The density matrix renormalization group for ab initio quantum chemistry

Abstract

Abstract. During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational cost are given special attention: the orbital choice and ordering, and the exploitation of the symmetry group of the Hamiltonian. With these considerations, the QC-DMRG algorithm allows to find numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals. PACS

Second-Order Self-Consistent-Field Density-Matrix Renormalization Group

“…Suffering from an exponential growth 7 of the FCI expansion with respect to increasing values of N and L, active orbital spaces beyond CAS (18,18) are out of reach for CASSCF based on traditional configuration interaction (CI) expansions.…”

On the multi-reference nature of plutonium oxides: PuO22+, PuO2, PuO3 and PuO2(OH)2

“…[9,[13][14][15][16][17][18][19] However, albeit DFT is in principle capable of treating open-shell molecules with multi-reference character, [20] it is known that the currently available density functional approximations often perform poorly in such cases. [12,21] It is therefore preferable to employ from the outset multireference approaches such as the Complete-Active-Space Self-Consistent-Field (CASSCF) method and the Density Matrix Renormalization Group (DMRG) algorithm [22][23][24][25][26][27][28][29][30][31] in order to obtain a qualitatively correct zeroth-order wave function for these systems.…”

A transformed framework for dynamic correlation in multireference problems

“…It is now possible to describe the correlation in the active orbitals for active spaces with up to 50 orbitals, to produce a multireference active space wavefunction |Ψ 0 ⟩ that is formally the sum of many determinants. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] In these cases, the remaining challenge is to efficiently describe the correlation outside of the active space, involving the external orbitals. We refer to this as the dynamic correlation problem in a multireference setting.…”