Can optical spectroscopy directly elucidate the ground state of C20?

Electron-vibrational renormalization in fullerenes through ab initio and machine learning methods

The effect of nuclear vibrations on the electronic eigenvalues and the HOMO-LUMO gap is known for several kinds of carbon-based materials, like diamond, diamondoids, carbon nanoclusters, carbon nanotubes and others, like hydrogen-terminated oligoynes and polyyne. However, it has not been widely analysed in another remarkable kind which presents both theoretical and technological interest: fullerenes. In this article we present the study of the HOMO, LUMO and gap renormalizations due to zero-point motion of a relatively large number (163) of fullerenes and fullerene derivatives. We have calculated this renormalization using density-functional theory with the frozen-phonon method, finding that it is non-negligible (above 0.1 eV) for systems with relevant technological applications in photovoltaics and that the strength of the renormalization increases with the size of the gap. In addition, we have applied machine learning methods for classification and regression of the renormalizations, finding that they can be approximately predicted using the output of a computationally cheap ground state calculation. Our conclusions are supported by recent research in other systems.

An improved descriptor of cluster stability: application to small carbon clusters

The mass spectra of gas-phase clusters in cluster beams have a rich structure where the relative heights of the peaks compared to peaks corresponding to the clusters of neighboring sizes reveal the stability of the clusters as a function of size N. In an analysis of the published mass spectrum of carbon cluster cations CN+ with N ≤ 16 we have employed the most common descriptor of cluster stability, which is based on the comparison of the total energy of the cluster of size N with the averaged energies of clusters with sizes N + 1 and N - 1. These energies have been obtained from density functional calculations. The comparison between the stability function and the mass spectrum leaves some experimental features unexplained; in particular, the correlation with the detailed variation of the height of the mass peaks as a function of size N is not satisfactory. We then propose a novel stability descriptor which improves the features substantially, in particular the correlation with the detailed variation of the height of the mass peaks. The new stability index is based on the comparison of the atom-evaporation energy of the cluster of size N with the averaged atom-evaporation energies of clusters with sizes N + 1 and N - 1. The substantial improvement achieved is attributed to the fact that evaporation energies are quantities directly connected with the processes controlling the cluster abundances in the beam.

Photoabsorption spectra of boron nitride fullerenelike structures

Optical absorption spectra have been calculated for a series of boron nitride fullerenelike cage structures BnNn of sizes n=12-36. The method used is a real-time, real-space implementation of the time-dependent density-functional theory, involving the full time propagation of the time-dependent Kohn-Sham equations. The spectra are found to be a possible tool for distinguishing between different boron nitride fullerene species and isomers. The trends and differences in the spectra are found to be related to the general geometry of the molecules. Comparison between local-density and generalized-gradient approximations for electron exchange-correlation functionals shows that both of them produce essentially the same spectral characteristics.

Molecular Engineering in Symmetric End-Substituted Oligothiophene Derivatives: Analysis of Condensed-Phase Photoemission Spectra Using Semiempirical Hartree−Fock Calculations

The electronic structures of two series of end-capped thiophene oligomers, one set containing the electron-deficient dimesitylboryl end-cap and one containing the electron-rich triaryl amine end-cap, have been modeled using semiempirical quantum chemical calculations and the results used to assign features in the photoemission spectra of the materials in the condensed phase. For the thiophene oligomers end-capped with the electron-deficient dimesitylboryl moieties, the energy of the occupied frontier orbitals is largely governed by pi-type orbitals of the thiophene repeat units in the oligothiophene main chain. Conversely, in oligomers end-capped with electron-rich triarylamine moieties, the occupied frontier orbital energies are largely governed by orbital states of heavily mixed character associated with thiophene pi-type systems and the low-lying nitrogen lone pairs of end capping groups.

Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-

High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C(20) and C(20)(-). The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method (with cc-pVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/cc-pVDZ [CCSD(T)-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/cc-pVTZ [MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C(20) isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C(20)(-) at T=0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C(20)(-). Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures (e.g., finite-size carbon nanotubes, nano-onions, or nanohorns). The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C(20) and C(20)(-) at high temperatures. Finally, photoelectron spectra (PES) for the anionic C(20)(-) isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C(20)(-) isomers.

Quantum Chemical Methods for the Investigation of Photoinitiated Processes in Biological Systems: Theory and Applications

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.

Photoabsorption spectra of Ti8C12 metallocarbohedrynes: Theoretical spectroscopy within time-dependent density functional theory

The photoabsorption spectra of several of the most stable isomers of the Ti8C12 metallocarbohedryne are calculated using time-dependent density functional theory. Several ground-state magnitudes have been also calculated, such as cohesive energies, electronic gaps between the highest occupied and lowest unoccupied molecular orbitals, and static polarizabilities. Since significant differences are found among the photoabsorption spectra of the different isomers in the low energy region (0-5 eV), we propose the comparison of experimental and the calculated absorption spectra as a tool to elucidate the isomers that appear to form in the experiments. Between 10 and 13 eV all the spectra show a region of high absorption that we identify as due to collective electronic excitations. The existence of this prominent feature explains the occurrence of delayed ionization and delayed ion emission phenomena observed in previous experiments.

C20 Carbon Clusters: Fullerene–Boat–Sheet Generation, Mass Selection, Photoelectron Characterization

Electron-impact ionization in a time-of-flight mass spectrometer of C(20)H(0-3)Br(14-12) probes-secured from C(20)H(20) dodecahedrane by a "brute-force" bromination protocol-provided bromine-free C(20)H(0-2(3)) anions in amounts that allowed the clean mass-separation of the hydrogen-free C(20) (-) ions and the photoelectron (PE) spectroscopic characterization as C(20) fullerene (electron affinity (EA)=2.25+/-0.03 eV, vibrational progressions of 730+/-70). The extremely strained C(20) fullerene ions surfaced as kinetically rather stable entities (lifetime of at least the total flight time of 0.4 ms); they only very sluggishly expel a C(2) unit. The HOMO and LUMO are suggested to be almost degenerate (DeltaE=0.27 eV). The assignment as a fullerene was corroborated by the PE characterization of the C(20) bowl (EA=2.17+/-0.03 eV, vibrational progression of 2060+/-50 cm(-1)) analogously generated from C(20)H(10) corannulene (C(20)H(1-3)Br(9-8) samples) and comparably stable. Highly resolved low-temperature PE spectra of the known C(20) ring (EA=2.49+/-0.03 eV, vibrational progressions 2022+/-45 and 455+/-30 cm(-1)), obtained from graphite, display an admixture of, most probably, a bicyclic isomer (EA=3.40+/-0.03 eV, vibrational progression 455+/-30 cm(-1)). The C(20) (+(-)) and C(20)H(2) (+(-)) cluster ions generated from polybrominated perylene (C(20)H(0-2)Br(12-10)) have (most probably) retained the planar perylene-type skeleton (sheet, EA=2.47+/-0.03 eV, vibrational progressions of 2089+/-30 and 492+/-30 cm(-1) and EA=2.18+/-0.03 eV, vibrational progressions of 2105+/-30 and 468+/-30 cm(-1)).

Quater-, Quinque-, and Sexithiophene Organogelators: Unique Thermochromism and Heating-Free Sol-Gel Phase Transition

A series of quater-, quinque-, and sexithiophene derivatives bearing two cholesteryl groups at the alpha-position, which are abbreviated as 4 T-(chol)(2), 5 T-(chol)(2), and 6 T-(chol)(2), respectively, have been synthesized. It has been found that these oligothiophene derivatives act as excellent organogelators for various organic fluids and show the unique thermochromic behaviors through the sol-gel phase transition. It was shown on the basis of extensive investigations, performed with UV-visible spectroscopy, circular dichroism (CD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and atomic force microscopy (AFM), that these gelators self-assemble into the one-dimensional structures in the organogels, in which the pi-block moieties of the oligothiophenes are stacked in an H-aggregation mode. Surprisingly, an AFM image shows that 4 T-(chol)(2) forms unimolecular fibers in a left-handed helical sense, whereby one pitch of the helical fiber is constructed by 400-540 4 T-(chol)(2) molecules. Very interestingly, the conformational change in the oligothiophene moieties can be visually detected: for example, 6 T-(chol)(2) shows a specific absorption maximum in the gel (lambda(max) = 389 nm) and in the solution (lambda(max) = 439 nm). In addition, a sol-gel phase transition of the 6 T-(chol)(2) gel was implemented by addition of oxidizing and reducing reagents such as FeCl(3) and ascorbic acid, respectively. The stimuli-responsive functionality of the oligothiophene-based organogels makes them promising candidates for switchable opto- and electronic soft materials.

The planar-to-tubular structural transition in boron clusters from optical absorption

The optical response of the lowest-energy isomers of the B20 family is calculated using time-dependent density-functional theory within a real-space, real-time scheme. Significant differences are found among the absorption spectra of the clusters studied. We show that these differences can be easily related to changes in the overall geometry. Optical spectroscopy is thus an efficient tool to characterize the planar-to-tubular structural transition, known to be present in these boron-based systems.

TIME-DEPENDENT DENSITY FUNCTIONAL THEORY

Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.