Quantum-information analysis of electronic states of different molecular structures

Abstract

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between entanglement and interaction localization. We also discuss the application of the configuration interaction based dynamically extended active space procedure which significantly reduces the effective system size and accelerates the speed of convergence for complicated molecular electronic structures to a great extent. Our results indicate the importance of taking entanglement among molecular orbitals into account in order to devise an optimal orbital ordering and carry out efficient calculations on transition metal clusters. We propose a recipe to perform DMRG calculations in a black-box fashion and we point out the connections of our work to other tensor network state approaches.

The ab-initio density matrix renormalization group in practice

“…[71][72][73] Graph techniques had earlier been examined in the DMRG ordering problem, 5 but a detailed study of the Fiedler vector was first presented by Barcza et al in Ref. 25. The derived ordering can be obtained as follows.…”

“…Since then, many groups have independently implemented and improved on the ab-initio DMRG algorithm. Some of these improvements include parallelization, 8,20 nonAbelian symmetry and spin-adaptation, 7,[21][22][23] orbital ordering 5,[24][25][26] and optimization, 9,27-29 more sophisticated initial guesses, 5,24,25,30,31 better noise algorithms, 5,32 extrapolation procedures, 5,33,34 response theories, 35,36 as well as the combination of the DMRG with various other quantum chemistry methods such as perturbation theory, 37 canonical transformations, 38 configuration interaction, 39 and relativistic Hamiltonians. 40 In the ecosystem of quantum chemistry, the DMRG occupies a unique spot.…”

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

“…Furthermore, for bent PuO 2+ 2 , 12 occupied orbitals (5 in A 1 , 2 in B 1 , 4 in B 2 and 1 in A 2 ) and 8 additional virtual orbitals (3 in A 1 , 2 in B 1 , 2 in B 2 , and 1 in A 2 ) were added to the CASSCF active space, resulting in DMRG (26,26). For PuO 3 , we included 16 occupied orbitals (7 in A 1 , 3 in B 1 , 5 in B 2 and 1 in A 2 ) and 6 virtual orbitals (3 in A 1 , 2 in B 1 and 1 in B 2 ) with respect to CASSCF, increasing it to DMRG (34,26). The CASSCF active space of PuO 2 (OH) 2 was extended by 20 occupied orbitals (10 in A and 10 in B) and 11 virtual orbitals (6 in A and 5 in B), yielding DMRG (42,35).…”

“…[34] The initial guess was generated using the dynamically extended-active-space procedure (DEAS). [32] For block states m > 512, we used the dynamic block state selection (DBSS) approach [76,77] and set the quantum information loss χ = 10 −5 and the minimum number of block states m min = 512, while the maximum number was set to m max = {1024, 2048}.…”

“…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.…”