What we can learn from the norms of one-particle density matrices, and what we can't: Some results for interstate properties in model singlet fission systems

Journal of Physical Chemistry A

Volumn 118, Issue 51, 2014, Pages 11943-11955

  Matsika, Spiridoula ^a   Feng, Xintian ^b   Luzanov, Anatoliy V ^c   Krylov, Anna I ^b  

^a Temple University   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^c INSTITUTE FOR SINGLE CRYSTALS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONIC PROPERTIES; ETHYLENE; GEOMETRY; MOLECULAR VIBRATIONS; WAVE FUNCTIONS;

COULOMB OPERATORS; LOCAL ENVIRONMENTS; MOLECULAR GEOMETRIES; NON-ADIABATIC COUPLING; PARTICLE DENSITIES; RELATIVE ORIENTATION; STACKED CONFIGURATION; TRANSITION DIPOLE MOMENTS;

DIMERS;

EID: 84906876610     PISSN: 10895639     EISSN: 15205215     Source Type: Journal    
DOI: 10.1021/jp506090g     Document Type: Article

References (65)

1. McWeeny, R. Methods of Molecular Quantum Mechanics, 2nd ed.; Academic Press: New York, 1992.
2. Davidson, E. R. Reduced Density Matrices in Quantum Chemistry; Academic Press, New York, 1976.
3. Mestechkin, M. M. Metod matritsy plotnosti v teorii molekul; Naukova Dumka, Kiev, Ukraine, 1977.
4. Helgaker, T.; Jørgensen, P.; Olsen, J. Molecular electronic structure theory; John Wiley & Sons: New York, 2000.
5. pq.
6. Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory; McGraw-Hill: New York, 1989.
7. Bader, R. F. W. Atoms in molecules - Quantum theory; Oxford University Press: Oxford, U.K., 1990.
8. Weinhold, F.; Landis, C. R. Discovering Chemistry with Natural Bond Orbitals; John Wiley & Sons, Hoboken, NJ, USA, 2012.
9. Glendening, E. D.; Badenhoop, J. K.; Weinhold, F. Natural resonance theory: II. Natural bond order and valency. J. Comput. Chem. 1998, 19, 610-627.
10. Takatsuka, K.; Fueno, T.; Yamaguchi, K. Distribution of odd electrons in ground-state molecules. Theor. Chim. Acta 1978, 48, 175-183.
11. Head-Gordon, M. Characterizing unpaired electrons from the one-particle density matrix. Chem. Phys. Lett. 2003, 372, 508-511.
12. Luzanov, A. V.; Prezhdo, O. V. Analysis of multiconfigurational wave functions in terms of hole-particle distributions. J. Chem. Phys. 2006, 124, No. 224109.
13. Head-Gordon, M.; Grana, A. M.; Maurice, D.; White, C. A. Analysis of electronic transitions as the difference of electron attachment and detachment densities. J. Phys. Chem. 1995, 99, 14261-14270.
14. Luzanov, A. V.; Zhikol, O. A. Electron invariants and excited state structural analysis for electronic transitions within CIS, RPA, and TDDFT models. Int. J. Quantum Chem. 2010, 110, 902-924.
15. Luzanov, A. V.; Zhikol, O. A. In Practical aspects of computational chemistry I: An overview of the last two decades and current trends; Leszczynski, J., Shukla, M. K., Eds.; Springer: Berlin, 2012; p 415.
16. Plasser, F.; Lischka, H. Analysis of excitonic and charge transfer interactions from quantum chemical calculations. J. Chem. Theory Comput. 2012, 8, 2777-2789.
17. Bravaya, K.; Khrenova, M. G.; Grigorenko, B. L.; Nemukhin, A. V.; Krylov, A. I. The effect of protein environment on electronically excited and ionized states of the green fluorescent protein chromophore. J. Phys. Chem. B 2011, 8, 8296-8303.
18. Luzanov, A. V. The structure of the electronic excitation of molecules in quantum-chemical models. Russ. Chem. Rev. 1980, 49, 1033-1048.
19. Luzanov, A. V.; Sukhorukov, A. A.; Umanskii, V. E. Application of transition density matrix for analysis of excited states. Theor. Exp. Chem. 1976, 10, 354-361.
20. Tretiak, S.; Mukamel, S. Density matrix analysis and simulation of electronic excitations in conjugated and aggregated molecules. Chem. Rev. 2002, 102, 3171-3212.
21. Feng, X.; Luzanov, A. V.; Krylov, A. I. Fission of entangled spins: An electronic structure perspective. J. Phys. Chem. Lett. 2013, 4, 3845-3852.
22. Kolomeisky, A. B.; Feng, X.; Krylov, A. I. A simple kinetic model for singlet fission: A role of electronic and entropic contributions to macroscopic rates. J. Phys. Chem. C 2014, 118, 5188-5195.
23. Feng, X.; Kolomeisky, A. B.; Krylov, A. I. Dissecting the effect of morphology on the rates of singlet fission: Insights from theory. J. Phys. Chem. C 2014, DOI: 10.1021/jp505942k.
24. Jagau, T.-C.; Zuev, D.; Bravaya, K. B.; Epifanovsky, E.; Krylov, A. I. A fresh look at resonances and complex absorbing potentials: Density matrix based approach. J. Phys. Chem. Lett. 2014, 5, 310-315.
25. Yarkony, D. R. Diabolical conical intersections. Rev. Mod. Phys. 1996, 68, 985-1013.
26. Yarkony, D. R. Conical intersections: Diabolical and often misunderstood. Acc. Chem. Res. 1998, 31, 511-518.
27. Yarkony, D. R. Conical intersections: The new conventional wisdom. J. Phys. Chem. A 2001, 105, 6277-6293.
28. Lengsfield, B. H.; Saxe, P.; Yarkony, D. R. On the evaluation of nonadiabatic coupling matrix-elements using SA-MCSCF/CI wave functions and analytic gradient methods. 1. J. Chem. Phys. 1984, 81, 4549-4553.
29. Saxe, P.; Lengsfield, B. H.; Yarkony, D. R. On the evaluation of non-adiabatic coupling matrix-elements for large-scale CI wave-functions. Chem. Phys. Lett. 1985, 113, 159-164.
30. Lischka, H.; Dallos, M.; Szalay, P. G.; Yarkony, D. R.; Shepard, R. Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism. J. Chem. Phys. 2004, 120, 7322-7329.
31. Tapavicza, E.; Bellchambers, G. D.; Vincent, J. C.; Furche, F. Ab initio non-adiabatic molecular dynamics. Phys. Chem. Chem. Phys. 2013, 15, 18336-18348.
32. Fatehi, S.; Alguire, E.; Shao, Y.; Subotnik, J. E. Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance. J. Chem. Phys. 2011, 135, No. 234105.
33. Zhang, X.; Herbert, J. M. Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory. J. Chem. Phys. 2014, http://dx.doi.org/10.1063/1.4891984.
34. Domcke, W. D., Yarkony, D. R., Köppel, H., Eds. Conical intersections. Electronic structure, dynamics and spectroscopy; World Scientific: Singapore, 2004.
35. Helgaker, T.; Coriani, S.; Jørgensen, P.; Kristensen, K.; Olsen, J.; Ruud, K. Recent advances in wave function-based methods of molecular-property calculations. Chem. Rev. 2012, 112, 543-631.
36. Lengsfield, B. H., III; Yarkony, D. R. Nonadiabatic interactions between potential energy surfaces: Theory and applications. Adv. Chem. Phys. 1992, 82, 1-72.
37. Dallos, M.; Lischka, H.; Shepard, R.; Yarkony, D. R.; Szalay, P. G. Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. II. Minima on the crossing seam: Formaldehyde and the photodimerization of ethylene. J. Chem. Phys. 2004, 120, 7330-7339.
38. Ichino, T.; Gauss, J.; Stanton, J. F. Quasidiabatic states described by coupled-cluster theory. J. Chem. Phys. 2009, 130, No. 174105.
39. Smith, M. B.; Michl, J. Singlet fission. Chem. Rev. 2010, 110, 6891-6936.
40. Smith, M. B.; Michl, J. Recent advances in singlet fission. Annu. Rev. Phys. Chem. 2013, 64, 361-368.
41. Johnson, J. C.; Nozik, A. J.; Michl, J. The role of chromophore coupling in singlet fission. Acc. Chem. Res. 2013, 46, 1290-1299.
42. When treating an operator in a nonorthonormal AO basis, one should distinguish (as in tensor calculus) covariant, contravariant, and regular matrices of the operator. Within quantum chemistry context these peculiarities are discussed in ref 65.
43. Zuev, D.; Jagau, T.-C.; Bravaya, K. B.; Epifanovsky, E.; Shao, Y.; Sundstrom, E.; Head-Gordon, M.; Krylov, A. I. Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks. J. Chem. Phys. 2014, 141, No. 024102.
44. Pieniazek, P. A.; Arnstein, S. A.; Bradforth, S. E.; Krylov, A. I.; Sherrill, C. D. Benchmark full configuration interaction and EOM-IP-CCSD results for prototypical charge transfer systems: Noncovalent ionized dimers. J. Chem. Phys. 2007, 127, No. 164110.
45. Amos, T.; Woodward, M. Configuration interaction wave-functions for small π systems. J. Chem. Phys. 1969, 50, 119-123.
46. Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach. Chem. Phys. 1980, 48, 157-173.
47. Casanova, D.; Slipchenko, L. V.; Krylov, A. I.; Head-Gordon, M. Double spin-flip approach within equation-of-motion coupled cluster and configuration interaction formalisms: Theory, implementation and examples. J. Chem. Phys. 2009, 130, No. 044103.
48. Casanova, D.; Head-Gordon, M. Restricted active space spin-flip configuration interaction approach: Theory, implementation and examples. Phys. Chem. Chem. Phys. 2009, 11, 9779-9790.
49. Bell, F.; Zimmerman, P. M.; Casanova, D.; Goldey, M.; Head-Gordon, M. Restricted active space spin-flip (RAS-SF) with arbitrary number of spin-flips. Phys. Chem. Chem. Phys. 2013, 15, 358-366.
50. Ohno, K. Some remarks on the Pariser-Parr-Pople method. Theor. Chim. Acta 1964, 2, 219-227.
51. Ramasecha, S.; Soos, Z. G. Optical excitations of even and odd polyenes with molecular PPP correlations. Synth. Met. 1984, 9, 283-294.
52. Luzanov, A. V.; Wulfov, A. L.; Krouglov, V. O. A wavefunction operator approach to the full-CI problem. Chem. Phys. Lett. 1992, 197, 614-619.
53. Lischka, H.;, et al. COLUMBUS, an ab initio electronic structure program, release 7.0; 2012.
54. Lischka, H.; et al. High-level multireference methods in the quantum-chemistry program system COLUMBUS: Analytic MRCISD and MR-AQCC gradients and MR-AQCC-LRT for excited states, GUGA spin-orbit CI and parallel CI density. Phys. Chem. Chem. Phys. 2001, 3, 664-673.
55. Krylov, A. I.; Gill, P. M. W. Q-Chem: An engine for innovation. WIREs Comput. Mol. Sci. 2013, 3, 317-326.
56. Shao, Y.; Fusti-Molnar, L.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S.; Gilbert, A. T. B.; Slipchenko, L. V.; Levchenko, S. V.; O'Neill, D. P.; et al. Advances in Methods and Algorithms in a Modern Quantum Chemistry Program Package. Phys. Chem. Chem. Phys. 2006, 8, 3172-3191.
57. Izmaylov, A. F.; Mendive-Tapia, D.; Bearpark, M. J.; Robb, M. A.; Tully, J. C.; Frisch, M. J. Nonequilibrium Fermi golden rule for electronic transitions through conical intersections. J. Chem. Phys. 2011, 135, No. 234106.
58. Lee, M. H.; Dunietz, B. D.; Geva, E. Calculation from first principles of intramolecular golden-rule rate constants for photo-induced electron transfer in molecular donor-occeptor systems. J. Phys. Chem. C 2013, 117, 23391-23401.
59. Luzanov, A. V. In Many-body problem in quantum chemistry; Mestechkin, M. M., Ed.; Naukova Dumka: Kiev, Ukraine, 1987; p 53.
60. Prezhdo, O. V.; Rossky, P. J. Evaluation of quantum transition rates from quantum-classical molecular dynamics simulations. J. Chem. Phys. 1997, 107, 5863-5878.
61. Desouter-Lecomte, M.; Lorquet, J. C. Nonadiabatic interactions in unimolecular decay. IV. Transition probability as a function of the Massey parameter. J. Chem. Phys. 1979, 71, 4391-4403.
62. Luzanov, A. V. Spin-free quantum chemistry: What one can gain from Fock's cyclic symmetry. Int. J. Quantum Chem. 2011, 111, 4042-4066.
63. Clark, A. E.; Davidson, E. R. Local spin. J. Chem. Phys. 2001, 115, 7382-7340.
64. Luzanov, A. V.; Prezhdo, O. V. High-order entropy measures and spin-free quantum entanglement for molecular problems. Mol. Phys. 2007, 105, 2879-2891.
65. Head-Gordon, M.; Maslen, P. E.; White, C. A. A tensor formulation of many-electron theory in a nonorthogonal single particle basis. J. Chem. Phys. 1998, 108, 616-625.