Spin-adapted density matrix renormalization group algorithms for quantum chemistry

Abstract

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.

Self-assembling tensor networks and holography in disordered spin chains

“…Their original manifestation, the density-matrix renormalization group (DMRG) [7], is now understood to be based on a variational update of a matrix product state (vMPS) [8,9], and has found applications in a wide range of fields such as quantum chemistry [10] and quantum information [11] as well as condensed matter physics [12]. More recent developments have extended the methods to, e.g., critical systems [13], two-dimensional lattices [14][15][16], and topologically ordered states [17].…”

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

“…We here focus on DMRG, 20,21 a variational method which minimizes the energy of a wavefunction parametrized as a matrix product state (MPS). 22,23 DMRG can handle active spaces of around [30][31][32][33][34][35][36][37][38][39][40] orbitals, and in some cases even up to 100 [24][25][26][27][28][29][30][31][32][33][34] . However, by themselves the mentioned methods are not efficient for obtaining quantitative accuracy and for this dynamic correlation must also be calculated.…”

A state interaction spin-orbit coupling density matrix renormalization group method

“…Otherwise, the algorithm is the same as the usual density matrix sweep evaluation, as described, for example, in Ref. 35.…”

“…N, respectively, and the total wavefunction |Ψ⟩ recouples these into a spin-pure state for the whole lattice. 35,98,99 It is sufficient then to work only with the multiplet space rather than the state space, and individual 2S + 1 spin states and their matrix elements can be regenerated using Clebsch-Gordon coefficients and the Wigner-Eckart theorem. The reduced wavefunction in the multiplet space is written as…”

“…In transition metal systems, active spaces with up to 50 orbitals can be routinely converged to chemical accuracy. 26,28,29,31,34,35,[38][39][40][41]43,44,48 In this work, we describe a method to combine a treatment of spin-orbit coupling with a density matrix renormalization group description of the electronically near-degenerate individual states. We use a state interaction approach, [53][54][55][56][57][58] whereby DMRG wavefunctions are determined for spinpure electronic states, and the Hamiltonian with spin-orbit coupling is recomputed within this basis and diagonalized.…”