Institute of Physics, Technical University of Lodz, Lodz, Pologne

Lundi 3 Décembre 2012, 14

bibliothèque LCT, tour 12 - 13, 4e étage

There exists a plethora of quantum chemistry methods for computing excitation energies of molecules but none of them is fully satisfactory. It is either due to the unfavorable computational scaling or inability to provide reliable results for some excitations. For example, it is known that time-dependent density functional theory (TD-DFT) in the adiabatic approximation is rather accurate for low lying excitations but Rydberg states, charge transfer or double excitations usually pose a serious problem. Especially the excitations of a strong double character are either not predicted at all by TD-DFT or they are in large error.

The recently proposed time-dependent method based on one-electron density matrix functional (time-dependent density matrix functional theory TD-DMFT) [1,2] is, in principle, more suitable for predicting double excitations than TD-DFT but it has been shown for the hydrogen molecule that the adiabatic approximation to TD-DMFT introduces a large error to some double excitations [3,4].

The equation-of-motion method of Rowe [5] offers yet another way of obtaining excitation energies from the ground state reduced density matrices. Including only single excitations in the excitation operator and employing the Hartree-Fock vacuum lead to RPA equations (equivalent to time-dependent Hartree-Fock). Using a correlated vacuum state leads to a so-called Extended RPA (ERPA). We show that for a twoelectron system ERPA is equivalent to the adiabatic TD-DMFT equations. Contrary to what could be expected, ERPA is not exact for two-electron systems. It is due to a violation of the killer condition. Including some double excitations in the excitation operator fixes the problem. Guided by those findings we proposed a method named ERPA2 that includes some doubly exciting operators and employs reduced density matrices (first- and second-particle) obtained from a geminal theory. It will be shown that ERPA2 yields accurate excitations for small molecules. In particular, it is capable of reproducing double excitations (although with varying accuracy). It also performs well for potential energy curves of excited states. The computational cost of ERPA2 is only slightly higher than that of RPA [6].

[1] K. Pernal, O. Gritsenko, and E. J. Baerends, Phys. Rev. A 2007, 75, 012506.

[2] K. Pernal, K. J. H. Giesbertz, O. Gritsenko, and E. J. Baerends, J. Chem. Phys. 2007, 127, 214101.

[3] K. J. H. Giesbertz, E. J. Baerends, and O. V. Gritsenko, Phys. Rev. Lett. 2008, 101, 033004.

[4] K. J. H. Giesbertz, K. Pernal, O. Gritsenko, and E. J. Baerends, J. Chem. Phys. 2009, 130, 114104.

[5] D. J. Rowe, Rev. Mod. Phys. 1968, 40, 153.

[6] K. Chatterjee and K. Pernal, J. Chem. Phys. 2012, 137, XXXX.