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Emission Energies and Stokes Shifts for Single Polycyclic Aromatic Hydrocarbon Sheets in Comparison to the Effect of Excimer Formation
Abstract
Emission spectra of paradigmatic single-sheet polycyclic aromatic hydrocarbons (PAHs), pyrene, circum-1-pyrene, coronene, circum-1-coronene and circum-2-coronene and Stokes shifts were computed and compared with previously calculated comparable data for relaxed excimer structures using the SOS-ADC(2), TD-B3LYP and TD-CAM-B3LYP methods with multireference DFT/MRCI data as benchmark. Vertical emission transitions and Stokes shifts were extrapolated to infinite PAH size. Comparison of Stokes shifts computed from theoretical monomer and dimer data confirm assumptions that relaxed excimers are responsible for the unusually large Stokes shifts in carbon dots observed in experimental investigations.
... Single-reference SOS-ADC(2) and TD-CAM-B3LYP methods provide reasonably good results, although with wrong ordering states. 114,160 The performances of different methods were also tested on doped models. In the case of nitrogen doping in pyrene, single reference methods describe reasonably well the system but fail in describing the higher excited states because of their multireference character, thus suggesting a possible bias in the evaluation of internal conversion processes. ...
... 112 It is worth noting that in their benchmark studies, the group of Lischka also underlined that the multireference calculations produce good results but at a high computational cost. 113,114,160,236,240 These results were also reported in a very recent review of Otyepka and co-workers, on computational approaches to understand photoluminescence of CDs. 23 Among the conclusions, the authors underlined the need for close collaboration between experimentalists and theoreticians to develop a multiscale cost-affordable approach to explain and predict the structural and optical properties of CNDs, a statement that also inspires the present review. ...
... Among the optical properties accessible to computational methods and largely exploited to validate a model, we find the HL gap (see, for example, Tepliakov et al. 82 ) and the character of the considered transitions (such as charge transfer or excimer resonance). 114,160 Also electronic DoS 57 and fingerprinting vibrational modes 51 are sometimes exploited to validate the models. However, the lack of knowledge of CND structure, the typical polydispersity of the nanoparticles, and the typically low control of their composition in terms of purity and reproducibility represent a limitation and challenge for the model validation effort. ...
Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.
... The vertical S 1 → S 0 emission energies ( Fig. 5 ) can be obtained with the SR approaches for most cases. These methods have, indeed, been recently used to explain unusually large Stokes shifts observed in the emission spectra of CDs by emission from excimer aggregates formed by stacking rather than from the monomer emission [250] . ...
... On the other hand, large structural models can cover many features of CDs, but their size heavily limits the available armament of compu- Fig. 9. A) Geometry differences (nm) between S 1 and S 0 states of pyrene and NTOs for the S 1 → S 0 transition. Reprinted with permission from [250] . Copyright 2019 American Chemical Society. ...
Carbon dots (CDs), including graphene quantum dots, carbon nanodots, carbon quantum dots, and carbonized polymer dots, belong to extensively studied nanomaterials with a very broad application potential resulting from their bright photoluminescence (PL), high (photo)stability, low toxicity and great biocompatibility. However, the design of CDs with tailored properties is still hampered by a fairly limited understanding of the CD PL, which stems from their rather complex structure and variability of the PL centers. Theoretical calculations provide valuable insights into the nature of the excited states and the source of PL. In this review, we focus on state-of-the-art theoretical methods for the description of absorption and PL of CDs and their limitations, along with providing an overview of theoretical studies addressing structural models and the electronic structure of various types of CDs in the context of their overall optical properties. Besides the assessment of the current state of knowledge, we also highlight the opportunity for further advancements in the field.
... Similar findings concerning Stokes shifts were reported previously for various polycyclic aromatic hydrocarbon (PAH) excimers. 69 The total CT characteristics of the S 1 state is increased from the values computed for the vertical excitations as well. The decreased interchain distance increases the total CT value from ∼0.2e (PPV 2 , Table I) for the vertical excitation to 0.5e for sandwich PPV 2 and PPV 3 and then decreases somewhat for PPV 4 . ...
Benchmark ab initio calculations have been performed for poly(p-phenylenevinylene) (PPV) dimers, a paradigmatic material for studying excitation energy transfer mechanisms. Second-order Møller–Plesset perturbation theory was utilized with the scaled opposite spin approach (SOS-MP2) and correlation consistent basis sets to determine the geometric properties and interaction energies in the ground state. Vertical excitations and optimized structures for the S1 state were computed using the SOS second-order algebraic diagrammatic construction method. For the ground state properties, extrapolation to the complete basis set (CBS) limit and correction for the basis set superposition error (BSSE) were performed. While all results computed with different basis sets and considering BSSE correction or not agreed at the CBS limit, a strong bias was observed either using augmented basis sets or BSSE corrections, proving that these approaches are not advisable for calculating intermolecular distances and interaction energies with smaller basis sets. The lower states for vertical excitations were largely local excitons where the hole/electron pair was confined to single chains. For higher excited states, interchain charge transfer (CT) states were also observed. Geometry optimization of the S1 state led to significant reductions in the intermolecular distances and energetic stabilization, with Stokes shifts between 1.4 eV and 0.9 eV (with increasing chain length), and significant CT values between 0.5e and 0.4e.
Tunable photoluminescence has been observed in hexagonal boron nitride quantum dots (BNQDs), but the underlying luminescence mechanism remains elusive. In this study, we examine excited-state properties of several functionalized BNQDs models using density functional theory (DFT), time-dependent DFT, and multistate complete active space second-order perturbation theory (MS-CASPT2) methods. Unlike reported graphene quantum dots, photoluminescence of BNQDs is not affected by their sizes (<2.5 nm). Instead, the embedded single sp3 carbon atom connecting different functional groups can tune emission colors of BNQDs, whose emission wavelength cover full range of visible light and even extend toward near-infrared region. Further analysis reveals that both exciton self-trapping and electron-hole separation decrease HOMO-LUMO energy gaps, leading to large Stokes shifts. Moreover, uneven and even hybridizations induce blue- and red-shifted emission spectra. These findings provide novel insights into full-spectrum emission of BNQDs modified with functional groups.
Diketopyrrolopyrrole (DPP) is a pivotal functional group to tune the physicochemical properties of novel organic photoelectronic materials. Among multiple uses, DPP-thiophene derivatives forming a dimer through a vinyl linker were recently shown to quench the fluorescence observed in their isolated monomers. Here, we explain this fluorescence quenching using computational chemistry. The DPP-thiophene dimer has a low-lying doubly excited state that is not energetically accessible for the monomer. This state delays the fluorescence allowing internal conversion to occur first. We characterize the doubly excited state wavefunction by systematically changing the derivatives to tune the π-scaffold size and the acceptor and donor characters. The origin of this state's stabilization is related to the increase in the π-system and not to the charge-transfer features. This analysis delivers core conceptual information on the electronic properties of organic chromophores arranged symmetrically around a vinyl linker, opening new ways to control the balance between luminescence and internal conversion.
This chapter describes the historical and current state of affairs of optical and chiroptical properties of helicenes. Hexahelicene, composed of six benzene rings, has been an exemplar for experimental (synthetic) and theoretical (computational) challenges that affords and explains the exceptional chiroptical responses such as very large optical rotation (OR) value, which is briefly described at the beginning of the chapter. Then, all of the fundamental chiroptical properties such as optical rotatory dispersion (ORD), electronic circular dichroism (ECD), vibrational circular dichroism (VCD), Raman optical activity (ROA), and circularly polarized luminescence (CPL) of hexahelicenes are summarized. Because of the favorable chiroptical properties of helicenes, structure–chiroptical property relationships have been extensively examined for helicene derivatives through the structural modifications, for instance, by an elongation of helices. Molecular symmetry wields more substantial impact on the chiroptical responses of helicenes that are experimentally obtained by the fusion of multiple helicene moieties in double, triple, quintuple, and higher multiple helicenes. Finally, the effect of substitution of skeletal carbon and peripheral hydrogen atoms of helicenes is discussed with emphasis on vibronic effect in the ECD and CPL spectra.
Carbon dots (CDs) are novel fluorescent nanoparticles that combine intense emission of visible light with eco-friendly and inexpensive carbon-based composition. In this work, CDs are synthesized trough a glycothermal treatment of resorcinol (1,3-hydroxybenzene) in air atmosphere. The presence of catalysts (NaOH and H2SO4) increases the reaction rate, promoting a faster and massive production of nanoparticles. The spectroscopic monitoring of fluorescence during CD synthesis, supported by a DFT study, allows to depict the formation and structural evolution of OH terminated polycyclic aromatic hydrocarbons (PAHs) from resorcinol polycondensation. In purified CDs, PAHs embedded in the amorphous carbogenic core are responsible for an intense green fluorescence emission with a quantum yield up to ∼40%. Such band exhibits high resistance to UV photobleaching, attributed to the physical protection of the carbogenic matrix. Finally, adding a strong acid/base to the CD solution, the CD fluorescence can be cyclically quenched/restored (due to reversible aggregation), suggesting the convenient use of such CDs in on/off sensors or stimulus-responding devices.
Diketopyrrolopyrrole (DPP) is a pivotal functional group to tune the physicochemical properties of novel organic photoelectronic materials. Among its multiple uses, DPP-thiophene derivatives forming a dimer through a vinyl linker were recently shown to quench the fluorescence observed in their isolated monomers. Here, we explain this fluorescence quenching using computational chemistry. The DPP-thiophene dimer has a low-lying doubly excited state that is not energetically accessible for the monomer. This state delays the fluorescence allowing internal conversion to occur first. We characterize the doubly excited state wavefunction by systematically changing the derivatives to tune the pi-scaffold size and the acceptor and donor characters. The origin of this state's stabilization is related to the increase in the π-system and not to the charge-transfer features. This analysis delivers core conceptual information on the electronic properties of organic chromophores arranged symmetrically around a vinyl linker, opening new ways to control the balance between luminescence and internal conversion.
We assess recent TD-DFT methods on excimers and highlight shortcomings of current strategies to treat dispersion in excited states.
Extended quantum chemical calculations were performed for the tetracene dimer to provide benchmark results, analyze the excimer survival process, and explore the possibility of using long-range-corrected (LC) time-dependent second-order density functional tight-biding (DFTB2) for this system. Ground- and first-excited-state optimized geometries, vertical excitations at relevant minima, and intermonomer displacement potential energy curves (PECs) were calculated for these purposes. Ground-state geometries were optimized with the scaled-opposite-spin (SOS) second-order Møller–Plesset perturbation (MP2) theory and LC-DFT (density functional theory) and LC-DFTB2 levels. Excited-state geometries were optimized with SOS-ADC(2) (algebraic diagrammatic construction to second-order) and the time-dependent approaches for the latter two methods. Vertical excitations and PECs were compared to multireference configuration interaction DFT (DFT/MRCI). All methods predict the lowest-energy S0 conformer to have monomers parallel and rotated relative to each other and the lowest S1 conformer to be of a displaced-stacked type. LC-DFTB2, however, presents some relevant differences regarding other conformers for S0. Despite some state-order inversions, overall good agreement between methods was observed in the spectral shape, state character, and PECs. Nevertheless, DFT/MRCI predicts that the S1 state should acquire a doubly excited-state character relevant to the excimer survival process and, therefore, cannot be completely described by the single reference methods used in this work. PECs also revealed an interesting relation between dissociation energies and the intermonomer charge-transfer interactions for some states.
Functionalization of quantum carbon dots (QCDs) and graphene quantum dots (GQDs) is a popular way to tune their optical spectra increasing their potential applicability in material science and biorelated disciplines. Based on the experimental observation, functionalization by fluorine atoms induces substantial shifts in absorption and emission spectra and an intensity increase. Understanding of the effects due to fluorine functionalization at the atomic scale level is still challenging due to the complex structure of fluorinated QCDs. In this work, the effect of covalent edge-fluorination and fluorine anion doping on absorption and emission spectra of prototypical polycyclic aromatic hydrocarbons pyrene and circum-pyrene has been investigated. The ways to achieve efficient red-shifts in the UV spectra and obtaining reasonable intensities stood in the focus of the work. High-level quantum chemical methods based on density functional theory/multireference configuration interaction (DFT/MRCI) and single-reference second-order algebraic diagrammatic construction (ADC(2)) and density functional theory (DFT) using the CAM-B3LYP functional have been used for this purpose. The calculations show that doping with the fluoride anion can have significant effects on the electronic spectrum. However, the effect of the fluoride ion is strongly dependent on its position with respect to the QCD. The localization above the GQDs causes large red-shifts to both the absorption and emission of spectra of GQDs, while in-plane localization leads to only negligible shifts and a tendency to dissociation after electronic excitation. Thus, large red-shifts, observed in complexes with F-, are obtained due to the introduction of new excited states with large CT character not yet been considered previously in this context, although they have the potential to significantly influence the photophysics of quantum dots. Doping by edge fluorination redshifts the spectra only slightly. This study provides insights on fluorine-doped GQDs, which is conducive to promoting its rational design and controllable synthesis.
Tuning of the electronic spectra of carbon dots by means of inserting heteroatoms into the π-conjugated polycyclic aromatic hydrocarbon (PAH) system is a popular tool to achieve a broad range of absorption and emission frequencies. Especially nitrogen atoms have been used successfully for that purpose. Despite the significant progress achieved with these procedures, the prediction of specific shifts in the UV-vis spectra and the understanding of the electronic transitions is still a challenging task. In this work, high-level quantum chemical methods based on multireference (MR) and single-reference (SR) methods have been used to predict the effect of different nitrogen doping patterns inserted into the prototypical PAH pyrene on its absorption spectrum. Furthermore, a simple classification scheme based on valence bond (VB) theory and the Clar sextet rule in combination with the harmonic oscillator measure of aromaticity (HOMA) index was applied to arrange the different doping structures into groups and rationalize their electronic properties. The results show a wide variety of mostly redshifts in the spectra as compared to the pristine pyrene case. The most interesting doping structures with the largest red shifts leading to absorption energies below one eV could be readily explained by the occurrence of diradical VB structures in combination with Clar sextets. Moreover, analysis of the electronic transitions computed with MR methods showed that several of the low-lying excited states possess double-excitation character, which cannot be realized by the popular SR methods and, thus, are simply absent in the calculated spectra.
In the past two decades, the combined density functional theory and multireference configuration interaction (DFT/MRCI) method has developed from a powerful approach for computing spectral properties of singlet and triplet excited states of large molecules into a more general multireference method applicable to states of all spin multiplicities. In its original formulation, it shows great efficiency in the evaluation of singlet and triplet excited states which mainly originate from local one‐electron transitions. Moreover, DFT/MRCI is one of the few methods applicable to large systems that yields the correct ordering of states in extended π‐systems where double excitations play a significant role. A recently redesigned DFT/MRCI Hamiltonian extends the application range of the method to bi‐chromophores such as hydrogen‐bonded or π‐stacked dimers and loosely coupled donor–acceptor systems. In conjunction with a restricted‐open shell Kohn–Sham optimization of the molecular orbitals, even electronically excited doublet and quartet states can be addressed. After a short outline of the general ideas behind this semi‐empirical method and a brief review of alternative approaches combining density functional and multireference wavefunction theory, formulae for the DFT/MRCI Hamiltonian matrix elements are presented and the adjustments of the two‐electron contributions are discussed. The performance of the DFT/MRCI variants on excitation energies of organic molecules and transition metal compounds against experimental or ab initio reference data is analyzed and case studies are presented which show the strengths and limitations of the method. Finally, an overview over the properties available from DFT/MRCI wavefunctions and further developments is given.
This article is categorized under:
• Electronic Structure Theory > Density Functional Theory
• Electronic Structure Theory > Semiempirical Electronic Structure Methods
• Software > Quantum Chemistry
Graphene quantum dots (GQDs) are promising materials in a variety of optical applications, such as bioimaging and photovoltaics, but such applications are hindered by the poor understanding of their optical properties, in particular under the influence of functional groups. By theoretically studying the effects of the surface functionalization of oxygen-containing groups (-COC-, -OH, -OCH3, -COOH, and -COCH3) on the optical properties of a GQD, we found that the absorption and emission properties of the systems vary significantly depending on the chemisorption sites of the functional group. Remarkably, given that the optical gap of the GQD is just 2.68 eV, the optical gap difference between two GQD oxide isomers can be as large as 2.39 eV. The notably small optical gaps (<0.66 eV) in specific GQD oxide configurations indicate that each kind of these chemical groups may greatly facilitate non-radiative decay in photo-excited GQDs, consequently causing diminished photoluminescence efficiency. All the optical features in the GQD oxides are rationalized by electronic structure modifications upon the chemisorption of the oxygen-containing group(s) on the GQD surface. The functional group-coverage influence and Stokes shifting are also revealed. This study sheds light on the experimental inconsistencies regarding the roles of O-containing groups in affecting the optics of GQDs and related materials and provides a valuable reference for further experiments.
The advantages conferred by the physical, optical and electrochemical properties of graphene-based nanomaterials have contributed to the current variety of ultrasensitive and selective biosensor devices. In this review, we present the points of view on the intrinsic properties of graphene and its surface engineering concerned with the transduction mechanisms in biosensing applications. We explain practical synthesis techniques along with prospective properties of the graphene-based materials, which include the pristine graphene and functionalized graphene (i.e., graphene oxide (GO), reduced graphene oxide (RGO) and graphene quantum dot (GQD). The biosensing mechanisms based on the utilization of the charge interactions with biomolecules and/or nanoparticle interactions and sensing platforms are also discussed, and the importance of surface functionalization in recent up-to-date biosensors for biological and medical applications.
Carbon-based organic electronics are a technology, with the potential of complementing and substituting opto-electronic devices based on inorganic semiconductors and metals. In the group of organic semiconductors, carbon allotropes come with outstanding opto-electric properties and are remarkable candidates for novel applications like printed electronics via solution-processing on mechanically flexible, robust and light weight substrates, while reducing the environmental impact. Carbon allotropes like fullerenes, graphene quantum dots (GQD), carbon nanotubes (CNT), graphene and also diamond are especially interesting for photodetectors due to their tunable bandgap, high absorption coefficients and high charge carrier mobilites. These unique opto-electric properties of the allotropes, which strongly depend on their molecular dimensionality (0D, 1D, 2D and 3D), allow each allotrope to be used in a preferential range. Hence, relying on the intrinsic properties of carbon allotropes or by hybridization, carbon-based photodetectors are built for a spectral bandwidth, reaching from gamma-rays to THz radiation. This review highlights the recent advances in photodetectors based on fullerenes, GQDs, CNTs, graphene and diamond, with the focus on room temperature-operated devices. The versatility of multi-dimensional carbon allotropes is outstanding, and promising results outline the maturing of all carbon-based photodetection across the technologically relevant wavelengths.
Graphene quantum dots (GQDs) are a new class of fluorescent reporters promising various novel applications including bio-imaging, optical sensing and photovoltaics. They have recently attracted enormous interest owing to their extraordinary and tunable optical, electrical, chemical and structural properties. The widespread use of GQDs, however, is hindered by the current poor understanding of their photoluminescence (PL) mechanisms. Using density-functional theory (DFT) and time-dependent DFT calculations, we reveal that the PL of a GQD can be sensitively tuned by its size, edge configuration, shape, attached chemical functionalities, heteroatom doping and defects. In addition, it is discovered that the PL of a large GQD consisting of heterogeneously hybridized carbon network is essentially determined by the embedded small sp2 clusters isolated by sp3 carbons. This study not only provides explanation to the previous experimental observations but also provides insightful guidance to develop methods for controllable synthesis and engineering of GQDs.
To obtain graphene-based fluorescent materials, one of the effective approaches is to convert one-dimensional (1D) graphene to 0D graphene quantum dots (GQDs), yielding an emerging nanolight with extraordinary properties due to their remarkable quantum confinement and edge effects. In this review, the state-of-the-art knowledge of GQDs is presented. The synthetic methods were summarized, with emphasis on the top-down routes which possess the advantages of abundant raw materials, large scale production and simple operation. Optical properties of GQDs are also systematically discussed ranging from the mechanism, the influencing factors to the optical tunability. The current applications are also reviewed, followed by an outlook on their future and potential development, involving the effective synthetic methods, systematic photoluminescent mechanism, bandgap engineering, in addition to the potential applications in bioimaging, sensors, etc.
Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self‐consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients.
The photodynamics of a C60-dithiapyrene donor-acceptor conjugate were compared with the corresponding C60-pyrene conjugate. The photoinduced charge separation and subsequent charge recombination processes were examined by time-resolved fluorescence measurements on the picosecond timescale and transient absorption measurements on the picosecond and microsecond timescales with detection in the visible and near-infrared regions. We have observed quite long lifetimes (i.e., up to 1.01 ns) for the photogenerated charge-separated state in a C60-dithiapyrene dyad without the need for i) a long spacer between the two moieties, or ii) a gain in aromaticity in the radical ion pair.
Carbon dots (CDs), as a new type of luminescent zero-dimensional carbon nanomaterial, have been applied in a variety of fields. Currently, functionalization of CDs is an extremely useful method for effectively tuning their intrinsic structure and surface state. Heteroatom doping and surface modification are two functionalization strategies for improving the photophysical performance and broadening the range of applications for fluorescent CDs. Heteroatom doping in CDs can be used to tune their intrinsic properties, which has received significant research interests because of its simplicity. Surface modification can be applied for varying active sites and the functional groups on the CDs surface, which can endow fluorescent CDs with the unique properties resulting from functional ligand. In this review, we summarize the structural and physicochemical properties of functional CDs. We focused our review on the latest developments in functionalization strategies for CDs and discuss the detailed characteristics of different functionalization methods. Ultimately, we hope to inform researchers on the latest progress in functionalization of CDs and provide perspectives on future developments for functionalization of CDs and their potential applications.
Five paradigmatic polycyclic aromatic hydrocarbons (PAHs) (pyrene, circum-1-pyrene, coronene, circum-1-coronene, and circum-2-coronene) are used for studying the performance of three single-reference methods {scaled opposite-spin-algebraic diagrammatic construction to second-order [SOS-ADC(2)], time-dependent (TD)-B3LYP, and TD-Coulomb-attenuating method (CAM)-B3LYP} and three multireference (MR) methods [density functional theory/multireference configuration interaction (DFT/MRCI), strongly contracted-n-electron valence state perturbation theory to second order (NEVPT2), and spectroscopy oriented configuration interaction (SORCI)]. The performance of these methods was evaluated by comparison of the calculated vertical excitation energies with experiments, where available. DFT/MRCI performs best and thus was used as a benchmark for other approaches where experimental values were not available. Both TD-B3LYP and NEVPT2 agree well with the benchmark data. SORCI performs better for coronene than for pyrene. SOS-ADC(2) does reasonably well in terms of excitation energies for smaller systems, but the error increases somewhat as the size of the system gets bigger. The natural transition orbital analysis for SOS-ADC(2) results indicated that at least two configurations were essential to characterize most of the lower-case electronic states. TD-CAM-B3LYP gives the largest errors for excitation energies and also gives an incorrect order of the lowest two states in circum-1-pyrene. A strong density increase of dark states was observed in the UV spectra with increasing size except for the lowest few states which remained well separated. An extrapolation of the UV spectra to infinite PAH size for S1, S2, and the first bright state based on the coronene series was made. The extrapolated excitation energies closest to experimental measurements on graphene quantum dots were obtained by TD-CAM-B3LYP.
The study of electronically excited states of stacked polycyclic aromatic hydrocarbons (PAHs) is of great interest due to promising applications of these compounds as luminescent carbon nanomaterials such as graphene quantum dots (GQDs) and carbon dots (CDs). In this study, the excited states and excitonic interactions are described in detail based on four CD model dimer systems of pyrene, coronene, circum-1-pyrene and circum-1-coronene, respectively. Two multi-reference methods, DFT/MRCI and SC-NEVPT2, and two single-reference methods, ADC(2) and CAM-B3LYP have been used for excited states calculations. The DFT/MRCI method has been used as benchmark method to evaluate the performance of the other ones. All methods produce useful lists of excited states. However, an overestimation of excitation energies and inverted ordering of states, especially concerning the bright HOMO-LUMO excitation, is observed. In the pyrene-based systems, the first bright state appears among the first four states whereas the number of dark states is significantly larger for the coronene-based systems. Fluorescence emission properties are addressed by means of geometry optimization in the S1 state. Inter sheet distances for the S1 state decrease in comparison to the corresponding ground-state values. These reductions are largest for the pyrene dimer and decrease significantly for the larger dimers. Several minima have been determined on the S1 energy surface for most of the dimers. The largest variability in emission energies is found for the pyrene dimer whereas in the other cases a more regular behavior of the emission spectra is observed.
The combination of density functional theory and multireference configuration interaction (DFT/MRCI) is a well-established semi-empirical method suitable for computing spectral properties of large molecular systems. To this day, three different Hamiltonians and various parameter set combinations exist. These DFT/MRCI variants are well tried and tested when it comes to electronic excitations of organic molecules. For transition metal complexes, systematic benchmarks against experimental data are missing, however. Here we present an assessment of the DFT/MRCI variants and of time-dependent, linear-response density functional theory (TDDFT) for a diverse set of ligand-centered, metal-to-ligand charge transfer, metal-centered, and ligand-to-metal charge transfer (LMCT) excitations on 21 3d and 4d complexes comprising 10 small inorganic and 11 larger metalorganic compounds with closed-shell ground states. In the course of this assessment, we realized that the excitation energies of transition metal complexes can be very sensitive with respect to the details of the damping function that scales off-diagonal matrix elements. This scaling is required in DFT/MRCI to avoid double counting of dynamic electron correlation. These insights lead to a new Hamiltonian, denoted R2018, with improved performance on transition metal compounds, while the results for organic molecules are nearly unaffected by the modified damping function. Two parameter sets were optimized for this Hamiltonian: One set is to be used in conjunction with the standard configuration selection threshold of 1.0 E
h
and a second set is for use with a selection threshold of 0.8 E
h
which leads to shorter wave function expansions. The R2018 Hamiltonian in standard parameterization achieves root-mean-square errors (RMSEs) of merely 0.15 eV for the metalorganic complexes, followed by 0.20 eV for the original DFT/MRCI ansatz, and 0.25 eV for the redesigned DFT/MRCI approach. In comparison, TDDFT gives a much larger RMSE of 0.46 eV for metalorganic complexes. None of the DFT/MRCI variants yields convincing results for small oxides and fluorides which exhibit LMCT transitions. Here, TDDFT performs better. If the oxides and fluorides are excluded from the inorganic test set, satisfactory agreement can be achieved, with RMSE values between 0.26 eV and 0.30 eV for DFT/MRCI and 0.34 eV for TDDFT. The performance of the original and the new DFT/MRCI Hamiltonians deteriorates only slightly, when a tighter selection threshold is chosen, thus enabling the computation of reliable spectral properties even for large metalorganic complexes.
In recent decade, carbon dots have drawn intensive attention in its own right and triggered substantial investigation. Carbon dots manifest superior merits including excellent bio-compatibility for both in vitro and in vivo, resistance to photo-bleaching, being easy to surface functionalization and bio-conjugation, outstanding colloidal stability, eco-friendly synthesis, and low cost. All of these endow them the high potential to replace the conventional unsatisfied florescent heavy meal contained semiconductor quantum dots or organic dyes. Even though the picture of their photoluminescence mechanism is still controversial, carbon dots have already exhibited versatile applications. In this article, we summarize and review the recent progress achieved in the field of carbon dots, where we provide the comprehensive summary and discussion on synthesis methods and emission mechanisms in section 2 and 3 respectively. We also present the applications achieved from carbon dots in bio-imaging, drug-delivery, microfluidics, light emitting diode (LED), sensing, logic gates, and chiral photonics etc.. Some unaddressed issues, challenges, and prospects of carbon dots are discussed and displayed in the last section. We envision that carbon dots will eventually go to market and become a strong competitor to some currently used fluorescent materials. It is our hope that this review can provide insight into both the fundamental research and practical applications of carbon dots.
Unexpectedly discovered photoluminescence of carbon nanoparticles attracted attention of many researchers and resulted in a variety of applications. Meantime the origin of their emission is still obscure, and the majority of discussions proceed around their molecular and/or excitonic emissive states. Performing cryogenic studies down to 10 K, we did not observe any signatures of suppressed molecular relaxations – the spectra remained broad showing large unaltered Stokes shift and temperature-independent emission intensities and lifetimes below 80 K with a weak dependence above this value. We demonstrate that the most general feature of carbon nanoparticles, the very large Stokes shifts and considerable differences between absorption and excitation spectra, are the result of formation of the dynamic defect, the self-trapped Frenkel exciton. It looks like the distorted domain of H-aggregate due to the exciton-lattice interaction and the local overheating caused by the exciton relaxation. In addition, at low temperatures the long-lifetime spectral component was found; it was attributed to phosphorescence. The obtained results present a strong support for the excitonic nature of fluorescence of nanocarbon materials.
Carbon dots (CDs) are a stable and highly biocompatible fluorescent material offering great application potential in cell labeling, optical imaging, LED diodes, and optoelectronic technologies. Because their emission wavelengths provide the best tissue penetration, red-emitting CDs are of a particular interest for applications in biomedical technologies. Current synthetic strategies enabling red-shifted emission include increasing the CD particle size (sp2 domain) by a proper synthetic strategy and tuning the surface chemistry of CDs with suitable functional groups (e.g., carboxyl). Here we present an elegant route for preparing full-color CDs with well-controllable fluorescence at blue, green, yellow, or red wavelengths. The two-step procedure involves the synthesis of a full-color emitting mixture of CDs from citric acid and urea in formamide followed by separation of the individual fluorescent fractions by column chromatography based on differences in CD charge. Red-emitting CDs, which had the most negative charge, were separated as the last fraction. The trend in the separation, surface charge, and red-shift of photoluminescence was caused by increasing amount of graphitic nitrogen in the CD structure as was clearly proved by XPS, FT-IR, Raman spectroscopy, and DFT calculations. Importantly, graphitic nitrogen generates midgap states within the HOMO-LUMO gap of the un-doped systems, resulting in significantly red-shifted light absorption that in turn gives rise to fluorescence at the low-energy end of the visible spectrum. The presented findings identify graphitic nitrogen as another crucial factor that can red-shift the CD photoluminescence.
Graphene quantum dots, the next generation carbon based nanomaterials, due to their outstanding physical, chemical and biological properties, have shown potential in revolutionizing the future of nanomedicine and biotechnology. Their strong size-dependent photoluminescence (PL) and the presence of reactive groups on the GQD surface, which allow their multimodal conjugation with various functional groups and biologically active molecules, make them ideal candidates for cancer diagnosis and treatment. GQDs have been loaded with drugs and labeled with tumor-targeting ligand units that are able to specifically recognize cancer receptors exposed on the cancer cell surface by generating new therapies that are able to allow a more efficient targeted delivery of anticancer agents while minimizing their distribution in healthy tissues, as well as the development of new imaging agents for the in vitro and in vivo diagnosis of several types of cancer. Here, we review the recent advances in the study of the application of GQDs as nanoplatforms for anticancer therapy, taking into account the methods used for their synthesis and functionalization procedures, which can deeply affect their biocompatibility and their electronic and optical features. The biosafety and toxicity aspects of these nanomaterials at cellular and animal levels, mainly related to their size and the kind and degree of surface functionalization, are also discussed.
Graphene quantum dots (GQDs) have generated enormous excitement because of their superiority in chemical inertness, biocompatibility and low toxicity. Due to quantum confinement and edge effects, GQDs have excellent properties, attracting extensive attention from scientists in the field of chemistry, physics, materials, biology, and other interdisciplinary sciences. In this review, we aimed to present a comprehensive view on the synthesis of GQDs for biological applications. We highlighted the potential methods like acid oxidation, hydrothermal and solvothermal reactions, microwave-assisted methods, electrochemical oxidation, as well as pyrolysis and carbonization for successful preparation of GQDs. Meanwhile, four representative types of the biomedical applications based on GQDs, such as bioimaging, biosensing, drug delivery, and antimicrobial materials, were introduced and discussed in detail. This work will be highly useful for quickly getting knowledge and experience for synthesizing various GQDs, and develop advanced strategies for creating novel functional GQD-based nanomaterials for further applications in biomedicine, materials science, analytical science, and optical nanodevices.
Graphene has emerged as a champion material for a variety of applications cutting across multiple disciplines in science and engineering. Graphene and its derivatives have displayed huge potential as a biosensing material due to their unique physicochemical properties, good electrical conductivity, optical properties, biocompatibility, ease of functionalization, and flexibility. Their widespread use in making biosensors has opened up new possibilities for early diagnosis of life-threatening diseases and real-time health monitoring. Following an introduction and discussion on the significance of fabrication protocols and assembly, this review is intended to assess why graphene is suitable to build better biosensors, the working of existing biosensing schemes and their current status toward commercialization for wearable diagnostic and prognostic devices. We believe this review will provide a critical insight for harnessing graphene as a suitable biosensor for the clinical diagnostics, its future prospects and challenges ahead.
In recent years, graphene quantum dots (GQDs) have been recognized as an attractive building block for electronic, photonic, and bio-molecular device applications. This paper reports the current status of studies on the novel properties of GQDs and their hybrids with conventional and low-dimensional materials for device applications. In this review, more emphasis is placed on the structural, electronic, and optical properties of GQDs, and device structures based on the combination of GQDs with various semiconducting/insulating materials such as graphene, silicon dioxide, Si quantum dots, silica nanoparticles, organic materials, and so on. Because of GQDs' unique properties, their hybrid structures are employed in high-efficiency devices, including photodetectors, solar cells, light-emitting diodes, flash memory, and sensors.
Graphene is a novel two-dimensional (2D) material composed of one atomic thick planar sheet of sp2-bonded carbon atoms perfectly arranged in a honeycomb lattice which has exceptional photonic and electronic properties. We believe that the true potential of graphene also lies in optical sensors especially for bio-chemical sensing in health care sector. The large surface area of graphene is able to enhance the surface loading of desired bio-chemical molecules. Whenever the bio-molecules comes in contact with graphene, the fermi level will shifts either p-type or n-type resulting in change in opto-electronic properties. The most important factors in graphene based optical sensing is lowering the limit of detection (LOD) and increasing the specificity in label-free bio-chemical sensing. This article comprehensively and critically reviews the emerging graphene optical bio-chemical sensors. We firstly elaborate their opto-electronic properties, fabrication, numerical model and simulation, and then review various sensing applications such as single cell detection, neural imaging and optogenetics, colorimetric multifunctional sensors, cancer diagnosis, protein and DNA sensing, and gas sensing. Finally, current and future trends of graphene optical bio-chemical sensors are discussed.
The molecular origin of the photoluminescence of carbon dots (CDs) is not known. This restricts the design of CDs with desired optical properties. We have synthesized CDs starting from carbohydrates by employing a simple synthesis method. We were able to demonstrate that the CDs are composed of aggregated hydroxymethylfurfural (HMF) derivatives. The optical properties of these CDs are quite unique. These CDs exhibit an excitation-independent PL emission maximum in the orange-red region (λ ∼ 590 nm). These CDs also exhibit excitation as well as monitoring wavelength-independent single exponential PL decay. These observations indicate that only one type of chromophore (HMF derivative) is present within the CDs. Several HMF derivatives are aggregated within the CDs; therefore, the aggregated structure cause a large Stokes shift (∼150 nm). By several control experiments, we showed that the same aggregated chromophore unit (HMF derivative), and not the individual fluorophores, is the fluorescing unit. The emission maximum and the single exponential PL lifetime are independent of the polarity of the medium. The existence of a low-lying trap state could be reduced quite significantly. A model has been proposed to explain the interesting steady state and dynamical photoluminescence behaviour of the CDs. As the molecular origin of their photoluminescence is known, CDs with desired optical properties can be designed.
Photoluminescent nanosized allotropes of carbon have attracted considerable interest because of their diverse optical properties depending on their crystal structure, size, and morphology, and chemical functionalization. Here, we present the first critical review covering the photoluminescence (PL) properties, their control, and origin in various carbon allotropes and their composites. Different mechanisms by which carbon nanostructures exhibit PL are discussed, involving excitonic PL in carbon nanotubes, thermally activated delayed fluorescence in spherical fullerenes, the presence of impurity-vacancy color centers in nanodiamonds, aromatic sp2 domains in reduced graphene oxide, and surface chromophores or defect-related PL in carbon dots. We critically analyze the intrinsic and external effects affecting the PL properties (spectral shift, decay, quantum yield) from both experimental data and theoretical calculations. The key parameters addressed include, for example, the type and content of impurity elements in nanodiamonds (NV and SiV centers), chemical composition in reduced graphene oxides, external effects (temperature, solvent) in C60 fullerene, structural type (single-wall versus multi-wall carbon nanotubes), and the roles of doping and surface functional groups in the PL behavior of carbon/graphene dots.
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
The knowledge gap on how different types of nitrogen centers affect the optical properties of N-doped carbon dots (CDs) hinders the rational design and synthesis of these nanostructures. We present a systematic theoretical study of 1 nm small CD models containing nitrogen and oxygen functional groups designed to explore the effects of various nitrogen centers on the absorption characteristics of CDs. Graphitic nitrogen is shown to have an electron-doping effect that alters the systems’ electronic energy levels and causes pronounced red-shift of their absorption spectra. Other kinds of nitrogens including pyridinic, pyrrolic, and amino centers had no appreciable effects on the CDs’ absorption properties.
Carbon dots (CDs) have attracted rapidly growing interest in recent years due to their unique and tunable optical properties, the low cost of fabrication and their wide-spread uses. However, due to the complex structure of CDs, both the molecular ingredients and the intrinsic mechanisms governing photoluminescence of CDs are poorly understood. Among other features, a large Stokes shift of over 100 nm and a photoluminescence spectrally dependent on the excitation wavelength, have so far not been adequately explained. In this paper we investigate the properties of CDs and develop a model system to mimic the optical properties of the CDs. This system was comprised of three types of polycyclic aromatic hydrocarbon (PAH) molecules with fine-tuned concentrations embedded in a polymer matrix. We show the Stokes shift to be due to the self-trapping of an exciton in the PAH network. The width and the excitation dependence of the emission comes from a selective excitation of PAHs with slightly different energy gaps and from energy transfer between them. These insights will help to tailor the optical properties of CDs and help their implementation into applications, e.g. light-emitting devices and biomarkers. This could also lead to "artificial" tunable carbon dots by locally modifying the composition and consequently the optical properties of composite PAH films.
At present, the actual mechanism of the photoluminescence (PL) of fluorescent carbon dots (CDs) is still an open debate among researchers. Because of the variety of CDs, it is highly important to summarize the PL mechanism for these kinds of carbon materials; doing so can guide the development of effective synthesis routes and novel applications. This review will focus on the PL mechanism of CDs. Three types of fluorescent CDs were involved: graphene quantum dots (GQDs), carbon nanodots (CNDs), and polymer dots (PDs). Four reasonable PL mechanisms have been confirmed: the quantum confinement effect or conjugated π-domains, which are determined by the carbon core; the surface state, which is determined by hybridization of the carbon backbone and the connected chemical groups; the molecule state, which is determined solely by the fluorescent molecules connected on the surface or interior of the CDs; and the crosslink-enhanced emission (CEE) effect. To give a thorough summary, the category and synthesis routes, as well as the chemical/physical properties for the CDs, are briefly introduced in advance.
The time-dependent density functional theory (TD-DFT) double-hybrid methods TD-B2-PLYP and TD-B2GP-PLYP are applied to five linear and 12 nonlinear polycyclic aromatic hydrocarbons. The absolute errors compared to experiment for the two lowest-lying 1La and 1Lb excited states are evaluated and it is also tested whether the energetic order of those states and their energy difference is reproduced correctly. The results are compared to published CC2, global hybrid, and long-range corrected hybrid TD-DFT results. The two double-hybrids outmatch the other methods in terms of absolute and relative accuracy without an empirical adjustment of parameters. Although of different electronic character, both types of states are described on an equal footing by the double-hybrids. Particularly, the B2GP-PLYP functional yields very good results, which is in accordance with previous benchmarks.
The excited states of a diverse set of molecules are examined using a collection of newly implemented analysis methods. These examples expose the particular power of three of these tools: (i) natural difference orbitals (the eigenvectors of the difference density matrix) for the description of orbital relaxation effects, (ii) analysis of the one-electron transition density matrix in terms of an electron-hole picture to identify charge resonance and excitonic correlation effects, and (iii) state-averaged natural transition orbitals for a compact simultaneous representation of several states. Furthermore, the utility of a wide array of additional analysis methods is highlighted. Five molecules with diverse excited state characteristics are chosen for these tasks: pyridine as a prototypical small heteroaromatic molecule, a model system of six neon atoms to study charge resonance effects, hexatriene in its neutral and radical cation forms to exemplify the cases of double excitations and spin-polarization, respectively, and a model iridium complex as a representative metal organic compound. Using these examples a number of phenomena, which are at first sight unexpected, are highlighted and their physical significance is discussed. Moreover, the generality of the conclusions of this paper is verified by a comparison of single- and multireference ab initio methods.
A procedure for a detailed analysis of excited states in systems of interacting chromophores is proposed. By considering the one-electron transition density matrix, a wealth of information is recovered that may be missed by manually analyzing the wave function. Not only are the position and spatial extent given, but insight into the intrinsic structure of the exciton is readily obtained as well. For example, the method can differentiate between excitonic and charge resonance interactions even in completely symmetric systems. Four examples are considered to highlight the utility of the approach: interactions between the n$pi$* states in a formaldehyde dimer, excimer formation in the naphthalene dimer, stacking interaction in an adenine dimer, and the excitonic band structure in a conjugated phenylenevinylene oligomer.
Within the framework of the many-body Green's-function method we present a new approach to the polarization propagator for finite Fermi systems. This approach makes explicit use of the diagrammatic perturbation expansion for the polarization propagator, and reformulates the exact summation in terms of a simple algebraic scheme, referred to as the algebraic diagrammatic construction (ADC). The ADC defines in a natural way a set of approximation schemes (nth-order ADC schemes) which represent infinite partial summations exact up to nth order of perturbation theory. In contrast to the random-phase-approximation (RPA)-like schemes, the corresponding mathematical procedures are essentially Hermitian eigenvalue problems in limited configuration spaces of unperturbed excited configurations. Explicit equations for the first- and second-order ADC schemes are derived. These schemes are thoroughly discussed and compared with the Tamm-Dancoff approximation and RPA schemes.
An effective Hamiltonian in a basis of spin- and space-symmetry adapted configuration state functions (CSF), which includes information from Kohn–Sham density functional theory (DFT), is used to calculate configuration interaction (CI) wave functions for the electronic states of molecules. The method emphasizes on states of multiconfigurational character which cannot be represented by conventional DFT. The CI matrix elements are constructed empirically by using the exact operator and corrections from DFT. Both the optimized KS orbitals from the parent determinant and the corresponding KS potential from the parent state density are used. Depending on their energy gap the CI off-diagonal elements between CSF are exponentially scaled to zero to avoid double counting of electron correlation. The selection of the most important CSF describing nondynamical correlation effects and the use of an approximate resolution of the identity (RI) for the evaluation of the two-electron integrals allows a very efficient DFT/MRCI treatment of molecules with several hundreds of electrons. As applications, the prediction of excitation energies for singlet and triplet states of organic molecules and transition metal complexes, the calculation of electronic circular dichroism spectra and investigations of the energetics of diradicals are presented. It is found, that the new DFT/MRCI approach gives results of high accuracy (rms errors for relative energies <0.2 eV) comparable to those from sophisticated ab initio treatments. © 1999 American Institute of Physics.
A new implementation of the approximate coupled cluster singles and doubles method CC2 is reported, which is suitable for large scale integral-direct calculations. It employs the resolution of the identity (RI) approximation for two-electron integrals to reduce the CPU time needed for calculation and I/O of these integrals. We use a partitioned form of the CC2 equations which eliminates the need to store double excitation cluster amplitudes. In combination with the RI approximation this formulation of the CC2 equations leads to a reduced scaling of memory and disk space requirements with the number of correlated electrons (n) and basis functions (N) to, respectively, O(N2) and O(nN2), compared to O(n2N2) in previous implementations. The reduced CPU, memory and disk space requirements make it possible to perform CC2 calculations with accurate basis sets on large molecules, which would not be accessible with conventional implementations of the CC2 method. We present an application to vertical excitation energies of alkenes C2nH2n+2, for n=1-12, and report results for the lowest lying dipole-allowed transitions for the TZVPP basis sets, which for n=12 contain 1108 basis functions. Comparison with conventional CC2 results for the smaller alkenes show that for CC2 ground state energies and for excitation energies of valence states, the error due to the RI approximation is negligible compared to the usual basis set error, if auxiliary basis sets are used, which have been optimized for MP2 energy calculations.
The excited states of polycyclic aromatic hydrocarbons (PAH) with up to 28 π-electrons have been investigated in the framework of time-dependent density functional theory (TDDFT). Calculations of the two lowest-lying singlet–singlet and the lowest-lying singlet–triplet excitation energies for sixteen molecules of very different structure are used to assess the accuracy and applicability of the method. The gradient corrected BP86 and hybrid-type B3LYP functionals together with the large cc-pVTZ AO basis set have been used. In general it is found that TDDFT should be used with caution for the singlet states of these large unsaturated π-systems. The TDDFT approach underestimates the excitation energies for states with dominant ionic character () with a mean absolute deviation (MAD) of 0.18 eV (B3LYP) and 0.49 eV (BP86), respectively. The MAD for covalent (B3LYP: 0.24 eV, BP86: 0.12 eV) and (B3LYP: 0.04 eV, BP86: 0.05 eV) states are significantly smaller. The TDDFT results are also compared with those from a semi-empirical time-dependent Pariser–Parr–Pople (TDPPP) treatment which is found to be very accurate ( eV) for the systems considered. The TDDFT errors are analyzed in a simplified valence-bond picture derived from the TDPPP data. It is shown that the TDDFT errors correlate linearly with the estimated ioniticity of the states which may open a route to correct TDDFT results or to improve existing functionals.
Fluorescence excitation and SVL fluorescence spectra of jet-cooled coronene are reported. Many weaker lines have been observed in addition to the well-known strong e28 basis in the S1 region. The excitation spectrum exhibits extensive combinations with an a1g (1372-cm-1) mode; otherwise it has few progressions and combinations. Fundamental frequencies in S0 and S1 are extracted with fluorescence spectroscopy. Some modes have been assigned. Fluorescence lifetimes of many SVL in S1 have been measured. Due to the high symmetry of coronene, fluorescence spectra remain relatively simple and neat even for vibrationally relaxed excited states. More subtle manifestations of IVR in fluorescence spectra were observed and interpreted.
A practical polarization propagator method devised for the treatment of valence electron excitations in atoms and molecules is presented. This method, referred to as (second-order) algebraic-diagrammatic construction (ADC(2)), allows for a theoretical description of single and double excitations consistently through second and first order, respectively, of perturbation theory. The computational scheme is essentially an eigenvalue problem of a Hermitian secular matrix defined with respect to the space of singly and doubly excited configurations. The configuration space is smaller (more compact) than that of comparable configuration interaction (CI) expansions and the method leads to size-consistent results. The performance of the ADC(2) method is tested in exemplary applications to Ne, Ar and CO, where detailed comparison can be made with experiment and previous theoretical results. While the accuracy of the absolute excitation energies is only moderate, a very satisfactory description is obtained for the relative energies and, in particular, for the spectral intensities. Aspects related to the Thomas-Reiche-Kuhn sum rule and the equivalence of the dipole-length and dipole-velocity forms of the transition moments are discussed. Due to the relatively small computational expense and the possibility of a direct ADC(2) formulation this method should prove particularly useful in applications to large molecules.
Previous attempts to combine Hartree–Fock theory with local density‐functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.
Full TDDFT combined with the commonly used hybrid functional B3LYP has been known to greatly underestimate the 1La excitation energies of large linear acenes. This has cast doubt on the TDDFT results for the similar 1La-type state in other conjugated π-systems. Although increasing the amount of Hartree–Fock (HF) exchange energy in the employed functional could improve the excitation energy estimation of the 1La state, it would worsen the results for another lowest-lying excited state,1Lb. Calculations of absorption and emitting energies relative to the 1La states for a series of linear acenes showed that a TDDFT scheme incorporating the Tamm–Dancoff approximation (TDDFT/TDA) could decrease the estimation errors by a factor of about 50%, but keep the levels of 1Lb states almost unchanged. Thus, the TDDFT/TDA scheme gives an overall description for the low-lying excited states of linear acenes significantly better than the full TDDFT does. Furthermore, 16 nonlinear polycyclic aromatic hydrocarbons (PAHs) with various structures were examined to confirm the superiority of the TDDFT/TDA over the full TDDFT in its ability to describe the 1La states for conjugated π-systems of large size. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008
The electronic spectrum of alternant polycyclic aromatic hydrocarbons (PAHs) includes two singlet excited states that are often denoted 1 L a and 1 L b . Time-dependent density functional theory (TD-DFT) affords reasonable excitation energies for the 1 L b state in such molecules, but often severely underestimates 1 L a excitation energies and fails to reproduce observed trends in the 1 L a excitation energy as a function of molecular size. Here, we examine the performance of long-range-corrected (LRC) density functionals for the 1 L a and 1 L b states of various PAHs. With an appropriate choice for the Coulomb attenuation parameter, we find that LRC functionals avoid the severe underestimation of the 1 L a excitation energies that afflicts other TD-DFT approaches, while errors in the 1 L b excitation energies are less sensitive to this parameter. This suggests that the 1 L a states of certain PAHs exhibit some sort of charge-separated character, consistent with the description of this state within valence-bond theory, but such character proves difficult to identify a priori. We conclude that TD-DFT calculations in medium-size, conjugated organic molecules may involve significant but hard-to-detect errors. Comparison of LRC and non-LRC results is recommended as a qualitative diagnostic.
The basic structure of the program system TURBOMOLE for SCF - including first and second analytical derivatives with respect to nuclear coordinates - and MP2 calculations is briefly described. The program takes full advantage of all discrete point group symmetries and has only modest - and (partially) adjustable - I/O and background storage requirements. The performance of TURBOMOLE is documented for demonstrative applications.
The result of a calculation of excited states, be it via configuration interaction methods or density functional response theory, is a set of coefficients describing the contribution that individual orbital excitations make to the total transition. Often times, there is no dominant amplitude describing the transition, making its qualitative description difficult. Natural transition orbitals dramatically simplify the situation by providing a compact representation of the transition density matrix. This is accomplished using the corresponding orbital transformation of Amos and Hall, which renders the transition density matrix diagonal and provides a unique correspondence between the excited ‘particle’ and empty ‘hole’.
Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen Møller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
This work presents theory, implementation, and validation of excited state properties obtained from time-dependent density functional theory (TDDFT). Based on a fully variational expression for the excited state energy, a compact derivation of first order properties is given. We report an implementation of analytic excited state gradients and charge moments for local, gradient corrected, and hybrid functionals, as well as for the configuration interaction singles (CIS) and time-dependent Hartree-Fock (TDHF) methods. By exploiting analogies to ground state energy and gradient calculations, efficient techniques can be transferred to excited state methods. Benchmark results demonstrate that, for low-lying excited states, geometry optimizations are not substantially more expensive than for the ground state, independent of the molecular size. We assess the quality of calculated adiabatic excitation energies, structures, dipole moments, and vibrational frequencies by comparison with accurate experimental data for a variety of excited states and molecules. Similar trends are observed for adiabatic excitation energies as for vertical ones. TDDFT is more robust than CIS and TDHF, in particular, for geometries differing significantly from the ground state minimum. The TDDFT excited state structures, dipole moments, and vibrational frequencies are of a remarkably high quality, which is comparable to that obtained in ground state density functional calculations. Thus, yielding considerably more accurate results at similar computational cost, TDDFT rivals CIS as a standard method for calculating excited state properties in larger molecules. (C) 2002 American Institute of Physics.
The optoelectronic and excitonic properties in a series of linear acenes (naphthalene up to heptacene) are investigated using range-separated methods within time-dependent density functional theory (TDDFT). In these rather simple systems, it is well-known that TDDFT methods using conventional hybrid functionals surprisingly fail in describing the low-lying L(a) and L(b) valence states, resulting in large, growing errors for the L(a) state and an incorrect energetic ordering as a function of molecular size. In this work, we demonstrate that the range-separated formalism largely eliminates both of these errors and also provides a consistent description of excitonic properties in these systems. We further demonstrate that reoptimizing the percentage of Hartree-Fock exchange in conventional hybrids to match wave function-based benchmark calculations still yields serious errors, and a full 100% Hartree-Fock range separation is essential for simultaneously describing both of the L(a) and L(b) transitions. From an analysis of electron-hole transition density matrices, we finally show that conventional hybrid functionals over-delocalize excitons and underestimate quasiparticle energy gaps in the acene systems. The results of our present study emphasize the importance of both a range-separated and asymptotically correct contribution of exchange in TDDFT for investigating optoelectronic and excitonic properties, even for these simple valence excitations.
Time-dependent double-hybrid density functional methods are evaluated for the calculation of vertical singlet-singlet valence excitation energies of a wide variety of organic molecules. Beside the already published TD-B2-PLYP method, an analogous approach based on the recently published ground state B2GP-PLYP functional is presented for the first time. Double-hybrid functionals contain a hybrid-GGA-like part for which a conventional TDDFT linear response treatment is carried out. The thus obtained excitation energies are afterwards corrected by adding a non-local correlation portion, which is based on an CIS(D) type excited state perturbative correction. Both, TD-B2-PLYP and TD-B2GP-PLYP, are first applied to the 142 vertical singlet excitation energies in a benchmark set by Schreiber et al., that contains small and medium sized organic molecules. In a second part, a new benchmark set composed of five large organic dyes is proposed. Accurate reference values are derived from experimental 0-0 excitation energies in solution. A back-correction scheme based on TDDFT computations is presented by which solvent, relaxation and vibrational effects are removed, yielding experimental vertical gas phase excitation energies with an estimated accuracy of about +/-0.1 eV. The TD-B2-PLYP, TD-B2GP-PLYP and a variety of conventional TDDFT methods are then applied to this new benchmark set. The results for both considered test sets show that the new double-hybrid approaches yield the smallest mean absolute deviations of 0.22 eV for the first benchmark set and 0.19 eV (TD-B2-PLYP) and 0.16 eV (TD-B2GP-PLYP) for the new organic dye test set. Apart from a break-down of the perturbative correction for very high-lying transitions (larger than 8 eV), it is generally found that the double-hybrid functionals show high robustness and accuracy that cannot be obtained with conventional density functionals (e.g. B3-LYP).
Unexpected failures of the popular time-dependent DFT (TDDFT) method for the pi --> pi* excited A A states (see figure) of large aromatic molecules are reported. A very probable reason for this behaviour is the underestimated interaction of important ionic components in the corresponding L-a-state wavefunctions with current standard functionals.
A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Møller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite-spin second order energy (SOS-MP2), where MP2 is Møller-Plesset theory, yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the fifth order computational steps associated with MP2 theory, even without exploiting any spatial locality. A fourth order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.
The development of nanotechnology using organic materials is one of the most intellectually and commercially exciting stories of our times. Advances in synthetic chemistry and in methods for the investigation and manipulation of individual molecules and small ensembles of molecules have produced major advances in the field of organic nanomaterials. The new insights into the optical and electronic properties of molecules obtained by means of single-molecule spectroscopy and scanning probe microscopy have spurred chemists to conceive and make novel molecular and supramolecular designs. Methods have also been sought to exploit the properties of these materials in optoelectronic devices, and prototypes and models for new nanoscale devices have been demonstrated. This Review aims to show how the interaction between synthetic chemistry and spectroscopy has driven the field of organic nanomaterials forward towards the ultimate goal of new technology.