Mr. Maldonado,

The DFTs for "routine applications" cannot vary "a lot"! You just compare absolute accuracy of theoretical methods with experimental methods like UV, IR (conventional) or DSC for thermodynamics most probably, which provide analytical information at high uncertainty comparing with the differences of many theoretical levels towards selected properties.

For instance:

1. UV-VIS spectroscopy (and Fs one) both in solution and in solid-state analysis, even in the cases when instrumental resolution is 0.1 nm, provides broad overlapped bands with different origin. So that, determination of band position needs application of chemometrics. For a complex patterns, the application of chemometric methods yields to errors 4-7 nm. For prediction of intensities even the errors are significantly higher. Furthermore there are possible effects of shifting of band due to specific solute-solvent and solute-solute interactions; concentration; tautomerism; intra-molecular H-bonds, and so forth.

In other words experimentally you cannot distinguish unambiguously lmax of a broad band. Is it 200 nm or 203 nm, exactly, for example? Lmax = 200 nm corresponds to E = 6.2 eV, while Lmax = 203 to E = 6.1084 eV. Or the difference of both Lmaxs is 0.0916 eV. The difference between M11-L and M06 for aromatics is within 0.03-0.33 eV. Because of electronic spectra depends on molecular factors (including different molecular conformations, particularly in solution; different CT effects) as above mentioned and environmental ones (phase, solvent, T, P and s.o.). The reliability of UV-VIS varied about 99 - 95 % comparing with theoretical data. In other words you can distinguish for example cases when the differences is 0.33 eV or about 9 nm (lmax = 203 and 192 nm), but not cases when the differences is 0.03 eV (or 203 and 202.007 nm). On the other hand the optimized geometry do not explicitly correspond to the real geometry in solution. And definitively the optimized geometry do not corresponds to solid-state molecular conformations. Or to predict solid-state spectra even higher deviations are expected depending on molecular conformation which you have taken as "most probable" one.

Then, the computations of electronic spectra of a set possible conformations yield to an average UV-VIS/Fs profile, where errors of Lmax are within the frame of above mentioned 7-9 nm (even 15 nm for complex molecular geometries). Same is valid for computations in solution where there should take into account different approaches (PCMs, mixed-solvation and s.o.)

The accuracies M06-2X and PBE0 is comparable (difference ca. 0.01 eV) as well as accuracies of M11 and M06 (ca. 0.03 eV), towards predicting ES. Between B3LYP and M06 the differences are about 0.05 eV. Same is valid for pairs B3LYP/M06-2X (0.05 eV). While betwee PBE0 and B3LYP 0.04 eV.

In those cases the differences in Lmax [nm] should be Dlmax 0.65 - 1.7 nm for VEEs.

If you have employed TDDFT B3PW91/SDD the UV-VIS spectra in solution have shown difference Lmax = 5.8 nm between theory and experiments (Ref. 1).

2. Towards, IR-spectra even operating with an instrumental resolution 0.05 cm-1 for example, if you have compared your computational data, again lies the problem about molecular geometry; phases; temperatures and inter/intra-molecular hydrogen bonds. On the other hand experimentally if you have not operate by polarized light, but used conventional FTIR, you cannot assign unambiguously your experimental bands to corresponding modes. And thus you have significant inaccuracy comparing your theoretical data with experimental ones. Moreover, in experimental FTIR spectra, there are series effect such as overtones; combinational modes; Davidov's splitting effect, Evans' hole effects, Fermi-resonance and so fort. For a complex molecule, only using conventional FTIR the experimental assignment is highly speculative task a well. Despite relatively not so broad profile of IR-bands, again arises question about errors of chemometrics used (determining bands positions and intensities). And thus again there is level of uncertainty. But smaller level, then this one of UV-VIS/Fs methods. If you would like to compare theory with experiment, then you should correlate selected set of IR-bands, but accounting for all possible effects to the IR-band position and intensity as well as assigned by polarized measurements, not conventional FTIR spectroscopy. Otherwise, you shall obtain significant unreliability of your conclusions about the accuracy of the different theoretical methods.

3. Towards your thermochemical data, the level of uncertainty of DSC for example, obtaining heat capacity is about 0.015 J.g-1.K-1. The computation by B3LYP and B3PW91, for example, give differences in DH 0.38 and 0.40 (0.02 difference), meaning that those values are again comparable with uncertainty of DSC as experimental method. The errors by chemometrics applied, again occur.

The data about B3LYP and M06, for example, are about 0.5 eV (or 48.24 kJ.mol-1 or 11.53 kcal.mol-1):

TOTAL ENERGY (B3LYP) = -75.9316984189

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TOTAL POTENTIAL ENERGY = -151.5545004683

TOTAL KINETIC ENERGY = 75.6228020494

VIRIAL RATIO (V/T) = 2.0040846988

TOTAL ENERGY (M06) = -75.9489608698

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TOTAL POTENTIAL ENERGY = -151.5752011394

TOTAL KINETIC ENERGY = 75.6262402696

VIRIAL RATIO (V/T) = 2.0042673099

4. Predicting thermodynamics, there is important to take into account can you neglect the nonadiabatic coupling of electronic, vibrational and magnetic degrees. For some systems they cannot be neglected. And thus you shall obtain again unreliability of the data comparing with experiments even using a theoretical level swith generally high accuracy.

If you would like to obtain an unambiguous information about accuracy of theoretical methods, you need high resolution mass spectrometric data (by ESI(MALDI) - Orbitrap-MS or FTICR-MS). The accuracy is in six sign after the decimal sign determining the MS peak position. In this context, you have received in fact an absolute intensity and peak position, and thus - exact thermodynamics.

Ref. 1. B.Ivanova, M. Spiteller, Title: Linear and nonlinear optical Zn(II)-metal-organic materials. Correlation between molecular structure, crystal structure and chemical-physical properties, GRIN Verlag, Muenchen, 2015, pp. 1-353, ISBN 978-3-668-11137-0:

http://www.grin.com/en/e-book/310619/linear-and-nonlinear-optical-zn-ii-metal-organic-materials-correlation

Dear Bojidarka B. Ivanova.

Thanks for you thorough reply!

It will be very useful not only to me, but to everyone willing to dive into DFT, or to delve a little deeper In these methods.

Best regards!

Mauricio Maldonado

Concerning the possible problems related to experimental data mentioned in an earlier response: these problems are usually avoided by studying gas-phase spectra, potentially even of cold molecules as can be prepared in molecular beams. Such data is available for a wide range of molecules. Experimental studies only get more tricky e.g. for larger biomolecules. Anyhow, vibrational and electronic excitation bands can be usually clearly identified (depending on the method even with rotational resolution) and, perhaps by comparison with DFT calculations, also assigned. Such data does not have 'high uncertainty' and should, whenever possible, be used as reference to check for the validity of the theoretical approach.