# Determination of the non-relativistic energy spectrum of molecular hydrogen ions H2+ and HD+

### Abstract

To solve the fundamental problems of physics, chemistry, biology and other sciences, which include many day-to-day practical tasks, it is necessary to have research methods that allow us determining the qualitative and quantitative composition of a substance, its structure, properties and other parameters in wide ranges of temperature and pressure, various aggregative states, at low and high concentrations and other physical conditions. A universal method that satisfies all these conditions is spectroscopy. Spectroscopy is the section of physics engaged in the study of the structure of matter using electromagnetic research, absorbed, emitted, scattered or reflected by the object of study. Electromagnetic radiation, decomposed by wavelength or energy, forms a spectrum. All modern studies on the spectra of electromagnetic radiation are based on quantum theory, and thus molecular spectroscopy is based on quantum laws.In this paper, we use the exponential expansion of the wave functions with the variational basis set type exp(–anR–bnr1–gnrn) for the systematic calculation of non-relativistic bound state energy hydrogen molecular ion H2+ and HD+. We perform calculations for the state with the total orbital angular momentum L=0-4 with a full set of vibrational quantum numbers n=0-10.

### References

1. B. Grémaud, D. Delande, and N. Billy, J. Phys. B: At. Mol. Opt. Phys., 31, 383 (1998).

2. S. Schiller and C. Lämmerzahl, Phys. Rev. A 68, 053406 (2003).

3. D.L. Farnham, R.S. Van Dyck, and P. B. Schwinberg, Phys. Rev. Lett. 75, 3598-3601 (1995).

4. C.M. Rosenthal, Chem. Phys. Lett. 10, 381-386 (1971).

5. J.J. Griffin and J.A. Wheeler, Phys. Rev. 108, 311 (1957).

6. A.J. Thakkar and V.H. Smith, Phys. Rev. A 15, 1 (1977).

7. T.K. Rebane and O.N. Yusupov, JETP, 71, 1050 (1990).

8. V.I. Korobov, D. Bakalov and H.J. Monkhorst, Phys. Rev A 59, R919 (1999).

9. A.M. Frolov and V.H. Smith, Jr., J. Phys. B 28, L449 (1995).

10. V.I. Korobov, Phys. Rev.A 61 064503 (2000).

11. V.I. Korobov, Phys. Rev. A 66, 024501 (2002).

12. D.H. Bailey, ACM Trans. Math. Software 19, 288 (1993).

13. S. Schiller and V. Korobov, Phys.Rev. A 71, 032505 (2005).

14. V.I. Korobov, Phys. Rev. A 70, 012505 (2000).

15. V.I. Korobov, Phys. Rev. A 73, 024502 (2006).

16. M.M. Cassar and G.W.F. Drake, J. Phys. B 37, 2485 (2004).

17. V.I. Korobov, Phys. Rev. A 61, 064503 (2000).

18. A.M. Frolov and V. H. Smith, Jr., J. Phys. B: At. Mol. Opt., 28, L449 (1995).

19. V.I. Korobov, D. Bakalov, and H.J. Monkhorst, Phys. Rev. A 59, R919 (1999).

20. V.I. Korobov, Phys. Rev. A 74, 052506 (2006).

2. S. Schiller and C. Lämmerzahl, Phys. Rev. A 68, 053406 (2003).

3. D.L. Farnham, R.S. Van Dyck, and P. B. Schwinberg, Phys. Rev. Lett. 75, 3598-3601 (1995).

4. C.M. Rosenthal, Chem. Phys. Lett. 10, 381-386 (1971).

5. J.J. Griffin and J.A. Wheeler, Phys. Rev. 108, 311 (1957).

6. A.J. Thakkar and V.H. Smith, Phys. Rev. A 15, 1 (1977).

7. T.K. Rebane and O.N. Yusupov, JETP, 71, 1050 (1990).

8. V.I. Korobov, D. Bakalov and H.J. Monkhorst, Phys. Rev A 59, R919 (1999).

9. A.M. Frolov and V.H. Smith, Jr., J. Phys. B 28, L449 (1995).

10. V.I. Korobov, Phys. Rev.A 61 064503 (2000).

11. V.I. Korobov, Phys. Rev. A 66, 024501 (2002).

12. D.H. Bailey, ACM Trans. Math. Software 19, 288 (1993).

13. S. Schiller and V. Korobov, Phys.Rev. A 71, 032505 (2005).

14. V.I. Korobov, Phys. Rev. A 70, 012505 (2000).

15. V.I. Korobov, Phys. Rev. A 73, 024502 (2006).

16. M.M. Cassar and G.W.F. Drake, J. Phys. B 37, 2485 (2004).

17. V.I. Korobov, Phys. Rev. A 61, 064503 (2000).

18. A.M. Frolov and V. H. Smith, Jr., J. Phys. B: At. Mol. Opt., 28, L449 (1995).

19. V.I. Korobov, D. Bakalov, and H.J. Monkhorst, Phys. Rev. A 59, R919 (1999).

20. V.I. Korobov, Phys. Rev. A 74, 052506 (2006).

Published

2018-10-30

How to Cite

BEKBAEV, A.K. et al.
Determination of the non-relativistic energy spectrum of molecular hydrogen ions H2+ and HD+.

**Recent Contributions to Physics (Rec.Contr.Phys.)**, [S.l.], v. 67, n. 4, p. 11-17, oct. 2018. ISSN 2663-2276. Available at: <https://bph.kaznu.kz/index.php/zhuzhu/article/view/957>. Date accessed: 01 nov. 2020.
Section

Theoretical Physics. Nuclear and Elementary Particle Physics. Astrophysics