Quantum chemistry using the density matrix renormalization group

(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

Section: [Fe 2 S 2 (Sch 3 ) 4 ] 3 − Clustermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Nakatani

Wouters

Neck

et al. 2014

“…[6][7][8][9][10][11] After early attempts to use the DMRG as a full configuration interaction (FCI) method for small molecules, 7,10,[12][13][14] it was recognised that DMRG is best used to describe non-dynamical correlation in active spaces. The DMRG algorithm exhibits a cost scaling of O(k 3 …”

Section: Introductionmentioning

confidence: 99%

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

Sharma¹,

Chan²

2012

282

392

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions ofŜ 2 , and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one-and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe 2 S 2 , [Fe 2 S 2 (SCH 3 ) 4 ] 2− , and Cr 2 systems. In the case of Fe 2 S 2 , the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe 2 S 2 (SCH 3 ) 4 ] 2− , we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr 2 we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.

“…[3][4][5][6][7][8][9][10][11][12][13][14][15] Developing from its roots in condensed matter, its earliest application to chemical problems used the semi-empirical π-electron Pariser-Parr-Pople Hamiltonian. [16][17][18] White and Martin introduced the first efficient formulation of the DMRG algorithm for ab-initio Hamiltonians (using some algorithmic contributions from Xiang 19 ) and the ab-initio density matrix renormalization group method was born.…”

Section: Introductionmentioning

confidence: 99%

The ab-initio density matrix renormalization group in practice

Olivares‐Amaya

Nakatani

et al. 2015

355

552

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice. C 2015 AIP Publishing LLC. [http://dx