This chapter discusses density functional methods for excited states. Density functional theory (DFT) is nowadays one of the most popular methods for ground state electronic structure calculations in quantum chemistry and solid state physics. A number of commercial programs are available, and DFT calculations of ground state energies, structures, and many other properties are routinely performed by nonexperts in (bio-)chemistry, physics, and materials sciences. The chapter focuses on the use of time-dependent density functional theory (TDDFT). Algorithms to compute spectra and excited state properties are also reviewed. The chapter describes the steps necessary in a TDDFT excited state calculation and some timing for typical applications are presented. Further the chapter also summarizes the performance of TDDFT excitation energies, transition moments, and excited state properties. Specific applications are surveyed that included compounds such as aromatic systems and fullerenes, porphyrins and related compounds, transition metal compounds, metal and semiconductor clusters, organic polymers, and biologically relevant systems.

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Density functional methods for excited states: equilibrium structure and electronic spectra

After a brief introduction to the theory of time-dependent density functional theory (TDDFT), an overview is given of the recent literature on calculations of the electronic absorption spectra of transition-metal complexes. Various types of complexes are treated – organometallic complexes with carbonyl and cyclopentadienyl ligands, oxo and halide complexes (Werner complexes), metal α-diimine complexes and metallotetrapyrroles. The performance of the various GGA and hybrid functionals is discussed, as well as that of special shape-corrected functionals for the Kohn-Sham potential. The TM complexes are outside of the range of molecules for which B3LYP is parameterized, and this functional does not perform better than pure GGAs. The statistical average of the orbital dependent potentials (SAOP) functional for the Kohn-Sham potential appears to perform best. The strong dependence of the excitation energies on metal-ligand distances is stressed. A consequence is that a full assessment of the accuracy of the TDDFT method will have to include a full vibronic interaction treatment. A conservative estimate is that the accuracy of the best TDDFT methods for TM complexes, where errors of several tenths of an eV often occur, is somewhat lower than for simple benchmark molecules like N2, CO, and CH2O, where errors are often of the order of 0.1–0.2 eV.

Excitation energies of metal complexes with time-dependent density functional theory

Semiconducting thin films were grown on quartz substrates and crystalline silicon wafers, using dilithium phthalocyanine and the organic ligands 2,6-dihydroxyanthraquinone and 2,6-diaminoanthraquinone as the starting compounds. The films, thus obtained, were characterized by Fourier Transform infrared (FTIR), fast atomic bombardment (FAB+) mass and ultraviolet-visible (UV-Vis) spectroscopies. The surface morphology of these films was analyzed by means of atomic force microscopy (AFM) and scanning electron microscopy (SEM). It was found that the temperature-dependent electric current in all cases showed a semiconductor behavior with conductivities on the order of 10⁻⁶·S cm⁻¹, whereas the highest value corresponded to the thin film based upon the bidentate amine. The Tauc and Cody optical band gap values of thin films were calculated from the absorption coefficients and were found to be around 1.5 eV, with another strong band between 2.3 and 2.43 eV, arising from non-direct transitions. The curvature in the Tauc plot influencing the determination of the optical gap, the Tauc optical gap corresponding to the thicker film is smaller. The dependence of the Cody optical gap on the film thickness was negligible.

https://www.mdpi.com/1420-3049/17/9/10000/pdf

Determination of the Optical GAP in Thin Films of Amorphous Dilithium Phthalocyanine Using the Tauc and Cody Models

The excited-state photodynamics of intrasupramolecular photoinduced electron transfer was investigated in a series of hydrogen-bonded supramolecular complexes composed of diprotonated 2,3,5,7,8,10,12,13,15,17,18,20-dodecaphenylporphyrin (H4DPP2+) and electron donors bearing a carboxylate group. The formation of supramolecular complexes was examined by spectroscopic measurements. The binding constants obtained by spectroscopic titration indicate the strong binding (108−1010 M−2) even in a polar and coordinating solvent, benzonitrile (PhCN). The crystal structure of the supramolecular assembly using ferrocenecarboxylate (FcCOO−) was determined to reveal a new structural motif involving two-point and single-point hydrogen bonding among saddle-distorted H4DPP2+ dication and two FcCOO− anions. Femtosecond laser flash photolysis was applied to investigate the photodynamics in the hydrogen-bonded supramolecular complexes. Rate constants obtained were evaluated in light of the Marcus theory of electron transfer, ...

Structure and photoinduced electron transfer dynamics of a series of hydrogen-bonded supramolecular complexes composed of electron donors and a saddle-distorted diprotonated porphyrin

pH-Controlled Self-Assembling of meso-Tetrakis(4-sulfonatophenyl)porphyrin−Chitosan Complexes

The ground-state structure, electronic spectrum and conformational inversion of porphyrin diacid (H4P2+) have been studied with the density functional theory. In accord with available crystallographic data of related compounds, the most stable structure of H4P2+ molecule is the one bearing a saddle-distorted porphyrin ring (D2d symmetry), with the four pyrrole rings tilted up and down alternatively with respect to the porphyrin mean plane. Electronic absorption spectrum of H4P2+ was studied by time-dependent DFT method, and the calculations were compared with the solution experimental results. The computations correctly predict excitation energies and oscillator strengths at least for the first and second excited states. The conformational inversion between the two conjugate D2d structures was studied, and a multi-step process was proposed. The structures of transition states and intermediates as well as the inversion barriers were calculated.

Density functional theory investigation of porphyrin diacid: electronic absorption spectrum and conformational inversion

Density functional theory study on the geometric, electronic and vibrational structures of alkali metal porphyrin complexes

Density functional theory investigations of geometries and electronic spectra of lithium phthalocyanines

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Density functional theory investigation of porphyrin diacid: electronic absorption spectrum and conformational inversion

Density functional theory study on the geometric, electronic and vibrational structures of alkali metal porphyrin complexes

Density functional theory investigations of geometries and electronic spectra of lithium phthalocyanines