Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology pp 101-118 | Cite as
Application of the Uniformly Charged Sphere Stabilization for Calculating the Lowest 1S Resonances of H−
Conference paper
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.
Keywords
Resonance Energy Resonance Parameter Stabilization Curve Slater Determinant Lower Resonance
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Notes
Acknowledgements
The study has been carried out with the financial support of the Russian Foundation for Basic Research, grant No. 12-03-00821.
References
- 1.Nicolaides CA (2010) Theory and state-specific methods for the analysis and computation of field-free and field-induced unstable states in atoms and molecules. In: Nicolaides CA, Brändas E (eds) Unstable states in the continuous spectra, Part I: analysis, concepts, methods, and results. Advances in quantum chemistry, vol 60. Elsevier, Amsterdam, pp 163–267, and references therein CrossRefGoogle Scholar
- 2.Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press, Cambridge CrossRefGoogle Scholar
- 3.Nicolaides CA, Brändas E (eds) (2012) Unstable states in the continuous spectra, Part II: interpretation, theory and applications. Advances in quantum chemistry, vol 63. Elsevier, Amsterdam Google Scholar
- 4.Sabelli NH, Gislason EA (1984) SCF study of the lowest \(^{2}\varSigma_{u}^{+}\) resonance of \({H}_{2}^{-}\). J Chem Phys 81:4002–4007 CrossRefGoogle Scholar
- 5.DeRose E, Gislason EA, Sabelli NH (1985) A new method for computing properties of negative ion resonances with application to \(^{2}\varSigma_{u}^{+}\) states of \(H_{2}^{-}\). J Chem Phys 82:4577–4584 CrossRefGoogle Scholar
- 6.Chao JS-Y, Falcetta MF, Jordan KD (1990) Application of the stabilization method to the \({N}_{2}^{-} (1^{2}\varPi_{g} )\) and Mg −(12 Π) temporary anion states. J Chem Phys 93:1125–1135 CrossRefGoogle Scholar
- 7.Izmaylov AF, Adamson SO, Zaitsevskii A (2004) Multipartitioning many-body perturbation theory calculations on temporary anions: applications to \({N}_{2}^{-}\) and CO −. J Phys B, Atom Mol Phys 37:2321–2329 CrossRefGoogle Scholar
- 8.Izmaylov AF, Shchegoleva LN, Scuseria GE, Zaitsevskii A (2005) Ab initio study of temporary anions of benzene and fluorobenzenes using the multipartitioning many-body perturbation theory. Phys Chem Chem Phys 7:3933–3937 CrossRefGoogle Scholar
- 9.Adamson S et al. (2007) Multiscale multiphysics non-empirical approach to calculation of light emission properties of chemically active non-equilibrium plasma: application to Ga-I3 system. J Phys D, Appl Phys 40:3857–3881 CrossRefGoogle Scholar
- 10.Simons J (2008) Molecular anions. J Phys Chem A 112:6401–6511, and references therein CrossRefGoogle Scholar
- 11.Adamson SO, Deminskii MA et al. (2010) The role of dissociative electron attachment to metal halides in a low pressure glow discharge. Russ J Phys Chem B 4:1–7 CrossRefGoogle Scholar
- 12.Simons J (2011) Theoretical study of negative molecular ions. Annu Rev Phys Chem 62:107–128, and references therein CrossRefGoogle Scholar
- 13.Watson RE (1958) Analytic Hartree-Fock solutions for \({O}_{2}^{-}\). Phys Rev 111:1108–1110 CrossRefGoogle Scholar
- 14.Liebman JF, Yeager DL, Simons J (1977) A simple approach to predicting resonance levels. Chem Phys Lett 48:227–232 CrossRefGoogle Scholar
- 15.Hazi AU, Taylor HS (1970) Stabilization method of calculating resonance energies: model problem. Phys Rev A 1:1109–1120 CrossRefGoogle Scholar
- 16.Lefebvre R (1985) Box quantization and resonance determination: the multichannel case. J Phys Chem 89:4201–4206 CrossRefGoogle Scholar
- 17.Kukulin VI, Krasnopolsky VM, Horác̆ek J (1989) Resonances in atomic physics. In: Kukulin VI, Krasnopolsky VM, Horác̆ek J (eds) Theory of resonances. Principles and applications. Academia, Praha, pp 303–340, and references therein Google Scholar
- 18.Adamson S, Kharlampidi D, Dementiev A (2008) Stabilization of resonance states by an asymptotic Coulomb potential. J Chem Phys 128:024101, and references therein CrossRefGoogle Scholar
- 19.Kharlampidi DD, Dementiev AI, Adamson SO (2010) Using of stabilization by uniformly charged sphere for resonance states calculations. Russ J Phys Chem A 84:611–616 CrossRefGoogle Scholar
- 20.Adamson SO, Kharlampidi DD, Dement’ev AI (2011) Calculation of the parameters of resonance states using stabilization with non-Coulomb potentials. Russ J Phys Chem B 5:915–920 CrossRefGoogle Scholar
- 21.Jolicard G, Austin E (1986) Optical potential method of calculating resonance energies and widths. Chem Phys 103:295–302 CrossRefGoogle Scholar
- 22.Jolicard G, Leforestier C, Austin E (1988) Resonance states using the optical potential model. Study of Feshbach resonances and broad shape resonances. J Chem Phys 88:1026–1031 CrossRefGoogle Scholar
- 23.Callaway J (1978) The variational method in atomic scattering. Phys Rep 45:89–173, and references therein CrossRefGoogle Scholar
- 24.Ho YK (1981) Complex-coordinate calculations for doubly excited states of two-electron atoms. Phys Rev A 23:2137–2149 CrossRefGoogle Scholar
- 25.Pathak A, Kingston AE, Berrington KA (1988) Resonances in H − associated with the n=2,3 and 4 hydrogenic thresholds. J Phys B, At Mol Opt Phys 21:2939–2951 CrossRefGoogle Scholar
- 26.Scholz T, Scott P, Burke PG (1988) Electron-hydrogen-atom scattering at intermediate energies. J Phys B, Atom Mol Phys 21:L139–LI45 CrossRefGoogle Scholar
- 27.Ho YK (1990) High-lying doubly excited states of H −. J Phys B, At Mol Opt Phys 23:L71–L78 CrossRefGoogle Scholar
- 28.Botero J, Shertzer J (1992) Direct numerical solution of the Schrodinger equation for quantum scattering problems. Phys Rev A 46:R1155–R1158 CrossRefGoogle Scholar
- 29.Sadeghpour HR (1992) Resonant electron-hydrogen atom scattering using hyperspherical coordinate method. J Phys B, At Mol Opt Phys 25:L29–L35 CrossRefGoogle Scholar
- 30.Shertzer J, Botero J (1994) Finite-element analysis of electron-hydrogen scattering. Phys Rev A 49:3673–3679 CrossRefGoogle Scholar
- 31.Gien TT (1998) Observation of a triplet D-wave resonance below the n=2 H excitation threshold in electron-hydrogen scattering. J Phys B, At Mol Opt Phys 31:L629–L635 CrossRefGoogle Scholar
- 32.Gien TT (1998) Feshbach resonances below the n=2 H excitation threshold in electron—hydrogen scattering. J Phys B, At Mol Opt Phys 31:L1001–L1008 CrossRefGoogle Scholar
- 33.Bylicki M, Nicolaides C (2000) Theoretical resolution of the H − resonance spectrum up to the n=4 threshold. II. States of 1 S and 1 D symmetries. Phys Rev A 61:052509 CrossRefGoogle Scholar
- 34.Zhang SB, Wang JG, Janev RK (2010) Electronhydrogen-atom elastic and inelastic scattering with screened Coulomb interaction around the n=2 excitation threshold. Phys Rev A 81:032707 CrossRefGoogle Scholar
- 35.Warner CD, King GC, Hammond P, Slevin J (1986) Resonance structure in elastic scattering of electrons from atomic hydrogen. J Phys B, At Mol Opt Phys 19:3297–3308 CrossRefGoogle Scholar
- 36.Burke PG, Taylor AJ (1966) Correlation in the elastic and inelastic S-wave scattering of electrons by H and He+. Proc Phys Soc Lond 88:549–562 CrossRefGoogle Scholar
- 37.Burke PG, Seaton MJ (1971) In: Alder B, Frenbach S, Rotenberg M (eds) Methods in computational physics. Atomic and molecular scattering, vol 10. Academic Press, New York. Chap. 1, and references therein Google Scholar
- 38.Harris FE, Michels HH (1971) In: Alder B, Frenbach S, Rotenberg M (eds) Methods in computational physics. Atomic and molecular scattering, vol 10. Academic Press, New York. Chap. 4, and references therein Google Scholar
- 39.Matese JJ, Oberoi RS (1971) Choosing pseudostates in the close-coupling formalism for electron-atomic-hydrogen system. Phys Rev A 4:569–579 CrossRefGoogle Scholar
- 40.Abramowitz M, Stegun I (eds) (1964) Handbook of mathematical functions with formulas, graphs, and mathematical tables. NBS app math series, vol 55. Government Printing Office, Washington Google Scholar
- 41.Bateman H, Erdlyi A (1953) Higher transcendental functions, vols 1, 2. McGraw-Hill, New-York Google Scholar
- 42.O-ohata K, Taketa H, Huzinaga S (1966) Gaussian expansions of atomic orbitals. J Phys Soc Jpn 21:2306–2313 CrossRefGoogle Scholar
- 43.Hehre WJ, Ditchfield R, Stewart RF, Pople JA (1970) Self-consistent molecular orbital methods. IV. Use of Gaussian expansions of Slater-type orbitals. Extension to second-row molecules. J Chem Phys 52:2769–2773 CrossRefGoogle Scholar
- 44.Widmark P-O, Persson BJ, Roos BO (1991) Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions. Theor Chim Acta 79:419–432 CrossRefGoogle Scholar
- 45.Sadlej AJ (1992) Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties. Theor Chim Acta 81:339–354 CrossRefGoogle Scholar
- 46.Wallis A, McElwain DLS, Pritchard HO (1969) The variation method and the algebraic eigenvalue problem. Int J Quant Chem 3:711–722 CrossRefGoogle Scholar
- 47.Moncrieff D, Wilson S (2005) Computational linear dependence in molecular electronic structure calculations using universal basis sets. Int J Quant Chem 101:363–371, and references therein CrossRefGoogle Scholar
- 48.Yoshida T (1995) Computation of Kummer functions U(a,b,x) for large argument x by using the τ-method. Inf Process Soc Jpn 36:2335–2342 Google Scholar
- 49.Temme NM (1983) The numerical computation of the confluent hypergeometric function U(a,b,z). Numer Math 41:63–82 CrossRefGoogle Scholar
- 50.Maier CH, Cederbaum LS (1980) A spherical-box approach to resonances. J Phys B, Atom Mol Phys 13:L119–L124 CrossRefGoogle Scholar
- 51.Gersbacher R, Broad JT (1990) Resonances in helium photoionisation. J Phys B 23:365–384 CrossRefGoogle Scholar
- 52.Guseinov II, Mamedov BA (2004) Evaluation of incomplete Gamma functions using downward recursion and analytical relations. J Math Chem 36:341–346 CrossRefGoogle Scholar
- 53.Eyring H, Walter J, Kimball GE (1944) Quantum chemistry. Wiley, New York Google Scholar
- 54.Holøien E, Midtdal J (1955) On a metastable energy state of the negative helium ion. Proc Phys Soc A 68:815–823 CrossRefGoogle Scholar
- 55.Condon EU, Shortley GH (1959) The theory of atomic spectra, 6th edn. Cambridge University Press, Cambridge Google Scholar
- 56.Schwartz C (1962) Importance of angular correlations between atomic electrons. Phys Rev 126:1015–1019 CrossRefGoogle Scholar
- 57.Goldman SP (1997) Accurate modified configuration interaction calculations for many electron systems made easy. Phys Rev Lett 78:2325–2328, and references therein CrossRefGoogle Scholar
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