Linear Polyacenes Research Articles

Predictive potential of eigenvalues-based graphical indices for determining thermodynamic properties of polycyclic aromatic hydrocarbons with applications to polyacenes

For the structure–property modeling of thermodynamic properties of polycyclic aromatic hydrocarbons (PAHs), this paper explores the effectiveness of a specific class of graphical indices defined based on eigenvalues, also known as valency-spectral graphical indices. The 30 lower PAHs have been selected as test molecules. The heat capacity (Cp) and entropy (So) are the standard choices for characterizing thermodynamic properties due to their close correlation with the thermodynamic properties of a similar nature. A computer-dependent method is proposed to calculate valency-spectral indices of chemical graphs, and it is employed to compute the indices for our test molecules. The statistical inferences reveal an unexpected finding for the Estrada harmonic energy, a less familiarized spectral descriptor within the research community, outperforming all the existing descriptors, followed by the positive & negative inertia indices. The Estrada harmonic energy achieved the highest mean correlation coefficient of ρ>0.99. On the other hand, well-studied descriptors such as Laplacian energy and adjacency energy still maintained their effectiveness in correlating the thermodynamic properties of PAHs; however, they were significantly outperformed by the Estrada harmonic energy. The three best valency-spectral indices are employed in the structure–property modeling of thermodynamic properties of linear polyacenes.

Exploring Aromaticity: From Linear Polyacene to Helicene

Exploring Aromaticity: From Linear Polyacene to Helicene

Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications

This paper considers all the commonly occurring distance-related graphical indices and investigates their potential to predict thermodynamic properties of benzenoid hydrocarbons (BHs). Customarily, the entropy So and the heat capacity Cp have been chosen to be the representatives of thermodynamic characteristics. For test molecules, the lower 30 BHs have been opted and it is justified because the experimental data of both Cp and So is publicly available and the number 30 is sufficiently large enough to validate statistical inferences. In this paper, firstly, we propose a computer-dependent computational method to compute all distance-related (including eccentricity-related as well as valency-distance-related indices) of chemical graphs. The computational technique is employed further to evaluate the distance-related topological indices available in the literature. The statistical inferences suggested certain unexpected results as the less-studied distance descriptors such as the second atom-bond connectivity (ABC2) index, the total eccentricity (ζ) index, and the eccentric-connectivity (ξ) index outperform the well-researched descriptors such as the Szeged (Sz), the Wiener W, the Padmakar-Ivan (PI) indices generate poor correlation power. Among the best descriptors for correlating thermodynamic characteristics of BHs, only the ABC2 index showcases the mean correlation coefficient ρ>0.95 which is the minimum threshold for application of a descriptor in structure–property as well as structure–activity (QSPR/QSAR) modeling. The five best distance descriptors are then employed in detailed statistical analysis and most appropriate regression models suggested by the data are non-linear. The applications of the analysis are presented in correlation of the entropy So and the heat capacity Cp of linear polyacenes.

Features of obtaining and properties of thin films organic semiconductors

In recent decades, thin films of organic semiconductors (OS), or, as they are also called, organic molecular crystals, have attracted special attention in connection with a number of proposals for their use in functional units of modern electronics, and therefore in modern technological equipment. At the same time, the optical, electrophysical and photoelectric properties of OS are very important, which are determined both by the structure of organic molecules, that is, the starting material, and by the crystal structure of condensates, that is, by the technological conditions of film production. In this regard, this article presents the results of studies of some properties of OS and the technology of obtaining thin films based on them. OS are characterized by weak intermolecular bonds of the Van der Baals type, which causes the low energy of their crystal lattice. In this regard, the electronic structure of individual molecules during the formation of a crystal does not change significantly, and the properties of the crystals almost completely preserve the individual features of the molecules in combination with new properties caused by their collective interaction. This determines the main features of optical and electrophysical properties of OS, their energy structure of neutral and ionized states. In this article, it is experimentally confirmed that the planar structure of atoms of molecular crystals, in particular, linear acenes, and therefore the number of π-electrons responsible for exciton absorption in the visible region of the spectrum determines the position of the edge of their own optical absorption. It was also confirmed that the long-wavelength shift of the optical absorption edge of thin films of phthalocyanines is observed when atoms of heavy elements, for example, lead, are introduced into the molecule. When atoms of lighter elements are introduced into the phthalocyanine molecule, their planarity is not disturbed, and the long-wavelength shift of the edge is much smaller. An explanation of such changes is presented based on the interaction of foreign atoms with the π-electron system of phthalocyanine rings of neighboring molecules. The significant influence of the technological parameters of production, in particular the temperature of the substrate during thermal sputtering, on the crystal structure and optical properties of thin films of linear polyacenes and metallophthalocyanines has been demonstrated and substantiated. The possibility of controlling and presetting the necessary properties of thin-film condensates of molecular crystals is shown.

Curious Case of Singlet Triplet Gaps in Nonlinear Polyaromatic Hydrocarbons

The singlet triplet (ST) gap of linear polyacenes decays exponentially with the system size as a result of extended conjugation and reducing highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps. These low ST gaps can ideally be leveraged toward energy applications but are hindered by the decreasing stability of the systems. Thus, there is the need to understand the ST gap of nonlinear polyacenes, which are markedly more stable than their linear counterparts. Here, we show that the ST gaps of the nonlinear polyacenes do not decrease with the system size and have no correlation with the HOMO-LUMO gaps or increased conjugation. The reason behind this is identified as the high multireference character of the triplet high-spin state. These unprecedented results are in stark contrast to the observations in linear polyacenes and are due to the combined effects of topology and geometrical factors.

Photophysics of Dibenzo[a,l]pentacene upon Monomer to Thin Film Transformation: Enhanced Visible Light Absorption and Ultrafast Singlet Fission

Linear polyacenes and their derivatives are well-recognized organic semiconductors because of their fascinating singlet fission (SF) property. However, higher polyacenes (e.g., pentacene and hexacene) suffer from poor chemical stability. Herein, we present photophysics of a nonlinearly fused analogue of heptacene, namely, dibenzo[a,l]pentacene in monomer and thin film forms. Nonlinear fusion of benzene rings at two sides of the linear pentacene core results in a weaker and blue-shifted absorption. Interestingly, thin film formation introduces a substantial red shift of absorption along with ∼5 times enhancement in absorption strength due to the cooperative intermolecular interaction in the solid state. Femtosecond and nanosecond pump–probe experiments reveal that the thin film of DBPn undergoes fast singlet fission (a time constant of ∼5.2 ps) to the triplet pair state, followed by dissociation to long-lived free triplets in hundreds of picoseconds with near-unity SF yield. Endowed with higher solubility and better photostability as compared to pentacene, observation of fast and efficient singlet fission makes DBPn a potential candidate for organic photovoltaic applications.

On the Laplacians for Strong Product Graphs Based on Polyacene Graphs

Let Hn be the molecular graph of a linear polyacene chain. In this paper, we introduce a kind of linear polyacene cylinder graph which is the strong product of two automorphism polyacene graphs Hn and Next, we obtain that the Laplacian spectrum of consists of the eigenvalues of symmetric matrices LA and LS of order according to the decomposition theorem of Laplacian characteristic polynomial. Furthermore, by applying the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, we study the Kirchhoff index and the number of spanning trees, and derive their explicit expressions in terms of n for the graph

Spin-Flip Pair-Density Functional Theory: A Practical Approach To Treat Static and Dynamical Correlations in Large Molecules

We present a practical approach to treat static and dynamical correlation accurately in large multiconfigurational systems. The static correlation is taken into account by using the spin-flip approach, which is well-known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (J. Comput. Theor. Chem., 2014, 10, 3669). External relaxations are performed in the spin-flip calculations through a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals, and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.

Resistance Distances in Linear Polyacene Graphs

The resistance distance between any two vertices of a connected graph is defined as the net effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. In this article, using electric network approach and combinatorial approach, we derive exact expression for resistance distances between any two vertices of polyacene graphs.

Total non-lewis structures: An application to predict the stability and reactivity of linear and angular polyacenes

In the present work, the total non-Lewis structure (TNLS) is introduced for describing the stability and reactivity of linear and angular polyacenes. TNLS of a molecule is derived from the natural bond orbital theory representing the antibonding orbitals and/or electron delocalization of π∗ orbitals. To verify this application, we obtained the TNLS values of thirteen linear and angular polyacenes and evaluated with other quantitative aromaticity probes based on reactivities, energetics, geometrics, and magnetic properties. Our results show that there is a remarkable second-order polynomial correlation between TNLS and seven popular global measures of aromaticity including hardness, resonance energy, aromatic stabilization energy, harmonic oscillator measure of aromaticity, magnetic susceptibility exaltation, global magnetic characteristics, and mean polarizability. By increasing the TNLS values of the systems the reactivity increases and stability decreases. It is worth mentioning that the angular polyacenes produce less TNLS values than the linear systems with the same number of benzene rings. Therefore, it can be stated that TNLS values confirmed with Clar’s rule which in general prove the angular polyacenes are more stable than linear ones.

Catacondensed Chemical Hexagonal Complexes: A Natural Generalisation of Benzenoids

Catacondensed benzenoids (those benzenoids having no carbon atom belonging to three hexagonal rings) form the simplest class of polycyclic aromatic hydrocarbons (PAH). They have a long history of study and are of wide chemical importance. In this paper, mathematical possibilities for natural extension of the notion of a catacondensed benzenoid are discussed, leading under plausible chemically and physically motivated restrictions to the notion of a catacondensed chemical hexagonal complex (CCHC). A general polygonal complex is a topological structure composed of polygons that are glued together along certain edges. A polygonal complex is flat if none of its edges belong to more than two polygons. A connected flat polygonal complex determines an orientable or nonorientable surface, possibly with boundary. A CCHC is then a connected flat polygonal complex all of whose polygons are hexagons and each of whose vertices belongs to at most two hexagonal faces. We prove that all CCHC are Kekulean and give formulas for counting the perfect matchings in a series of examples based on expansion of cubic graphs in which the edges are replaced by linear polyacenes of equal length. As a preliminary assessment of the likely stability of molecules with CCHC structure, all-electron quantum chemical calculations are applied to molecular structures based on several CCHC, using either linear or kinked unbranched catafused polyacenes as the expansion motif. The systems examined all have closed shells according to Huckel theory and all correspond to minima on the potential surface, thus passing the most basic test for plausibility as a chemical species.

Singlet-Triplet Energy Gaps of Organic Biradicals and Polyacenes with Auxiliary-Field Quantum Monte Carlo.

The energy gap between the lowest-lying singlet and triplet states is an important quantity in chemical photocatalysis, with relevant applications ranging from triplet fusion in optical upconversion to the design of organic light-emitting devices. The ab initio prediction of singlet-triplet (ST) gaps is challenging due to the potentially biradical nature of the involved states, combined with the potentially large size of relevant molecules. In this work, we show that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can accurately predict ST gaps for chemical systems with singlet states of highly biradical nature, including a set of 13 small molecules and the ortho-, meta-, and para- isomers of benzyne. With respect to gas-phase experiments, ph-AFQMC using CASSCF trial wave functions achieves a mean averaged error of ∼1 kcal/mol. Furthermore, we find that in the context of a spin-projection technique, ph-AFQMC using unrestricted single-determinant trial wave functions, which can be readily obtained for even very large systems, produces equivalently high accuracy. We proceed to show that this scalable methodology is capable of yielding accurate ST gaps for all linear polyacenes for which experimental measurements exist, that is, naphthalene, anthracene, tetracene, and pentacene. Our results suggest a protocol for selecting either unrestricted Hartree-Fock or Kohn-Sham orbitals for the single-determinant trial wave function, based on the extent of spin-contamination. These findings pave the way for future investigations of specific photochemical processes involving large molecules with substantial biradical character.

Combining Pair-Density Functional Theory and Variational Two-Electron Reduced-Density Matrix Methods.

Complete active space self-consistent field (CASSCF) computations can be realized at polynomial cost via the variational optimization of the active-space two-electron reduced-density matrix (2-RDM). Like conventional approaches to CASSCF, variational 2-RDM (v2RDM) driven CASSCF captures nondynamical electron correlation in the active space, but it lacks a description of the remaining dynamical correlation effects. Such effects can be modeled through a combination of v2RDM-CASSCF and on-top pair-density functional theory (PDFT). The resulting v2RDM-CASSCF-PDFT approach provides a computationally inexpensive framework for describing both static and dynamical correlation effects in multiconfigurational and strongly correlated systems. On-top pair-density functionals can be derived from familiar Kohn-Sham exchange-correlation (XC) density functionals through the translation of the v2RDM-CASSCF reference densities [ Li Manni et al. J. Chem. Theory Comput. 2014 , 10 , 3669 - 3680 ]. Translated and fully translated on-top PDFT versions of several common XC functionals are applied to the potential energy curves of N2, H2O, and CN-, as well as to the singlet/triplet energy splittings in the linear polyacene series. Using v2RDM-CASSCF-PDFT and the translated PBE functional, the singlet/triplet energy splitting of an infinitely long acene molecule is estimated to be 4.87 kcal mol-1.

Analytic Energy Gradients for Variational Two-Electron Reduced-Density Matrix Methods within the Density Fitting Approximation

Analytic energy gradients are presented for a variational two-electron reduced-density-matrix-driven complete active space self-consistent field (v2RDM-CASSCF) procedure that employs the density fitting (DF) approximation to the two-electron repulsion integrals. The DF approximation significantly reduces the computational cost of v2RDM-CASSCF gradient evaluation, in terms of both the number of floating-point operations and memory requirements, enabling geometry optimizations on much larger chemical systems than could previously be considered at this level of theory [ Maradzike et al., J. Chem. Theory Comput. , 2017 , 13 , 4113 - 4122 ]. The efficacy of v2RDM-CASSCF for computing equilibrium geometries and harmonic vibrational frequencies is assessed using a set of 25 small closed- and open-shell molecules. Equilibrium bond lengths from v2RDM-CASSCF differ from those obtained from configuration-interaction-driven CASSCF (CI-CASSCF) by 0.62 and 0.05 pm, depending on whether the optimal reduced-density matrices from v2RDM-CASSCF satisfy two-particle N-representability conditions (PQG) or PQG plus partial three-particle conditions (PQG+T2), respectively. Harmonic vibrational frequencies, which are obtained by finite differences of v2RDM-CASSCF analytic energy gradients, similarly demonstrate that quantitative agreement between v2RDM- and CI-CASSCF requires the consideration of partial three-particle N-representability conditions. Lastly, optimized geometries are obtained for the lowest-energy singlet and triplet states of the linear polyacene series up to dodecacene (C50H28), in which case the active space is comprised of 50 electrons in 50 orbitals. The v2RDM-CASSCF singlet-triplet energy gap extrapolated to an infinitely long linear acene molecule is found to be 7.8 kcal mol-1.

Numerical Nuclear Second Derivatives on a Computing Grid: Enabling and Accelerating Frequency Calculations on Complex Molecular Systems.

The computation of nuclear second derivatives of energy, or the nuclear Hessian, is an essential routine in quantum chemical investigations of ground and transition states, thermodynamic calculations, and molecular vibrations. Analytic nuclear Hessian computations require the resolution of costly coupled-perturbed self-consistent field (CP-SCF) equations, while numerical differentiation of analytic first derivatives has an unfavorable 6 N ( N = number of atoms) prefactor. Herein, we present a new method in which grid computing is used to accelerate and/or enable the evaluation of the nuclear Hessian via numerical differentiation: NUMFREQ@Grid. Nuclear Hessians were successfully evaluated by NUMFREQ@Grid at the DFT level as well as using RIJCOSX-ZORA-MP2 or RIJCOSX-ZORA-B2PLYP for a set of linear polyacenes with systematically increasing size. For the larger members of this group, NUMFREQ@Grid was found to outperform the wall clock time of analytic Hessian evaluation; at the MP2 or B2LYP levels, these Hessians cannot even be evaluated analytically. We also evaluated a 156-atom catalytically relevant open-shell transition metal complex and found that NUMFREQ@Grid is faster (7.7 times shorter wall clock time) and less demanding (4.4 times less memory requirement) than an analytic Hessian. Capitalizing on the capabilities of parallel grid computing, NUMFREQ@Grid can outperform analytic methods in terms of wall time, memory requirements, and treatable system size. The NUMFREQ@Grid method presented herein demonstrates how grid computing can be used to facilitate embarrassingly parallel computational procedures and is a pioneer for future implementations.

A method for computing the edge-hyper-Wiener index of partial cubes and an algorithm for benzenoid systems

The edge-hyper-Wiener index of a connected graph G is defined as WWe(G)=1/2 ?{e,f}?E(G) d(e,f) + 1/2 ? {e,f}?E(G)d(e,f)2. We develop a method for computing the edge-hyper-Wiener index of partial cubes, which constitute a large class of graphs with a lot of applications. It is also shown how the method can be applied to trees. Furthermore, an algorithm for computing the edge-hyper-Wiener index of benzenoid systems is obtained. Moreover, the algorithm is used to recalculate already known closed formulas for the edge-Wiener index and the edge-hyper-Wiener index of linear polyacenes. Finally, the method is presented on a benzenoid system with more complicated structure.

Comprehensive study of the correlations that exist among the members of the [n]cyclacene series and the Möbius[n]cyclacene series

ABSTRACTCyclacenes are the smallest substructures of carbon nanotubes used in modelling studies. The systematics that exists between Hückel molecular orbital eigenvalues and eigenvectors of cyclacenes are delineated. This study of cyclacenes combines the interconnection of concepts of complementarity theorem, characteristic and matching polynomial recursion equations, embedding, greater than twofold symmetry and doubly degenerate eigenvalues, open-shell singlet character, and pairing theorem. Proof that cyclacenes have more open-shell (diradical) character than do polyacenes is also provided by the sum total of this work. Mirror-plane scission of even-ring cyclacenes gives linear polyacene fragments. This shows that the properties of the successor linear polyacene must be contained in the precursor cyclacene. Corresponding Möbius[n]cyclacene isomers display contrasting and unusual comparative properties. A partial list of contrasting properties include alternant (cyclacenes) versus nonalternant (Möbius[n]cyclacene) polyenes, presence of Hamiltonian circuits in Möbius[n]cyclacene and presence of oscillatory electronic properties in cyclacenes.

A DFT study on 1,4‐dihydro‐1,4‐azaborinine annulated linear polyacenes: Absorption spectra, singlet‐triplet energy gap, aromaticity, and HOMO–LUMO energy modulation

Linear polyacene (LPA) mimics containing multiple heterocycles have been computationally designed by annulating 1,4-dihydro-1,4-azaborinine moieties to benzene (aB1 -aB5 ), naphthalene (aN1 -aN5 ), anthracene (aA1 -aA5 ), and tetracene (aT1 -aT5 ) cores. DFT studies conducted on them using M06L/6-311++G(d,p) method reveal a perfect planar structure for all and suggest the utilization of nitrogen lone pairs for aromatic π-electron delocalization. The computed values of aromaticity indices such as HOMA, NICS, and dehydrogenation energy (Edh ) of heterocycles support strong aromatic character for each six-membered ring in the LPA mimics. On the basis of the minimum value of the molecular electrostatic potential (Vmin ) observed on each LPA unit in the LPA mimics, the extended delocalization of π-electrons is verified. The energetic parameter Edh showed strong linear correlation with HOMA, NICS and Vmin parameters, which strongly supports the multidimensional character of aromaticity in LPA mimics. The electronic property modification is shown by the theoretical absorption spectra data and singlet-triplet energy gap (ΔEST ). The bandgap and ΔEST tunings are achieved for LPA mimics by selecting appropriate number of azaborinine type units and the size of LPA core used for annulation. © 2017 Wiley Periodicals, Inc.

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

ABSTRACTWe describe the implementation of orbital optimisation for the models in the perfect pairing hierarchy. Orbital optimisation, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the π space. While local minima and σ-π symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the π subspace, as well as in the full σπ valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimised orbitals are used. PH is found to yield good agreement with previously published density matrix renormalisation group data in the π space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger basis sets or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

π-electron content of rings in polycyclic conjugated compounds – A valence bond based measure of local aromaticity

In 2004 Randić and Balaban employed Kekulé structures to assess the π-electron content (EC) of rings in benzenoid hydrocarbons. In this paper we showed how ab initio Valence Bond (VB) calculations based on the set of Kekulé structures of a given polycyclic conjugated molecule can be used to obtain more accurate π-electron contents of rings (VB-EC) as the true computed weights of the Kekulé structures are used, instead of postulating that all Kekulé structures have equal weights as in the EC formula. In the case of benzenoid hydrocarbons, the values of VB-EC and EC are very close. The main difference is found for linear polyacenes, for which, contrary to the EC, the VB-EC values predict that the inner rings are more aromatic than the terminal rings. The original EC method has also the disadvantage that it cannot be applied to heterocyclic conjugated molecules. It was shown that the VB-EC method can be used to assess the local aromaticity in aza derivatives of naphthalene. The calculated VB-EC values were compared with several other aromaticity indices, namely: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six center delocalization index (SCI) and nucleus independent chemical shifts (NICS). The best correlation was found between the VB-EC and SCI, implying that these two indices carry similar information on the local aromaticity.