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 `_