Focal Point Analysis of the Singlet–Triplet Energy Gap of Octacene and Larger Acenes

Detection of diheptacendiyl diradical intermediate in the cycloreversion of diheptacene to heptacene

Cycloreversion of diheptacenes, the covalently bound dimers of heptacene, in the solid state produces heptacene. In addition, diheptacendiyl diradical can be detected by ESR spectroscopy. The diradical has a small singlet-triplet energy gap of -0.02 kJ mol-1 (-4.8 × 10-3 kcal mol-1) in favor of the singlet state and is persistent in solid heptacene.

Chemically accurate singlet-triplet gaps of organic chromophores and linear acenes by the random phase approximation and σ-functionals

Predicting the energy differences between different spin-states is challenging for many widely used ab initio electronic structure methods. We here assess the ability of the direct random phase approximation (dRPA), dRPA plus two different screened second-order exchange (SOX) corrections, and σ-functionals to predict adiabatic singlet-triplet gaps. With mean absolute deviations of below 0.1 eV to experimental reference values, independent of the Kohn-Sham starting point, dRPA and σ-functionals accurately predict singlet-triplet gaps of 18 organic chromophores. The addition of SOX corrections to dRPA considerably worsens agreement with experiment, adding to the mounting evidence that dRPA+SOX methods are not generally applicable beyond-RPA methods. Also for a series of linear acene chains with up to ten fused rings, dRPA, and σ-functionals are in excellent agreement with coupled-cluster single double triple reference data. In agreement with advanced multi-reference methods, dRPA@PBE and σ-functional@PBE predict a singlet ground state for all chain lengths, while dRPA@PBE0 and σ-functional@PBE0 predict a triplet ground state for longer acenes. Our work shows dRPA and σ-functionals to be reliable methods for calculating singlet-triplet gaps in aromatic molecules.

Intruder-free cumulant-truncated driven similarity renormalization group second-order multireference perturbation theory

Accurate multireference electronic structure calculations are important for constructing potential energy surfaces. Still, even in the case of low-scaling methods, their routine use is limited by the steep growth of the computational and storage costs as the active space grows. This is primarily due to the occurrence of three- and higher-body density matrices or, equivalently, their cumulants. This work examines the effect of various cumulant truncation schemes on the accuracy of the driven similarity renormalization group second-order multireference perturbation theory. We test four different levels of three-body reduced density cumulant truncations that set different classes of cumulant elements to zero. Our test cases include the singlet-triplet gap of CH2, the potential energy curves of the XΣg+1 and AΣu+3 states of N2, and the singlet-triplet splittings of oligoacenes. Our results show that both relative and absolute errors introduced by these cumulant truncations can be as small as 0.5 kcal mol-1 or less. At the same time, the amount of memory required is reduced from O(NA6) to O(NA5), where NA is the number of active orbitals. No additional regularization is needed to prevent the intruder state problem in the cumulant-truncated second-order driven similarity renormalization group multireference perturbation theory methods.

New Density Matrix Renormalization Group Approaches for Strongly Correlated Systems Coupled with Large Environments

Thanks to the high compression of the matrix product state (MPS) form of the wave function and the efficient site-by-site iterative sweeping optimization algorithm, the density matrix normalization group (DMRG) and its time-dependent variant (TD-DMRG) have been established as powerful computational tools in accurately simulating the electronic structure and quantum dynamics of strongly correlated molecules with a large number (10^1-2) of quantum degrees of freedom (active orbitals or vibrational modes). However, the quantitative characterization of the quantum many-body behaviors of realistic strongly correlated systems requires a further consideration of the interaction between the embedded active subsystem and the remaining correlated environment, e.g., a larger number (10^2-3) of external orbitals in electronic structure or infinite condensed-phase phononic modes in nucleus dynamics. To this end, we introduced three new post-DMRG and TD-DMRG approaches, namely (1) DMRG2sCI-MRCI and DMRG2sCI-ENPT by the reconstruction of selected configuration interaction (sCI) type of compact reference function from DMRG coefficients and the use of externally contracted MRCI (multireference configuration interaction) and Epstein-Nesbet perturbation theory (ENPT), without recourse to the expensive high order n-electron reduced density matrices (n-RDMs). (2) DMRG combined with RR-MRCI (renormalized residue-based MRCI), which improves the computational accuracy and efficiency of internally contracted (ic) MRCI by renormalizing the contracted bases with small-sized buffer environment(s) of a few external orbitals as probes based on quantum information theory. (3) HM (hierarchical mapping)-TD-DMRG in which a large environment is reduced to a small number of renormalized environmental modes (which accounts for the most vital system-environment interactions) through stepwise mapping transformation. These advances extend the efficacy of highly accurate DMRG/TD-DMRG computations to the quantitative characterization of the electronic structure and quantum dynamics in realistic strongly correlated systems coupled with large environments and are reviewed in this paper.

Anti-ohmic nanoconductors: myth, reality and promise

The recent accomplishment in the design of molecular nanowires characterized by increasing conductance with length has led to the origin of an extraordinary new family of molecular junctions referred to as "anti-ohmic" wires. Herein, this highly desirable, non-classical behavior, has been examined for molecules long-enough to exhibit pronounced diradical character in their ground state within the unrestricted DFT formalism with spin symmetry breaking. We demonstrate that highly conjugated acenes signal higher resistance in an open-shell singlet (OSS) configuration as compared to their closed-shell counterparts. This anomaly has been further proven for experimentally certified cumulene wires, which reveals phenomenal modulation in the transport characteristics such that an increasing conductance is observed in the closed-shell limit, while higher cumulenes in the OSS ground state yield regular decay of conductance.

Closed-shell and open-shell dual nature of singlet diradical compounds

Unlike triplet diradicals, singlet diradicals can vary in diradical character from 0 % to 100 % depending on linker units that allow two formally unpaired electrons to couple covalently. In principle, the electronic structure of singlet diradicals can be described as a quantum superposition of closed-shell and open-shell structures. This means that, depending on the external environment, singlet diradicals can behave as either closed-shell or open-shell species. This paper summarizes our progress in understanding the electronic structure of π-conjugated singlet diradical molecules in terms of closed-shell and open-shell dual nature. We first discuss the coexistence of intra- and intermolecular covalent bonding interactions in the π-dimer of a singlet diradical molecule. The intra- and intermolecular coupling of two formally unpaired electrons are related to closed-shell and open-shell nature of singlet diradical, respectively. Then we demonstrate the coexistence of the covalent bonding interactions in the one-dimensional stack of singlet diradical molecules having different diradical character. The relative strength of the interactions is varied with the magnitude of singlet diradical index y 0. Finally, we show the dual reactivity of a singlet diradical molecule, which undergoes rapid [4 + 2] and [4 + 4] cycloaddition reactions in the dark at room temperature. Closed-shell and open-shell nature endow the singlet diradical molecule with the reaction manner as diene and diradical species, respectively.

del Campo J. Charge delocalization error in Piris Natural Orbital Functionals

Piris Natural Orbital Functionals (PNOF) have been recognized as a low-scaling alternative to study strong correlated systems. In this work, we address the performance of the fifth functional (PNOF5) and the seventh functional (PNOF7) to deal with another common problem, the charge delocalization error. The effects of this problem can be observed in charged systems of repeated well-separated fragments, where the energy should be the sum of the charged and neutral fragments, regardless of how the charge is distributed. In practice, an energetic overstabilization of fractional charged fragments leads to a preference for having the charge delocalized throughout the system. To establish the performance of PNOF functionals regarding charge delocalization error, charged chains of helium atoms and the W4-17-MR set molecules were used as base fragments and their energy, charge distribution and correlation regime were studied. It was found that PNOF5 prefers localized charge distributions, while PNOF7 improves the treatment of interpair static correlation and tends to the correct energetic limit for several cases, although a preference for delocalized charge distributions may arise in highly strong correlation regimes. Overall, it is concluded that PNOF functionals can simultaneously deal with static correlation and charge delocalization errors, resulting in a promising choice to study charge-related problems.

Benzo-Extended Cyclohepta[def]fluorene Derivatives with Very Low-Lying Triplet States

Open-shell non-alternant polycyclic hydrocarbons (PHs) are attracting increasing attention due to their promising applications in organic spintronics and quantum computing. Herein we report the synthesis of three cyclohepta[def]fluorene-based diradicaloids (1-3), by fusion of benzo rings on its periphery for the thermodynamic stabilization, as evidenced by multiple characterization techniques. Remarkably, all of them display a very narrow optical energy gap (E_g ^opt =0.52-0.69 eV) and persistent stability under ambient conditions (t_1/2 =11.7-33.3 h). More importantly, this new type of diradicaloids possess a low-lying triplet state with an extremely small singlet-triplet energy gap, as low as 0.002 kcal mol^-1 , with a clear dependence on the molecular size. This family of compounds thus offers a new route to create non-alternant open-shell PHs with high-spin ground states, and opens up novel possibilities and insights into understanding the structure-property relationships.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.

TAO-DFT fictitious temperature made simple

Over the past few years, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys., 2012, 136, 154104] has been proved to be an efficient electronic structure method for investigating the ground-state properties of large electronic systems with strong static correlation effects. In TAO-DFT, the strength of static correlation in an electronic system at zero temperature is closely related to the so-called fictitious temperature (i.e., the temperature of the corresponding noninteracting reference system). In this work, we propose a simple model to define the optimal system-independent fictitious temperature of a given energy functional in TAO-DFT. Besides, we employ this model to determine the optimal system-independent fictitious temperature of a global hybrid functional in TAO-DFT as a function of the fraction of exact exchange. In addition, we adopt TAO-DFT with various global hybrid functionals and system-independent fictitious temperatures to explore the ground-state properties of several electronic systems with strong static correlation effects, such as the linear acenes and cyclic carbon chains. Furthermore, we discuss the role of exact exchange and an optimal system-independent fictitious temperature in TAO-DFT. Owing to the much reduced self-interaction error, TAO-DFT with exact exchange and an optimal system-independent fictitious temperature can accurately predict the radical character and bond length alternation of cyclic carbon chains (with even number of carbon atoms), which are challenging problems for traditional electronic structure methods.

Optimal system-independent fictitious temperature θ of TAO-GH as a function of the fraction of exact exchange a_x.

Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection

The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced density matrices. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe₃S₄ cluster.

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.

Accurate singlet-triplet gaps in biradicals via the spin averaged anti-Hermitian contracted Schrödinger equation

The accurate description of biradical systems, and in particular the resolution of their singlet-triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schrödinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet-triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature.

Energetics of Formation of Cyclacenes from 2,3-Didehydroacenes and Implications for Astrochemistry

The carriers of the diffuse interstellar bands (DIBs) are still largely unknown although polycyclic aromatic hydrocarbons, carbon chains, and fullerenes are likely candidates. A recent analysis of the properties of n-acenes of general formula C4n+2 H2n+4 suggested that these could be potential carriers of some DIBs. Dehydrogenation reactions of n-acenes after absorption of an interstellar UV photon may result in dehydroacenes. Here the reaction energies and barriers for formation of n-cyclacenes from 2,3-didehydroacenes (n-DDA) by intramolecular Diels-Alder reaction to dihydro-etheno-cyclacenes (n-DEC) followed by ejection of ethyne by retro-Diels-Alder reactions are analyzed using thermally assisted occupation density functional theory (TAO-DFT) for n=10-20. It is found that the barriers for each of the steps depend on the ring strain of the underlying n-cyclacene, and that the ring strain of n-DEC is about 75 % of that of the corresponding n-cyclacene. In each case, ethyne extrusion is the step with the highest energy barrier, but these barriers are smaller than CH bond dissociation energies, suggesting that formation of cyclacenes is an energetically conceivable fate of n-acenes after multiple absorption of UV photons.

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

Acenes, consisting of linearly fused benzene rings, are an important fundamental class of organic compounds with various applications. Hexacene is the largest acene that was synthesized and isolated in the 20th century. The next largest member of the acene family, heptacene, was observed in 2007 and since then significant progress in preparing acenes has been reported. Significantly larger acenes, up to undecacene, could be studied by means of low-temperature matrix isolation spectroscopy with in situ photolytic generation, and up to dodecacene by means of on-surface synthesis employing innovative precursors and highly defined crystalline metal surfaces under ultrahigh vacuum conditions. The review summarizes recent experimental and theoretical advances in the area of acenes that give a significantly deeper insight into the fundamental properties and nature of the electronic structure of this fascinating class of organic compounds.

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = −2JS_i · S_j) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term jS², the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H₂ under a covalent bond dissociation, C, O, Si, NH, OH⁺, CH₂, NF, O₂, and triple bond dissociated N₂ molecule revealed that the BxB can compute the J value within 1 kcal mol⁻¹ of errors with less computational costs than conventional quantum phase estimation-based approaches.

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol⁻¹ of energy tolerance.

Excitation energies from thermally assisted-occupation density functional theory: Theory and computational implementation

The time-dependent density functional theory (TDDFT) has been broadly used to investigate the excited-state properties of various molecular systems. However, the current TDDFT heavily relies on outcomes from the corresponding ground-state DFT calculations, which may be prone to errors due to the lack of proper treatment in the non-dynamical correlation effects. Recently, thermally assisted-occupation DFT (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)], a DFT with fractional orbital occupations, was proposed, explicitly incorporating the non-dynamical correlation effects in the ground-state calculations with low computational complexity. In this work, we develop TDTAO-DFT, which is a TD, linear-response theory for excited states within the framework of TAO-DFT. With tests on the excited states of H₂, the first triplet excited state (1³Σ_u ⁺) was described well, with non-imaginary excitation energies. TDTAO-DFT also yields zero singlet-triplet gap in the dissociation limit for the ground singlet (1¹Σ_g ⁺) and the first triplet state (1³Σ_u ⁺). In addition, as compared to traditional TDDFT, the overall excited-state potential energy surfaces obtained from TDTAO-DFT are generally improved and better agree with results from the equation-of-motion coupled-cluster singles and doubles.

Extrapolating Unconverged GW Energies up to the Complete Basis Set Limit with Linear Regression

The GW approximation to the electronic self-energy is now a well-recognized approach to obtain the electron quasiparticle energies of molecules and, in particular, their ionization potential and electron affinity. Though much faster than the corresponding wavefunction methods, the GW energies are still affected by slow convergence with respect to the basis completeness. This limitation hinders a wider application of the GW approach. Here, we show that we can reach the complete basis set limit for the cumbersome GW calculations solely based on fast preliminary calculations with an unconverged basis set. We introduce a linear model that correlates the molecular orbital characteristics and the basis convergence error for a large database of approximately 600 states in 104 organic molecules that contain H, C, O, N, F, P, S, and Cl. The model employs molecular-orbital-based non-linear descriptors that encode efficiently the chemical space offering outstanding transferability. Using a low number of descriptors (17) the performance of this extrapolation procedure is superior to that of the earlier more physically motivated approaches. The predictive power of the method is finally demonstrated for a selection of large acceptor molecules.

Global and local aromaticity of acenes from the information-theoretic approach in density functional reactivity theory

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characterizing the molecular electron density distribution. Based on the correlation analysis of six conventional aromaticity indices with eight information-theoretic quantities, we examined the aromaticity of acenes from both global and local perspectives. From the global aromaticity viewpoint, our results suggest that different descriptors based on various physicochemical properties are intrinsically dependent. A novel laminated feature ruling local aromaticity of acenes has been unveiled, from which we found that the distance from the terminal rings plays the critical role. Based on the shape of the correlation plots between the conventional aromaticity indices and information-theoretic quantities, the latter could be separated into three subgroups. The seemingly contradictory results from global and local aromaticity perspectives not only present us the uniqueness of the acene systems but all demonstrate the effectiveness of the information-theoretic approach from density functional reactivity theory. Besides strengthening the validity of a series of new aromaticity descriptors, our results should lead to more clear insights into the chemical significance of the information-theoretic quantities.

Automatic Construction of the Initial Orbitals for Efficient Generalized Valence Bond Calculations of Large Systems

We propose an efficient general strategy for generating initial orbitals for generalized valence bond (GVB) calculations which makes routine black-box GVB calculations on large systems feasible. Two schemes are proposed, depending on whether the restricted Hartree-Fock (RHF) wave function is stable (scheme I) or not (scheme II). In both schemes, the first step is the construction of active occupied orbitals and active virtual orbitals. In scheme I, active occupied orbitals are composed of the valence orbitals (the inner core orbitals are excluded), and the active virtual orbitals are obtained from the original virtual space by requiring its maximum overlap with the virtual orbital space of the same system at a minimal basis set. In scheme II, active occupied orbitals and active virtual orbitals are obtained from the set of unrestricted natural orbitals (UNOs), which are transformed from two sets of unrestricted HF spatial orbitals. In the next step, the active occupied orbitals and active virtual ones are separately transformed to localized orbitals. Localized occupied and virtual orbital pairs are formed using the Kuhn-Munkres (KM) algorithm and are used as the initial guess for the GVB orbitals. The optimized GVB wave function is obtained using the second-order self-consistent-field algorithm in the GAMESS program. With this procedure, GVB energies have been obtained for the lowest singlet and triplet states of polyacenes (up to decacene with 96 pairs) and the singlet ground state of two di-copper-oxygen-ammonia complexes. We have also calculated the singlet-triplet gaps for some polyacenes and the relative energy between two di-copper-oxygen-ammonia complexes with the block-correlated second-order perturbation theory based on the GVB reference.

Density matrix renormalization group pair-density functional theory (DMRG-PDFT): singlet-triplet gaps in polyacenes and polyacetylenes

The density matrix renormalization group (DMRG) is a powerful method to treat static correlation.

The density matrix renormalization group (DMRG) is a powerful method to treat static correlation. Here we present an inexpensive way to calculate correlation energy starting from a DMRG wave function using pair-density functional theory (PDFT). We applied this new approach, called DMRG-PDFT, to study singlet–triplet gaps in polyacenes and polyacetylenes that require active spaces larger than the feasibility limit of the conventional complete active-space self-consistent field (CASSCF) method. The results match reasonably well with the most reliable literature values and have only a moderate dependence on the compression of the initial DMRG wave function. Furthermore, DMRG-PDFT is significantly less expensive than other commonly applied ways of adding additional correlation to DMRG, such as DMRG followed by multireference perturbation theory or multireference configuration interaction.

Externally-Contracted Multireference Configuration Interaction Method Using a DMRG Reference Wave Function

The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry makes it practical to evaluate static correlation in a large active space, while dynamic correlation provides a critical correction to the DMRG reference for strong-correlated systems and is usually obtained using multireference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use an active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with an active space larger than 30 orbitals and/or a large basis set because of high computation and storage costs of high-order reduced density matrices (RDMs) and the crucial dependence of the MRCI Hamiltonian dimension on the number of virtual orbitals. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use reconstructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA) [ Luo et al. J. Chem. Theory Comput. 2017 , 13 , 4699 - 4710 . ] and integrate it with MRCI by an external contraction (ec) scheme. This bypasses the bottleneck of computing high-order RDMs in traditional DMRG dynamic correlation methods with ic approximation, and the number of MRCI configurations is not dependent on the number of virtual orbitals. Therefore, the DMRG-ec-MRCI method is promising for dealing with a larger active space than 30 orbitals and large basis sets. We demonstrate the capability of our DMRG-ec-MRCI method in several benchmark applications, including the evaluation of the potential energy curve of Cr₂, single-triplet gaps of higher n-acene molecules, and the energy of the Eu-BTBP(NO₃)₃ complex.

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

We propose hybrid schemes incorporating exact exchange into thermally assisted-occupation-density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] for an improved description of nonlocal exchange effects. With a few simple modifications, global and range-separated hybrid functionals in Kohn-Sham density functional theory (KS-DFT) can be combined seamlessly with TAO-DFT. In comparison with global hybrid functionals in KS-DFT, the resulting global hybrid functionals in TAO-DFT yield promising performance for systems with strong static correlation effects (e.g., the dissociation of H₂ and N₂, twisted ethylene, and electronic properties of linear acenes), while maintaining similar performance for systems without strong static correlation effects. Besides, a reasonably accurate description of noncovalent interactions can be efficiently achieved through the inclusion of dispersion corrections in hybrid TAO-DFT. Relative to semilocal density functionals in TAO-DFT, global hybrid functionals in TAO-DFT are generally superior in performance for a wide range of applications, such as thermochemistry, kinetics, reaction energies, and optimized geometries.

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. We recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functional theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet-triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet-triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.

Tuning the HOMO-LUMO Energy Gap of Small Diamondoids Using Inverse Molecular Design

Functionalized diamondoids show great potential as building blocks for various new optoelectronic applications. However, until now, only simple mono and double substitutions were investigated. In this work, we considered up to 10 and 6 sites for functionalization of the two smallest diamondoids, adamantane and diamantane, respectively, in search for diamondoid derivatives with a minimal and maximal HOMO-LUMO energy gap. To this end, the energy gap was optimized systematically using an inverse molecular design methodology based on the best-first search algorithm combined with a Monte Carlo component to escape local optima. Adamantane derivatives were found with HOMO-LUMO gaps ranging from 2.42 to 10.63 eV, with 9.45 eV being the energy gap of pure adamantane. For diamantane, similar values were obtained. The structures with the lowest HOMO-LUMO gaps showed apparent push-pull character. The push character is mainly formed by sulfur or nitrogen dopants and thiol groups, whereas the pull character is predominantly determined by the presence of electron-withdrawing nitro or carbonyl groups assisted by amino and hydroxyl groups via the formation of intramolecular hydrogen bonds. In contrast, maximal HOMO-LUMO gaps were obtained by introducing numerous electronegative groups.

Tuning for Visible Fluorescence and Near-Infrared Phosphorescence on a Unimolecular Mechanically Sensitive Platform via Adjustable CH-π Interaction

CH-π interaction-assisted alignment of organic conjugated systems has played an important role to regulate molecular electronic and photophysical properties, whereas harnessing such a smart noncovalent interaction into the tuning of unimolecular complex emissive bands covering a wide spectral region remains a challenging research topic. Since the tuning for visible and near-infrared emissive properties in a single π-functional platform relates to its multicolor luminescent behaviors and potential superior application in analysis, bioimaging, and sensing, herein, we report a proportional control of the singlet and triplet emissions that cover visible and near-infrared spectral regions, respectively, can be straightforwardly achieved by CH-π interaction-assisted self-assembly at the unimolecular level. Employing an octathionaphthalene-based single luminophore as a prototype, we find that a strength-adjustable CH-π interaction-assisted self-assembly can be established in mixed DMF/H₂O and in the film state. The hybridization of planar local excited and intramolecular charge transfer transitions occurs on the basis, allowing a competitive inhibition to the intersystem crossing process to generate a complex emission composed of visible fluorescence and near-infrared phosphorescence. Furthermore, reversible mechanochromic and mechanoluminescent conversions of the corresponding solid sample can both be observed to rely on a corresponding self-assembly alternation. These results can probably provide new visions for the development of future intelligent and multifunctional luminescent materials.

Nature of ground and electronic excited states of higher acenes

Higher acenes have drawn much attention as promising organic semiconductors with versatile electronic properties. However, the nature of their ground state and electronic excited states is still not fully clear. Their unusual chemical reactivity and instability are the main obstacles for experimental studies, and the potentially prominent diradical character, which might require a multireference description in such large systems, hinders theoretical investigations. Here, we provide a detailed answer with the particle-particle random-phase approximation calculation. The (1)Ag ground states of acenes up to decacene are on the closed-shell side of the diradical continuum, whereas the ground state of undecacene and dodecacene tilts more to the open-shell side with a growing polyradical character. The ground state of all acenes has covalent nature with respect to both short and long axes. The lowest triplet state (3)B2u is always above the singlet ground state even though the energy gap could be vanishingly small in the polyacene limit. The bright singlet excited state (1)B2u is a zwitterionic state to the short axis. The excited (1)Ag state gradually switches from a double-excitation state to another zwitterionic state to the short axis, but always keeps its covalent nature to the long axis. An energy crossing between the (1)B2u and excited (1)Ag states happens between hexacene and heptacene. Further energetic consideration suggests that higher acenes are likely to undergo singlet fission with a low photovoltaic efficiency; however, the efficiency might be improved if a singlet fission into multiple triplets could be achieved.

Perimeter ring currents in benzenoids from Pauling bond orders

It is shown that the ring currents in perimeter hexagonal rings of Kekulean benzenoids, as estimated within the Randić conjugated-circuit model, can be calculated directly without tedious pairwise comparison of Kekulé structures or Kekulé counting for cycle-deleted subgraphs. Required are only the Pauling bond orders of perimeter bonds and the number of Kekulé structures of the benzenoid, both readily available from the adjacency matrix of the carbon skeleton. This approach provides easy calculation of complete current maps for benzenoids in which every face has at least one bond on the perimeter (as in the example of cata-condensed benzenoids), and allows qualitative evaluation of the main ring-current contributions to (1)H chemical shifts in general benzenoids. A combined Randić-Pauling model for correlation of ring current and bond length through bond order is derived and shown to be consistent with resilience of current under bond alternation.

Benchmarking semiempirical, Hartree–Fock, DFT, and MP2 methods against the ionization energies and electron affinities of short- through long-chain [n]acenes and [n]phenacenes

Vertical and adiabatic ionization energies (IEs) and electron affinities (EAs) were calculated for the n = 1–10 [n]acenes using a wide range of semiempirical, Hartree–Fock, density functional, and second-order Moller–Plesset perturbation theory model chemistries. None of the model chemistries examined was able to accurately predict the IEs or EAs for both short- through long-chain [n]acenes, as well as for extrapolations to the polymeric limit, when compared to available experimental and benchmark theoretical data. Except for 6-31G(d), the choice of the basis set does not affect B3LYP results significantly. Analogous calculations using a suite of eight modern and (or) popular density functionals for the n = 1–10 [n]phenacenes revealed similar problems in estimating the IEs and EAs of these compounds, with the sole exception of the M062X functional for adiabatic IEs and potentially the APFD, B3LYP, and MN12SX functionals for adiabatic EAs. The poor IE/EA prediction performance for the parent [n]acenes and [n]phenacenes may extend to their substituted derivatives and heteroatom-substituted analogs. Consequently, caution should be exercised in the application of non-high-level calculations for estimating the IE/EA of these important classes of materials.

Polyradical Character of Triangular Non-Kekulé Structures, Zethrenes, p-Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison: An Extended Multireference Study

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 π-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 π-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.

Electronic Properties of Zigzag Graphene Nanoribbons Studied by TAO-DFT

Accurate prediction of the electronic properties of zigzag graphene nanoribbons (ZGNRs) has been very challenging for conventional electronic structure methods due to the presence of strong static correlation effects. To meet the challenge, we study the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy (i.e., a measure of polyradical character) of hydrogen-terminated ZGNRs with different widths and lengths using our recently developed thermally-assistedoccupation density functional theory (TAO-DFT) [Chai, J.-D. J. Chem. Phys. 2012, 136, 154104], a very efficient method for the study of large strongly correlated systems. Our results are in good agreement with the available experimental and high-accuracy ab initio data. The ground states of ZGNRs are shown to be singlets for all the widths and lengths investigated. With the increase of ribbon length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy increase monotonically. On the basis of the calculated orbitals and their occupation numbers, the longer ZGNRs are shown to possess increasing polyradical character in their ground states, where the active orbitals are mainly localized at the zigzag edges.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit

In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree-Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates.

Electronic and Optical Properties of the Narrowest Armchair Graphene Nanoribbons Studied by Density Functional Methods

In the present study, a series of planar poly(p-phenylene) (PPP) oligomers with n phenyl rings (n = 1–20), designated as n-PP, are taken as finite-size models of the narrowest armchair graphene nanoribbons with hydrogen passivation. The singlet-triplet energy gap, vertical ionization potential, vertical electron affinity, fundamental gap, optical gap, and exciton binding energy of n-PP are calculated using Kohn-Sham density functional theory and time-dependent density functional theory with various exchange-correlation density functionals. The ground state of n-PP is shown to be singlet for all the chain lengths studied. In contrast to the lowest singlet state (i.e., the ground state) of n-PP, the lowest triplet state of n-PP and the ground states of the cation and anion of n-PP are found to exhibit some multi-reference character. Overall, the electronic and optical properties of n-PP obtained from the ωB97 and ωB97X functionals are in excellent agreement with the available experimental data.

Thermally-assisted-occupation density functional theory with generalized-gradient approximations

We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computational efficiency for systems with strong static correlation effects, TAO-LDA and TAO-GGAs are applied to study the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy) of acenes with different number of linearly fused benzene rings (up to 100), which is very challenging for conventional electronic structure methods. The ground states of acenes are shown to be singlets for all the chain lengths studied here. With the increase of acene length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy (i.e., a measure of polyradical character) increase monotonically.

Theoretical design of tetra(arenediyl)bis(allyl) derivatives as model compounds for Cope rearrangement transition states

Delocated structures bearing 2.3–2.5 Å C⋯C bonds are preferred for some tetra(arenediyl)bis(allyl) systems.

Effect of electric field on the electronic and magnetic properties of a graphene nanoribbon/aluminium nitride bilayer system

The effect of an external electric field on the electronic and magnetic properties of the heterostructure of zigzag graphene nanoribbons (ZGNRs) placed on an aluminium nitride nanosheet (AlNNS) is studied using density functional theory (DFT).