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Constricted Variational Density Functional Theory Approach to the Description of Excited States

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Density-Functional Methods for Excited States

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 368))

Abstract

We review the theoretical foundation of constricted variational density functional theory and illustrate its scope through applications.

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Notes

  1. 1.

    See the chapter “Ensemble DFT approach to excited states of strongly correlated molecular systems” by M. Filatov.

  2. 2.

    See Sect. 3.1 from part S1 of supporting information in Ziegler et al. [27].

  3. 3.

    See Sect. 3.3 from part S1 of supporting information in Ziegler et al. [27].

  4. 4.

    See Sect. 3.2 from part S1 of supporting information in Ziegler et al. [27].

  5. 5.

    See Sect. 3.4 from part S1 of supporting information in Ziegler et al. [27].

  6. 6.

    See Sect. 4.1 from part S1 of supporting information in Ziegler et al. [27].

  7. 7.

    See Sect. 3.0 from part S2 of supporting information in Ziegler et al. [27].

References

  1. Jensen F (2006) Introduction to computational chemistry. Wiley, New York

    Google Scholar 

  2. Helgaker T, Jørgensen P, Olsen J (2000) Molecular electronic-structure theory. Wiley, New York

    Book  Google Scholar 

  3. Runge E, Gross EKU (1984) Density functional theory for time-dependent systems. Phys Rev Lett 52:997

    Article  CAS  Google Scholar 

  4. Casida ME (1995) In: Chong DP (ed) Recent advances in density functional methods. World Scientific, Singapore, pp 155–193

    Chapter  Google Scholar 

  5. van Gisbergen SJA, Snijders JG (1995) A density functional theory study of frequency dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules. J Chem Phys 103:9347

    Article  Google Scholar 

  6. Petersilka M, Grossmann UJ, Gross EKU (1996) Excitation energies from time-dependent density-functional theory. Phys Rev Lett 76:12

    Article  Google Scholar 

  7. Bauernschmitt R, Ahlrichs R (1996) Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory. Chem Phys Lett 256:454

    Article  CAS  Google Scholar 

  8. Furche F (2001) On the density matrix based approach to time-dependent density functional response theory. J Chem Phys 114:5882

    Google Scholar 

  9. Furche F, Ahlrichs R (2002) Adiabatic time-dependent density functional methods for excited state properties. J Chem Phys 117:7433

    Article  CAS  Google Scholar 

  10. Romaniello P, Sangalli D, Berger JA, Sottile F, Molinari LG, Reining L, Onida G (2009) Double excitations in finite systems. J Chem Phys 130:044108

    Article  CAS  Google Scholar 

  11. Gritsenko O, Baerends EJ (2009) Double excitation effects in non-adiabatic time-dependent theory with an analytic construction of the exchange correlation kernel in the common energy denominator energy approximation. Phys Chem 11:4640

    CAS  Google Scholar 

  12. Jacquemin D, Wathelet V, Perpète EA, Adamo C (2009) Extensive TD-DFT benchmark: singlet excited states of organic molecules. J Chem Theory Comput 5:2420

    Article  CAS  Google Scholar 

  13. Jacquemin D, Perpète EA, Ciofini I, Adamo C (2009) Accurate simulation of optical properties in dyes. Acc Chem Res 42:326

    Article  CAS  Google Scholar 

  14. Jacquemin D, Perpete EA, Scuseria GE, Ciofini I, Adamo C (2008) TD-DFT performance for the visible absorption spectra of organic dyes: conventional versus long range hybrids. J Chem Theory Comput 4:123–135

    Article  CAS  Google Scholar 

  15. Grimme S, Neese F (2007) Double-hybrid density functional theory for excited electronic states of molecules. J Chem Phys 127:154116

    Article  Google Scholar 

  16. Send R, Valsson O, Filippi C (2011) Electronic excitations of simple cyanine dyes: reconciling density functional and wave function methods. J Chem Theory Comput 7:444

    Article  CAS  Google Scholar 

  17. Jacquemin D, Perpete EA, Ciofini I, Adamo C, Valero R, Zhao Y, Truhlar DG (2010) On the performances of the M06 family of density functionals for electronic excitation energies. J Chem Theory Comput 6:2071

    Article  CAS  Google Scholar 

  18. Moore B II, Autschbach J (2013) Longest-wavelength electronic excitations of linear cyanines: the role of electron delocalization and of approximations in time-dependent density functional theory. J Chem Theory Comput 9:4991

    Article  Google Scholar 

  19. Schipper PRT, Gritsenko OV, van Gisberger SJA, Baerends EJ (2000) Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials. J Chem Phys 112:1344

    Article  CAS  Google Scholar 

  20. Likura H, Tsuneda T, Tanai T, Hirao K (2001) A long-range correction scheme for generalized-gradient-approximation exchange functionals. J Chem Phys 115:3540

    Article  Google Scholar 

  21. Song J-W, Watson MA, Hirao K (2009) An improved long-range corrected hybrid functional with vanishing Hartree–Fock exchange at zero interelectronic distance (LC2gau-BOP). J Chem Phys 131:144108

    Article  Google Scholar 

  22. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118:8207

    Article  CAS  Google Scholar 

  23. Baer R, Neuhauser D (2005) Density functional theory with correct long-range asymptotic behavior. Phys Rev Lett 94:043002

    Article  Google Scholar 

  24. Dreuw A, Weisman J, Head-Gordon M (2003) Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange. J Chem Phys 119:2943

    Article  CAS  Google Scholar 

  25. Tozer D (2003) Relationship between long-range charge transfer error and integer discontinuity error in Kohn Sham theory. J Chem Phys 119:12697

    Article  CAS  Google Scholar 

  26. Krykunov M, Ziegler T (2013) Self-consistent formulation of constricted variational density functional theory with orbital relaxation. Implementation and application. J Chem Theory Comput 9:2761

    Article  CAS  Google Scholar 

  27. Ziegler T, Krykunov M, Cullen J (2012) The implementation of a self-consistent constricted variational density functional theory for the description of excited states. J Chem Phys 136:124107

    Article  Google Scholar 

  28. Cullen J, Krykunov M, Ziegler T (2011) The formulation of a self-consistent constricted variational density functional theory for the description of excited states. Chem Phys 391:11

    Article  CAS  Google Scholar 

  29. Ziegler T, Seth M, Krykunov M, Autschbach J, Wang F (2009) On the relation between time-dependent and variational density functional theory approaches for the determination of excitation energies and transition moments. J Chem Phys 130:154102

    Article  Google Scholar 

  30. Krykunov M, Seth M, Ziegler T (2014) Derivation of the RPA (random phase approximation) equation of ATDDFT (adiabatic time dependent density functional ground state response theory) from an excited state variational approach based on the ground state functional. J Chem Phys 140:18A502

    Article  Google Scholar 

  31. Ziegler T, Krykunov M (2010) On the calculation of charge transfer transitions with standard density functionals using constrained variational density functional theory. J Chem Phys 133:074104

    Article  Google Scholar 

  32. Ziegler T, Seth M, Krykunov M, Autschbach J, Wang F (2008) A revised electronic Hessian for approximate time-dependent density functional theory. J Chem Phys 129:184114

    Article  Google Scholar 

  33. Stein T, Kronik L, Baer R (2009) Reliable prediction of charge transfer excitations in molecular complexes using time-dependent density functional theory. J Am Chem Soc 131:2818

    Article  CAS  Google Scholar 

  34. Cave RJ, Zhang F, Maitra NT, Burke K (2004) A dressed time-dependent density functional treatment of the 21A states of butadiene and hexatriene. Chem Phys Lett 389:39

    Article  CAS  Google Scholar 

  35. Mazur G, Wlodarczyk R (2009) Application of the dressed time-dependent density functional theory for the excited states of linear polyenes. J Comp Chem 30:811

    Article  CAS  Google Scholar 

  36. Elliott P, Goldson S, Canahui C, Maitra NT (2011) Perspectives on double-excitations in TDDFT. Chem Phys 391:110

    Article  CAS  Google Scholar 

  37. Slater JC, Wood JH (1971) Statistical exchange and the total energy of a crystal. Int J Quant Chem Suppl 4:3

    Google Scholar 

  38. Slater JC (1972) Statistical exchange-correlation in the self-consistent field. Adv Quant Chem 6:1

    Article  CAS  Google Scholar 

  39. Kowalczyk T, Yost SR, Van Voorhis T (2011) Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes. J Chem Phys 134:054128

    Article  Google Scholar 

  40. Ziegler T, Rauk R, Baerends EJ (1977) On the calculation of multiplet energies by the Hartree-Fock-Slater method. Theor Chim Acta 43:261

    Article  CAS  Google Scholar 

  41. Ziegler T, Rauk A, Baerends EJ (1976) The electronic structure of tetrahedral oxo-complexes. The nature of the “charge transfer” transitions. J Chem Phys 16:209

    CAS  Google Scholar 

  42. Gilbert A, Besley N, Gill P (2008) J Phys Chem A 122:13164

    Article  Google Scholar 

  43. Besley N, Gilbert A, Gill P (2009) Self-consistent-field calculations of core excited states. J Chem Phys 130:124308-1

    Article  Google Scholar 

  44. Park YC, Krykunov M, Seidu I, Ziegler T (2014) On the relation between adiabatic time dependent density functional theory (TDDFT) and the ΔSCF-DFT method. Introducing a numerically stable ΔSCF-DFT scheme for local functionals based on constricted variational DFT. Mol Phys 112:661

    Google Scholar 

  45. Gavnholt J, Olsen T, Engelund M, Schiøtz J (2008) Δ self-consistent field method to obtain potential energy surfaces of excited molecules on surfaces. J Phys Rev B 78:075441/1

    Article  CAS  Google Scholar 

  46. Liu TQ, Han WG, Himo FG, Ullmann M, Bashford D, Toutchkine A, Hahn KM, Noodleman L (2004) Density functional vertical self-consistent reaction field theory for solvatochromism studies of solvent-sensitive dyes. Phys Chem A 108:3545

    Article  CAS  Google Scholar 

  47. Ceresoli D, Tosatti E, Scandolo S, Santoro G, Serra S (2004) Trap** of excitons at chemical defects in polyethylene. J Chem Phys 121:6478

    Article  CAS  Google Scholar 

  48. Zhekova H, Seth M, Ziegler T (2014) Application of time dependent and time independent density functional theory to the first π to π* transition in cyanine dyes. Int J Quant Chem 114:1019

    Article  CAS  Google Scholar 

  49. Ziegler T (2011) A chronical about the development of electronic structure theories for transition metal complexes. Struct Bond 47:1

    Article  Google Scholar 

  50. von Barth U (1979) Local-density theory of multiplet structure. Phys Rev A 20:1693

    Article  Google Scholar 

  51. Gunnarsson O, Lundqvist BI (1976) Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys Rev B 13:4274

    Article  CAS  Google Scholar 

  52. Levy M, Perdew JP (1985) Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms. Phys Rev A 32:2010

    Article  CAS  Google Scholar 

  53. Gaudoin R, Burke K (2005) Lack of Hohenberg-Kohn theorem for excited states. Phys Rev Lett 93:173001

    Article  Google Scholar 

  54. Oliveira LN, Gross EKU, Kohn W (1988) Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom. Phys Rev A 37:2821

    Article  CAS  Google Scholar 

  55. Filatov M, Shaik S (1998) Spin-restricted density functional approach to the open-shell problem. Chem Phys Lett 288:689

    Article  CAS  Google Scholar 

  56. Filatov M, Shaik S (1999) Spin-restricted density functional approach to the open-shell problem. Chem Phys Lett 304:429

    Article  CAS  Google Scholar 

  57. Filatov M, Huix-Rotllant M (2014) Description of electron transfer in the ground and excited states of organic donor–acceptor systems by single-reference and multi-reference density functional methods. J Chem Phys 141:024112

    Article  Google Scholar 

  58. Gidopoulos NI, Papaconstantinou PG, Gross EKU (2002) Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom. Phys Rev Lett 88:03300

    Article  Google Scholar 

  59. Gross EKU, Oliveira LN, Kohn W (1988) Spurious interactions, and their correction, in the ensemble-Kohn-Sham scheme for excited states. Phys Rev A 37:2809

    Article  CAS  Google Scholar 

  60. Levy M, Nagy A (1999) Variational density-functional theory for an individual excited state. Phys Rev Lett 83:4361

    Article  CAS  Google Scholar 

  61. Görling A, Levy M (1993) Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. Phys Rev B 47:13105

    Article  Google Scholar 

  62. Ziegler T, Krykunov M, Autschbach J (2014) Derivation of the RPA (random phase approximation) equation of ATDDFT (adiabatic time dependent density functional ground state response theory) from an excited state variational approach based on the ground state functional. J Chem Theory Comput 10:3980

    Article  CAS  Google Scholar 

  63. Ziegler T, Krykunov M, Cullen J (2011) The application of constricted variational density functional theory to excitations involving electron transitions from occupied lone-pair orbitals to virtual π* orbitals. J Chem Theory Comput 7:2485

    Article  CAS  Google Scholar 

  64. Krykunov M, Grimme S, Ziegler T (2012) Accurate theoretical description of the 1La and 1Lb excited states in acenes using the all order constricted variational density functional theory method and the local density approximation. J Chem Theory Comput 8:4434

    Article  CAS  Google Scholar 

  65. Zhekova H, Krykunov M, Autschbach J, Ziegler T (2014) Applications of time dependent and time independent density functional theory to the first π to π* transition in cyanine dyes. J Chem Theory Comput 10:3299

    Article  CAS  Google Scholar 

  66. Seidu I, Krykunov M, Ziegler T (2014) Applications of time-Ù‐dependent and time-Ù‐ independent density functional theory to Rydberg transitions. J Phys Chem A ASAP. doi:10.1021/jp5082802

  67. Wang F, Ziegler T (2004) Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential. J Chem Phys 121:12191-1

    Google Scholar 

  68. Wang F, Ziegler T (2005) The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies. J Chem Phys 122:074109-1

    Google Scholar 

  69. Wang F, Ziegler T (2006) Use of noncollinear exchange-correlation potentials in multiplet resolutions by time-dependent density functional theory. Int J Quant Chem 106:2545–2550

    Article  CAS  Google Scholar 

  70. Hirata S, Head-Gordon M (1999) Time-dependent density functional theory within the Tamm-Dancoff approximation. Chem Phys Lett 291:314

    Google Scholar 

  71. Amos AT, Hall GG (1961) Single determinant wave functions. Proc R Soc A 263:483

    Article  Google Scholar 

  72. Martin RLJ (2003) Natural transition orbitals. J Chem Phys 118:4775

    Article  CAS  Google Scholar 

  73. Schreiber M, Silva-Junior M, Sauer S, Thiel W (2008) Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. J Chem Phys 128:134110

    Article  Google Scholar 

  74. Platt JR (1949) Classification of spectra of Cata condensed hydrocarbons. J Chem Phys 17:484

    Article  CAS  Google Scholar 

  75. Grimme S, Parac M (2003) Substantial errors from time-dependent density functional theory for the calculation of excited states of large π systems. Chemphyschem 4:292

    Article  CAS  Google Scholar 

  76. Parac M, Grimme S (2003) TDDFT of the lowest excitation energies of polycyclic aromatic hydrocarbons. Chem Phys 292:11

    Article  CAS  Google Scholar 

  77. Jacquemin D, Wathelet V, Perpete EA, Adamo C (2009) Assessment of functionals for TD-DFT calculations of singlet-triplet calculations. J Chem Theory 5:2420

    Article  CAS  Google Scholar 

  78. Goerigk L, Grimme S (2010) Assessment of TD-DFT methods and of various spin scaled CIS (D) and CC2 versions for the treatment of low-lying valence excitations of large organic dyes. J Chem Phys 132:184103

    Article  Google Scholar 

  79. Richard RM, Herbert JM (2011) Time-dependent density-functional description of the 1La state in polycyclic aromatic hydrocarbons: charge-transfer character in disguise? J Chem Theory Comput 7:1296

    Article  CAS  Google Scholar 

  80. Ziegler T, Rauk A (1977) On the calculation of bonding energies by the Hartree-Fock-Slater method. Theor Chim Acta (Berl) 46:1

    Article  CAS  Google Scholar 

  81. Pople JA, Krishnan R, Schlegel HB, Binkley JS (1979) Derivative studies in configuration interaction theory. Int J Quant Chem S13:225

    Google Scholar 

  82. Fletcher R (1980) Practical methods of optimization, vol 1. Wiley, New York

    Google Scholar 

  83. Fischer H, Almlöf J (1992) General methods for geometry and wave function optimization. J Phys Chem 96:9768

    Article  CAS  Google Scholar 

  84. Prochorow J, Tramer AJ (1967) Photoselection study of charge transfer complexes. J Chem Phys 47:775

    Article  CAS  Google Scholar 

  85. Frey JE, Andrews AM, Ankoviac DG et al (1990) Charge-transfer complexes of tetracyanoethylene with cycloalkanes, alkenes, and alkynes and some of their aryl derivatives. J Org Chem 55:606

    Article  CAS  Google Scholar 

  86. Merrifield RE, Phillips WD (1958) Cyanocarbon chemistry. II.1 Spectroscopic studies of the molecular complexes of tetracyanoethylene. J Am Chem Soc 80:2778

    Article  Google Scholar 

  87. Masnovi JM, Seddon EA, Kochi JK (1984) Electron transfer from anthracenes. Comparison of photoionization, charge-transfer excitation and electrochemical oxidation. Can J Chem 62:2552

    Article  CAS  Google Scholar 

  88. Hanazaki I (1972) Vapor-phase electron donor–acceptor complexes of tetracyanoethylene and of sulfur dioxide. J Phys Chem 76:1982

    Article  CAS  Google Scholar 

  89. Garcia-Cuesta I, Sanchez de Meras AMJ, Koch H (2003) Coupled cluster calculations of the vertical excitation energies of tetracyanoethylene. J Chem Phys 118:8216

    Article  CAS  Google Scholar 

  90. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58:1200

    Article  CAS  Google Scholar 

  91. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098

    Article  CAS  Google Scholar 

  92. Perdew JP, Wang Y (1986) Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys Rev B 33:8822

    Article  Google Scholar 

  93. Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785

    Article  CAS  Google Scholar 

  94. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865

    Article  CAS  Google Scholar 

  95. Hammer B, Hansen LB, Norskøv JK (1999) Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Phys Rev B 59:7413

    Article  Google Scholar 

  96. Zhang Y, Yang W (1998) Comment on “generalized gradient approximation made simple”. Phys Rev Lett 80:890

    Article  CAS  Google Scholar 

  97. Gritsenko OV, Schipper PRT, Baerends EJ (1999) Approximation of the exchange-correlation Kohn–Sham potential with a statistical average of different orbital model potentials. Chem Phys Lett 302:199

    Article  CAS  Google Scholar 

  98. Grüning M, Gritsenko OV, van Gisbergen SJA, Baerends EJ (2001) Shape corrections to exchange-correlation Kohn-Sham potentials by gradient-regulated seamless connection of model potentials for inner and outer region. J Chem Phys 114:652

    Article  Google Scholar 

  99. Filatov M (2013) Assessment of density functional methods for obtaining geometries at conical intersections in organic molecules. J Chem Theory Comput 9:4526

    Article  CAS  Google Scholar 

  100. Ziegler T (1983) Extension of the statistical energy expression to multi-determinantal wave functions. In: Dahl JP, Avery J (eds) Density functional theory of atoms, molecules and solids. Plenum, New York

    Google Scholar 

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Acknowledgement

T.Z. would like to thank the Canadian government for a Canada research chair in theoretical inorganic chemistry and NSERC for financial support.

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Authors and Affiliations

  1. Department of Chemistry, University of Calgary, Calgary, AB, Canada, T2N1N4

    Tom Ziegler, Mykhaylo Krykunov, Issaka Seidu & Young Choon Park

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  1. Tom Ziegler
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Correspondence to Tom Ziegler .

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Editors and Affiliations

  1. Institut de Chimie Radicalaire, Université d'Aix-Marseille, Marseille, France

    Nicolas Ferré

  2. Inst. für Physikalische und Theoretische Chemie, Universität Bonn, Bonn, Germany

    Michael Filatov

  3. Institut für Physikalische und Theoretische Chemie, Goethe-Universität Frankfurt am Main, Frankfurt, Germany

    Miquel Huix-Rotllant

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Ziegler, T., Krykunov, M., Seidu, I., Park, Y.C. (2014). Constricted Variational Density Functional Theory Approach to the Description of Excited States. In: Ferré, N., Filatov, M., Huix-Rotllant, M. (eds) Density-Functional Methods for Excited States. Topics in Current Chemistry, vol 368. Springer, Cham. https://doi.org/10.1007/128_2014_611

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