References
A detailed description of the parallel DMRG algorithm implemented in block2 can be found in the following paper
Zhai, H., Chan, G. K. L. 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. L. 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
Zhai, H., Chan, G. K. A comparison between the one- and two-step spin-orbit coupling approaches based on the ab initio Density Matrix Renormalization Group. The Journal of Chemical Physics 2022, 157, 164108. doi: 10.1063/5.0107805
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
Time-Dependent DMRG
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
Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B., Verstraete, F. Unifying time evolution and optimization with matrix product states. Physical Review B 2016, 94, 165116. doi: 10.1103/PhysRevB.94.165116
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
Guo, S., Watson, M. A., Hu, W., Sun, Q., Chan, G. K. L. N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and a trimer model of poly (p-phenylenevinylene). Journal of Chemical Theory and Computation 2016, 12, 1583-1591. doi: 10.1021/acs.jctc.5b01225
DMRG-SC-NEVPT2
Roemelt, M., Guo, S., Chan, G. K. L. A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions. The Journal of Chemical Physics 2016, 144, 204113. doi: 10.1063/1.4950757
Sokolov, A. Y., Guo, S., Ronca, E., Chan, G. K. L. Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes. The Journal of Chemical Physics 2017, 146, 244102. doi: 10.1063/1.4986975
DMRG-CASPT2
Kurashige, Y., Yanai, T. Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: Theory and application to the study of chromium dimer. The Journal of Chemical Physics 2011, 135, 094104. doi: 10.1063/1.3629454
Wouters, S., Van Speybroeck, V., Van Neck, D. DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes. The Journal of Chemical Physics 2016, 145, 054120. doi: 10.1063/1.4959817
Nakatani, N., Guo, S. Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations. The Journal of Chemical Physics 2017, 146, 094102. doi: 10.1063/1.4976644
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., Cimiraglia, R., Malrieu J.-P. N-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. The Journal of chemical physics 2002, 117, 9138-9153. doi: 10.1063/1.1515317
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