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note
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The rank of a linear operator A acting in a carrier space S equals to the dimensionality of the image space span{Ax}, x ε S. Note that the following alternative representation of the excitation operator from Eq. (3): R′ (f)≡|f〉〈0|+A(1̂-|0〉〈0|), where A is any operator, does not ensure the unit rank of the operator R(f)|g〈 = |f〉〈0|g〈 = 0, R′(f)〈〉g〉 = |f〈〉0|g〉 + A(1̂|g〉 - |0〉〈0〈|g〉)=A|g) for any state g〉 |0〉. Note that the operators R(f) and R′(f) act differently on |0̃〈, and that R′(f) does not satisfy Eqs. (5) and (6).
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22
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0942266434
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ff′|0〉〈0|.
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note
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+ are ionizing or electron attaching.
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31
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0942288125
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note
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6 for the CISD and the CCSD models). Practically, however, the truncated EOM-CC model is superior to the CI truncated at the same level because effects of higher excitations are "folded in" through the similarity transformation (21) into the effective Hamiltonian H̄. The role of the similarity transformation is to achieve more compact representation of vectors R̃,L̃. For example, if T is not truncated and is a solution of CC equations in a full multielectron space, the reference determinant |0̃〉 is an eigenstate of H̄ with the exact eigenvalue.
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s = 1/2 determinants. This procedure yields doublets and low-spin components of quartet states.
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This feature is not present in most of the available EOM-CCSD implementations. We have found this type of calculation to be very helpful in testing the correctness of our implementation of the EOM-SF methods.
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