Introduction to the density matrix renormalization group ansatz in quantum chemistry - Chan, Garnet Kin-Lic; Dorando, Jonathan J.; Ghosh, Debashree; Hachmann, Johannes; Neuscamman, Eric; Wang, Haitao; Yanai, Takeshi (Frontiers in Quantum Systems in Chemistry and Physics, 2008)
The Density Matrix Renormalisation Group (DMRG) is an electronic structure method that has recently been applied to ab-initio quantum chemistry. Even at this early stage, it has enabled the solution of many problems that would previously have been intractable with any other method, in particular, multireference problems with very large active spaces. Historically, the DMRG was not originally formulated from a wavefunction perspective, but rather in a Renormalisation Group (RG) language. However, it is now realised that a wavefunction view of the DMRG provides a more convenient, and in some cases more powerful, paradigm. Here we provide an expository introduction to the DMRG ansatz in the context of quantum chemistry.

Orbital optimization in the density matrix renormalization group, with applications to polyenes and ss-carotene - Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi; Chan, Garnet Kin-Lic (Journal of Chemical Physics, 2008)

Accelerating convergence in iterative solution for large-scale complete active space self-consistent-field calculations - Yanai, Takeshi; Kurashige, Yuki; Ghosh, Debashree; Chan, Garnet Kin-Lic (International Journal of Quantum Chemistry, 2009)
An algorithm that accelerates the convergence of the iterative optimization of the complete active space self-consistent field (CASSCF) wavefunction so as to find a optimum solution in fewer macroiterations is described. The algorithm is oriented to large-scale CASSCF problems that are to be solved with a combination of density matrix renormalization group (DMRG) method for the configuration interaction (CI) process. The algorithm is based on the alternating (or two-step) CASSCF optimization in which the CI and molecular orbital (MO) parameters are optimized separately. Convergence ratio is improved by finding further optimized MOs from a linear extrapolation of the MO sets of the iteration history. The acceleration results in fewer diagonalizations in a total CASSCF calculation to save a considerable computational cost. The convergence performance is examined in a couple of realistic applications on SiC(3) and poly (phenyl)carbenes. For poly(phenyl)carbenes, the large-size CASSCF calculations with CAS(30e,30o) that entails full pi valence space as well as sp(2) orbital space of carbenes are performed by using the practical implementation of DMRG-CASSCF in conjunction with the acceleration technique. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2178-2190, 2009

Study of cumulant approximations to n-electron valence multireference perturbation theory - Zgid, Dominika; Ghosh, Debashree; Neuscamman, Eric; Chan, Garnet Kin-Lic (Journal of Chemical Physics, 2009)
We investigate the possibility of reducing the complexity of multireference perturbation theory through cumulant based approximations to the high-order density matrices that appear in such theories. Our test cases show that while the cumulant approximated forms are degraded in accuracy relative to the parent theory and exhibit intruder state problems that must be carefully handled, they may provide a route to a simple estimation of dynamic correlation when the parent perturbation theory is infeasible. Nonetheless, further work is clearly needed on better approximations to the denominators in the perturbation theory.