References

If you find block2 useful in your research, please cite the paper

  • Zhai, H.; Larsson, H. R.; Lee, S.; Cui, Z.; Zhu, T.; Sun, C.; Peng, L.; Peng, R.; Liao, K.; Tölle, J.; Yang, J.; Li, S.; Chan, G. K.-L. Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond. The Journal of Chemical Physics 2023, 159, 234801. doi: 10.1063/5.0180424

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. doi: 10.1063/5.0050902

For large site DMRG-MRCI/MRPT, 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. doi: 10.1021/acs.jctc.1c00957

For DMRG with spin-orbit-coupling, please cite

  • Zhai, H.; Chan, G. K.-L. 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

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