23. Marques M, Maitra N, Noguiera F, Gross EKU, Rubio A (2011) Fundamentals of timedependent density-functional theory, Lecture Notes in Physics, vol 837. Springer, Berlin
24. Ullrich CA (2012) Time-dependent density-functional theory: concepts and applications.
Oxford University Press, Oxford
25. Runge E, Gross EKU (1984) Density functional theory for time-dependent systems. Phys Rev
Lett 52:997
26. van Leeuwen R (1999) Mapping from densities to potentials in time-dependent densityfunctional theory. Phys Rev Lett 82:3863
27. Maitra NT, Todorov TN, Woodward C, Burke K (2010) Density-potential mapping in timedependent density-functional theory. Phys Rev A 81:042525
28. Ruggenthaler M, van Leeuwen R (2011) Global fixed-point proof of time-dependent densityfunctional theory. Europhys Lett 95:13001
29. Ruggenthaler M, Glesbertz KJH, Penz M, van Leeuwen R (2012) Density-potential mappings
in quantum dynamics. Phys Rev A 85:052504
30. Ruggenthaler M, Nielsen SEB, van Leeuwen R (2013) Analytic density functionals with
initial-state dependence. Phys Rev A 88:022512
31. Vignale G (2008) Real-time resolution of the causality paradox of time-dependent densityfunctional theory. Phys Rev A 77(6):1. doi:10.1103/PhysRevA.77.062511
32. Messud J, Dinh PM, Reinhard P, Suraud E (2011) The generalized SIC-OEP formalism and
the generalized SIC-Slater approximation (stationary and time-dependent cases). Ann Phys
(Berlin) 523:270
33. Rajagopal AK (1996) Time-dependent variational principle and the effective action in
density-functional theory and Berrys phase. Phys Rev A 54:3916
34. van Leeuwen R (1998) Causality and symmetry in time-dependent density-functional theory.
Phys Rev Lett 80:1280
35. van Leeuwen R (2001) Key concepts in time-dependent density-functional theory. Int J Mod
Phys 15:1969
36. Mukamel S (2005) Generalized time-dependent density-functional-theory response functions
for spontaneous density fluctuations and nonlinear response: resolving the causality paradox.
Phys Rev A 024503
37. Mosquera MA (2013) Action formalism in time-dependent density-functional theory.
Phys Rev B 88:022515
38. Casida ME (1995) Time-dependent density-functional response theory for molecules. In:
Chong DP (ed) Recent advances in density functional methods, Part I. World Scientific,
Singapore, p 155
39. Casida ME (1996) Time-dependent density functional response theory of molecular systems:
theory, computational methods, and functionals. In: Seminario J (ed) Recent developments
and applications of modern density functional theory. Elsevier, Amsterdam, p 391
40. L€ owdin PO (1964) Studies in perturbation theory. Part VI. Contraction of secular equations.
J Mol Spectr 14:112
41. Onida G, Reining L, Rubio A (2002) Electronic excitations: density-functional versus manybody Greens-function approaches. Rev Mod Phys 74:601
42. Reining L, Olevano V, Rubio A, Onida G (2002) Excitonic effects in solids described by
time-dependent density-functional theory. Phys Rev Lett 88:066404
43. Sottile F, Olevano V, Reining L (2003) Parameter-free calculation of response functions in
time-dependent density-functional theory. Phys Rev Lett 91:056402
44. Marini A, Sole RD, Rubio A (2003) Bound excitons in time-dependent density-functional
theory: optical and energy-loss spectra. Phys Rev Lett 91:256402
45. Stubner R, Tokatly IV, Pankratov O (2004) Excitonic effects in time-dependent densityfunctional theory: an analytically solvable model. Phys Rev B 70:245119
46. von Barth U, Dahlen NE, van Leeuwen R, Stefanucci G (2005) Conserving approximations in
time-dependent density functional theory. Phys Rev B 72:235109
MBPT Insights About and Corrections to TD-DFT
57
24. Ullrich CA (2012) Time-dependent density-functional theory: concepts and applications.
Oxford University Press, Oxford
25. Runge E, Gross EKU (1984) Density functional theory for time-dependent systems. Phys Rev
Lett 52:997
26. van Leeuwen R (1999) Mapping from densities to potentials in time-dependent densityfunctional theory. Phys Rev Lett 82:3863
27. Maitra NT, Todorov TN, Woodward C, Burke K (2010) Density-potential mapping in timedependent density-functional theory. Phys Rev A 81:042525
28. Ruggenthaler M, van Leeuwen R (2011) Global fixed-point proof of time-dependent densityfunctional theory. Europhys Lett 95:13001
29. Ruggenthaler M, Glesbertz KJH, Penz M, van Leeuwen R (2012) Density-potential mappings
in quantum dynamics. Phys Rev A 85:052504
30. Ruggenthaler M, Nielsen SEB, van Leeuwen R (2013) Analytic density functionals with
initial-state dependence. Phys Rev A 88:022512
31. Vignale G (2008) Real-time resolution of the causality paradox of time-dependent densityfunctional theory. Phys Rev A 77(6):1. doi:10.1103/PhysRevA.77.062511
32. Messud J, Dinh PM, Reinhard P, Suraud E (2011) The generalized SIC-OEP formalism and
the generalized SIC-Slater approximation (stationary and time-dependent cases). Ann Phys
(Berlin) 523:270
33. Rajagopal AK (1996) Time-dependent variational principle and the effective action in
density-functional theory and Berrys phase. Phys Rev A 54:3916
34. van Leeuwen R (1998) Causality and symmetry in time-dependent density-functional theory.
Phys Rev Lett 80:1280
35. van Leeuwen R (2001) Key concepts in time-dependent density-functional theory. Int J Mod
Phys 15:1969
36. Mukamel S (2005) Generalized time-dependent density-functional-theory response functions
for spontaneous density fluctuations and nonlinear response: resolving the causality paradox.
Phys Rev A 024503
37. Mosquera MA (2013) Action formalism in time-dependent density-functional theory.
Phys Rev B 88:022515
38. Casida ME (1995) Time-dependent density-functional response theory for molecules. In:
Chong DP (ed) Recent advances in density functional methods, Part I. World Scientific,
Singapore, p 155
39. Casida ME (1996) Time-dependent density functional response theory of molecular systems:
theory, computational methods, and functionals. In: Seminario J (ed) Recent developments
and applications of modern density functional theory. Elsevier, Amsterdam, p 391
40. L€ owdin PO (1964) Studies in perturbation theory. Part VI. Contraction of secular equations.
J Mol Spectr 14:112
41. Onida G, Reining L, Rubio A (2002) Electronic excitations: density-functional versus manybody Greens-function approaches. Rev Mod Phys 74:601
42. Reining L, Olevano V, Rubio A, Onida G (2002) Excitonic effects in solids described by
time-dependent density-functional theory. Phys Rev Lett 88:066404
43. Sottile F, Olevano V, Reining L (2003) Parameter-free calculation of response functions in
time-dependent density-functional theory. Phys Rev Lett 91:056402
44. Marini A, Sole RD, Rubio A (2003) Bound excitons in time-dependent density-functional
theory: optical and energy-loss spectra. Phys Rev Lett 91:256402
45. Stubner R, Tokatly IV, Pankratov O (2004) Excitonic effects in time-dependent densityfunctional theory: an analytically solvable model. Phys Rev B 70:245119
46. von Barth U, Dahlen NE, van Leeuwen R, Stefanucci G (2005) Conserving approximations in
time-dependent density functional theory. Phys Rev B 72:235109
MBPT Insights About and Corrections to TD-DFT
57