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I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations


Winter, Nicholas Wilhelm (1970) I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DCXZ-TX32.


Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)1S, (1s2s)3S, and (1s2s)1S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z2 +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z2)a.u.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Chemistry
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemistry
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McKoy, Basil Vincent (advisor)
  • Goddard, William A., III (co-advisor)
  • Pitzer, Robert M. (co-advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:10 November 1969
Record Number:CaltechTHESIS:09112015-100730009
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9150
Deposited By: Benjamin Perez
Deposited On:11 Sep 2015 19:26
Last Modified:09 Nov 2022 19:20

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