Integrals occurring in problems of molecular structure
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References
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J. Slater, “Atomic shielding constants,” Phys. Rev., v. 36, 1930, p. 57-64.
- Klaus Rüdenberg, A study of two-center integrals useful in calculations on molecular structure. II. The two-center exchange integrals, J. Chem. Phys. 19 (1951), 1459–1477. MR 47211, DOI 10.1063/1.1748101 Y. Sugiura, “Über die Eigenschaften des Wasserstoff Moleküls in Grundzustande,” Zeit. Phys., v. 45, 1927, p. 484-492. C. Zener & V. Guillemin, “The $B$-state of the hydrogen molecule,” Phys. Rev., v. 34, 1929, p. 999-1009. J. H. Bartlett, “Orbital valency,” Phys. Rev., v. 37, 1931, p. 507-531. N. Rosen, “Calculation of interactions between atoms with $s$-electrons,” Phys. Rev., v. 38, 1931, p. 255-276; “The normal state of the hydrogen molecule,” Phys. Rev., v. 38, 1931, p. 2099-2114. H. M. James, “Wave-mechanical treatment of the ${\operatorname {Li} _2}$ molecule,” Jn. Chem. Phys., v. 2, 1934, p. 794-810.
- M. P. Barnett and C. A. Coulson, The evaluation of integrals occurring in the theory of molecular structure. Parts I & II, Philos. Trans. Roy. Soc. London Ser. A 243 (1951), 221–249. MR 40489, DOI 10.1098/rsta.1951.0003 A. S. Coolidge, “A quantum mechanics treatment of the water molecule,” Phys. Rev., v. 42, 1932, p. 189-209. E. W. Hobson, Spherical and Ellipsoidal Harmonics. Cambridge University Press, London, 1931.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746 (a) A. L. Sklar, “The near ultraviolet absorption of substituted benzenes,” Jn. Chem. Phys., v. 7, 1939, p. 984-993. (b) M. Goeppert Mayer & K. J. McCallum, “Calculation of the absorption spectrum of Wurster’s salts,” Rev. Mod. Phys., v. 14, 1942, p. 248-258. (c) R. S. Mulliken, “Quelques aspects de la théorie des orbitals moléculaires,” Journ. Chim. Phys., v. 46, 1949, p. 497-542, 675-713. (d) J. F. Mulligan, “LCAO self-consistent field calculation of the ground state of carbon dioxide,” Jn. Chem. Phys., v. 19, 1951, p. 347-362. (e) S. L. Altmann, “$\pi - \sigma$ electronic states in molecules I. The Hückel approximation,” Roy. Soc. London, Proc., v. 210A, 1952, p. 327-343. (f) E. Scrocco & O. Salvetti, “Studio dell’ integrale di scambio e di ricerca di formule approximate per alcuni integrali che si incontrano nei problemi di struttura molecolare,” La Ricerca Scientifica, v. 23, 1953, p. 98-107. (g) C. R. Mueller & H. Eyring, “The overlap average and central field approximations,” Jn. Chem. Phys., v. 19, 1951, p. 934-938. (h) H. Preuss, “Abschätzung für Zweizentren-integrale,” Zeit. f. Naturforschung, v. 8a, 1953, p. 270-272. (i) C. R. Mueller, “Semilocalised orbitals IV. Relationship of $n$-center orbitals, two-center orbitals, and bond properties,” Jn. Chem. Phys., v. 20, p. 1600-1604.
- R. O. Brennan and J. F. Mulligan, Two-center hetero-nuclear hybrid Coulomb-exchange integrals, J. Chem. Phys. 20 (1952), 1635–1644. MR 52592, DOI 10.1063/1.1700230
- A. Fletcher, J. C. P. Miller, and L. Rosenhead, An Index of Mathematical Tables, McGraw-Hill Book Co., New York; Scientific Computing Service Ltd., London, 1946. MR 0018419, DOI 10.1090/s0025-5718-45-99069-7 J. F. Mulligan—reference (12d).
- C. C. J. Roothaan, A study of two-center integrals useful in calculations on molecular structure. I, J. Chem. Phys. 19 (1951), 1445–1458. MR 47210, DOI 10.1063/1.1748100 K. Rüdenberg—reference (2). Quantum-mechanical methods in valence theory, Sept. 1951, Nat. Acad. Sci. and Office of Naval Research, New York.
Additional Information
- © Copyright 1954 American Mathematical Society
- Journal: Math. Comp. 8 (1954), 203-212
- MSC: Primary 65.0X
- DOI: https://doi.org/10.1090/S0025-5718-1954-0064473-9
- MathSciNet review: 0064473