On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies

Fabian J., Nepraš M.

In order to disclose the validity of former phenomenological interpretations and rules concerning the spectral absorption feature of antraquinone dyes, electronic wave functions of 9,10-antraquinone and some derivatives have been subjected to the configuration analysis (CA). The calculations demonstrate the possibilities and limitations of the different approaches. The results enable us to make the consistent interpretation in terms of molecular fragments.

Tarte P.

Averkiev B.B., Zhao Y., Truhlar D.G.

The structures of Pd(PH 3 ) 2 and Pt(PH 3 ) 2 complexes with ethene and conjugated C n H n  + 2 systems ( n  = 4, 6, 8, and 10) were studied. Their binding energies were calculated using both wave function theory (WFT) and density functional theory (DFT). Previously it was reported that the binding energy of the alkene to the transition metal does not depend strongly on the size of the conjugated C n H n  + 2 ligand, but that DFT methods systematically underestimate the binding energy more and more significantly as the size of the conjugated system is increased. Our results show that recently developed density functionals predict the binding energy for these systems much more accurately. New benchmark calculations carried out by the coupled cluster method based on Brueckner orbitals with double excitations and a quasiperturbative treatment of connected triple excitations (BCCD(T)) with a very large basis set agree even better with the DFT predictions than do the previous best estimates. The mean unsigned error in absolute and relative binding energies of the alkene ligands to Pd(PH 3 ) 2 is 2.5 kcal/mol for the ωB97 and M06 density functionals and 2.9 kcal/mol for the M06-L functional. Adding molecular mechanical damped dispersion yields even smaller mean unsigned errors: 1.3 kcal/mol for the M06-D functional, 1.5 kcal/mol for M06-L-D, and 1.8 kcal/mol for B97-D and ωB97X-D. The new functionals also lead to improved accuracy for the analogous Pt complexes. These results show that recently developed density functionals may be very useful for studying catalytic systems involving Pd d 10 centers and alkenes.

Yang K., Zheng J., Zhao Y., Truhlar D.G.

Thirty four density functional approximations are tested against two diverse databases, one with 18 bond energies and one with 24 barriers. These two databases are chosen to include bond energies and barrier heights which are relevant to catalysis, and in particular the bond energy database includes metal-metal bonds, metal-ligand bonds, alkyl bond dissociation energies, and atomization energies of small main group molecules. Two revised versions of the Perdew–Burke–Ernzerhof (PBE) functional, namely the RPBE and revPBE functionals, widely used for catalysis, do improve the performance of PBE against the two diverse databases, but give worse results than B3LYP (which denotes the combination of Becke's 3-parameter hybrid treatment with Lee–Yang–Parr correlation functional). Our results show that the Minnesota functionals, M05, M06, and M06-L give the best performance for the two diverse databases, which suggests that they deserve more attention for applications to catalysis. We also obtain notably good performance with the τ-HCTHhyb, ωB97X-D, and MOHLYP functional (where MOHLYP denotes the combination of the OptX exchange functional as modified by Schultz, Zhao, and Truhlar with half of the LYP correlation functional).

Valero R., Gomes J.R., Truhlar D.G., Illas F.

The adsorption of small molecules such as NO or CO on surfaces of magnetic oxides containing transition metals is difficult to model by current density functional approximations. Two such oxides are NiO(100) and Ni-doped MgO(100). Here we compare the results of a theoretical model of the Ni-doped MgO(100) surface with experimental results on NiO(100), which introduces some uncertainty into a quantitative theory-experiment comparison. In the present work, we tested seven meta-GGA and hybrid metafunctionals, in particular, three developed by the Minnesota group (M05, M06-L, and M06), and TPSS, TPSSh, TPSSKCIS, and B1B95; six GGA functionals, including BP86, PBE, and four other functionals that are modifications of PBE (PBEsol, SOGGA, revPBE, and RPBE); five hybrid GGA functionals (B3LYP, PBE0, B97–2, B97–3, and MPWLYP1M); and one unconventional functional of the generalized gradient type with scaled correlation called MOHLYP. The Minnesota meta-GGA functionals were found in the past to be very good choices when transition metal atoms were present; the other functionals chosen are a selection from the most currently used and most promising sets of functionals for bulk solids and surfaces and for transition metals. The difficulty is due to the charge transfer between open shells in the case of NO and to the weak character of the interaction in the case of CO. It is shown that the M06 hybrid meta functional applied to NO or CO on a model of the Ni-doped MgO(100) surface is able to provide a good description of both adsorbate geometries and binding energies. The M06 vibrational frequency shifts are more accurate than for other functionals, but there is still room for improvement.

Caricato M., Trucks G.W., Frisch M.J., Wiberg K.B.

This work reports a comparison among wave function and DFT single reference methods for vertical electronic transition energy calculations toward singlet states, valence and Rydberg in nature. A series of 11 small organic molecules are used as test cases, where accurate experimental data in gas phase are available. We compared CIS, RPA, CIS(D), EOM-CCSD, and 28 multipurpose density functionals of the type LSDA, GGA, M-GGA, H-GGA, HM-GGA and with separated short and long-range exchange. The list of functionals is obviously not complete, but it spans more than 20 years of DFT development and includes functionals which are commonly used in the computation of a variety of molecular properties. Large differences in the results were found between the various functionals. The aim of this work is therefore to shed some light on the performance of the plethora of functionals available and compare them with some traditional wave function based methods on a molecular property of large interest as the transition energy.

Cao J., van Mourik T.

The M06-L density functional has been assessed for its ability to predict the correct structure of a Tyr–Gly conformer for which MP2/6-31+G(d) predicts a folded ‘closed book’ conformer, whereas a more open conformation is predicted by B3LYP/6-31+G(d). Potential energy profiles were determined by computing the energy for geometries optimised at various fixed values of a distance that controls the degree of foldedness of the structure. The M06-L/6-31G(d) and M06-L/6-31+G(d) methods yield excellent agreement with the reference df-LCCSD(T0)/aug-cc-pVTZ profile. Thus, M06-L manifests itself as a very promising method to investigate the potential energy surface of small peptides containing aromatic residues.

Fabian J.

To examine the strengths and limitations of the time-dependent density functional theory in calculating the absorption wavelengths of dye, 130, non-radical, radical and biradical coloured organic compounds, including perylenimide, porphyrin , azobenzene , quinone, croconaine, squaraine and push–pull-type colorants , were randomly selected. The first intense electronic transitions were satisfactorily calculated using time-dependent density functional theory. Whilst polymethine dyes behaved exceptionally, the calculated transition energies for cyanines, oxonols and various related dyes were systematically too large. Broken-symmetry unrestricted density functional calculations revealed the biradical character of several quinoid compounds derived from p -quinodimethane as well as that of some non-Kekulé-type structures.

Renge I.

A barely resolved structure can cause considerable loss of precision when locating the maxima of broad spectra. The centers of band envelopes were determined for the acetone n-pi* absorption in vapor, pure liquid, and solutions at 293 K. A complementary method of "band-halving" is proposed for accurate measurement of solvent-induced displacements. Solvent shifts span from -280 cm(-1) in CCl(4) to 465 cm(-1) in acetonitrile, and further to 1785 cm(-1) in hydrogen-bonding water, being negligible in n-alkanes. In the latter case the dispersive and induction shift components almost cancel mutually. Unbiased values of absolute frequency shifts will provide a reference to quantum chemical calculations, in particular, in nonpolar and weakly polar solvents where much controversy exists. The dipole moment in the excited state (mu(e) = 1.81 +/- 0.2 D, Deltamu = -1.81 D) and polarizability change (Deltaalpha = 0.6 +/- 0.2 A(3)) were estimated. A solvent set where the Onsager model is apparently applicable was used for the determination of mu(e). Remarkably, the bandwidth at half-maximum (fwhm) decreases in liquids, including water (6270 cm(-1)), as compared to vapor (6680 cm(-1)).

Świderek K., Paneth P.

Five iridium Ir(III) complexes have been studied using B3P86, B3LYP, M05, M06, M05-2X, and M06-2X functionals within configuration interaction singles (CIS) and time dependent density functional theory (TDDFT) formalisms with the aim of finding theory level that would allow for reliable prediction of emission properties. Knowledge of these properties prior to synthesis may significantly facilitate rational design of organic light-emitting diodes (OLEDs). Our results indicate that the M05-2X functional gives excellent results in this respect for the class of complexes studied here with the exception of the (bsn)2Ir(acac) complex. We have shown that the discrepancy between the theoretical and experimental values for this complex is due to the presence of the sulfur atom. Copyright © 2009 John Wiley & Sons, Ltd.

Mantina M., Valero R., Truhlar D.G.

As gold clusters increase in size, the preferred structure changes from planar to three-dimensional and, for anionic clusters, Aun−, the two-dimensional(2D)→three-dimensional (3D) transition is found experimentally to occur between n=11 and n=12. Most density functionals predict that planar structures are preferred up to higher n than is observed experimentally, an exception being the local spin density approximation. Here we test four relatively new functionals for this feature, in particular, M05, M06-L, M06, and SOGGA. We find that M06-L, M06, and SOGGA all predict the 2D→3D transition at the correct value of n. Since the M06-L and M06 functionals have previously been shown to be reasonably accurate for transition metal bond energies, main group atomization energies, barrier heights, and noncovalent interaction energies, and, since they are here shown to perform well for the s-d excitation energy and ionization potential of Au atoms and for the size of Aun− clusters at which the 2D→3D transition occurs, they are recommended for simulating processes catalyzed by gold clusters.

Jacquemin D., Wathelet V., Perpète E.A., Adamo C.

Extensive Time-Dependent Density Functional Theory (TD-DFT) calculations have been carried out in order to obtain a statistically meaningful analysis of the merits of a large number of functionals. To reach this goal, a very extended set of molecules (∼500 compounds, >700 excited states) covering a broad range of (bio)organic molecules and dyes have been investigated. Likewise, 29 functionals including LDA, GGA, meta-GGA, global hybrids, and long-range-corrected hybrids have been considered. Comparisons with both theoretical references and experimental measurements have been carried out. On average, the functionals providing the best match with reference data are, one the one hand, global hybrids containing between 22% and 25% of exact exchange (X3LYP, B98, PBE0, and mPW1PW91) and, on the other hand, a long-range-corrected hybrid with a less-rapidly increasing HF ratio, namely LC-ωPBE(20). Pure functionals tend to be less consistent, whereas functionals incorporating a larger fraction of exact exchange tend to underestimate significantly the transition energies. For most treated cases, the M05 and CAM-B3LYP schemes deliver fairly small deviations but do not outperform standard hybrids such as X3LYP or PBE0, at least within the vertical approximation. With the optimal functionals, one obtains mean absolute deviations smaller than 0.25 eV, though the errors significantly depend on the subset of molecules or states considered. As an illustration, PBE0 and LC-ωPBE(20) provide a mean absolute error of only 0.14 eV for the 228 states related to neutral organic dyes but are completely off target for cyanine-like derivatives. On the basis of comparisons with theoretical estimates, it also turned out that CC2 and TD-DFT errors are of the same order of magnitude, once the above-mentioned hybrids are selected.

Ribeiro R.F., Marenich A.V., Cramer C.J., Truhlar D.G.

Although continuum solvation models have now been shown to provide good quantitative accuracy for calculating free energies of solvation, questions remain about the accuracy of the perturbed solute electron densities and properties computed from them. Here we examine those questions by applying the SM8, SM8AD, SMD, and IEF-PCM continuum solvation models in combination with the M06-L density functional to compute the 14N magnetic resonance nuclear shieldings of CH3CN, CH3NO2, CH3NCS, and CH3ONO2 in multiple solvents, and we analyze the dependence of the chemical shifts on solvent dielectric constant. We examine the dependence of the computed chemical shifts on the definition of the molecular cavity (both united-atom models and models based on superposed individual atomic spheres) and three kinds of treatments of the electrostatics, namely the generalized Born approximation with the Coulomb field approximation, the generalized Born model with asymmetric descreening, and models based on approximate numerical solution schemes for the nonhomogeneous Poisson equation. Our most systematic analyses are based on the computation of relative 14N chemical shifts in a series of solvents, and we compare calculated shielding constants relative to those in CCl4 for various solvation models and density functionals. While differences in the overall results are found to be reasonably small for different solvation models and functionals, the SMx models SM8, and SM8AD, using the same cavity definitions (which for these models means the same atomic radii) as those employed for the calculation of free energies of solvation, exhibit the best agreement with experiment for every functional tested. This suggests that in addition to predicting accurate free energies of solvation, the SM8 and SM8AD generalized Born models also describe the solute polarization in a manner reasonably consistent with experimental 14N nuclear magnetic resonance spectroscopy. Models based on the nonhomogeneous Poisson equation show slightly reduced accuracy. Scaling the intrinsic Coulomb radii to larger values (as has sometimes been suggested in the past) does not uniformly improve the results for any kind of solvent model; furthermore it uniformly degrades the results for generalized Born models. Use of a basis set that increases the outlying charge diminishes the accuracy of continuum models that solve the nonhomogeneous Poisson equation, which we ascribe to the inability of the numerical schemes for approximately solving the nonhomogeneous Poisson equation to fully account for the effects of electronic charge outside the solute cavity.

Ferrighi L., Hammer B., Madsen G.K.

We present a density functional theory study of the energetics of isolated Aun+ (n = 5−10) and Aun− (n = 8−13) gold clusters. We compare our results to both theoretical and experimental values from the literature and find the use of meta-generalized gradient approximation (MGGA) functionals, in particular the M06-L functional, to be of importance in order to match experiment. The M06-L values suggest crossovers between 2D and 3D structures at n = 8 and 12 for cationic and anionic clusters, respectively. We suggest that the MGGA’s stronger tendency toward 3D structures arises from their smaller gradient enhancement. Moreover, we show how MGGAs, in contrast to generalize gradient approximations with smaller gradient enhancements, avoid overestimating the bond energies by combining the information contained in the reduced gradient and the kinetic energy. This allows MGGAs to treat differently the exchange enhancement in the decaying density and bonding regions.

Biczysko M., Panek P., Barone V.

Several recently introduced models rooted into the density functional theory and designed for the study of weakly bound molecular systems, with particular reference to the role of dispersion interactions, have been tested for their performances in prediction of vibrational properties for adenine molecule. Results obtained by semi-empirical correction for dispersion (DFT-D), semi-local density-functionals (M05-2X, M06-2X), and long-range correction scheme (LC-ωPBE, CAM-B3LYP) have been compared to the PT2 anharmonic frequencies computed by B3LYP functional and to the experimental results. From the tested computational models only the B3LYP-D/DM scheme provided quantitative agreement with the reference data and at the same time correctly described binding of adenine dimer.

Fan J., Fang R., Dong Y., Qi S., Yang L.

Gowda B.G., Revanasiddappa H.D., Iqbal M., Armaković S.J., Armaković S., Kollur S.P.

Yuktha Vijay U., Parakkal S.C., Datta R.

Bera A., Vennapusa S.R.

ABSTRACTWe perform a computational investigation to unravel the mechanisms of intramolecular thiol proton transfer and triplet formation in dithiotropolone. The S1 and S2 states are dipole‐forbidden, whereas S3 and S4 are dipole‐allowed states in this molecule. Upon initiating the nuclear wavepacket on S3, this molecule exhibits simultaneous S3 to S2/S1 internal conversion and S3‐T4 intersystem crossing. Further simulations reveal that the molecule shows ultrafast internal conversion in the triplet manifold, similar to its singlet dynamics. Apart from these decay processes in the Franck‐Condon region, this molecule can display thiol proton transfer via multiple singlet states due to low barrier energies along the reaction coordinate. The S1‐T4 and S3‐T5/T6 crossings upon the S‐H coordinate's elongation illustrate that the molecule can also show the triplet formation outside the Franck‐Condon region.

Wasif Baig M., Pederzoli M., Kývala M., Pittner J.

ABSTRACTA computational study of I‐BODIPY (2‐ethyl‐4,4‐difluoro‐6,7‐diiodo‐1,3‐dimethyl‐4‐bora‐3a,4a‐diaza‐s‐indacene) has been carried out to investigate its key photophysical properties as a potential triplet photosensitizer capable of generating singlet oxygen. Multireference CASPT2 and CASSCF methods have been used to calculate vertical excitation energies and spin–orbit couplings (SOCs), respectively, in a model (mono‐iodinated BODIPY) molecule to assess the applicability of the single‐reference second‐order algebraic diagrammatic construction, ADC(2), method to this and similar molecules. Subsequently, time‐dependent density functional theory (TD‐DFT), possibly within the Tamm–Dancoff approximation (TDA), using several exchange‐correlation functionals has been tested on I‐BODIPY against ADC(2), both employing a basis set with a two‐component pseudopotential on the iodine atoms. Finally, the magnitudes of SOC between excited electronic states of all types found have thoroughly been discussed using the Slater–Condon rules applied to an arbitrary one‐electron one‐center effective spin–orbit Hamiltonian. The geometry dependence of SOCs between the lowest‐lying states has also been addressed. Based on these investigations, the TD‐DFT/B3LYP and TD‐DFT(TDA)/BHLYP approaches have been selected as the methods of choice for the subsequent nuclear ensemble approach absorption spectra simulations and mixed quantum‐classical trajectory surface hopping (TSH) molecular dynamics (MD) simulations, respectively. Two bright states in the visible spectrum of I‐BODIPY have been found, exhibiting a redshift of the main peak with respect to unsubstituted BODIPY caused by the iodine substituents. Excited‐state MD simulations including both non‐adiabatic effects and SOCs have been performed to investigate the relaxation processes in I‐BODIPY after its photoexcitation to the state. The TSH MD simulations revealed that intersystem crossings occur on a time scale comparable to internal conversions and that after an initial phase of triplet population growth a “saturation” is reached where the ratio of the net triplet to singlet populations is about 4:1. The calculated triplet quantum yield of 0.85 is in qualitative agreement with the previously reported experimental singlet oxygen generation yield of 0.99 0.06.

Sadhukhan J., Mukherjee M., Chatterjee P., Datta A.

Krunić D., Armaković S., Bilić A., Armaković S.J., Gavanski L.

Song Y., Zhang N., Lei Y., Guo Y., Liu W.

Li J., Reid J.

This review provides an overview of predictive tools in asymmetric synthesis. The evolution of methods from simple qualitative pictures to complicated quantitative approaches is connected with the increased complexity of stereoselective synthesis.

Liu H., Liu Y., Jiang J., Ke Z.

Kwon S., Shong B.

Atomic layer deposition (ALD) of metals on oxide substrates often yields islandlike growth, undesirable toward conductor applications. Thus, enhancement of initial nucleation of metal ALD is of great importance. One potential solution reported is to functionalize the substrate surface with small molecules, such as trimethylaluminum (TMA) and aluminum chloride (AlCl3) before metal ALD, so that nucleation delay is reduced, and the coverage and conformality are enhanced. In this study, density functional theory calculations are utilized to elucidate the chemical mechanism toward a change of the reactivity of the surface toward metal ALD upon functionalization by TMA or AlCl3. Surface adsorption of a typical Pt ALD precursor, trimethyl(methylcyclopentadienyl)platinum (MeCpPtMe3), on an OH-terminated SiO2 surface is compared to its adsorption on AlCH3-terminated and AlCl-terminated surfaces. Considering rate-limiting steps on each surface, greater rates for adsorption of Pt are found for the organometallic-functionalized surfaces than the bare SiO2 surface, confirming the chemical enhancement effect by functionalization.

Belowar S., Rahamatolla M., Islam S., Jalil M.A., Hossain S., Saeed M.A., Rahman Bhuiyan M.M., Kazi F., Shekh S.

Qin M., Zhu W., Liu Y., Zhou X.

Benzothiadiazole and benzoxadiazole compounds including terminal groups with higher planarity have better hole-transporting properties.

Abhijith R., Datta R., Sakthivel S., Khaled J.M., Muthu S.

Yan G., Ma J., Qi S., Kirillov A.M., Yang L., Fang R.

The mechanism, regioselectivity, and chemoselectivity in a gold-catalyzed oxidative cyclization of diynones with alcohols to give furan-3-carboxylate derivatives were explored by density functional theory (DFT).