Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster–configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions—from which the EOM-CC expressions are derived—are determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.

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M0m2=limωXj2ωmωXj2ωmXj1;Xj2ωXj2=12S0mXj1Xj2+S0mXj2Xj1*,
where ωm = (EmE0) is an excitation energy corresponding to an excited state Cm and
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The CC-CI transition moments read
T0mXj1=νn[(μkt¯μk(0)sμkXj1(ωm))HF|H0T0|νn+(μkHF|H0T0|μksμkXj1(ωm))t¯νn(0)+HF|Xj1T0|νn+μkt¯μk(0)μk|[Xj1T0,|νnHF|]|HF]Cνnm,
Tm0Xj2=νnC¯mνnνn|Xj2T0|HF.
EOM-CC transition strengths are obtained by taking the CI transition strength expressions (in the diagonal representation) and replacing the eigenstates of the CI eigenvalue equation with the eigenstates of the EOM-CC eigenvalue equation,
M0m2=00CC|Xj1|0mCC0mCC|Xj2|00CC,
and the EOM-CC transition moments consequently read
T0mXj1=00CC|Xj1|0mCC=νn[(μkt¯μk(0)μk|Xj1T0|HF)t¯νn(0)+HF|Xj1T0|νn+μkt¯μk(0)μk|[Xj1T0,|νnHF|]|HF]Cνnm,
Tm0Xj2=0mCC|Xj2|00CC=νnC¯mνnνn|Xj2T0|HF.
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