## 3 Solving the METDSE Nonperturbatively via the State-Specific Expansion Approach
### The Meaning of the Term \"Electron Correlations\"  
As the title of our paper [14] shows, the concept of _electron correlation_ was at the core of our initial considerations and proposals aiming to connect the prospects of observable effects of electron dynamics to spectroscopy with attosecond resolution. At that time (2001), published statements regarding the possible connection of attosecond pulses to electron dynamics had not yet identified specific concepts and effects whose interrogation would require attosecond resolution. The general argument regarding the relevance of attosecond pulses simply invoked the classical picture of a 1 s Bohr electron of hydrogen going around a circle with a period of about 150 as. In order to explore the prospects of practical spectroscopic use of attosecond pulses for issues of time-resolved effects of electron dynamics on spectra, we identified as suitable candidates the doubly excited states (DESs) in the continuous spectrum of helium [1; 2; 3; 14; 15]. Helium is attractive to both theoreticians and experimentalists for practical reasons. By now, there are a number of publications in the area of attophysics with results on time-resolved spectra involving DESs of helium. In recent years, in the growing literature on themes of the nascent field of attosecond physics [29], the term _electron correlation_ is often used to describe a feature that is inextricably linked to electron dynamics studied with high temporal resolution. In order to avoid misunderstanding as to the meaning of this term, which is used in our work, I comment as follows:  
The term is not the same as \"_electron interactions_\", whose meaning is related to the obvious fact that there are two-electron operators of the atomic (molecular) Hamiltonian, nonrelativistic or relativistic. In other words, if, say, a calculation is carried out in the absence of the Coulomb operator \(1/r_{12}\), the result represents an artificial situation. In our theoretical and computational work on the electronic structure and properties of atoms and molecules, electron correlation is defined and computed in terms of wave functions, as outlined below. The term _electron correlation_ was coined by [PERSON] in his theory of the electron gas for metals in 1934 [30]. It was later picked up and first used in the literature of quantum chemistry in 1952 by [PERSON] and [PERSON] [31], in their configuration-interaction study of the \(1s^{2}\)\({}^{1}S\) state of helium. They defined it as the part of the exact solution of Equation (2) that remains after calculating the single-configuration HF wave function and energy. The same definition was later emphasized by [PERSON] [32] in his review article on electron correlation, which dealt with solving the eigenvalue of Equation (2) for ground states. The above definition is translated to the following standard equations of quantum chemistry:  
\[\Psi=\Phi^{HF}+\mathsf{X}^{corr},E=E^{HF}+E^{corr} \tag{4}\]where \(\Psi\) and \(E\) satisfy Equation (2). Equations (4) are valid for those states for which the HF equations are solvable. Furthermore, they are useful for those states for which the HF wave function is overwhelmingly dominant in the zero-order description of the exact eigenfunction. This normally occurs in many ground states of atoms and many closed-shell molecules in equilibrium. Therefore, in all those cases, and especially for ground states, the MEP becomes equivalent to the _electron correlation problem_ defined by Equation (4). When it comes to complicated cases of electronic structures with open subshells or of excited states, including resonance (autoionizing) states, where the mixing coefficients of a couple of configurations are large, the description of electron correlation in terms of Equation (4) has to be modified.