Abstract
Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρ(N)(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT virtually unavoidable, adiabatic approximation, the second problem is the reliable evaluation of the probabilities P(n)(t) of multiple photoinduced ionization, while the third problem (which TDDFT shares with other approaches) is the reliable description of continuum states of the electrons ejected in the process of ionization. In this paper time-dependent Dyson orbital theory (TDDOT) is proposed. Exact TDDOT equations of motion (EOMs) for time-dependent Dyson orbitals are derived, which are linear differential equations with just static, feasible potentials of the electron-electron interaction. No adiabatic approximation is used, which formally resolves the first TDDFT problem. TDDOT offers formally exact expressions for the complete evolution in time of the wavefunction of the outgoing electron. This leads to the correlated probability of single ionization P(1)(t) as well as the probabilities of no ionization (P(0)(t)) and multiple ionization of n electrons, P(n)(t), which formally solves the second problem of TDDFT. For two-electron systems a proper description of the required continuum states appears to be rather straightforward, and both P(1)(t) and P(2)(t) can be calculated. Because of the exact formulation, TDDOT is expected to reproduce a notorious memory effect, the "knee structure" of the non-sequential double ionization of the He atom.
Highlights
Real-time propagation of the electron density rN(x1,t) provides valuable information about dynamics of N-electron systems in strong rapidly changing electric fields
When t - N the propagation of the wavefunction in time will lead to a superposition of ion states times the oneelectron state describing the emitted electron, which is by definition the time-dependent Dyson orbital (DO) dk(x1,t)
The time-dependent DOs are defined by projection of the generic time-dependent wavefunction CN(t) onto the the stationary cation states C(jNÀ1)
Summary
Real-time propagation of the electron density rN(x1,t) provides valuable information about dynamics of N-electron systems in strong rapidly changing electric fields. This can seriously affect the quality of simulated electronic dynamics.[3,18,20,21] The paradigmatic memory effect is the famous ‘‘helium knee’’ indicating an enhancement of the non-sequential double ionization of the He atom by several orders of magnitude over what sequential ionization models would predict.[3,4] A second problem TDDFT is facing here is the reliable evaluation of the correlated timedependent probabilities Pn(t) of multiple ionizations, which in the case of He reduces to estimation of the probabilities P1(t) and P2(t) of single and double ionization, respectively. The time-dependent Dyson orbital theory (TDDOT) formally resolves the memory and multiple ionization problems (first and second of the above mentioned TDDFT problems) in the general N-electron case. TDDOT is expected to successfully reproduce the ‘‘helium knee’’ in the experimental ion yield curves.[46]
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