Hi All,
I have just read very recent paper "Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3d Transition Metals?" by Xuefei Xu, Wenjing Zhang, Mingsheng Tang and Donald Truhlar published in JCTC ("just accepted"). Here is the link:
http://pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00081
They looked how few DFT functionals perform for the dissociation energies of a set of diatomic, transition metal-containing molecules and compared this to the performance of a hierarchy of CC approximations (CCSD, CCSD(T), CCSDT, CCSDT(Q)). They concluded that CC, although much more elaborate and time consuming, are not better than modern DFT functionals. They also questioned benchmarks of DFT methods against CC for TM systems.
With the results they presented the conclusions are right. Of course, as they properly noted, if the experimental data change the trends can also be changed. As I'm personally interested in TM compounds and do a lot of calculations on these systems (DFT, single- and multireference wavefunction-based methods), I'm quite surprise that they make such strong statements.
First of all, I would never use CC methods for the molecules in question. Multireference treatment would be preferred. Linear molecules tend to have near-degenerate states. Most of the complexes we deal in real life have stronger ligands and way lower symmetry and consequently highly single-reference character. The latter, as properly pointed by authors, is not well defined. In fact, T1, M and B1 diagnostics used in the paper do not seem to correlate between each other.
In larger systems weak interactions tend to have really large impact and consistent solution for this problem is still not definitely done in DFT. The DFT errors here can reach more than deviations presented in the paper.
Although the paper is very solid, I'm a bit sceptical about the generality of conclusions made. I would be curious to hear your feelings about this paper and about benchmarks for transition metals in general.
All the best,
Adam
You are definitely right, WF-based highly correlated methods should be our lighthouse. Many functionals are well balanced (e.g. PBE0, wB97X etc.) and do offer great accuracy in most of the cases. There can always be pathological molecule, system, reaction where they fail dramatically. Multierference character is one of such situations. Weak interactions are second (they are not-so-week in fact, just look on many papers of Grimme). But I still do think that for real life applications comparisons with CC methods, even their local versions (for example DLPNOs of Neese et. al.), are still very valuable in calculations on TM molecules.
In my point of view and I asked this question a lot of time in my investigation.
How many dft methods should we develop for study every molecule with every different atoms? DFT methods have problems for many systems, and it is possible that we don't see it if we starts to use only DFT methods in our studies as reference. The problem I see is that we are working with comparison and relative methods and we need a strong reference for every compound because if I study a molecule and if only changing an atom, dft gives extremely different results it is not useful for all.
These dft will explain all transition metals with all different compounds and will we be sure that it is correct for all cases?
For me dft methods are fast but they are only correct if we take care of the results.
Dear Oleg,
you probably meant 'question on this paper' as I'm not the co-author ;) anyhow I think that the question raised in the work by Truhlar et al. is of great interest and it is worth to read the paper. Any further comments are welcome!
All the best,
Adam
One issue that springs to mind is that the basis sets used in the coupled cluster investigation are simply not large enough. They are only of def2-TZVPP (or aug-cc-pVTZ) quality, which is nowhere near converged for coupled cluster.
For TiH (see link below) D_e changes by ~1.5 kcal/mol between VTZ and the CBS limit. With the cc-pwCVTZ basis sets the core-valence correction can have the wrong sign(!).
For TiF the BSIE in D_e increases to 2.5 kcal/mol.
I think the main finding is actually that small basis set coupled cluster results shouldn't be trusted, but I think most people know that anyway.
http://scitation.aip.org/content/aip/journal/jcp/123/6/10.1063/1.1998907
Coupled Cluster theory have limitations, but are known and will be solution in next years, etc... But we know more about CC than dft. The strategy for CC and extrapolation is use better basis sets that will means that computational capacity will require increase and I hope it will be do it at same velocity that has been happening. But about DFT, there are a lot of methods, each one with very limitations and his accuracy very sensitive to change. The problem, in contrast to cc is: If I have a method, and I want to do it better, what can I do? It is sure that the change made will be better? And the answer to this questions seems to be to create a new dft method to solve a concrete problem and generate new ones.
I think they are not trying to say DFT is better, merely CC is not good enough.
Other than what you already pointed out, (CC doesn't treat multi reference well and very strong basis set dependency compared to DFT), I just want to point to note is the use of Mean Unsigned Error instead of RMS error, which is more standard practice. MUE error treats all error evenly regardless of size, while RMS on the other hand is most sensitive to large errors. MUE has a tendency to be less affected by a small number of outlier points with pathological errors, which will totally ruin the RMS error. One may suspect this would affect the comparison here.
Indeed, the basis set incompleteness error (BSIE) in DFT and CC is rather different. Probably the authors just wanted to use a typical protocol people would follow when benchmarking DFT, i.e. DFT with reasonable basis set (typically of TZ quality) and CCSD(+some treatment of T, rarely Q) with moderate basis set. However, if you can afford calculations like in the paper, then next step would be something that accounts for BSIE. One typically takes two point extrapolation, corrects with MP2/CBS or uses F12 approach. I just think it is unfair to stop at the level they done.
DFT has larger error spread and this would be quicker visible from RMS error, I agree. Probably one should always provide as much statistics as possible to avoid overinterpretation :)
I also do think that benchmarking with CC methods for TM compounds still has bright future because:
1) many complexes/reactions are still single-reference problems,
2) if 1) is not true then use MR-CC and if impossible then MRCI, NEVPT2, CASPT2 etc. At this point do not expect that DFT will do the job either. You can just be lucky.
3) whenever possible go to CBS. There are various ways to do so.
4) points 1-3 become more and more feasible with locally correlated methods, efficient parallel computing etc. we will definitely see explosion of wave function based results in the nearest future!
Mr. Kubas,
In the below stated book, we have performed a comparative presentation of the accuracy of the widely implemented theoretical approaches, in order to evaluate their applicabilty in prediction particularly of the vibrational properties, thermodynamics and kinetics of actinide complexes and processes observed in the nature.
If you pay attantion even only on the attachment, there is shown that accuracy towards experimental data of CC-based methods is within 20-40 cm-1. By contrast with may DFT approaches, including using the Truhlar's functionals has achieved accuracy within 0-4 cm-1.
1. B.Ivanova, M.Spiteller, Theoretical design for environmental sorption processes of actinides, LAP Lambert Academic Publishing ( 2014-11-12 ) , Saarbruecken, 2ß14, pp.1-268, ISBN: 978-3-659-63487-1
Dear Bojidarka,
thank you for your contribution. I have only one small question - were the DFT frequencies scaled? If yes, are these scaling factors from standard organic sets or specially derived for La/Ac groups? I'm just surprised that DFT has such small error - you still miss anharmonic effects, have small basis set etc. What about scaling of CC methods? Do you know how CCSD(T) frequencies con be improved (core-valence correlation, larger basis, higher order relativity treatment, anharmonicity)?
Thanks,
Adam
Mr Kubas,
Not only DFT, but ab initio, including CC-based methods use scaling factors. The last ones are usually employed for both computing of organics and inorganics, including complexes of f-elements such as for example the complex reported in [ref. 6] (attachment) and all those, summarized in our book, which I already has posted previously.
Furthermore the scaling factors vary within the frame of different theoretical levels. In this respect please find few useful references (attachment) and shown details about the most widely utilized scaling factors depending on theoretical levels. For organic compounds there is not shown the full literature research in this topic, but has significantly representative details about mostly employed theoretical levels for inorganics and organics, including radionuclides.
Towards improvement of CC-based methods, there have rather surprising data for organics that B3LYP/6-31+G** has given even better frequencies that CCSD(T)/cc-pVTZ (ref. 9). Commonly like in actinides already shown in my previous posting, there have been found differences between theoretical and experimental frequencies within 3-39 cm-1 (refs. 7;8a,b, attachment), so that again this information has confirmed that DFTs give significantly reliable information, even more accurate one, about structural parameters and optical properties for organics. Particularly we have employed for actinides B3PW91/SDD, using also scaling factors in the shown boundaries, which compared to our experimental vibrational spectra have shown a high level of reliability. Accounting only for the fact that B3PW91 has yielded to lower frequencies than B3LYP of about 2 cm-1, but IR-spectra are measured with resolution of +/- 2 cm-1 (ref.: B. Ivanova, M. Spiteller, Uranyl-water-containing complexes: solid-state UV-MALDI mass spectrometric and IR spectroscopic approach for selective quantitation, Environ Sci Pollut Res, DOI 10.1007/s11356-013-1892-6), meaning that the differences between both theoretical methods are within the frame of the error of experimental measurements.
By the way most of theoretical papers have comparison with known experimental data, but there has not discussion about exactly the resolution of the instruments, especially using old experimental datasets. Given that, the shown error boundaries for CC-methods, like DFT ones are relative ones, i.e. +/- xx (1, 2 or 4 cm-1) from resolution of IR-instruments. We have treated this question in our book as well. It is shown that few of reported errors of DFT methods are even lower than the given ones, because of there have cases that the authors have not accounted for phase of IR-spectra (solution, solid-state), resolution of the instrument or the chemometric approaches applied for the frequency determination, comparing known experimental literature data with their theoretical optimizations.
How can you obtain exact harmonic frequencies, dear colleagues, if system is unharmonic? (I mean comparison with experiment)
Hi Bojidarka, since you mentioned that the CCSD(T) calculation is done in cc-pVTZ level, it wouldn't be entirely surprising since CCSD(T) has notoriously slow convergence with respect to basis set. in general, one has to use basis set extrapolation when using cc-pVXZ to gain very accurate results, which is what these basis sets are designed for. If no extrapolation is done, we found that ANO basis sets yield significantly better results at similar basis size.
However, I think Adam's point is this: even exact ab initio calculations cannot obtain harmonic frequencies with that small magnitude an error compared to experimental values (even if we assume model harmonic frequencies can be obtained from rotational structures and vibrational progressions, which may not be possible for even moderately size systems). That is, even with full CI and complete basis, the error caused by higher order effects, Born-oppenheimer approximation, relativistic effects (including spin orbit couplings), rovibrational couplings etc can easily exceed 10cm-1. Insufficient treatment of core electrons usually account for even larger amount of error. For example, for system as light as water, relativistic effects can account for as much as 2.2cm-1 error and freezing core electron causes error of 5cm-1(J. Chem. Theory Comput., 2007, 3 (4), pp 1267–1274). For transition metal complexes relativistic effect can be magnitudes larger, and they also tend to have strong non-adiabatic effects as well.
DFT calculation here did not treat core electron polarization or correlation. Since DFT is reporting an error even lower than what can be achieved by exact nonrelativistic adiabatic calculation, what does the result even mean?
Xiaolei and Eugene got exactly my point of view. I would love to see same calculations including anharmonic effects, relativitity, large basis set and no-fc for CCSD(T) and see if DFT is still doing so well.
People struggled to get (very) highly accurate anharmonic frequencies of H2N2:
http://arxiv.org/pdf/physics/9808014.pdf
TZ -> QZ errors can be even more than 10 cm-1! Anharmonicity of more than 100 cm-1 is not rare...
First let's clarified, what we have experimentally observed by IR-spectroscopy - intensity versus "path". Applying FFT we have achieved transformation into a frequency domain. Or we have observable a "quantity" in a frequency domain. The application of model of harmonic oscillator, treating molecular vibration within the frame of a bond/s, incorporating f-force constant, presumably as a characteristic of the chemical bond, has yielded to conclusion that harmonic frequency has expressed well namely this, observable "quantity". But the force constant do not expressed nothing other than a change of potential energy as a function of the coordinates. So that we have treated the change of the energy as second derivatives towards the motion of nuclei. To obtain the fundamental vibrations, theoretically, we have accounted for anharmonic constants; or computing higher order derivatives of the energy.
Given that, in a more recent work, on prediction of force constants and fundamental frequencies of derivatives, containing BB triple bond [1], there has been shown exactly the reliability of this model. It has been used B3LYP/6-311G(d). The frequency obtained is 1628 cm-1. The experimental value is 1648 cm-1. Or the scaling factor is 0.98; a typical value for this theoretical level. The theoretical data have been compared with Raman spectra due to the symmetry of the molecules described, performing a correlative analysis with the frequencies and f-constants within the frame of a set of characteristic functional groups. Therefore there has a quantitative relationship as well, based on a chemometric approach.
[1] J. Boehnke, H. Braunschweig, P. Constantinidis, T. Dellermann, W. Ewing, I. Fischer, K. Hammond, F. Hupp, J. Mies, H. Schmitt, A. Vargas, Experimental Assessment of the Strengths of BB Triple Bonds, J. Am. Chem. Soc. 2015, 137, 1766-1769
Other work [2] employing B3LYP, B3PW91 and CCDC(T) at VTZ and VDZ approaches (attachment) accounting for above mentioned anharmonic constants, have shown differences towards experimental data within 1-22 cm-1 (B3LYP), 0-19 cm-1 (B3PW91) and 2-21 cm-1 (CCSD(T)). This result has confirmed that B3PW91/cc-pVTZ has yielded to a more reliable data, towards other methods described, like the previously shown data, which were on the base of B3LYP/6-31+G** (ref. 9 from the previous posting).
Particularly for rotational constants there have been found differences within 5.71-147 (B3LYP), 3.678-15 (B3PW91) and 1-28.88 (CCSD(T)) towards the experimental data set provided (Ref. 2, attachment, herein).
[2] Y. Sun, M. Wang, C. Yang, Y. Guo, Ab initio study of spectroscopic constants and anharmonic force field of FCO2 radical, J. Mol. Struct. THEOCHEM 951 (2010) 77-81.
There have data for employment of CCSD(T)/aug-cc-pVXZ (for X = T,Q,5), too, to predict fundamental frequencies, showing common accuracy of < 5 cm-1 and even achieved one of 1 cm-1[3]. But, on the one hand such as accuracy as shown (in the attachment herein and this previously posted one) is obtained by DFTs. On the other hand it is within the frame of the error of the measurements employing IR-spectrometers, as I already have pointed out, even operating at resolution of +/- 0.5 cm-1 (reference laser energy for example l = 1064.2 nm).
[3] Y. Pak, E. Sibert, R. Woods, Coupled cluster anharmonic force fields, spectroscopic constants, and vibrational energies of AIF3 and SiF3+, J. Chem. Phys. 107, 1997, 1717-1724.
In this respect, Mr. Kubis, I do not known the word "still" for DFTs in which context has been used. Accuracy of "0", 1, 3 or even 5 cm-1 for a relative large set of representative molecular objects, achieved with commercial software packages, employing experimental physical methods, exactly for example like IR-spectroscopy, where the results are unambigousely fully reproducible, furthermore quantitatively, even not qualitatively, means direct experimental evidencing. As well as extending to methods such as Raman, NIR, far-, THz and photoelectron spectroscopy, means high reliability and high reproducibility of the scientific information, employing DFTs.
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