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4 OPTICAL ROTATION, OPTICAL ROTATORY DISPERSION, ELECTRONIC CIRCULAR DICHROISM, AND VIBRATIONAL CIRCULAR DICHROISM

4 OPTICAL ROTATION, OPTICAL ROTATORY DISPERSION, ELECTRONIC CIRCULAR DICHROISM, AND VIBRATIONAL CIRCULAR DICHROISM

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OPTICAL ROTATION, OPTICAL ROTATORY DISPERSION



83



TABLE 2.11 Comparison of Experimental and Calculated Optical Rotationa for

Ketones and Alkenesb



O



O



O

O



a

b



[𝛼]D (Expt)



[𝛼]D (B3LYP)



[𝛼]D (Expt)



[𝛼]D (B3LYP)



−180



−251



−40



−121



−44



−85



−68



−99



+59



+23



−36



−50



+7



+13



−15



+27



[𝛼]D in deg. [dm. g/cm3 ]−1 .

Computed at B3LYP/6-31G*, see Ref. 68.



TABLE 2.12 Compounds for Which Calculated Optical Rotationa Disagree in Sign

with the Experimental Valueb



O



[𝛼]D (Expt)



[𝛼]D (Comp)



−15.9



3.6



6.6



−11.3



29.8



−10.1



O



O



O

a

b



[𝛼]D in deg. [dm g/cm3 ]−1 .

Computed at B3LYP/aug-cc-pVDZ//B3LYP/6-31G*, see Ref. 69.



[𝛼]D (Expt)



[𝛼]D (Comp)



−78.4



13.1



14.4



−9.2



−59.9



20.0



84



COMPUTED SPECTRAL PROPERTIES AND STRUCTURE IDENTIFICATION



B3LYP/aug-cc-pVDZ but for the CCSD computations, aug-cc-pVDZ was used for

carbon and oxygen, while cc-pVDZ was used for hydrogen. For the entire set of

compounds, the mean absolute deviations between the computed and experimental

[𝛼]D values are 31.7 for B3LYP and 56.5 for CCSD. This includes a very large error

of the CCSD prediction for (1S,4S)-norbornenone (exp: −1146, B3LYP: −1216,

CCSD: −740). Omitting this compound gives mean absolute deviations for both

methods of about 27. Sources of errors include (1) use of a relatively small basis set,

though examples with larger basis sets do not seem to be much improved, (2) lack

of triple or higher excitations, (3) neglect of vibration and temperature effects, and

(4) comparison of computed gas-phase values compared to experimental solution

phase values.

In a benchmark study of 45 compounds (including three organometallic

compounds), the effect of long-range corrections on ORs was tested.72 Neither

the CAM-B3LYP functional73 (which is a range-separated density functional)

nor LC-PBE0 preformed any better than B3LYP. In addition, the LPol-ds basis

set,74 a customized basis set proposed for OR computations, offers no general

improvement over the aug-cc-pVDZ basis set used in the other benchmark studies

mention above.

Grimme75 extended the double hybrid density functional formalism to be able to

compute ECD. For a test suite of six molecules, performance of B2PLYP is notably

better than for B3LYP.

Crawford67 highlights in his review article three particular studies that demonstrate the varied results one might expect to attain with computed optical activities.

In particular, he notes molecules where the CC approach performs much better

than DFT, where DFT performs better than CC, but for the wrong reason, and a

case where DFT appears to perform better than CC.

(P)-(+)-[4]-Triangulane 27, synthesized by de Meijere,76,77 exhibits amazing

optical activity: varying from 193 deg/[dm (g/ml)] at 589 nm to 648 deg/[dm (g/ml)]

at 365 nm. This is remarkable given its lack of a long wavelength chromophore or

chiral atom. B3LYP and CCSD computations of the OR of 27 were done at five

different wavelengths.78 B3LYP overestimates the value of [𝛼] by about 15 percent,

but CCSD underestimates the experimental values by less than 2 percent across the

wavelengths. It is readily apparent that CCSD outperforms B3LYP. The poor performance of the DFT method is linked to the first electronic excitation energy that

is too small (7.21 eV with CCSD vs 6.24 eV with B3LYP).



27



The ORD of (S)-methyloxirane shows a change of sign: −8.39 at 633 nm and

+7.39 at 355 nm.79 CCSD predicts a reasonable value at 633 nm but gets the wrong



OPTICAL ROTATION, OPTICAL ROTATORY DISPERSION



85



sign at the shorter wavelength.66 On the other hand, B3LYP does predict the sign

change. However, this seemingly correct result is due to (once again) underestimation of the excitation energy. The correct answer is obtained here with B3LYP but

for the wrong reason!

Lastly, [𝛼]D for (1S,4S)-norbornenone is −1146 deg/[dm (g/ml)]. B3LYP does a

very reasonable job in predicting a value of −1216. However, CCSD grossly underestimates this value at −740.65,71 Though B3LYP again underestimates the excitation energy, it appears to get the energy and rotational strength near the liquid-phase

values. This is a case where B3LYP outperforms CCSD.

The upshot here is that a standard method for computing ORs, ORD, ECD, and

VCD is still a work in progress. We next present a few case studies where computation has played a role in structure determination. The interested reader should use

these examples for guidance in performing his/her own computations.

2.4.1



Case Studies



2.4.1.1 Solvent Effect The method most widely utilized for computing optical activities is B3LYP/aug-cc-pVDZ, as advocated by the Stephens and Gaussian groups.64,69,71 Can one use a smaller, more computationally efficient basis

set? Is the neglect of solvent justified? To address these points, Rosini80 examined five related cyclohexene oxides with known absolute configuration and ORs.

Low energy conformations (within 2 kcal mol−1 of the minimum) were optimized

at in the gas-phase B3LYP/6-31G(d) and B3LYP/aug-cc-pVDZ. Geometries were

also reoptimized using PCM to simulate the solvent environment of the experiments. Both the gas- and solution-phase [𝛼]D values were computed with both basis

sets and Boltzmann averaged. We discuss the results for two of these compounds,

(+)-chaloxone 28 and (+)-epoxydon 29.

OH



OH

O

O



O

O



O



O



28



29



There are five low energy conformations of 28. The computed Boltzmannweighted ORs with both basis sets, in the gas and solution phases are listed in

Table 2.13. While the gas-phase B3LYP/6-31G(d) average value is far off the

experimental value, it does predict the correct sign, and since all of the five

conformers give rise to a positive rotation, any error in their relative energies will

not affect the overall sign of the rotation. The computed gas-phase value with

the larger basis set using geometries optimized with that basis set is in better

agreement with experiment. However, the solution-phase values are acceptable,

indicating the potential importance of including solvent effects.



86



COMPUTED SPECTRAL PROPERTIES AND STRUCTURE IDENTIFICATION



TABLE 2.13



Boltzmann-Weighted Values of [𝜶]D for 28 and 29

Gas



Solution



6-31G(d)// aug-cc-pVDZ// aug-cc-pVDZ// 6-31G(d)// aug-cc-pVDZ//

Cmpd 6-31G(d)

6-31G(d)

aug-cc-pVDZ 6-31G(d)

6-31G(d)

28

29



+378

−16



+372

+11



+333

+57



+318

+4



+322

+32



Expt

+271

+93



This is reinforced in the study of 29. Again, five low energy conformers were

optimized, and the Boltzmann-weighted [𝛼]D computed for gas and solution phases

are listed in Table 2.13. In this case, the small basis set performs very poorly. The

gas-phase B3LYP/6-31G(d) value of [𝛼]D is −16, predicting the wrong sign, let

alone the wrong magnitude. Things improve with the larger basis set, which predicts a value of +57. Since the lowest energy conformer is levorotatory and the other

four are dextrorotatory, the computed relative energies are key to getting the correct

prediction. This is made even more poignant with the solution results, where both

computations predict a positive rotation. In fact, if the PCM/B3LYP/aug-cc-pVDZ

geometries are used, the predicted rotation is +61. The bottom line is that 6-31G(d)

provides marginal results, but the larger aug-cc-pVDZ is much better suited for

computing ORs. Furthermore, inclusion of solvent effects within computation of

ORs and related properties are likely to be necessary.

2.4.1.2 Chiral Solvent Imprinting

Beratan and Wipf81 have examined

the role of solvent organization about a chiral molecule in producing optical

activity. They generated 1000 configurations of benzene arrayed about either (S)or (R)-methyloxirane via a Monte Carlo simulation. Each configuration was then

stripped off every benzene molecule greater than 0.5 nm from the center-of-mass

of methyloxirane, leaving usually 8–10 solvent molecules. The OR was then

computed at four wavelengths using TDDFT at BP86/SVP. (The authors note that

though the Gaussian group64,69,71 recommends B3LYP/aug-ccpVDZ, using the

nonhybrid density functional BP86 allows the use of resolution-of-the-identity

techniques that make the computations about six orders of magnitude faster—of

critical importance given the size of the clusters and the sheer number of them!)

OR is then obtained by averaging over the ensemble.

The computed ORs disagree with the experiment by about 50 percent in magnitude but have the correct sign across the four different wavelengths. Use of the

COSMO (implicit solvent) model provides the wrong sign at short wavelengths,

justifying the need of this microsolvation approach. Most intriguing is that the computed optical activity of the solvent molecules in the configuration about the solute,

but without including the central methyloxirane molecule, is nearly identical to that

of the whole cluster! In other words, the optical activity is due to the dissymmetric distribution of the solvent molecules about the chiral molecule, not the chiral

molecule itself! It is the imprint of the chiral molecule on the solvent ordering that



OPTICAL ROTATION, OPTICAL ROTATORY DISPERSION



87



accounts for nearly all of the optical activity. This provides considerable guidance

as to why computation of the optical activity of methyloxirane, described in the

previous section, is so fraught with difficulties.

In fact, a recent approach delineates just how much effort is needed to

obtain good results for the OR of methyloxirane. Cappelli and Barone82 have

developed a QM/MM procedure where methyloxirane is treated with DFT

(B3LYP/aug-cc-pVDZ). Then, 2000 arrangements of water about methyloxirane

were obtained from an MD simulation. For each of these configurations, a

supermolecule containing methyloxirane and all water molecules within 16 Å

was identified. The waters of the supermolecule were treated with a polarized

force field. This supermolecule is embedded into bulk water employing a

conductor-polarizable continuum model (C-PCM). Lastly, inclusion of vibrational

effects and averaging over the 2000 configurations gives a predicted OR at 589 nm

that is of the correct sign (which is not accomplished with a gas-phase or simple

PCM computation) and is within 10 percent of the correct value.

2.4.1.3 Plumericin and Prismatomerin Isolation and characterization of

plumericin led Albers-Schönberg and Schmid83 to assign it structure 30. Subsequent analysis of its ECD spectrum and comparison with computed semiempirical

spectrum suggested that the actual structure is the enantiomer of 30.84

O

O



H



O



H



H

H

O

O



O



O

H



O

O



H



H

30



O

H



OH

31



Stephens reexamined this compound, obtaining its experimental VCD spectrum. The four lowest energy conformers of 30 were optimized at B3LYP/6-31G*,

B3LYP/TZ2P, and B3PW91/TZ2P; their relative energies are very similar with

each method, and the Boltzmann population is dominated by just two conformers.

The VCD spectrum was computed at B3PW91/TZ2p for the two lowest energy

conformers and averaged together. This resulting VCD-computed spectrum is

in very close agreement with the experimental VCD spectrum, arguing for the

original structural assignment. Further confirmation was supplied by computing

the ECD spectrum at this same level and comparing it back to the earlier

experimental ECD spectrum; their agreement is also excellent.

Stephens85 next examined the related iridoid prismatomerin 31. The OR of

plumericin 30 is [𝛼]D = +204. The structurally related prismatomerin 31 has

[𝛼]D = −136, suggesting that the core polycyclic portion may have opposite



88



COMPUTED SPECTRAL PROPERTIES AND STRUCTURE IDENTIFICATION



absolute configuration. Stephens prepared the acetate of 31 and experimentally

determined its VCD spectrum. Using the same computational procedure as

described above, 16 low energy conformers of 21 were identified. The VCD spectrum for the 12 lowest energy conformers was then computed at B3PW91/TZ2p

and summed together using their Boltzmann weights. The computed spectrum

for the enantiomer with the same absolute configuration as 30 matches the

experimental spectrum. Thus, 30 and 31 have the same absolute configuration.

Stephens concludes with the warning that optical activity of analogous compounds

can be quite different and is not suitable for obtaining configuration information.

Rather, VCD is a much more suitable test, especially when experimental and

computed spectra are compared.

2.4.1.4 2,3-Hexadiene Wiberg et al.86 produced a tour-de-force experimental

and computational studies of the ORD of 2,3-hexadiene 32. This seemingly normal

compound offers some confounding problems!

The compound 2,3-hexadiene exists in three conformations, as shown in

Figure 2.2. The cis conformer is the lowest energy form, but the other two are

only 0.3 kcal mol−1 higher in energy (computed at G3), meaning that all three

will be present to a significant extent at 0 ∘ C. The OR for each conformer was

determined using B3LYP/aug-cc-pVDZ and CCSD/aug-ccpVDZ. (We use here

just the velocity gauge results.) While there is some disagreement in the values

determined by the two methods, what is most interesting is the large dependence

of [𝛼]D on the conformation (see Table 2.14).

The ORD spectrum of 32 was taken for neat liquid and in the gas phase. The

computed and experimental ORs are listed in Table 2.15. Two interesting points

can be made from this data. First, the optical activity of 32 is strongly affected



cis

(0.0)



gauche120

(0.269)



Figure 2.2



TABLE 2.14



Conformations and relative energies (G3) of 2,3-hexadiene 32.



Calculated [𝜶]D for 32

cis



B3LYP/aug-cc-pVDZ

CCSD/aug-cc-pVDZ

a



gauche240

(0.272)



205.2

208.5



gauche120



gauche240



Averagea



415.9

376.7



−179.8

−120.6



156.8

163.8



Boltzmann-weighted average based on the G3 energies listed in Figure 2.2.



OPTICAL ROTATION, OPTICAL ROTATORY DISPERSION



TABLE 2.15

of 32



89



Boltzmann-Weighted Computed and Experimental Optical Rotations

Computed



Experiment



nm



B3LYP



CCSD



Liquid



633

589

546

365

355



134.7

156.8

183.8

409.7

427.5



140.6

163.8

203.6

492.5

489.3



86.5

102.0

243.3



Gas

122



511



by phase. Second, the computed ORs, especially the CCSD values, are in fairly

good agreement with the gas-phase experimental values.

A hypothesis to account for the large difference in the gas- and liquid-phase

ORDs for 32 is that the conformational distribution changes with the phase. The

gas- and liquid-phase ORDs of 2,3-pentadiene, also examined in this study, show

the same strong phase dependence, even though this compound exists as only one

conformer. A Monte Carlo simulation of gas- and liquid-phase 2,3-pentadienes

was performed to assess potential differences in conformational distributions in the

two phases. Though the range of dihedral angle distributions spans about 60∘ , the

population distribution is nearly identical in the gas and liquid phases. Therefore,

conformation distribution cannot explain the difference in the gas and liquid ORDs.

The authors also tested for the vibrational dependence on the OR. While there is

a small correction due to vibrations, it is not enough to account for the differences

due to the phase. The origin of this phase effect remains unexplained.

2.4.1.5 Multilayered Paracyclophane The three-layer paracylophane 33

was synthesized and the two stereoisomers separated. The question facing

Kobayashi and colleagues87 was “is the (+)-isomer of R or S stereochemistry?”

Comparison of the computed and experimental ORs resolved the issue.



(R)-33



They located seven conformations of (R)-33 at B3LYP/TZVP and computed the

[𝛼]D values for each conformer. The lowest energy conformer has [𝛼]D = −171.7

deg/[dm (g/ml)], and all conformers have ORs that are negative, ranging from



90



COMPUTED SPECTRAL PROPERTIES AND STRUCTURE IDENTIFICATION



−124.4 to −221.8 deg/[dm (g/ml)]. These values are consistent with the experimental observation of the (−)-33 isomer, whose [𝛼]D = −123 deg/[dm (g/ml)]. The

computed CD spectrum of the seven (R)-33 conformations are similar to the experimental spectra of (−)-33. Thus, the two enantiomers are R-(−)-33 and S-(+)-33.

2.4.1.6 Optical Activity of an Octaphyrin The octaphyrin 34 has been prepared and its crystal structure and ECD spectra reported.88 The X-ray structure

identified the compound as having the M,M helical structure. The OR, however,

could not be determined.

Et



Et

Et



Et

Et



Et

Et

Et



N



NH



N

H



N

H



N



N



Et



N



Et



HN



Et



Et



Et

Et

Et



Et

34



Rzepa89 reported the computed ECD spectrum and optical activity of 34

and some related compounds. These computed spectra were obtained

using TD-DFT/B3LYP/6-31G(d) method with the C-PCM treatment of the

dichloromethane solvent. The computed ECD spectrum matches nicely with the

experimental one, except that the signs at 570 and 620 nm are opposite. Rzepa

suggests that either the compound is really of P,P configuration or the authors of

experimental work have erroneously switched their assignments.

The computed value of [𝛼]D of 34 is about −4000 deg/[dm (g/ml)]. However,

what is truly fantastic is the magnitude of the optical activity of the dication of

34 produced by loss of two electrons. This dication should be aromatic and it is

predicted to have [𝛼]1000 = −31,597 deg/[dm (g/ml)]!



2.5 INTERVIEW: JONATHAN GOODMAN



Interviewed August 28, 2012

Jonathan Goodman is Reader in Chemistry at the University of Cambridge

University and Clare College. He became interested in computational chemistry



INTERVIEW: JONATHAN GOODMAN



91



during his graduate studies with Professor Ian Paterson. He was exploring

the boron-mediated aldol condensation and wondered if computations might

be able to assist in rationalizing the selectivity they were observing in the

experiments. Goodman had the good fortune of meeting Scott Kahn who was

a post-doctoral associate at that time with Dudley Williams in a neighboring

laboratory. Kahn collaborated with Goodman and taught him how to perform

quantum computations. Despite the fact that they were limited by computational

resources to examining the reaction of the BH2 -mediated enolate of ethanol

with formaldehyde in the gas phase, a reaction decidedly different from their

experiments, the computations revealed a key new insight: the enol borinates

did not have to be flat, maximizing conjugation, but could be twisted! Goodman

remarked that “we weren’t expecting the calculations to tell us the answer; we

were hoping the calculations would give us an insight to how to think about

these systems.” Subsequent increases in computer power allowed them to go

to a seven heavy-atom system that permitted a “huge amount of additional

complexity.” This early success led to a post-doctoral stint with Clark Still

at Columbia where Goodman was able to continue to explore the interplay

between computations and experiments.

In establishing his own independent research program back at Cambridge,

Goodman aimed to find problems that were accessible to both experiment and

computations. Early on he developed an empirical rule: “If it’s easy to do the

experiment, it’s next to impossible to do the computations and vice versa.” In

his early studies, this meant the avoidance of transition metals and reactions

with strong solvent effects. His rule is not so strictly true today; the continued

improvement in computational hardware and algorithmic advances, especially

DFT, allows one to judiciously include transition metals and solvent effects.

However, Goodman suggests that this rule remains “ the reason why synthetic

chemistry often don’t do computations today: unless you have some experience with computations, it’s very difficult to tell a computation that will be

done in 10 min from one that will take a thousand years.” Some significant skill

remains in choosing an experiment where computations are tractable. He notes,

for example, that polymers remain a singular challenge.

Goodman considers his work in NMR analysis to be a significant scientific

achievement. This project was motivated by his experimental studies, in particular, answering the question “how do you know what you have made?” Goodman

feels that there is a “certain prejudice that this ought to be easy; it is straightforward to calculate the NMR spectrum, and get reasonable agreement.” But he

notes that problems crop up when isomers, especially diastereomers, are possible. “You have a set of computed NMR for the set of isomers and all are different

from each other—and different from the experiment! So which is which? How

sure can you be?” Working with his doctoral student Steven Smith, Goodman

developed statistical methods for not just assigning a structure but also providing a confidence measure. These techniques, especially DP4, have allowed for

uncovering misassigned spectra and structural identification of natural products.



92



COMPUTED SPECTRAL PROPERTIES AND STRUCTURE IDENTIFICATION



Goodman is generally pleased with the acceptance and uptake of the DP4 procedure, but recognizes that progress still is needed in making the method more

accessible, especially to synthetic chemists. He is focused on making the entire

process from computing the spectra to assigning the structure easier to accomplish. Goodman is especially eager to find a way to incorporate this process

within a laboratory notebook.

Goodman’s choice of merging cheminformatics with computations was

driven by his recognition of the closing gap between experiments and calculations. Goodman says “there has always been a tension between the experimental

chemist and the computational chemist: the computational guy thinks the

experimentalist should do the experiment better; the experimentalist thinks

the theoretician is out of touch with reality and should do something useful.

That’s where informatics comes in. It’s not just that you have a number, say a

diastereomer ratio of 9 : 1. The experiments and calculations will be different,

not just because they are measuring different things. Whether the different

things the experiment and calculation are telling you can be put together to

tell you more than you have individually; that’s informatics—getting a united

whole.” Interestingly, Goodman has essentially trained himself in informatics!

Goodman is quite modest regarding his contribution toward understanding

the role of the enzyme in catalysis, with Luis Simón, then a post doc in his

group. He nạvely thought that to catalyze a reaction, one should simply lower

the transition state, but he notes that he “needed to read Pauling more closely!”

His operating picture is now that “if a catalyst is brilliant at stabilizing the

TS but even better at stabilizing the ground state, then it will not be a good

catalyst—nature realizes this. Enzymes do not stabilize the TS as well as they

maximally could because they need to avoid stabilizing the ground state too.”

While he feels that this assessment seems “pretty obvious now,” he notes that

his papers in this area met with significant resistance from referees, they were

rejected many times, and that the publication process took more than a couple

of years.

Goodman expresses serious dismay regarding progress in the area of data

mining. He despairs that so much data is controlled by publishers and copyright

holders and this prevents our abilities to effectively mine this resource. “We

could know all sorts of stuff, but it’s just out of reach,” he says. “The task is

technically straightforward with enormous potential but we can’t do it because

of license restrictions and that’s frustrating. I need to collaborate with lawyers

as much as with chemists!” In collaboration with his Cambridge colleague Peter

Murray-Rust, they developed an experimental data checker for the Royal Society of Chemistry. He wistfully speaks about getting access to a large literature

backfile and “checking to see what data is good and what data is not.”

Goodman remains firm in his commitment to a high goal for computations:

“If we want to understand a reaction we need to be able to draw a picture on a

fume cupboard that an experimentalist will understand.”



REFERENCES



93



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