Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T02:18:55.169Z Has data issue: false hasContentIssue false

3 - Ab-initio quantum defects

Published online by Cambridge University Press:  07 October 2011

M. S. Child
M. S. Child
Affiliation:
University of Oxford
Get access

Summary

The previous chapter laid out the principles of multichannel quantum defect theory, showing in particular how knowledge of the quantum defects or scattering K-matrices are built into a unified theory of Rydberg spectroscopy and ionization dynamics. This chapter deals with the ab-initio determination of these quantum defects. We know from the discussion in Chapter 1 that they arise from interactions between the positive ion core and the Rydberg electron, which were seen to occur on a timescale far shorter than that of the molecular vibrations and rotations. It is therefore natural to compute them within the fixed nucleus Born–Oppenheimer approximation. Useful information on the lowest members of a given series may be obtained by traditional Hartree–Fock and configuration interaction techniques [1]. Carefully designed diffuse Rydberg orbitals are, however, required [2]. The resulting information is normally limited to the potential energy surfaces for principal quantum numbers n ≤ 4, from which it may be difficult to extract the desired forms of the quantum defects, as functions of the nuclear coordinates, particularly for polyatomic molecules. An alternative is to recognize that the distant outer parts of the Rydberg wavefunction may be expressed as Coulomb functions. Thus the ab-initio effort may be restricted to a finite volume, chosen to be large enough to allow a proper treatment of all Rydberg–core interactions [3, 4, 5, 6]. The inner and outer wavefunctions are then joined at the core boundary by a so-called R-matrix, from which the scattering K-matrix may be obtained directly, without reference to information on any potential energy surfaces.

Type
Chapter
Information
Theory of Molecular Rydberg States , pp. 45 - 89
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] A., Szabo and N. S., Ostlund, Modern Quantum Chemistry (Dover Publishing, 1996).Google Scholar
[2] R. J., Buenker and S. D., Peyerimhoff, Theor. Chim. Acta 35, 33 (1974).
[3] P. G., Burke and K. A., Berrington, Atomic and Molecular Processes: An R-Matrix Approach (IOP, 1993).Google Scholar
[4] W. M., Huo and F. A., Gianturco, eds, Computational Methods for Electron–Molecule Collisions (Plenum, 1955).Google Scholar
[5] M., Aymar, C. H., Greene and E., Luc-Koenig, Rev. Mod. Phys. 68, 1015 (1996).
[6] P. G., Burke, R-Matrix Theory of Atomic Collisions: Application to Atomic, Molecular and Optical Processes (Springer, 2011).Google Scholar
[7] L., Wolniewicz and K., Dressler, J. Chem. Phys. 100, 444 (1994).
[8] T., Detmer, P., Schneider and L. S., Cederbaum, J. Chem. Phys. 109, 9694 (1998).
[9] G., Staszewska and L., Wolniewicz, J. Mol. Spec. 169, 208 (2002).
[10] K. P., Huber and G., Herzberg, Constants of Diatomic Molecules (van Nostrand, 1979).Google Scholar
[11] R. S., Mulliken, JACS 88, 1849 (1966).
[12] J. T., Lewis, Proc. Phys. Soc. London 68, 632 (1955).
[13] L., Wolniewicz and G., Staszewska, J. Mol. Spec. 220, 45 (2003).
[14] H., Wind, J. Chem. Phys. 42, 2371 (1965).
[15] C., Jungen and O., Atabek, J. Chem. Phys. 66, 5584 (1977).
[16] R. S., Mulliken, Chem. Phys. Lett. 46, 197 (1977).
[17] M., Hiyama and M. S., Child, J. Phys. B 35, 1337 (2002).
[18] R., de Vivie and S. D., Peyerimhoff, J. Chem. Phys. 89, 3028 (1988).
[19] S. C., Ross and C., Jungen, Phys. Rev. A 49, 4353 (1994).
[20] A., Kirrander, D Phil thesis, Oxford University (2005).
[21] M. S., Child and M., Hiyama, J. Phys. B 40, 1233 (2007).
[22] A. U., Hazi, C., Derkits and J. N., Bardsley, Phys. Rev. A 27, 1751 (1983).
[23] S. L., Guberman, J. Chem. Phys. 78, 1404 (1983).
[24] S. C., Ross and C., Jungen, Phys. Rev. A 49, 4364 (1994).
[25] M. S., Child, Phil. Trans. Roy. Soc. London, A 355, 1623 (1997).
[26] D. M., Hirst and M. S., Child, Mol. Phys. 77, 463 (1992).
[27] G., Theodorakopoulos, I. D., Petsalakis and M. S., Child, J. Phys. B 29, 4543 (1996).
[28] B. M., Nestmann and S. D., Peyerimhoff, J. Phys. B 23, 773 (1990).
[29] B. M., Nestmann, R. M., Nesbet and S. D., Peyerimhoff, J. Phys. B 24, 5133 (1991).
[30] L. A., Morgan, J., Tennyson and C. J., Gillan, Comp. Phys. Commun. 114, 120 (1998).
[31] I., Rabadán and J., Tennyson, J. Phys. B 29, 3747 (1996).
[32] I., Rabadán and J., Tennyson, J. Phys. B 30, 1975 (1997).
[33] F. P., Billingsby, Chem. Phys. 3, 864 (1975).
[34] D. L., Albritton, A. L., Schmeltekopf and R. N., Zare, J. Chem. Phys. 71, 3271 (1979).
[35] C., Bloch, Nucl. Phys. 4, 503 (1957).
[36] E., Miescher and K. P., Huber, International Review of Science vol. 3. Physical Chemistry Series 2 (Butterworth, 1976).Google Scholar
[37] I., Rabadán and J., Tennyson, J. Phys. B 31, 4485 (1997).
[38] K., Kauffman, J. Phys. B 24, 2277 (1991).
[39] E. P., Wigner and L., Eisbud, Phys. Rev. 72, 29 (1947).
[40] P. J. A., Buttle, Phys. Rev. 160, 719 (1967).
[41] I. S., Gradsteyn and I. M., Ryzhik, Tables of Integrals, Series and Products (Academic Press, 1980).Google Scholar
[42] M., Abramowitz and I. A., Stegun, Handbook of Mathematical Functions (Dover, 1965).Google Scholar
[43] J. L., Jackson, Phys. Rev. 83, 301 (1951).
[44] D. E., Manolopoulos and R. E., Wyatt, Chem. Phys. Lett. 152, 23 (1988).
[45] A., Faure, J. M., Gorfinkel, L. A., Morgan and J., Tennyson, Comp. Commun. Phys. 144, 224 (2002).
[46] L. A., Morgan, C. J., Gillan, J., Tennyson and X., Chen, J. Phys. B 30, 4087 (1997).
[47] U., Fano and C. M., Lee, Phys. Rev. Lett. 31, 1573 (1973).
[48] C. H., Greene, Phys. Rev. A 28, 2209 (1983).
[49] H., Le Rouzo and G., Raseev, Phys. Rev. A 29, 1214 (1984).
[50] F., Robicheaux, Phys. Rev. A 43, 5946 (1991).
[51] M., Telmini and C., Jungen, Phys. Rev. A 68, 062704 (2003).
[52] S., Bezzaouia, M., Telmini and C., Jungen, Phys. Rev. A 70, 012713 (2004).
[53] F. H., Mies, Phys. Rev. A 20, 1773 (1979).
[54] M., Hiyama and M. S., Child, J. Phys. B 36, 4547 (2003).
[55] R., Galluser and K., Dressler, J. Chem. Phys. 76, 4311 (1982).
[56] J. K. G., Watson, Mol. Phys. 81, 277 (1994).
[57] C., Jungen, A. L., Roche and M., Arif, Phil. Trans. Roy. Soc. London, A 355, 1481 (1997).
[58] K. B., Laughlin, G. A., Blake, R. C., Cohen, D. C., Hoyde and R. J., Saykally, J. Chem. Phys. 90, 1358 (1989).
[59] C. M., Gittins, N. A., Harris, M., Hui and R. W., Field, Can. J. Phys. 79, 247 (2001).
[60] I., Dabrowski, D. W., Tokaryk, R. H., Lipson and J. K. G., Watson, J. Mol. Spec. 189, 95 (1998).
[61] C., Jungen and A. L., Roche, J. Chem. Phys. 110, 10791 (1999).
[62] C. W., Clark, Phys. Rev. A 20, 1875 (1979).
[63] R. W., Field, C. M., Gittins, N. A., Harris and C., Jungen, J. Chem. Phys. 122, 184314 (2005).
[64] M., Arif, C., Jungen and A. L., Roche, J. Chem. Phys. 106, 4102 (1997).
[65] C., Jungen and F., Texier, J. Phys. B 33, 2495 (2000).
[66] C., Jungen and A. L., Roche, Can. J. Phys. 79, 287 (2001).
[67] S. N., Altunata, S. L., Coy and R. W., Field, J. Chem. Phys. 123, 084318 (2005).
[68] S. N., Altunata, S. L., Coy and R. W., Field, J. Chem. Phys. 123, 084319 (2005).
[69] C. H., Greene, U., Fano and G., Strinati, Phys. Rev. A 19, 1485 (1979).
[70] C. H., Greene, A. R. P., Rau and U., Fano, Phys. Rev. A 26, 2441 (1982).
[71] A. R. P., Rau, Phys. Rev. A 38, 2255 (1988).

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Ab-initio quantum defects
  • M. S. Child, University of Oxford
  • Book: Theory of Molecular Rydberg States
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511994814.004
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Ab-initio quantum defects
  • M. S. Child, University of Oxford
  • Book: Theory of Molecular Rydberg States
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511994814.004
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Ab-initio quantum defects
  • M. S. Child, University of Oxford
  • Book: Theory of Molecular Rydberg States
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511994814.004
Available formats
×