Long-range Corrected Functionals Research Articles

A Theoretical Benchmark of the Geometric and Optical Properties for 3d Transition Metal Nanoclusters via Density Functional Theory.

Understanding structure-property relationships in atomically precise metal nanoclusters is vital in finding selective and tunable catalysts. In this study, density functional theory (DFT) was used to benchmark seven exchange correlation functionals at different basis sets for 17 atomically precise nanoclusters against experimentally determined geometries, band gaps, and optical gaps. The set contains both monometallic and bimetallic clusters that possess at least two types of 3d transition metals (specifically, Cu, Ni, Fe, or Co). The benchmark highlights that PBE0 is a good functional to use regardless of the basis set, and Minnesota functionals do well with respect to specific metals. Further, while long-range corrected functionals overestimate band and optical gaps, they model absorption features better than the other considered functionals. The study additionally looks at the photoinduced hydrogen evolution reaction (HER) and the CO2 reduction mechanism on nanoclusters reported from the literature.

Inverted Lowest Singlet and Triplet Excitation Energy Ordering of Graphitic Carbon Nitride Flakes.

In organic light-emitting diodes (OLEDs), only 25% of electrically generated excitons are in a singlet state, S1, and the remaining 75% are in a triplet state, T1. In thermally activated delayed fluorescence (TADF) chromophores the transition from the nonradiative T1 state to the radiative S1 state can be thermally activated, which improves the efficiency of OLEDs. Chromophores with inverted energy ordering of S1 and T1 states, S1 < T1, are superior to TADF chromophores, thanks to the absence of an energy barrier for the transition from T1 to S1. We benchmark the performance of time-dependent density functional theory using different exchange-correlation functionals and find that scaled long-range corrected double-hybrid functionals correctly predict the inverted singlet-triplet gaps of N-substituted phenalene derivatives. We then show that the inverted energy ordering of S1 and T1 is an intrinsic property of graphitic carbon nitride flakes. A design strategy of new chromophores with inverted singlet-triplet gaps is proposed. The color of emitted light can be fine-tuned through flake size and amine substitution on flake vertices.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning.

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional abinitio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level.

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Electronic absorption spectral analysis of chlorin-based dyad sensitizers by TD-DFT calculations

As part of our studies of chlorophyll-based sensitizers for solar energy applications, we recently synthesized two dyad panchromatic chromophores of chlorin-indoline (Chl-Ind) and chlorin-carotenoid (Chl-Car) conjugates aiming at the wider range of sunlight utilization. By comparing the absorption spectra of these dyad sensitizers in various solvents, we found that each chromophore unit in Chl-Ind showed drastic red-shift when measured in polar solvents, while the spectra of Chl-Car showed lesser solvent effects. To elucidate the origin of such solvatochromism by time dependent density functional theory (TD-DFT) calculations with molecular dynamics studies, we decided to compare the estimation results of TD-DFT/CAM-B3LYP (M06-2X and ωB97X-D)/6-31(d,p) using polarizable continuum model (H2O and THF) with the absorption spectra for Chl-Ind and Chl-Car, together with their sole chromophore units methyl trans-32-carboxy-pyropheophorbide-a (Chl), methyl ester of indoline dye D102 (Ind), and β–apo-8ʹ-carotenoic acid ethyl ester (Car). The results revealed that the unusual peak shifts of Chl and Ind moieties in Chl-Ind dyad could be most properly reproduced at ωB97X-D density functionals. This is likely because ωB97X-D contains dispersion-corrected and long-range corrected functionals. The destabilized HOMO−1 is expected to contribute to the red-shift of Ind peak in the dyad. Our results would provide useful information for the selection of computational methods to anticipate spectral characteristics of covalently-linked multi-chromophores in advance.

Conceptual DFT-Based Computational Peptidology, Pharmacokinetics Study and ADMET Report of the Veraguamides A-G Family of Marine Natural Drugs.

As a continuation of our research on the chemical reactivity, pharmacokinetics and ADMET properties of cyclopeptides of marine origin with potential therapeutic abilities, in this work our already presented integrated molecular modeling protocol has been used for the study of the chemical reactivity and bioactivity properties of the Veraguamides A–G family of marine natural drugs. This protocol results from the estimation of the conceptual density functional theory (CDFT) chemical reactivity descriptors together with several chemoinformatics tools commonly considered within the process of development of new therapeutic drugs. CP-CDFT is a branch of computational chemistry and molecular modeling dedicated to the study of peptides, and it is a protocol that allows the estimation with great accuracy of the CDFT-based reactivity descriptors and the associated physical and chemical properties, which can aid in determining the ability of the studied peptides to behave as potential useful drugs. Moreover, the superiority of the MN12SX density functional over other long-range corrected density functionals for the prediction of chemical and physical properties in the presence of water as the solvent is clearly demonstrated. The research was supplemented with an investigation of the bioactivity of the molecular systems and their ADMET (absorption, distribution, metabolism, excretion, and toxicity) parameters, as is customary in medicinal chemistry. Some instances of the CDFT-based chemical reactivity descriptors’ capacity to predict the pKas of peptides as well as their potential as AGE inhibitors are also shown.

Pseudospectral implementations of long-range corrected density functional theory.

We have implemented pseudospectral density-functional theory (DFT) with long-range corrected DFT functionals (PS-LRC) in quantum mechanics package Jaguar, and applied it in the calculations of geometry optimizations, dimmer interaction energies, polarizabilities and first-order hyperpolarizabilities, harmonic vibrational frequencies, S1 and T1 excitation energies, singlet-triplet gaps, charge transfer numbers, oscillator strengths, reaction barrier heights, electron-transfer couplings, and charge-transfer excitation energies. From our accuracy benchmark analysis, PS grids, PS dealiasing functions, PS atomic corrections, PS multigrid strategy, PS length scales, and PS cutoff scheme perform well in PS DFT with LRC density functionals with very small and ignorable deviations when compared to the conventional spectral (CS) method. The timing benchmark study of S1 excitation energy calculations of fullerenes (Cn , n up to 540) demonstrates that PS-LRC achieves 1.4-8.4-fold speedups in SCF, 22-32-fold speedups in Tamm-Dancoff approximation, and 6-15-fold speedups in total wall clock time with an average error 0.004 eV of excitation energies compared to the CS method.

A Systematic and Comparative Analysis of Four Major Classes of DFT Functionals to Compute Linear and Nonlinear Optical Properties of Benchmark Molecules

This study spotlights the fundamental insights about the systematic and comparative analysis of four famous hybrid classes of density functional theory (DFT) methods and their efficacy to calculate the linear and nonlinear optical (NLO) polarizabilities. For this study, urea and para-nitroaniline ([Formula: see text]-NA) molecular geometries are used as prototypes to calculate their linear and NLO properties. For comparative purposes, these molecules are often used as reference organic molecules for determination of NLO response properties and there is a dire need for such a benchmark database to be utilized by the researchers. We report systematically a range of functionals including hybrid (B3LYP, PBE1PBE, BH and HLYP), meta-hybrid (M06, M06-2X, M06-HF, M06-L), long-range corrected (CAM-B3LYP, LC-BLYP, LC-B97D, LC-B97D3) and functional with dispersion correction ([Formula: see text]B97, [Formula: see text]B97X, [Formula: see text]B97XD, HSEH1PBE). These groups are evaluated and their efficiency to calculate linear and NLO properties is graphically compared with each other. Overall, there are less deviations among different functionals for calculating dipole moments of [Formula: see text]-NA and urea while these deviations enhance as one moves from dipole moment to linear polarizability and nonlinear hyperpolarizabilities. In general, if we look at the trends, the polarizability values of B3LYP, M06-L, CAM-B3LYP and HSEH1PBE are relatively large and can be compared with each other. The dispersion corrected and long-range corrected functionals show more systematic deviations. For instance, among dispersion corrected functionals, the amplitudes of dipole moments, linear polarizability and NLO polarizabilities show an increasing trend as [Formula: see text]. It is also important to note that LC-B97D and LC-B97D3 of long-range corrected functional have observed exactly the same values of all the calculated parameters. A good agreement is being observed in static first and second hyperpolarizabilities of urea (B3LYP, M06-L, M06 and HSEH1PBE) and [Formula: see text]-NA (B3LYP, M06, M06-L, CAM-B3LYP and HSEH1PBE). Thus, we believe that the current investigation will provide the benchmark data of reference NLO molecules at different methods for theoretical community and molecular level insights for experimental community to design better NLO materials for hi-tech NLO applications.

Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem.

We calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r2) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee-Yang-Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee-Yang-Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.

Investigating functional performance and substituent effect in modelling molecular structure, UV-visible spectra, and optical properties of D-π-A conjugated organic dye molecules: a DFT and TD-DFT study

The molecular structure, UV-visible spectra, and optical properties of D-π-A conjugated organic dye molecules (Disperse Red 1 (DR1) and Disperse Red 73 (DR73)) were analyzed using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) and compared with azobenzene molecule to study the effect of donor and acceptor substituents on the molecular properties. The performance of DFT functionals is investigated using B3LYP hybrid functional and three long-range corrected functionals (CAM-B3LYP, LC-ω PBE, and ω B97XD) in conjunction with 6-31G(d,p) basis set. Using TD-DFT, we calculate the vertical excitation energies and transition dipole moment values for 100 excited states. These values were further utilized to calculate frequency dependent polarizability under sum-over-states (SOS) formalism and refractive index of these molecular systems. We observe that for azobenzene and DR1 molecules, ω B97XD predicted wavelengths corresponding to peak absorbance closest to the experimental results, while for DR73 molecule, B3LYP gave better prediction. Large polarizability response is also observed for these molecules (DR1 and DR73) in comparison to parent azobenzene structure due to charge transfer between donor and acceptor groups. For DR1 and DR73 molecules, αxx component of polarizability dominates in contrast to azobenzene where αyy dominates. The HOMO → LUMO transition during excitation contributes to the peak molecular response in simulated UV-visible spectra. The high polarizability response of selected D-π-A conjugated molecules in comparison to parent molecule suggests that these molecules are promising candidates for tailor-made photonic and optoelectronic device development. Graphical Abstract Functional and substituent effect on the optical response of D-π-A conjugated molecules modelled using DFT and TDDFT.

Simplified tuning of long-range corrected density functionals for use in symmetry-adapted perturbation theory

Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn-Sham orbitals, or SAPT0(KS), can be resurrected for semiquantitative purposes using long-range corrected density functionals whose asymptotic behavior is adjusted separately for each monomer. As in other contexts, correct asymptotic behavior can be enforced via "optimal tuning" based on the ionization energy theorem of density functional theory, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using a fast, convenient, and automated tuning procedure based on the size of the exchange hole. In conjunction with "extended" (X)SAPT methods that improve the description of dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.

Embedded equation-of-motion coupled-cluster theory for electronic excitation, ionisation, electron attachment, and electronic resonances

The projection-based quantum embedding method is applied to a comprehensive set of electronic states. We embed different variants of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory in density functional theory and investigate electronically excited states of valence, Rydberg, and charge-transfer character, valence- and core-ionised states, as well as bound and temporary radical anions. The latter states, which are unstable towards electron loss, are treated by means of a complex-absorbing potential. Besides transition energies, we present Dyson orbitals and natural transition orbitals for embedded EOM-CCSD. We benchmark the performance of the embedded EOM-CCSD methods against full EOM-CCSD using small organic molecules microsolvated by a varying number of water molecules as test cases. Our results illustrate that embedded EOM-CCSD describes ionisation and valence excitation very well and that these transitions are quite insensitive towards technical details of the embedding procedure. On the contrary, more care is required when dealing with Rydberg excitations or electron attachment. For the latter type of transition in particular, the use of long-range corrected density functionals is mandatory and truncation of the virtual orbital space proves to be difficult.

Non long-range corrected density functionals incorrectly describe the intensity of the CH stretching band in polycyclic aromatic hydrocarbons.

We present a comprehensive study of the most relevant numerical aspects influencing frequencies and intensities in the infrared spectrum of isolated polycyclic aromatic hydrocarbons (PAHs) regarding the overestimate of the IR CH-stretching bands. We use naphthalene as benchmark and show the validity of our results to different members of the PAH family. Our analysis relies on widely employed density functional theory methods and second-order vibrational perturbational theory for the computation of vibrational eigenstates. We have focused on the elucidation of the origin of the systematic overestimate of the intensities in the CH-stretching region. To rule out nonfundamental numerical errors, we have initially considered the influence of the electronic basis set and various other parameters on the different stages of the vibrational analysis. In a second stage, we have benchmarked the results of different density functional theory functionals with respect to the aforementioned overestimate taken as the ratio between the most prominent features of the spectrum, the CH-bending and the CH-stretching bands. Our results unambiguously indicate that the long-range correction plays a major role in this spurious numerical issue. More specifically, this phenomenon is due to an incorrect description of the charge distribution (and hence dipole) within the symmetrically relevant CH bonds. Long-range correction specifically remedies this issue. It improves the description of the intensities in the stretching region while at the same time it does not perturb significantly the rest of the spectrum. With respect to the frequencies, we have observed an overall improvement when compared to noncorrected functionals.

TD-DFT and Experimental Methods for Unraveling the Energy Distribution of Charge-Transfer Triplet/Singlet States of a TADF Molecule in a Frozen Matrix.

Reverse intersystem crossing (RISC) rate of a thermally activated delayed fluorescence (TADF) molecule is sensitive to the energy alignment of the singlet charge-transfer state (1CT), triplet charge-transfer state (3CT), and locally excited triplet state (3LE). However, the energy distribution of the charge-transfer states originating from the conformational distribution of TADF molecules in a solid matrix inevitably generated during the preparation of a solid sample due to the rotatable donor-acceptor linkage is rarely considered. Moreover, the investigation of the energy distribution of the 3CT state is both theoretically and experimentally difficult due to the triplet instabilities of time-dependent density functional (TD-DFT) calculations and difficulties in phosphorescence measurements, respectively. As a result, the relationships between conformational distribution, configurations of excited state transition orbitals, and excited state energies/dynamics have not been clearly explained. In this work, we determined the energy distribution of CT states of the TADF emitter TPSA in frozen toluene at 77 K by the measurement of time-resolved spectra in the full time range (1 ns to 30 s) of emission including prompt fluorescence, TADF, 3CT phosphorescence, and 3LE phosphorescence. We obtained the energy band of CT states where 1CT and 3CT states are distributed in the range of 2.85-3.00 and 2.64-2.96 eV, respectively. We tested various global hybrid and long-range corrected functionals for the TD-DFT calculation of 3CT energy of TPSA and found that only the M11 functional shows consistent results without triplet instability. We performed TD-DFT with the M11* functional optimized for a robust dihedral angle scan of 3CT states without triplet instability and reproduced the energy band structure obtained from the experiment. Through TD-DFT and experimental investigations, it is estimated that the dihedral angles of donor-acceptor (θD-A) and acceptor-linker (θA) of TPSA in frozen toluene lie within the range 70° ≤ θD-A ≤ 90° and 0° ≤ θA ≤ 30° respectively. Our results show that the dihedral angle distribution must be considered for further investigation of the photophysics of TADF molecules and the development of stable and efficient TADF emitters.

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.

Electronic transitions of tetrathiafulvalene oriented in polyethylene film. Near and vacuum UV synchrotron radiation polarization spectroscopy

The electronic spectrum of tetrathiafulvalene (TTF) oriented in a polyethylene film is characterized experimentally using synchrotron radiation linear dichroism from the near-UV to the vacuum-UV region to 56,500 cm–1 (177 nm). The non-planar TTF molecule is shown to have electronic transitions of significant intensity polarized along all three molecular symmetry axes. A procedure for processing linear dichroic data to obtain partial absorbance curves representing different polarization directions is exemplified. The overlapping contributions to eight individual spectral features are furthermore interpreted by the aid of time-dependent density functional theory using CAM-B3LYP/6-311++G(3df,3pd) with geometry optimized at the B3LYP / 6-311++G(3df,3pd) level within the C2v point group. Additional calculations using larger basis sets as well as other long-range corrected functionals (LC-ωPBE and ωB97XD) yielded similar results. The planar conformer with D2h symmetry is also considered and it is discussed that rapid equilibration via this transition state may contribute to the diffuse nature of some features of the electronic spectrum. The TTF molecule is a dynamic and 3-dimensional chromophore, and these characteristics may serve as a basis for understanding the optical properties of the numerous TTF-based materials finding applications in supramolecular chemistry, molecular electronics and beyond.

UV/Vis absorption spectrum calculations of benzo-1,2-dipyrene isomer using long-range corrected density functional theory

Anti- and syn-isomers of benzo-1,2-dipyrene were synthesized, and nonidentical experimental absorption spectra were observed. The B3LYP, B3LYP-D3, ωB97XD, and optimally tuned long-range corrected (LC) BOP functionals were assessed. B3LYP and B3LYP-D3 underestimated and ωB97XD overestimated the fundamental gaps and their following optical gaps in both isomers. The LC-BOP functional with the range separation parameter (µ=0.18) using the geometries optimized with LCgau-BOP + LRD reproduced the experimental absorption spectra of both isomers well. Therefore, in the case of the absorption spectrum calculation of the excimer-like isomers, it is significant to include both the weak interaction term and long-range Hartree-Fock exchange interaction appropriately.

Assessing the Tamm-Dancoff approximation, singlet-singlet, and singlet-triplet excitations with the latest long-range corrected double-hybrid density functionals.

We continue our work on the long-range corrected double-hybrid density functionals (LC-DHDFs) ωB2PLYP and ωB2GP-PLYP that we developed in the context of time-dependent (TD) Density Functional Theory (DFT) to enable the robust description of singlet-singlet excitations [M. Casanova-Páez, M. B. Dardis, and L. Goerigk, J. Chem. Theory Comput. 15, 4735 (2019)]. In our initial study, we only assessed the impact of a LC on BLYP-based DHDFs, and herein, we extend our understanding by providing the first test of PBE-based LC-DHDFs within the established TD-DHDF scheme. Moreover, this study is one of few that provides a direct comparison between TD-DHDFs and their faster Tamm-Dancoff-approximation variants (TDA-DHDFs). Most importantly, this is the first TDA-DHDF study since Grimme and Neese's TDA-B2PLYP [J. Chem. Phys. 127, 154116 (2007)] and the first work on TD-DHDFs that addresses singlet-triplet excitations. We show how the difference between TD-DHDFs and TDA-DHDFs is often negligible for singlet-singlet excitations, but how one has to apply TDA-DHDFs for triplet excitations. For both excitation types, the LC is beneficial to the BLYP-based DHDFs, but detrimental to the PBE-based ones. For local-valence and Rydberg excitations, ωB2PLYP and ωB2GP-PLYP as well as the global DHDF PBE-QIDH can be recommended. If a transition exhibits charge-transfer character, ωB2PLYP and ωB2GP-PLYP should be applied. An analysis of the gaps between the first singlet and triplet excited states of our systems revealed that there is room for further improvements to reach better robustness. Until that goal has been achieved, we recommend ωB2PLYP and ωB2GP-PLYP as some of the currently best TDA-DFT methods.

Nonlinear optical activity of imino-dyes with furan, thiophene or thiazole moieties as π-conjugated bridge: a computational investigation

ABSTRACT The electronic, linear and nonlinear optical properties of some heterocycle-containing imino-dyes, namely, the synthesised dyes 1–3 and the designed dye 4, were evaluated using suitable long-range corrected DFT functionals. HOMO–LUMO gaps, dipole moments, polarisabilities, and first hyperpolarisabilities were calculated using CAM-B3LYP, ωB97XD and LC-ωPBE methods combined with the 6-311++G(d,p) basis set using CAM-B3LYP/6-31G(d,p) optimised geometries. The calculated molecular hyperpolarisabilities, µβ, increase in the order 1 < 2 < 3 as expected experimentally. The enhancement of µβ when passing from dye 1 to dye 2 is due to the replacement of furan by thiophene and the increase of µβ when passing from dye 2 to dye 3 is due to the change of the thiophene position from the acceptor side to the donor side. Interestingly, the replacement of thiophene (dye 2) by thiazole (dye 4) leads to a notable increase of the NLO response. The electronic transitions data of dyes 1–4 were calculated at the CIS/6-31G(d,p) level of theory and the predicted order 1 < 2<3 < 4 of µβ values is conveniently explained using the two-level model based on the calculation of the dipole moment absolute change, |ΔµEG |, from the ground to the excited state. Consequently, dye 4 could be a promising candidate for organic NLO devices.