University of Chicago Laboratory of Molecular Structure and Spectra Technical Report: 1952-1953, Part 2 Page: 192
xxiv, 359 p. : diagrams, graphs, ill. ; 28 cm.View a full description of this report.
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RUEDENBERG, ROOTHAAN, AND JAUNZEMIS
which follows immediately from the definition (3.1):
Pb-a-B-P'-y--2E-1C a,+y be bpb-a-P'y--2E-1 6E (4.13)
Pb P,B+B' =, . (.13)
Eq. (4.13) permits us to calculate C1000 by successive differentiations of C1,000
namely, putting a = -1, B' = y = 6 = e = 0,we obtain
pb C-,1,P000 = b -1,0000 . (4.14)
If we substitute in Eq. (4.14) for C-1,0000 the expression (4.9), we see that, because
of Eqs. (4.12;5.1) the result may be written in the form
Pb- C-1,000 = A (-pb)G + (-1) A(pb)F + Pb -1,000 (4.15)
where the functions D 000(pa,pb) do not contain any exponential integrals or loga-
rithms. Hence we have proved the validity of Eq. (4.6) for the functions C 000
-1,,
namely
C-1,000 (PaPb) = D-1,000 (Pa'Pb) + E-1, 000(PaPb)F(Pa,Pb)
+ E-1,p000 _pa'Pb)G(pa'Pb) ; (4.16)
the functions E-1 ,000 are actually only functions of pb, and are given by
E-1,000 (apb) = (-Pb) A(pb) . (4.17)
We observe that Eq. (4.9) implies that
000
D,0 = 0; (;(.18)
we shall now proceed to find a recurrence scheme for the functions D 00 We start
with the relation
b-P-2[C-1,+2000+(+2)C_1,+100] Pb [C-1, 000+ 1,~ 000
00+ 00 000 l-nO0D 000
Pb-B-2[D-1,0+20 (B+2)D-1,p+1000 Pb [D-1,00+-1,-100
+ [AP+2 Pb)+(+2)Pb- 1AB+1 (-Pb)-A (-Pb )-B Pb- AB- 1 (-Pb )]G
+ (-1) [AB+2 Pb)-(B+2)pb -1A+ )-A (pb )+Pb-Ab-1 pb)]F , (4.19)
which follows directly from Eq. (4.15) and holds for B > O. The linear combination
of the C-functions in (4.19) is chosen so that the coefficients of the functions F192
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University of Chicago. Laboratory of Molecular Structure and Spectra. University of Chicago Laboratory of Molecular Structure and Spectra Technical Report: 1952-1953, Part 2, report, 1953~; Chicago, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc228353/m1/84/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.