We considered several well established low-cost quantum chemical methods ranging from minimal basis set Hartree-Fock to semiempirical MO based schemes for the calculation of general non-covalent interactions. We have developed a computationally more efficient va- lence variant of the HF-3c method and augmented the MSINDO method with corrections for London dispersion and hydrogen bonding interactions. Both schemes were imple-
Figure 5.8.: Mean absolute deviations (MAD) in kcal/mol for various low-cost methods on all investigated benchmark sets. The color code highlights the error relative to the mean binding energy of the corresponding test set.
mented in generally available program packages. The proposed methods were tested in comparison to other semiempirical approaches (DFTB3-D3, OM2-D3, PM6-D3H+, PM6- D3H4X, and PM7) regarding their performance for non-covalent interactions in various systems.
A summary of our investigations is shown in Figure 5.8 as mean absolute deviations in kcal/mol. In order to easily judge the results, we give the errors relative to the mean binding energy of the corresponding test set in the color code. To put these values into perspective, we also added values for a commonly used dispersion corrected density functional (PBE-D3) in the estimated basis set limit (’CBS’).
For the small organic systems (S22, S66x8) most methods perform well with MAD values close or below 1 kcal/mol. Note, however, that such values here correspond to typical relative errors of about 20-30 % while an MAD of <0.5 kcal/mol is required to bring the typical error down to a more acceptable 5-10% range. The halogenated systems are problematic for all minimal basis set methods, which probably can only be reduced by special correction schemes.
5.4. Results and Discussion The larger molecular complexes (L7, S30L) are more challenging, but most of the methods give very reasonable results in particular for neutral complexes. HF-3c and DFTB3-D3 perform excellent with relative errors below about 10%. Though PM7 was presented as successor of PM6, we cannot recommend it for large non-covalently bound systems with relative errors close to 50%.
The strategy of separately adjusting the short-range electronic potentials and the non- covalent corrections (as conducted in HF-3c and DFTB3-D3) seems to be superior to an over-fitting prone determination of all parameters on a huge reference set.
The X23 set of organic solids is most sensitive to the correct treatment of long-range interactions. All technically feasible and converging computations give good results with relative errors for sublimation energies ranging from 10 to 20%. The mean absolute deviation increases in the order PBE-D3, HF-3c, DFTB3-D3, MSINDO-D3H+.
Regarding the overall picture, we loose a factor of about two in accuracy for the semiem- pirical methods compared to first principle DFT results. At the same time, a computa- tional speed-up of two orders of magnitude is achieved. While we have analyzed the interaction energies in huge data sets, future benchmarks should also examine also struc- tures (molecular complexes as well as unit cells) provided by the low-cost methods in more detail. We have recently shown that the rotational constants of medium-sized molecules are well described by dispersion-corrected DFT and dispersion-corrected semiempirical methods.127 PM6 and PM7 geometries were also investigated for small NCI dimers273. This should be extended to larger and periodic systems because geometry optimization represents a main area of application of low-cost methods.
In conclusion, the here presented methods are ideally suited for large scale applications as either pre-screening tools or in a multi-level approach by combining ab-initio electronic energies with semiempirically derived thermostatistical corrections. In any case, due to the increased accuracy and meanwhile relative broad range of applicability, the future for low-cost quantum chemical methods for investigating non-covalent interactions in all their aspects seems bright.
Part IV.
Application to Organic and
Organometallic Crystals
In part II and III electronic structure methods for noncovalent interactions in general and for organic solids in particular have been presented. Part IV of this thesis focuses on explicit applications of these methods.
It has been shown that DFT-D2 cannot properly describe the relative gas phase con- formations and the crystal structure of ethyl acetate. In Chapter 6, we demonstrate that with modern dispersion corrections like the D3 model, the results can be significantly improved. In particular, the relative energies of the gas phase conformers are very close to the reference and the crystal geometry agrees reasonably well with the experimental structure. Interestingly, ethyl acetate does not crystallize in the gauche form (nearly isoenergetic with the most stable gas phase conformer), but in the trans conformer. The stability of the trans form is probably increased due to the increased number of hydrogen bonds compared to the other conformers. This study shows that DFT in combination with modern dispersion corrections can accurately describe both the gas and the solid phase of organic molecules.
The subsequent study on tribenzotriquinacene (TBTQ) and its methyl derivative (Me- TBTQ) has been conducted in close collaboration with experimental groups (Chapter 7). A refined X-ray geometry of TBTQ has been measured with subtle changes in the space group symmetry compared to earlier measurements. Specifically, a slight rotation between the stacked molecules could be detected which is not present in Me-TBTQ. DFT-D3 calculations could confirm this structure and assign the tilting to the three-dimensional packing dominated by intermolecular London dispersion interactions.
A most pronounced CPE was found for a zirconium complex presented in Chapter 8. The X-ray geometry of two complexes (differing only in substitution of a tert-butyl group with a trimethylsilyl group) was found to deviate significantly. Due to the coordination to
Figure 5.9.: Lewis structure of the seven-membered ring zirconium compound with differ- ing bond character in the gas and the solid state.
complex isomerization (from the gas to the solid state) is feasible (compare with structure in Figure 5.9). Our theoretical analysis revealed that the gas phase structure of both com- pounds is identical (allene-type), but with a slightly different barrier of the isomarization to the structure with triple-bond character (η2 alkyne). In the crystal, intermolecular London dispersion forces stabilize this structure which is unfavored in the gas phase. Be- cause of the metal center, this formally forbidden isomerization is feasible and consistently explains the measured structures. The hypothesis of a CPE induced bond isomerization was then confirmed by solid and liquid phase NMR measurements. The correct assign- ment of the NMR chemical shifts (and anisotropies) was guided by corresponding DFT calculations.
6. A Dispersion-Corrected Density
Functional Theory Case Study on
Ethyl Acetate: Conformers, Dimer,
and Molecular Crystal
Jan Gerit Brandenburg∗ and Stefan Grimme∗
Keywords: Density Functional Theory, Dispersion Corrections, Molecular Conformation, and Crystal Structure Prediction
Received 16th of August 2013, Published online 24th of September 2013 Reprinted (adapted) with permission from
J. G. Brandenburg and S. Grimme, Theor. Chem. Acc. 2013, 132, 1399.
— Copyright c 2013, Springer-Verlag Berlin Heidelberg. DOI 10.1007/s00214-013-1399-8
Own manuscript contribution
• Computations of gas phase conformers, dimer and the solid state • Interpretation of results
• Writing the manuscript
∗Mulliken Center for Theoretical Chemistry, Institut f¨ur Physikalische und Theoretische Chemie,
Abstract We present a dispersion corrected Density Functional Theory case study on recently reported apparently difficult systems (Boese et al., ChemPhysChem 14, 799 (2013)). The relative stability of the trans, gauche, and cis conformers of ethyl acetate, the dissociation energy of the (trans-trans) dimer, and the structure and electronic lat- tice energy of the corresponding molecular crystal is calculated. We utilize the general- ized gradient approximation density functionals PBE and BLYP, the hybrid functional B3LYP, and the double-hybrid functional B2PLYP. It is shown that all semilocal density functionals must be corrected for missing long-range electron correlation, a.k.a. London dispersion interaction. The performance of the ab initio dispersion correction DFT-D3 is excellent and significantly improves the results compared to the uncorrected functionals and compared to the older more empirical DFT-D2 correction. The three-body dispersion contribution to the lattice energy is 7 %, while its impact on the crystal geometry and the conformer energies is negligible. A nonlocal correction approach termed DFT-NL is also tested and shows good performance comparable to the DFT-D3 results. Overall, it is shown that dispersion corrected Density Functional Theory can accurately describe the properties of ethyl acetate in various states ranging from single molecule conformers to the infinite periodic molecular crystal.