The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges

Abstract

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison to other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, in particular its time-dependent formulation and the application to vibrational spectroscopy.

Hardware efficient quantum algorithms for vibrational structure calculations

“…Alternatively, the computational cost of VCI can be reduced with non-linear wavefunction parametrizations. This is the case, for example, of the vibrational Density Matrix Renormalization Group (vDMRG) 16,17 which encodes the wavefunction as a matrix product state, 18 or of VCC. 11 The emerging development of quantum computers has refreshed the prospect of computing energies of large molecules by leveraging the exponentially-large multi-qubit Hilbert space.…”

“…Alternatively, the computational cost of VCI can be reduced with non-linear wavefunction parametrizations. This is the case, for example, of the vibrational Density Matrix Renormalization Group (vDMRG) 16 , 17 which encodes the wavefunction as a matrix product state, 18 or of VCC. 11 …”

Chemical insights into the electronic structure of Fe(II) porphyrin using FCIQMC, DMRG, and generalized active spaces

“…Orbital entanglement measures [5][6][7][8][9][10] based on DMRG for quantum chem-istry [11][12][13][14][15][16][17][18][19][20][21] provide a clear description of correlation effects that differentially stabilize the 3 E g over the 5 A 1g spin state. Furthermore, in order to directly relate the role of the CT configurations to the triplet-quintet spin-gap, a strategy has been designed to selectively allow or forbid ligand-to-metal and metalto-ligand CT excitations within the CAS (32,34) configuration interaction expansion, while letting the rest of the wave function relax within the FCIQMC method [22,23] and orbitals relax self-consistently.…”

Chemical insights into the electronic structure of Fe(II) porphyrin using FCIQMC, DMRG, and generalized active spaces

“…Orbital entanglement measures [9,10,11,12,13,14] based on DMRG for quantum chemistry [15,16,17,18,19,20,21,22,23,24,25] provide a clear description of correlation effects that differentially stabilize the 3 E g over the 5 A 1g spin state. Furthermore, in order to directly relate the role of the CT configurations to the triplet-quintet spin-gap, a strategy has been designed to selectively allow or forbid ligand-to-metal and metal-to-ligand CT excitations within the CAS (32,34) configuration interaction expansion, while letting the rest of the wave function relax within the FCIQMC method [26,27] and orbitals relax self-consistently.…”