This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note that besides functional approximations, the KS-DFT empty states need to be corrected for the derivative discontinuity of the potential upon infinitesimal electron addition. Such derivative discontinuity is usually neglected by approximate functionals which also tend to downshift further the orbital energies of empty states.
- 2.
Otherwise, an infinitesimal transfer of charge δf > 0 from the highest occupied orbital to a state of energy ε i < ε ℋ would decrease the total energy by an amount (ε i – ε ℋ)δf < 0.
- 3.
Reference [49] also highlights the limitations of conventional DFT approximations in capturing static correlation in spin-degenerate systems (the H2 dissociation problem). Self-interaction errors arising from fractional occupations are nevertheless distinct from static correlation errors arising from fractional spins. In this work, only the self-interaction problem is addressed.
- 4.
Koopmans’ theorem has been originally proven for the HF method considering frozen orbitals [109]. Here we refer to this case as the restricted Koopmans theorem. The generalized version of the theorem has been introduced later [110] in order to include orbital relaxation. We note in passing that the generalized Koopmans theorem is a property of the exact many-body Green’s function G. The performance of GW approximations in this regard has been recently discussed by Bruneval [48]. In fact, when adopting the Lehmann representation, the poles of G, playing the role of (Dyson) orbital energies, are exactly given by total energy differences corresponding to many-body states with different number of particles (with one electron added or removed).
- 5.
One could rely on other definitions to measure the lack of Koopmans compliance. In particular, (30) has recently been exploited in [64] within the frozen orbital approximation. The comparative assessment of these closely related definitions is beyond the scope of this introductory review and will be discussed in detail elsewhere.
- 6.
It is very instructive to note that the linear-response DFT + U method of Cococcioni and de Gironcoli [57] is obtained from a similar expansion to evaluate the U parameters for the N I preselected orbitals χ Ii of the Ith atom. In fact, in its simplest form, the nonlinearity correction reads
$$ {E}_U\left[{f}_1,{f}_2,\dots, {\varphi}_1,{\varphi}_2,\dots \right]={\displaystyle \sum_{I=1}^{N_{\mathrm{atom}}}{\displaystyle \sum_{i=1}^{N_I}{\scriptscriptstyle \frac{U_{Ii}}{2}}{n}_{Ii}\left(1-{n}_{Ii}\right)}} $$with
$$ {U}_{Ii}={\displaystyle \int {d}^3\mathbf{r}{d}^3{\mathbf{r}}^{\mathbf{\prime}}{d}^3{\mathbf{r}}^{\mathbf{{\prime\prime}}}\left|{\chi}_{Ii}\right|{}^2\left(\mathbf{r}\right){\tilde{\varepsilon}}^{-1}\left(\mathbf{r},{\mathbf{r}}^{\mathbf{\prime}}\right){f}_{\mathrm{Hxc}}\left({\mathbf{r}}^{\mathbf{\prime}},{\mathbf{r}}^{\mathbf{{\prime\prime}}}\right)\left|{\chi}_{Ii}\right|{}^2\left({\mathbf{r}}^{\mathbf{{\prime\prime}}}\right)}\kern1em \mathrm{and}\kern1em {n}_{Ii}={\displaystyle \sum_{j=1}^{+\infty }{f}_j\left|\left\langle {\chi}_{Ii}\Big|{\varphi}_j\right\rangle \right|{}^2.} $$The spirit of the Koopmans-compliant correction is identical with the advantage of not requiring preselected atomic orbitals.
- 7.
We note that in Figs. 2 and 4 that we have used the Koopmans-compliant functional defined in (40), where the α screening coefficient has been included. We have adopted the same value for α in both figures. If no α were used [(35)], the K panel in Fig. 2 would show a flat curve, while that of Fig. 4 would display a negative slope as the HF method.
- 8.
For instance, one could compute the average dielectric screening coefficient related to the orbital ψ i through
$$ {\alpha}_i=\frac{{\displaystyle \int {d}^3\mathbf{r}{d}^3{\mathbf{r}}^{\mathbf{\prime}}{d}^3{\mathbf{r}}^{\mathbf{{\prime\prime}}}\left|{\psi}_i\right|{}^2\left(\mathbf{r}\right){\tilde{\varepsilon}}^{-1}\left(\mathbf{r},{\mathbf{r}}^{\mathbf{\prime}}\right){f}_{\mathrm{Hxc}}\left({\mathbf{r}}^{\mathbf{\prime}},{\mathbf{r}}^{\mathbf{{\prime\prime}}}\right)\left|{\psi}_i\right|{}^2\left({\mathbf{r}}^{\mathbf{{\prime\prime}}}\right)}}{{\displaystyle \int {d}^3\mathbf{r}{d}^3{\mathbf{r}}^{\mathbf{\prime}}\left|{\psi}_i\right|{}^2\left(\mathbf{r}\right){f}_{\mathrm{Hxc}}\left(\mathbf{r},{\mathbf{r}}^{\mathbf{\prime}}\right)\left|{\psi}_i\right|{}^2\left({\mathbf{r}}^{\mathbf{\prime}}\right)}}+\cdots, $$where it is understood that each quantity that appears in the integrals must be calculated self-consistently.
- 9.
The same approach is adopted when computing virtual orbital levels and band gaps within, e.g., hybrid DFT and DFT+U approximations.
- 10.
A detailed sensitivity analysis of this approximation is presented in [62].
References
Allen SM, Thomas EL (1999) The structure of materials, MIT series in materials science and engineering. Wiley, New York
Martin RM (2008) Electronic structure: basic theory and practical methods. Cambridge University Press, Cambridge
Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136(3B):B864–B871. doi:10.1103/PhysRev.136.B864
Eschrig H (2003) The fundamentals of density functional theory. Edition am Gutenbergplatz, Leipzig
Lieb EH (1983) Density functionals for coulomb systems. Int J Quant Chem 24(3):243–277. doi:10.1002/qua.560240302
Baroni S, de Gironcoli S, Dal Corso A (2001) Phonons and related crystal properties from density-functional perturbation theory. Rev Mod Phys 73:515–562. doi:10.1103/RevModPhys.73.515
Payne MC, Arias TA, Joannopoulos JD (1992) Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev Mod Phys 64(4):1045–1097. doi:10.1103/RevModPhys.64.1045
Perdew JP, Levy M, Balduz JL (1982) Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys Rev Lett 49(23):1691–1694. doi:10.1103/PhysRevLett.49.1691
Chong DP, Gritsenko OV, Baerends EJ (2002) Interpretation of the Kohn Sham orbital energies as approximate vertical ionization potentials. J Chem Phys 116(5):1760. doi:10.1063/1.1430255
Casida M (1995) Generalization of the optimized-effective-potential model to include electron correlation – a variational derivation of the Sham–Schluter equation for the exact exchange-correlation potential. Phys Rev A 51(3):2005–2013
Casida M, Huix-Rotllant M (2012) Progress in time-dependent density-functional theory. Annu Rev Phys Chem 63(1):287–323. doi:10.1146/annurev-physchem-032511-143803
Runge E, Gross EKU (1984) Density-functional theory for time-dependent systems. Phys Rev Lett 52(12):997–1000. doi:10.1103/PhysRevLett.52.997
Onida G, Reining L, Rubio A (2002) Electronic excitations: density-functional versus many-body greens-function approaches. Rev Mod Phys 74(2):601–659. doi:10.1103/RevModPhys.74.601
Dreuw A, Weisman JL, Head-Gordon M (2003) Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange. J Chem Phys 119(6):2943. doi:10.1063/1.1590951
Himmetoglu B, Marchenko A, Dabo I, Cococcioni M (2012) Role of electronic localization in the phosphorescence of iridium sensitizing dyes. J Chem Phys 137(15):154309. doi:10.1063/1.4757286
Maitra NT (2005) Undoing static correlation: long-range charge transfer in time-dependent density-functional theory. J Chem Phys 122(23):234104. doi:10.1063/1.1924599
Tozer DJ (2003) Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn Sham theory. J Chem Phys 119(24):12697. doi:10.1063/1.1633756
Faleev S, van Schilfgaarde M, Kotani T (2004) All-electron self-consistent GW approximation: application to Si, MnO, and NiO. Phys Rev Lett 93(12):126406. doi:10.1103/PhysRevLett.93.126406
Godby R, Schlüter M, Sham L (1988) Self-energy operators and exchange-correlation potentials in semiconductors. Phys Rev B 37(17):10159–10175. doi:10.1103/PhysRevB.37.10159
Hedin L (1965) New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys Rev 139(3A):A796–A823. doi:10.1103/PhysRev.139.A796
Hybertsen M, Louie S (1986) Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys Rev B 34(8):5390–5413. doi:10.1103/PhysRevB.34.5390
van Schilfgaarde M, Kotani T, Faleev S (2006) Quasiparticle self-consistent GW theory. Phys Rev Lett 96(22):226402. doi:10.1103/PhysRevLett.96.226402
Zakharov O, Rubio A, Blase X, Cohen M, Louie S (1994) Quasiparticle band structures of six II-VI compounds: ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe. Phys Rev B 50(15):10780–10787. doi:10.1103/PhysRevB.50.10780
Albrecht S, Onida G, Reining L (1997) Ab initio calculation of the quasiparticle spectrum and excitonic effects in Li2O. Phys Rev B 55(16):10278–10281. doi:10.1103/PhysRevB.55.10278
Albrecht S, Reining L, Del Sole R, Onida G (1998) Ab initio calculation of excitonic effects in the optical spectra of semiconductors. Phys Rev Lett 80(20):4510–4513. doi:10.1103/PhysRevLett.80.4510
Rohlfing M, Louie S (1998) Excitonic effects and the optical absorption spectrum of hydrogenated Si clusters. Phys Rev Lett 80(15):3320–3323. doi:10.1103/PhysRevLett.80.3320
Tiago M, Northrup J, Louie S (2003) Ab initio calculation of the electronic and optical properties of solid pentacene. Phys Rev B 67(11):115212. doi:10.1103/PhysRevB.67.115212
Donnelly RA, Parr RG (1978) Elementary properties of an energy functional of the first-order reduced density matrix. J Chem Phys 69(10):4431. doi:10.1063/1.436433
Gilbert T (1975) Hohenberg–Kohn theorem for nonlocal external potentials. Phys Rev B 12(6):2111–2120. doi:10.1103/PhysRevB.12.2111
Lathiotakis NN, Sharma S, Helbig N, Dewhurst JK, Marques MAL, Eich F, Baldsiefen T, Zacarias A, Gross EKU (2010) Discontinuities of the chemical potential in reduced density matrix functional theory. Z Phys Chem 224(3–4):467–480. doi:10.1524/zpch.2010.6118
Sharma S, Dewhurst JK, Shallcross S, Gross EKU (2013) Spectral density and metal-insulator phase transition in Mott insulators within reduced density matrix functional theory. Phys Rev Lett 110(11):116403. doi:10.1103/PhysRevLett.110.116403
Burke K (2012) Perspective on density functional theory. J Chem Phys 136(15):150901. doi:10.1063/1.4704546
Becke AD (1993) A new mixing of Hartree–Fock and local density-functional theories. J Chem Phys 98(2):1372. doi:10.1063/1.464304
Livshits E, Baer R (2007) A well-tempered density functional theory of electrons in molecules. Phys Chem Chem Phys 9(23):2932. doi:10.1039/b617919c
Kümmel S, Kronik L (2008) Orbital-dependent density functional: theory and applications. Rev Mod Phys 80(1):3–60. doi:10.1103/RevModPhys.80.3
Baer R, Livshits E, Salzner U (2010) Tuned range-separated hybrids in density functional theory. Annu Rev Phys Chem 61(1):85–109. doi:10.1146/annurev.physchem.012809.103321
Refaely-Abramson S, Baer R, Kronik L (2011) Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional. Phys Rev B 84(7):075144. doi:10.1103/PhysRevB.84.075144
Cococcioni M (2002) A LDA + U study of selected iron compounds. PhD thesis, SISSA, Trieste http://www.sissa.it/cm
Cococcioni M, Gironcoli SD (2005) Linear response approach to the calculation of the effective interaction parameters in the lda + u method. Phys Rev B 71(3):035105. doi:10.1103/PhysRevB.71.035105
Kulik H, Cococcioni M, Scherlis D, Marzari N (2006) Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach. Phys Rev Lett 97(10):103001. doi:10.1103/PhysRevLett.97.103001
Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):A1133–A1138. doi:10.1103/PhysRev.140.A1133
Janak J (1978) Proof that ∂E/∂n i = ε i in density-functional theory. Phys Rev B 18(12):7165–7168. doi:10.1103/PhysRevB.18.7165
Cancès E (2001) Self-consistent field algorithms for Kohn Sham models with fractional occupation numbers. J Chem Phys 114(24):10616. doi:10.1063/1.1373430
Marzari N, Vanderbilt D, Payne M (1997) Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators. Phys Rev Lett 79(7):1337–1340. doi:10.1103/PhysRevLett.79.1337
Cancès E, Le Bris C (2000) Can we outperform the DIIS approach for electronic structure calculations? Int J Quant Chem 79(2):8290
Yang W, Zhang Y, Ayers PW (2000) Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett 84(22):5172
Mori-Sánchez P, Cohen A, Yang W (2006) Many-electron self-interaction error in approximate density functionals. J Chem Phys 125:201102
Bruneval F (2009) GW approximation of the many-body problem and changes in the particle number. Phys Rev Lett 103(17):176403. doi:10.1103/PhysRevLett.103.176403
Cohen AJ, Mori-Sanchez P, Yang W (2008) Insights into current limitations of density functional theory. Science 321(5890):792–794. doi:10.1126/science.1158722
Mori-Sánchez P, Cohen A, Yang W (2008) Localization and delocalization errors in density functional theory and implications for band-gap prediction. Phys Rev Lett 100(14):146401. doi:10.1103/PhysRevLett.100.146401
Mori-Sánchez P, Cohen AJ, Yang W (2006) Many-electron self-interaction error in approximate density functionals. J Chem Phys 125(20):201102. doi:10.1063/1.2403848
Ruzsinszky A, Perdew JP, Csonka GI, Vydrov OA, Scuseria GE (2006) Spurious fractional charge on dissociated atoms: pervasive and resilient self-interaction error of common density functionals. J Chem Phys 125(19):194112. doi:10.1063/1.2387954
Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York
Ayers PW, Morrison RC, Parr RG (2005) Fermi–Amaldi model for exchange-correlation: atomic excitation energies from orbital energy differences. Mol Phys 103(15–16):2061–2072. doi:10.1080/00268970500130183
Perdew J (1990) Size-consistency, self-interaction correction, and derivative discontinuity in density functional theory. In: Advances in quantum chemistry, vol 21. Elsevier, San Diego, California. pp 113–134
Kowalczyk T, Yost SR, Voorhis TV (2011) Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes. J Chem Phys 134(5):054128. doi:10.1063/1.3530801
Cococcioni M, de Gironcoli S (2005) Linear response approach to the calculation of the effective interaction parameters in the LDA + U method. Phys Rev B 71(3):035105. doi:10.1103/PhysRevB.71.035105
Cohen AJ, Mori-Sánchez P, Yang W (2012) Challenges for density functional theory. Chem Rev 112(1):289–320. doi:10.1021/cr200107z
Hachmann J, Olivares-Amaya R, Atahan-Evrenk S, Amador-Bedolla C, Sanchez-Carrera RS, Gold-Parker A, Vogt L, Brockway AM, Aspuru-Guzik A (2011) The Harvard clean energy project: large-scale computational screening and design of organic photovoltaics on the world community grid. J Phys Chem Lett 2(17):2241–2251. doi:10.1021/jz200866s
Lany S, Zunger A (2010) Generalized Koopmans density functional calculations reveal the deep acceptor state of NO in ZnO. Phys Rev B 81(20):205209. doi:10.1103/PhysRevB.81.205209
Salzner U, Baer R (2009) Koopmans springs to life. J Chem Phys 131(23):231101. doi:10.1063/1.3269030
Dabo I, Ferretti A, Park CH, Poilvert N, Li Y, Cococcioni M, Marzari N (2013) Donor and acceptor levels of organic photovoltaic compounds from first principles. Phys Chem Chem Phys 15:685. doi:10.1039/c2cp43491a
Dabo I, Ferretti A, Poilvert N, Li Y, Marzari N, Cococcioni M (2010) Koopmans condition for density-functional theory. Phys Rev B 82(11):115121. doi:10.1103/PhysRevB.82.115121
Kraisler E, Kronik L (2013) Piecewise linearity of approximate density functionals revisited: implications for frontier orbital energies. Phys Rev Lett 110(12):126403. doi:10.1103/PhysRevLett.110.126403
Perdew JP, Zunger A (1981) Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B 23(10):5048–5079. doi:10.1103/PhysRevB.23.5048
Körzdörfer T, Kümmel S, Mundt M (2008) Self-interaction correction and the optimized effective potential. J Chem Phys 129(1):014110. doi:10.1063/1.2944272
Krieger J, Li Y, Iafrate G (1992) Construction and application of an accurate local spin-polarized Kohn–Sham potential with integer discontinuity: exchange-only theory. Phys Rev A 45(1):101–126. doi:10.1103/PhysRevA.45.101
Gatti M, Olevano V, Reining L, Tokatly IV (2007) Transforming nonlocality into a frequency dependence: a shortcut to spectroscopy. Phys Rev Lett 99(5):057401
Ferretti A, Cococcioni M, Marzari N (2013) Submitted
Cohen AJ, Mori-Sanchez P, Yang W (2007) Development of exchange-correlation functionals with minimal many-electron self-interaction error. J Chem Phys 126(19):191109. doi:10.1063/1.2741248
Pederson M, Heaton R, Lin C (1984) Local density Hartree–Fock theory of electronic states of molecules with self interaction correction. J Chem Phys 80:1972
Stengel M, Spaldin N (2008) Self-interaction correction with Wannier functions. Phys Rev B 77(15):155106
Marzari N, Vanderbilt D (1997) Maximally localized generalized Wannier functions for composite energy bands. Phys Rev B 56(20):12847–12865
Wannier GH (1937) The structure of electronic excitation levels in insulation crystals. Phys Rev 52:191–197
Messud J, Dinh P, Reinhard PG, Suraud E (2009) On the exact treatment of time-dependent self-interaction correction. Ann Phys 324:955–976
Vydrov O, Scuseria G, Perdew J (2007) Tests of functionals for systems with fractional electron number. J Chem Phys 126:154109
Körzdörfer T (2011) On the relation between orbital-localization and self-interaction errors in the density functional theory treatment of organic semiconductors. J Chem Phys 134:094111
Chan M, Ceder G (2010) Efficient band gap prediction for solids. Phys Rev Lett 105(19):196403. doi:10.1103/PhysRevLett.105.196403
Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Corso AD, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) Quantum espresso: a modular and open-source software project for quantum simulations of materials. J Phys Condens Mat 21(39):395502
Li Y, Dabo I (2011) Electronic levels and electrical response of periodic molecular structures from plane-wave orbital-dependent calculations. Phys Rev B 84(15):155127
Perdew J, Levy M (1983) Physical content of the exact Kohn–Sham orbital energies - band-gaps and derivative discontinuities. Phys Rev Lett 51(20):1884–1887
Perdew J, Levy M (1997) Comment on “significance of the highest occupied Kohn–Sham eigenvalue”. Phys Rev B 56(24):16021–16028
Blase X, Attaccalite C, Olevano V (2011) First-principles GW calculations for fullerenes, porphyrins, phthalocyanine, and other molecules of interest for organic photovoltaic applications. Phys Rev B 83(11):115103. doi:10.1103/PhysRevB.83.115103
Tiago ML, Kent PRC, Hood RQ, Reboredo FA (2008) Neutral and charged excitations in carbon fullerenes from first-principles many-body theories. J Chem Phys 129(8):084311
Foerster D, Koval P, Sánchez-Portal D (2011) An O (N3) implementation of Hedin’s GW approximation for molecules. J Chem Phys 135:074105
Pines D (1963) Elementary excitations in solids. W.A. Benjamin, New York
Pines D, Nozières P (1989) The theory of quantum liquids. Addison-Wesley, New York
Onida G, Reining L, Rubio A (2002) Electronic excitations: density-functional versus many-body Green’s-function approaches. Rev Mod Phys 74(2):601–659
Ferretti A, Mallia G, Martin-Samos L, Bussi G, Ruini A, Montanari B, Harrison N (2012) Ab initio complex band structure of conjugated polymers: effects of hybrid density functional theory and GW schemes. Phys Rev B 85(23):235105. doi:10.1103/PhysRevB.85.235105
Curtiss L, Raghavachari K, Redfern P, Pople J (1997) Assessment of gaussian-2 and density functional theories for the computation of enthalpies of formation. J Chem Phys 106(3):1063–1079
National Institute of Standards and Technology (NIST) (2013). Computational chemistry comparison and benchmark database, http://cccbdb.nist.gov
Kadantsev ES, Stott MJ, Rubio A (2006) Electronic structure and excitations in oligoacenes from ab initio calculations. J Chem Phys 124(13):134901
Piancastelli M, Kelly M, Chang Y, McKinley J, Margaritondo G (1987) Benzene adsorption on low-temperature silicon: a synchrotron-radiation photoemission study of valence and core states. Phys Rev B 35(17):9218–9221. doi:10.1103/PhysRevB.35.9218
Trofimov AB, Zaitseva IL, Moskovskaya TE, Vitkovskaya NM (2008) Theoretical investigation of photoelectron spectra of furan, pyrrole, thiophene, and selenole. Chem Heterocycl Comp 44(9):1101–1112. doi:10.1007/s10593-008-0159-5
Coropceanu V, Malagoli M, da Silva D, Gruhn N, Bill T, Bredas J (2002) Hole- and electron-vibrational couplings in oligoacene crystals: intramolecular contributions. Phys Rev Lett 89(27):275503. doi:10.1103/PhysRevLett.89.275503
CRC (2009) CRC handbook of chemistry and physics. CRC, Boca Raton
Kramida A, Ralchenko Y, Reader J, NIST ASD Team (2013) NIST atomic spectra database
Mehlhorn W, Breuckmann B, Hausamann D (1977) Electron spectra of free metal atoms. Phys Scrip 16(5–6):177
Shirley D, Martin R, Kowalczyk S, McFeely F, Ley L (1977) Core-electron binding energies of the first thirty elements. Phys Rev B 15(2):544
Banna M, Wallbank B, Frost D, McDowell C, Perera J (1978) Free atom core binding energies from X-ray photoelectron spectroscopy. II. Na, K, Rb, Cs, and Mg. J Chem Phys 68:5459
Perera J, Frost D, McDowell C, Ewig C, Key R, Banna M (1982) Atomic and ionic core binding energies of selected levels in the alkaline earths from X-ray photoelectron spectroscopy and Dirac–Fock calculations. J Chem Phys 77:3308
Chen H, Pan Y, Groh S, Hagan T, Ridge D (1991) Gas-phase charge-transfer reactions and electron affinities of macrocyclic, anionic nickel complexes: Ni (salen), Ni (tetraphenylporphyrin), and derivatives. J Am Chem Soc 113(7):2766–2767
Schiedt J, Weinkauf R (1997) Photodetachment photoelectron spectroscopy of mass selected anions: anthracene and the anthracene-H2O cluster. Chem Phys Lett 266(1):201–205
Crocker L, Wang T, Kebarle P (1993) Electron affinities of some polycyclic aromatic hydrocarbons, obtained from electron-transfer equilibria. J Am Chem Soc 115(17):7818–7822. doi:10.1021/ja00070a030
Prinzbach H, Weller A, Landenberger P, Wahl F, Worth J, Scott L, Gelmont M, Olevano D, von Issendorff B (2000) Gas-phase production and photoelectron spectroscopy of the smallest fullerene, C-20. Nature 407(6800):60–63
Yang S, Pettiette C, Conceicao J, Cheshnovsky O, Smalley R (1987) Ups of buckminsterfullerene and other large clusters of carbon. Chem Phys Lett 139(3):233–238
Wang XB, Ding CF, Wang LS (1999) High resolution photoelectron spectroscopy of C60. J Chem Phys 110:8217–8220
Wang XB, Woo HK, Huang X, Kappes M, Wang LS (2006) Direct experimental probe of the on-site coulomb repulsion in the doubly charged fullerene anion c702-. Phys Rev Lett 96(14):143002. doi:10.1103/PhysRevLett.96.143002
Zsabo A, Ostlund NS (1996) Modern quantum chemistry: introduction to advanced electronic structure theory. Dover, New York
Phillips J (1961) Generalized Koopmans theorem. Phys Rev 123(2):420
Acknowledgements
The authors are indebted to M. Cococcioni, N. Poilvert, G. Borghi, N. L. Nguyen, C.-H. Park, M. Marqués, E. K. U. Gross, S. de Gironcoli, and S. Baroni for valuable discussions and relevant suggestions. ID acknowledges partial support from the French National Research Agency through Grant ANR 12-BS04-0001 PANELS (Photovoltaics from Ab-initio Novel Electronic-structure Simulations). AF acknowledges partial support from Italian MIUR through Grant FIRB-RBFR08FOAL_001.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dabo, I., Ferretti, A., Marzari, N. (2014). Piecewise Linearity and Spectroscopic Properties from Koopmans-Compliant Functionals. In: Di Valentin, C., Botti, S., Cococcioni, M. (eds) First Principles Approaches to Spectroscopic Properties of Complex Materials. Topics in Current Chemistry, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/128_2013_504
Download citation
DOI: https://doi.org/10.1007/128_2013_504
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-55067-6
Online ISBN: 978-3-642-55068-3
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)