Skip to main content
SpringerLink
Log in

Methods for Computing Ro-vibrational Energy Levels

  • Chapter
  • First Online:
Practical Aspects of Computational Chemistry IV

  • 1055 Accesses

Abstract

In this article I review methods for computing ro-vibrational energy levels of small polyatomic molecules. The principal impediment to the calculation of energy levels is the size of the required basis set. If one uses a product basis the Hamiltonian matrix for a four-atom molecule is too large to store in core memory. Iterative methods enable one to use a product basis to compute energy levels (and spectra) without storing a Hamiltonian matrix. Despite the advantages of iterative methods it is not possible, using product basis functions, to calculate ro-vibrational spectra of molecules with more than four atoms. A recent method combining contracted basis functions and the Lanczos algorithm is described.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aliev MR, Watson JKG (1985) Molecular spectroscopy: modern research, vol 3

    Google Scholar 

  2. Carter S, Handy NC (1986) Comput Phys Rep 5:115

    Article  CAS  Google Scholar 

  3. Tennyson J (1986) Comput Phys Rep 4:1

    Article  Google Scholar 

  4. Bačić Z, Light JC (1989) Annu Rev Phys Chem 40:469

    Article  Google Scholar 

  5. Sibert EL (1990) Int Rev Phys Chem 9:1

    Article  CAS  Google Scholar 

  6. Carrington T Jr (1998) Encyclopedia of computational chemistry, von Ragué Schleyer P (ed), vol 5. Wiley, New York

    Google Scholar 

  7. Spectrochim (2002) Acta Part A 58 A special issue on First principles rovibrational spectroscopy

    Google Scholar 

  8. Watson JKG (1968) Mol Phys 15:479–490

    Article  CAS  Google Scholar 

  9. Romanowski H, Bowman JM, Harding L (1985) J Chem Phys 82:4155

    Article  CAS  Google Scholar 

  10. Carter S, Culik SJ, Bowman JM (1997) J Chem Phys 107:10458

    Article  CAS  Google Scholar 

  11. Carter S, Bowman JM, Handy NC (1998) Theor Chem Acta 100:191

    Article  CAS  Google Scholar 

  12. Bowman JM, Carter S, Huang X (2003) Int Rev Phys Chem 22:533–549

    Article  CAS  Google Scholar 

  13. Bowman JM, Carter S, Handy NC(2005) Theory and applications of computational chemistry: the first forty years, Dykstra C et al (ed), Chapter 11. Elsevier, New York

    Google Scholar 

  14. Oyanagi C, Yagi K, Taketsugu T, Hirao K (2006) J Chem Phys 124:064311

    Article  Google Scholar 

  15. Chapuisat X, Iung C (1992) Phys Rev A 45:6217–6235

    Article  Google Scholar 

  16. Gatti F, Iung C, Menou M, Justum Y, Nauts A, Chapuisat X (1998) J Chem Phys 108:8804

    Article  CAS  Google Scholar 

  17. Iung C, Gatti F, Viel A, Chapuisat X (1999) Phys Chem Chem Phys 1:3377

    Article  CAS  Google Scholar 

  18. Mladenović M (2000) J Chem Phys 112:1070–1081

    Article  Google Scholar 

  19. Mladenović M (2000) J Chem Phys 112:1082–1095

    Article  Google Scholar 

  20. Bramley MJ, Carrington T Jr (1993) J Chem Phys 99:8519

    Article  CAS  Google Scholar 

  21. Mladenović M (2000) J Chem Phys 112:1070

    Article  Google Scholar 

  22. Mladenović M (2000) J Chem Phys 112:1082

    Article  Google Scholar 

  23. Chapuisat X, Iung C (1992) Phys Rev A 45:6217

    Article  Google Scholar 

  24. Sutcliffe BT (1982) Current aspects of quantum chemistry. In: Carbo R (ed) Studies in theoretical and physical chemistry, vol 21. Elsevier, Amsterdam, pp 99–125

    Google Scholar 

  25. Sutcliffe BT, Tennyson J (1991) Int J Quant Chem 39:183

    Article  CAS  Google Scholar 

  26. Tennyson J, Sutcliffe BT (1982) J Chem Phys 77:4061

    Article  CAS  Google Scholar 

  27. Brocks G, Van Der Avoird A, Sutcliffe BT, Tennyson J (1983) Mol Phys 50:1025

    Article  CAS  Google Scholar 

  28. Xantheas SS, Sutcliffe BT (1995) J Chem Phys 103:8022

    Article  CAS  Google Scholar 

  29. Handy NC (1987) Mol Phys 61:207

    Article  CAS  Google Scholar 

  30. Gatti F, Iung C, Leforestier C, Chapuisat X (1999) J Chem Phys 111:7236

    Article  CAS  Google Scholar 

  31. Gatti F, Munoz C, Iung C (2001) J Chem Phys 114:8275

    Article  CAS  Google Scholar 

  32. Wang X-G, Carrington T Jr (2004) J Chem Phys 121:2937

    Article  CAS  Google Scholar 

  33. Zare RN (1988) Angular momentum. Wiley, New York

    Google Scholar 

  34. Wang X-G, Carrington T Jr (2000) J Chem Phys 113:7097–7101

    Article  CAS  Google Scholar 

  35. Laane J, Harthcock MA, Killough PM, Bauman LE, Cooke JM (1982) J Mol Spec 91:286; Harthcock MA, Laane J (1982) J Mol Spectrosc 91:300

    Google Scholar 

  36. Meyer R (1979) J Mol Spectrosc 76:266

    Article  CAS  Google Scholar 

  37. McCoy AB, Burleigh DC, Sibert EL (1991) J Chem Phys 95:7449

    Article  CAS  Google Scholar 

  38. Lauvergnat D, Nauts A (2002) J Chem Phys 116:8560

    Article  CAS  Google Scholar 

  39. Mátyus E, Czakó G, Császár AG (2009) J Chem Phys 130:134112

    Article  Google Scholar 

  40. Lauvergnat David (2002) J Chem Phys 116:8560

    Article  CAS  Google Scholar 

  41. Carter S, Handy NC (1988) Comput Phys Commun 51:49

    Article  CAS  Google Scholar 

  42. Bac̆ić Z, Light JC (1989) Annu Rev Phys Chem 40:469

    Google Scholar 

  43. Henderson JR, Tennyson J (1990) Chem Phys Lett 173:133

    Article  CAS  Google Scholar 

  44. Wu XT, McCoy AB, Hayes EF (1999) J Chem Phys 110:2354

    Article  CAS  Google Scholar 

  45. Qiu Y, Zhang JZH, Bac̆ić Z (1998) J Chem Phys 108:4804

    Google Scholar 

  46. Bahel A, Bac̆ić Z (1999) J Chem Phys 111:11164

    Google Scholar 

  47. Mladenović M (2002) Spectrochim Acta Part A 58:809

    Article  Google Scholar 

  48. Mladenović M (2002) Spectrochim Acta Part A 58:795

    Article  Google Scholar 

  49. Luckhaus D (2000) J Chem Phys 113:1329

    Article  CAS  Google Scholar 

  50. Bramley MJ, Handy NC (1993) J Chem Phys 98:1378

    Article  CAS  Google Scholar 

  51. Light JC, Carrington T Jr (2000) Adv Chem Phys 114:263

    Google Scholar 

  52. Bowman JM, Gazdy B (1991) J Chem Phys 94:454

    Article  CAS  Google Scholar 

  53. Carter S, Handy NC (2002) Mol Phys 100:681

    Article  CAS  Google Scholar 

  54. Koput J, Carter S, Handy N (2001) J Chem Phys 115:8345

    Article  CAS  Google Scholar 

  55. Handy NC, Carter S, Colwell SM (1999) Mol Phys 96:477

    Article  CAS  Google Scholar 

  56. Tennyson J, Sutcliffe BT (1986) Mol Phys 58:1067; Sutcliffe BT, Tennyson J (1986) Mol Phys 58:1053

    Google Scholar 

  57. Wang X-G, Carrington T Jr (2004) J Chem Phys 121:2937

    Article  CAS  Google Scholar 

  58. Carter S, Bowman JM, Handy NC (1998) Theor Chem Acc 100:191

    Google Scholar 

  59. Fábri C, Mátyus E, Császár AG (2011) J Chem Phys 134:074105

    Article  Google Scholar 

  60. Wang X-G, Carrington T Jr (2003) J Chem Phys 119:101

    Article  CAS  Google Scholar 

  61. Papousek D, Aliev MR (1982) Molecular vibrational-rotational spectra. Elsevier, Amsterdam

    Google Scholar 

  62. Wei H, Carrington T (1997) J Chem Phys 107:2813–2818

    Article  CAS  Google Scholar 

  63. Wei H, Carrington T Jr (1997) J Chem Phys 107:9493

    Article  CAS  Google Scholar 

  64. Wei H, Carrington T Jr (1998) Chem Phys Lett 287:289

    Article  CAS  Google Scholar 

  65. Wei H (2003) J Chem Phys 118:7208

    Article  CAS  Google Scholar 

  66. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1989) Numerical recipes. Cambridge University Press, Cambridge

    Google Scholar 

  67. Wyatt RE (1989) Adv Chem Phys 73:231

    Google Scholar 

  68. Koeppel H, Domcke W, Cederbaum LS (1984) Adv Chem Phys 57:59

    Google Scholar 

  69. Iung C, Leforestier C (1989) J Chem Phys 90:3198

    Article  CAS  Google Scholar 

  70. Bentley JA, Brunet J-P, Wyatt RE, Friesner RA, Leforestier C (1989) Chem Phys Lett 161:393

    Article  CAS  Google Scholar 

  71. Bramley MJ, Carrington T Jr (1993) J Chem Phys 99:8519

    Article  CAS  Google Scholar 

  72. Bramley MJ, Carrington T Jr (1994) J Chem Phys 101:8494

    Article  CAS  Google Scholar 

  73. Neuhauser D (1990) J Chem Phys 93:2611

    Article  CAS  Google Scholar 

  74. Lehoucq RB, Gray SK, Zhang D-H, Light JC (1998) Comput Phys Commun 109:15

    Article  CAS  Google Scholar 

  75. Mussa HY, Tennyson J (1998) J Chem Phys 109:10885

    Article  CAS  Google Scholar 

  76. Wall NR, Neuhauser D (1995) J Chem Phys 102:8011

    Article  CAS  Google Scholar 

  77. Mandelshtam VA, Taylor HS (1995) J Chem Phys 102:7390

    Article  CAS  Google Scholar 

  78. Mandelshtam VA, Taylor HS (1997) J Chem Phys 106:5085

    Article  CAS  Google Scholar 

  79. Yu H-G, Smith SC (1997) Ber Bunsenges Phys Chem 101:400

    Article  CAS  Google Scholar 

  80. Chen R, Guo H (1998) J Chem Phys 108:6068

    Article  CAS  Google Scholar 

  81. Golub GH, Van Loan CF (1989) Matrix computations. Johns Hopkins University Press, Baltimore

    Google Scholar 

  82. Friesner RA, Wyatt RE, Hempel C, Criner B (1986) J Comput Phys 64:220

    Article  Google Scholar 

  83. Manthe U, Koeppel H (1990) J Chem Phys 93:345

    Article  CAS  Google Scholar 

  84. Beck MH, Jaeckle A, Worth GA, Meyer H-D (2000) Phys Rep 324:1

    Article  CAS  Google Scholar 

  85. Pelaez D, Meyer H-D (2013) J Chem Phys 138:014108

    Article  Google Scholar 

  86. Manzhos S, Carrington T (2006) J Chem Phys 125:194105

    Article  Google Scholar 

  87. Manzhos S, Carrington T (2007) J Chem Phys 127:014103

    Article  Google Scholar 

  88. Manzhos S, Carrington T (2008) J Chem Phys 129:224104

    Article  Google Scholar 

  89. Pradhan JCMSE, Carreon-Macedo J-L, Brown A (2013) J Phys Chem A 117:6925

    Article  CAS  Google Scholar 

  90. Cullum JK, Willoughby RA (1985) Lanczos algorithms for large symmetric eigenvalue computations. Birkhäuser, Boston

    Google Scholar 

  91. Sorensen DC (1992) SIAM. J Math Anal Appl 13:357

    Google Scholar 

  92. Lehoucq RB, Sorensen DC, Yang C (1998) ARPACK USERS GUIDE: solution of large scale eigenvalue problems by implicitly restarted Arnoldi methods. SIAM, Philadelphia

    Book  Google Scholar 

  93. Baglama J, Calvetti D, Reichel L (1996) BIT 36:400

    Article  Google Scholar 

  94. Huang S, Carrington T Jr (1999) Chem Phys Lett 312:311–318

    Article  CAS  Google Scholar 

  95. Roy P-N, Carrington T Jr (1996) Chem Phys Lett 257:98–104

    Article  CAS  Google Scholar 

  96. Bunker PR (1998) Symmetry Per Jensen molecular, spectroscopy, 2nd edn. NRC Research Press, Ottawa

    Google Scholar 

  97. Wang X-G, Carrington T Jr (2001) J Chem Phys 114:1473

    Article  CAS  Google Scholar 

  98. Chen R, Guo H (2001) J Chem Phys 114:1467

    Article  CAS  Google Scholar 

  99. Wang X-G, Carrington T Jr (2001) J Chem Phys 115:9781

    Article  CAS  Google Scholar 

  100. Wang X-G, Carrington T Jr (2003) J Chem Phys 118:6946–6956

    Article  CAS  Google Scholar 

  101. Bramley MJ, Carrington T Jr (1994) J Chem Phys 101:8494

    Article  CAS  Google Scholar 

  102. Wang X-G, Carrington T Jr (2002) J Chem Phys 117:6923

    Article  CAS  Google Scholar 

  103. Chapuisat X, Belfhal A, Nauts A (1991) J Mol Spectrosc 149:274

    Article  CAS  Google Scholar 

  104. Wu XT, Hayes EF (1997) J Chem Phys 107:2705

    Article  CAS  Google Scholar 

  105. Friesner RA, Bentley JA, Menou M, Leforestier C (1993) J Chem Phys 99:324

    Article  CAS  Google Scholar 

  106. Viel A, Leforestier C (2000) J Chem Phys 112:1212

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Natural Sciences and Engineering Research Council of Canada

Author information

Authors and Affiliations

  1. Chemistry Department, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Tucker Carrington

Authors
  1. Tucker Carrington
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tucker Carrington .

Editor information

Editors and Affiliations

  1. Dept of Chemistry, Jackson State Univ, Jackson, Mississippi, USA

    Jerzy Leszczynski

  2. US Army Engr Research & Development, Jackson State University, Vicksburg, USA

    Manoj K. Shukla

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this chapter

Cite this chapter

Carrington, T. (2016). Methods for Computing Ro-vibrational Energy Levels. In: Leszczynski, J., Shukla, M. (eds) Practical Aspects of Computational Chemistry IV. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7699-4_5

Download citation

Publish with us

Policies and ethics

Search

Navigation