Tensor product methods and entanglement optimization for ab initio quantum chemistry

Abstract

The treatment of high-dimensional problems such as the Schr€ odinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods-developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools-can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic "New wavefunction methods and entanglement optimizations in quantum

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.…”

“…Furthermore, when combined with concepts of quantum information theory, DMRG allows us to quantify orbital entanglement [32] and orbital-pair correlations [30,[33][34][35][36][37][38][39] that enable us to gain a better understanding of electron correlation effects, [36,40,41] elucidate chemical bonding in molecules, [37,[42][43][44][45][46][47] and detect changes in the electronic wave function. [48][49][50] The suitability of DMRG for helping to understand the electronic structure of actinides can be seen in a recent study of the changes in the ground-state for the CUO molecule when diluted in different noble gas matrices.…”

Density matrix renormalization group with efficient dynamical electron correlation through range separation

“…To exploit this advantage, an increasing number of quantum-chemistry DMRG implementations have emerged since the late 1990s . Methods, with (DMRG-SCF) and without (DMRG-CI) a simultaneous optimization of the orbital basis, were devised and a few comprehensive reviews are a) Electronic mail: erik.hedegard@phys.chem.ethz.ch b) Electronic mail: hjj@sdu.dk c) Electronic mail: markus.reiher@phys.chem.ethz.ch also available [28][29][30][31][32][33][34][35] . Yet, even with larger active orbital spaces at hand, essential parts of the remaining dynamical electron correlation cannot be efficiently accounted for within a DMRG framework.…”

Polarizable Embedding Density Matrix Renormalization Group

“…[18,19] In state-specific excited state optimizations, the treatment of static correlation effects is of high importance as excited states typically display large static correlation effects. One of the most capable methods to recover static correlation is the density matrix renormalization group (DMRG) algorithm [46][47][48][49][50][51][52][53][54][55][56][57]. Our group recently reported the implementation of an efficient second-generation DMRG program [58][59][60][61][62] which relies entirely on matrix product operators.…”