The multiconfiguration time-dependent Hartree method generalized to the propagation of density operators

The multiconfiguration time-dependent Hartree (MCTDH) method is formulated for density operators and applied to their numerical propagation. We introd uce two types of MCTDH density operators which are expanded in different ki nds of so-called single-particle density operators. The latter may either b e hermitian, or else represent ket-bra products of so-called single-particl e functions. For both types of MCTDH expansions of density operators we der ive equations of motion employing the Dirac-Frenkel/MacLachlan variational principle. Further an alternative set of equations of motion for the second type of density operators is proposed, which is not based on a variational principle but derived by taking partial traces. We thus obtain three sensi ble approaches within the framework of the MCTDH method which differ in the ir performance and properties. We investigate these approaches and their pr operties analytically and numerically. Our numerical results refer to a mod el of vibronic-coupling dynamics in the pyrazine molecule representing coup led electronic states with four vibrational modes and two and three electro nic states respectively. We analyze the closed-system dynamics for this mod el with temperature-dependent initial states. The influence of temperature on state populations, on correlation functions and on absorption spectra is discussed. We assess the numerical performance of two of the three approac hes and find that both can be very efficiently applied to investigate the t ype of systems studied here. (C) 1999 American Institute of Physics. [S0021 -9606(99)30343-3].