Chapter 7 The Density Matrix Renormalization Group in Quantum Chemistry

Annual Reports in Computational Chemistry

Volumn 5, Issue , 2009, Pages 149-162

  Chan, Garnet Kin Lic ^a   Zgid, Dominika ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

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

Indexed keywords

EID: 69349086548     PISSN: 15741400     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-1400(09)00507-6     Document Type: Review

References (53)

1. White S.R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69 19 (1992) 2863
2. White S.R. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48 14 (1993) 10345
3. Schollwöck U. The density-matrix renormalization group. Rev. Mod. Phys. 77 1 (2005) 259
4. Hallberg, K. Density matrix renormalization: a review of the method and its applications. In Theoretical Methods for Strongly Correlated Electrons (eds D. Sénéchal, A.-M. Tremblay, and C. Bourbonnais), CRM Series in Mathematical Physics. Springer, New York, 2003.
5. Hallberg K.A. New trends in density matrix renormalization. Adv. Phys. 55 5 (2006) 477
6. Fannes M., Nachtergaele B., and Werner R.F. Finitely correlated states on quantum spin chains. Comm. Math. Phys. 144 3 (1992) 443
7. Fannes M., Nachtergaele B., and Werner R.F. Finitely correlated pure states. J. Funct. Anal. 120 2 (1994) 511-534
8. Östlund S., and Rommer S. Thermodynamic limit of density matrix renormalization. Phys. Rev. Lett 75 19 (1995) 3537
9. Rommer S., and Östlund S. Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group. Phys. Rev. B 55 4 (1997) 2164
10. Chan G.K.L. An algorithm for large scale density matrix renormalization group calculations. J. Chem. Phys. 120 7 (2004) 3172
11. Chan G.K.L., Kállay M., and Gauss J. State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. J. Chem. Phys. 121 13 (2004) 6110
12. Hachmann J., Cardoen W., and Chan G.K.L. Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group. J. Chem. Phys. 125 14 (2006) 144101
13. Chan G.K.L., and Head-Gordon M. Highly correlated calculations with a polynomial cost algorithm: a study of the density matrix renormalization group. J. Chem. Phys. 116 11 (2002) 4462
14. Legeza O., and Sólyom J. Optimizing the density-matrix renormalization group method using quantum information entropy. Phys. Rev. B 68 19 (2003) 195116
15. Moritz G., Hess B.A., and Reiher M. Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings. J. Chem. Phys. 122 2 (2005) 024107
16. Rissler J., Noack R.M., and White S.R. Measuring orbital interaction using quantum information theory. Chem. Phys. 323 2-3 (2006) 519
17. Dorando J.J., Hachmann J., and Chan G.K.L. Targeted excited state algorithms. J. Chem. Phys. 127 8 (2007) 084109
18. Hachmann J., Dorando J.J., Avilés M., and Chan G.K.L. The radical character of the acenes: a density matrix renormalization group study. J. Chem. Phys. 127 13 (2007) 134309
19. Wilson K.G. The renormalization group: critical phenomena and the kondo problem. Rev. Mod. Phys. 47 4 (1975) 773
20. Wilson K.G. The renormalization group and critical phenomena. Rev. Mod. Phys. 55 3 (1983) 583
21. Chan G.K.L. Density matrix renormalisation group Lagrangians. Phys. Chem. Chem. Phys. 10 (2008) 3454
22. Ramasesha S., Pati S.K., Krishnamurthy H.R., Shuai Z., and Brédas J.L. Low-lying electronic excitations and nonlinear optic properties of polymers via symmetrized density matrix renormalization group method. Synth. Met. 85 1-3 (1997) 1019
23. Yaron D., Moore E.E., Shuai Z., and Brédas J.L. Comparison of density matrix renormalization group calculations with electron-hole models of exciton binding in conjugated polymers. J. Chem. Phys. 108 17 (1998) 7451
24. Shuai Z., Brédas J.L., Saxena A., and Bishop A.R. Linear and nonlinear optical response of polyenes: a density matrix renormalization group study. J. Chem. Phys. 109 6 (1998) 2549
25. Fano G., Ortolani F., and Ziosi L. The density matrix renormalization group method: Application to the PPP model of a cyclic polyene chain. J. Chem. Phys. 108 22 (1998) 9246
26. Bendazzoli G.L., Evangelisti S., Fano G., Ortolani F., and Ziosi L. Density matrix renormalization group study of dimerization of the pariserparrpople model of polyacetilene. J. Chem. Phys. 110 2 (1999) 1277
27. Raghu C., Anusooya Pati Y., and Ramasesha S. Structural and electronic instabilities in polyacenes: density-matrix renormalization group study of a long-range interacting model. Phys. Rev. B 65 15 (2002) 155204
28. Raghu C., Anusooya Pati Y., and Ramasesha S. Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model. Phys. Rev. B 66 3 (2002) 035116
29. Pariser R., and Parr R. A semi-empirical theory of the electronic spectra and electronic structure of complex unsaturated molecules, I. J. Chem. Phys. 21 (1953) 466
30. Pariser R., and Parr R. A semi-empirical theory of the electronic spectra and electronic structure of complex unsaturated molecules. II. J. Chem. Phys. 21 (1953) 767
31. Pople J.A. Electron interaction in unsaturated hydrocarbons. Trans. Faraday Soc 49 (1953) 1375
32. Paldus J., Takahashi M., and Cho R.W.H. Coupled-cluster approach to electron correlation in one dimension: cyclic polyene model in delocalized basis. Phys. Rev. B 30 (1984) 4267
33. Paldus J., Čížek J., and Takahashi M. Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory. Phys. Rev. A 30 (1984) 2193-2209
34. White S.R., and Martin R.L. Ab initio quantum chemistry using the density matrix renormalization group. J. Chem. Phys. 110 9 (1999) 4127
35. Mitrushenkov A.O., Fano G., Ortolani F., Linguerri R., and Palmieri P. Quantum chemistry using the density matrix renormalization group. J. Chem. Phys. 115 15 (2001) 6815
36. Legeza O., Röder J., and Hess B.A. Controlling the accuracy of the density-matrix renormalization-group method: the dynamical block state selection approach. Phys. Rev. B 67 12 (2003) 125114
37. Zgid D., and Nooijen M. On the spin and symmetry adaptation of the density matrix renormalization group method. J. Chem. Phys. 128 (2008) 014107
38. 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.
39. Daul S., Ciofini I., Daul C., and White S.R. Full-CI quantum chemistry using the density matrix renormalization group. Int. J. Quantum Chem. 79 6 (2000) 331
40. Mitrushenkov A.O., Linguerri R., Palmieri P., and Fano G. Quantum chemistry using the density matrix renormalization group II. J. Chem. Phys. 119 8 (2003) 4148
41. Legeza O., Röder J., and Hess B.A. Qc-DMRG study of the ionic-neutral curve crossing of life. Mol. Phys. 101 13 (2003) 2019
42. Chan G.K.L., and Head-Gordon M. Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrödinger equation for water. J. Chem. Phys. 118 19 (2003) 8551
43. Moritz G., and Reiher M. Construction of environment states in quantum-chemical density-matrix renormalization group calculations. J. Chem. Phys. 124 3 (2006) 034103
44. Moritz G., Wolf A., and Reiher M. Relativistic DMRG calculations on the curve crossing of cesium hydride. J. Chem. Phys. 123 18 (2005) 184105
45. Moritz G., and Reiher M. Decomposition of density matrix renormalization group states into a Slater determinant basis. J. Chem. Phys. 126 24 (2007) 244109
46. Marti K.H., Ondík I.M., Moritz G., and Reiher M. Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters. J. Chem. Phys. 128 (2008) 014104
47. Yanai, T., Kurashige, Y., Ghosh, D., Chan, G.K-L. Accelerating convergence in iterative solutions of large active-space self-consistent field calculations. Int. J. Quantum Chem., 2009, 109, 2178-90.
48. Ghosh D., Hachmann J., Yanai T., and Chan G.K.L. Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene. J. Chem. Phys. 128 (2008) 144117
49. Zgid D., and Nooijen M. Obtaining the two-body density matrix in the density matrix renormalization group method. J. Chem. Phys. 128 (2008) 144115
50. 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, 0306058v1, 2003.
51. Chan G.K.L., and Van Voorhis T. Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes. J. Chem. Phys. 122 20 (2005) 204101
52. Dorando, J.J., Hachmann, J., Chan G.K-L. Analytic response theory for the density matrix renormalization group. J. Chem. Phys. 2009, 130(18), 184111.
53. Zgid D., and Nooijen M. The density matrix renormalization group self-consistent field method: Orbital optimization with the density matrix renormalization group method in the active space. J. Chem. Phys. 128 (2008) 144116