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.

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.

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 (13Σu +) was described well, with non-imaginary excitation energies. TDTAO-DFT also yields zero singlet-triplet gap in the dissociation limit for the ground singlet (11Σg +) and the first triplet state (13Σu +). 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.

Impact of non-empirically tuning the range-separation parameter of long-range corrected hybrid functionals on ionization potentials, electron affinities, and fundamental gaps.

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.

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.

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions.

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.

SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters.

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.

Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections.

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.

Assessment of asymptotically corrected model potentials for charge-transfer-like excitations in oligoacenes.

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.

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.

Salicylaldehyde built fluorescent probe for dual sensing of Al3+, Zn2+ ions: Applications in latent fingerprint, bio-imaging & real sample analysis.

This Schiff base chemosensor (SNN) detected dual ions, Al3+ and Zn2+ ions selectively. Fluorescence spectrum investigations showed that Al3+ ions increased fluorescence intensity, notably at 493 nm. Introducing Zn2+ 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 Al3+/Zn2+ 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 + Al3+ and SNN + Zn2+ complexations had a 1:1 stoichiometry. DFT, LC-HRMS, and 1H NMR titration confirm this conclusion. The probe SNN's limit of detection (LOD) for Al3+/Zn2+ 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 Al3+ and Zn2+ ions.

Impact of metal and anion substitutions on the hydrogen storage properties of M-BTT metal-organic frameworks.

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.

Restoration of the derivative discontinuity in Kohn-Sham density functional theory: an efficient scheme for energy gap correction.

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.

Assessment of density functional methods with correct asymptotic behavior.

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.

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.

Significant role of the DNA backbone in mediating the transition origin of electronic excitations of B-DNA--implication from long range corrected TDDFT and quantified NTO analysis.

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.

Assessment of density functional approximations for the hemibonded structure of the water dimer radical cation.

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.

Density functional theory with fractional orbital occupations.

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.

Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections.

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.

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.