Quantum chemical study on the circular dichroism spectra and specific rotation of donor-acceptor cyclophanes

The structures of donor,acceptor-substituted cyclophanes were optimized by DFT and MP2 methods and compared with the X-ray crystallographic structures. The electronic circular dichroism (CD) spectra of these chiral cyclophanes were simulated by time dependent density functional theory (TD-DFT) with several functionals including different amounts of "exact" Hartree-Fock exchange. The experimental oscillator and rotatory strengths were best reproduced by the BH-LYP/TZV2P method. The specific rotation and vibrational circular dichroism (VCD) spectra were also calculated at the BH-LYP/aug-cc-pVDZ and B3-LYP/6-31G(d) levels, respectively, and compared with the experimental data. Better performance was obtained with the ECD, rather than the specific rotation or the VCD spectral calculations in view of the computation time and accuracy for the determination of absolute configuration (AC). The exciton coupling model can be applied only for the cyclophanes without CT-character. However, the split pattern found in the experiment does not appear to originate from a simple two-transition coupling, indicating that this method should be applied with caution to the AC determination. This conclusion was supported by the TD-DFT investigations of the transition moments and the roles of excited-state electronic configuration associated with these split bands. Cyclophanes with donor-acceptor interactions showed Cotton effects at the CT band and couplets at the 1La and 1Lb bands. Although the degree of charge transfer between the rings is very small, as revealed by a Mulliken-Hash analysis, the split Cotton effects are due to a large separation in energy of the donor and acceptor orbitals. The effect of the distance and angle between the donor and acceptor moieties in model (intermolecular) CT complexes on the calculated CD spectra was also studied and compared with those obtained for various paracyclophanes.     

Experimental and theoretical study of the CD spectra and conformational properties of axially chiral 2,2'-, 3,3'-, and 4,4'-biphenol ethers

New chiral biphenol ethers (Biph22, Biph33, and Biph44), carrying (R)-methylpropyloxy groups at 2,2'-, 3,3'-, and 4,4'-positions of biphenyl, were prepared. The introduced peripheral chiral groups in these biphenol ethers induce an (averaged) axial chirality to give predominant aR- or aS-rotamers. The chiroptical properties of these axially chiral biphenol ethers in polar and nonpolar solvents were determined experimentally and were compared with the corresponding theoretical values to determine their conformational behavior in solution. Geometry optimization at the DFT-D/TZV2P level and subsequent time-dependent density functional theory (TD-DFT) at the BH-LYP/TZV2P level treatments to obtain rotatory strengths revealed that 6 out of 18 conformers (aR-Tg-, aR-Tg+, aR-G+t, aS-Tg-, aS-Tg+, and aS-G+t) are crucial to reproduce the experimental circular dichroism (CD) spectra and optical rotations. Although biphenyl molecules are in conformational equilibrium with varying interplanar angles in solution, our static approach to the prediction of the experimental CD spectra is simply based on pairs of thermally populated, local-minimum structures, that is, the dynamic behavior of the systems or the vibrational wave functions are not considered. The relative energies computed at the SCS-MP2/TZVPP level in the gas phase or in acetonitrile solution using the conductor-like screening model (COSMO) were found to be accurate enough to calculate the thermal population of the relevant conformers. Although most of the CD signals mutually cancel out each other between a pair of aR- and aS-rotamers, the remaining Cotton effects due to a small preference for a single rotamer produce characteristic CD spectra. In general (and somewhat unexpectedly), the delicate cancellation effects in the CD spectra are accurately described by the theoretical approach, and the simulated CD spectra are in excellent agreement with the experimental ones though observed rotatory strengths being always smaller (by 5-20 times) than the theoretical data. Accordingly, slight preferences for the P (or aR)-configuration for Biph22 and M-configuration for Biph33 and Biph44 are determined. The preference for the opposite isomer in the case of Biph22 is due to larger attractive intramolecular interactions between the chiral alkyl groups. This is also consistent with the lower oxidation potential found for Biph22 (DeltaE approximately 0.1 V), as compared with those for Biph33 and Biph44. The CT complex formation of Biph22-44 with various acceptors was also studied by UV-vis and CD spectroscopic methods.     

Axial chirality of donor-donor, donor-acceptor, and tethered 1,1'-binaphthyls: a theoretical revisit with dynamics trajectories

The circular dichroism (CD) spectra of (R)-2,2'-dimethoxy-1,1'-binaphthyl (DD) and its untethered and tethered donor-acceptor analogues (DA and DA7-DA9) were investigated experimentally and theoretically. The experimental CD spectra of DD and DA resembled each other in several aspects, displaying a positive-positive-negative Cotton effect pattern in the (1)L(b)-(1)L(a) region and a strong negative couplet at the (1)B(b) band, but significantly differed in transition energy and rotatory strength. The couplet amplitude (A) of the main band was 1.6 times larger in DA than in DD, despite the comparable extinction coefficients and seemingly analogous conformations. An additional positive Cotton effect was observed at the CT (CT) band for donor-acceptor binaphthyl DA. Our theoretical prediction of the CD spectra of binaphthyls involves three sequential first principle quantum mechanics (QM) calculations. Thus, the geometry optimizations of a series of conformers with varying dihedral angles were performed by the dispersion-corrected DFT-D method using the B97-D functional and the TZV2P basis set. The potential curve as a function of the dihedral angle (θ) was obtained by using the SCS-MP2/TZVPP single-point energy calculations with and without application of the solvent correction. The CD spectrum of each conformer was independently calculated by the second-order approximate coupled cluster calculation (CC2 method) using the TZVPP basis sets and the resolution of the identity (RI-J) approximation. The (net) theoretical CD spectrum was obtained by averaging over all possible conformers, where the dynamics trajectories based on the relative SCS-MP2 energies were taken into account. By using 17 possible conformers at θ varying from 50 to 130° by 5° intervals, the experimental CD spectra were successfully reproduced in a quantitative manner, enabling us to characterize properly almost all of the important spectral features and chiroptical properties. The two-state model, reported previously, turned out to have led to the right answer with wrong reasons. The couplet sign and amplitude A are critical functions of θ and can be used not only for (qualitatively) determining the absolute configuration but also for quantitatively analyzing the binaphthyl conformations. The angle dependence of A was already argued in the classical coupled oscillator and exciton chirality theories to provide reasonable structure elucidations but only in a qualitative or semiquantitative manner. Our method is able to predict the A value quantitatively as a function of θ. For tethered binaphthyls DA7-DA9, particular care should be exercised in the conformational assessment based on the classical treatment because the amplitude A was shown to be significantly affected by the existence of the tether itself. In the present method, the couplet amplitude A was nicely related to the dihedral angle θ of DA and DD by the state-of-the-art ab initio calculations, enabling us to gain the quantitative information about the conformation of axially chiral binaphthyls. The Cotton effect at the CT band also serves as a complementary clue for elucidating the conformation of donor-acceptor binaphthyls.     

Time-dependent density functional calculations of optical rotatory dispersion including resonance wavelengths as a potentially useful tool for determining absolute configurations of chiral molecules

The optical rotations for six organic molecules (verbenone, fenchone, camphor, nopinone, Tr?ger's base, dimethyl-cyclopropane) and the transition metal complex [Co(en)(3)](3+) were calculated as a function of wavelength using time-dependent density functional theory (TDDFT). In the calculations, a realistic behavior of the optical rotation in the vicinity of an electronic transition was obtained by using a phenomenological damping parameter of the order of 0.2 eV (0.007 au). In comparison with experiment, for the molecules studied here the sign and order of magnitude of the optical rotation as well as the excitation energies were reasonably well reproduced in most computations. These findings apply to the investigated wavelength ranges typically between about 200 and 650 nm even when using comparatively small basis sets. Such calculations might therefore routinely be applied to help assigning the absolute configurations of chiral molecules. Supplementary calculations of the circular dichroism (CD) and comparison with experimental CD were used for further assessment of the optical rotation calculations. In particular, a combined study of optical rotation and CD turned out to be useful in cases where the optical rotatory dispersion in a specific energy range exhibits a considerable blue or red shift or where it is difficult to reproduce because of an interplay of several competing Cotton effects. The influence of basis set, density functional, and the damping parameter was also investigated.     

DFT studies using supercells and projector-augmented waves for structure, energetics, and dynamics of glycine, alanine, and cysteine

A large variety of gas phase conformations of the amino acids glycine, alanine, and cysteine is studied by numerically efficient semi-local gradient-corrected density functional theory calculations using a projector-augmented wave scheme and periodic boundary conditions. Equilibrium geometries, conformational energies, dipole moments, vibrational modes, and IR optical spectra are calculated from first principles. A comparison of our results with values obtained from quantum-chemistry methods with localized basis sets and nonlocal exchange-correlation functionals as well as with experimental data is made. For conformations containing strong intramolecular hydrogen bonds deviations in their energetic ordering occur, which are traced back to different treatments of spatial nonlocality in the exchange-correlation functional. However, even for these structures, the comparison of calculated and measured vibrational frequencies shows satisfying agreement.     

Role and effective treatment of dispersive forces in materials: Polyethylene and graphite crystals as test cases

A semiempirical addition of dispersive forces to conventional density functionals (DFT-D) has been implemented into a pseudopotential plane-wave code. Test calculations on the benzene dimer reproduced the results obtained by using localized basis set, provided that the latter are corrected for the basis set superposition error. By applying the DFT-D/plane-wave approach a substantial agreement with experiments is found for the structure and energetics of polyethylene and graphite, two typical solids that are badly described by standard local and semilocal density functionals.     

Theoretical and experimental studies on circular dichroism of carbo[n]helicenes

The chiroptical properties of a series of carbo[n]helicenes (n = 4-10) were investigated by the state-of-the-art approximate coupled cluster and density functional theory calculations. The theoretical calculation at the RI-CC2/TZVPP//DFT-D2-B97-D/TZVP level nicely reproduced the experimental CD spectra in both excitation energy and rotational strength without any shift or scaling. These calculations afforded the electric and the magnetic transition dipole moment vectors in [n]helicenes, allowing us to discuss the observed rotational strengths as a function of the number of benzene rings. Although the observed CD intensity was not immediately correlated to any of the calculated parameters, the anisotropy (g) factor of the (1)B(b) band and the specific rotation were found inversely proportional to n and nicely correlated with the helical pitch, but discontinuous at n = 6, where the aromatic rings start to overlap. In contrast, the g factor at the (1)B(a) band was rather insensitive to n. It was also revealed that the excitation energies of the (1)B(b) and (1)B(a) bands are inversely proportional to n over the entire range of n examined. The theoretical predictions also enabled us to rectify the erroneous experimental CD spectra of [5]- and [6]helicenes reported earlier, by using the enantiopure samples resolved by chiral HPLC.     

Theoretical study on the chiroptical optical properties of chiral fullerene C60 derivative

Time-dependent density functional theory (TDDFT) calculations have been used to investigate UV/CD spectra and nonlinear optical (NLO) property of the C(60)-fullerene bisadduct (R,R,(f,s)A)-[CD(+)280] for the first time. The electron transition natures of the four main measured bands are analyzed, and their results are used to designate the excited states involved in an electron-transfer process of the studied compound. On a comparative scale, the predicted excitation energies and oscillator strengths are in reasonable agreement with the observed values, demonstrating the efficiency of TDDFT in predicting the localized and charge transfer transitions. The good agreement between the experimental and the simulated CD spectra shows that TDDFT calculations can be used to assign the absolute configurations (ACs) of chiral fullerene C(60) derivatives with high confidence. The observed large dissymmetry ratio g (g = Δε/ε) at about 700 nm results from the orbital characters of the local fullerene excited state, which leads to large transition magnetic dipole moment and small transition electronic dipole moment. The different functionals and solvent effects on UV/CD spectra were also considered. The studied compound has a possibility to be an excellent second-order NLO material from the standpoint of transparency and large second-order polarizability value.     

Determination of the absolute configuration of [3(2)](1,4)barrelenophanedicarbonitrile using concerted time-dependent density functional theory calculations of optical rotation and electronic circular dichroism

The technique of time-dependent density functional theory (TDDFT) has very recently been applied to the calculation of both transparent spectral region optical rotations and electronic circular dichroism (CD). Here, we report the concerted application of the new methodologies to the determination of the absolute configuration (AC) of [3(2)](1,4)barrelenophanedicarbonitrile, 1, the first optically active barrelenophane. 1 is conformationally flexible: the two three-carbon bridges of 1 can each exhibit two conformations, leading to three inequivalent conformations of 1: a, b, and c. Conformational structures and energies are predicted using DFT at the B3LYP/6-31G level. Comparison of the calculated structures to structures obtained via X-ray crystallography of (+)-1 shows that (remarkably) all three conformations a-c are simultaneously present in crystalline (+)-1. The sodium D line specific rotations, [alpha](D), and CD spectra of a-c are calculated using TDDFT at the B3LYP/aug-cc-pVDZ level. Comparison of the conformationally averaged specific rotation and CD spectrum to the experimental data of Matsuda-Sentou and Shinmyozu leads to the AC 9S,12S(+)/9R,12R(-). The same AC is obtained both from [alpha](D) and from the CD, strongly supporting its reliability.     

Electronic Structure and Circular Dichroism of Natural Alboatisins Isolated from Aerial Parts of Isodon Albopilosus: DFT and TDDFT Study

The stable conformations of a series of bioactive molecules, (?)-alboatisins A?C, are identified via Monte Carlo searching with the MMFF94 molecular mechanics force field. Then, the optical rotation (OR) values, vibrational circular dichroism (VCD), and electronic circular dichroism (ECD) spectra were calculated using the gradient-corrected density functional theory method. The vibrational and transition modes of molecular chirality were explored in terms of their microscopic origin. The calculated specific rotations are in agreement with the experimental values. From the OR analysis, it was concluded that optical rotation values areregulated by hydroxyl substitution. Vibrations occurring on the chiral skeleton may cause strong absorption in VCD spectra; VCD spectra are thus the spectral response to deformation vibrations on the chiral carbon skeleton. The lowest-energy negative Cotton effect is caused by σ→π^* transition. Frontier molecular orbital analysis showed that strong ECD absorptions are produced when the dominant transition on the chiral skeleton is asymmetric; ECD spectra show the result of transitions lacking asymmetry on the chiral skeleton.     

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.     

Theoretical study of valance photoelectron spectra of hypoxanthine, xanthine, and caffeine using direct symmetry-adapted cluster/configuration interaction methodology

UV photoelectron spectra of hypoxanthine, xanthine, and caffeine, up to 20 eV, were calculated and compared with the experimental spectra reported in literature. The calculations were performed using a novel version of the quantum mechanical symmetry-adapted cluster/configuration interaction (SAC-CI) method termed, direct SAC-CI. The Duning/Huzinaga valance double-zeta D95+(d,p) Gaussian basis set was also employed with this method. The ionization energies and intensities were calculated, and the corresponding spectral bands were assigned. Natural bonding orbital (NBO) calculations were employed for better spectral band assignment. The calculated ionization energies and intensities reasonably produced the experimental photoelectron spectra.     

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.     

Absolute configuration of conformationally flexible cis-dihydrodiol metabolites by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations

We have determined the absolute configurations of conformationally flexible cis-dihydrodiol metabolites (cis-1,2-dihydroxy-3,5-cyclohexadienes), bearing different substituents (e.g., Br, F, CF3, CN, Me) in 3- and 5-positions, by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations. Convergent results were obtained by both methods in eight out of ten cases. For the difficult cases, where either conformer population and/or chiroptical properties (calculated rotational strengths of the long-wavelength Cotton effect or optical rotations) of contributing conformers remain inconclusive, the absolute configuration could still be correctly assigned based on one of the biased properties (either ECD or optical rotation). This approach appears well-suited for a broad spectrum of conformationally flexible chiral molecules.     

A benchmark for non-covalent interactions in solids

A benchmark for non-covalent interactions in solids (C21) based on the experimental sublimation enthalpies and geometries of 21 molecular crystals is presented. Thermal and zero-point effects are carefully accounted for and reference lattice energies and thermal pressures are provided, which allow dispersion-corrected density functionals to be assessed in a straightforward way. Other thermal corrections to the sublimation enthalpy (the 2RT term) are reexamined. We compare the recently implemented exchange-hole dipole moment (XDM) model with other approaches in the literature to find that XDM roughly doubles the accuracy of DFT-D2 and non-local functionals in computed lattice energies (4.8 kJ/mol mean absolute error) while, at the same time, predicting cell geometries within less than 2% of the experimental result on average. The XDM model of dispersion interactions is confirmed as a very promising approach in solid-state applications.     

Absolute configuration in 4-alkyl- and 4-aryl-3,4-dihydro-2(1H)-pyrimidones: a combined theoretical and experimental investigation

Structural features (orientation of the carboxyl group, ring puckering), electronic absorption, and circular dichroism spectra of 4-alkyl- and 4-aryl-dihydropyrimidones 1-5 are calculated by semiempirical (AM1, INDO/S), ab initio (HF/6-31G, CIS/6-31G, RPA/6-31G), and density functional theory (B3LYP/6-31G) methods. These calculations allow an assignment of the absolute configuration by comparison of simulated and experimental CD spectra. Although the ab initio methods greatly overestimate electronic transition energies, the general appearance of the experimental CD spectra is quite nicely reproduced by these calculations. Thus, comparison of experimental with calculated CD spectra is a reliable tool for the assignment of the absolute configuration. For 4-methyl derivatives 1, the first enantiopure DHPM examples with no additional aromatic substituent, the stereochemistry at C4 provided by the theoretical results is confirmed by X-ray structure determination of the diastereomeric salt 6. Additional support is the consistent HPLC elution order found for all investigated DHPMs on a cellulose-derived chiral stationary phase.     

Benchmarking density functional methods against the S66 and S66x8 datasets for non-covalent interactions

Dispersion-corrected density functional theory is assessed on the new S66 and S66x8 benchmark sets for non-covalent interactions. In total, 17 different density functionals are evaluated. Two flavors of our latest additive London-dispersion correction DFT-D3 and DFT-D3(BJ), which differ in their short-range damping functions, are tested. In general, dispersion corrections are again shown to be crucial to obtain reliable non-covalent interaction energies and equilibrium distances. The corrections strongly diminish the performance differences between the functionals, and in summary most dispersion-corrected methods can be recommended. DFT-D3 and DFT-D3(BJ) also yield similar results but for most functionals and intermolecular distances, the rational Becke-Johnson scheme performs slightly better. Particularly, the statistical analysis for S66x8, which covers also non-equilibrium complex geometries, shows that the Minnesota class of functionals is also improved by the D3 scheme. The best methods on the (meta-)GGA or hybrid- (meta-)GGA level are B97-D3, BLYP-D3(BJ), PW6B95-D3, MPW1B95-D3 and LC-ωPBE-D3. Double-hybrid functionals are the most accurate and robust methods, and in particular PWPB95-D3 and B2-PLYP-D3(BJ) can be recommended. The best DFT-D3 and DFT-D3(BJ) approaches are competitive to specially adapted perturbation methods and clearly outperform standard MP2. Comparisons between S66, S22 and parts of the GMTKN30 database show that the S66 set provides statistically well-behaved data and can serve as a valuable tool for, for example, fitting purposes or cross-validation of other benchmark databases.     

Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data

Due to their position-dependent exact exchange admixture, local hybrid functionals offer a higher flexibility and thus the potential for more universal and accurate exchange correlation functionals compared to global hybrids with a constant admixture, as has been demonstrated in previous work. Yet, the local hybrid constructions used so far do not account for the inclusion of dispersion-type interactions. As a first exploratory step toward a more general approach that includes van der Waals-type interactions with local hybrids, the present work has added DFT-D3-type corrections to a number of simple local hybrid functionals. Optimization of only the s(8) and s(r,6) parameters for the S22 set provides good results for weak interaction energies but deteriorates the excellent performance of the local hybrids for G3 atomization energies and for classical reaction barriers. A combined optimization of the two DFT-D3 parameters with one of the two parameters of the spin-polarized local mixing function (LMF) of a local hybrid for a more general optimization set provides simultaneously accurate dispersion energies, improved atomization energies, and accurate reaction barriers, as well as excellent alkane protobranching ratios. For other LMFs, the improvements of such a combined optimization for the S22 energies have been less satisfactory. The most notable advantage of the dispersion-corrected local hybrids over, for example, a B3LYP-D3 approach, is in the much more accurate reaction barriers.     

Structure and properties of metal-exchanged zeolites studied using gradient-corrected and hybrid functionals. II. Electronic structure and photoluminescence spectra

The influence of the choice of the exchange-correlation functional (semilocal gradient corrected or hybrid functionals) on the electronic properties of metal-exchanged zeolites has been investigated for Cu- and Co-exchanged chabazite. The admixture of exact exchange in hybrid functionals increases the fundamental gap of purely siliceous chabazite, leading to better agreement with experiment and many-body perturbation theory for close-packed SiO(2) polymorphs where detailed experimental information is available. For the metal-exchanged chabazite the increased exchange splitting strongly influences the position of the cation states relative to the framework bands-in general, gradient-corrected functionals locate the occupied cation states close to the valence-band maximum of the framework, while hybrid functionals shift the occupied cation states to larger binding energies and the empty states to higher energies within the fundamental gap. The photoluminescence spectra have been analyzed using fixed-moment total-energy calculations for excited spin states in structurally relaxed and frozen geometries. The geometrical relaxation of the excited states leads to large differences in excitation and emission energies which are more pronounced in calculations using hybrid functionals. Due to the stronger relaxation effects calculated with hybrid functionals, the large differences in the electronic spectra calculated with both types of functionals are not fully reflected in the photoluminescence spectra.