1. Could you explain the significance of your article to the non-specialist?

Recently the time-dependent density matrix functional theory (TD-DMFT) has been formulated that enables one to obtain frequency-dependent response properties and excitation energies of atoms and molecules from energy functionals of one-electron reduced density matrix (one-matrix). The success of TD-DMFT hinges on both the quality of the functional and adiabatic approximations made to TD-DMFT equations. The importance of these two factors has been investigated in the paper. It has been revealed that the adiabatic approximations that reproduce the response properties at the low-frequency limit are superior to those with the incorrect zero-frequency limit. Additionally, a practical algorithm for obtaining excitation energies, which can be applied for any one-matrix functional has been presented and discussed.

2. What has motivated you to conduct this work?

Approximations to TDDMFT have been only recently proposed and they have not been numerically investigated. On the other hand, practical computational scheme for obtaining excitation energies from these approximations has been missing. Until now approximate density matrix functionals have not been employed for computation of the dynamic response properties or excitation energies.

3. Where do you see this work developing in the future?

The methods presented in the paper can be applied for other density matrix functionals to test their quality. Moreover, the presented results may incite a development of the corrected coupling matrix entering TD-DMFT equations (in analogy to the exchange-correlation kernels in time-dependent density functional theory) that, in conjunction with the existing energy functionals, would provide accurate excitation energies.

4. Are there any particular challenges facing future research in this area?

At the moment the main challenge in time-dependent density matrix functional theory lies in the development of an exchange-correlation functional that would not break the spatial symmetry of the one-electron density matrix and improve the description of the excitation energies.