K. Museth et C. Leforestier, ON THE DIRECT COMPLEX SCALING OF MATRIX-ELEMENTS EXPRESSED IN A DISCRETE VARIABLE REPRESENTATION - APPLICATION TO MOLECULAR RESONANCES, The Journal of chemical physics, 104(18), 1996, pp. 7008-7014
We present an extension of a method initially proposed by Moiseyev and
Corcoran [Phys. Rev. A 20, 814 (1978)] to a direct continuation of th
e matrix elements of a real Hamiltonian operator expressed in a contra
cted, discrete variable representation type basis set. It is based on
the identity which relates the matrix elements of a complex scaled pot
ential between real basis set functions to those of the unscaled poten
tial between backward scaled basis functions. The method is first appl
ied to the study of the resonances of a one dimensional model by means
of complex scaling. It is shown that the resulting matrix elements of
the scaled potential are no longer diagonal in the DVR. This paradox
is discussed and shown to be of no practical consequence in the formul
ation. The scheme is then extended to the direct complex scaling of a
two dimensional Hamiltonian operator expressed in a contracted basis s
et built through the successive adiabatic reduction method of Bacic an
d Light. Results show that, due to the use of a numerical continuation
, slightly larger grids have to be used as compared to the case of an
analytic continuation where the potential is available. (C) 1996 Ameri
can Institute of Physics.