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Journal of Molecular Structure: THEOCHEM 851 (2008) 313–318

Quantitative study and visualization of spherical 2(N + 1)2

homoaromaticity by through space NMR shieldings (TSNMRS)

Erich Kleinpeter *, Andreas Koch

Chemisches Institut, Universitat Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Golm, Germany

Received 26 October 2007; received in revised form 20 November 2007; accepted 20 November 2007Available online 14 January 2008

Abstract

The through space NMR shielding (TSNMRS) values of adamantane, the 2(N + 1)2 spherical (4c,2e) homoaromatic compounds1,3-dehydro-5,7-adamantandiyl dication (C10H12

2þ) and 1,3-dehydro-5,7-cubandiyl dication (C8H42þ), and the (6c,8e) homoaromatic

compound 2,2 0,4,4 0,6,6 0,8,8 0,10,10 0-dehydroadamantane tetracation (C10H44þ) have been ab initio calculated, employing the NICS

concept, and visualized as iso-chemical shielding surfaces (ICSSs). TSNMRS values can be successfully employed to study both theendohedral and exohedral aromaticity/antiaromaticity of the compounds studied.� 2007 Elsevier B.V. All rights reserved.

Keywords: Through space NMR shielding values; Ab initio calculation; GIAO; NICS; Spherical aromaticity

1. Introduction

The 2(N + 1)2 electron counting rule can be used to pre-dict the aromaticity of the three-dimensional delocalized sys-tems with near spherical geometry [1–3]. Following thisconcept, the spherical homoaromaticity of the systems withtwo (N = 0) and eight (N = 1) mobile electrons of theadamantane and cubane skeletons have been studied [4].It was found out that, among the systems studied, 1,3-dehy-dro-5,7-adamantandiyl dication (C10H12

2þ) 2 and 1,3-dehydro-5,7-cubandiyl dication (C8H4

2þ) 3 (four-center

two-electron systems – 4c,2e), and 2,2 0,4,4 0,6,6 0,8,8 0,10,10 0-dehydroadamantane tetracation (C10H4

4þ) 4 (six-centereight-electron system – 6c,8e) were characterized as stronglyaromatic by their highly negative NICS values at thecenters of the molecules (2 – 49.5 ppm, 3 – 38.1 ppm and 4

– 60.4 ppm), cf. Scheme 1 [4].The NICS values [5] on a grid around the molecules

can be calculated as well to provide an insight aboutthe diatropic and paratropic regions of the molecules

0166-1280/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2007.11.029

* Corresponding author. Tel.: +49 331 977 5210; fax: +49 331 977 5064.E-mail address: kp@chem.uni-potsdam.de (E. Kleinpeter).

[6]; these through space NMR shieldings (TSNMRS) werevisualized [7] as iso-chemical-shielding surfaces (ICSSs)and employed to study the aromaticity of planar[8] as wellas the aromaticity/antiaromaticity of spherical system-ful-lerenes [9].

Of significant note though, there have been some recentdevelopments of NICS [5] showing that none of the variousmethods can safely assign aromaticity [10] and nonmeasur-able parameters have proven generally to be not generallysuitable for quantitative evaluation of aromaticity [11]. Inaddition, the conventional interpretation of deshielded 1Hchemical shifts for aromatic protons has proven to bedue to reasons other than deshielding ring current effects[12] and thus they are not reliable indicators of aromaticityas well [13]. For example, NICS analysis was shown to leadto an incorrect prediction of aromaticity for the cyclop-ropenyl anion [14].

The goal of this study was to calculate the TSNMRSvalues for the cations 2–4 (and adamantane 1 as a ref-erence compound, cf. Scheme 1) in order to visualizeand determine quantitatively both the endo- and exohe-dral shielding/deshielding regions of the spherical sys-tems 1–4.

-1.0

0.0

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netic

shi

eldi

ng-1.0

0.0

1.0

2.0

3.0

4.0

Mag

netic

shi

eldi

ng

Fig. 2. Variation of the through space NMR shielding with the distancefrom the center of adamantane 1 through the C–H bonds of thebridgeheads (–r–) and through the 6-membered rings middle points(–j–).

2+

4+H

HH

H

HH

HH

H H

HH

HH

HH

H

HH

H

H

HH

H H

HH

HH

H H

HHH

H

2+

1 2

3 4

Scheme 1. Compounds studied.

314 E. Kleinpeter, A. Koch / Journal of Molecular Structure: THEOCHEM 851 (2008) 313–318

2. Results and discussion

First, as a kind of reference, the TSNMRs values of ada-mantane were calculated and visualized as ICSS in Fig. 1.In addition, NICS values on the lines starting from the cen-ter of adamantane (NICS �1.1 ppm shielding) and movingthrough the C–H bridgehead protons (Fig. 2, upper plot)and the middle points of the 6-membered rings (Fig. 2,lower plot) were also calculated. The endohedral region isshielded up to 2.3 ppm (at ca. 1.2 A). Exohedral of theadamantane carbon cage, regions of both shielding(ICSS = 0.1 ppm at ca. 4.4 A) and deshielding (ICSS =

Fig. 1. Visualization of the through space NMR shielding cones of adamantaneand red +0.1 ppm deshielding). (For interpretation of the references to colour i

�0.1 ppm at 4.9 A), respectively, are observed; the effects,however, are rather small, comparable with the anisotropiceffect of the C–C single bond, calculated by the samemethod.[15] This behavior proved to be different subjectto endohedral and exohedral TSNMRS values in thecharged species 2–4.

The TSNMR shielding behavior on the surface of theadamantyl dication 2(C10H12

2þ) does change (cf. Figs. 3

1 as iso-chemical-shielding surfaces (yellow represents �0.1 ppm shieldingn this figure legend, the reader is referred to the web version of this paper.)

Fig. 3. Visualization of the through space NMR shielding cones of 1,3-dehydro-5,7-adamantandiyl dication (C10H122þ) 2 as iso-chemical-shielding surfaces

(yellow represents �0.1 ppm shielding and red +0.1 ppm deshielding). (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this paper.)

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Fig. 4. Variation of the through space NMR shielding with the distancefrom the center of 1,3-dehydro-5,7-adamantandiyl dication (C10H12

2þ) 2

through the sp2 carbon atoms (–j–) and through the 6-membered ringsmiddle points (–r–); lower two graphs are expansions of the top graph.

E. Kleinpeter, A. Koch / Journal of Molecular Structure: THEOCHEM 851 (2008) 313–318 315

and 4) with respect to both the sign and direction of theICSSs as compared with adamantane: ICSSs of �0.1 ppm(shielding) from the center through the sp2 carbon atomsat 3.9 A and ICSS = 0.1 ppm (deshielding) from the centerthrough the 6-membered ring middle points at 4.5 A,respectively, were obtained (cf. Figs. 3 and 4). Endohedral-ly, however, dramatic changes due to the spherical aroma-ticity of C10H12

2þ were found and visualized in Fig. 4: Thestrong aromaticity at the center [4] (NICS = �49.8 ppm)remains almost constant until reaching the walls (van derWaals radii of carbon atoms); with the distance from thecenter of the molecule through the 6-membered ring middlepoints (cf. Fig. 4) it drops gradually reachingICSS = �0.1 ppm at ca. 4.5 A. On the other hand, themagnetic shielding decreases with the distance from thecenter of the dication 2 through the sp2 carbon atoms sothat it crosses the zero line, reaches the minimum at ca.3.1 A and finally approaches zero at ca. 3.9 A(ICSS = 0.1 ppm). At the largest extension the deshieldingis as low as 0.14 ppm.

The TSNMRS values as visualized as ICSSs of thestructurally similar homoaromatic 4c,2e and 6c,8e com-pounds C8H4

2þ 3 and C10H44þ 4, respectively, look very

similar but different from 1 and 2, respectively (cf. Figs.5–8). Endohedrally, the spherical aromaticity proveddifferent[4] (NICS at center �38.1 ppm – 3 and�60.4 ppm – 4), but, as in 2, it remains almost con-stant until reaching the walls; after crossing the carbonvan der Waals radii, it drops gradually (cf. Figs. 6 and8). External of the carbon cages, 3 and 4 exhibit thesame but stronger anisotropic behavior as comparedwith 1 and 2 (cf. Figs. 5 and 7): a deshielding wasfound moving from the center through the C–H bonds[ICSS = 0.1 ppm at 5.9 A (3) and 8.3 A (4)], whereas ashielding was observed moving through the 4-memberedrings in 3 and the 6-membered rings middle points in

Fig. 5. Visualization of the through space NMR shielding cones of 1,3-dehydro-5,7-cubandiyl dication (C8H42þ) 3 as iso-chemical-shielding surfaces (yellow

represents �0.1 ppm shielding and red +0.1 ppm deshielding). (For interpretation of the references to colour in this figure legend, the reader is referred tothe web version of this paper.)

-5

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35

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Fig. 6. Variation of the through space NMR shielding with the distancefrom the center of 1,3-dehydro-5,7-cubandiyl dication (C8H4

2þ) 3 throughthe sp2 carbon atoms (–j–) and through the 4-membered rings middlepoints (–r–); lower two graphs are expansions of the top graph.

316 E. Kleinpeter, A. Koch / Journal of Molecular Structure: THEOCHEM 851 (2008) 313–318

4, respectively, [ICSS = �0.1 ppm at 4.8 A (3) and 8.0 A(4)] (cf. Figs. 5–8). Deshielding proves to be strongestat 3.6 A being 0.8 ppm in 3 and 2.5 ppm in 4. In termsof spherical aromaticity, the 4c,8e homoaromaticity of4 proves, as expected, to be stronger than the 4c,2ehomoaromaticity of 3. This is true both for the endohe-dral [4] and the exohedral regions of the carbon cages.From the illustrative point of view, the visualization ofthe shielding/deshielding regions, as illustrated by thecorresponding ICSSs external of the studied carboncages, looks even more impressive (cf. Figs. 5and 6).

The adamantyl dication C10H122þ 2 proves to be the

only one of the studied ions 2–4,[16]which was synthe-sized and whose magnetic properties were measured:its protons resonate at d 3.8 ppm and the 13C chemicalshift of the quaternary carbons, sharing the positivecharges, is shifted upfield to 6.6 ppm (the CH2 carbonsresonate at 35.6 ppm). The spectra were recorded insevere conditions (superacid media, external TMS); thechemical shifts, calculated for the gas state [d(1H)2.8 ppm; d(13C) 4.8 and 36.2 ppm, respectively], are ingood agreement already at this level of theory; 13Cchemical shifts probably deviate from the experimentbecause the chemical shift of internal TMS in superacid,as a reference, is unknown. However, if considering thedifference [29 ppm (exp.) and 31.4 ppm (calc.)] the agree-ment is fine.

Employing the same approach, we calculated thechemical shifts d(1H) of 10.3 ppm and d(13C) of 103.1and 41.5 ppm, respectively, for 3, and d(1H) of13.9 ppm and d(13C) of 81.1 and 31.7 ppm, respectively,for 4. Both the 1H and 13C NMR spectra of 3 and 4

prove to be dramatically different from those of 2. Itwould be a challenge to synthesize 3 and 4 and to checktheir NMR spectra.

Fig. 7. Visualization of the through space NMR shielding cones of 2,2 0,4,4 0,6,6 0,8,8 0,10,10 0-dehydroadamantane tetracation (C10H44þ) 4 as iso-chemical-

shielding surfaces (yellow represents �0.1 ppm shielding and red +0.1 ppm deshielding). (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this paper.)

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Fig. 8. Variation of the through space NMR shielding with the distancefrom the center of 2,2 0,4,4 0,6,6 0,8,8 0,10,10 0-dehydroadamantane tetraca-tion (C10H4

4þ) 4 through the sp2 carbon atoms (–j–) and through the6-membered rings middle points (–r–); the lower two graphs areexpansions of the top graph.

E. Kleinpeter, A. Koch / Journal of Molecular Structure: THEOCHEM 851 (2008) 313–318 317

3. Computational details

The quantum chemical calculations were carried outusing the GAUSSIAN 03 program package [17]. All com-pounds were fully optimized using the FCMP2/6-31G*

level of theory [18]. Nucleus-independent chemical shift(NICS in ppm) [19] values were computed on the basis ofMP2/6-31G* geometries of 1–4 using the GIAO methodat the HF/6-31G* theory level [20]. To calculate the NICS,ghost atoms were placed on a lattice of �10 to +10 A witha step size of 0.5 A in the three directions of the Cartesiancoordinate system. The zero points of the coordinate sys-tem were positioned at the centers of the carbon cages in1–4. The resulting 68000 NICS values, thus obtained, wereanalyzed and visualized by the SYBYL7.2 [21] molecularmodeling software; two different iso-chemical-shieldingsurfaces (ICSSs) of �0.1 ppm shielding (yellow) and 0.1deshielding (red) were used to visualize the through spaceNMR shieldings (TSNMRS) both endohedral and externalof the carbon cages of 1–4. All calculations were carriedout on SGI workstations.

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[16] M. Bremer, P.v.R. Schleyer, K. Schotz, M. Kausch, M. Schindler, M.Angew, Angew. Chem., Int. Ed. Engl. 26 (1987) 761.

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[18] C. Møller, M.S. Plesset, Phys. Rev. 46 (1934) 618.[19] P.von R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.J.R. von E.

Hommes, J. Am. Chem. Soc. 118 (1996) 6317.[20] The lattice points (‘‘ghost atoms’’) should be sensor points only

without energy contribution in the present calculations. Only if HFcalculations are applied this proved to be true; in case of electroncorrelation calculations, the ‘‘ghost atoms’’ get their own electrondensity and are of some influence on the energy of the studiedmolecule hereby. In these cases the TSNMRS surfaces proved to getheavily distorted.

[21] SYBYL 7.2 Tripos Inc. 1699 South Hanley Road, St. Louis, Missouri63144, USA, 2006.