Density matrix renormalization

In modest sized systems, we can treat the nondynamic correlation in an active space. For systems with up to 14 orbitals, the complete-active-space self-consistent field (CASSCF) theory provides a very satisfactory description [2, 3]. More recently, the ab initio density matrix renormalization group (DMRG) theory has allowed us to obtain a balanced description of nondynamic correlation for up to 40 active orbitals and more [4-13]. CASSCF and DMRG potential energy... 

S. R. White and R. L. Martin, Ab initio quantum chemistry using the density matrix renormalization group. J. Chem. Phys. 110, 4127 (1998). 

G. K.-L. Chan, An algorithm for large scale density matrix renormalization group calculations. J. Chem. Phys. 120, 3172 (2004). 

The Density Matrix Renormalization Group in Quantum Chemistry... 

Abstract The density matrix renormalization group (DMRG) is an electronic structure... 

Keywords strongly correlated electrons nondynamic correlation density matrix renormalization group post Hartree-Fock methods many-body basis matrix product states complete active space self-consistent field electron correlation... 

Hallberg, K. Density matrix renormalization a review of the method and its applications. In Theoretical Methods for Strongly Correlated Electrons (eds D. Senechal, A.-M. Tremblay, and... 

Ostlund, S., Rommer, S. Thermodynamic limit of density matrix renormalization. Phys. Rev. Lett 1995, 75(19), 3537. 

Rommer, S., Ostlund, S. Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group. Phys. Rev. B 1997, 55(4), 2164. 

Chan, G.K.L., Kallay, M., Gauss, J. State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. J. Chem. Phys. 2004, 121(13), 6110. 

Legeza, O., Solyom, J. Optimizing the density-matrix renormalization group method using quantum information entropy. Phys. Rev. B 2003, 68(19), 195116. 

Moritz, G., Hess, B.A., Reiher, M. Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings. J. Chem. Phys. 2005,122(2), 024107. 

Hachmann, J., Dorando, J.J., Aviles, M., Chan, G.K.L. The radical character of the acenes a density matrix renormalization group study. J. Chem. Phys. 2007, 127(13), 134309. 

Ramasesha, S., Pati, S.K., Krishnamurthy, H.R., Shuai, Z., Bredas, J.L. Low-lying electronic excitations and nonlinear optic properties of polymers via symmetrized density matrix renormalization group method. Synth. Met. 1997, 85(1-3), 1019. 

Fano, G., Ortolani, F., Ziosi, L. The density matrix renormalization group method Application to the PPP model of a cyclic polyene chain. J. Chem. Phys. 1998, 108(22), 9246. 

Raghu, C., Anusooya Pati, Y., Ramasesha, S. Structural and electronic instabilities in polyacenes density-matrix renormalization group study of a long-range interacting model. Phys. Rev. B 2002, 65(15), 155204. 

Kurashige, Y., Yanai, T. High-performance ab initio density matrix renormalization group method applicability to large-scale multireference problems for metal compounds. J. Chem. Phys. 2009, 130(23), 234114. 

Daul, S., Ciofini, I., Daul, C., White, S.R. Full-CI quantum chemistry using the density matrix renormalization group. Int. J. Quantum Chem. 2000, 79(6), 331. 

Zgid, D., Nooijen, M. Obtaining the two-body density matrix in the density matrix renormalization group method. J. Chem. Phys. 2008, 128, 144115. 

Mitrushenkov, A.O., Fano, G., Linguerri, R., Palmieri, P. On the possibility to use non-orthogonal orbitals for density matrix renormalization group calculations in quantum chemistry. arXiv.cond-mat, 0306058vl, 2003. 

Chan, G.K.L., Van Voorhis, T. Density-matrix renormalization-group algorithms with nonortho-gonal orbitals and non-Hermitian operators, and applications to polyenes. J. Chem. Phys. 2005, 122(20), 204101. 

Here p iaa occ, L() (respectively p iaa unocc, L()) represents the probability of the atomic configuration of site i, where the orbital a with spin a is occupied (resp. unoccupied) and where L[ is a configuration of the remaining orbitals of this site. This result is similar to the expression obtained by Biinemann et al. [22], but it is obtained more directly by the density matrix renormalization (5). To obtain the expression of the qiaa factors, an additional approximation to the density matrix of the uncorrelated state was necessary. This approximation can be viewed as the multiband generalization of the Gutzwiller approximation, exact in infinite dimension [23]... 

Among the technical methods proper to the one dimensional geometry, one may cite the Bethe ansatz [19], the bosonization techniques [18], and, more recently, the Density-Matrix Renormalization Group (DMRG) method (20, 21] and a closely related scheme which is directy considered in this note, the Recurrent Variational Approach (RVA) [22, 21], The two first methods are analytical and the third one is numerical the RVA method is in between. 

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