Dispersion forces in chirality recognition - a density

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Dispersion forces in chirality recognition - a densityfunctional and wave function theory study of diols

Xaiza Aniban,‡a Beppo Hartwig,‡a Axel Wuttke,a Ricardo A. Mataa*

a Institut fur Physikalische Chemie, Georg-August-Universitat Gottingen, Tammannstr. 6, 37077 Gottingen,Germany. E-mail: [email protected]

‡ These authors contributed equally to this work.

Contents

1 DFT data 1

2 WFT data 4

3 Geometry analysis data 53.1 Intermolecular hydrogen bond (A), EDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Intermolecular hydrogen bond (A), CHexDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3 Intermolecular hydrogen bond (A), Pinacol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.4 Generation of density plots in Figure 4 of the main text. . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Structures 9

References 10

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2021

1 DFT data

0 200 400 600 800 1000 1200tavg(aVQZ) / tavg(XXXX)

0

2

4

6

8

10

E avg

(aVQ

Z) /

kJ m

ol1

DunningVDZaVDZVTZaVTZVQZaVQZAhlrichsdef2-SVPma-def2-SVPdef2-SVPDdef2-TZVP

ma-def2-TZVPdef2-TZVPDdef2-QZVPma-def2-QZVPdef2-QZVPDJensenpcseg-1aug-pcseg-1pcseg-2aug-pcseg-2pcseg-3

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

Fig. S1: Overview of the average energy difference relative to the Dunning aVQZ (aug-cc-pVQZ) basis set depend-ing on the fraction of the computational time of aVQZ and each tested basis set. The fully augmentedDunning basis sets (aug-cc-pVXZ) as well as the non augmented variants (cc-pVXZ) were tested[1,2].Furthermore the def2-XZVP Ahlrichs[3] family of basis sets were tested as well as the minamlly aug-mented variants of Zheng et al.[4] and the property optimized heavily augmented variants of Rappoportet al.[5]. Additionally the augmented (aug-pcseg-X) and non augmented (pcseg-X) Jensen basis sets weretested[6]. The aug-pcseg-3 calculations did not converge. All calculations were made for a total of 8different ethanediol dimers and then averaged. For comparable timings each calculation was done on thesame node.

1

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'

hom3ahom3a'hom3b'hom2''

het4het3het3'

het3b'het2''

9.4 9.8 6.5

7.5 6.4 6.6

6.1 5.5 4.6

8.3 6.6 4.6

8.0 8.8 5.3

8.2 6.0

8.0 8.9

0.0 0.0 0.0

5.4 4.3 3.4

4.9 4.6 2.3

7.5 8.6 3.0

7.6 8.7 6.5

a)no D3(BJ,abc)

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

10.0 10.4 9.3

11.0 9.7 11.7

9.1 8.8 10.3

13.8 11.5 13.5

13.0 10.4

11.3 12.5 13.9

8.8 11.8

0.0 0.0 0.0

9.3 8.6 7.2

12.9 13.8 9.3

9.9 12.4 11.1

b) D3(BJ,abc)0

2

4

6

8

10

12

0

2

4

6

8

10

12

E0,m

in / kJ mol

1(a) BP86

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

9.3 6.3

7.4 6.4 7.0

6.0 5.6 5.1

8.4 6.9 5.5

9.1 6.3

7.5 7.9 7.0

7.0 8.7

0.0 0.0 0.0

5.4 4.4 3.8

5.0 4.8 2.8

7.1 8.4 3.3

6.9 8.4 6.5

a)no D3(BJ,abc)

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

9.8 10.2 8.2

10.0 8.8 10.5

8.1 7.9 8.8

12.2 10.2 10.7

12.0 9.5

9.9 10.9 12.3

7.7 10.6

0.0 0.0 0.0

8.1 6.6

7.9 7.5 6.2

10.6 11.9 7.3

8.6 10.9 9.4

b) D3(BJ,abc)0

2

4

6

8

10

12

0

2

4

6

8

10

12

E0,m

in / kJ mol

1

(b) PBE

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

8.6 5.4

5.9 5.3 6.2

4.6 4.7 4.8

6.3 5.4 4.4

8.6 5.7

5.4 6.0 6.0

6.0 7.9

0.0 0.0 0.0

3.6 3.1 3.0

3.5 3.9 2.2

4.8 6.4 2.2

5.4 6.7 6.3

a)no D3(BJ,abc)

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

9.6 9.5 7.0

8.2 7.3 9.2

6.5 6.7 7.8

9.5 8.1 8.9

11.2 9.1

7.1 8.3 10.3

6.3 9.4

0.0 0.0 0.0

6.0 4.9

6.2 6.2 5.1

7.8 9.2 5.5

6.4 8.7 8.7

b) D3(BJ,abc)0

2

4

6

8

10

12

0

2

4

6

8

10

12

E0,m

in / kJ mol

1

(c) PBE0

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

7.8 4.9

4.1 3.2 3.6

2.9 2.7 2.3

3.9 2.9 0.8

6.1 2.3

3.0 3.2 2.5

6.4 7.5

0.0 0.0 0.7

1.7 1.1 0.7

1.6 1.6 0.0

2.8 3.6 0.0

4.3 5.1 5.4

a)no D3(BJ,abc)

Cyclohexanediol

EthanediolPinacol

hom4hom3hom3'


het4het3het3'

het3b'het2''

9.7 9.8 7.0

8.2 7.2 8.3

6.5 6.7 7.1

9.1 8.0 7.9

11.1 8.4

6.8 8.0 9.4

7.3 10.6

0.0 0.0 0.0

5.8 4.8 4.8

5.9 5.9 4.2

7.6 8.9 4.9

6.9 9.3 9.6

b) D3(BJ,abc)0

2

4

6

8

10

12

0

2

4

6

8

10

12

E0,m

in / kJ mol

1

(d) B3LYP

Fig. S2: Overview of the DFT results with (b)) and without D3(BJ,abc) (a)) for cyclohexanediol, ethanedioland pinacol. The energies given are always relative to the minimum energy conformer and zero pointcorrected. Grey squares indicate unstable conformers.

2

a) ethanediol

b) cyclohexanediol

c) pinacol

Fig. S3: Identical analysis as was done in Fig. 9 of the main text for ethanediol a), cyclohexanediol b) and pinacolc) at the B3LYP level of computation.

3

2 WFT data

0

2

4

6

8

het-h

om g

ap /

kJ m

ol1

0.0LMP2-d

6.6

0.0LMP2-E

1.9

0.0SCS-d

4.0

0.0SCS-E

4.6

a) ethanediol

0

2

4

6

8

het-h

om g

ap /

kJ m

ol1

0.0LMP2-d

5.3

0.0LMP2-E

1.8

0.0SCS-d

3.1

0.0SCS-E

3.9

b) cyclohexanediol

0

2

4

6

8

het-h

om g

ap /

kJ m

ol1

0.0LMP2-d

7.0

0.0LMP2-E

4.5

0.0SCS-d

5.2

0.0SCS-E

4.2

c) pinacol

Fig. S4: Comparison of the LMP2-d and SCS-LMP2-d het-hom gap with the corresponding results purely basedon the dispersion energy (LMP2-E and SCS-LMP2-E). The dispersion energy gap can also be inferredfrom Fig. 12 of the main text for SCS-LMP2 and figure S5 for LMP2.

4

het2'

'he

t3 b'he

t3he

t3' het4

hom2''

hom3 b'

hom3

hom3'

hom3a

hom3a

'ho

m4

35

30

25

20

15

10

5

0

E Disp

/ kJ

mol

1

11.2

4.8

12.7

3.5

14.9

4.1

14.1

3.9

18.7

4.9

11.4

4.8

12.8

3.7

14.5

3.7

14.0

4.0

13.1

4.7

13.9

4.1

17.5

4.3

a) ethanediolOH groupsbackbone

het2'

'he

t3 b'he

t3he

t3' het4

hom2''

hom3 b'

hom3

hom3'

hom3a

hom3a

'ho

m4

35

30

25

20

15

10

5

0

E Disp

/ kJ

mol

1

12.3

6.9

13.3

5.1

15.5

5.0

14.6

5.0

19.8

6.2

12.6

7.3

13.7

5.9

15.2

4.9

14.6

5.8

13.3

6.5

18.7

5.5

b) cyclohexanediolOH groupsbackbone

het2'

'he

t3 b'he

t3he

t3' het4

hom2''

hom3 b'

hom3

hom3'

hom3a

hom3a

'ho

m4

35

30

25

20

15

10

5

0

E Disp

/ kJ

mol

1

13.5

9.4

14.5

7.9

15.5

7.9

21.2

9.7

12.9

7.4

15.6

7.9

14.9

8.3

13.2

8.4

17.0

8.2

18.2

8.2

c) pinacolOH groupsbackbone

Fig. S5: Energy fragmentation of the dispersion energy at the LMP2-d level of computation for ethanediol (a)),cyclohexanediol (b)) and pincaol (c)). A zero energy value indicates that a conformer either convergesto a different one or exhibits an imaginary frequency. The performed analysis is analogous to that ofFig. 12 of the main text.

3 Geometry analysis data

3.1 Intermolecular hydrogen bond (A), EDO

Tab. S1: Intermolecular H-bonding optimized at LMP2/aug-cc-pVTZ,H=cc-pVTZ.

Molecular System with dispersion without dispersion

het2” 1.983 1.983 2.133 2.133het3b’ 2.188 2.031 1.892 2.532 2.112 2.000het3 1.905 1.998 1.899 2.045 2.152 2.063het3’ 1.928 1.976 1.920 2.085 2.131 2.100het4 1.959 1.959 1.959 1.959 2.111 2.111 2.111 2.111hom2 1.926 1.973 2.081 2.145hom3a 1.841 1.972 2.065 1.956 2.215 2.244hom3a’ 1.822 1.961 2.021 2.034 3.390 2.046hom3b’ 2.145 1.983 1.886 2.491 2.083 2.006hom3 1.847 1.980 1.959 1.956 2.154 2.136hom3’ 1.876 1.971 1.961 2.004 2.159 2.135

5

Tab. S2: Intermolecular H-bonding optimized at B3LYP/aug-cc-pVTZ,H=cc-pVTZ.


het2” 1.939 1.939 1.980 1.980het3b’ 2.141 1.988 1.876 2.203 2.046 1.915het3 1.881 1.973 1.865 1.925 2.008 1.911het3’ 1.885 1.943 1.877 1.913 2.000 1.935het4 1.951 1.951 1.951 1.951 1.997 1.997 1.997 1.997hom2” 1.898 1.932 1.957 1.977hom3a 1.810 1.926 2.018 1.832 1.998 2.091hom3a’ 1.792 1.916 2.001 1.811 2.018 2.044hom3b’ 2.062 1.956 1.864 2.114 2.024 1.909hom3 1.828 1.940 1.916 1.852 2.015 1.987hom3’ 1.841 1.935 1.921 1.870 2.019 1.990

Tab. S3: Intermolecular H-bonding optimized at SCS-LMP2/aug-cc-pVTZ,H=cc-pVTZ.


het2” 2.052 2.052 2.178 2.178het3b’ 2.255 2.083 1.944 2.510 2.152 2.030het3 1.968 2.059 1.964 2.079 2.181 2.096het3’ 1.997 2.038 1.992 2.119 2.161 2.133het4 2.024 2.024 2.024 2.024 2.144 2.144 2.144 2.144hom2” 1.992 2.051 2.116 2.196hom3a 1.897 2.051 2.140 1.987 2.250 2.288hom3a’ 1.866 2.075 2.102 2.063 3.474 2.073hom3b’ 2.232 2.031 1.937 2.499 2.112 2.035hom3 1.900 2.044 2.026 1.986 2.183 2.169hom3’ 1.936 2.039 2.025 2.035 2.188 2.166

3.2 Intermolecular hydrogen bond (A), CHexDO



het2” 2.002 2.002 2.175 2.175het3b’ 2.176 2.002 1.873 2.378 2.131 2.007het3 1.910 1.988 1.898 2.089 2.139 2.077het3’ 1.960 1.956 1.921 2.140 2.122 2.106het4 1.939 1.939 1.939 1.939 2.099 2.099 2.099 2.099hom2” 2.013 1.947 2.196 2.142hom3a 1.869 1.907 2.065 2.011 2.203 2.301hom3b’ 2.174 1.957 1.880 2.415 2.087 2.024hom3 1.866 1.952 1.942 1.987 2.153 2.159hom3’ 1.923 1.959 1.948 2.055 2.172 2.173

6







3.3 Intermolecular hydrogen bond (A), Pinacol



het2” 1.982 1.982 2.394 2.394het3b’ 2.192 2.069 1.883 2.361 2.298 2.081het3’ 1.975 1.980 1.995 2.223 2.207 2.256het4 1.963 1.963 1.963 1.963 2.185 2.185 2.185hom3b’ 1.906 2.099 2.090 2.193 2.306 2.313hom4 1.887 1.887 2.343 2.343 2.091 2.091 2.733 2.733



het2” 1.965 1.964 2.066 2.066het3b’ 2.173 2.014 1.853 2.226 2.138 1.937het3’ 1.909 1.948 1.923 1.999 2.053 2.055het4 1.950 1.950 1.950 1.950 2.036 2.036 2.036 2.036hom3b’ 1.916 1.986 2.094 2.014 2.055 2.234hom4 1.864 1.878 2.462 2.181 1.966 1.975 2.788 2.359

7



het2” 2.054 2.054 2.430 2.430het3b’ 2.232 2.144 1.948 2.364 2.331 2.109het3’ 2.056 2.048 2.075 2.243 2.235 2.277het4 2.035 2.035 2.035 2.035 2.212 2.212 2.212 2.212hom3b’ 2.029 2.155 2.159 2.220 2.322 2.335hom4 1.953 1.953 2.473 2.475 2.113 2.113 2.758 2.757

3.4 Generation of density plots in Figure 4 of the main text.

To illustrate how the intermolecular O–H bond distance is affected once dispersion contributions are neglected, akernel density estimate (KDE) plot was employed. This allows a nice visualization of the distribution of the O–Hvalues we have and is analogous to a histogram. The data in KDE are represented using a continuous probabilitydensity curve in one or more dimensions.

Since the values of the O–H bond distances in the previous tables are within 3 decimal places, the bin widthchosen to represent the data was 0.001. This permits each value to be represented in each bin, so higher frequencyindicated in the plots are representatives of several repeated O–H bond distances. In this section, the analogoushistogram is reflected so as to show how the data looks like before employing the continuous probability densitycurve via KDE.

1.50 1.75 2.00 2.25 2.50 2.75 3.000

2

4

6

Etha

nedi

ol

LMP2

1.50 1.75 2.00 2.25 2.50 2.75 3.00

B3LYP

1.50 1.75 2.00 2.25 2.50 2.75 3.00

SCS-LMP2

with dispersionwithout dispersion

1.50 1.75 2.00 2.25 2.50 2.75 3.000

2

4

6

Cyclo

hexa

nedi

ol

1.50 1.75 2.00 2.25 2.50 2.75 3.00 1.50 1.75 2.00 2.25 2.50 2.75 3.00

1.50 1.75 2.00 2.25 2.50 2.75 3.000

2

4

6

Pina

col

1.50 1.75 2.00 2.25 2.50 2.75 3.00 1.50 1.75 2.00 2.25 2.50 2.75 3.00Intermolecular O-H Bond / Å

Fig. S6: Histogram counterpart of Figure 4 of the main text.

8

4 Structures

hom3 hom3aFig. S7: Comparison of the more orthogonal arrangement of the C-C backbone of hom3 and the more parallel

one of hom3a.

(a) S4 axis facing the viewer (b) S4 axis, side view (c) S4 axis rotated 90 degreeswith respect to b

Fig. S8: Dispersion interaction density of het4 EDO viewed in different perspectives of its S4 symmetry.

9

References

[1] T. H. Dunning, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron throughneon and hydrogen”, J. Chem. Phys. 1989, 90, 1007–1023.

[2] R. A. Kendall, T. H. Dunning, R. J. Harrison, “Electron affinities of the first-row atoms revisited. Systematicbasis sets and wave functions”, J. Chem. Phys. 1992, 96, 6796–6806.

[3] F. Weigend, R. Ahlrichs, “Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple ZetaValence Quality for H to Rn: Design and Assessment of Accuracy”, Phys. Chem. Chem. Phys. 2005, 7, 3297.

[4] J. Zheng, X. Xu, D. G. Truhlar, “Minimally augmented Karlsruhe basis sets”, Theor. Chem. Acc. 2011, 128,295–305.

[5] D. Rappoport, F. Furche, “Property-optimized Gaussian basis sets for molecular response calculations”, J.Chem. Phys. 2010, 133, 134105.

[6] F. Jensen, “Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent BasisSets”, J. Chem. Theory Comput. 2014, 10, 1074–1085.

10

https://doi.org/10.1063/1.456153

https://doi.org/10.1063/1.462569

https://doi.org/10.1039/b508541a

https://doi.org/10.1007/s00214-010-0846-z

https://doi.org/10.1063/1.3484283

https://doi.org/10.1063/1.3484283

https://doi.org/10.1021/ct401026a

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Dispersion forces in chirality recognition - a density