References¶
A detailed description of the parallel DMRG algorithm implemented in block2 can be found in the following paper
Zhai, H., Chan, G. K. Low communication high performance ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2021, 154, 224116.
Please cite this paper if you find block2 useful in your research. For the large site code, please cite
Larsson, H. R., Zhai, H., Gunst, K., Chan, G. K. L. Matrix product states with large sites. Journal of Chemical Theory and Computation 2022, 18, 749-762.
You can find a bibtex file in CITATIONS.bib.
The other algorithms implemented in block2 are based on the following papers.
Qauntum Chemisty DMRG¶
Chan, G. K.-L.; Head-Gordon, M. Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group. The Journal of Chemical Physics 2002, 116, 4462–4476. doi: 10.1063/1.1449459
Sharma, S.; Chan, G. K.-L. Spin-adapted density matrix renormalization group algorithms for quantum chemistry. The Journal of Chemical Physics 2012, 136, 124121. doi: 10.1063/1.3695642
Wouters, S.; Van Neck, D. The density matrix renormalization group for ab initio quantum chemistry. The European Physical Journal D 2014, 68, 272. doi: 10.1140/epjd/e2014-50500-1
Parallelization¶
Chan, G. K.-L. An algorithm for large scale density matrix renormalization group calculations. The Journal of Chemical Physics 2004, 120, 3172–3178. doi: 10.1063/1.1638734
Chan, G. K.-L.; Keselman, A.; Nakatani, N.; Li, Z.; White, S. R. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2016, 145, 014102. doi: 10.1063/1.4955108
Stoudenmire, E.; White, S. R. Real-space parallel density matrix renormalization group. Physical Review B 2013, 87, 155137. doi: 10.1103/PhysRevB.87.155137
Zhai, H., Chan, G. K. Low communication high performance ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2021, 154, 224116. doi: 10.1063/5.0050902
Spin-Orbit Coupling¶
Sayfutyarova, E. R., Chan, G. K. L. A state interaction spin-orbit coupling density matrix renormalization group method. The Journal of Chemical Physics 2016, 144, 234301. doi: 10.1063/1.4953445
Sayfutyarova, E. R., Chan, G. K. L. Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group. The Journal of Chemical Physics 2018, 148, 184103. doi: 10.1063/1.5020079
Green’s Function¶
Ronca, E., Li, Z., Jimenez-Hoyos, C. A., Chan, G. K. L. Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians. Journal of Chemical Theory and Computation 2017, 13, 5560-5571. doi: 10.1021/acs.jctc.7b00682
Finite-Temperature DMRG¶
Feiguin, A. E., White, S. R. Finite-temperature density matrix renormalization using an enlarged Hilbert space. Physical Review B 2005, 72, 220401. doi: 10.1103/PhysRevB.72.220401
Feiguin, A. E., White, S. R. Time-step targeting methods for real-time dynamics using the density matrix renormalization group. Physical Review B 2005, 72, 020404. doi: 10.1103/PhysRevB.72.020404
Linear Response¶
Sharma, S., Chan, G. K. Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states. Journal of Chemical Physics 2014, 141, 111101. doi: 10.1063/1.4895977
Perturbative Noise¶
White, S. R. Density matrix renormalization group algorithms with a single center site. Physical Review B 2005, 72, 180403. doi: 10.1103/PhysRevB.72.180403
Hubig, C., McCulloch, I. P., Schollwöck, U., Wolf, F. A. Strictly single-site DMRG algorithm with subspace expansion. Physical Review B 2015, 91, 155115. doi: 10.1103/PhysRevB.91.155115
Particle Density Matrix¶
Ghosh, D., Hachmann, J., Yanai, T., Chan, G. K. L. Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene. The Journal of Chemical Physics 2008, 128, 144117. doi: 10.1063/1.2883976
Multi-Reference Correlation Theories¶
Szalay, P. G.; Müller, T.; Gidofalvi, G.; Lischka, H.; Shepard, R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chemical Reviews 2012, 112, 108-181. doi: 10.1021/cr200137a
Gdanitz, R. J., Ahlrichs, R. The Averaged Coupled-Pair Functional (ACPF): A Size-Extensive Modification of MR CI(SD). Chemical Physics Letters 1988, 143, 413-420. doi: 10.1016/0009-2614(88)87388-3
Szalay, P. G., Bartlett, R. J. Multi-Reference Averaged Quadratic Coupled-Cluster Method: A Size-Extensive Modification of Multi-Reference CI. Chemical Physics Letters 1993, 214, 481-488. doi: 10.1016/0009-2614(93)85670-J
Laidig, W. D.; Bartlett, R. J. A Multi-Reference Coupled-Cluster Method for Molecular Applications. Chemical Physics Letters 1984, 104, 424-430. doi: 10.1016/0009-2614(84)85617-1
Laidig, W. D., Saxe, P., Bartlett, R. J. The Description of N 2 and F 2 Potential Energy Surfaces Using Multireference Coupled Cluster Theory. The Journal of Chemical Physics 1987, 86, 887-907. doi: 10.1063/1.452291
Angeli, C., Cimiraglia, R., Evangelisti, S., Leininger, T., Malrieu, J.-P. Introduction of N-Electron Valence States for Multireference Perturbation Theory. J. Chem. Phys. 2001, 114, 10252–10264. doi: 10.1063/1.1361246
Angeli, C., Pastore, M., Cimiraglia, R. New Perspectives in Multireference Perturbation Theory: The n-Electron Valence State Approach. Theor Chem Account 2007, 117, 743–754. doi: 10.1007/s00214-006-0207-0
Fink, R. F. The Multi-Reference Retaining the Excitation Degree Perturbation Theory: A Size-Consistent, Unitary Invariant, and Rapidly Convergent Wavefunction Based Ab Initio Approach. Chemical Physics 2009, 356, 39-46. doi: 10.1016/j.chemphys.2008.10.004
Fink, R. F. Two New Unitary-Invariant and Size-Consistent Perturbation Theoretical Approaches to the Electron Correlation Energy. Chemical Physics Letters 2006, 428, 461–466. doi: 10.1016/j.cplett.2006.07.081
Sharma, S., Chan, G. K.-L. Communication: A Flexible Multi-Reference Perturbation Theory by Minimizing the Hylleraas Functional with Matrix Product States. The Journal of Chemical Physics 2014, 141, 111101. doi: 10.1063/1.4895977
Sharma, S., Alavi, A. Multireference Linearized Coupled Cluster Theory for Strongly Correlated Systems Using Matrix Product States. The Journal of Chemical Physics 2015, 143, 102815. doi: 10.1063/1.4928643
Sharma, S., Jeanmairet, G., Alavi, A. Quasi-Degenerate Perturbation Theory Using Matrix Product States. The Journal of Chemical Physics 2016, 144, 034103. doi: 10.1063/1.4939752
Larsson, H. R., Zhai, H., Gunst, K., Chan, G. K. L. Matrix product states with large sites. Journal of Chemical Theory and Computation 2022, 18, 749-762. doi: 10.1021/acs.jctc.1c00957
Determinant Coefficients¶
Lee, S., Zhai, H., Sharma, S., Umrigar, C. J., Chan, G. K. Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD (T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources. Journal of Chemical Theory and Computation 2021, 17, 3414-3425. doi: 10.1021/acs.jctc.1c00205
Perturbative DMRG¶
Guo, S., Li, Z., Chan, G. K. L. Communication: An efficient stochastic algorithm for the perturbative density matrix renormalization group in large active spaces. The Journal of chemical physics 2018, 148, 221104. doi: 10.1063/1.5031140
Guo, S., Li, Z., Chan, G. K. L. A perturbative density matrix renormalization group algorithm for large active spaces. Journal of chemical theory and computation 2018, 14, 4063-4071. doi: 10.1021/acs.jctc.8b00273
Orbital Reordering¶
Olivares-Amaya, R.; Hu, W.; Nakatani, N.; Sharma, S.; Yang, J.;Chan, G. K.-L. The ab-initio density matrix renormalization group in practice. The Journal of Chemical Physics 2015, 142, 034102. doi: 10.1063/1.4905329