Computational Organic Chemistry, Second Edition – what’s new in Chapters 1-4

Second Edition Steven Bachrach 15 Apr 2014 No Comments

In this and the next post I discuss some of the new materials in the Second Edition of my book Computational Organic Chemistry. Every chapter has been updated, meaning that the topics from the First Edition that remain in this Second Edition (and that’s most of them) have been updated with any new relevant work that have appeared since 2007, when the First Edition was published. What I present in this and the next post are those sections or chapters that are entirely new. This post covers chapters 1-4 and the next post covers chapters 5-9.

Chapter 1: Quantum Mechanics for Organic Chemistry

The section on Density Functional Theory has been expanded and updated to include

  • a presentation of Jacob’s ladder, Perdew’s organizational model of the hierarchy of density
    functionals
  • a discussion of dispersion corrections, principally Grimme’s “-D” and “-D3” corrections
  • a discussion of Grimme’s double hybrid functions and Martin’s DSD-DFT method (dispersion corrected, spin-component scaled double hybrid)
  • and a brief discussion of functional selection

The discussion of basis set superposition error (BSSE) is expanded and includes intramolecular BSSE. A new section has been added to discuss QM/MM methods including ONIOM. The discussion of potential energy surfaces is expanded, including presentation of more complicated surfaces that including valley-ridge inflection (VRI) points. Lastly, the chapter concludes with an interview of Prof. Stefan Grimme.

Chapter 2. Computed Spectral Properties and Structure Identification

This is essentially a brand new chapter dealing with how computed spectral properties have been used in structural identification. The chapter begins with a presentation of computed structural features (bond lengths and angles) and how they compare with experiment. Next, I present some studies of computer IR spectra and their use in structure identification. The bulk of this chapter deals with NMR. I present methods for computing NMR with scaling techniques. The statistical methods of Goodman (CP1 and DP4) are described in the context of discriminating stereoisomers. The section ends with five case studies where computed NMR spectra were used to identify chemical structure. Next, computed optical activity including ORD and ECD and VCD used for structure determination are described through 6 case studies. This chapter ends with an interview of Prof. Jonathan Goodman.

Chapter 3. Fundamentals of Organic Chemistry

The main addition to this chapter is an extensive discussion of alkane isomerism, and the surprising failure of many standard density functionals (including B3LYP) to properly account for isomer energies. The work in this area led to the recognition of the importance of dispersion and medium-range correlation, and the development of new functionals and dispersion corrections. Other new sections include a case study of the acidity of amino acids (especially cysteine and tyrosine where the most acidic proton in the gas phase is not the carboxylic acid proton), and two added studies of aromaticity: (a) the competition between aromaticity and strain and (b) π-π stacking.

Chapter 4. Pericyclic Reactions

The chapter is updated from the first addition with two major additions. First, a section on bispericyclic reactions is added. This type of reaction is important in the context of a number of reactions that display dynamic effects (see Chapter 8). Second, the notion of transition state distortion energy as guiding reaction selectivity is described.

The highlights of the new materials in Chapters 5-9 will appear in the next blog post.

Second Edition of Computational Organic Chemistry released!

Second Edition Steven Bachrach 14 Apr 2014 1 Comment

The second edition of my book Computational Organic Chemistry has finally been published. The book is available directly from the publisher (Wiley) or from Amazon.

The book web page (http://www.comporgchem.com) has been largely updated to reflect the new content: the complete Table of Contents is available as are links to all of the citations. I hope to have all of the molecules added to the web site soon. (All of the materials associated with the First Edition of the book are still available through this same site.)

You’ll notice the great cover for the Second Edition. The image is of the molecular complex designed by Iwamoto and co-workers,1 which I blogged about in this post. The image was prepared by my sister Lisa! (You can see more of her work here.)

The book contains a lot of updated materials along with a great deal of new sections and chapters. The next couple of blog posts will go into some detail about what is new in the Second Edition.

I do want to thank all of the commenters to my blog for their encouragement towards both maintaining this blog service and writing the Second Edition. The many comments helped inform my selections of new materials to include in the new edition.

I hope you enjoy the book and as always I welcome any and all comments and feedback!

References

(1) Iwamoto, T.; Watanabe, Y.; Sadahiro, T.; Haino, T.; Yamago, S. "Size-Selective Encapsulation of C60 by [10]Cycloparaphenylene: Formation of the Shortest Fullerene-Peapod," Angew. Chem. Int. Ed. 2011, 50, 8342-8344, DOI: 10.1002/anie.201102302

Structure of benzene dication

Aromaticity &MP Steven Bachrach 08 Apr 2014 2 Comments

Benzene is certainly one of the most iconic chemical compounds – its planar hexagonal structure is represented often in popular images involving chemists, and its alternating single and double bonds the source of one of chemistry’s most mythic stories: Kekule’s dream of a snake biting its own tail. So while the structure of benzene is well-worn territory, what of the structure of the benzene dication? Jasik, Gerlich and Rithova probe that question using a combined experimental and computational approach.1

The experiment involves generation of the benzene dication at low temperature and complexed
to helium. Then, using infrared predissociation spectroscopy (IRPD), they obtained a spectrum that suggested two different structures.

Next, employing MP2/aug-cc-pVTZ computations, they identified a number of possible geometries, and the two lowest energy singlet dications have the geometries shown in Figure 1. The first structure (1) has a six member ring, but the molecule is no longer planar. Lying a bit lower in energy is 2, having a pentagonal pyramid form. The combination of the computed IR spectra of each of these two structures matches up extremely well with the experimental spectrum.

1

2

Figure 1. MP2/aug-cc-pVTZ geometries of benzene dication 1 and 2.

References

(1) Jašík, J.; Gerlich, D.; Roithová, J. "Probing Isomers of the Benzene Dication in a Low-Temperature Trap," J. Am. Chem. Soc. 2014, 136, 2960-2962, DOI: 10.1021/ja412109h.

Structure determination: Quercusnin A

NMR Steven Bachrach 01 Apr 2014 No Comments

Here’s another nice example of the use of computed NMR spectra to aid in structure identification. Quercusnin A was identified in an extract of dried sapwood from the oak tree Quercus crispula. The NMR sectrum along with structural comparison to the previously determined extract vescalagin, led the authors to the structure 1.1


1

To aid in determining the absolute stereochemistry as centers 1’ and A8, the authors employed a computational approach. Conformers of the four diastereomers (RR, RS, SR, SS) were optimized first with molecular mechanics, then the low energy conformers were reoptimized at AM1, and then finally all of the conformers within 6 kcal mol-1 of the lowest energy structure were reoptimized at PCM(acetone)/B3LYP/6-31G(d,p). The 1H and 13C NMR chemical shifts for all of the structures that contribute greater than 1% to the Boltzmann population were computed at PCM(acetone)mPW1PW91/6-311+G(2d,p)//B3LYP/6-31G(d,p). The DP4 probability (see this post) identified the (1’S,A8R) isomer with 100% probability for matching up with the experimental NMR spectrum. Additionally, the computed ECD spectrum matches nicely with the experimental spectra for this same stereoisomer. The lowest energy conformer of 1 is shown in Figure 1.

1

Figure 1. PCM(acetone)/B3LYP/6-31G(d,p) structure of the lowest energy conformer of 1.

References

(1) Omar, M.; Matsuo, Y.; Maeda, H.; Saito, Y.; Tanaka, T. "New Metabolites of C-Glycosidic Ellagitannin from Japanese Oak Sapwood," Org. Lett. 2014, 16, 1378–1381, DOI: 10.1021/ol500146a.

InChIs

1: InChI=1S/C36H24O22/c37-11-2-8-15(24(44)20(11)40)16-9(3-12(38)21(41)25(16)45)36(53)56-29-14(5-54-32(8)49)55-33(50)10-4-13(39)22(42)26(46)19(10)30-17-6(34(51)57-30)1-7-18(23(17)43)31(58-35(7)52)28(48)27(29)47/h1-4,14,27-31,37-48H,5H2/t14-,27-,28-,29-,30-,31+/m1/s1
InChIKey=PTEZCLBSJBUWFI-LJBUUXJGSA-N

Corannulene bowl inversion inside a host

annulenes &host-guest Steven Bachrach 20 Mar 2014 No Comments

The concept of complementarity between enzyme and substrate, especially the transition state for reactions at the substrate, is a key element of Pauling’s model for enzymatic activity. Koshland’s “induced fit” modification suggests that the enzyme might change its structure during the binding process to either destabilize the reactant or help stabilize the TS. These concepts are now tested in a very nice model by Stoddart, Siegel and coworkers.1

Stoddart recently reported the host compound ExBox4+ 1 and demonstrated that it binds planar polycyclic aromatic hydrocarbons.2 (I subsequently reported DFT computations on this binding.) The twist in this new paper is the binding of corranulene 2 inside ExBox4+ 1. Corranulene is bowl-shaped, with a bowl inversion barrier of 11.5 kcal mol-1 (10.92 kcal mol-1 at B97D/Def2-TZVPP).

The corranulene bowl is too big to fit directly into 1 without some distortions. The x-ray structure of the complex of 1 with 2 inside shows the width of 1 expanding by 0.87 Å and the bowl depth of 2 decreasing by 0.03 Å. The B97D/Def2-TZVPP optimized geometry of this complex (shown in Figure 1) shows similar distortions – the width of 1 increases by 0.37 Å (gas) or 0.29 Å (acetone solution), while the bowl depth of 2 decreases by 0.03 Å (gas) or 0.02 Å (solution).

ground state

transition state

Figure 1. B97D/Def2-TZVPP optimized geometries of the complex of 2 inside 1 (a) ground state and (b) transition state.

The calculated structure of the bowl inversion transition state of 2 inside of 1 is shown in Figure 1. 2 is planar at the TS. The experimental inversion barrier (determined by variable temperature NMR line shift analysis) is 7.88 kcal mol-1, while the calculated barrier is 8.77 kcal mol-1. The reduction in the bowl inversion barrier of 2 inside of 1 is therefore about 2.5 kcal mol-1. The authors argue that this barrier reduction can be attributed to about 0.5 kcal mol-1 of destabilization of the ground state of 2 along with 2 kcal mol-1 of stabilization of the transition state afforded by the host. This study thus confirms the notions of a host reducing a barrier (through both transition state stabilization and ground state destabilization) and induced fit.

References

(1) Juríček, M.; Strutt, N. L.; Barnes, J. C.; Butterfield, A. M.; Dale, E. J.; Baldridge, K. K.; Stoddart, J. F.; Siegel, J. S. "Induced-fit catalysis of corannulene bowl-to-bowl inversion," Nat. Chem. 2014, 6, 222-228, DOI: 10.1038/nchem.1842.

(2) Barnes, J. C.; Juríček, M.; Strutt, N. L.; Frasconi, M.; Sampath, S.; Giesener, M. A.; McGrier, P. L.; Bruns, C. J.; Stern, C. L.; Sarjeant, A. A.; Stoddart, J. F. "ExBox: A Polycyclic Aromatic Hydrocarbon Scavenger," J. Am. Chem. Soc. 2012, 135, 183-192, DOI: 10.1021/ja307360n.

(3) Bachrach, S. M. "DFT Study of the ExBox·Aromatic Hydrocarbon Host–Guest Complex," J. Phys. Chem. A 2013, 117, 8484-8491, DOI: 10.1021/jp406823t.

InChIs

1: InChI=1S/C48H40N4/c1-2-38-4-3-37(1)33-49-25-17-45(18-26-49)41-9-11-43(12-10-41)47-21-29-51(30-22-47)35-39-5-7-40(8-6-39)36-52-31-23-48(24-32-52)44-15-13-42(14-16-44)46-19-27-50(34-38)28-20-46/h1-32H,33-36H2/q+4
InChIKey=ZMELWAYDWQWNOQ-UHFFFAOYSA-N

2: InChI=1S/C20H10/c1-2-12-5-6-14-9-10-15-8-7-13-4-3-11(1)16-17(12)19(14)20(15)18(13)16/h1-10H
InChIKey=VXRUJZQPKRBJKH-UHFFFAOYSA-N

The complex PES for sesquiterpene formation

non-classical &terpenes Steven Bachrach 13 Mar 2014 2 Comments

Hong and Tantillo1 report a real tour de force computational study of multiple pathways along the routes towards synthesis of a variety of sesquiterpenes. The starting point is the bisabolyl cation 1, and a variety of rearrangements, cyclizations, proton and hydride transfers are examined to convert it into such disparate products as barbatene 2, widdradiene 3, and champinene 4. The pathways are explored at mPW1PW91/6-31+G(d,p)//B3LYP/6-31+G(d,p). Some new pathways are proposed but the main points are the sheer complexity of the C15H25+ potential energy surface and the interconnections between potential intermediates.

References

(1) Hong, Y. J.; Tantillo, D. J. "Branching Out from the Bisabolyl Cation. Unifying Mechanistic Pathways to Barbatene, Bazzanene, Chamigrene, Chamipinene, Cumacrene, Cuprenene, Dunniene, Isobazzanene, Iso-γ-bisabolene, Isochamigrene, Laurene, Microbiotene, Sesquithujene, Sesquisabinene, Thujopsene, Trichodiene, and Widdradiene Sesquiterpenes," J. Am. Chem. Soc. 2014, 136, 2450-2463, DOI: 10.1021/ja4106489.

InChIs

1: InChI=1S/C15H25/c1-12(2)6-5-7-14(4)15-10-8-13(3)9-11-15/h6,8,15H,5,7,9-11H2,1-4H3/q+1
InChIKey=YKHXORRQMGBNFI-UHFFFAOYSA-N

2: InChI=1S/C15H24/c1-11-6-9-13(2)10-12(11)14(3)7-5-8-15(13,14)4/h6,12H,5,7-10H2,1-4H3/t12-,13-,14+,15-/m0/s1
InChIKey=RMKQBFUAKZOVPQ-XQLPTFJDSA-N

3: InChI=1S/C15H24/c1-12-6-7-13-14(2,3)9-5-10-15(13,4)11-8-12/h6-7H,5,8-11H2,1-4H3/t15-/m0/s1
InChIKey=SJUIWFYSWDVOEQ-HNNXBMFYSA-N

4: InChI=1S/C15H24/c1-11-6-9-15-10-12(11)14(15,4)8-5-7-13(15,2)3/h6,12H,5,7-10H2,1-4H3/t12-,14-,15-/m1/s1
InChIKey=XRDHEPAYTVHOPC-BPLDGKMQSA-N

Enhancing the acidity of proline – application to organocatalysis

Acidity Steven Bachrach 04 Mar 2014 3 Comments

Organocatalysis affected by proline is an extremely active research area, and computational chemists have made considerable contributions (see Chapter 5.3 of my book – and this is expanded on in the 2nd edition which should be out in just a few months). Most importantly, the Houk-List model1 for the catalysis was largely developed on the basis of computations.

Recent experiments have indicated cocatalysts that can hydrogen bond to proline may increase the catalytic effect, including the enantioselectivity. Xue and co-workers have examined a series of potential cocatalysts for their ability to enhance the acidity of proline.2 This is important in that a proton transfer is a component to the key step of the Houk-List model.

The cocatalysts examined included such compounds as 1-6. The deprotonation energy of proline with the associated cocatalysts was compared with that of proline itself. The energies were computed at M06-2x/6-311++G(2df,2p)//B3LYP/6-31+G(d) with the SMD treatment of five solvents. The structure of 5 with proline is shown in Figure 1.

5 with proline

5 with proline conjugate base

Figure 1. M06-2x/6-311++G(2df,2p)//B3LYP/6-31+G(d) optimized structure of 5 with proline and its conjugate base.

The effect of the cocatalysts is striking. In the gas phase, these additives decrease the pKa of proline by 15 – 70 pKa units, with 2 showing the largest effect. In solvent, the effect of the cocatalyst is attenuated, especially in more polar solvents, but still a considerable decrease in the pKa is seen (as much as a 12 pKa unit increase in acidity). Further exploration of potential cocatalysts seems fully warranted.

References

(1) Allemann, C.; Gordillo, R.; Clemente, F. R.; Cheong, P. H.-Y.; Houk, K. N. "Theory of Asymmetric Organocatalysis of Aldol and Related Reactions:  Rationalizations and Predictions," Acc. Chem. Res. 2004, 37, 558-569, DOI: 10.1021/ar0300524.

(2) Xue, X.-S.; Yang, C.; Li, X.; Cheng, J.-P. "Computational Study on the pKa Shifts in Proline Induced by Hydrogen-Bond-Donating Cocatalysts," J. Org. Chem. 2014, 79, 1166–1173, DOI: 10.1021/jo402605n.

InChIs

1: InChI=1S/CH4N2O/c2-1(3)4/h(H4,2,3,4)
InChIKey=XSQUKJJJFZCRTK-UHFFFAOYSA-N

2: InChI=1S/CH5N3/c2-1(3)4/h(H5,2,3,4)/p+1
InCiKey=ZRALSGWEFCBTJO-UHFFFAOYSA-O

3: InChI=1S/C4H4N2O2/c5-1-2(6)4(8)3(1)7/h5-6H2
InChIKey=WUACDRFRFTWMHE-UHFFFAOYSA-N

4: InChI=1S/C13H12N2S/c16-13(14-11-7-3-1-4-8-11)15-12-9-5-2-6-10-12/h1-10H,(H2,14,15,16)
InChIKey=FCSHMCFRCYZTRQ-UHFFFAOYSA-N

5: InChI=1S/C20H14O2/c21-17-11-9-13-5-1-3-7-15(13)19(17)20-16-8-4-2-6-14(16)10-12-18(20)22/h1-12,21-22H
InChIKey=PPTXVXKCQZKFBN-UHFFFAOYSA-N

6: InChI=1S/C7H13N3/c1-3-8-7-9-4-2-6-10(7)5-1/h1-6H2,(H,8,9)/p+1
InChIKey=FVKFHMNJTHKMRX-UHFFFAOYSA-O

Proline: InChI=1S/C5H9NO2/c7-5(8)4-2-1-3-6-4/h4,6H,1-3H2,(H,7,8)/t4-/m0/s1
InChIKey= ONIBWKKTOPOVIA-BYPYZUCNSA-N

Computing OR: norbornenone

DFT &Optical Rotation Steven Bachrach 25 Feb 2014 2 Comments

Optical activity is a major tool for identifying enantiomers. With recent developments in computational techniques, it is hoped that experiments combined with computations will be a powerful tool for determining absolute configuration. The recent work of Lahiri, et al. demonstrates the scope of theoretical work that is still needed to really make this approach broadly applicable.1

They prepared (1R,4R)-norbornenone 1 and measured its optical rotation in the gas phase and in dilute solutions of acetonitrile and cyclohexane. The specific rotations at three different wavelengths are listed in Table 1. Of first note is that though there is some small differences in solution, as expected, there really is substantial differences between the gas- and solution phases. Thus cautionary point 1: be very careful of comparing solution phase experimental optical activity with computed gas phase predictions.


1

Table 1. Experimental and computed specific rotation of 1.

 

355.0 nm

589.3 nm

633.0 nm

Gas phase

Expt

6310

755

617

B3LYP

10887

1159

944

CCSD

3716

550

453

Acetonitrile solution

Expt

8607

950

776

PCM/B3LYP

11742

1277

1040

Cyclohexane solution

Expt

9159

981

799

PCM/B3LYP

11953

1311

1069

For the computations, the geometry of 1 was optimized at B3LYP/aug-cc-pVTZ (see Figure 1. The OR was computed at B3LYP with different basis sets, finding that the difference in the predicted specific rotation at 598.3nm differs only quite little (90.6 deg dm-1 (g/mL)-1) between the computations using aug-cc-pVTZ and aug-cc-pVQZ) suggesting that the basis set limit has been reached. The gas –phase computed values at B3LYP and CCSD are also shown in Table 1. Though these computations do get the correct sign of the rotation, they are appreciably off of the experimental values, and the percent error varies with wavelength. Cautionary point 2: it is not obvious what is the appropriate computational method to compute OR, and beware of values that seem reasonable at one wavelength – this does not predict a good agreement at a different wavelength.

Figure 1. Optimized geometry of 1 at B3LYP/aug-cc-pVTZ.

Lastly, computed solution values of the OR were performed with PCM and B3LYP. These values are given in Table 1. Again the agreement is poor. So cautionary point 3: computed (PCM) solution OR
may be in quite poor agreement with experiment.

Often the culprit to poor agreement between computed and experimental OR is attributed to omitted vibrational effects, but in this case, because 1 is so rigid, one might not expect too much error to be caused by the effects of vibrations. So the overall result – we need considerable work towards addressing how to accurately compute optical activity!

References

(1) Lahiri, P.; Wiberg, K. B.; Vaccaro, P. H.; Caricato, M.; Crawford, T. D. "Large Solvation Effect in the Optical Rotatory Dispersion of Norbornenone," Angew. Chem. Int. Ed. 2014, 53, 1386-1389, DOI: 10.1002/anie.201306339.

InChIs

1: InChI=1S/C7H8O/c8-7-4-5-1-2-6(7)3-5/h1-2,5-6H,3-4H2/t5-,6+/m1/s1
InChIKey=HUQXEIFQYCVOPD-RITPCOANSA-N

Monosaccharide PES

sugars Steven Bachrach 18 Feb 2014 1 Comment

The conformational space of monosaccharides is amazingly complex. If we consider just the pyranose form, the ring can in principal exist as a chair, a half-chair, skew (or twist boat) and boat form, for a total of 38 puckering configurations. Layer on top of this the axial and equatorial positions of the hydroxyl and methylhydroxyl groups, and then the rotamers of these substituents, and one is faced with a dauntingly vast space. It is just this space that Beckham and co-workers1 take on for α- and β-glucose, β-xylose, β-mannose and β-acetylglucosamine.

For each sugar, and for each of the 38 puckering configurations, full rotamer scans for each of the substituents led to 27,702 conformations of each of the four monosaccharides, and 36,936 conformations of β-acetylglucosamine. This totals to over 123,000 geometry optimizations that were carried out at M06-2x/6-31G(d). Then taking the structures within 5 kcal mol-1 of the lowest energy structure for ­each pucker, they reoptimized at M06-2X/6-31+G(d,p). Pruning once again those structures that were above 5 kcal mol-1 of the minimum, they performed CCSD(T)/6-311+G(d,p)//B3LYP/6-311+G(2df,p) computations. What a tour de force!

The results of these conformational space surveys are not terribly exciting. The substituents do make a difference in dictating the most and least favorable structures and the activation barriers for interconversion of ring forms.

These PESs will be quite useful in understanding carbohydrate conformations and the role these may play in their chemistry. But the point of bringing this paper to your attention is the tremendously complex, detailed PES that is uncovered, representing the scale of what can be done with modern computers and modern algorithms.

References

(1) Mayes, H. B.; Broadbelt, L. J.; Beckham, G. T. "How Sugars Pucker: Electronic Structure Calculations Map the Kinetic Landscape of Five Biologically Paramount Monosaccharides and Their Implications for Enzymatic Catalysis," Journal of the American Chemical Society 2013, 136, 1008-1022, DOI: 10.1021/ja410264d.

InChIs

α-glucose: InChI=1S/C6H12O6/c7-1-2-3(8)4(9)5(10)6(11)12-2/h2-11H,1H2/t2-,3-,4+,5-,6+/m1/s1
InChIKey: WQZGKKKJIJFFOK-DVKNGEFBSA-N

β-glucose: InChI=1S/C6H12O6/c7-1-2-3(8)4(9)5(10)6(11)12-2/h2-11H,1H2/t2-,3-,4+,5-,6-/m1/s1
InChIKey=WQZGKKKJIJFFOK-VFUOTHLCSA-N

β-xylose: InChI=1S/C5H10O5/c6-2-1-10-5(9)4(8)3(2)7/h2-9H,1H2/t2-,3+,4-,5-/m1/s1
InChIKey=SRBFZHDQGSBBOR-KKQCNMDGSA-N

β-mannose: InChI=1S/C6H12O6/c7-1-2-3(8)4(9)5(10)6(11)12-2/h2-11H,1H2/t2-,3-,4+,5+,6-/m1/s1
InChIKey=WQZGKKKJIJFFOK-RWOPYEJCSA-N

β-acetylglucosamine: InChI=1S/C8H15NO6/c1-3(11)9-5-7(13)6(12)4(2-10)15-8(5)14/h4-8,10,12-14H,2H2,1H3,(H,9,11)/t4-,5-,6-,7-,8-/m1/s1
InChIKey=OVRNDRQMDRJTHS-FMDGEEDCSA-N

Testing for method performance using rotational constants

Grimme Steven Bachrach 11 Feb 2014 No Comments

The importance of dispersion in determining molecular structure, even the structure of a single medium-sized molecule, is now well recognized. This means that quantum methods that do not account for dispersion might give very poor structures.

Grimme1 takes an interesting new twist towards assessing the geometries produced by computational methods by evaluating the structures based on their rotational constants B0 obtained from microwave experiments. He uses nine different molecules in his test set, shown in Scheme 1. This yields 25 different rotational constants (only one rotational constant is available from the experiment on triethylamine). He evaluates a number of different computational methods, particularly DFT with and without a dispersion correction (either the D3 or the non-local correction). The fully optimized geometry of each compound with each method is located to then the rotational constants are computed. Since this provides Be values, he has computed the vibrational correction to each rotational constant for each molecule, in order to get “experimental” Be values for comparisons.

Scheme 1.

Grimme first examines the basis set effect for vitamin C and aspirin using B3LYP-D3. He concludes that def2-TZVP or lager basis sets are necessary for reliable structures. However, the errors in the rotational constant obtained at B3LYP-D3/6-31G* is at most 1.7%, and even with CBS the error can be as large as 1.1%, so to my eye even this very small basis set may be completely adequate for many purposes.

In terms of the different functionals (using the DZVP basis set), the best results are obtained with the double hybrid B2PLYP-D3 functional where the mean relative deviation is only 0.3%; omitting the dispersion correction only increases the mean error to 0.6%. Common functionals lacking the dispersion correction have mean errors of about 2-3%, but with the correction, the error is appreciably diminished. In fact B3LYP-D3 has a mean error of 0.9% and B3LYP-NL has an error of only 0.6%. In general, the performance follows the Jacob’s Ladder hierarchy.

References

(1) Grimme, S.; Steinmetz, M. "Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase," Phys. Chem. Chem. Phys. 2013, 15, 16031-16042, DOI: 10.1039/C3CP52293H.

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