Long-range Corrected Hybrid Functionals Research Articles

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange–correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

The Role of Range-Separated Correlation in Long-Range Corrected Hybrid Functionals.

The extensive application of long-range corrected hybrid functionals highlights the importance of further improving their accuracy. Unlike common long-range corrected hybrid functionals mainly focusing on the exchange part, range-separated correlation and its role in long-range corrected hybrid functionals are the main concerns of this work. To this end, we present theory on the derivation of the range-separated correlation, whose reliability and validity are proved by the agreement with the full CI on the test of the short-range correlation energy. The tests on various properties indicate that the long-range part of the LYP functional cannot effectively capture the long-range correlation effect required in LC-BLYP, whose absence instead results in a better XC functional. This new functional significantly improves LC-BLYP on all the tests in this work, with an accuracy on par with or even greater than the widely recognized CAM-B3LYP method for some applications, while maintaining the important -1/r asymptotic behavior of the XC potential. The advances and insights gained in this work are useful for the application and development of long-range corrected hybrid functionals, while emphasizing the significance of developing effective and low-cost long-range correlation functionals.

Evaluation of charge-transfer rates in fullerene-based donor-acceptor dyads with different density functional approximations.

The shift towards renewable energy is one of the main challenges of this generation. Dye-sensitized solar cells (DSSCs), based on donor-acceptor architectures, can help in this transition as they present excellent photovoltaic efficiencies yet cheap and simple manufacturing. For molecular heterojunction DSSCs, donor-acceptor pairs are linked in a covalent manner, which facilitates their tailoring and rational design. Nevertheless, reliable computational characterization of charge transfer rate constants (kCT) is needed to speed this development process up. In this context, the performance of time-dependent density functional theory for the calculation of kCT values in donor-acceptor fullerene-based dyads has not been benchmarked yet. Herein, we present a detailed analysis on the performance of seven well-known density functional approximations (DFAs) for this type of system, focusing on several parameters such as the reorganization energies (λ), electronic couplings (VDA), and Gibbs energies (ΔG0CT), as well as the final rate constants. The amount of exact exchange at short range (SR) and long range (LR) electron-electron distances (and the transition from the SR to LR) turned out to be key for the success of the prediction. The tuning of these parameters improves significantly the performance of current DFAs.

Charge transfer and nonlinear optical properties of anthraquinone D-π-A dyes in relation with the DFT based molecular descriptors and perturbational potential

The static and dynamic NLO properties of Anthraquinone based (D-π-A) dyes are determined by using the Density Functional Theory in ten different functionals. Five global hybrids and five long-range corrected hybrid functionals used based on Hartree-fork exchange contribution. The investigation of vertical excitation is also performed in the equivalent set of functionals. The elaborate study of molecular configuration i.e. intramolecular charge transfer character is analyzed by Frontier Molecular Orbital study, bond length alternation, bond order alternation, molecular electrostatic potential plot, quinoidal character (δr), and electrophilicity index (ω). Benchmarking studies are initiated with the standard deviation method and, the functionals BHHLYP and ωB97 resulted as the suitable functionals for determining the NLO properties of anthraquinone based dyes. The less studied reactivity descriptor hyper-hardness (Γ) and perturbation potential (Vo) is also explored and correlated with the NLO properties. The substitution effect on NLO properties is further confirmed by Hammett constant and excited state Hammett substituent constant.

Design of novel tellurium and selenium containing semiconducting polymers using quantum mechanical tools

Structural, optical and electronic properties of the two novel donor-acceptor-donor type conjugated polymers based on 4,7-di(selenophen-2-yl)benzo[c][1,2,5]selenadiazole (SeSeSe) and 4,7-di(tellurophen-2-yl)benzo[c][1,2,5]telluradiazole (TeTeTe) are investigated by means of quantum chemical calculations utilizing conventional and long-range corrected hybrid functionals. The lowest energy structures of the SeSeSe and TeTeTe monomers and oligomers are revealed through conformational analysis, while their electronic properties are obtained from density functional theory (DFT) molecular orbital calculations and optical properties are obtained from the time dependent DFT (TD-DFT) calculations for UV–vis absorption spectra. Electronic band gaps that directly affect the semiconducting properties of these novel polymers are calculated by using linear regression analysis of DFT data, and also periodic boundary conditions calculations (PBC-DFT). Our results indicate that SeSeSe and TeTeTe polymers have considerably lower band gap values than that of their furan-, thiophene-, benzooxadiazole- and benzothiadiazole-based analogs. The novel SeSeSe and TeTeTe polymers with improved optical and electronic properties may have an important role in the near future, especially for the optoelectronic and photovoltaic applications.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals

The performance of non-empirically tuned long-range corrected hybrid functionals for the prediction of vertical ionization potentials (IPs) and electron affinities (EAs) is assessed for a set of 24 organic acceptor molecules. Basis set-extrapolated coupled cluster singles, doubles, and perturbative triples [CCSD(T)] calculations serve as a reference for this study. Compared to standard exchange-correlation functionals, tuned long-range corrected hybrid functionals produce highly reliable results for vertical IPs and EAs, yielding mean absolute errors on par with computationally more demanding GW calculations. In particular, it is demonstrated that long-range corrected hybrid functionals serve as ideal starting points for non-self-consistent GW calculations.

Long-Range Corrected DFT Meets GW: Vibrationally Resolved Photoelectron Spectra from First Principles.

We propose an entirely nonempirical and computationally efficient scheme to calculate highly reliable vibrationally resolved photoelectron spectra for molecules from first principles. To this end, we combine nonempirically tuned long-range corrected hybrid functionals with non-self-consistent many-body perturbation theory in the G0W0 approximation and a Franck-Condon multimode analysis based on DFT-calculated frequencies. The vibrational analysis allows for a direct comparison of the GW-calculated spectra to gas-phase ultraviolet photoelectron measurements of neutral and anionic molecules, respectively. Direct comparison of the calculated peak maxima with experiment yields mean absolute errors below 0.1 eV for ionization potentials, electron affinities, and fundamental gaps, clearly outperforming commonly used G0W0 approaches at similar numerical costs.

Can gap tuning schemes of long-range corrected hybrid functionals improve the description of hyperpolarizabilities?

Long-range corrected hybrid density functionals (LC-DFT), with range separation parameters optimally tuned to obey Koopmans' theorem, are used to calculate the first-order hyperpolarizabilities of prototypical charge-transfer compounds p-nitroaniline (PNA) and dimethylamino nitrostilbene (DANS) in the gas phase and various solvents. It is shown that LC-DFT methods with default range separation parameters tend to underestimate hyperpolarizabilities (most notably in solution) and that the tuning scheme can sharply improve results, especially in the cases when the standard LC-DFT errors are largest. Nonetheless, we also identify pathological cases (two pyrrole derivatives) for which LC-DFT underestimates the hyperpolarizabilities, regardless of tuning. It is noted that such pathological cases do not follow the usual inverse relation between the hyperpolarizability and amount of exact exchange, and thus this behavior may serve as a diagnostic tool for the adequacy of LC-DFT.

Prediction of the linear and nonlinear optical properties of tetrahydronaphthalone derivatives via long-range corrected hybrid functionals

The linear and nonlinear optical (NLO) properties of methoxybenzylidene (1) and thiophen-2-ylmethylidene (2) tetrahydronaphthalone derivatives are studied using long-range corrected density functional theory (LC-DFT). The calculated hyperpolarisabilities indicate that both compounds have measurable NLO properties (approximately one to two times the hyperpolarisability of p-nitroaniline). Charge-transfer indices and time-dependent DFT calculations suggest that the NLO properties are a result of a charge-transfer excitation, which is typical in conjugated donor–acceptor structures. The ultraviolet–visible spectra of 1 and 2 are also predicted using gap-fitting schemes, and these data are used to assess how accurately the hyperpolarisabilities of 1 and 2 could be estimated by the solvatochromic method.

Theoretical Study of the Local and Charge-Transfer Excitations in Model Complexes of Pentacene-C60 Using Tuned Range-Separated Hybrid Functionals.

The characteristics of the electronic excited states and the charge-transfer processes at organic-organic interfaces play an important role in organic electronic devices. However, charge-transfer excitations have proven challenging to describe with conventional density functional theory (DFT) methodologies due to the local nature of the exchange-correlation potentials often employed. Here, we examine the excited states of model pentacene-C60 complexes using time-dependent DFT with, on one hand, one of the most popular standard hybrid functionals (B3LYP) and, on the other hand, several long-range corrected hybrid functionals for which we consider both default and nonempirically tuned range-separation parameters. The DFT results based on the tuned functionals are found to agree well with the available experimental data. The results also underline that the interface geometry of the complex has a strong effect on the energies and ordering of the singlet and triplet charge-transfer states.

Organic electronic materials: recent advances in the DFT description of the ground and excited states using tuned range-separated hybrid functionals.

CONSPECTUS: Density functional theory (DFT) and its time-dependent extension (TD-DFT) are powerful tools enabling the theoretical prediction of the ground- and excited-state properties of organic electronic materials with reasonable accuracy at affordable computational costs. Due to their excellent accuracy-to-numerical-costs ratio, semilocal and global hybrid functionals such as B3LYP have become the workhorse for geometry optimizations and the prediction of vibrational spectra in modern theoretical organic chemistry. Despite the overwhelming success of these out-of-the-box functionals for such applications, the computational treatment of electronic and structural properties that are of particular interest in organic electronic materials sometimes reveals severe and qualitative failures of such functionals. Important examples include the overestimation of conjugation, torsional barriers, and electronic coupling as well as the underestimation of bond-length alternations or excited-state energies in low-band-gap polymers. In this Account, we highlight how these failures can be traced back to the delocalization error inherent to semilocal and global hybrid functionals, which leads to the spurious delocalization of electron densities and an overestimation of conjugation. The delocalization error for systems and functionals of interest can be quantified by allowing for fractional occupation of the highest occupied molecular orbital. It can be minimized by using long-range corrected hybrid functionals and a nonempirical tuning procedure for the range-separation parameter. We then review the benefits and drawbacks of using tuned long-range corrected hybrid functionals for the description of the ground and excited states of π-conjugated systems. In particular, we show that this approach provides for robust and efficient means of characterizing the electronic couplings in organic mixed-valence systems, for the calculation of accurate torsional barriers at the polymer limit, and for the reliable prediction of the optical absorption spectrum of low-band-gap polymers. We also explain why the use of standard, out-of-the-box range-separation parameters is not recommended for the DFT and/or TD-DFT description of the ground and excited states of extended, pi-conjugated systems. Finally, we highlight a severe drawback of tuned range-separated hybrid functionals by discussing the example of the calculation of bond-length alternation in polyacetylene, which leads us to point out the challenges for future developments in this field.

Accurate description of torsion potentials in conjugated polymers using density functionals with reduced self-interaction error

We investigate the torsion potentials in two prototypical π-conjugated polymers, polyacetylene and polydiacetylene, as a function of chain length using different flavors of density functional theory. Our study provides a quantitative analysis of the delocalization error in standard semilocal and hybrid density functionals and demonstrates how it can influence structural and thermodynamic properties. The delocalization error is quantified by evaluating the many-electron self-interaction error (MESIE) for fractional electron numbers, which allows us to establish a direct connection between the MESIE and the error in the torsion barriers. The use of non-empirically tuned long-range corrected hybrid functionals results in a very significant reduction of the MESIE and leads to an improved description of torsion barrier heights. In addition, we demonstrate how our analysis allows the determination of the effective conjugation length in polyacetylene and polydiacetylene chains.

Comparative assessment of density functionals for excited-state dipole moments

In this Letter, we report on the performance of density functionals in computing (π,π∗) excited-state dipole moments of several photochromic molecules. The studied set of theoretical approximations encompasses GGA, hybrid and long-range corrected hybrid functionals. The CC2 coupled-cluster model and a large, property-oriented basis set are used to determine the reference values. The preliminary results of calculations of geometric derivatives of dipole moment difference, between the (π,π∗) excited state and the ground state, are also presented.

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.

Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections.

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.

Assessment of the performance of tuned range-separated hybrid density functionals in predicting accurate quasiparticle spectra

Long-range corrected hybrid functionals that employ a nonempirically tuned range-separation parameter have been demonstrated to yield accurate ionization potentials and fundamental gaps for a wide range of finite systems. Here, we address the question of whether this high level of accuracy is limited to the highest occupied/lowest unoccupied energy levels to which the range-separation parameter is tuned or whether it is retained for the entire valence spectrum. We examine several \ensuremath{\pi}-conjugated molecules and find that orbitals of a different character and symmetry require significantly different range-separation parameters and fractions of exact exchange. This imbalanced treatment of orbitals of a different nature biases the resulting eigenvalue spectra. Thus, the existing schemes for the tuning of range-separated hybrid functionals, while providing for good agreement between the highest occupied energy level and the first ionization potential, do not achieve accuracy comparable to reliable ${G}_{0}$${W}_{0}$ computations for the entire quasiparticle spectrum.

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.

Structure and electronic spectral property of coumarin–chalcone hybrids: A comparative study using conventional and long-range corrected hybrid functionals

The structures and electronic absorption spectra of a series of coumarin–chalcone hybrids have been investigated with density functional theory (DFT) and time-dependent density functional theory (TDDFT). Standard hybrid (PBE1PBE and BHHLYP), hybrid meta (BMK, M06, M06-2X and M06-HF) and long-range corrected hybrid (CAM-B3LYP) functionals have been chosen for calculations. The relative performance of the seven exchange–correlation functionals has been discussed and it turns out that, within the selected TDDFT framework, BMK emerges as the most efficient hybrid functional for coumarin–chalcone hybrids with a mean absolute error (MAE) of 0.16 eV (21.0 nm). Based on BMK results, the structure-spectra relationship and the effects of substituent, solvent and elongation of the conjugate chain on electronic spectra have been discussed. The experimentally observed substitution and solvent effects are well reproduced by calculation. The results reveal that the lowest energy transitions should be of intramolecular charge transfer (ICT) nature, which predominantly correspond to the π → π * transitions from HOMO to LUMO.

Scalar Relativistic Computations of Nuclear Magnetic Shielding and g-Shifts with the Zeroth-Order Regular Approximation and Range-Separated Hybrid Density Functionals.

Density functional theory (DFT) calculations of NMR chemical shifts and molecular g tensors with Gaussian-type orbitals are implemented via second-order energy derivatives within the scalar relativistic zeroth order regular approximation (ZORA) framework. Nonhybrid functionals, standard (global) hybrids, and range-separated (Coulomb-attenuated, long-range corrected) hybrid functionals are tested. Origin invariance of the results is ensured by use of gauge-including atomic orbital (GIAO) basis functions. The new implementation in the NWChem quantum chemistry package is verified by calculations of nuclear shielding constants for the heavy atoms in HX (X = F, Cl, Br, I, At) and H2X (X = O, S, Se, Te, Po) and (125)Te chemical shifts in a number of tellurium compounds. The basis set and functional dependence of g-shifts is investigated for 14 radicals with light and heavy atoms. The problem of accurately predicting (19)F NMR shielding in UF6-nCln, n = 1-6, is revisited. The results are sensitive to approximations in the density functionals, indicating a delicate balance of DFT self-interaction vs correlation. For the uranium halides, the range-separated functionals are not clearly superior to global hybrids.

Reinvestigation of the Reaction of Ethylene and Singlet Oxygen by the Approximate Spin Projection Method. Comparison with Multireference Coupled-Cluster Calculations

We quantify a spin contamination error caused by a broken-symmetry (BS) method on the geometry at the stationary points and barrier heights of the [2 + 2] reaction between singlet oxygen and ethylene, which goes through a diradical intermediate. Several hybrid GGA, hybrid meta-GGA, and long-range corrected hybrid functionals, O3LYP, B3LYP, PBE0, MPW1B95, BHandHLYP, and omegaB97X, are examined to elucidate their original nature without the spin contamination error. For that purpose, the geometry of each reaction step for the BS state as well as its total energy is corrected by using an approximate spin projection method. The CCSD and CCSD(T) single-point calculations are also carried out at optimized geometries at the DFT level to confirm the results of the DFT methods. The single-point calculations by means of Mukherjee's multireference coupled cluster with single and double excitations at CASSCF(10e,8o)-optimized geometries are also presented to assess the DFT methods. After the energy and geometry corrections, the barrier height of each functional is consistent with conventional closed-shell-type reactions even in the reaction involving singlet diradical species. We also find that the spin contamination error on the geometric change is not negligible especially at the early stage of the reaction ( approximately 3 kcal/mol), where the triplet state is the ground state.