Time-dependent density functional interacting electrons

The study of behavior of many-electron systems such as atoms, molecules, and solids under the action of time-dependent (TD) external fields, which includes interaction with radiation, has been an important area of research. In the linear response regime, where one considers the external held to cause a small perturbation to the initial ground state of the system, one can obtain many important physical quantities such as polarizabilities, dielectric functions, excitation energies, photoabsorption spectra, van der Waals coefficients, etc. In many situations, for example, in the case of interaction of many-electron systems with strong laser held, however, it is necessary to go beyond linear response for investigation of the properties. Since a full theoretical description based on accurate solution of TD Schrodinger equation is not yet within the reach of computational capabilities, new methods which can efficiently handle the TD many-electron correlations need to be explored, and time-dependent density functional theory (TDDFT) is one such valuable approach. 

Time-dependent density functional theory (TDDFT) as a complete formalism [7] is a more recent development, although the historical roots date back to the time-dependent Thomas-Fermi model proposed by Bloch [8] as early as 1933. The first and rather successful steps towards a time-dependent Kohn-Sham (TDKS) scheme were taken by Peuckert [9] and by Zangwill and Soven [10]. These authors treated the linear density response of rare-gas atoms to a time-dependent external potential as the response of non-interacting electrons to an effective time-dependent potential. In analogy to stationary KS theory, this effective potential was assumed to contain an exchange-correlation (xc) part, r,c(r, t), in addition to the time-dependent external and Hartree terms ... 

The treatment in terms of induced current is in the mainstream of modem development of the time-dependent density functional theory (TDDFT). Moreover, the current density formalism has been proposed [4] as a variant of TDDFT. The evolution of current density presents properly the response of electrons on an external field. In general words, such a strong basis is promising for a theoretical treatment of many aspects of ion interactions with atoms, molecules and solids. 

The theory in which the susceptibility is formally defined for jellium surfaces is the time-dependent density functional theory (TDDFT). In this theory, the susceptibility for interacting electrons (also called screened susceptibility) x(q, z, z ) is related to the susceptibility for non-interacting (independent) electrons Xo(q, ta, q z, z ) via the integral equation... 

Time-Dependent Density Functional Theory (TD-DFT) simulations in adiabatic approximation, carried out on a prototype terthiophene oxidized in the inner position (Raganato et al., 2004), indicated that the oxidation of the thiophene ring leads to the formation of new interactions in the LUMO orbital. The kinetic energy of the electrons in this orbital is lowered, while the energy of the electrons in the HOMO orbital is almost unchanged. As a consequence, the electron affinity of the whole molecule is increased. 

M. Schreiber, M.R. Silva-Junior, S.P.A Sauer, W. Thiel, Benchmarks for electronically excited states CASPT2, CC2, CCSD, and CCS, J. Chem. Phys. 128 (2008) 134110 M.R. Sflva-Junior, M. Schreiber, S.P.A. Sauer, W. Thiel, Benchmarks for electronically excited states Time-dependent density functional theory and density functional theory based multireference configuration interaction, J. Chem. Phys. 129 (2008) 104103 S.P.A. Sauer, M. Schreiber, M.R. Silva-Junior, W. Thiel, Benchmarks for Electronically Excited States A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods CCSDR(3) versus CCS, J. Chem. Theory Comput. 5 (2009) 555 M.R. Silva-Junior, S.P.A. Sauer, M. Schreiber, W. Thiel, Basis set effects on coupled cluster benchmarks of electronically excited states CCS, CCSDR(3) and CC2, Mol. Phys. 108 (2010) 453 M.R. Silva-Junior, M. Schreiber, S.P.A. Sauer, W. Thiel, Benchmarks of electronically excited states basis set effects on CASPT2 results, J. Chem. Phys. 133 (2010) 174318. 

Roewer G, Herzog U, Trommer K, Muller E, Friihauf S (2002) Silicon Carbide - A Survey of Synthetic Approaches, Properties and Applications 101 59-136 Rosa A, Ricciardi G, Gritsenko O, Baerends EJ (2004) Excitation Energies of Metal Complexes with Time-dependent Density Functional Theory 112 49-116 Rosokha SV, Kochi JK (2007) X-ray Structures and Electronic Spectra of the it-Halogen Complexes between Halogen Donors and Acceptors with it-Receptors. 126 137-160 Rowan SJ, Mather PT (2008) Supramolecular Interactions in the Formation of Thermotropic Liquid Crystalline Polymers. 128 119-149... 

As follows from the form of the QM/MM Hamiltonian (Eq. 5.8), any electronic structure method can be used for describing the QM and MM parts of the system. Applications discussed in the following session mainly deal with understanding photochemistry in the condensed phase, with a common choice of the excited state methods from the equation of motion coupled cluster (EOM-CC) family [61-64], time-dependent density functional theory (TD-DFT) [65-66], or configuration interaction (Cl) methods. The MM Hamiltonian is represented by either EFPl or EFP Hamiltonian from Eq. 5.1 or Eq. 5.7. //qm-mm coupling term in the QM/EFPl... 

Table 12 Vertical excitation energies (in eV) for N2- TDLDA and TDGGA represent results from time-dependent density-functional calculations with either a local-density (LDA) or a generalized-gradient (GGA) approximation, whereas TDHF are similar results from time-dependent Hartree-Fock calculations. MRCCSD, SOPPA, MRTDHF are results from sophisticated configuration-interaction calculations, and CIS are less sophisticated configuration-interaction calculations. The final state and the electronic excitation are also shown and the results are compared with experimental values (Exp.). The results are from ref. 89...

In this chapter we present an introductory overview of the basic theoretical concepts of computational molecular photoph rsics. First, the nature and properties of electronic excitations are considered, with special attention to transition moments and vibrational contributions. Then, the main photophysical processes involving the electronic excited states are examined, focusing in particular on nonradiative deactivation phenomena. Finally, we present a brief review of computational methods commonly applied for the description of molecular excitations. Special emphasis is given to the configuration-interaction (Cl) method and the time-dependent density functional theory (TD-DFT), discussing some technical details and outlining advantages and limitations. 

Hirata, S., Head-Gordon, M., and Bartlett, R. J. (1999) Configuration interaction singles, time-dependent Hartree-Fock, and time-dependent density functional theory for the electronic excited states of extended systems,/ Chem. Phys., Ill, 10774-10791. 

Silva-Junior, M. R., Schreiber, M., Sauer, S. P. A., and Thiel, W. [2008] Benchmarks for electronically excited states Time-dependent density functional theory and density functional theory based multireference configuration interaction, / Chem. Phys., 129, 104103/ 1-14. 

While the continuous body description of the metal is exploited, the molecule is treated atomistically by standard electronic structure techniques, such as time-dependent Hartree-Fock (TD-HF) or time-dependent density functional theory (TD-DFT) (see Sec. 4.4.2), and the electromagnetic interaction is included in the molecular Hamiltonian. This is a promising route not only to bypass inaccuracies related to the classical dipole model for the molecule, but also to go toward an ab initio molecular plasmonics. At present, this model has been explored mostly in the polarizable continuum model (PCM) group [51, 52, 54-58], but recently other implementations have been proposed [59]. 

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