Skip to main content

The Floating Spherical Gaussian Orbital Method

  • Chapter
Methods of Electronic Structure Theory

Part of the book series: Modern Theoretical Chemistry ((MTC,volume 3))

Abstract

One important object of molecular quantum mechanics is the calculation of the stationary state energies of molecular systems as functions of the geometrical configuration of their nuclei. By finding the energy minima one can predict the equilibrium geometric form of molecules, including internuclear distances and bond angles. The procedure implies the use of the Born-Oppenheimer approx­imation which is known to be excellent for the ground electronic state of most molecules.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. F. Schaefer III,The Electronic Structure of Atoms and Molecules, Addison-Wesley Publishing Co., Reading, Mass. (1972).

    Google Scholar 

  2. L. C. Snyder and H. Basch, Molecular Wave Functions and Properties, John Wiley and Sons, New York (1972).

    Google Scholar 

  3. W. G. Richards, T. E. H. Walker, and R. K. Hinkley, A Bibliography of Ab Initio Molecular Wave Function, Oxford University Press, London (1972).

    Google Scholar 

  4. F. E. Harris, Quantum chemistry, Annu. Rev. Phys. Chem. 23, 415–438 (1972); also previous reviews referenced therein.

    Article  CAS  Google Scholar 

  5. C. C. J. Roothaan, New developments in molecular orbital theory, Rev. Mod. Phys. 23,69 (1951).

    Article  CAS  Google Scholar 

  6. G. G. Hall, The molecular orbital theory of chemical valency. VIII.A method of calculating ionization potentials, Proc. R. Soc. London, Ser. A 205,541 (1951).

    Article  CAS  Google Scholar 

  7. E. Clementi and D. R. Davis, Electronic structure of large molecular systems, J. Comput. Phys. 2,223 (1967).

    Google Scholar 

  8. J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 1, McGraw-Hill Book Co., New York (1963).

    Google Scholar 

  9. P.-O. Löwdin, On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals, J. Chem. Phys. 18, 365 (1950).

    Article  Google Scholar 

  10. S. F. Boys, Electronic wave functions. I. A general method of calculation for the stationary states of any molecular system, Proc. R. Soc. London, Ser. A 200,542 (1950).

    Article  CAS  Google Scholar 

  11. I.Shavitt, The gaussian function in calculations in statistical mechanics and quantum mechanics, Methods Comput. Phys. 2,1 (1963).

    Article  Google Scholar 

  12. H. Preuss, Bemerkungen zum Self-consistent-field-Verfahren and zur Methode der Konfigurationenwechselwirkung in der Quantenchemie, Z. Natwforsch. 11a,823 (1956).

    CAS  Google Scholar 

  13. J.L. Whitten, Gaussian expansion of hydrogen-atom wave functions, J. Chem. Phys. 39,349 1963.

    Article  CAS  Google Scholar 

  14. W. J. Hehre, R. F. Stewart, and J. A. Pople, Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of Slater-type atomic orbitals, J. Chem. Phys. 51, 2657 (1969).

    Article  CAS  Google Scholar 

  15. R. P. Hosteny, R. R. Gilman, T. H. Dunning, A. Pipano, and I.Shavitt, Comparison of Slater and contracted Gaussian basis sets in SCF and CI calculations on H20, Chem Phys. Lett. 7,325 (1970).

    Article  CAS  Google Scholar 

  16. V. Fock, Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems, Z. Phys.61, 126 (1930); see also Ref. 5.

    Article  Google Scholar 

  17. C. Edmiston and K. Ruedenberg, Localized atomic and molecular orbitals, Rev. Mod. Phys.35, 457 (1963).

    Article  CAS  Google Scholar 

  18. D. Peters, Computation of the SCF molecular orbital wavefunction in terms of localized orbitals, J. Chem. Phys.46, 4427 (1967).

    Article  CAS  Google Scholar 

  19. J. R. Hoyland, Ab initio bond-orbital calculations. I. Application to methane, ethane, propane and propylene, J. Am. Chem. Soc.90, 2227 (1968).

    Article  CAS  Google Scholar 

  20. J. H. Letcher and T. H. Dunning, Localized orbitals. I. б- bonds J. Chem. Phys. 48, 4538 (1968).

    Article  CAS  Google Scholar 

  21. R. D. Brown, A quantum-mechanical treatment of aliphatic compounds. Part I. Paraffins, J Chem. Soc.1953, 2615 (1953).

    Article  Google Scholar 

  22. W. C. Herndon, Unparameterized localized orbital calculations for saturated hydrocarbons, Chem. Phys. Lett.10, 460 (1971).

    Article  CAS  Google Scholar 

  23. G. N. Lewis, The atom and the molecule, J. Am. Chem. Soc.38, 762 (1916)

    Article  CAS  Google Scholar 

  24. G. N. Lewis, Valence and the Structure of Atoms and Molecules, Chemical Catalog Co., New York (1923).

    Google Scholar 

  25. G. E. Kimball and G. F. Neumark, Use of Gaussian wave functions in molecular calculations, J. Chem. Phys.26, 1285 (1957).

    Article  CAS  Google Scholar 

  26. G. F. Neumark, Free Cloud Approximation to Molecular Orbital Calculation, Ph.D. disserta­tion, Columbia University (1951); University Microfilms Publication No. 2845.

    Google Scholar 

  27. H. Preuss, Ein neues Programm zur quantentheoretischen Berechnung von Molekülen and Atomsystem. I. Grundlagen, Mol. Phys. 8, 157 (1964).

    Article  Google Scholar 

  28. A. A. Frost, B. H. Prentice III, and R. A. Rouse, A simple floating localized orbital model of molecular structure, J. Am. Chem. Soc.89, 3064 (1967).

    Article  CAS  Google Scholar 

  29. A. A. Frost, Floating spherical Gaussian orbital model of molecular structure. I. Computa­tional procedure. LiH as an example, J. Chem. Phys.47, 3707 (1967).

    Article  CAS  Google Scholar 

  30. A. A. Frost, Floating spherical Gaussian orbital model of molecular structure. II. One- and two-electron-pair systems, J. Chem. Phys.47, 3714 (1967).

    Article  CAS  Google Scholar 

  31. A. A. Frost, A floating spherical Gaussian orbital model of molecular structure. III. First-row atom hydrides, J. Phys. Chem.72, 1289 (1968).

    Article  CAS  Google Scholar 

  32. A. A. Frost and R. A. Rouse, A floating spherical Gaussian orbital model of molecular structure. IV. Hydrocarbons, J. Am. Chem. Soc.90, 1965 (1968).

    Article  CAS  Google Scholar 

  33. A. A. Frost, R. A. Rouse, and L. Vescelius, A floating spherical Gaussian orbital model of molecular structure. V. Computer programs, Int. J. Quantum Chem. IIS, 43 (1968).

    Google Scholar 

  34. R. A. Rouse and A. A. Frost, Floating spherical Gaussian orbital model of molecular structure. VI. Double-Gaussian modification, J. Chem. Phys.50, 1705 (1969).

    Article  CAS  Google Scholar 

  35. A. A. Frost, A floating spherical Gaussian orbital model of molecular structure VII. Borazane and diborane, Theor. Chim. Acta18, 156 (1970).

    Article  CAS  Google Scholar 

  36. S. Y. Chu and A. A. Frost, Floating spherical Gaussian orbital model of molecular structure. VIII. Second-row atom hydrides, J. Chem. Phys. 54, 760 (1971).

    Article  CAS  Google Scholar 

  37. S. Y. Chu and A. A. Frost, Floating spherical Gaussian orbital model of molecular structure. IX. Diatomic molecules of first-row and second-row atoms, J. Chem. Phys. 54, 764 (1971).

    Article  CAS  Google Scholar 

  38. A. A. Frost, The potential energy surface of the H3 system using floating Gaussian orbitals, Adv. Chem. Phys.21, 65 (1971).

    Article  CAS  Google Scholar 

  39. J. L. Nelson and A. A. Frost, A floating spherical Gaussian orbital model of molecular structure. X. C3 and C4 saturated hydrocarbons and cyclobutane, J. Am. Chem. Soc. 94, 3727 (1972).

    Article  CAS  Google Scholar 

  40. J. L. Nelson, and A. A. Frost, A floating spherical Gaussian orbital model of molecular structure. ESCA chemical shifts for inner shell electrons for small hydrocarbons, Chem. Phys. Lett. 13, 610 (1972).

    Article  CAS  Google Scholar 

  41. M. Afzal and A. A. Frost, A floating spherical Gaussian orbital model of molecular structure. XII. Analysis of energy terms affecting the geometry of the water molecule, Mt. J. Quantum Chem. VII, 51 (1973).

    Article  Google Scholar 

  42. J. L. Nelson and A. A. Frost, Local orbitals for bonding in ethane, Theor. Chim. Acta29, 75 (1973).

    Article  CAS  Google Scholar 

  43. J. L. Nelson, C. C. Cobb, and A. A. Frost, FSGO investigation of several conformers of cyclopentane, J. Chem. Phys.60, 712 (1974).

    Article  CAS  Google Scholar 

  44. J. Bicerano and A. A. Frost, FSGO calculations of octahydrotriborate anion and tetraborane, Theor. Chim. Acta35, 71 (1974).

    Article  Google Scholar 

  45. L. Vescelius and A. A. Frost, Ellipsoidal Gaussian molecular calculations, J. Chem. Phys.61, 2983 (1974).

    Article  CAS  Google Scholar 

  46. L. Shipman and R. E. Christoffersen, High speed evaluation of F o (x), Comput. Phys. Commun. 2, 201 (1971).

    Article  CAS  Google Scholar 

  47. D. B. Neumann, H. Basch, R. L. Kornegay, L. C. Snyder, J. W. Moskowitz, C. Hornback, and S. P. Liebmann, Polyatom (Version 2) System of Programs for Quantitative Theoretical Chemistry, Program 199, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Indiana, 1972.

    Google Scholar 

  48. M. A. Robb and I. G. Csizmadia, The generalized separated electron pair model. III. An application to three localization schemes for CO, Int. J. Quantum Chem.6, 367 (1972).

    Article  CAS  Google Scholar 

  49. M. A. Robb, W. J. Haines, and I. G. Csizmadia, A theoretical definition of the “size” of electron pairs and its stereochemical implications, J. Am. Chem. Soc.95, 42 (1973).

    Article  CAS  Google Scholar 

  50. P. E. Cade and W. M. Huo, Electronic structure of diatomic molecules. VI. A. Hartree-Fock wavefunctions and energy quantities for the ground states of the first-row hydrides, AH, J.Chem. Phys. 47, 614 (1967).

    Article  CAS  Google Scholar 

  51. M. Jungen, Das “floating Gaussian orbital”-Modell als Hilfsmittel zur interpretation von Photoelektronen-Spektren, Theor. Chim. Acta22, 255 (1971).

    Article  CAS  Google Scholar 

  52. P. H. Blustin and J. W. Linnett, Applications of a simple molecular wavefunction. Part 1. Floating spherical Gaussian orbital calculations for propylene and propane, J. Chem. Soc., Faraday Trans. 2, 70, 274 (1974).

    Article  CAS  Google Scholar 

  53. G. G. Hall, Point charge models for molecular properties, Chem. Phys. Lett. 20, 501 (1973).

    Article  CAS  Google Scholar 

  54. A. D. Tait and G. G. Hall, Point charge models for LiH, CH4 and H2O, Theor. Chim. Acta 31, 311 (1973).

    Article  CAS  Google Scholar 

  55. L. L. Shipman, Derivation of a total charge and dipole moment-preserving population analysis for FSGO wavefunctions, Chem. Phys. Lett.31, 361 (1975).

    Article  CAS  Google Scholar 

  56. T. D. Davis and A. A. Frost, FSGO investigation of several conformers of cyclohexane, J. Am. Chem. Soc.97, 7410 (1975).

    Article  CAS  Google Scholar 

  57. P. H. Blustin and J. W. Linnett, Applications of a simple molecular wavefunction. Part 2. Torsional barrier in ethane, J. Chem. Soc., Faraday Trans. 2 70, 290 (1974).

    Article  CAS  Google Scholar 

  58. J. R. Easterfield and J. W. Linnett, Applications of a simple molecular wavefunction, Part 4. The force fields of BH4 -, CH4 and NH4 +, J. Chem. Soc., Faraday Trans. 2 70, 317 (1974).

    Article  CAS  Google Scholar 

  59. S. L. Schulman, Ab initio Calculation of Spectroscopic Constants Using the FSGO Model, Ph.D. dissertation, Northwestern University, Evanston, Illinois (1973).

    Google Scholar 

  60. J. Easterfield and J. W. Linnett, The ions FL; and the possibility of LiHn + and BeHn +, Chem. Commun. 1970, 64.

    Google Scholar 

  61. J. Easterfield and J. W. Linnett, Theoretical calculations on the ion cluster Li(H2)n + and BeH(H2)n +, Nature 226, 141 (1970).

    Article  Google Scholar 

  62. W. D. Erickson and J. W. Linnett, Gaussian orbital calculations of solids. Crystalline lithium hydride, J. Chem. Soc., Faraday Trans. 2 68, 693 (1972).

    Article  Google Scholar 

  63. W. D. Erickson and J. W. Linnett, An ab initio Gaussian orbital calculation of the (100) surface of crystalline lithium hydride, Proc. R. Soc. London, Ser. A331, 347 (1972).

    Article  CAS  Google Scholar 

  64. P. H. Blustin and J. W. Linnett, Applicatons of a simple molecular wavefunction. Part 3. Ethyl and propyl carbonium ions, J. Chem. Soc., Faraday Trans. 2 70, 297 (1974).

    Article  CAS  Google Scholar 

  65. R. A. Suthers and J. W. Linnett, On the localized nature of FSGO wavefunctions, Chem. Phys. Lett.25, 84 (1974).

    Article  CAS  Google Scholar 

  66. N. K. Ray, Floating spherical Gaussian orbital model calculation for LiH2 +, Li2H+ and Li3 +, J. Chem. Phys.52, 463 (1970).

    Article  CAS  Google Scholar 

  67. N. K. Ray, Theoretical study of the structure of protonated ethane (C2H7 +), Theoret. Chim. Acta23, 111 (1971).

    Article  CAS  Google Scholar 

  68. I. Tamássy-Lentei and J. Szaniszló, Calculation of the proton affinity of several small molecules by the FSGO method, Acta Phys. Acad. Sci. Hung.35, 201 (1974).

    Article  Google Scholar 

  69. I. Tamássy-Lentei and J. Szaniszló, Interaction of atoms and ions with two electrons, Acta Phys. Chim. Debrecina. 18, 61 (1972).

    Google Scholar 

  70. B. Tinland and C. Decoret, An ab initio study of the conformation of 1,4-dioxadience, J. Mol. Struct. 9,205 (1971).

    Article  CAS  Google Scholar 

  71. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory, McGraw-Hill Book Co., New York (1970), p. 58.

    Google Scholar 

  72. W. A. Lathan, W. J. Hehre, and J. A. Pople, Molecular orbital theory of the electronic structure of organic compounds. VI. Geometries and energies of small hydrocarbons, J. Am. Chem. Soc. 93,808 (1971).

    Article  Google Scholar 

  73. J. Katriel and G. Adam, Comparative study of ellipsoidal Gaussians: H2 and He2 ++ J. Chem. Phys. 53,302 (1970).

    Article  CAS  Google Scholar 

  74. G. Simons and A. K. Schwartz, Floating ellipsoidal Gaussian orbital computations on small molecules, J. Chem. Phys. 60,2272 (1974).

    Article  CAS  Google Scholar 

  75. P. T. van Duijnen and D. B. Cook, Ab initio calculations with small ellipsoidal gaussian basis sets. I and II, Mol. Phys. 21, 475 (1971)

    Article  Google Scholar 

  76. P. T. van Duijnen and D. B. Cook, Ab initio calculations with small ellipsoidal gaussian basis sets. I and II, Mol. Phys. 22, 637 (1971).

    Article  Google Scholar 

  77. S. Rothenberg and H. F. Schaefer III, Methane as a numerical experiment for polarization basis function selection, J. Chem. Phys. 54,2764 (1971).

    Article  CAS  Google Scholar 

  78. J. C. Barthelat and P. Durand, Orbitales moléculaires localisées: structure électronique de la molecule de methane, Theoret. Chim. Acta 27, 109 (1972).

    Article  CAS  Google Scholar 

  79. L. P. Tan and J. W. Linnett, The lone-pair orbital in NH3 and the calculation of the HNH angle, J. Chem. Soc. D. 1973, 736.

    Google Scholar 

  80. K. Muller, private communication, 1972.

    Google Scholar 

  81. H. Preuss, Das SCF-MO-P(LCGO)-Verfahren and seine Varianten, Int. J. Quantum Chem. II, 651 (1968).

    Article  Google Scholar 

  82. P. Schmittinger, Das Wassermolekül nach dem SCF-MO-P(LCGO)-Verfahren, Z. Natur­forsch. 26a,1411 (1971).

    Google Scholar 

  83. B. Ford, G. G. Hall, and J. C. Packer, Molecular modelling with spherical Gaussians, Int. J. Quantum Chem. IV, 533 (1970).

    Article  Google Scholar 

  84. M. Tropis and P. Durand, Description des orbitales Π- et IT de la molecule d’ethylene par une base réduite de fonctions Gaussionnes sphériques, C. R. Acad. Sci. Paris C276, 1775 (1973).

    Google Scholar 

  85. R. M. Archibald, D. R. Armstrong, and P. G. Perkins, Molecular calculations using spherical Gaussian orbitals. Part 1.—Optimisation of the atomic parameters for first-row atoms, J. Chem. Soc., Faraday Trans. 2 70, 1557 (1974).

    Article  CAS  Google Scholar 

  86. P. H. Blustin and J. W. Linnett, Applications of a simple molecular wavefunction. Part 5 —Floating spherical Gaussian orbital open-shell calculations: Introduction, J. Chem. Soc., Faraday Trans. 2 70, 327 (1974).

    Article  CAS  Google Scholar 

  87. R. E. Christoffersen, D. W. Genson, and G. M. Maggiora, Ab initio calculations on large molecules using molecular fragments. Hydrocarbon characterizations, J. Chem. Phys. 54, 239 (1971).

    Article  CAS  Google Scholar 

  88. R. E. Christoffersen, Ab initio calculations on large molecules, Adv. Quantum Chem. 6, 333 (1972).

    Article  CAS  Google Scholar 

  89. L. L. Shipman and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Model peptide studies. Polypeptides of glycine, J. Am. Chem. Soc. 95, 1408, 4733 (1973).

    Article  CAS  Google Scholar 

  90. T. D. Davis, G. M. Maggiora, and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Unrestricted Hartree–Fock calculations on the low- lying states of formaldehyde and its radical ions, J. Am. Chem. Soc. 96, 7878 (1974).

    Article  CAS  Google Scholar 

  91. G. Nicolas and P. Durand, Orbitales moléculaires localisées ou fonctions de Loge et approxi­mation de Mulliken, C. R. Acad. Sci. Paris C272, 1482 (1971).

    Google Scholar 

  92. J. C. Barthelet and P. Durand, Pseudopotentials and localized molecular orbitals. Application to the methane molecule, Chem. Phys. Lett. 16, 63 (1972).

    Article  Google Scholar 

  93. A. T. Amos and J. A. Yaffe, The Frost model and perturbation theory, Chem. Phys. Lett. 31, 57 (1975).

    Article  CAS  Google Scholar 

  94. E. R. Talaty, A. K. Schwartz, and G. Simons, Simple ab initio studies of the isomers of N2H2, Li2O, C3H4 and O3, J. Am. Chem. Soc. 97, 972 (1975).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer Science+Business Media New York

About this chapter

Cite this chapter

Frost, A.A. (1977). The Floating Spherical Gaussian Orbital Method. In: Schaefer, H.F. (eds) Methods of Electronic Structure Theory. Modern Theoretical Chemistry, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0887-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-0887-5_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0889-9

  • Online ISBN: 978-1-4757-0887-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics