Orbital entanglement in bond-formation processes

Journal of Chemical Theory and Computation

Volumn 9, Issue 7, 2013, Pages 2959-2973

  Boguslawski, Katharina ^a   Tecmer, Paweł ^a   Barcza, Gergely ^b   Legeza, Örs ^b   Reiher, Markus ^a  

^a ETH ZURICH   (Switzerland)

^b WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84880023063     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct400247p     Document Type: Article

References (89)

1. Löwdin, P.-O. Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects Phys. Rev. 1955, 97, 1509-1520
2. Löwdin, P.-O. Advances in Chemical Physics; Wiley & Sons, Inc.: 1958; Vol. I, Chapter Review of Different Approaches and Discussion of Some Current Ideas, pp 209-321.
3. Bartlett, R. J.; Stanton, J. F. Applications of Post-Hartree-Fock Methods: A Tutorial Rev. Comput. Chem. 1994, 5, 65-169
4. Bartlett, R. J.; Musiał, M. Coupled-Cluster Theory in Quantum Chemistry Rev. Mod. Phys. 2007, 79, 291-350
5. Sinanoǧlu, O.; Tuan, D. F. Many-Electron Theory of Atoms and Molecules. III. Effect of Correlation on Orbitals J. Chem. Phys. 1963, 38, 1740-1748
6. Roos, B.; Taylor, P. R. A Complete Active Space SCF Method-(CASSCF) Using a Density Matrix Formulated Super-CI Approach Chem. Phys. 1980, 48, 157-173
7. Andersson, K.; Malmqvist, P.-A.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. Second-Order Perturbation Theory with a CASSCF Reference Function J. Chem. Phys. 1990, 94, 5483-5488
8. Andersson, K.; Malmqvist, P.-A.; Roos, B. O. Second-Order Perturbation Theory with a Complete Active Space Self-Consistent Field Reference Function J. Chem. Phys. 1992, 96, 1218-1226
9. Pulay, P. A Perspective on the CASPT2 Method Int. J. Quantum Chem. 2011, 111, 3273-3279
10. Ivanov, V. V.; Lyakh, D. I.; Adamowicz, L. Multireference State-Specific Coupled-Cluster Methods. State-of-the-Art and Perspectives Phys. Chem. Chem. Phys. 2009, 11, 2355-2370
11. Jeziorski, B. Multireference Coupled-Cluster Ansatz Mol. Phys. 2010, 108, 3043-3054
12. Lyakh, D. I.; Musiał, M.; Lotrich, V. F.; Bartlett, J. Multireference Nature of Chemistry: The Coupled-Cluster View Chem. Rev. 2012, 112, 182-243
13. Köhn, A.; Hanauer, M.; Mück, L. A.; Jagau, T.-C.; Gauss, J. State-Specific Multireference Coupled-Cluster Theory WIREs Comput. Mol. Sci. 2013, 3, 176-197
14. Jiang, W.; DeYonker, N. J.; Wilson, A. K. Multireference Character for 3d Transition-Metal-Containing Molecules J. Chem. Theory Comput. 2012, 8, 460-468
15. Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods Int. J. Quantum Chem. 1989, 23, 199-207
16. 2 and FNNF and the Transition State Structure for FNNF Cis-Trans Isomerization Theor. Chim. Acta 1989, 75, 81-98
17. Leininger, M. L.; Nielsen, I. M. B.; Crawford, T. D.; Janssen, C. L. A New Diagnostic for Open-Shell Coupled-Cluster Theory Chem. Phys. Lett. 2000, 328, 431-436
18. Lee, T. J.; Head-Gordon, M.; Rendell, A. P. Investigation of a Diagnostic for Perturbation Theory. Comparison to the T1 Diagnostic of Coupled-Cluster Theory Chem. Phys. Lett. 1995, 243, 402-408
19. Nielsen, I. M. B.; Janssen, C. L. Double-Substitution-Based Diagnostics for Coupled-Cluster and Møller-Plesset Perturbation Theory Chem. Phys. Lett. 1999, 310, 568-576 (Pubitemid 129592684)
20. Lee, T. J. Comparison of the T1 and D1 Diagnostics for Electronic Structure Theory: a New Definition for the Open-Shell D1 Diagnostic Chem. Phys. Lett. 2003, 372, 362-367 (Pubitemid 36507353)
21. Ziesche, P. Correlation Strength and Information Entropy Int. J. Quantum Chem. 1995, 56, 363-369
22. Luzanov, A. V.; Prezhdo, O. V. Irreducible Charge Density Matrices for Analysis of Many-Electron Wave Functions Int. J. Quantum Chem. 2005, 102, 582-601 (Pubitemid 40566728)
23. Huang, Z.; Kais, S. Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations Chem. Phys. Lett. 2005, 413, 1-5 (Pubitemid 41252359)
24. Huang, Z.; Wang, H.; Kais, S. Entanglement and Electron Correlation in Quantum Chemistry Calculations J. Mod. Opt. 2006, 53, 2543-2558 (Pubitemid 44662447)
25. Juhász, T.; Mazziotti, D. A. The Cumulant Two-Particle Reduced Density Matrix as a Measure of Electron Correlation and Entanglement J. Chem. Phys. 2006, 125, 174105
26. Luzanov, A. V.; Prezhdo, O. High-Order Entropy Measures and Spin-Free Quantum Entanglement for Molecular Problems Mol. Phys. 2007, 105, 2879-2891 (Pubitemid 351194999)
27. Kais, S. In Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules; Mazziotti, D. A., Ed.; John Wiley & Sons, Inc.: 2007; pp 493-535.
28. Greenman, L.; Mazziotti, D. A. Strong Electron Correlation in the Decomposition Reaction of Dioxetanone with Implications for Firefly Bioluminescence J. Chem. Phys. 2010, 133, 164110
29. Alcoba, D. R.; Bochicchio, R. C.; Lain, L.; Torre, A. On the Measure of Electron Correlation and Entanglement in Quantum Chemistry Based on the Cumulant of the Second-Order Reduced Density Matrix J. Chem. Phys. 2010, 133, 144104
30. Pelzer, K.; Greenman, L.; Gidofalvi, G.; Mazziotti, D. A. Strong Correlation in Acene Sheets from the Active-Space Variational Two-Electron Reduced Density Matrix Method: Effects of Symmetry and Size J. Phys. Chem. A 2011, 115, 5632-5640
31. Ivanov, V. V.; Lyakh, D. I.; Adamowicz, L. New Indices for Describing the Multi-Configurational Nature of the Coupled Cluster Wave Function Mol. Phys. 2005, 103, 2131-2139 (Pubitemid 41647950)
32. Takatsuka, K.; Fueno, T.; Yamaguchi, K. Distribution of Odd Electrons in Ground-State Molecules Theor. Chim. Acta 1978, 183, 175-183
33. Staroverov, V. N.; Davidson, E. R. Distribution of Effectively Unpaired Electrons Chem. Phys. Lett. 2000, 330, 161-168
34. Bochicchio, R.; Torre, A.; Lain, L. Comment on 'Characterizing Unpaired Electrons from One-Particle Density Matrix' [M. Head-Gordon, Chem. Phys. Lett. 372 (2003) 508-511] Chem. Phys. Lett. 2003, 380, 486-487
35. Head-Gordon, M. Reply to comment on 'Characterizing Unpaired Electrons from the One-Particle Density Matrix' Chem. Phys. Lett. 2003, 380, 488-489
36. Hachmann, J.; Dorando, J. J.; Avilés, M.; Chan, G. K.-L. The Radical Character of the Acenes: A Density Matrix Renormalization Group Study J. Chem. Phys. 2007, 127, 134309
37. Boguslawski, K.; Tecmer, P.; Legeza, O.; Reiher, M. Entanglement Measures for Single- and Multireference Correlation Effects J. Phys. Chem. Lett. 2012, 3, 3129-3135
38. Legeza, O.; Sólyom, J. Optimizing the Density-Matrix Renormalization Group Method Using Quantum Information Entropy Phys. Rev. B 2003, 68, 195116
39. Legeza, O.; Sólyom, J. Two-Site Entropy and Quantum Phase Transitions in Low-Dimensional Models Phys. Rev. Lett. 2006, 96, 116401
40. Rissler, J.; Noack, R. M.; White, S. R. Measuring Orbital Interaction Using Quantum Information Theory Chem. Phys. 2006, 323, 519-531
41. Legeza, O.; Sólyom, J. Quantum Data Compression, Quantum Information Generation, and the Density-Matrix Renormalization-Group Method Phys. Rev. B 2004, 70, 205118
42. Barcza, G.; Noack, R. M.; Sólyom, J.; Legeza, O. Generalized Correlation Functions and Entanglement Patterns. Entanglement topology of strongly correlated systems; Korrelationstage MPIPKS: Dresden, 2011
43. Schollwöck, U. The Density-Matrix Renormalization Group Rev. Mod. Phys. 2005, 77, 259-315 (Pubitemid 41490660)
44. Legeza, O.; Noack, R.; Sólyom, J.; Tincani, L. In Computational Many-Particle Physics; Fehske, H.; Schneider, R.; Weiße, A., Eds.; Lect. Notes Phys.; Springer: Berlin/Heidelerg, 2008; Vol. 739, pp 653-664.
45. Marti, K. H.; Reiher, M. The Density Matrix Renormalization Group Algorithm in Quantum Chemistry Z. Phys. Chem. 2010, 224, 583-599
46. Chan, G. K.-L.; Sharma, S. The Density Matrix Renormalization Group in Quantum Chemistry Annu. Rev. Phys. Chem. 2011, 62, 465-481
47. White, S. R. Density Matrix Formulation for Quantum Renormalization Groups Phys. Rev. Lett. 1992, 69, 2863-2866
48. Veryazov, V.; Widmark, P.-O. Relativistic Atomic Natural Orbital Type Basis Sets for the Alkaline and Alkaline-Earth Atoms Applied to the Ground-State Potentials for the Corresponding Dimers Theor. Chem. Acc. 2003, 111, 345-351 (Pubitemid 38659639)
49. Hess, B. A. Relativistic Electronic-Structure Calculations Employing a 2-Component No-Pair Formalism With External-Fields Projection Operators Phys. Rev. A 1986, 33, 3742
50. Wolf, A.; Reiher, M.; Hess, B. A. The Generalized Douglas-Kroll Transformation J. Chem. Phys. 2002, 117, 9215-9226
51. Reiher, M.; Wolf, A. Exact Decoupling of the Dirac Hamiltonian. I. General Theory J. Chem. Phys. 2004, 121, 2037-2047
52. Reiher, M.; Wolf, A. Exact Decoupling of the Dirac Hamiltonian. II. The Generalized Douglas-Kroll-Hess Transformation up to Arbitrary Order J. Chem. Phys. 2004, 121, 10945-10956 (Pubitemid 40020632)
53. Siegbahn, P. E. M.; Almlöf, J.; Heiberg, A.; Roos, B. O. The Complete Active Space SCF (CASSCF) Method in a Newton-Raphson Formulation with Application to the HNO Molecule J. Chem. Phys. 1981, 74, 2384-2396
54. Knowles, P. J.; Werner, H.-J. An Efficient Second-Order MC-SCF Method for Long Configuration Expansions Chem. Phys. Lett. 1985, 115, 259-267
55. Werner, H.-J.; Knowles, P. J. A Second Order Multiconfiguration SCF Procedure with Optimum Convergence J. Chem. Phys. 1985, 82, 5053-5063
56. Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; MOLPRO, Version 2010.1, a Package of Ab initio Programs; Cardiff University: Cardiff, United Kingdom, and University of Stuttgart: Stuttgart, Germany, 2010.
57. Moritz, G.; Wolf, A.; Reiher, M. Relativistic DMRG Calculations on the Curve Crossing of Cesium Hydride J. Chem. Phys. 2005, 123, 184105
58. Werner, H.-J. Third-Order Multireference Perturbation Theory-The CASPT3 Method Mol. Phys. 1996, 89, 645-661 (Pubitemid 126454689)
59. Altmann, S. L.; Herzig, P. Point-Group Theory Tables; Oxford: 1994; p 361.
60. Legeza, O. QC-DMRG-Budapest, A Program for Quantum Chemical DMRG Calculations; HAS RISSPO Budapest: 2000-2013.
61. Barcza, G.; Legeza, O.; Marti, K. H.; Reiher, M. Quantum-Information Analysis of Electronic States of Different Molecular Structures Phys. Rev. A 2011, 83, 012508
62. Legeza, O.; Röder, J.; Hess, B. A. Controlling the Accuracy of the Density-Matrix Renormalization-Group Method: The Dynamical Block State Selection Approach Phys. Rev. B 2003, 67, 125114
63. Valiev, M.; Bylaska, E.; Govind, N.; Kowalski, K.; Straatsma, T.; van Dam, H.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. de Jong, W. NWChem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations Comput. Phys. Commun. 2010, 181, 1477-1489
64. van Dam, H.; de Jong, W.; Bylaska, E.; Govind, N.; Kowalski, K.; Straatsma, T.; Valiev, M. NWChem: Scalable Parallel Computational Chemistry Rev. Comput. Mol. Sci. 2011, 1, 888-894
65. NWChem 6.1. http://www.nwchem-sw.org (accessed December 20, 2012).
66. Hirata, S. Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories J. Phys. Chem. A 2003, 107, 9887-9897
67. Hirata, S. Higher-Order Equation-of-Motion Coupled-Cluster Methods J. Phys. Chem. 2004, 121, 51-60
68. Hirata, S.; Fan, P.-D.; Auer, A. A.; Nooijen, M.; Piecuch, P. Combined Coupled-Cluster and Many-body Perturbation Theories J. Phys. Chem. 2004, 121, 12197-12208
69. Kowalski, K.; Krishnamoorthy, S.; Olson, R.; Tipparaju, V.; Apra, E. Scalable Implementations of Accurate Excited-State Coupled Cluster Theories: Application of High-Level Methods to Porphyrin-Based Systems; In: International Conference for High Performance Computing, Networking, Storage and Analysis. Seatle, USA, November, 12-18, 2011. http://ieeexplore.ieee.org/xpls/abs-all.jsp? arnumber=6114418&tag=1 (accessed May 9, 2013).
70. 2 J. Chem. Phys. 1991, 94, 1264-1270
71. Mitrushenkov, A. O.; Fano, G.; Ortolani, F.; Linguerri, R.; Palmieri, P. Quantum Chemistry Using the Density Matrix Renormalization Group J. Chem. Phys. 2001, 115, 6815-6821 (Pubitemid 33028807)
72. Chan, G. K.-L.; Kállay, M.; Gauss, J. State-of-the-Art Density Matrix Renormalization Group and Coupled Cluster Theory Studies of the Nitrogen Binding Curve J. Chem. Phys. 2004, 121, 6110-6116
73. Shepard, R.; Minkoff, M. Optimization of Nonlinear Wave Function Parameters Int. J. Quantum Chem. 2006, 106, 3190-3207 (Pubitemid 44726700)
74. 2 by the Reduced Multireference Coupled-Cluster Method J. Chem. Phys. 2008, 129, 054104
75. Shepard, R.; Kedziora, G. S.; Lischka, H.; Shavitt, I.; Müller, T.; Szalay, P. G.; Kállay, M.; Seth, M. The Accuracy of Molecular Bond Lengths Computed by Multireference Electronic Structure Methods Chem. Phys. 2008, 349, 37-57
76. 2: A Multi-Reference Coupled Cluster Study on the Potential Energy Surfaces of Ground and Excited States Mol. Phys. 2009, 107, 143-155
77. 2? The Renormalized CCSDT(Q) Study Chem. Phys. Lett. 2001, 344, 176-184 (Pubitemid 33640188)
78. Fang, T.; Shen, J.; Li, S. Block Correlated Coupled Cluster Method with a Complete-Active-Space Self-Consistent-Field Reference Function: the Formula for General Active Spaces and its Applications for Multibond Breaking Systems J. Chem. Phys. 2008, 128, 224107
79. 2 J. Chem. Phys. 1985, 82, 1413-1419
80. 2 Chem. Phys. 1985, 98, 381-386
81. 2O J. Chem. Phys. 1998, 108, 637-648 (Pubitemid 128598578)
82. 2 Chem. Phys. Lett. 2001, 344, 165-175 (Pubitemid 33640187)
83. Ivanov, V. V.; Adamowicz, L.; Lyakh, D. I. Dissociation of the Fluorine Molecule: CASCCSD Method and Other Many-Particle Models Int. J. Quantum Chem. 2006, 106, 2875-2880 (Pubitemid 44726725)
84. Musiał, M.; Bartlett, R. J. Critical Comparison of Various Connected Quadruple Excitation Approximations in the Coupled-Cluster Treatment of Bond Breaking J. Chem. Phys. 2005, 122, 224102
85. 2 Potential Energy Surfaces Using Multireference Coupled Cluster Theory J. Chem. Phys. 1987, 86, 887-907
86. Carnell, M.; Peyerimhoff, S. D.; Hess, B. A. Ab Initio MRDCI Calculations on the Cesium Hydride (CsH) Molecule Z. Phys. D. At., Mol. Clusters 1989, 333, 317-333
87. Zrafi, W.; Oujia, B.; Berriche, H.; Gadea, F. Evaluation of the Adiabatic Correction for LiH, RbH and CsH Molecules J. Mol. Struct.: THEOCHEM 2006, 777, 87-97
88. Zrafi, W.; Khelif, N.; Oujia, B.; Gadea, F. X. Theoretical Study of the CsH Molecule: Adiabatic and Diabatic Potential Energy Curves and Dipole Moments J. Phys. B: At. Mol. Opt. Phys. 2006, 39, 3815-3832 (Pubitemid 44403619)
89. Yan, L.; Qu, Y.; Liu, C.; Wang, J.; Buenker, R. J. Ab Initio Many-Electron Study for the Low-Lying States of the Alkali Hydride Cations in the Adiabatic Representation J. Chem. Phys. 2012, 136, 124304