Electronic Properties of Triangle-Shaped Graphene Nanoflakes from TAO-DFT.
ABSTRACT: Reliable prediction of the properties of nanosystems with radical nature has been tremendously challenging for common computational approaches. Aiming to overcome this, we employ thermally-assisted-occupation density functional theory (TAO-DFT) to investigate various electronic properties (e.g., singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, active orbital occupation numbers, and visualization of active orbitals) associated with a series of triangle-shaped graphene nanoflakes with n fused benzene rings at each side (denoted as n-triangulenes), which can be extended from triangulene. According to our TAO-DFT results, the ground states of n-triangulenes are singlets for all the values of n studied (n = 3, 5, 7, 9, ..., and 21). Moreover, the larger the values of n, the more significant the polyradical nature of n-triangulenes. There are approximately (n - 1) unpaired electrons for the ground state of n-triangulene. The increasing polyradical nature of the larger n-triangulenes should be closely related to the fact that the active orbitals tend to be mainly concentrated at the periphery of n-triangulenes, apparently increasing with the molecular size.
Project description:Owing to the presence of strong static correlation effects, accurate prediction of the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, active orbital occupation numbers, and real-space representation of active orbitals) of cyclacenes with n fused benzene rings (n?=?4-100) has posed a great challenge to traditional electronic structure methods. To meet the challenge, we study these properties using our newly developed thermally-assisted-occupation density functional theory (TAO-DFT), a very efficient method for the study of large systems with strong static correlation effects. Besides, to examine the role of cyclic topology, the electronic properties of cyclacenes are also compared with those of acenes. Similar to acenes, the ground states of cyclacenes are singlets for all the cases studied. In contrast to acenes, the electronic properties of cyclacenes, however, exhibit oscillatory behavior (for n???30) in the approach to the corresponding properties of acenes with increasing number of benzene rings. On the basis of the calculated orbitals and their occupation numbers, the larger cyclacenes are shown to exhibit increasing polyradical character in their ground states, with the active orbitals being mainly localized at the peripheral carbon atoms.
Project description:It has been extremely difficult for traditional theoretical methods to adequately predict the properties of systems possessing radical character (i.e., multi-reference systems), especially for multi-reference systems at the nanoscale. To circumvent this, we employ thermally-assisted-occupation density functional theory (TAO-DFT) to predict the electronic properties of Möbius cyclacenes, with the number of fused benzene rings (n) ranging from 8 to 100. In addition, to investigate the significance of Möbius topology, we also compare these properties with the respective properties of cyclacenes and acenes, containing the same number of fused benzene rings. From our TAO-DFT results, Möbius cyclacenes, cyclacenes, and acenes have singlet ground states for all the cases examined. However, unlike acenes, the electronic properties of Möbius cyclacenes and cyclacenes display clear oscillation patterns when n is small (e.g., n ≤ 10 for Möbius cyclacenes and n ≤ 23 for cyclacenes), and converge to the respective properties of acenes when n greatly exceeds 30. The polyradical character of the ground states of Möbius cyclacenes should increase with the molecular size, intimately correlated with the localization of active orbitals at the edges of molecules.
Project description:It remains rather difficult for traditional computational methods to reliably predict the properties of nanosystems, especially for those possessing pronounced radical character. Accordingly, in this work, we adopt the recently formulated thermally-assisted-occupation density functional theory (TAO-DFT) to study two-atom-wide linear boron nanoribbons l-BNR[2,n] and two-atom-wide cyclic boron nanoribbons c-BNR[2,n], which exhibit polyradical character when the n value (i.e., the number of boron atoms along the length of l-BNR[2,n] or the circumference of c-BNR[2,n]) is considerably large. We calculate various electronic properties associated with l-BNR[2,n] and c-BNR[2,n], with n ranging from 6 to 100. Our results show that l-BNR[2,n] and c-BNR[2,n] have singlet ground states for all the n values examined. The electronic properties of c-BNR[2,n] exhibit more pronounced oscillatory patterns than those of l-BNR[2,n] when n is small, and converge to the respective properties of l-BNR[2,n] when n is sufficiently large. The larger the n values, the stronger the static correlation effects that originate from the polyradical nature of these ribbons. Besides, the active orbitals are found to be delocalized along the length of l-BNR[2,n] or the circumference of c-BNR[2,n]. The analysis of the size-dependent electronic properties indicates that l-BNR[2,n] and c-BNR[2,n] can be promising for nanoelectronic devices.
Project description:In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a ?-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet containing varying polyradical character in their singlet ground state. The first class of structures already have open-shell character because of their high-spin ground state, which follows from the bonding pattern, whereas for the second class the open-shell character is generated either because of the competition between the closed-shell quinoid Kekulé and the open-shell singlet biradical resonance structures or the topology of the ?-electron arrangement of the non-Kekulé form. High-level ab initio calculations based on multireference theory have been carried out to compute singlet-triplet splitting for the above-listed compounds and to provide insight into their chemical reactivity based on the polyradical character by means of unpaired densities. Unrestricted density functional theory and Hartree-Fock calculations have been performed for comparison also in order to obtain better insight into their applicability to these types of complicated radical systems.
Project description:The electronic absorption spectra, ground-state geometries and electronic structures of symmetric and asymmetric squaraine dyes (SQD1-SQD4) were investigated using density functional theory (DFT) and time-dependent (TD-DFT) density functional theory at the B3LYP/6-311++G** level. The calculated ground-state geometries reveal pronounced conjugation in these dyes. Long-range corrected time dependent density functionals Perdew, Burke and Ernzerhof (PBE, PBE1PBE (PBE0)), and the exchange functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh) with 6-311++G** basis set were employed to examine optical absorption properties. In an extensive comparison between the optical data and DFT benchmark calculations, the BEP functional with 6-311++G** basis set was found to be the most appropriate in describing the electronic absorption spectra. The calculated energy values of lowest unoccupied molecular orbitals (LUMO) were 3.41, 3.19, 3.38 and 3.23 eV for SQD1, SQD2, SQD3, and SQD4, respectively. These values lie above the LUMO energy (-4.26 eV) of the conduction band of TiO? nanoparticles indicating possible electron injection from the excited dyes to the conduction band of the TiO? in dye-sensitized solar cells (DSSCs). Also, aromaticity computation for these dyes are in good agreement with the data obtained optically and geometrically with SQD4 as the highest aromatic structure. Based on the optimized molecular geometries, relative positions of the frontier orbitals, and the absorption maxima, we propose that these dyes are suitable components of photovoltaic DSSC devices.
Project description:We have applied DMC to evaluate relative stability of the possible electronic configurations of an isolated FePc under D 4h symmetry, considering some fixed nodes generated from different methods. They predict A 2g ground state consistently, supporting preceding DFT studies, with confidence overcoming the ambiguity about exchange-correlation (XC) functionals. By comparing DMC with several XC, we clarified the importance of the short-range exchange to describe the relative stability. We examined why the predicted A 2g is excluded from possible ground states in the recent ligand field based model. Simplified assumptions made in the superposition model are identified to give unreasonably less energy gain for A 2g when compared with the reality. The state is found to have possible reasons for the stabilization, reducing the occupations from an unstable anti-bonding orbital, avoiding double occupation of a spatially localized orbital, and gaining exchange energy by putting a triplet spin pair in degenerate orbitals.
Project description:It has been extremely difficult for conventional computational approaches to reliably predict the properties of multi-reference systems (i.e., systems possessing radical character) at the nanoscale. To resolve this, we employ thermally-assisted-occupation density functional theory (TAO-DFT) to predict the electronic and hydrogen storage properties of Li-terminated linear boron chains (Li2Bn), with n boron atoms (n?=?6, 8, …, and 16). From our TAO-DFT results, Li2Bn, which possess radical character, can bind up to 4 H2 molecules per Li, with the binding energies in the desirable regime (between 20 and 40?kJ/mol per H2). The hydrogen gravimetric storage capacities of Li2Bn range from 7.9 to 17.0?wt%, achieving the ultimate goal of the United States Department of Energy. Accordingly, Li2Bn could be promising media for storing and releasing H2 at temperatures much higher than the boiling point of liquid nitrogen.
Project description:Narrow HOMO-LUMO gaps and high charge-carrier mobilities make larger acenes potentially high-efficient materials for organic electronic applications. The performance of such molecules was shown to significantly increase with increasing number of fused benzene rings. Bulk quantities, however, can only be obtained reliably for acenes up to heptacene. Theoretically, (oligo)acenes and (poly)acenes are predicted to have open-shell singlet biradical and polyradical ground states, respectively, for which experimental evidence is still scarce. We have now been able to dramatically lower the HOMO-LUMO gap of acenes without the necessity of unfavorable elongation of their conjugated ??system, by incorporating two boron atoms into the anthracene skeleton. Stabilizing the boron centers with cyclic (alkyl)(amino)carbenes gives neutral 9,10-diboraanthracenes, which are shown to feature disjointed, open-shell singlet biradical ground states.
Project description:Sulfur K-edge X-ray absorption spectroscopy (XAS) spectra of the monodentate sulfate complexes [MII(itao)(SO4)(H2O)0,1] (M = Co, Ni, Cu) and [Cu(Me6tren)(SO4)] exhibit well-defined preedge transitions at 2479.4, 2479.9, 2478.4, and 2477.7 eV, respectively, despite having no direct metal-sulfur bond, while the XAS preedge of [Zn(itao)(SO4)] is featureless. The sulfur K-edge XAS of [Cu(itao)(SO4)] but not of [Cu(Me6tren)(SO4)] uniquely exhibits a weak transition at 2472.1 eV, an extraordinary 8.7 eV below the first inflection of the rising K-edge. Preedge transitions also appear in the sulfur K-edge XAS of crystalline [MII(SO4)(H2O)] (M = Fe, Co, Ni, and Cu, but not Zn) and in sulfates of higher-valent early transition metals. Ground-state density functional theory (DFT) and time-dependent DFT (TDDFT) calculations show that charge transfer from coordinated sulfate to paramagnetic late transition metals produces spin polarization that differentially mixes the spin-up (?) and spin-down (?) spin orbitals of the sulfate ligand, inducing negative spin density at the sulfate sulfur. Ground-state DFT calculations show that sulfur 3p character then mixes into metal 4s and 4p valence orbitals and various combinations of ligand antibonding orbitals, producing measurable sulfur XAS transitions. TDDFT calculations confirm the presence of XAS preedge features 0.5-2 eV below the rising sulfur K-edge energy. The 2472.1 eV feature arises when orbitals at lower energy than the frontier occupied orbitals with S 3p character mix with the copper(II) electron hole. Transmission of spin polarization and thus of radical character through several bonds between the sulfur and electron hole provides a new mechanism for the counterintuitive appearance of preedge transitions in the XAS spectra of transition-metal oxoanion ligands in the absence of any direct metal-absorber bond. The 2472.1 eV transition is evidence for further radicalization from copper(II), which extends across a hydrogen-bond bridge between sulfate and the itao ligand and involves orbitals at energies below the frontier set. This electronic structure feature provides a direct spectroscopic confirmation of the through-bond electron-transfer mechanism of redox-active metalloproteins.
Project description:The nature of chemical bonds of ruthenium(Ru)-quinine(Q) complexes, mononuclear [Ru(trpy)(3,5-t-Bu(2)Q)(OH(2))](ClO(4))(2) (trpy = 2,2':6',2''-terpyridine, 3,5-di-tert-butyl-1,2-benzoquinone) (1), and binuclear [Ru(2)(btpyan)(3,6-di-Bu(2)Q)(2)(OH(2))](2+) (btpyan = 1,8-bis(2,2':6',2''-terpyrid-4'-yl)anthracene, 3,6-t-Bu(2)Q = 3,6-di-tert-butyl-1,2-benzoquinone) (2), has been investigated by broken-symmetry (BS) hybrid density functional (DFT) methods. BS DFT computations for the Ru complexes have elucidated that the closed-shell structure (2b) Ru(II)-Q complex is less stable than the open-shell structure (2bb) consisting of Ru(III) and semiquinone (SQ) radical fragments. These computations have also elucidated eight different electronic and spin structures of tetraradical intermediates that may be generated in the course of water splitting reaction. The Heisenberg spin Hamiltonian model for these species has been derived to elucidate six different effective exchange interactions (J) for four spin systems. Six J values have been determined using total energies of the eight (or seven) BS solutions for different spin configurations. The natural orbital analyses of these BS DFT solutions have also been performed in order to obtain natural orbitals and their occupation numbers, which are useful for the lucid understanding of the nature of chemical bonds of the Ru complexes. Implications of the computational results are discussed in relation to the proposed reaction mechanisms of water splitting reaction in artificial photosynthesis systems and the similarity between artificial and native water splitting systems.