Chapter 5
Application of the Uniformly Charged Sphere
Stabilization for Calculating the Lowest 1 S
Resonances of H −
S.O. Adamson, D.D. Kharlampidi, and A.I. Dementiev
Abstract The uniformly charged sphere stabilization method has been used to calculate the lowest 1 S resonances of H − . It was shown that this method is sensitive to
the choice of basis set and parameters of the stabilization potential. The conclusion
on the suitability of this method for calculating resonance energies and widths is
based on the analysis of our computational results.
5.1 Introduction
Considering the progress in development of the direct methods for resonance calculations [1–3], the uniformly charged sphere stabilization (UCS-stabilization) approach now can be considered as the simple “first-aid” tool for the estimation of
resonance parameters of molecular negative ions [4–12]. This method, based on the
ideas from the previous works [13, 14], has two advantages distinguishing it from
the other stabilization techniques [1, 10, 12, 15–17]. First, the calculations may be
carried out by almost all modern quantum chemistry programs, including multireference ab initio methods. Secondly, the scope of this approach isn’t limited to
consideration of only the single-channel problem (but up to now there are no examples of multi-channel calculations). On the other hand, for a long time this method
was applied in the absence of the theoretical base proving possibility to estimate
the resonance energy and width using only the known parameters of the potential,
and the energies of the discrete levels. Later it was shown, that these parameters
allow to estimate the amplitudes of the incoming and outgoing waves of the partial
solution [18–20]. One more lack of this method is the absence of recommendations
for creating the optimal computational scheme (the construction of the single- and
many-particle functions, choice of the external potential parameters, etc.).
S.O. Adamson (B)
Department of Chemistry, Lomonosov Moscow State University, Leninskie Gory 1,
Moscow 119991, Russia
e-mail: sergey.o.adamson@gmail.com
S.O. Adamson
MIPT, Moscow, Russia
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_5,
© Springer International Publishing Switzerland 2013
101
Application of the Uniformly Charged Sphere
Stabilization for Calculating the Lowest 1 S
Resonances of H −
S.O. Adamson, D.D. Kharlampidi, and A.I. Dementiev
Abstract The uniformly charged sphere stabilization method has been used to calculate the lowest 1 S resonances of H − . It was shown that this method is sensitive to
the choice of basis set and parameters of the stabilization potential. The conclusion
on the suitability of this method for calculating resonance energies and widths is
based on the analysis of our computational results.
5.1 Introduction
Considering the progress in development of the direct methods for resonance calculations [1–3], the uniformly charged sphere stabilization (UCS-stabilization) approach now can be considered as the simple “first-aid” tool for the estimation of
resonance parameters of molecular negative ions [4–12]. This method, based on the
ideas from the previous works [13, 14], has two advantages distinguishing it from
the other stabilization techniques [1, 10, 12, 15–17]. First, the calculations may be
carried out by almost all modern quantum chemistry programs, including multireference ab initio methods. Secondly, the scope of this approach isn’t limited to
consideration of only the single-channel problem (but up to now there are no examples of multi-channel calculations). On the other hand, for a long time this method
was applied in the absence of the theoretical base proving possibility to estimate
the resonance energy and width using only the known parameters of the potential,
and the energies of the discrete levels. Later it was shown, that these parameters
allow to estimate the amplitudes of the incoming and outgoing waves of the partial
solution [18–20]. One more lack of this method is the absence of recommendations
for creating the optimal computational scheme (the construction of the single- and
many-particle functions, choice of the external potential parameters, etc.).
S.O. Adamson (B)
Department of Chemistry, Lomonosov Moscow State University, Leninskie Gory 1,
Moscow 119991, Russia
e-mail: sergey.o.adamson@gmail.com
S.O. Adamson
MIPT, Moscow, Russia
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_5,
© Springer International Publishing Switzerland 2013
101