P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.80, issue.3B, pp.864-871, 1964.
DOI : 10.1088/0370-1328/80/5/307

W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.119, issue.4A, pp.1133-1138, 1965.
DOI : 10.1103/PhysRev.119.1153

T. Deutsch and L. Genovese, Wavelets for electronic structure calculations, ??cole th??matique de la Soci??t?? Fran??aise de la Neutronique, vol.12, pp.33-76, 2011.
DOI : 10.1051/sfn/201112004

URL : http://www.neutron-sciences.org/articles/sfn/pdf/2011/01/sfn201112004.pdf

L. Bhaarathi-natarajan, M. E. Genovese, T. Casida, O. N. Deutsch, C. Burchak et al., Wavelet-based linear-response time-dependent density-functional theory, Chemical Physics, vol.402, pp.29-40, 2012.
DOI : 10.1016/j.chemphys.2012.03.024

J. Brabec, L. Lin, M. Shao, N. Govind, C. Yang et al., Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT, Journal of Chemical Theory and Computation, vol.11, issue.11, pp.5197-5208, 2015.
DOI : 10.1021/acs.jctc.5b00887

G. Gamow, Zur Quantentheorie des Atomkernes, Zeitschrift f???r Physik, vol.51, issue.3-4, pp.204-212, 1928.
DOI : 10.1007/BF01343196

A. J. Siegert, On the Derivation of the Dispersion Formula for Nuclear Reactions, Physical Review, vol.166, issue.8, pp.750-752, 1939.
DOI : 10.1098/rspa.1938.0093

R. Santra and L. S. Cederbaum, Non-Hermitian electronic theory and applications to clusters, Physics Reports, vol.368, issue.1, pp.1-117, 2002.
DOI : 10.1016/S0370-1573(02)00143-6

T. Berggren and P. Lind, Resonant state expansion of the resolvent, Physical Review C, vol.11, issue.2, pp.768-778, 1993.
DOI : 10.1016/0029-5582(59)90293-7

P. Lind, Completeness relations and resonant state expansions, Physical Review C, vol.39, issue.5, pp.1903-1920, 1993.
DOI : 10.1103/PhysRevC.39.1020

P. Lind, R. J. Liotta, T. Maglione, and . Vertse, Resonant state expansions of the continuum. Zeitschrift für Physik A Hadrons and Nuclei, pp.231-236, 1994.

D. R. Hartree, The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods, Mathematical Proceedings of the Cambridge Philosophical Society, vol.24, issue.01, pp.89-110, 1928.
DOI : 10.1017/S0305004100011919

V. Fock, Näherungsmethode zur lösung des quantenmechanischen mehrkörperproblems . Zeitschrift für Physik, pp.126-148, 1930.
DOI : 10.1007/bf01340294

J. C. Slater, Note on Hartree's Method, Physical Review, vol.35, issue.2, pp.210-211, 1930.
DOI : 10.1103/PhysRev.35.210.2

P. John, K. Perdew, and . Schmidt, Jacob's ladder of density functional approximations for the exchange-correlation energy, AIP Conference Proceedings, vol.577, issue.1, pp.1-20, 2001.

J. P. Perdew, A. Ruzsinszky, J. Tao, N. Viktor, G. E. Staroverov et al., Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits, The Journal of Chemical Physics, vol.23, issue.6, 2005.
DOI : 10.1002/jcc.20078

L. Kronik, T. Stein, S. Refaely-abramson, and R. Baer, Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals, Journal of Chemical Theory and Computation, vol.8, issue.5, pp.1515-1531, 2012.
DOI : 10.1021/ct2009363

R. M. Martin, Electronic structure : basic theory and practical methods Description de l'éditeur http, 2004.
DOI : 10.1017/CBO9780511805769

E. Runge and E. K. Gross, Density-Functional Theory for Time-Dependent Systems, Physical Review Letters, vol.140, issue.12, pp.997-1000, 1984.
DOI : 10.1103/PhysRev.140.A1133

J. Theilhaber, Ab initio simulations of sodium using time-dependent densityfunctional theory [22] So Hirata and Martin Head-Gordon. Time-dependent density functional theory within the Tamm?Dancoo approximation, Physical Review B Chemical Physics Letters, vol.46, issue.314, pp.129903-4291, 1992.

S. H. Vosko, L. Wilk, and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Canadian Journal of Physics, vol.58, issue.8, pp.1200-1211, 1980.
DOI : 10.1139/p80-159

M. Valiev, J. Eric, N. Bylaska, K. Govind, . Kowalski et al., NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations, Computer Physics Communications, vol.181, issue.9, pp.1811477-1489, 2010.
DOI : 10.1016/j.cpc.2010.04.018

K. P. Huber and G. Herzberg, IV, Constants of Diatomic Molecules, Molecular Spectra and Molecular Structure, 1979.

J. Oddershede, N. E. Grüner, and G. H. Diercksen, Comparison between equation of motion and polarization propagator calculations, Chemical Physics, vol.97, issue.2-3, pp.303-310, 1985.
DOI : 10.1016/0301-0104(85)87039-7

C. Jamorski, M. E. Casida, and D. R. Salahub, as a case study, The Journal of Chemical Physics, vol.69, issue.13, pp.5134-5147, 1996.
DOI : 10.1063/1.460038

R. Bauernschmitt and R. Ahlrichs, Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory, Chemical Physics Letters, vol.256, issue.4-5, pp.454-464, 1996.
DOI : 10.1016/0009-2614(96)00440-X

E. Mark, C. Casida, K. C. Jamorski, D. R. Casida, and . Salahub, Molecular excitation energies to high-lying bound states from time-dependent densityfunctional response theory : Characterization and correction of thetime-dependent local density approximation ionization threshold, The Journal of Chemical Physics, vol.108, issue.11, pp.4439-4449, 1998.

T. Grabo, M. Petersilka, and E. K. Gross, Molecular excitation energies from timedependent density functional theory, Journal of Molecular Structure : THEOCHEM, vol.501, pp.353-367, 2000.
DOI : 10.1016/s0166-1280(99)00445-5

F. Furche and R. Ahlrichs, Adiabatic time-dependent density functional methods for excited state properties, The Journal of Chemical Physics, vol.100, issue.16, pp.7433-7447, 2002.
DOI : 10.1139/v93-199

Y. Tawada, T. Tsuneda, S. Yanagisawa, T. Yanai, and K. Hirao, A long-range-corrected time-dependent density functional theory, The Journal of Chemical Physics, vol.120, issue.18, pp.8425-8433, 2004.
DOI : 10.1021/ic00277a030

J. G. Michael, P. Peach, T. Benneld, D. J. Helgaker, and . Tozer, Excitation energies in density functional theory : an evaluation and a diagnostic test, The Journal of chemical physics, vol.128, issue.4, p.44118, 2008.

P. Elliott, F. Furche, and K. Burke, Excited States from Time-Dependent Density Functional Theory, Reviews in computational chemistry, vol.48, issue.65, p.91, 2009.
DOI : 10.1007/BF01351576

URL : http://arxiv.org/abs/cond-mat/0703590

S. Egon, P. Nielsen, J. Jörgensen, and . Oddershede, Transition moments and dynamic polarizabilities in a second order polarization propagator approach, The Journal of Chemical Physics, vol.73, issue.12, pp.6238-6246, 1980.

J. W. Cooley, An improved eigenvalue corrector formula for solving the Schrödinger equation for central elds [38] Nimrod Moiseyev. Non-Hermitian quantum mechanics, Mathematics of Computation, vol.15, issue.76, pp.363-374, 1961.

T. Berggren, On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes, Nuclear Physics A, vol.109, issue.2, pp.265-287, 1968.
DOI : 10.1016/0375-9474(68)90593-9

T. Berggren, Completeness relations, Mittag-Leffler expansions and the perturbation theory of resonant states, Nuclear Physics A, vol.389, issue.2, pp.261-284, 1982.
DOI : 10.1016/0375-9474(82)90519-X

W. Romo, Resonant-state perturbation formalisims, Nuclear Physics A, vol.398, issue.3, pp.525-543, 1983.
DOI : 10.1016/0375-9474(83)90300-7

T. Vertse, R. Curutchet, and . Liotta, Approximate treatment of the continuum, Physical Review C, vol.32, issue.6, pp.2605-2616, 1990.
DOI : 10.1146/annurev.ns.32.120182.000433

T. Berggren, Expectation value of an operator in a resonant state, Physics Letters B, vol.373, issue.1-3, pp.1-4, 1996.
DOI : 10.1016/0370-2693(96)00132-3

G. Jolicard and E. J. Austin, Optical potential stabilisation method for predicting resonance levels, Chemical Physics Letters, vol.121, issue.1-2, pp.106-110, 1985.
DOI : 10.1016/0009-2614(85)87164-5

U. Riss and H. Meyer, Calculation of resonance energies and widths using the complex absorbing potential method, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.26, issue.23, p.4503, 1993.
DOI : 10.1088/0953-4075/26/23/021

J. Aguilar and J. M. Combes, A class of analytic perturbations for one-body Schr??dinger Hamiltonians, Communications in Mathematical Physics, vol.10, issue.5, pp.269-279, 1971.
DOI : 10.2307/1970331

E. Balslev and J. M. Combes, Spectral properties of many-body Schr??dinger operators with dilatation-analytic interactions, Communications in Mathematical Physics, vol.12, issue.5, pp.280-294, 1971.
DOI : 10.2307/1970331

B. Simon, The definition of molecular resonance curves by the method of exterior complex scaling, Physics Letters A, vol.71, issue.2-3, pp.211-214, 1979.
DOI : 10.1016/0375-9601(79)90165-8

N. Rom, N. Lipkin, and N. Moiseyev, Optical potentials by the complex coordinate method, Chemical Physics, vol.151, issue.2, pp.199-204, 1991.
DOI : 10.1016/0301-0104(91)80101-M

A. Cerioni, L. Genovese, I. Duchemin, and T. Deutsch, Accurate complex scaling of three dimensional numerical potentials, The Journal of Chemical Physics, vol.138, issue.20, p.2013
DOI : 10.1002/andp.201200062

L. Genovese, A. Cerioni, M. Morinière, and T. Deutsch, Identiication of resonant states via the generalized virial theorem. arXiv, 2015.

D. W. Sprung, H. Wu, and J. Martorell, Poles, bound states, and resonances illustrated by the square well potential, American Journal of Physics, vol.64, issue.2, pp.136-144, 1996.
DOI : 10.1119/1.18131

H. M. Nussenzveig, The poles of the S-matrix of a rectangular potential well of barrier, Nuclear Physics, vol.11, pp.499-521, 1959.
DOI : 10.1016/0029-5582(59)90293-7

B. Belchev, S. G. Neale, and W. M. , This research was supported in part by an NSERC Undergraduate Summer Research Award (SGN) and an NSERC Discovery Grant (MAW)., Canadian Journal of Physics, vol.73, issue.11, pp.1127-1140, 2011.
DOI : 10.1007/BF02725104

URL : http://arxiv.org/pdf/1110.4902

R. Zavin and N. Moiseyev, One-dimensional symmetric rectangular well: from bound to resonance via self-orthogonal virtual state, Journal of Physics A: Mathematical and General, vol.37, issue.16, p.4619, 2004.
DOI : 10.1088/0305-4470/37/16/011

S. Klaiman and N. Moiseyev, The absolute position of a resonance peak, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.43, issue.18, p.185205, 2010.
DOI : 10.1088/0953-4075/43/18/185205

R. G. Newton, Analytic Properties of Radial Wave Functions, Journal of Mathematical Physics, vol.11, issue.9, pp.319-347, 1960.
DOI : 10.1103/PhysRev.107.1103

A. Goldberg, H. M. Schey, and J. L. Schwartz, Computer-Generated Motion Pictures of One-Dimensional Quantum-Mechanical Transmission and Reflection Phenomena, American Journal of Physics, vol.35, issue.3, pp.177-186, 1967.
DOI : 10.1119/1.1973991

S. Mohr, L. E. Ratclii, P. Boulanger, L. Genovese, D. Caliste et al., Daubechies wavelets for linear scaling density functional theory, The Journal of Chemical Physics, vol.140, issue.20, pp.140-2014
DOI : 10.1103/PhysRevB.82.035431

URL : https://hal.archives-ouvertes.fr/hal-01334186

L. E. Ratclii, N. D. Hine, and P. D. Haynes, Calculating optical absorption spectra for large systems using linear-scaling density functional theory, Physical Review B, vol.84, issue.16, p.165131, 2011.
DOI : 10.1103/PhysRevB.51.9668

R. N. Silver, H. Roeder, A. F. Voter, and J. D. Kress, Kernel Polynomial Approximations for Densities of States and Spectral Functions, Journal of Computational Physics, vol.124, issue.1, pp.115-130, 1996.
DOI : 10.1006/jcph.1996.0048