Multiconfiguration second-order perturbation theory approach to strong electron correlation in chemistry and photochemistry

Wiley Interdisciplinary Reviews: Computational Molecular Science

Volumn 2, Issue 4, 2012, Pages 585-603

  Roca Sanjuán, Daniel ^a   Aquilante, Francesco ^a   Lindh, Roland ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84860207352     PISSN: 17590876     EISSN: 17590884     Source Type: Journal    
DOI: 10.1002/wcms.97     Document Type: Review

References (121)

1. Gagliardi L, Roos BO. Multiconfigurational quantum chemical methods for molecular systems containing actinides. Chem Soc Rev 2007, H36:893-903.
2. Roos BO. Multiconfigurational quantum chemistry for ground and excited states. In: Shukla MK, Leszczynski J, ed. Radiation Induced Molecular Phenomena in Nucleic Acids. Amsterdam: Springer; 2007, 125-156.
3. Kotliar G, Savrasov S. Model Hamiltonians and first principles electronic structure calculations. In: Tsvelik AM, ed. New Theoretical Approaches to Strongly Correlated Systems. New York: Kluwer Academic/Plenum; 2001, 259-301.
4. Georges A, Kotliar G, Krauth W, Rozenberg MJ. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev Mod Phys 1996, 68:13-125.
5. White SR. Density-matrix algorithms for quantum renormalization-groups. Phys Rev B 1993, 48:10345-10356.
6. Marti KH, Ondik IM, Moritz G, Reiher M. Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters. J Chem Phys 2008, 128:014104.
7. Ghosh D, Hachmann J, Yanai T, Chan GKL. Orbital optimization in the density matrix renormalization group, with applications to polyenes and ss-carotene. J Chem Phys 2008, 128:144117.
8. Wiggins P, Williams JAG, Tozer DJ. Excited state surfaces in density functional theory: a new twist on an old problem. J Chem Phys 2009, 131:91101.
9. Tsuchimochi T, Henderson TM, Scuseria GE, et al. Constrained-pairing mean-field theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree-Fock theory. J Chem Phys 2010, 133:134108.
10. Mazziotti DA. Large-scale semidefinite programming for many-electron quantum mechanics. Phys Rev Lett 2011, 106:083001.
11. Roos BO. Methods in quantum chemistry II. Adv Chem Phys 1987, 69:399.
12. Andersson K, Malmqvist PA, Roos BO. Second-order perturbation-theory with a CASSCF reference function. J Chem Phys 1990 94:5483.
13. Pedersen TB, Aquilante F, Lindh R. Density fitting with auxiliary basis sets from Cholesky decompositions. Theor Chem Acc 2009, 124:1-10.
14. Aquilante F, Gagliardi L, Pedersen TB, Lindh, R. Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. J Chem Phys 2009, 130:154107.
15. Aquilante F, Lindh R, Pedersen TB. Analytic derivatives for the Cholesky representation of the two-electron integrals. J Chem Phys 2008, 129:34106.
16. Aquilante F, Lindh R, Pedersen TB. Unbiased auxiliary basis sets for accurate two-electron integral approximations. J Chem Phys 2007, 127:114107.
17. Aquilante F, Malmqvist PA, Pedersen TB, Chosh, A, Roos, BO. Cholesky decomposition based multiconfigurational second order perturbation theory (CD-CASPT2): application to the spin state energetics of CoIII(diiminato)(NPh). J Chem Theory Comput 2008, 4:694-702.
18. Aquilante F, Pedersen TB, Lindh R, Roos BO, Sánchez de Merás A, Koch H. Accurate ab initio density fitting for multiconfigurational self-consistent field methods. J Chem Phys 2008, 129:24113.
19. La Macchia G, Aquilante F, Veryazov V, Roos BO, Gagliardi L. Bond length and bond order in one of the shortest Cr-Cr bonds. Inorg Chem 2008, 47:11455-11457.
20. 2 with a Cu(I)-alpha-ketocarboxylate. J Chem Theory Comput 2009, 5:2967-2976.
21. Aquilante F, Pedersen TB, Lindh R. Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals. J Chem Phys 2007, 126:194106.
22. Aquilante F, Pedersen TB, Sánchez de Merás A, Koch H. Fast non-iterative orbital localization for large molecules. J Chem Phys 2006, 125:174101.
23. Aquilante F, Todorova TK, Gagliardi L, Pedersen TB, Roos BO. Systematic truncation of the virtual space in multiconfigurational perturbation theory. J Chem Phys 2009, 131:34113.
24. La Macchia G, Manni GL, Todorova TK, Brynda M, Aquilante F, Roos BO, Gagliardi L. On the analysis of the Cr-Cr multiple bond in several classes of dichromium compounds. Inorg Chem 2010, 49:5216-5222.
25. Nakano H. Quasidegenerate perturbation theory with multiconfigurational self-consistent-field reference functions. J Chem Phys 1993, 99:7983.
26. Aquilante F, Boman L, Boström J, Koch H, Lindh R, Sánchez de Merán A, Pedersen TB. Cholesky decomposition techniques in electronic structure theory. In: Zalesny R, Papadopoulos MG, Mezey PG, Leszczynski J, eds. Challenges and Avances in Computational Chemistry and Physics. Vol. 13. Springer; 2011, 301.
27. Shiozaki T, Werner HJ. Communication: second-order multireference perturbation theory with explicit correlation: CASPT2-F12. J Chem Phys 2010, 133:141103.
28. Angeli C, Cimiraglia R, Evangelisti S, Leininger T, Malrieu JP. Introduction of n-electron valence states for multireference perturbation theory. J Chem Phys 2001, 114:10252.
29. Angeli C, Borini S, Cestari M, Cimiraglia R. A quasidegenerate formulation of the second order n-electron valence state perturbation theory approach. J Chem Phys 2004, 121:4043.
30. Havenith RWA, Taylor PR, Angeli C, Cimiraglia R, Ruud K. Calibration of the n-electron valence state perturbation theory approach. J Chem Phys 2004, 120:4619.
31. Ghigo G, Roos BO, Malmqvist PA. A modified definition of the zeroth-order Hamiltonian in multiconfigurational perturbation theory (CASPT2). Chem Phys Lett 2004, 396:142-149.
32. Aquilante F, De Vico L, Ferre N, Ghigo G, Malmqvist PA, Neogrady P, Pedersen TB, Pitonak M, Reiher M, Roos BO, et al. Software news and update MOLCAS 7: the next generation. J Comput Chem 2010; 31;224-247.
33. Queralt N, Taratiel D, de Graaf C, Caballol R, Cimiraglia R, Angeli C. On the applicability of multireference second-order perturbation theory to study weak magnetic coupling in molecular complexes. J Comput Chem 2008, 29:994-1003.
34. Suaud N, Bonnet ML, Boilleau C, Labeguerie P, Guihery N. Light-induced excited spin state trapping: ab initio study of the physics at the molecular level. J Am Chem Soc 2009, 131:715-722.
35. Kepenikian M, Robert V, Le Guennic B. What zeroth-order Hamiltonian for CASPT2 adiabatic energetics of Fe(II)N6 architectures? J Chem Phys 2009, 131:114702.
36. Finley J, Malmqvist PA, Roos BO, Serrano-Andrés L. The multi-state CASPT2 method. Chem Phys Lett 1998, 288:299-306.
37. Serrano-Andrés L, Merchán M, Lindh R. Computation of conical intersections by using perturbation techniques. J Chem Phys 2005, 122:104107.
38. Roos BO, Andersson K, Fülscher P, Malmqvist PA, Serrano-Andrés L. Multiconfigurational perturbation theory: applications in electronic spectroscopy. Adv Chem Phys 1996, 93:219-331.
39. ISI Web of Knowledge, Thomson Reuters.
40. Bernardi F, Olivucci M, Robb MA. Conical intersections as a mechanistic feature of organic-photochemistry. Pure Appl Chem 1995; 67:783-789.
41. Serrano-Andrés L, Roca-Sanjuán D, Olaso-González G. Recent trends in computational photochemistry. In: Albani A, ed. Photochemistry. Specialist Periodical Reports. Vol 38. London: The Royal Society; 2011, 11.
42. Serrano-Andrés L, Merchán M. Spectroscopy: applications. In: Shleyer PVR, Jorgensen WL, Shaeffer III HF, Schreiner PR, Thiel W, Glen R, eds. Encyclopedia of Computational Chemistry. Chichester: John Wiley & Sons; 2004.
43. Merchán M, Serrano-Andrés L. Ab initio methods for excited states. In: Olivucci M, ed. Computational Photochemistry. Amsterdam: Elsevier; 2005.
44. Pérez-Hernández G, González L, Serrano-Andrés L. Rydberg or valence? The long-standing question in the UV absorption spectrum of 1, 1′-bicyclohexylidene. Chem Phys Chem 2008, 9:2544-2549.
45. Rubio M, Serrano-Andrés L, Merchán M. Excited states of the water molecule: analysis of the valence and Rydberg character. J Chem Phys 2008, 128:104305.
46. Buendía-Atencio C, Leyva V, Gonzalez L. Thermochemistry and UV spectroscopy of alkyl peroxynitrates. J Phys Chem A 2010, 114:9537-9544.
47. Corral I, Gonzalez L. Theoretical investigation of anthracene-9, 10-endoperoxide vertical singlet and triplet excitation spectra. J Comput Chem 2008, 29:1982-1991.
48. Liu YJ, Zhao, ZX, Bai FQ, Song MX, Zhang HX, Sun CC. Theoretical studies on the low-lying electronic states of the diazomethyl (HCNN) radical and its ions. J Mol Struct 2010, 955:145-151.
49. Zhao ZX, Hou CY, Shu X, Zhang HX, Sun CC. A CASSCF/CASPT2 study on the low-lying excited states of HSiCN, HSiNC and their ions. Theor Chem Acc 2009, 124:85-93.
50. Serrano-Andrés L, Merchán M. Quantum chemistry of the excited state: 2005 overview. J Mol Struct 2005, 729:99-108.
51. Olivucci M. Computational Photochemistry. Amsterdam: Elsevier; 2005.
52. Delchev VB, Sobolewski AL, Domcke W. Comparison of the non-radiative decay mechanisms of 4-pyrimidinone and uracil: an ab initio study. Phys Chem Chem Phys 2010, 12:5007-5015.
53. Conti I, Garavelli M, Orlandi G. Deciphering low energy deactivation channels in adenine. J Am Chem Soc 2009, 131:16108-16118.
54. Serrano-Andrés L, Merchán M, Borin AC. A three-state model for the photophysics of guanine. J Am Chem Soc 2008, 130:2473-2484.
55. Serrano-Andrés L, Merchán M. Are the five natural DNA/RNA base monomers a good choice from natural selection? A photochemical perspective. J Photochem Photobiol C: Photochem Rev 2009, 10:21-32.
56. Frutos LM, Markmann A, Sobolewski AL, Domcke W. Photoinduced electron and proton transfer in the hydrogen-bonded pyridine-pyrrole system. J Phys Chem B 2007, 111:6110-6112.
57. Marazzi M, Sancho U, Castano O, Domcke W, Frutos LM. Photoinduced proton transfer as a possible mechanism for highly efficient excited-state deactivation in proteins. J Phys Chem Lett 2010, 1:425-428.
58. Boggio-Pasqua M, Groenhof G, Schafer LV, Grubmuller H, Robb MA. Ultrafast deactivation channel for thymine dimerization. J Am Chem Soc 2007, 129:10996-10997.
59. Blancafort L, Migani A. Modeling thymine photodimerizations in DNA. Mechanism and correlation diagrams. J Am Chem Soc 2007, 129:14540-14541.
60. Roca-Sanjuán D, Olaso-González G, González-Ramírez I, Serrano-Andrés L, Merchán M. Molecular basis of DNA photodimerization: intrinsic production of cyclobutane cytosine dimers. J Am Chem Soc 2008, 130:10768-10779.
61. Serrano-Pérez JJ, González-Ramírez I, Coto PB, Merchán M, Serrano-Andrés L. Theoretical insight into the intrinsic ultrafast formation of cyclobutane pyrimidine dimers in UV-irradiated DNA. Thymine versus cytosine. J Phys Chem B 2008, 112:14096-14098.
62. González-Ramírez I, Roca-Sanjuán D, Climent T, Serrano-Pérez JJ, Merchán M, Serrano-Andrés L. On the photoproduction of DNA/RNA cyclobutane pyrimidine dimers. Theor Chem Acc 2011, 128:705-711.
63. Cembran A, González-Luque R, Serrano-Andrés L, Merchán M, Garavelli M. About the intrinsic photochemical properties of the 11-cis retinal chromophore: computational clues for a trap state and a lever effect in Rhodopsin catalysis. Theor Chem Acc 2007, 118:173-183.
64. Coto PB, Roca-Sanjuán D, Serrano-Andrés L, Martín-Pendás A, Martí S, Andrés J. Toward understanding the photochemistry of photoactive yellow protein: a CASPT2/CASSCF and quantum theory of atoms in molecules combined study of a model chromophore in vacuo. J Chem Theor Comput 2009, 5:3032-3038.
65. Altoe P, Haraszkiewicz N, Gatti FG, Wiering PG, Frochot C, Brouwer AM, Balkowski G, Shaw D, Woutersen S, Buma WJ, et al. Multistate photo-induced relaxation and photoisomerization ability of fumaramide threads: a computational and experimental study. J Am Chem Soc 2009, 131:104-117.
66. Assmann M, Pérez-Hernández G, González L. On the light-driven isomerization of a model asymmetric molecular rotor: conformations and conical intersections of 2-cyclopentylidene-tetrahydrofuran. J Phys Chem A 2010, 114:9342-9348.
67. Sinicropi A, Martin E, Ryazantsev M, Helbing J, Briand J, Sharma D, Leonard J, Haacke S, Cannizzo A, Chergui M, et al. An artificial molecular switch that mimics the visual pigment and completes its photocycle in picoseconds. Proc Natl Sci USA 2008, 105:17642-17647.
68. Meng QY, Huang MB, Chang HB. Theoretical study on the predissociation mechanism of CO2+ (C 2Sg+). J Phys Chem A 2009, 113:12825-12830.
69. Chen BZ, Chang HB, Huang MB. Dissociation of the OCS+ ion in low-lying electronic states studied using multiconfiguration second-order perturbation theory. J Chem Phys 2006, 125:054310.
70. Ding L, Chen XB, Fang WH. Ultrafast asynchronous concerted excited-state intramolecular proton transfer and photodecarboxylation of o-acetylphenylacetic acid explored by combined CASPT2 and CASSCF studies. Org Lett 2009, 11:1495-1498.
71. Shen X, Yang XL, Zhang XR, Cui ZJ, Kricka LJ, Stanley PE. Bioluminescence and chemiluminescence: Biology and Scientific Applications. Singapoure: World Scientific; 2009.
72. Gundermann KD. Chemilumineszenz Organicher Verbindungen. Berlin/Heidelberg/New York: Springer; 1968.
73. Isobe H, Yamanaka S, Kuramitsu S, Yamaguchi K. Regulation mechanism of spin-orbit coupling in charge-transfer-induced luminescence of imidazopyrazinone derivatives. J Am Chem Soc 2007, 130:132-149.
74. Isobe H, Takano Y, Okumura M, Kuramitsu S, Yamaguchi K. Mechanism insights in charge-transfer-induced luminescence of 1, 2-dioxetanones with a substituent of low oxidation potential. J Am Chem Soc 2005, 127:8667-8679.
75. De Vico L, Liu YJ, Krogh JW, Lindh R. Chemiluminescence of 1, 2-dioxetane. Reaction mechanism uncovered. J Phys Chem A 2007, 111:8013-8019.
76. Liu FY, Liu YJ, De Vico L, Lindh R. Theoretical study of the chemiluminescent decomposition of dioxetanone. J Am Chem Soc 2009, 131:6181-6188.
77. Liu FY, Liu YJ, De Vico L, Lindh R. A CASSCF/CASPT2 approach to the decomposition of thiazole-substituted dioxetanone: substitution effects and charge-transfer induced electron excitation. Chem Phys Lett 2009, 484:69-75.
78. Chung LW, Hayashi, S, Lundberg M, Nakatsu T, Kato H, Morokuma K. Mechanism of efficient firefly bioluminescence via adiabatic transition state and seam of sloped conical intersection. J Am Chem Soc 2008, 130:12880-12881.
79. Douglas M, Kroll NM. Quantum electrodynamical corrections to fine structure of helium. Ann Phys 1974, 82:89-155.
80. Hess BA. Relativistic electronic-structure calculations employing a 2-component no-pair formalism with external-field projection operators. Phys Rev A 1986, 33:3742-3748.
81. Malmqvist PA, Roos BO, Schimmelpfennig B. The restricted active space (RAS) state interaction approach with spin-orbit coupling. Chem Phys Lett 2002, 357:230-240.
82. Raab J, Roos BO. Excitation energies for transition metal atoms-a comparison between coupled cluster methods and second-order perturbation theory. Adv Quantum Chem 2005, 48:421-433.
83. Roos BO, Malmqvist PA. On the effects of spin-orbit coupling on molecular properties: dipole moment and polarizability of PbO and spectroscopic constants for the ground and excited states. Adv Quantum Chem 2004, 47:37-49.
84. Vancoillie S, Rulisek L, Neese F, Pierloot K. Theoretical description of the structure and magnetic properties of nitroxide-Cu(II)-nitroxide spin triads by means of multiconfigurational ab initio calculations. J Phys Chem A 2009, 113:6149-6157.
85. Vancoillie S, Zhao HL, Radon M, Pierloot K. Performance of CASPT2 and DFT for relative spin-state energetics of heme models. J Chem Theor Comput 2010, 6:576-582.
86. Vancoillie S, Chalupsky J, Ryde U, Solomon EI, Pierloot K, Neese F, Rulisek L. Multireference ab initio calculations of g tensors for trinuclear copper clusters in multicopper oxidases. J Phys Chem B 2010, 114:7692-7702.
87. Vancoillie S, Pierloot K. A multiconfigurational perturbation theory study of the electronic structure and EPR g values of an oxomolybdenum enzyme model complex. Theor Chem Acc 2009, 124:251-259.
88. +, and plastocyanin. J Phys Chem A 2008, 112:4011-4019.
89. Pierloot K, Zhao HL, Vancoillie S. Copper corroles: the question of noninnocence. Inorg Chem 2010, 49:10316-10329.
90. Roos BO, Malmqvist PA, Gagliardi L. Exploring the actinide-actinide bond: theoretical studies of the chemical bond in Ac2, Th2, Pa2, and U2. J Am Chem Soc 2006, 128:17000-17006.
91. Roos BO, Borin AC, Gagliardi L. Reaching the maximum multiplicity of the covalent chemical bond. Angew Chem Int Ed 2007, 46:1469-1472.
92. Gagliardi L, Roos BO. Quantum chemical calculations show that the uranium molecule U2 has a quintuple bond. Nature 2005, 433:848-851.
93. Borin AC, Gobbo JP, Roos BO. Electronic structure and chemical bonding in W2 molecule. Chem Phys Lett 2010, 490:24-28.
94. Borin AC, Gobbo JP, Roos BO. Electronic structure and chemical bonding in the ground states of Tc2 and Re2. Mol Phys 2009, 107:1035-1040.
95. Roos BO, Pyykkö P. Bonding trends in molecular compounds of lanthanides: the double-bonded carbene cations LnCH2+ (Ln = Sc, Y, La-Lu). Chem Eur J 2010, 16:270-275.
96. Todorova TK, Gagliardi L, Walensky JR, Miller KA, Evans WJ. DFT and CASPT2 analysis of polymetalic Uranium nitride and oxide complexes: how theory can help when X-ray analysis is inadequate. J Am Chem Soc 2010, 132:12397-12403.
97. Ungur L, van der Heuvel W, Chibotaru LF. Ab initio investigation of the non-collinear magnetic structure and the lowest magnetic excitations in dysprosium triangles. New J Chem 2009, 33:1224-1230.
98. Feltham HLC, Lan YH, Klöwer F, Ungur L, Chibotaru LF, Powell AK, Brooker S. A non-sandwiched macrocyclic monolanthanide single-molecule magnet: the key role of axiality. Chem Eur J 2011, 17:4362-4365.
99. Blancafort L, Migani A. Water effect on the excited-state decay paths of singlet excited cytosine. J Photochem Photobiol A: Chem 2007, 190:283-289.
100. Serrano-Pérez JJ, Serrano-Andrés L, Merchán M. A theoretical insight into the photophysics of psoralen. J Chem Phys 2006, 124:124502.
101. Borin AC, Serrano-Andrés L, Ludwig V, Coutinho K, Canuto S. Theoretical electronic spectra of 2-aminopurine in vapor and in water. Int J Quantum Chem 2006, 106:2564-2577.
102. Ludwig V, da Costa ZM, do Amaral MS, Borin AC, Canuto S, Serrano-Andrés L. Photophysics and photostability of adenine in aqueous solution: a theoretical study. Chem Phys Lett 2010, 492:164-169.
103. Roca-Sanjuán D, Olaso-González G, Rubio M, Coto PB, Merchán M, Ferré N, Ludwig V, Serrano-Andrés L. DNA nucleobase properties and photoreactivity: modeling environmental effects. Pure Appl Chem 2009, 81:743-754.
104. Roca-Sanjuán D, Olaso-González G, Coto PB, Merchán M, Serrano-Andrés L. Modeling hole transfer in DNA. II. Molecular basis of charge transport in the DNA chain. Theor Chem Acc 2010, 126:177-183.
105. Chen SF, Liu YJ, Navizet I, Ferré N, Fang WH, Lindh R. Systematic theoretical investigation on the light emitter of firefly. J Chem Theor Comput 2011, 7:798-803.
106. Navizet I, Liu YJ, Ferré N, Xiao HY, Fang WH, Lindh R. Color-tuning mechanism of firefly investigated by multi-configurational perturbation method. J Am Chem Soc 2010, 132:706-712.
107. Strambi A, Coto PB, Ferré N, Olivucci M. Effects of water re-location and cavity trimming on the CASPT2//CASSCF/AMBER excitation energy of Rhodopsin. Theor Chem Acc 2007, 118:185-191.
108. Schapiro I, Ryazantsev MN, Ding WJ, Huntress MM, Melaccio F, Andruniow T, Olivucci M. Computational Photobiology and beyond. Aust J Chem 2010, 63:413-429.
109. Tomasello G, Olaso-González G, Altoe P, Stenta M, Serrano-Andrés L, Merchán M, Orlandi G, Bottoni A, Garavelli M. Electrostatic control of the photoisomerization efficiency and optical properties in visual pigments: on the role of counterion quenching. J Am Chem Soc 2009, 131:5172-5186.
110. Trueba A, García-Lastra JM, de Graaf C, García-Fernández P, Barriuso MT, Aramburu JA, Moreno M. Jahn-Teller effect in Ag2+ doped KCl and NaCl: is there any influence of the host lattice? Chem Phys Lett 2006, 430:51-55.
111. Swerts B, Chibotaru LF, Lindh R, Seijo L, Barandiaran Z, Clima S, Pierloot K, Hendrickx MFA. Embedding fragment ab initio model potentials in CASSCF/CASPT2 calculations of doped solids: implementation and applications. J Chem Theor Comput 2008, 4:586-594.
112. Rozgonyi T, Gonzalez L. A two-dimensional wavepacket study of the nonadiabatic dynamics of CH2BrCl. J Phys Chem A 2008, 112:5573-5581.
113. Asturiol D, Lasorne B, Robb MA, Blancafort L. Photophysics of the pi, pi* and n, pi* states of thymine: MS-CASPT2 minimum-energy paths and CASSCF on-the-fly dynamics. J Phys Chem A 2009, 113:10211-10218.
114. Polli D, Altoe P, Weingart O, Spillane KM, Manzoni C, Brida D, Tomasello G, Orlandi G, Kukura P, Mathies RA, et al. Conical intersection dynamics of the primary photoisomerization event in vision. Nature 2010, 467:440-443.
115. Frutos LM, Andruniow T, Santoro F, Ferré N, Olivucci M. Tracking the excited-state time evolution of the visual pigment with multiconfigurational quantum chemistry. Proc Natl Sci USA 2007, 104:7764-7769.
116. Malmqvist PA, Pierloot K, Shahi ARM, Cramer CJ, Gagliardi L. The restricted active space (RAS) state interaction approach with spin-orbit coupling. J Chem Phys 2008, 128:2041092.
117. Shahi ARM, Cramer CJ, Gagliardi L. Second-order perturbation theory with complete and restricted active space reference functions applied to oligomeric unsaturated hydrocarbons. Phys Chem Chem Phys 2009, 11:10964-10972.
118. Li Manni G, Aquilante F, Gagliardi L. Strong correlation treated via effective hamiltonians and perturbation theory. J Chem Phys 2011, 134:034114.
119. Shepard R, Gidofalvi G, Hovland PD. An effective recursive algorithm to compute wave function optimization gradients for the graphically contracted function method. Int J Quantum Chem 2010, 110:2938-2948.
120. Andersson K, Roos BO. In: Yarkony DR, ed. Modern Electronic Structure Theory. Singapore: World Scientific; 1995, 55.
121. Roos BO. In: Dykstra CE, Frenking G, Kim K, Scuseria G, eds. Theory and Applications of Computational Chemistry: The First Forty Years. Amsterdam: Elsevier; 2005, 725.