Dynamical Density-Matrix Renormalization Group

Eric Jeckelmann, H. Benthien

Satoshi Nishimoto, Florian Gebhard, Eric Jeckelmann

Enrico Ronca, Zhendong Li, Carlos A. Jiménez-Hoyos +1 more

We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context to compute dynamical correlation functions of correlated systems. We analyze the strengths and weaknesses of the two methods in small model problems and propose two simple improved formulations, DDMRG ++ and td-DMRG ++, that give increased accuracy at the same bond dimension at a nominal increase in cost. We apply DDMRG ++ to obtain the oxygen core-excitation energy in the water molecule in a quadruple-zeta quality basis, which allows us to estimate the remaining correlation error in existing coupled cluster results. Further, we use DDMRG ++ to compute the local density of states and gaps and td-DMRG ++ to compute the complex polarization function, in linear hydrogen chains with up to 50 H atoms, to study metallicity and delocalization as a function of bond length.

Haibo Ma, Ulrich Schollwöck, Zhigang Shuai

Imam S. Wahyutama, Henrik R. Larsson

Compared to ground-state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground-state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of matrix-product-state representation for complex-valued nonsinglet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a σ character to one with a π character within less than a femtosecond.

R. M. Noack, Steven R. White