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19
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85038198816
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Let us mention here that these rules are based on the definitions (16) and (17), which differ by a normalization factor from those used in Part I. Indeed, while [formula omitted], where [formula omitted], holds (see Part I for definitions of [formula omitted] and U), we have [formula omitted], where [formula omitted]. Consequently, the final expressions for the matrix elements of the A and B matrices differ by a factor of 2. Since we investigate positive definiteness of the respective quadratic form, the normalization used has no importance whatsoever.
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In fact, should we wish to use the same normalization as in Part I, we would have only to change the rule (a), replacing factor [formula omitted] by a factor [formula omitted] Since, in the open-shell case, it is advantageous to refrain from normalizing the individual components of the complete variational function, we do not normalize them even in the closed-shell case in order to stress this fact.
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21
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85038204938
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The other doublet linear combination interacts with the ground state while, of course, the third one, which is a pure quartet, does not interact with ground-state function.
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22
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84951143397
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It would seem on first sight that the terms [formula omitted] in [formula omitted] could be disregarded since these terms give zeros in the product with [formula omitted]
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However, the product of these terms with [formula omitted] yields biexcited (pseudomonoexcited) states, which must be properly taken into account.
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23
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85038200776
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We skeletons (diagrams) are drawn with a rectangular-shaped end vertex in order to distinguish them on the first sight from T skeletons.
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This is not very essential in this simple case, when we have only one particle in the open shell, but for the sake of consistency with more general cases, we use this convention even here.]
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24
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85038203085
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Due to typesetting difficulties, special brackets, rather than a horizontal bar above the term, are used to designate complex conjugate quantities in Eqs. (77a) and (77b).
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26
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85038193770
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If more than one negative root is obtained from the stability eigenvalue problem, this means, in general, that for each one we can find another new HF solution.
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12
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