Ab Initio Density Functional vs Hartree Fock Predictions for the Structure of [18]-Annulene: Computational Evidence for Bond Localization and Diminished Ring Currents in Bicycloannelated [18]-Annulenes.

Kim K. Baldridge and Jay S. Siegel*

[*] Dr. Kim K. Baldridge

San Diego Supercomputer Center, P.O. Box 85608, San Diego, California 92186-9784

Professor. Jay S. Siegel

Department of Chemistry, University of California-San Diego, La Jolla, California 92093- 0358. Fax: 619/534 5383

e-mail: jss@chem.ucsd.edu

[**] This work was supported by the US National Science Foundation.

Justification: Although computational chemistry has become an everyday part of chemistry there remain seemingly simple hydrocarbon structures, such as the higher annulenes, that cannot be correctly predicted without the implementation of higher order basis sets and dynamical electron correlation. This study establishes the threshold levels for the correct prediction of a delocalized [18]-annulene, a classic in aromatic chemistry. Computations of 2,8,14-trisbicyclo[2.1.1]hexeno-[18]-annulene at the same level of theory predict a clear bond localized structure and set a new synthetic challenge for novel aromatic chemistry.

Keywords: Ab initio and density functional theory computations, bond localization, [18]-annulene, aromaticity, NMR ring current.

 

Ab Initio Density Functional vs Hartree Fock Predictions for the Structure of [18]-Annulene: Computational Evidence for Bond Localization and Diminished Ring Currents in Bicycloannelated [18]-Annulenes.

Kim K. Baldridge and Jay S. Siegel

On the basis of steric exclusion arguments, Mislow predicted in 1952 that higher annulenes should not be planar and therefore should not enjoy "aromatic" stabilization. This plausible prediction came from weighing the known high energetic costs for a molecule to adopt sub-van der Waals contacts and extended angles against what at that time was a more vague estimation of the aromatic stabilization energy. Indeed, only through clever subversions, such as Vogel's methano [10]- and [14]-annulenes and Boekelheide and Mitchell's dimethyldihydropyrenes, do we gain insight into stable members n=2, 3 of Hückel's 4n+2 hydrocarbons. Although the highly reactive [10]- and [14]-annulenes could be prepared, it was Sondheimer's synthesis and characterization of the relatively stable [18]-annulene (1) that provided unambiguous evidence that "aromatic" character could out-weight steric effects in simple annulenes.

During the time period that these novel higher annulenes were being synthesized and characterized, no ab initio computations were presented that correctly predicted their structure. Baumann and Haddon had proposed early on that dynamical electron correlation would be needed to handle the higher annulene structures, but the computational effort was not expended. In the last few years, computations including electron correlation have been performed on all cis [10]-annulene, but experimental comparison is limited in this system. Very recently, density functional methods have been shown to predict accurately the structure and energy of dimethyldihyropyrene and derivatives, Kekulene, and syn and anti bismethano-[14]-annulene. Schulman and Disch showed that MP2 single point analysis of the energies of symmetry constrained Restricted Hartree-Fock optimized geometries for 1 favored a D6h structure, but as of yet no correlated ab initio structure predictions exist and no reliable computational level for higher order aromatics has been established. The present study, as well as the accompanying paper, demonstrates the suitability of hybrid restricted Hartree-Fock/density functional methods to predict the structure of 1 and proposes a bicyloannelated derivative of 1 with a bond localized geometry.

Figure 1. Schematic of the structure and history of higher annulenes.[1-6]

In the absence of dynamical electron correlation, 1 (HF/DZV(2d,p)) is predicted to be D3 bond localized with average double and single bond lengths of 1.339 and 1.472 Å, respectively (Table I). Thus, at this level the potential energy surface along the bond localization coordinate is predicted to be a double-welled potential. Addition of dynamical electron correlation, by either MP2 or DFT methods, dramatically lowers the energy of the D6h structure such that the potential energy surface becomes a single well; no stationary points of D3h or D3 symmetry are found at correlated levels. The molecular geometry predicted by the correlated computations (B3PW91/d95(2df,2p)) agrees well with Cruickshank's recently determined disorder-modeled crystal structure of 1 at 110K. Imperative is the use correlated methods and extensive polarization functions in order to predict the molecular geometry with experimental accuracy.

[Insert Table I]

Bicyclic annelation induces bond localization in benzene and dimethyldihydropyrene. The special nature of 1, being on the border of the breakdown in the Hückel 4n+2 rule, makes it a natural target for further examination of the bond localizing effect of bicyclic annelations, and symmetry considerations favored the choice of 2,8,14-trisbicyclo[2.1.1]hexeno-[18]-annulene (2) for investigation.

HF/6-31G(2d,p) computations on 2 predict a double-well potential energy surface with respect to a bond localization coordinate, with an energetic preference for the exo double of 30.4 kcal/mol; however, implementation of methods that include dynamical electron correlation (B3PW91/d95(d,p)) predict a single-well potential energy surface centered about a regularly alternate structure with double bonds exo to the bicyclic annelations (Table II). The degree of bond localization can conveniently be measured by the difference in the average double and single bond lengths (0 pm 1; 6.8 pm 2). The preference for the exo double bonds and magnitude of bond localization is analogous to results found for annelated benzenes and dimethyldihydropyrenes. Bond localization in 2 suggests a significant loss in ring current, thus, the large anisotropy reflected in the difference in chemical shift between inner and outer protons of 1 should be substantially diminished for the protons of 2. Density Functional GIAO computations of the NMR properties of 1 and 2 corroborate these qualitative predictions.

Focusing first on 1, we find that the predicted signal for outer protons falls within 0.4 ppm of experiment; however, the prediction for the inner protons is off by several ppm at all computational levels attempted. Sondheimer noted a strong temperature dependence of the chemical shift of the inner protons. The discrepancy between experiment and theory may arise in part from temperature factors or because the ring current is over estimated at these computational levels. A redetermination of the low temperature high field NMR of 1 and a computational study of hexahydrocoronene should shed some light on this question. Nonetheless, similar computations of the NMR properties of 2 show an unequivocal loss of ring current compared to 1; the difference in chemical shift between exo and endo protons is calculated to be reduced from 23.6 ppm for 1 to 14.8 ppm for 2 (BPW91/6-311G(df,p//BPW91/d95(d)). Thus, bicyclic annelation is directly associated with bond localization and loss of ring current.

[Insert Table II]

Aromatic stabilization is another factor to be assessed in bond localized annulenes.[12] Prediction of the energy of the homodesmic reaction 1 by DFT methods (17.95 kcal/mol [22.9 kcal/mol corrected]) agrees reasonably well with experiment (19.0 kcal/mol)., Comparison of the DFT energies for the homodesmic reactions 1 and 2 show that 2 lacks the stability of 1 vis a vis similar fragmentation analysis.

In conclusion, the aromatic character of annulenes higher than benzene is attenuated by severe steric interactions. Bicyclic annelation, as in 2, significantly reduces, the geometrical bond delocalization, ring current and stabilization energy of 1. These novel structural, energetic, and spectroscopic predictions should motivate the synthesis and characterization of 2.

References.

[47] Energy value in brackets includes the thermal and scaled zero-point vibrational energy corrections for 1.

 

 

 

Table I. Computational and Experimental Structural Parameters for 1.

   

D6h

   

D6h

D3h

D3

 

Parametere

BPW91/

d95(d)

B3PW91/

d95(d,p)

B3PW91/

d95(2df,2p)

MP2/

d95(d)

RHF/

dzv(2d,p)a

RHF/

dzv(2d,p)b

RHF/

dzv(2d,p)c

Exptald

                 

C1-C2

1.407

1.400

1.391

1.403

1.388

1.479

1.476

1.385

C2-C3

1.424

1.417

1.409

1.419

1.404

1.336

1.335

1.405

C1-C18

         

1.345

1.341

 

C17-C18

         

1.458

1.463

 

C1-C2-C3

124.2

124.1

124.2

123.9

124.0

124.0

123.8

 

C18-C1-C2

128.5

128.2

128.4

127.8

128.1

127.9

126.9

123.9

C17-C 18-C1

         

123.8

123.4

127.9

d(avg)

1.413

1.406

1.397

1.408

1.393

1.407

1.405

1.395

bond alt.g

0.0

0.0

0.0

0.0

0.0

13.0

13.3

0.0

rel. E

-

-

-

-

23.4

1.7

0.0

-

NMR H(exo)f

9.8

 

9.7

     

5.8

9.3

NMR H(endo)f

-13.8

 

-15.3

     

-2.3

-3

 

aStationary point with 1 imaginary frequencies (8782 I).

bStationary point with 3 imaginary frequencies (177.7 I, 177.7 I, 172.8 I).

cStationary point with a positive definite force constant matrix.

dGeometries from X-ray (reference 43), shifts from NMR (reference 46).

eparameter values are averages over symmetry equivalent types; distances in Å, angles in degrees, energies in kcal/mol, chemical shifts in ppm from TMS (computationally this is based on an extrapolation from the chemical shielding tensors for a reference set of compounds fit to their experiemental shifts).

fNMR calculations were done using the indicated geometry at BPW91/6-311G(df,p) for RHF and NLDFT methods, and B3PW91/6-311G(df,p) for hybrid DFT methods (reference 18).

gbond alt. = [avg. d(1-2), d(3-4), ..., d(17-18)] - [avg. d(2-3), d(4-5), ..., d(18-1)] in pm; for six-fold symmetry bond alt. is symmetry restricted to 0.

 

 

 

Table II. Computational Structural Parameters for 2.

Parametera

BPW91/

d95(d)

B3PW91/

d95(d,p)

RHF/

6-31G(2d,p)

RHF/

6-31G(2d,p)

     

'endo'

'exo'

         

C1-C2

1.426

1.429

1.334

1.460

C2-C3

1.405

1.385

1.473

1.339

C1-C18

1.383

1.365

1.443

1.326

C17-C18

1.459

1.462

1.348

1.496

C1-C2-C3

124.3

124.0

123.9

124.1

C18-C1-C2

130.5

130.1

130.4

130.0

C17-C18-C1

126.2

126.0

126.5

125.8

d(avg)

1.414

1.406

1.396

1.401

bond alt.b

4.7

6.8

11.4

14.2

rel. E

-

--

30.4

0.0

NMR H(exo)c

8.8

     

NMR H(endo)c

-6.0

     
         

aparameter values are averages over symmetry equivalent types; distances in Å, angles in degrees, energies in kcal/mol, chemical shifts in ppm from TMS (computationally this is based on an extrapolation from the chemical shielding tensors for a reference set of compounds fit to their experiemental shifts).

bbond alt. = [avg. d(1-2), d(3-4), ..., d(17-18)] - [avg. d(2-3), d(4-5), ..., d(18-1)] in pm; for six-fold symmetry bond alt. is symmetry restricted to 0.

cNMR calculation was done at the indicated geometry using BPW91/6-311G(df,p).

 

 

 

Table of Contents Insert

Higher order annulenes, such as [18]annulene, are finally managable by hybrid RHF/density functional ab initio computations. The structure, NMR chemical shifts,and stabilization energies of 1 and 2 are calculated and compared in this study.