A perturbation approach is used to analyze the natural transition orbital method proposed by Smith and Day for computing ionization potentials. The results are carried to third order in the electronic interaction and a comparison is made with the diagrammatic method of Cederbaum. Two of the thirdhyphen;order terms included in the natural transition orbital method which contribute to the rsquo;rsquo;particle partrsquo;rsquo; of the selfhyphen;energy are found to differ from Cederbaumrsquo;s diagrammatic terms by multiplicative factors.
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