*Corresponding author. Fax:#44-141-330-4888.E-mail address: brian@chem.gla.ac.uk (B. Webster).1Present address: Radiation Laboratory, University of Notre

Dame, Notre Dame, IN 46556, USA.

Physica B 289}290 (2000) 598}602

A theoretical investigation of the e!ect of a sodium cationon the proton}electron hyper"ne coupling constants of the

cyclohexadienyl radical and some consequences for themuonium-substituted cyclohexadienyl radical, C

6H

6Mu,

formed in zeolites

Brian Webster!,*, Roderick M. Macrae",1

!Chemistry Department, University of Glasgow, Glasgow, G12 8QQ, UK"Muon Science Laboratory, RIKEN, Wako, Saitama, Japan 351-0198

Abstract

The isotropic hyper"ne coupling constants A*40

for the protons in the cyclohexadienyl radical, C6H

7, are calculated

using ab initio molecular orbital methods. Taking all single excitations from a restricted open shell Hartree}Fockcon"guration, (CIS), the calculated value for A

*40at the methylenic protons is 93.0 MHz. The presence of a sodium cation

reduces A*40

for the methylenic proton of C6H

7on the same side of the ring as Na` by 18.2 MHz. For the other

methylenic proton the presence of Na` enhances the value of A*40

by 30.8 MHz and the C6H

7ring shows signi"cant

distortion. ( 2000 Published by Elsevier Science B.V. All rights reserved.

Keywords: Cyclohexadienyl radical; C6H

6Mu in zeolites

1. Introduction

There is a wealth of experimental data on themuonium-substituted cyclohexadienyl radicalC

6H

6Mu, formed by addition of muonium to ben-

zene in both gaseous and condensed phases [1}3].Although electronically identical with the radicalC

6H

7, the muonium label permits the detection of

the species by transverse "eld lSR spectroscopyand avoided level crossing resonance. It also per-turbs the radical's vibrational structure yieldingimportant information related to the dynamics ofintramolecular motion and how this motion is in-#uenced by the radical's environment. Current ex-perimental interest focuses upon the creation ofC

6H

6Mu radicals in various zeolites where the

radical is formed in an environment containingmetal cations [4,5].

The hyper"ne coupling constant, in particularthe isotropic component, A

*40, is commonly used to

investigate a radical's behaviour as a function ofexternal variables such as the temperature and

0921-4526/00/$ - see front matter ( 2000 Published by Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 9 1 - X

chemical environment. For muonium-substitutedradicals values for A

*40are usually scaled by

0.3141, the ratio of the proton and muon magneticmoments, to facilitate comparisons with the protonanalogues. For C

6H

6Mu in the liquid phase

at 25.13C the observed value of A*40

is 514.409(13)MHz for the muon and the reduced value, A@

*40,

is 161.591 MHz [2]. This compares with thevalue 134.6 MHz for the methylenic proton ofC

6H

7in the liquid phase at an ambient temper-

ature [6]. In the gas phase at 403C for C6H

6Mu the

reduced value, A@*40

, for the muon is 159.4 MHzwhile for the methylenic proton A

*40is 124.9 MHz

[3]. The purpose of this investigation is to obtaina rough estimate of the e!ect of a sodium cation inthe vicinity of C

6H

6Mu in a zeolite upon the values

of A@*40

for the muon and A@*40

for the methylenicproton.

2. Methods and results

2.1. The cyclohexadienyl radical

The cyclohexadienyl radical in its electronicground state has C

2vsymmetry and therefore has

a plane of symmetry coincident with the nodalplane of the ring p-system. The methylenic protonspositioned above and below this plane therefore arechemically equivalent. In the ground electronicstate the odd electron occupies a molecular orbitalcomposed solely of the 2p atomic orbitals centredat the ortho- and para-carbon atoms together with1s orbitals centred at the H atoms of the methylenicgroup. Using a 6-311G(p) basis an ROHF calcu-lation using the program GAMESS [7] indicatesthat the 2p orbital at the para carbon makes thedominant contribution to this SOMO at the equi-librium geometry. The isotropic component of thehyper"ne interaction A

*40is proportional to un-

paired spin density at a selected nucleus and for thiscase has a calculated value of 40.9 MHz at themethylenic protons. Accurate calculations of thehyper"ne interaction in C

6H

7are indeed scarce.

Chipman using the CIS approach, that is taking allsingle excitations from a restricted open shell Har-tree}Fock con"guration, obtained a result of96.7 MHz for A

*40at the methylenic protons [8].

More recently, Perera et al. using a coupled clustertechnique calculated a value of 116.6 MHz for thesame quantity [9].

Here using the program MELD [10] and theCIS approach with a 6-311G(p) basis, the cal-culated value for A

*40is 93.0 MHz at the methylenic

protons of C6H

7. Since this calculation only in-

volves single excitations from an ROHF referencecon"guration there is no proper consideration ofelectron correlation and one does not expect toobtain an exact agreement with the observed valuesfor A

*40. Obviously, taking all single and double

excitations, as in CISD, or including some tripleexcitations improves the wave function. Howeverwith a 6-311G(p) basis such calculations becomevery large and in view of the objective, to investi-gate the e!ect of Na` upon the values of A

*40for the

methylenic protons of C6H

7, we will proceed at the

CIS level. An alternative approach using the pro-gram Gaussian 98 [11] is to take a density func-tional approximation, like UB-PW91(Beckeexchange functional [12] with a Perdew and Wangcorrelational functional [13]). We are surprised to"nd that despite such approximations the cal-culated values of A

*40obtained by this method at all

of the protons in C6H

7are in very good accord

with observation, as is evident from Table 1. Thereasons for this agreement are not clear at presentand we include this result only for interest.

2.2. The species C6H7Na`

We consider now the e!ect of placing a Na` ionin the proximity of the C

6H

7ring taking the CIS

approach. Clearly, in real zeolite systems, otheraspects of the surroundings will also in#uence theradical's electronic structure and dynamics, eitherdirectly through intermolecular forces or indirectlyby perturbing the electronic structure of the metalion. However, this model system allows the use ofhigh-level computational techniques and shouldalso be su$cient at least qualitatively for futureconsiderations of vibrational e!ects.

The computed ROHF energy of C6H

7Na` at

the equilibrium geometry is !392.906067 hartree,which compared with a calculated energy of C

6H

7at its equilibrium geometry of !231.208589 har-tree and the energy of Na` equalling!161.664236

B. Webster, R.M. Macrae / Physica B 289}290 (2000) 598}602 599

Table 1Calculated values of the isotropic hyper"ne coupling constant, A

*40/MHz, for di!erent protons in the cyclohexadienyl radical C

6H

7and

the species C6H

7Na`.

Proton Exp.! UB-PW91 C6H

7ROHF C

6H

7CIS C

6H

7CIS C

6H

7Na`

C6H

76-311G(d,p) 6-311G(p) 6-311G(p) 6-311G(p)

A*40

(CH2) 134.6 139.2 40.9 93.0 123.8, 74.8

A*40

(o) (!)25.2 !24.2 0.0 !22.7 !22.7A

*40(m) 7.5 6.4 0.0 6.3 6.1

A*40

(p) (!)36.8 !31.9 0.0 !50.4 !49.5

!Ref. [6]

Fig. 1. The geometry of C6H

7Na` calculated at the ROHF

level.

hartree, indicates that C6H

7Na` is stabilised by

!0.033242 hartree or !87.3 kJ mol~1. Fig. 1shows the equilibrium structure calculated forC

6H

7Na` with the Na` ion situated o!-centre of

the ring, in a vertical plane containing the para-carbon atom, the methylenic carbon atom andNa`. The calculated internuclear distances are276 pm from Na` to the para-carbon atom and 328pm to the methylenic carbon atom and the inter-nuclear angle at Na` is 573. The dimensions of theC

6H

7ring are scarcely a!ected by the presence of

the ion and the C}H bonds of the ring and methyl-enic group hardly alter in length; compared witha methylenic C}H distance of 108.7 pm in C

6H

7the methylenic C}H distance for the bond on theopposite side to the ion increases to 108.8 pm andthat on the same side reduces to 108.4 pm. A keychange is the tilting of the para-carbon away fromthe Na`. Whereas for C

6H

7the distance from the

para carbon atoms to the methylene protons is 367

pm, in C6H

7Na` this distance is 355 pm to the

H on the opposite side of the ring to Na` and379 pm to the H on the same side as Na`. Tooversimplify, this geometrical e!ect could resultfrom electrostatic repulsion related to the fact thatsome of the carbon atoms have a slight increase innegative charge compared with the charges inC

6H

7and the hydrogen atoms a slight increase in

positive charge. Notably at the para carbon atom,where in C

6H

7the Mulliken population yields

a charge of !0.04 units and #0.03 units at theH in the para C}H bond, and these values alter to!0.12 units, and #0.10 units, respectively, inC

6H

7Na`. The calculated charge at Na` is #0.88

units.We see from Table 1 that the calculated values of

A*40

at all of the ring protons are hardly a!ected bythe presence of the cation. The #exing of the ring inC

6H

7Na` as we have seen brings a methylenic

hydrogen atom in closer proximity to the 2p orbitalcentred at the para carbon atom and this results ina distinction in the A

*40values calculated at the

methylenic protons. At the proton on the oppositeside to the cation the calculated value for A

*40is

123.8 MHz while for the proton on the same sideA*40

is 74.8 MHz, using a 6-311G(p) basis, whichcompares with a value of 93.0 MHz for the C

6H

7radical at the CIS level. For interest we add thattaking the UB-PW91 density functional approxi-mation yields similar results for the methylenicprotons though with higher computed A

*40values,

of 195 MHz and 102 MHz, respectively, inC

6H

7Na` compared with 139 MHz in C

6H

7.

These DFT studies will be described elsewhere inan investigation of the e!ect of complexation with

600 B. Webster, R.M. Macrae / Physica B 289}290 (2000) 598}602

2QuickTime animation showing a normal vibration ofC

6H

6Na` is viewable at: http://rmm.riken.go.jp/sta!/

RMM/cyclohex.html.

Na` and other metal ions on the normal modes ofC

6H

6Mu.2

3. Conclusions

The isotropic hyper"ne coupling constant for theprotons of the methylenic group of the cyc-lohexadienyl radical are signi"cantly altered by thepresence of an Na` cation. When an H atom issubstituted by Mu in the methylenic group ofC

6H

7it is well-known that there is a signi"cant

isotope e!ect on the value of A*40

. This is usuallyattributed to muon zero-point vibrational e!ectsthat increase the C}Mu distance. For this reasonthe methylenic site distant from Na` is likely to bepreferred by the muon. Clearly, however, the ob-served site ratio will also be in#uenced by forma-tion kinetics and ring-#ip rates. As theenhancement in A

*40due to Na` found here is

primarily electronic in origin, we can obtain roughestimates for the reduced muon and proton hyper-"ne coupling constants of bound C

6H

6Mu by cor-

recting the experimental gas-phase values using thedi!erence between the calculated CIS couplings forthe near and distant methylene protons inC

6H

7Na` and the calculated value for C

6H

7.

These di!erences are simply #30.8 MHz for theproton distant to Na` and !18.2 MHz for thenearside proton. Now taking the observed valuesfor C

6H

6Mu, Ref. [3], for Mu on the far side with

respect to Na` (likely to be the majority site), thereduced muon coupling of 159.4 MHz is enhancedby 30.8 MHz and A@

*40"190.2 MHz. Similarly, the

proton coupling of 124.9 MHz is decreased by18.2 MHz when A

*40"106.7 MHz. With Mu on

the near side A@*40

decreases to 141.2 MHz, andA

*40increases to 155.7 MHz. Since the CIS ap-

proach, de"cient of any proper treatment of elec-tron correlation, yielded a value of A

*40for C

6H

7which was lower than observed, perhaps these esti-mates should be regarded as lower limits. It will beinteresting to see how these rough estimates for

A*40

compare with the experimental investigationsin progress on C

6H

6Mu in sodium zeolites [5].

Acknowledgements

RMM acknowledges the award of a RIKENfellowship.

References

[1] E. Roduner, The Positive Muon as a Probe in Free Rad-ical Chemistry, Lecture Notes in Chemistry, Vol. 49,Springer, Berlin, 1988.

[2] D. Yu, P.W. Percival, J. Brodovitch, S. Leung, R.F. Kie#, K.Venkateswaran, S.F.J. Cox, Chem. Phys. 142 (1990) 229.

[3] D.G. Fleming, D.J. Arseneau, J. Pan, M.Y. Shelley, M.Senba, P.W. Percival, Appl. Magn. Reson. 13 (1997) 181.

[4] M. Stolmar, E. Roduner, J. Am. Chem. Soc. 120 (1998) 583.[5] D.G. Fleming, personal communication.[6] K. Eiben, R.H. Schuler, J. Chem. Phys. 62 (1975) 3093.[7] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert,

M.S. Gorgon, J.J. Jensen, S. Koseki, N. Matsunaga, K.A.Nyugen, S. Su, T.L. Windus, M. Dupuis, J. Montgomery,J. Comput. Chem. 14 (1993) 1347.

[8] D.M. Chipman, J. Phys. Chem. 96 (1992) 3294.[9] S.A. Perera, L.N. Salemi, R.J. Bartlett, J. Chem. Phys. 106

(1997) 4061.[10] E.R. Davidson, Quantum Chemistry Group, Indiania Uni-

versity, 1991; QCPE, program 580.[11] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria,

M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Mon-tgomery, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich,J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O.Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi,B. Mennucci, C. Pomelli, C. Adamo, S. Cli!ord, J. Och-terski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma,D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Fore-sman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A.Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L.Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng,A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W.Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres,M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian 98,Revision A.6, Gaussian Inc., Pittsburgh, PA, 1998.

[12] A.D. Becke, Phys. Rev. A 38 (1988) 3098.[13] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1982) 1324.

Comments

E. Roduner:I wonder whether the Na` cation is located in the symmetry planeperpendicular to the radical or whether it is owset in the direction

B. Webster, R.M. Macrae / Physica B 289}290 (2000) 598}602 601

of the ortho carbons. Secondly, did you calculate the bindingenergy of the cation?

M. Macrae:The Na` cation is owset by a small amount towards the para carbonin the optimized geometry, in other words away from the methylene

group. The binding energy was not explicitly calculated, butfrom the low frequency of the radical-ion stretching modes (such asthe **trampoline++ mode at about 186 cm~1) it appears that thepotential well is fairly shallow.

602 B. Webster, R.M. Macrae / Physica B 289}290 (2000) 598}602