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Internal coordinates and orthogonality: features of the pseudoinverse of the Eliashevich–Wilsonian B-matrix

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Abstract

It is shown that the system of unit vectors corresponding to the internal coordinates is non-orthogonal generally. The deduction starts with the well-known orthonormality of unit vectors of the Cartesian coordinates. The crucial point of the GDIIS method is discussed regarding a “partially isomorphic” relationship between two vector spaces. Some features of the pseudoinverse of the Eliashevich–Wilsonian matrix B are deduced and discussed: these are analogous to the conditions formulated originally for the elements of the B-matrix.

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References

  1. Wilson EB Jr, Decius JC, Cross PC (1955) Molecular vibrations. McGraw-Hill, New York

    Google Scholar 

  2. Boлькeнштeйн MB, Гpибoв ЛA, Eльяшeвич MA, Cтeпaнoв БИ (1972) Кoлeбaния мoлeкyл. Hayкa, Mocквa (in Russian)

    Google Scholar 

  3. Califano S (1976) Vibrational states. Wiley, London

    Google Scholar 

  4. Fogarasi G, Zhou X, Taylor PW, Pulay P (1992) J Am Chem Soc 114:8191

    Article  CAS  Google Scholar 

  5. Casimir HBG (1931) Dissertation, Leyden

  6. Eckart C (1935) Phys Rev 47:552

    Article  CAS  Google Scholar 

  7. Sayvetz A (1939) J Chem Phys 6:383

    Article  Google Scholar 

  8. Eliashevich M (1940) C. R. Acad Sci URSS 28:605

    Google Scholar 

  9. Wilson EB Jr (1941) J Chem Phys 9:76

    Article  CAS  Google Scholar 

  10. Moore EH (1920) Bull Am Math Soc 26:394

    Google Scholar 

  11. Penrose R (1955) Proc Cambridge Phil Soc 51:406

    Article  Google Scholar 

  12. Pulay P, Fogarasi G, Pang F, Boggs JE (1979) J Am Chem Soc 101:2550

    Article  CAS  Google Scholar 

  13. Fogarasi G, Pulay P (1985) Ab initio calculation of force fields and vibrational spectra. In: Durig JR (ed) Vibrational spectra and structure, vol 14. Elsevier, Amsterdam, p 125

    Google Scholar 

  14. Crawford B Jr (1952) J Chem Phys 20:977

    Article  CAS  Google Scholar 

  15. Mirsky L (1990) An introduction to linear algebra. Dover, New York

    Google Scholar 

  16. Pulay P, Fogarasi G, Zhou X, Taylor PW (1990) Vibr Spectrosc 1:159

    Article  CAS  Google Scholar 

  17. Császár P, Pulay P (1984) J Mol Struct 114:31

    Article  Google Scholar 

  18. Malhiot RJ, Ferigle SM (1954) J Chem Phys 22:717

    Article  CAS  Google Scholar 

  19. Woodward LA (1972) Introduction to the theory of molecular vibrations and vibrational spectroscopy. Oxford University Press, Oxford

    Google Scholar 

  20. Winnewisser BP, Watson JKG (2001) J Mol Spectrosc 205:227

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors are grateful to Dr. László Párkányi (Research Centre for Natural Sciences of the Hungarian Academy of Sciences) and to Dr. Lajos László, Dr. Tibor Pasinszki and János Eőri (Eötvös Loránd University, Budapest) for the valuable discussions and help.

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Authors and Affiliations

  1. Department of Inorganic Chemistry, Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest, 1117, Hungary

    F. Kalincsák & G. Pongor

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  1. F. Kalincsák
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  2. G. Pongor
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Correspondence to G. Pongor.

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Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan”.

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Kalincsák, F., Pongor, G. Internal coordinates and orthogonality: features of the pseudoinverse of the Eliashevich–Wilsonian B-matrix. Theor Chem Acc 134, 108 (2015). https://doi.org/10.1007/s00214-015-1713-8

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  • DOI: https://doi.org/10.1007/s00214-015-1713-8

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