This work tries to show the significant competence and functionality of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) as theoretical approaches, supporting experimental measurements in various fields of physics from astrophysics to surface science, to study the electronic structure and spectroscopic properties of molecules and clusters: Silicon nanocrystals: Due to their optical properties, silicon nanocrystals have attracted considerable attention in astrophysics. In this work, the optical properties of H-passivated silicon nanocrystals are determined by the energetics of the frontier orbitals and their dependence on the deformation in the relaxed excited state, using DFT and TD-DFT. The Jahn-Teller effect in the lowest excited state results in a distortion toward tetragonal symmetry, contributing significantly to the red shift of the photoluminescence (PL) spectra. Therefore, the deformation in the relaxed excited state consists of a symmetry conserving part and of a symmetry-breaking distortion from Td toward D2d. For nanocrystals up to a diameter of 1.5 nm, we project the deformations at the minima of the excited state potential surface onto the different symmetries, allowing for a discrimination of the respective contributions to the total Stokes shift. The results show a quantitative agreement between the TD-DFT calculations of PL gap and the observed PL energies better than 0.2 eV. It is also seen that the large PL linewidth is the fundamental property of each cluster, not of ensemble average over clusters of different size. 2,3-Benzofluorene: We have presented new theoretical results on the absorption spectroscopy of 2,3-benzofluorene (Bzf) for the transition from the ground state, S0, to the first electronically excited singlet state, S1, to support the measurements of S1(1A´) <- S0(1A´) absorption spectrum of jet-cooled Bzf. The potential energy surfaces (PESs) of the S(n=0,1,2) states of Bzf have been investigated with calculations based on DFT and TD-DFT. At the B3LYP/TZ level of theory, TD-DFT does not deliver a realistic difference between the excited S1 and S2 potential energy surfaces, a problem which can be avoided by introducing a reference geometry (q*) where this difference coincides with the observation. In this geometry, an expression for the Herzberg-Teller corrected intensities of the vibronic bands is proposed, allowing a straightforward assignment of the observed a′ modes below 900 cm−1, including realistic calculated intensities. In spite of the difficulties caused by the small energy difference between the S1 and S2 states, we have obtained a reasonable theoretical absorption spectrum based on a TD-DFT approach applied to the slightly modified molecular geometry. Although the agreement between the theoretical and observed spectra is very good only for vibrational modes with frequencies lower than 900 cm−1, we consider our calculations to be the best approach to an ab initio study realized for Bzf until now since only parametrized force fields had been used before. (Ni–, Pd–, Pt–) Phthalocyanine: We studied the HOMO–LUMO gap shrinking in order to investigate the tip-induced polarization in scanning tunneling spectroscopy (STS) of d8 (Ni, Pd, and Pt) phthalocyanines. By means of DFT, the electronic structure and vibronic properties of single neutral NiPc, PdPc, and PtPc and their singly and doubly ionized cations and anions have been calculated. Interestingly, the position of the HOMO decreases systematically with increasing the atomic number of the central metal atom. The first ionization energies of neutral molecules increase by changing the central metal atom, while the electron affinities remain constant. This causes an increase in the HOMO–LUMO gap. These results show a clear correlation to experimental observations. Furthermore, partitioning of the reorganization energy, corresponding to the photoelectron spectra of the first and second ionizations of studied molecules, into normal mode contributions shows that the major contributions are due to several vibrational modes with a1g symmetry and energies lower than 1600 cm−1. The results reveal that the reorganization energy due to the singly positive ionization in the studied molecules is about one order of magnitude less than other reorganization energies, which makes these metal–phthalocyanines more attractive as electron donor for intramolecular electron transfer in electron acceptor–donor systems.

This work tries to show the significant competence and functionality of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) as theoretical approaches, supporting experimental measurements in various fields of physics from astrophysics to surface science, to study the electronic structure and spectroscopic properties of molecules and clusters: Silicon nanocrystals: Due to their optical properties, silicon nanocrystals have attracted considerable attention in astrophysics. In this work, the optical properties of H-passivated silicon nanocrystals are determined by the energetics of the frontier orbitals and their dependence on the deformation in the relaxed excited state, using DFT and TD-DFT. The Jahn-Teller effect in the lowest excited state results in a distortion toward tetragonal symmetry, contributing significantly to the red shift of the photoluminescence (PL) spectra. Therefore, the deformation in the relaxed excited state consists of a symmetry conserving part and of a symmetry-breaking distortion from Td toward D2d. For nanocrystals up to a diameter of 1.5 nm, we project the deformations at the minima of the excited state potential surface onto the different symmetries, allowing for a discrimination of the respective contributions to the total Stokes shift. The results show a quantitative agreement between the TD-DFT calculations of PL gap and the observed PL energies better than 0.2 eV. It is also seen that the large PL linewidth is the fundamental property of each cluster, not of ensemble average over clusters of different size. 2,3-Benzofluorene: We have presented new theoretical results on the absorption spectroscopy of 2,3-benzofluorene (Bzf) for the transition from the ground state, S0, to the first electronically excited singlet state, S1, to support the measurements of S1(1A´) <- S0(1A´) absorption spectrum of jet-cooled Bzf. The potential energy surfaces (PESs) of the S(n=0,1,2) states of Bzf have been investigated with calculations based on DFT and TD-DFT. At the B3LYP/TZ level of theory, TD-DFT does not deliver a realistic difference between the excited S1 and S2 potential energy surfaces, a problem which can be avoided by introducing a reference geometry (q*) where this difference coincides with the observation. In this geometry, an expression for the Herzberg-Teller corrected intensities of the vibronic bands is proposed, allowing a straightforward assignment of the observed a′ modes below 900 cm−1, including realistic calculated intensities. In spite of the difficulties caused by the small energy difference between the S1 and S2 states, we have obtained a reasonable theoretical absorption spectrum based on a TD-DFT approach applied to the slightly modified molecular geometry. Although the agreement between the theoretical and observed spectra is very good only for vibrational modes with frequencies lower than 900 cm−1, we consider our calculations to be the best approach to an ab initio study realized for Bzf until now since only parametrized force fields had been used before. (Ni–, Pd–, Pt–) Phthalocyanine: We studied the HOMO–LUMO gap shrinking in order to investigate the tip-induced polarization in scanning tunneling spectroscopy (STS) of d8 (Ni, Pd, and Pt) phthalocyanines. By means of DFT, the electronic structure and vibronic properties of single neutral NiPc, PdPc, and PtPc and their singly and doubly ionized cations and anions have been calculated. Interestingly, the position of the HOMO decreases systematically with increasing the atomic number of the central metal atom. The first ionization energies of neutral molecules increase by changing the central metal atom, while the electron affinities remain constant. This causes an increase in the HOMO–LUMO gap. These results show a clear correlation to experimental observations. Furthermore, partitioning of the reorganization energy, corresponding to the photoelectron spectra of the first and second ionizations of studied molecules, into normal mode contributions shows that the major contributions are due to several vibrational modes with a1g symmetry and energies lower than 1600 cm−1. The results reveal that the reorganization energy due to the singly positive ionization in the studied molecules is about one order of magnitude less than other reorganization energies, which makes these metal–phthalocyanines more attractive as electron donor for intramolecular electron transfer in electron acceptor–donor systems.