Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states

Abstract

(2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster. © 2014 AIP Publishing LLC. [http://dx

Complete active space second-order perturbation theory with cumulant approximation for extended active-space wavefunction from density matrix renormalization group

“…· p q r s t u (12) · p q r s t u · For s = 1: (Using the site-2 lattice configuration) 20) p ≤ q r s t u (21) p q r s t u (22) · p q r s t u (23) p ≤ q · r s t u (24) p q r s t u (25) · p q r s t u (26) p · q r s t u (27) · q q r s t u (28) · · p q r s t u approach undergoes a moderate complexity computation. This k-dependence is still higher than that of the cost for determining the DMRG wavefunction, while the evaluation of 3-RDM does not become a bottleneck in practice.…”

“…Over the past decades, the applicability of quantum chemical DMRG has been studied for various molecular systems, ranging from basic molecules, such as water molecule, 3,6,7 to polymeric organic systems, such as polyenes, 10,11,14,23 acenes, 12,13 polycarbenes, 17,45 graphene nanoribbons, 47 etc. Inorganic chemical systems are also included in the application domain, such as chromium dimer, 5,27,44,46,51,53 dicopper-dioxygen isomers, 35,44,55 tetranuclear manganese cluster, 49 2Fe-2S/ 4Fe-4S clusters, 21,22 etc; their full single-shell (or even double-shell) valence d-block configurations can be highly correlated using the DMRG method with such a great accuracy to account for the full quantum degrees of freedom and with an affordable computational cost.…”

Equation of Motion Theory for Excited States in Variational Monte Carlo and the Jastrow Antisymmetric Geminal Power in Hilbert Space

“…Such methods include configuration interaction singles (CIS) [10], time-dependent density functional theory (TDDFT) [10], equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) [11], and linear-response DMRG [12]. These methods typically have more favorable cost-scalings than those based on CASSCF, allowing them to reach larger molecules, but they usually lack the advantage of systematic improvability.…”

The ab-initio density matrix renormalization group in practice

“…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.…”