We propose new methods for using contracted basis functions in conjunction with the Lanczos algorithm to calculate vibrational (or rovibrational) spectra. As basis functions we use products of eigenfunctions of reduced-dimension Hamiltonians obtained by freezing coordinates at equilibrium. The basis functions represent the desired wave functions well, yet are simple enough that matrix-vector products may be evaluated efficiently. The methods we suggest obviate the need to transform from the contracted to an original product basis each time a matrix-vector product is evaluated. For HOOH the most efficient of the methods we present is about an order of magnitude faster than a product basis Lanczos calculation.
REFERENCES
1.
Spectrochim. Acta Part A 58, (2002), a special issue on “First Principles Rovibrational Spectroscopy”.
2.
T. Carrington, Jr., in Encyclopedia of Computational Chemistry, edited by P. von Ragué Schleyer (Wiley, New York, 1998), Vol. 5.
3.
4.
5.
6.
7.
8.
W. H. Press et al., in Numerical Recipes, 1st ed. (Cambridge University Press, Cambridge, England, 1989), Chap. 11.
9.
10.
11.
G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, 1989).
12.
13.
14.
15.
A.
McNichols
and T.
Carrington
, Jr., Chem. Phys. Lett.
202
, 464
(1993
).16.
M. J.
Bramley
and T.
Carrington
, Jr., J. Chem. Phys.
99
, 8519
(1993
).17.
M. J.
Bramley
and T.
Carrington
, Jr., J. Chem. Phys.
101
, 8494
(1994
).18.
19.
T. P.
Grozdanov
, V. A.
Mandelshtam
, and H. S.
Taylor
, J. Chem. Phys.
103
, 7990
(1995
).20.
V. A.
Mandelshtam
and H. S.
Taylor
, J. Chem. Phys.
102
, 7390
(1995
).21.
V. A.
Mandelshtam
and H. S.
Taylor
, J. Chem. Phys.
106
, 5085
(1997
).22.
H.-G.
Yu
and S. C.
Smith
, Ber. Bunsenges. Phys. Chem.
101
, 400
(1997
).23.
24.
S.-W.
Huang
and T.
Carrington
, Jr., J. Chem. Phys.
112
, 8765
(2000
).25.
26.
R. A.
Friesner
, R. E.
Wyatt
, C.
Hempel
, and B.
Criner
, J. Comput. Phys.
64
, 220
(1986
).27.
28.
29.
R. A.
Friesner
, J. A.
Bentley
, M.
Menou
, and C.
Leforestier
, J. Chem. Phys.
99
, 324
(1993
).30.
31.
32.
X.
Chapuisat
, A.
Belfhal
, and A.
Nauts
, J. Mol. Spectrosc.
149
, 274
(1991
).33.
F.
Gatti
, C.
Iung
, M.
Menou
, Y.
Justum
, A.
Nauts
, and X.
Chapuisat
, J. Chem. Phys.
108
, 8804
(1998
).34.
35.
36.
37.
38.
39.
40.
X. T.
Wu
, A. B.
McCoy
, and E. F.
Hayes
, J. Chem. Phys.
110
, 2354
(1999
).41.
Y.
Qiu
, J. Z. H.
Zhang
, and Z.
Bačić
, J. Chem. Phys.
108
, 4804
(1998
).42.
43.
44.
45.
46.
47.
48.
49.
50.
N. C.
Handy
, S.
Carter
, and S. M.
Colwell
, Mol. Phys.
96
, 477
(1999
).51.
52.
53.
J.
Antikainen
, R. A.
Friesner
, and C.
Leforestier
, J. Chem. Phys.
102
, 1270
(1995
).54.
See, for example,
A.
Bakasov
, T.-K.
Ha
, and M.
Quack
, J. Chem. Phys.
109
, 7263
(1998
).55.
56.
B.
Fehrensen
, D.
Luckhaus
, and M.
Quack
, Chem. Phys. Lett.
300
, 312
(1999
).57.
58.
59.
X.-G. Wang, T. Carrington, Jr., M. Quack, and M. Willeke, J. Chem. Phys. (to be published).
60.
R. N. Zare, Angular Momentum (Wiley, New York, 1988).
61.
62.
J. J. Dongarra, I. S. Duff, D. C. Sorensen, and H. A. van der Vorst, Numerical Linear Algebra for High-Performance Computers (SIAM, Philadelphia, 1998).
63.
J. Cullum and R. A. Willoughby, Lanczos Algorithm for Large Symmetric Eigenvalue Computations (Birkhäuser, Boston, 1985).
64.
S.-W.
Huang
and T.
Carrington
, Jr., J. Chem. Phys.
112
, 8765
(2000
).65.
B.
Kuhn
, T. R.
Rizzo
, D.
Luckhaus
, M.
Quack
, and M.
Suhm
, J. Chem. Phys.
111
, 2565
(1999
).66.
67.
68.
M. J.
Bramley
, J. W.
Tromp
, T.
Carrington
, Jr., and G. C.
Corey
, J. Chem. Phys.
100
, 6175
(1994
).69.
70.
This content is only available via PDF.
© 2002 American Institute of Physics.
2002
American Institute of Physics
You do not currently have access to this content.
