Skip to main content
Top

2013 | OriginalPaper | Chapter

5. Application of the Uniformly Charged Sphere Stabilization for Calculating the Lowest 1 S Resonances of H

Authors : S. O. Adamson, D. D. Kharlampidi, A. I. Dementiev

Published in: Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference 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 CrossRef 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 CrossRef
2.
go back to reference Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press, Cambridge CrossRef Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press, Cambridge CrossRef
3.
go back to reference 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 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
4.
go back to reference Sabelli NH, Gislason EA (1984) SCF study of the lowest \(^{2}\varSigma_{u}^{+}\) resonance of \({H}_{2}^{-}\). J Chem Phys 81:4002–4007 CrossRef Sabelli NH, Gislason EA (1984) SCF study of the lowest \(^{2}\varSigma_{u}^{+}\) resonance of \({H}_{2}^{-}\). J Chem Phys 81:4002–4007 CrossRef
5.
go back to reference 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 CrossRef 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 CrossRef
6.
go back to reference 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 CrossRef 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 CrossRef
7.
go back to reference 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 CrossRef 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 CrossRef
8.
go back to reference 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 CrossRef 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 CrossRef
9.
go back to reference 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 CrossRef 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 CrossRef
10.
go back to reference Simons J (2008) Molecular anions. J Phys Chem A 112:6401–6511, and references therein CrossRef Simons J (2008) Molecular anions. J Phys Chem A 112:6401–6511, and references therein CrossRef
11.
go back to reference 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 CrossRef 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 CrossRef
12.
go back to reference Simons J (2011) Theoretical study of negative molecular ions. Annu Rev Phys Chem 62:107–128, and references therein CrossRef Simons J (2011) Theoretical study of negative molecular ions. Annu Rev Phys Chem 62:107–128, and references therein CrossRef
13.
go back to reference Watson RE (1958) Analytic Hartree-Fock solutions for \({O}_{2}^{-}\). Phys Rev 111:1108–1110 CrossRef Watson RE (1958) Analytic Hartree-Fock solutions for \({O}_{2}^{-}\). Phys Rev 111:1108–1110 CrossRef
14.
go back to reference Liebman JF, Yeager DL, Simons J (1977) A simple approach to predicting resonance levels. Chem Phys Lett 48:227–232 CrossRef Liebman JF, Yeager DL, Simons J (1977) A simple approach to predicting resonance levels. Chem Phys Lett 48:227–232 CrossRef
15.
go back to reference Hazi AU, Taylor HS (1970) Stabilization method of calculating resonance energies: model problem. Phys Rev A 1:1109–1120 CrossRef Hazi AU, Taylor HS (1970) Stabilization method of calculating resonance energies: model problem. Phys Rev A 1:1109–1120 CrossRef
16.
go back to reference Lefebvre R (1985) Box quantization and resonance determination: the multichannel case. J Phys Chem 89:4201–4206 CrossRef Lefebvre R (1985) Box quantization and resonance determination: the multichannel case. J Phys Chem 89:4201–4206 CrossRef
17.
go back to reference 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 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
18.
go back to reference Adamson S, Kharlampidi D, Dementiev A (2008) Stabilization of resonance states by an asymptotic Coulomb potential. J Chem Phys 128:024101, and references therein CrossRef Adamson S, Kharlampidi D, Dementiev A (2008) Stabilization of resonance states by an asymptotic Coulomb potential. J Chem Phys 128:024101, and references therein CrossRef
19.
go back to reference 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 CrossRef 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 CrossRef
20.
go back to reference 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 CrossRef 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 CrossRef
21.
go back to reference Jolicard G, Austin E (1986) Optical potential method of calculating resonance energies and widths. Chem Phys 103:295–302 CrossRef Jolicard G, Austin E (1986) Optical potential method of calculating resonance energies and widths. Chem Phys 103:295–302 CrossRef
22.
go back to reference 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 CrossRef 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 CrossRef
23.
go back to reference Callaway J (1978) The variational method in atomic scattering. Phys Rep 45:89–173, and references therein CrossRef Callaway J (1978) The variational method in atomic scattering. Phys Rep 45:89–173, and references therein CrossRef
24.
go back to reference Ho YK (1981) Complex-coordinate calculations for doubly excited states of two-electron atoms. Phys Rev A 23:2137–2149 CrossRef Ho YK (1981) Complex-coordinate calculations for doubly excited states of two-electron atoms. Phys Rev A 23:2137–2149 CrossRef
25.
go back to reference 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 CrossRef 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 CrossRef
26.
go back to reference Scholz T, Scott P, Burke PG (1988) Electron-hydrogen-atom scattering at intermediate energies. J Phys B, Atom Mol Phys 21:L139–LI45 CrossRef Scholz T, Scott P, Burke PG (1988) Electron-hydrogen-atom scattering at intermediate energies. J Phys B, Atom Mol Phys 21:L139–LI45 CrossRef
27.
go back to reference Ho YK (1990) High-lying doubly excited states of H −. J Phys B, At Mol Opt Phys 23:L71–L78 CrossRef Ho YK (1990) High-lying doubly excited states of H . J Phys B, At Mol Opt Phys 23:L71–L78 CrossRef
28.
go back to reference Botero J, Shertzer J (1992) Direct numerical solution of the Schrodinger equation for quantum scattering problems. Phys Rev A 46:R1155–R1158 CrossRef Botero J, Shertzer J (1992) Direct numerical solution of the Schrodinger equation for quantum scattering problems. Phys Rev A 46:R1155–R1158 CrossRef
29.
go back to reference Sadeghpour HR (1992) Resonant electron-hydrogen atom scattering using hyperspherical coordinate method. J Phys B, At Mol Opt Phys 25:L29–L35 CrossRef Sadeghpour HR (1992) Resonant electron-hydrogen atom scattering using hyperspherical coordinate method. J Phys B, At Mol Opt Phys 25:L29–L35 CrossRef
30.
go back to reference Shertzer J, Botero J (1994) Finite-element analysis of electron-hydrogen scattering. Phys Rev A 49:3673–3679 CrossRef Shertzer J, Botero J (1994) Finite-element analysis of electron-hydrogen scattering. Phys Rev A 49:3673–3679 CrossRef
31.
go back to reference 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 CrossRef 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 CrossRef
32.
go back to reference 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 CrossRef 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 CrossRef
33.
go back to reference 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 CrossRef 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 CrossRef
34.
go back to reference 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 CrossRef 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 CrossRef
35.
go back to reference 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 CrossRef 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 CrossRef
36.
go back to reference 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 CrossRef 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 CrossRef
37.
go back to reference 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 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
38.
go back to reference 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 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
39.
go back to reference Matese JJ, Oberoi RS (1971) Choosing pseudostates in the close-coupling formalism for electron-atomic-hydrogen system. Phys Rev A 4:569–579 CrossRef Matese JJ, Oberoi RS (1971) Choosing pseudostates in the close-coupling formalism for electron-atomic-hydrogen system. Phys Rev A 4:569–579 CrossRef
40.
go back to reference 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 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
41.
go back to reference Bateman H, Erdlyi A (1953) Higher transcendental functions, vols 1, 2. McGraw-Hill, New-York Bateman H, Erdlyi A (1953) Higher transcendental functions, vols 1, 2. McGraw-Hill, New-York
42.
go back to reference O-ohata K, Taketa H, Huzinaga S (1966) Gaussian expansions of atomic orbitals. J Phys Soc Jpn 21:2306–2313 CrossRef O-ohata K, Taketa H, Huzinaga S (1966) Gaussian expansions of atomic orbitals. J Phys Soc Jpn 21:2306–2313 CrossRef
43.
go back to reference 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 CrossRef 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 CrossRef
44.
go back to reference 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 CrossRef 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 CrossRef
45.
go back to reference Sadlej AJ (1992) Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties. Theor Chim Acta 81:339–354 CrossRef Sadlej AJ (1992) Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties. Theor Chim Acta 81:339–354 CrossRef
46.
go back to reference Wallis A, McElwain DLS, Pritchard HO (1969) The variation method and the algebraic eigenvalue problem. Int J Quant Chem 3:711–722 CrossRef Wallis A, McElwain DLS, Pritchard HO (1969) The variation method and the algebraic eigenvalue problem. Int J Quant Chem 3:711–722 CrossRef
47.
go back to reference 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 CrossRef 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 CrossRef
48.
go back to reference 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 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
49.
go back to reference Temme NM (1983) The numerical computation of the confluent hypergeometric function U(a,b,z). Numer Math 41:63–82 CrossRef Temme NM (1983) The numerical computation of the confluent hypergeometric function U(a,b,z). Numer Math 41:63–82 CrossRef
50.
go back to reference Maier CH, Cederbaum LS (1980) A spherical-box approach to resonances. J Phys B, Atom Mol Phys 13:L119–L124 CrossRef Maier CH, Cederbaum LS (1980) A spherical-box approach to resonances. J Phys B, Atom Mol Phys 13:L119–L124 CrossRef
51.
go back to reference Gersbacher R, Broad JT (1990) Resonances in helium photoionisation. J Phys B 23:365–384 CrossRef Gersbacher R, Broad JT (1990) Resonances in helium photoionisation. J Phys B 23:365–384 CrossRef
52.
go back to reference Guseinov II, Mamedov BA (2004) Evaluation of incomplete Gamma functions using downward recursion and analytical relations. J Math Chem 36:341–346 CrossRef Guseinov II, Mamedov BA (2004) Evaluation of incomplete Gamma functions using downward recursion and analytical relations. J Math Chem 36:341–346 CrossRef
53.
go back to reference Eyring H, Walter J, Kimball GE (1944) Quantum chemistry. Wiley, New York Eyring H, Walter J, Kimball GE (1944) Quantum chemistry. Wiley, New York
54.
go back to reference Holøien E, Midtdal J (1955) On a metastable energy state of the negative helium ion. Proc Phys Soc A 68:815–823 CrossRef Holøien E, Midtdal J (1955) On a metastable energy state of the negative helium ion. Proc Phys Soc A 68:815–823 CrossRef
55.
go back to reference Condon EU, Shortley GH (1959) The theory of atomic spectra, 6th edn. Cambridge University Press, Cambridge Condon EU, Shortley GH (1959) The theory of atomic spectra, 6th edn. Cambridge University Press, Cambridge
56.
go back to reference Schwartz C (1962) Importance of angular correlations between atomic electrons. Phys Rev 126:1015–1019 CrossRef Schwartz C (1962) Importance of angular correlations between atomic electrons. Phys Rev 126:1015–1019 CrossRef
57.
go back to reference Goldman SP (1997) Accurate modified configuration interaction calculations for many electron systems made easy. Phys Rev Lett 78:2325–2328, and references therein CrossRef Goldman SP (1997) Accurate modified configuration interaction calculations for many electron systems made easy. Phys Rev Lett 78:2325–2328, and references therein CrossRef
Metadata
Title
Application of the Uniformly Charged Sphere Stabilization for Calculating the Lowest 1 S Resonances of H −
Authors
S. O. Adamson
D. D. Kharlampidi
A. I. Dementiev
Copyright Year
2013
DOI
https://doi.org/10.1007/978-3-319-01529-3_5

Premium Partner