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

Computational Studies of Dimerization of [n]-Cyclacenes

Cyclacenes, C4nH2n, consist of n linearly fused benzene rings that are arranged to result in a closed nanohoop structure. Cyclacenes are thus the cyclic versions of acenes and have so far escaped synthesis. In order to estimate the tendency of [n]-cyclacenes (6 ≤ n ≤ 20) to undergo dimerization, which is assumed to be a major pathway of degradation under oxygen-free conditions, we here report the energy of dimerization as computed by density functional theory using spin-restricted, spin-unrestricted, and thermally assisted-occupation (TAO) formalisms. It is found that the energy of dimerization increases with increasing size of n but that this increase is not monotonic for the smaller members of the series. This is due to the combination of the cryptoannulenic effect and the inherent strain of the cyclacenes. The energy of dimerization of the largest member inspected, [20]-cyclacene, is -59.3 kcal/mol, while we expect it to converge to -46 kcal/mol for n → ∞ based on comparison with data obtained for 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.

Gas Phase Ionization Energy of Heptacene

The ionization energy is a fundamental property that is relevant to charge transport in organic semiconductors. We report adiabatic ionization energies (AIEs) of heptacene at 6.21 and 7.20 eV for the X̃+B2g and Ã+Au states, respectively, as the next larger member of the acene series using mass- and isomer-selective double imaging photoelectron photoion coincidence spectroscopy. The X̃+ state energy decreases monotonically with an increase in size within the homologous series of acenes and approaches an asymptotic limit [AIE(polyacene) = 5.94 ± 0.06 eV] based on a fit with an exponential decay function. As byproducts of heptacene formation from cycloreversion of diheptacenes, 5,18-, 7,16-, and 6,17-dihydroheptacene can be detected, and their AIE is similar to that of their largest acene subunit (anthracene and tetracene, respectively), in very good agreement with computational treatments.

Electronic Properties of Graphene Nano-Parallelograms: A Thermally Assisted Occupation DFT Computational Study

In this computational study, we investigate the electronic properties of zigzag graphene nano-parallelograms (GNPs), which are parallelogram-shaped graphene nanoribbons of various widths and lengths, using thermally assisted occupation density functional theory (TAO-DFT). Our calculations revealed a monotonic decrease in the singlet-triplet energy gap as the GNP length increased. The GNPs possessed singlet ground states for all the cases examined. With the increase of GNP length, the vertical ionization potential and fundamental gap decreased monotonically, while the vertical electron affinity increased monotonically. Some of the GNPs studied were found to possess fundamental gaps in the range of 1-3 eV, lying in the ideal region relevant to solar energy applications. Besides, as the GNP length increased, the symmetrized von Neumann entropy increased monotonically, denoting an increase in the degree of the multi-reference character associated with the ground state GNPs. The occupation numbers and real-space representation of active orbitals indicated that there was a transition from the nonradical nature of the shorter GNPs to the increasing polyradical nature of the longer GNPs. In addition, the edge/corner localization of the active orbitals was found for the wider and longer GNPs.

Entropy is a good approximation to the electronic (static) correlation energy

For an electronic system, given a mean field method and a distribution of orbital occupation numbers that are close to the natural occupations of the correlated system, we provide formal evidence and computational support to the hypothesis that the entropy (or more precisely -σS, where σ is a parameter and S is the entropy) of such a distribution is a good approximation to the correlation energy. Underpinning the formal evidence are mild assumptions: the correlation energy is strictly a functional of the occupation numbers, and the occupation numbers derive from an invertible distribution. Computational support centers around employing different mean field methods and occupation number distributions (Fermi-Dirac, Gaussian, and linear), for which our claims are verified for a series of pilot calculations involving bond breaking and chemical reactions. This work establishes a formal footing for those methods employing entropy as a measure of electronic correlation energy (e.g., i-DMFT [Wang and Baerends, Phys. Rev. Lett. 128, 013001 (2022)] and TAO-DFT [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)]) and sets the stage for the widespread use of entropy functionals for approximating the (static) electronic correlation.

Real-Time Extension of TAO-DFT

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Polyradical character assessment using multireference calculations and comparison with density-functional derived fractional occupation number weighted density analysis

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties. In this work, the unpaired electron densities and numbers of unpaired electrons (NU values) calculated at the high-level multireference averaged quadratic coupled-cluster (MR-AQCC) method are used to develop a test set to assess the capabilities of different biradical descriptors based on density functional theory. A benchmark collection of 29 different compounds has been selected. The DFT descriptors contain primarily the fractional occupation number weighted electron density (FOD) based on simplified thermally-assisted-occupation density functional theory (TAO-DFT) calculations, but the singlet-triplet energy difference and other descriptors denoted as y0 and nLUNO have been considered as well. After adjustment of the literature-recommended finite temperatures, a very good, detailed agreement between unpaired density and FOD analysis is observed which is also manifested in excellent statistical correlations. The other two descriptors also show good correlations even though the absolute scaling is not satisfactory. A new linear fit of FOD data to the MR-AQCC reference values leads to an improved regression relation for determining the recommended finite temperature value in dependence of the Hartree-Fock exchange. This provides the basis for fast and reliable assessment of the biradical character of many classes of PAHs without the need for performing computationally extended MR calculations.

TAO-DFT with the Polarizable Continuum Model

For the ground-state properties of gas-phase nanomolecules with multi-reference character, thermally assisted occupation (TAO) density functional theory (DFT) has recently been found to outperform the widely used Kohn-Sham DFT when traditional exchange-correlation energy functionals are employed. Aiming to explore solvation effects on the ground-state properties of nanomolecules with multi-reference character at a minimal computational cost, we combined TAO-DFT with the PCM (polarizable continuum model). In order to show its usefulness, TAO-DFT-based PCM (TAO-PCM) was used to predict the electronic properties of linear acenes in three different solvents (toluene, chlorobenzene, and water). According to TAO-PCM, in the presence of these solvents, the smaller acenes should have nonradical character, and the larger ones should have increasing polyradical character, revealing striking similarities to the past findings in the gas phase.

Electronic Properties of Hexagonal Graphene Quantum Rings from TAO-DFT

The reliable prediction of electronic properties associated with graphene nanosystems can be challenging for conventional electronic structure methods, such as Kohn-Sham (KS) density functional theory (DFT), due to the presence of strong static correlation effects in these systems. To address this challenge, TAO (thermally assisted occupation) DFT has been recently proposed. In the present study, we employ TAO-DFT to predict the electronic properties of n-HGQRs (i.e., the hexagonal graphene quantum rings consisting of n aromatic rings fused together at each side). From TAO-DFT, the ground states of n-HGQRs are singlets for all the cases investigated (n = 3-15). As the system size increases, there should be a transition from the nonradical to polyradical nature of ground-state n-HGQR. The latter should be intimately related to the localization of active TAO-orbitals at the inner and outer edges of n-HGQR, which increases with increasing system size.

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study

Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

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.

Covalently Bonded Fullerene Nano-Aggregates (C60)n: Digitalizing Their Energy–Topology–Symmetry

Fullerene dimers and oligomers are attractive molecular objects with an intermediate position between the molecules and nanostructures. Due to the size, computationally assessing their structures and molecular properties is challenging, as it currently requires high-cost quantum chemical techniques. In this work, we have jointly studied energies, topological (Wiener indices and roundness), and information theoretic (information entropy) descriptors, and have obtained regularities in triad ‘energy–topology–symmetry’. We have found that the topological indices are convenient to indicating the most and least reactive atoms of the fullerene dimer structures, whereas information entropy is more suitable to evaluate odd–even effects on the symmetry of (C60)n. Quantum chemically assessed stabilities of selected C120 structures, as well as linear and zigzag (C60)n, are discussed.

Electronic Properties of Carbon Nanobelts Predicted by Thermally-Assisted-Occupation DFT

Accurate prediction of properties of large-scale multi-reference (MR) electronic systems remains difficult for traditional computational methods (e.g., the Hartree-Fock theory and Kohn-Sham density functional theory (DFT)). Recently, thermally-assisted-occupation (TAO)-DFT has been demonstrated to offer reliable description of electronic properties of various large-scale MR electronic systems. Consequently, in this work, TAO-DFT is used to unlock the electronic properties associated with C-Belt[n] (i.e., the carbon nanobelts containing n fused 12-membered carbon rings). Our calculations show that for all the system sizes reported (n = 4-24), C-Belt[n] have singlet ground states. In general, the larger the size of C-Belt[n], the more pronounced the MR character of ground-state C-Belt[n], as evident from the symmetrized von Neumann entropy and the occupation numbers of active TAO-orbitals. Furthermore, the active TAO-orbitals are delocalized along the circumference of C-Belt[n], as evident from the visualization of active TAO-orbitals.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

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.

TAO-DFT-Based Ab Initio Molecular Dynamics

Recently, AIMD (ab initio molecular dynamics) has been extensively employed to explore the dynamical information of electronic systems. However, it remains extremely challenging to reliably predict the properties of nanosystems with a radical nature using conventional electronic structure methods (e.g., Kohn-Sham density functional theory) due to the presence of static correlation. To address this challenge, we combine the recently formulated TAO-DFT (thermally-assisted-occupation density functional theory) with AIMD. The resulting TAO-AIMD method is employed to investigate the instantaneous/average radical nature and infrared spectra of n-acenes containing n linearly fused benzene rings (n = 2-8) at 300 K. According to the TAO-AIMD simulations, on average, the smaller n-acenes (up to n = 5) possess a nonradical nature, and the larger n-acenes (n = 6-8) possess an increasing radical nature, showing remarkable similarities to the ground-state counterparts at 0 K. Besides, the infrared spectra of n-acenes obtained with the TAO-AIMD simulations are in qualitative agreement with the existing experimental data.

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.

TAO-DFT investigation of electronic properties of linear and cyclic carbon chains

It has been challenging to adequately investigate the properties of nanosystems with radical nature using conventional electronic structure methods. We address this challenge by calculating the electronic properties of linear carbon chains (l-CC[n]) and cyclic carbon chains (c-CC[n]) with n = 10-100 carbon atoms, using thermally-assisted-occupation density functional theory (TAO-DFT). For all the cases investigated, l-CC[n]/c-CC[n] are ground-state singlets, and c-CC[n] are energetically more stable than l-CC[n]. The electronic properties of l-CC[n]/c-CC[n] reveal certain oscillation patterns for smaller n, followed by monotonic changes for larger n. For the smaller carbon chains, odd-numbered l-CC[n] are more stable than the adjacent even-numbered ones; c-CC[[Formula: see text]]/c-CC[4m] are more/less stable than the adjacent odd-numbered ones, where m are positive integers. As n increases, l-CC[n]/c-CC[n] possess increasing polyradical nature in their ground states, where the active orbitals are delocalized over the entire length of l-CC[n] or the whole circumference of c-CC[n].

Finite-temperature-based time-dependent density-functional theory method for static electron correlation systems

In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems.

TAO-DFT Study on the Electronic Properties of Diamond-Shaped Graphene Nanoflakes

At the nanoscale, it has been rather troublesome to properly explore the properties associated with electronic systems exhibiting a radical nature using traditional electronic structure methods. Graphene nanoflakes, which are graphene nanostructures of different shapes and sizes, are typical examples. Recently, TAO-DFT (i.e., thermally-assisted-occupation density functional theory) has been formulated to tackle such challenging problems. As a result, we adopt TAO-DFT to explore the electronic properties associated with diamond-shaped graphene nanoflakes with n = 2-15 benzenoid rings fused together at each side, designated as n-pyrenes (as they could be expanded from pyrene). For all the n values considered, n-pyrenes are ground-state singlets. With increasing the size of n-pyrene, the singlet-triplet energy gap, vertical ionization potential, and fundamental gap monotonically decrease, while the vertical electron affinity and symmetrized von Neumann entropy (which is a quantitative measure of radical nature) monotonically increase. When n increases, there is a smooth transition from the nonradical character of the smaller n-pyrenes to the increasing polyradical nature of the larger n-pyrenes. Furthermore, the latter is shown to be related to the increasing concentration of active orbitals on the zigzag edges of the larger n-pyrenes.

Electronic Properties of Triangle-Shaped Graphene Nanoflakes from TAO-DFT

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.

Electronic Properties of Linear and Cyclic Boron Nanoribbons from Thermally-Assisted-Occupation Density Functional Theory

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.

Local Density Approximation for the Short-Range Exchange Free Energy Functional

Analytical expressions for the exchange free energy per particle of the uniform electron gas (UEG) associated with the short-range (SR) interelectronic interaction at the low- and high-temperature limits are examined, yielding an accurate analytical parametrization for the SR exchange free energy per particle of the UEG as a function of the uniform electron density, temperature, and range-separation parameter. This parametrization constitutes the local density approximation for the SR exchange free energy functional, which can be the first step toward finding generally accurate range-separated hybrid functionals in both finite-temperature density functional theory and thermally assisted-occupation density functional theory.

Electronic Properties of Möbius Cyclacenes Studied by Thermally-Assisted-Occupation Density Functional Theory

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.

Electronic properties of the coronene series from thermally-assisted-occupation density functional theory

To fully utilize the great potential of graphene in electronics, a comprehensive understanding of the electronic properties of finite-size graphene flakes is essential. While the coronene series with n fused benzene rings at each side (designated as n-coronenes) are possible structures for opening a band gap in graphene, their electronic properties are not yet fully understood. Nevertheless, because of their radical character, it remains very difficult to reliably predict the electronic properties of the larger n-coronenes with conventional computational approaches. In order to circumvent this, the various electronic properties of n-coronenes (n = 2-11) are investigated using thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys., 2012, 136, 154104], a very efficient electronic structure method for studying nanoscale systems with strong static correlation effects. The ground states of the larger n-coronenes are shown to be polyradical singlets, where the active orbitals are mainly localized at the zigzag edges.

Electronic and Hydrogen Storage Properties of Li-Terminated Linear Boron Chains Studied by TAO-DFT

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 (Li₂B_n), with n boron atoms (n = 6, 8, …, and 16). From our TAO-DFT results, Li₂B_n, 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 Li₂B_n range from 7.9 to 17.0 wt%, achieving the ultimate goal of the United States Department of Energy. Accordingly, Li₂B_n could be promising media for storing and releasing H₂ at temperatures much higher than the boiling point of liquid nitrogen.

Effect of Li Termination on the Electronic and Hydrogen Storage Properties of Linear Carbon Chains: A TAO-DFT Study

Accurate prediction of the electronic and hydrogen storage properties of linear carbon chains (C n ) and Li-terminated linear carbon chains (Li2C n ), with n carbon atoms (n = 5-10), has been very challenging for traditional electronic structure methods, due to the presence of strong static correlation effects. To meet the challenge, we study these properties using our newly developed thermally-assisted-occupation density functional theory (TAO-DFT), a very efficient electronic structure method for the study of large systems with strong static correlation effects. Owing to the alteration of the reactivity of C n and Li2C n with n, odd-even oscillations in their electronic properties are found. In contrast to C n , the binding energies of H2 molecules on Li2C n are in (or close to) the ideal binding energy range (about 20 to 40 kJ/mol per H2). In addition, the H2 gravimetric storage capacities of Li2C n are in the range of 10.7 to 17.9 wt%, satisfying the United States Department of Energy (USDOE) ultimate target of 7.5 wt%. On the basis of our results, Li2C n can be high-capacity hydrogen storage materials that can uptake and release hydrogen at temperatures well above the easily achieved temperature of liquid nitrogen.

Self-consistent determination of the fictitious temperature in thermally-assisted-occupation density functional theory

We propose a self-consistent scheme for the determination of the fictitious temperature in thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys., 2012, 136, 154104].