.
Stock
,
J. Chem. Phys.
112
,
10282
(
2000
).
15.
A. R.
Walton
and
D. E.
Manolopoulos
,
Mol. Phys.
87
,
961
(
1996
).
16.
V. I.
Filinov
,
Nucl. Phys.
A271
,
717
(
1986
).
17.
N.
Makri
and
W. H.
Miller
,
Chem. Phys. Lett.
139
,
10
(
1987
).
18.
F.
Grossman
,
V. A.
Mandelshtam
,
H. S.
Taylor
, and
J. S.
Briggs
,
Chem. Phys. Lett.
279
,
355
(
1997
).
19.
A. L.
Kaledin
and
W. H.
Miller
,
J. Chem. Phys.
118
,
7174
(
2003
).
20.
A. L.
Kaledin
and
W. H.
Miller
,
J. Chem. Phys.
119
,
3078
(
2003
).
21.
J.
Main
,
P. A.
Dando
,
D.
Belkic
, and
H. S.
Taylor
,
J. Phys. A
33
,
1247
(
2000
).
22.
J. A.
Cadzow
,
IEEE Trans. Acoust., Speech, Signal Process.
36
,
49
(
1988
).
23.
S. D.
Kunikeev
and
H. S.
Taylor
,
J. Phys. Chem. A
108
,
743
(
2004
).
24.
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 1992).
25.
G. H. Golub and C. V. Loan, Matrix Computations, 3rd ed. (Johns Hop-kins University Press, 1996).
26.
Y.
Li
,
K. J. R.
Liu
, and
J.
Razavilar
,
IEEE Trans. Signal Process.
45
,
481
(
1997
).
27.
F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1974).
28.
E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations(McGraw-Hill, New York, 1955).
29.
J. K. G.
Watson
,
Mol. Phys.
15
,
479
(
1968
).
30.
J. M.
Bowman
,
A.
Wierzbicki
, and
J.
Zuniga
,
Chem. Phys. Lett.
150
,
269
(
1988
).
31.
K.
Husimi
,
Proc. Phys. Math. Soc. Jpn.
22
,
264
(
1940
).
This content is only available via PDF.
You do not currently have access to this content.