Abstract
A finite element method in Cartesian coordinates in three dimensions is described to solve the time-dependent Schrödinger equation for H +2 in the presence of time-dependent electromagnetic fields. The ionization rates, nonlinear optical polarizabilities and harmonic generation spectrum of H +2 have been calculated for field directions parallel or perpendicular to the hydrogen molecule ion axis. Comparisons of the present numerical results with previously published calculations show that the finite element method reproduces perturbative results and can treat nonperturbativity arbitrary intense short pulses as it includes automatically both bound and continuum electronic states.
Similar content being viewed by others
References
A.D. Bandrauk (ed.),Atomic Molecular Processes with Short Intense Laser Pulses, NATO ASI, Vol. B171 (Plenum Press, New York, 1988).
A.D. Bandrauk and S.C. Wallace (eds.),Coherence Phenomena in Atoms and Molecules in Laser Fields, NATO ASI, Vol. B278 (Plenum Press, New York, 1992).
A.D. Bandrauk,Molecules in Laser Fields (Marcel Dekker, New York, 1993).
J.L. Krause, K.J. Schafer and K.C. Kulander, Chem. Phys. Lett.178 (1991) 573.
S. Chelkowski, T. Zuo and A.D. Bandrauk, Phys. Rev. A46 (1992) 5342.
M.S. Pinzola, C.J. Bottrell and C. Bottcher, J. Opt. Soc. Am. B7 (1990) 659.
P.L. Devries, J. Opt. Soc. Am. B7 (1990) 519.
K.C. Kulander, Phys. Rev. A36 (1987) 2726.
P.H. Buchsbaum, A. Zavriyev, H.G. Muller and D.W. Schumacher, Phys. Rev. Lett. 64 (1990) 1883.
A.D. Bandrauk and M.L. Sink, Chem. Phys. Lett. 57 (1978) 569; J. Chem. Phys. 74 (1981) 1110.
E. Aubanel, A.D. Bandrauk and P. Rancourt, Chem. Phys. Lett.197 (1992) 419.
H. Yu, A.D. Bandrauk and V. Sonnad, in ref. [2], p. 31.
H. Yu, A.D. Bandrauk and V. Sonnad, Part I of this paper, J. Math. Chem. 15 (1994) 273.
M. Horbatsch, Phys. Rev. A44 (1991) 5346.
J.H. Eberly, Q. Su and J. Javanainen, Phys. Rev. Lett. 62 (1989) 881.
K. LaGattuta, Phys. Rev. A41 (1991) 5157.
B.A. Finlayson, Method of Weighted Residues (Academic Press, New York, 1974).
O.C. Zinkiewicz and K. Morgan,Finite Elements and Approximation (Wiley, New York, 1983).
D. Sundholm, J. Olsen and S.A. Alexander, J. Chem. Phys. 96 (1992) 5229.
D. Heinemann, A. Rosen and B. Fricke, Chem. Phys. Lett.166 (1990) 627.
D. Heinemann, B. Fricke and D. Kolb, J. Chem. Phys. 38 (1988) 4994.
T. Inoshita, Phys. Rev. B41 (1990) 180.
H. Murakami, V. Sonnad and E. Clementi, Int. J. Quant. Chem. 42 (1992) 785.
G. Hammerlin and K.H. Hoffmann, Numerical Methods (Springer, New York, 1991).
A.D. Becke, J. Chem. Phys. 76 (1982) 6037.
A.D. Becke and R.M. Dickson, J. Chem. Phys. 92 (1990) 3610.
E. Clementi (ed.),Modern Technique in Computational Chemistry: MOTECC90 (1990) chap. 12.
J.K. Cullum and R.A. Willoughby,Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. II, Program (Birkhauser, New York, 1985).
M.G. Duffy, SIAM. J. Numer. Anal. 19 (1982) 1260.
I.L. Levine,Quantum Chemistry, 3rd Ed. (Allyn and Bacon, Newton, Massachusetts, 1983).
H. Yu, A.D. Bandrauk and V. Sonnad, to appear in Chem. Phys. Lett. (1994).
A.D. Bandrauk and H. Shen, J. Chem. Phys. 99 (1993) 1185.
N.C. Manakov, M.A. Preobrazhenskii and L.P. Rapoport, Opt. Spectr. 35 (1973) 14.
C.A. Nicolaides, T. Mercouris and G. Aspromallis, J. Opt. Soc. Am. B7 (1990) 494.
Y. Justum, A. Maquet and Y. Heno, Phys. Rev. A41 (1990) 2791.
L.L. Boyle, A.D. Buckingham, R.L. Disch and D.A. Dunmur, J. Chem. Phys. 45 (1966) 1318.
P. Sitz and R. Yaris, J. Chem. Phys. 48 (1968) 3546.
P.R. Taylor, T.J. Lee, J.E. Rice and J. Almlof, Chem. Phys. Lett.163 (1989) 359.
M. Jaszunski and D.L. Yeager, Phys. Rev. A40 (1989)1651.
J.E. Rice, P.R. Taylor, T.J. Lee and J. Almlof, J. Chem. Phys. 94 (1991) 4972.
R.B. Miller and S.E. Harris, IEEE J. Quant. Electr. QE-9 (1973) 470.
D.M. Bishop, J. Pipin and J.N. Silverman, Mol. Phys. 59 (1986) 165.
L. Adamowicz and R.J. Bartlett, J. Chem. Phys. 84 (1986) 4988.
D.M. Bishop and B. Lam, Chem. Phys. Lett. 134 (1987) 283.
D.M. Bishop and L.M. Cheung, J. Phys. B11 (1978) 3133.
D.M. Bishop, Rev. Mod. Phys. 62 (1990) 343.
D.M. Bishop and L.M. Cheung, J. Phys. B12 (1979) 3135.
P.R. McEachran, S. Smith and M. Cohen, Can. J. Chem. 52 (1974) 3463.
Y.R. Shen,The Principles ofNonlinear Optics (Wiley, New York, 1984).
M. Ferry, A. L'Huillier, X. Li, L.A. Lompr/'e, G. Mainfray and C. Manus, J. Phys. B21 (1988) L31.
X.F. Li, A. L'Huillier, M. Ferry, L.A. Lompré, G. Mainfray, Phys. Rev. A39 (1989) 3751.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yu, H., Bandrauk, A.D. & Sonnad, V. Application of the finite element method to time-dependent quantum mechanics: II. H +2 in a laser field. J Math Chem 15, 287–301 (1994). https://doi.org/10.1007/BF01277566
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01277566