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

  • 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

  • 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., 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