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Recently, oriented external electric fields (OEEFs) have earned much attention due to the possibility of tuning the properties of electronic systems. From a theoretical perspective, one can resort to electronic structure calculations to understand how the direction and strength of OEEFs affect the properties of electronic systems. However, for multi-reference (MR) systems, calculations employing the popular Kohn-Sham density functional theory with the traditional semilocal and hybrid exchange-correlation energy functionals can yield erroneous results. Owing to its decent compromise between accuracy and efficiency for MR systems at the nanoscale (i.e., MR nanosystems), in this study, thermally assisted occupation density functional theory (TAO-DFT) is adopted to explore the electronic properties of n -acenes ( n = 2-10), containing n linearly fused benzene rings, in OEEFs, where the OEEFs of various electric field strengths are applied along the long axes of n -acenes. According to our TAO-DFT calculations, the ground states of n -acenes in OEEFs are singlets for all the cases examined. The effect of OEEFs is shown to be significant on the vertical ionization potentials and vertical electron affinities of ground-state n -acenes with odd-number fused benzene rings. Moreover, the MR character of ground-state n -acenes in OEEFs increases with the increase in the acene length and/or the electric field strength.

This Schiff base chemosensor (SNN) detected dual ions, Al 3+ and Zn 2+ ions selectively. Fluorescence spectrum investigations showed that Al 3+ ions increased fluorescence intensity, notably at 493 nm. Introducing Zn 2+ ions caused a significant blue shift of roughly ∼65 nm at a wavelength of 434 nm, resulting in a notable change in fluorescence intensity. When binding Al 3+ /Zn 2+ ions, the SNN receptor uses three methods. Inhibition of photoinduced electron transfer (PET), excited state intramolecular proton transfer (ESIPT), and restriction of CN isomerization. The jobs plot method found that SNN + Al 3+ and SNN + Zn 2+ complexations had a 1:1 stoichiometry. DFT, LC-HRMS, and 1 H NMR titration confirm this conclusion. The probe SNN's limit of detection (LOD) for Al 3+ /Zn 2+ ions was 3.99 nM and 1.33 nM. Latent fingerprint (LFP), food samples, pharmaceutical products, and E. coli pathogen bio-imaging have all used the SNN probe to identify Al 3+ and Zn 2+ ions., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

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.

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.

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.

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.

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., Competing Interests: There are no conflicts of interest to declare., (This journal is © The Royal Society of Chemistry.)

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.

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.

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., (Copyright © 2020 Li and Chai.)

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 H 2 , the first triplet excited state (1 3 Σ 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 (1 1 Σ g + ) and the first triplet state (1 3 Σ 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.

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].

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.

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., Competing Interests: The authors declare no competing financial interest.

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.

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., Competing Interests: The authors declare no competing financial interest.

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.

Non-empirically tuning the range-separation parameter (ω) of long-range corrected (LC) hybrid functionals in improving the accuracy of vertical ionization potentials (IPs), vertical electron affinities (EAs), and fundamental gaps (FGs) is investigated. Use of default ω values gives the best overall property predictions employing the Δ self-consistent field (ΔSCF) approach, if sufficiently large basis set is used. Upon tuning, IP (HOMO) (i.e., the IP estimated from the negative of HOMO energy via DFT Koopmans' theorem) with the IP (ΔSCF) (i.e., the IP obtained from the ΔSCF approach) the accuracy of IP (HOMO) significantly improves however a reciprocal phenomenon is not observed. An interesting observation is that EA (LUMO) (i.e., the EA estimated from the negative of LUMO energy) is more accurate than EA (ΔSCF), if the ω value is in the range of 0.30 to 0.50 bohr -1 . © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

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., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

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 (Li 2 B n ), with n boron atoms (n = 6, 8, …, and 16). From our TAO-DFT results, Li 2 B n , which possess radical character, can bind up to 4 H 2 molecules per Li, with the binding energies in the desirable regime (between 20 and 40 kJ/mol per H 2 ). The hydrogen gravimetric storage capacities of Li 2 B n range from 7.9 to 17.0 wt%, achieving the ultimate goal of the United States Department of Energy. Accordingly, Li 2 B n could be promising media for storing and releasing H 2 at temperatures much higher than the boiling point of liquid nitrogen.

Accurate prediction of the electronic and hydrogen storage properties of linear carbon chains (C n ) and Li-terminated linear carbon chains (Li 2 C 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 Li 2 C n with n, odd-even oscillations in their electronic properties are found. In contrast to C n , the binding energies of H 2 molecules on Li 2 C n are in (or close to) the ideal binding energy range (about 20 to 40 kJ/mol per H 2 ). In addition, the H 2 gravimetric storage capacities of Li 2 C 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, Li 2 C 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.

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 H 2 and N 2 , 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.

We propose a short- and long-range corrected (SLC) hybrid scheme employing 100% Hartree-Fock exchange at both zero and infinite interelectronic distances, wherein three SLC hybrid density functionals with the D3 dispersion corrections (SLC-LDA-D3, SLC-PBE-D3, and SLC-B97-D3) are developed. SLC-PBE-D3 and SLC-B97-D3 are shown to be accurate for a very diverse range of applications, such as core ionization and excitation energies, thermochemistry, kinetics, noncovalent interactions, dissociation of symmetric radical cations, vertical ionization potentials, vertical electron affinities, fundamental gaps, and valence, Rydberg, and long-range charge-transfer excitation energies. Relative to ωB97X-D, SLC-B97-D3 provides significant improvement for core ionization and excitation energies and noticeable improvement for the self-interaction, asymptote, energy-gap, and charge-transfer problems, while performing similarly for thermochemistry, kinetics, and noncovalent interactions.

Owing to the presence of strong static correlation effects, accurate prediction of the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, active orbital occupation numbers, and real-space representation of active orbitals) of cyclacenes with n fused benzene rings (n = 4-100) has posed a great challenge to traditional electronic structure methods. To meet the challenge, we study these properties using our newly developed thermally-assisted-occupation density functional theory (TAO-DFT), a very efficient method for the study of large systems with strong static correlation effects. Besides, to examine the role of cyclic topology, the electronic properties of cyclacenes are also compared with those of acenes. Similar to acenes, the ground states of cyclacenes are singlets for all the cases studied. In contrast to acenes, the electronic properties of cyclacenes, however, exhibit oscillatory behavior (for n ≤ 30) in the approach to the corresponding properties of acenes with increasing number of benzene rings. On the basis of the calculated orbitals and their occupation numbers, the larger cyclacenes are shown to exhibit increasing polyradical character in their ground states, with the active orbitals being mainly localized at the peripheral carbon atoms.

Due to the presence of strong static correlation effects and noncovalent interactions, accurate prediction of the electronic and hydrogen storage properties of Li-adsorbed acenes with n linearly fused benzene rings (n = 3-8) has been very challenging for conventional electronic structure methods. To meet the challenge, we study these properties using our recently developed thermally-assisted-occupation density functional theory (TAO-DFT) with dispersion corrections. In contrast to pure acenes, the binding energies of H2 molecules on Li-adsorbed acenes are in the ideal binding energy range (about 20 to 40 kJ/mol per H2). Besides, the H2 gravimetric storage capacities of Li-adsorbed acenes are in the range of 9.9 to 10.7 wt%, satisfying the United States Department of Energy (USDOE) ultimate target of 7.5 wt%. On the basis of our results, Li-adsorbed acenes can be high-capacity hydrogen storage materials for reversible hydrogen uptake and release at ambient conditions.

We investigate the role of Kekulé and non-Kekulé structures in the radical character of alternant polycyclic aromatic hydrocarbons (PAHs) using thermally-assisted-occupation density functional theory (TAO-DFT), an efficient electronic structure method for the study of large ground-state systems with strong static correlation effects. Our results reveal that the studies of Kekulé and non-Kekulé structures qualitatively describe the radical character of alternant PAHs, which could be useful when electronic structure calculations are infeasible due to the expensive computational cost. In addition, our results support previous findings on the increase in radical character with increasing system size. For alternant PAHs with the same number of aromatic rings, the geometrical arrangements of aromatic rings are responsible for their radical character.

We investigate the potential energy curves of rare-gas dimers with various ranges and strengths of interparticle interactions (nuclear-electron, electron-electron, and nuclear-nuclear interactions). Our investigation is based on the highly accurate coupled-cluster theory associated with those interparticle interactions. For comparison, the performances of the corresponding Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and density functional theory are also investigated. Our results reveal that when the interparticle interactions retain the long-range Coulomb tails, the nature of van der Waals interactions in the rare-gas dimers remains similar. By contrast, when the interparticle interactions are sufficiently short-range, the conventional van der Waals interactions in the rare-gas dimers completely disappear, yielding purely repulsive potential energy curves.

By incorporating the nonempirical strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] in the underlying expression of four existing hybrid and double-hybrid models, we propose one hybrid (SCAN0) and three double-hybrid (SCAN0-DH, SCAN-QIDH, and SCAN0-2) density functionals, which are free from any fitted parameters. The SCAN-based double-hybrid functionals consistently outperform their parent SCAN semilocal functional for self-interaction problems and noncovalent interactions. In particular, SCAN0-2, which includes about 79% of Hartree-Fock exchange and 50% of second-order Møller-Plesset correlation, is shown to be reliably accurate for a very diverse range of applications, such as thermochemistry, kinetics, noncovalent interactions, and self-interaction problems.

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.

We examine the performance of the asymptotically corrected model potential scheme on the two lowest singlet excitation energies of acenes with different numbers of linearly fused benzene rings (up to 5), employing both the real-time time-dependent density functional theory and the frequency-domain formulation of linear-response time-dependent density functional theory. The results are compared with the experimental data and those calculated using long-range corrected hybrid functionals and others. The long-range corrected hybrid scheme is shown to outperform the asymptotically corrected model potential scheme for charge-transfer-like excitations.

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.

Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to the asymptote of the exchange-correlation potential, such as the highest occupied molecular orbital energies and Rydberg excitation energies of molecules. To provide a comprehensive comparison, we investigate the performance of the two schemes and others on a very wide range of applications, including asymptote problems, self-interaction-error problems, energy-gap problems, charge-transfer problems and many others. The LC hybrid scheme is shown to consistently outperform the AC model potential scheme. In addition, to be consistent with the molecules collected in the IP131 database [Y.-S. Lin, C.-W. Tsai, G.-D. Li and J.-D. Chai, J. Chem. Phys., 2012, 136, 154109], we expand the EA115 and FG115 databases to include, respectively, the vertical electron affinities and fundamental gaps of the additional 16 molecules and develop a new database, AE113 (113 atomization energies), consisting of accurate reference values for the atomization energies of the 113 molecules in IP131. These databases will be useful for assessing the accuracy of density functional methods.

Microporous metal-organic frameworks are a class of materials being vigorously investigated for mobile hydrogen storage applications. For high-pressure storage at ambient temperatures, the M(3)[(M(4)Cl)(3)(BTT)(8)](2) (M-BTT; BTT(3-) = 1,3,5-benzenetristetrazolate) series of frameworks are of particular interest due to the high density of exposed metal cation sites on the pore surface. These sites give enhanced zero-coverage isosteric heats of adsorption (Q(st)) approaching the optimal value for ambient storage applications. However, the Q(st) parameter provides only a limited insight into the thermodynamics of the individual adsorption sites, the tuning of which is paramount for optimizing the storage performance. Here, we begin by performing variable-temperature infrared spectroscopy studies of Mn-, Fe-, and Cu-BTT, allowing the thermodynamics of H(2) adsorption to be probed experimentally. This is complemented by a detailed DFT study, in which molecular fragments representing the metal clusters within the extended solid are simulated to obtain a more thorough description of the structural and thermodynamic aspects of H(2) adsorption at the strongest binding sites. Then, the effect of substitutions at the metal cluster (metal ion and anion within the tetranuclear cluster) is discussed, showing that the configuration of this unit indeed plays an important role in determining the affinity of the framework toward H(2). Interestingly, the theoretical study has identified that the Zn-based analogs would be expected to facilitate enhanced adsorption profiles over the compounds synthesized experimentally, highlighting the importance of a combined experimental and theoretical approach to the design and synthesis of new frameworks for H(2) storage applications.

From the perspective of perturbation theory, we propose a systematic procedure for the evaluation of the derivative discontinuity (DD) of the exchange-correlation energy functional in Kohn-Sham (KS) density functional theory, wherein the exact DD can in principle be obtained by summing up all the perturbation corrections to infinite order. Truncation of the perturbation series at low order yields an efficient scheme for obtaining the approximate DD. While the zeroth-order theory yields a vanishing DD, the first-order correction to the DD can be expressed as an explicit universal functional of the ground-state density and the KS lowest unoccupied molecular orbital density, allowing the direct evaluation of the DD in the standard KS method without extra computational cost. The fundamental gap can be predicted by adding the estimated DD to the KS gap. This scheme is shown to be accurate in the prediction of the fundamental gaps for a wide variety of atoms and molecules.

By incorporating the improved empirical atom-atom dispersion corrections from DFT-D3 [Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys.2010, 132, 154104], two long-range corrected (LC) hybrid density functionals are proposed. Our resulting LC hybrid functionals, ωM06-D3 and ωB97X-D3, are shown to be accurate for a very wide range of applications, such as thermochemistry, kinetics, noncovalent interactions, frontier orbital energies, fundamental gaps, and long-range charge-transfer excitations, when compared with common global and LC hybrid functionals. Relative to ωB97X-D [Chai, J.-D.; Head-Gordon, M. Phys. Chem. Chem. Phys.2008, 10, 6615], ωB97X-D3 (reoptimization of ωB97X-D with improved dispersion corrections) is shown to be superior for nonbonded interactions, and similar in performance for bonded interactions, while ωM06-D3 is shown to be superior for general applications.

Due to the severe self-interaction errors associated with some density functional approximations, conventional density functionals often fail to dissociate the hemibonded structure of the water dimer radical cation (H(2)O)(2)(+) into the correct fragments: H(2)O and H(2)O(+). Consequently, the binding energy of the hemibonded structure (H(2)O)(2)(+) is not well-defined. For a comprehensive comparison of different functionals for this system, we propose three criteria: (i) the binding energies, (ii) the relative energies between the conformers of the water dimer radical cation, and (iii) the dissociation curves predicted by different functionals. The long-range corrected (LC) double-hybrid functional, ωB97X-2(LP) [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2009, 131, 174105], is shown to perform reasonably well based on these three criteria. Reasons that LC hybrid functionals generally work better than conventional density functionals for hemibonded systems are also explained in this work.

We systematically investigate the possible complex transition origin of electronic excitations of giant molecular systems by using the recently proposed QNTO analysis [J.-H. Li, J.-D. Chai, G. Y. Guo and M. Hayashi, Chem. Phys. Lett., 2011, 514, 362.] combined with long-range corrected TDDFT calculations. Thymine (Thy) related excitations of a B-DNA biomolecule are then studied as examples, where the model systems have been constructed by extracting from the perfect or an X-ray crystal (PDB code 3BSE) B-DNA structure with at least one Thy included. In the first part, we consider the systems composed of a core molecular segment (e.g. Thy, or di-Thy) and a surrounding physical/chemical environment of interest (e.g. backbone, adjacent stacking nucleobases) in gas phase and examine how the excitation properties of the core vary in response to the environment. We find that the orbitals contributed by the DNA backbone and surrounding nucleobases often participate in a transition of Thy-related excitations affecting their composition, absorption energy, and oscillator strength. A vast number of strongly backbone-orbital involved excitations are also found at an absorption wavelength below ∼180 nm predicted by TD-ωB97X. In the second part, we take into account geometrically induced variation of the excitation properties of various B-DNA segments, e.g. di-Thy, dTpdT etc., obtained from different sources (ideal and 3BSE). It is found that the transition origin of several Thy-related excitations of these segments is sensitive to slight conformational variations, suggesting that DNA with thermal motions may from time to time exhibit very different photo-induced physical and/or chemical processes.

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H(2) and N(2), and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.

We propose a long-range corrected hybrid meta-generalized-gradient approximation (GGA) functional, based on a global hybrid meta-GGA functional, M05 [Y. Zhao, N. E. Schultz, and D. G. Truhlar, J. Chem. Phys. 123, 161103 (2005)], and empirical atom-atom dispersion corrections. Our resulting functional, ωM05-D, is shown to be accurate for a very wide range of applications, such as thermochemistry, kinetics, noncovalent interactions, equilibrium geometries, frontier orbital energies, fundamental gaps, and excitation energies. In addition, we present three new databases, IP131 (131 ionization potentials), EA115 (115 electron affinities), and FG115 (115 fundamental gaps), consisting of experimental molecular geometries and accurate reference values, which will be useful in the assessment of the accuracy of density functional approximations.

Objective: To observe the effect of astragaloside on oxidative low-density lipoprotein (Ox-LDL) mediated oxidative damage of endothelial progenitor cells (EPCs)., Methods: Peripheral blood mononuclear cells(PBMCs) were isolated by Ficoll density gradient centrifugation, and EPCs were identified by flow cytometry. Adherent cells were collected after seven-day incubation and randomly divided into the normal control group, the Ox-LDL group (as the model group, at the dose of 100 microg/mL), the low, middle, and high astragaloside groups (with 100 microg/mL Ox-LDL plus 2, 10, and 50 microg/mL astragaloside). Twenty-four h later, the proliferation and adhesion capabilities of EPCs were observed using MTT colorimetry and the adhesion capability detection. Levels of superoxide dismutase (SOD) and malonaldehyde (MDA) in the cell supernate of each group were determined., Results: After Ox-LDL damage, the proliferative and adhesive capacities of EPCs were significantly injured (53 +/- 8 vs 42 +/- 6, 0.49 +/- 0.12 vs 0.37 +/- 0.02, both P<0.05). The SOD content obviously decreased (21.95 +/- 1.43 vs 14.76 +/- 3.99, P<0.01), the MDA content obviously increased (3.72 +/- 0.30 vs 5.57 +/- 0.64, P<0.01). After intervened by astragaloside for 24 h, the proliferative and adhesive capacities of EPCs were significantly improved. The SOD contents of astragaloside intervention groups were obviously improved and the MDA content obviously lowered., Conclusions: Astragaloside showed significant protection on Ox-LDL damaged EPCs. Its mechanism might be correlated with antioxidative damage.

In this study, we examined the protective effects of Danshen both on endothelial progenitor cells (EPCs) in patients with hypercholesterolemia and on in-vitro EPCs of healthy volunteers. In the clinical study, we randomly divided 24 subjects with hypercholesterolemia into two groups (the control group and the Danshen-treated group). At the end of two weeks of treatment, the EPC cellular functions of both groups were tested. The results indicated that, compared to the control group, EPCs in the Danshen-treated group showed significantly better cellular functions, which was manifested in the cloning number, the proliferation capacity, the number of EPC adhesions, and cell migration. In the subsequent in-vitro experiments, EPCs were treated with vehicle, oxidized low-density lipoprotein (Ox-LDL, 100 microg/ml), or Ox-LDL (100 microg/ml) plus different concentrations of Danshen (Danshensu 2, 10, or 50 microg/ml, respectively) for 24 h. The results showed that Danshen treatments can prevent the detrimental effects of Ox-LDL on EPC cellular functions measured by proliferation capacity (0.24+/-0.08, 0.37+/-0.11, 0.30+/-0.04 vs. 0.13+/-0.02, P<0.05, P<0.01, and P<0.01, respectively), and adhesion ability (63.00+/-11.60, 70.00+/-10.80, 85.50+/-11.41 vs. 40.50+/-6.85, all P<0.01). Compared to the group treated with Ox-LDL alone, Danshen treatment significantly decreased the lipid peroxidation end product malondialdehyde (MDA) [(4.34+/-0.54), (3.98+/-0.47), (3.46+/-0.31) vs. (5.57+/-0.64) nmol/ml, all P<0.01], increased the production of superoxide dismutase (SOD) [(29.74+/-0.71), (31.09+/-0.83), (30.41+/-0.65) vs. (14.76+/-3.99) U/ml, all P<0.01], and lowered the expression of interleukin-6 (IL-6) [(24.62+/-7.69), (27.04+/-3.14), (33.38+/-18.86) vs. (230.67+/-33.53) pg/ml, all P<0.01] and tumor necrosis factor-alpha (TNF-alpha) [(41.72+/-6.10), (17.02+/-6.82), (3.73+/-2.26) vs. (228.71+/-41.53) pg/ml, all P<0.01] in Ox-LDL treated EPCs. These results suggest that Danshen may exert a protective effect through its antioxidant and anti-inflammatory features.

We extend the range of applicability of our previous long-range corrected (LC) hybrid functional, omegaB97X [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by second-order Moller-Plesset (many-body) perturbation theory. This LC "double-hybrid" density functional, denoted as omegaB97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calculations (as well as training set results), omegaB97X-2 yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree-Fock exchange, omegaB97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as symmetric homonuclear radical cations.

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, omegaB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, omegaB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as omegaB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

The recently proposed new family of "double-hybrid" density functionals [Grimme, S. J. Chem. Phys. 2006, 124, 34108] replaces a fraction of the semi-local correlation energy by a non-local correlation energy expression that employs the Kohn-Sham orbitals in second-order many-body perturbation theory. These functionals have provided results of high accuracy over a wide range of properties but fail to accurately describe long-range van der Waals interactions. In this work, a distance-dependent scaling factor for the non-local correlation energy is introduced to address this problem, and two new double-hybrid density functionals are proposed. The new functionals are optimized with the finite cc-pVTZ basis on training sets of atomization energies and intermolecular interaction energies. They are compared against (scaled) second-order Møller-Plesset perturbation theories and popular density functionals including the hybrid-GGA functional B3-LYP and the first double-hybrid functional (B2-PLYP). Tests are performed on an extensive set including reaction energies, barrier heights, weakly interacting complexes, transition-metal systems, molecular geometries, and harmonic vibrational frequencies. Within the cc-pVTZ atomic orbital basis, we have demonstrated the ability to find a parametrization scheme which is simultaneously able to describe thermochemistry and weakly bound systems with a satisfactory degree of accuracy.

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.