The Application of Wave Functions Containing Interelectron Coordinates I the G

Peter Walsh

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^ v. (0. )g I = dQ.
^" "of«j'«o w is the appropriate weighting function for the angle which appears in the volume element.
The system of Equations (^. 5) must be solved simultaneously, and in practice an iteration procedure is used to solve them. Since the inter- electron coordinates which enter into g do not depend strongly upon the angles, the iteration of Equations (^. 5) converges quite rapidly if a reasonable guess is originally made for the angles.
Writing r. . As the value of r. . At r. ..., 0. , a. We now have for I ijo ij 10 10 10 {k. 6) I^(Z) = g(r^20' ""150' ••■ ' Vl^no^ J ^^^'^1' ^2^ •*• ' ""-^ ^^ n Note the dependence of I upon Z in Equations (^. L) and (4. 6). With large Z the exponential variation of f is so strong that only those regions near the nucleus contribute to I. As long as g is monotonic this means that Equation (4. 1) reduces to (^. 7) 1(00) = g(o, o, o) I .. I f dV .
- 19 This is exactly the form vhich Equation (^. 6) assumes at large Z and that expression is thus exact at Z equal to infinity.

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