www.elsevier.com/locate/chemphys

Chemical Physics 310 (2005) 85–96

Vibrational spectra of methyllithium and its aggregates: anew interpretation from ab initio anharmonic calculations

Neil Gohaud, Didier Begue *, Claude Pouchan *

Laboratoire de Chimie Structurale, UMR 5624, FR2606 IPREM, Universite de Pau et des Pays de l�Adour, IFR, Rue Jules Ferry,

BP27540, 64075 Pau Cedex, France

Received 5 July 2004; accepted 4 October 2004Available online 18 November 2004

Abstract

The complete quartic force field of methyllithium (CH3Li) is computed at the B3LYP/cc-pVTZ level of theory. The vibrationalenergy levels calculated from a perturbational and a variational procedure are in agreement with the observed spectra except for theC–Li stretching and the symmetric methyl deformation modes for which a disagreement with the experimental assignment given byAndrews is apparent. This discrepancy between experiment and theory is so large that questions are raised either about a correctcharacterization of, or correct calculations for the monomeric species CH3Li. Our theoretical study of methyllithium aggregates(CH3Li)n, with n = 2,3,4 and 6, gives a new interpretation of the experimental data.� 2004 Elsevier B.V. All rights reserved.

1. Introduction

The characterization of methyllithium (CH3Li) hasbeen causing problems for well one 40 years. In 1961,West et al. [1] took up the study of the infrared spectrumof CH3Li because of disagreements in earlier studies.Their work extended the IR domain to between 300and 4000 cm�1 and completed this by the study of iso-topic substitutions, which is needed for an accurateassignment. Their study clearly showed several errorsin the assignments in previous work, mainly for the C–Li stretching mode: 514 versus 1052 cm�1 [2] or 880cm�1 [3]. Moreover, authors also observed a set of unex-pected frequencies that are abnormally low. As organo-metallic compounds have a tendency to aggregate (evenin the gas phase [4–7]), this observation was rationalizedby possible aggregation of the methyllithium molecules.

0301-0104/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2004.10.016

* Corresponding authors. Tel.: +33 5 59 78 40 52; fax: +33 5 59 7840 62.

E-mail addresses: didier.begue@univ-pau.fr (D. Begue), claude.pouchan@univ-pau.fr (C. Pouchan).

In order to avoid aggregation, Andrews and co-workers[8,9] proposed an experimental protocol which made itpossible to produce monomeric methyllithium, by con-tinuous reactions between methyl radicals and lithiumatoms, and recording the IR spectrum in a 15 K argonmatrix. Up to now, this experimental technique has be-come the standard procedure to generate the methyllith-ium monomer [8], mainly because it takes care of allspecies in the matrix, their concentrations, their isotopiccompositions and intensities of observed bands.

Unlike bench scientists, theoretical chemists have theluxury of studying any molecule that interests them, asthere are none of the practical issues that an experi-mentalist must faces. Nevertheless, theoretical chemistshave to choose carefully the computational conditions,so that they can describe accurately the desired proper-ties of the system. In the methyllithium case, there is,as far as we know, only one full theoretical vibrationalattempt recently published [10]. It deals with referencecalculations on the structural parameters and the har-monic frequencies obtained at the CCSD(T)/cc-pVQZ+aug(C) level. If the optimized geometry of the

86 N. Gohaud et al. / Chemical Physics 310 (2005) 85–96

molecule is in perfect agreement with the experimentalvalues recently obtained from the microwave spectra[11] (where only polar molecules can be detected; inthis case only the monomer meets this criterion), it isabsolutely not the case if one studies the vibrationalproperties, particularly if one focuses on both stretch-ing (C–Li) and deformation (CH3) modes. Althoughtheoretical frequencies obtained with the harmonicapproximation cannot be compared directly with theexperimental ones, this discrepancy between experimentand theory is large enough to question the correctcharacterization of the molecule. This discrepancy ledBreidung and Thiel [10] to carry out anharmonic calcu-lations. These computations were performed with useof a perturbational method, in which all appropriateinteractions are included, either perturbationally (inthe majority of cases) or by explicit matrix diagonaliza-tion when tests indicate that the perturbational treat-ment is no longer appropriate (i.e., in the case ofresonances). Their conclusion is essentially that reliablegas-phase values of the fundamental frequencies formonomeric methyllithium are needed. Neither calcula-tions on any of the isotopic species, namely, 12CH3Li,13CH3Li, CH3

6Li, CH37Li and their deuterium iso-

topes, nor taking account of the anharmonic correc-tions, which is known to be essential for thedescription of the C–H stretching modes, offer satisfac-tory explanations for the atypical discrepancies be-tween experiments and theory.

In this paper, after a brief presentation of the compu-tational methods used, we present the main theoreticaland experimental results currently known for themedium-size and controversial methyllithium system.Because of the unusually large differences and in orderto resolve the atypical experiment/theory discrepancy,we also present in the same section a complete vibra-tional anharmonic study of monomeric methyllithium.As organometallic compounds have a strong tendencyto aggregation, we present structural and harmonic re-sults for (CH3Li)n (n = 2,3, . . ., 6) clusters. In the light

Fig. 1. Internal and symmetry

of these results, a new interpretation of the experimentaldata is proposed at the end of this paper.

2. Computational methods

The calculation of molecular vibrations generally re-quires two steps: the first is the determination of ananharmonic potential function and, once the latter isdetermined, the second concerns the resolution of theSchrodinger vibrational equation for the system underconsideration.

For systems in which anharmonicity is small, it ispossible to write the potential function as a Taylorexpansion series in terms of curvilinear displacementcoordinates. This expansion series is often limited atthe fourth order. Quadratic, cubic, and quartic forceconstants are generally obtained either by fitting theelectronic energy data calculated by ab initio methodsfor various nuclear configurations close to the optimizedgeometry, or by a finite difference procedure for first orsecond derivatives of the electronic energy with respectto the nuclear coordinates. In both cases, the requirednumber of ab initio data points grows drastically withincreasing size of the molecule, so that it becomes diffi-cult to determine accurately a complete quartic forcefield for systems without symmetry containing morethan four atoms [12]. In order to reduce the number ofcalculations, we used in this work the procedure imple-mented in our code REGRESS EGHREGRESS EGH, the details of whichare described elsewhere [13,14]. Briefly, the strategy con-sists of including in the same process of linear regressionthe value of the energy and the corresponding first ana-lytical derivatives obtained at each point of a well-suitedgrid. In this way, for a five-atom molecular system with-out symmetry, 176 (energy + gradient) calculations interms of points (there is a redundancy nearly equals totwo corresponding to deformed geometric structures)are necessary for the complete determination of thequartic force field, i.e., 714 independent parameters.

coordinates for CH3Li.

N. Gohaud et al. / Chemical Physics 310 (2005) 85–96 87

Due to the C3v symmetry of CH3Li, only a set of six dis-placement coordinates (Fig. 1) were chosen for deter-mining the 152 independent and non-null forceconstants of the potential function [15]. In this case,about 40 (E + G) calculations in a well-suited simplexsum grid are required to obtain, from a generalizedleast-squares fitting, the complete quartic force field.

Calculations were carried out with use of Dunningcorrelation consistent pVTZ cartesian basis set [16].For geometry and harmonic wavenumber determinationCCSD(T) and CASSCF calculations were undertaken,for comparison with the DFT results and the experimen-tal data. The Becke [17] three-parameter exchange func-tional (B3) in combination with the Lee Yang and Parr[18] (LYP) correlation functional was used to describeCH3Li and five of its aggregates. Geometry optimiza-tion, energies and analytical first derivatives were ob-tained with use of the GAUSSIAN 98 suite ofprograms [19].

Regarding the treatment of the Schrodinger vibra-tional equation, the most common method found inthe literature is the perturbational approach [20]. Theprocedure is simple but the results are sensitive, in par-ticular with regard to the study of resonances such as,for example, Fermi�s and Darling-Denisson�s [21,22].Generally, when these last are not too significant, theseconditions of calculation are sufficient for determining(from a highly correlated wave functions by using atleast a triple f basis set) the position of the entire funda-mental and combination bands present in the mediumIR spectrum of small organic compounds with errorsof less than 2%. The Van Vleck perturbation theory,which was developed thereafter by Nielsen for the treat-ment of the ro-vibronic states, and the standard Ray-leigh–Schrodinger theory are the most common.Whichever the perturbational approach used, the gen-eral energy formula for the case of doubly degeneratevibrations as in CH3Li leads to the following truncatedDunham expansion:

Ev ¼Xs

xs vs þ1

2

� �þXt

xtðvt þ 1Þ

þXsPs0

xss0 vs þ1

2

� �vs0 þ

1

2

� �

þXs;t

xst vs þ1

2

� �ðvt þ 1Þ

þXtPt0

xtt0 ðvt þ 1Þðvt0 þ 1Þ þXtPt0

gtt0‘t‘t0 þ � � �

where x represents the harmonic frequency, the indices sand t refer to the non-degenerate and doubly degeneratemodes, respectively, ‘ the vibrational angular quantumnumber, x and g the anharmonicity constants that de-pend on cubic and quartic force constants, respectively.

These relations were generalized by various authors suchas Mills [23], Pliva [24] and recently validated by Willetsand Handy [20].

For a more comprehensive treatment, it is possibleto use a variational approach. However, for systemscontaining more than five atoms, it is generally difficultto use this solution because the treatment of the gigan-tic CI matrices is required. Recently, an intermediatesolution has been proposed that consists of the use ofmixed variation-perturbation methods [25,26], whichselect iteratively the vibrational states by using the per-turbation method in a reduced space that contains theuseful information. Nowadays, it is possible, thanks tothe development of average data processing, to workwith the whole vibrational information and thendevelop pure variational methods for the treatment ofmedium size systems. It is, on the other hand, neces-sary to optimize the variational algorithm in a differentway [27]. This approach consists of taking an inventoryof the vibrational states potentially needed for thedescription of the problem, taking into account thesymmetry of each state, and cutting the process intospectral windows. Consequently, the size of the matri-ces to be used is much reduced. In the case of CH3Li,although the number of vibrational states is very large,it is possible to treat the full space, thus variationalybuild in the active configurations basis. The spectralarea studied was cut into seven spectral windows gath-ering a few hundred states per window; thus, the size ofeach matrix to be diagonalized does not exceed 15,000configurations to obtain the 50 first converged eigen-values with an accuracy of 1 cm�1.

3. Results and discussion

3.1. Calculated geometry and harmonic wavenumbers in

connexion with experimental data

For more than 20 years, there has been debate overthe bonding structure of CH3Li, more precisely aboutthe nature of the C–Li bond [28,29]. From an experi-mental point of view, only two references exist aboutthe structure of CH3Li, namely, an infrared work [9],which estimates the C–Li bond length as 2.10 A, and amore recent work [11] dealing with microwave spectros-copy, where authors found an effective r0 bond length of1.959 A. From a theoretical point of view, it is impor-tant to notice that, whatever method or basis set chosen(Table 1), all the results are in very close agreement withthe microwave study ones.

Only the use of a poor quality basis set (DZVP) [32]leads to sizable overestimation of the C–Li bond length(about 3.5%), which is, nevertheless, within the experi-mental errors and not nearly as large as the discrepancyof results reported in the IR study [9]. Between our

Table 2Calculated harmonic vibrational frequencies (cm�1) at various levels oftheory

Methods x6 x3 x2 x5 x1 x4

B3LYP/6-311++G** [29]

466 630 1094 1453 2966 3028

B3LYP/6-311+G*[29] 449 628 1137 1478 2950 3005MP2/6-311G* [6] 462 628 1164 1510 3021 3106MP2/cc-pVTZ [30] 449 632 1096 1463 3028 3107MP2/cc-pVQZ+aug(C,H) [10]

433 628 1084 1456 3017 3102

CCSD(T)/cc-pVQZ+aug(C) [10]

430 628 1097 1452 2961 3031

CCSD(T)/MT(ae) [10] 435 640 1111 1459 2982 3050CASSCF(8/8)/6-311++G** [29]

465 576 1127 1486 2882 2956

CASSCF(8/8)/cc-pVTZ

448 591 1134 1485 2873 2943

CASSCF(10/13)/cc-pVTZ

432 611 1113 1410 2891 2938

CCSD(T)/-cc-pVTZ+aug(C) 425 624 1097 1451 2957 3023CCSD(T) all electron/cc-pVTZ+aug(C)

419 649 1103 1457 2986 3022

B3LYP/cc-pVTZ+aug(C) 427 632 1085 1445 2962 3016

Table 1Structural parameters for CH3Li; the values in the parentheses refer tothe use of augmented basis sets

Method/basis set rC–Li (A) rC–H (A) hHCH (�)

MP2 (all electron)/6-31+G* [7]

2.005 1.099 107.3

MP2/6-311G* [31] 1.994 1.099MP2/cc-pVTZ [30] 1.984 1.092 106.4B3LYP/DZVP [32] 2.030CCSD(T)/cc-pVQZ+aug(C) [10]

1.982 1.099 105.9

HF/cc-pVTZ+aug(C) 1.983 (1.985) 1.092 (1.092) 106.1 (106.3)CASSCF (8/8)/cc-pVTZ

2.025 1.112 106.5

CASSCF (10/13)/cc-pVTZ

1.998 1.111 105.7

B3LYP/cc-pVTZ+aug(C)

1.964 (1.965) 1.097 (1.097) 106.2 (106.2)

CCSD(T) all electron/cc-pVTZ+aug(C)

1.959 (1.959) 1.097 (1.097) 106.5 (105.7)

Exp: (deduced from)IR [9]

2.10 1.12

Exp: (effective r0)microwaves [11]

1.959 1.111 106.2

88 N. Gohaud et al. / Chemical Physics 310 (2005) 85–96

theoretical results (DFT B3LYP/cc-pVTZ and ab initioCCSD(T)/cc-pVTZ+aug(C)) and the CCSD(T)/cc-pVQZ+aug(C) one of Breidung and Thiel (Table 1),the average difference is less than 0.02 A. It is establishedthat, for a small molecular system, the precision of cal-culations obtained at the CCSD(T)/cc-pVXZ (X = T,Q) or similar level is about 0.015 A in comparison withexperimental data. We observe only a 0.005 A differencebetween our theoretical results and the microwave data

(effective r0 structure), thereby justifying the choice ofthe DFT method for the C–Li bond description.

One of the present problems about the spectroscopiccharacterization of methyllithium is that the experimen-tal reference put the C–Li stretching mode m3 at 530cm�1, a position that is lower by more than 100 cm�1

in comparison with all the best previous harmonic calcu-lations (Table 2).

Thirty years after the first IR detection, CASSCF(8/8)/6-311++G** calculations by Bare et al. [29] reportedan harmonic estimation of 576 cm�1, which is quiteatypical among all theoretical calculations (Table 2).Nevertheless, although this value is the closest to theexperimental one reported in argon matrix, it can notbe taken into account according to the followingreasons:

• First, the debate over the C–Li bond leads us toconsider the possibility of a mix between covalentand ionic character, which might justify the use ofa multiconfigurational method such as CASSCF.However, our results show that, whatever theCAS chosen, the total wave-function describingthe monomer is always developed for more than93% on one configuration, which corresponds tothe most stable state; thus, the use of such amethod is not really necessary.

• Second, it is well known that small size CASSCF (8/8in this case) wave functions predict too large bonddistances (2.025 A [29]) because they only correctthe dissociative behaviour of the system. LargerCASSCF (10/13 in our work) expansions involveconfigurations providing a better balance betweenbonding and anti-bonding effects, with as a resultmore reasonable values of the bond distance (1.998A; see Table 1). Then, it is this overestimation onrLi–C (which leads to an underestimation of the x2

harmonic vibration) that has led authors [29] to thinkthat CASSCF calculations were the first step to agood theoretical description of the C–Li bond andits corresponding vibrational mode.

Still about the m3 mode, it is significant to specifythat Grotjahn et al. [11] have recently estimated theC–Li stretching wavenumber in CH3Li from the ob-served rotational data to be 670 cm�1. This estimateis more in conformity with those obtained startingfrom ab initio calculations. Lastly, the harmonicstretching wavenumber of HCCLi [33] (a moleculefor which experimental data are quoted in [33]) wasestimated near 665 cm�1, i.e., in the same theoreticalpredicted area as for CH3Li. Many arguments there-fore seem to confirm the validity of our theoreticaldata.

More generally, for the whole of the fundamentalbands (Table 3), whatever the basis set used, B3LYP

Table 4B3LYP/cc-pVTZ anharmonic force field of CH3

7Li

/666 �372.84 /6666 �858.00 /2244 6.12/366 33.82 /3666 27.48 /2555 �9.54/266 229.60 /2666 89.76 /1255 5.08/566 �158.22 /5666 265.56 /1245 4.34/166 �100.82 /1666 108.42 /1112 57.00/466 �64.42 /4666 23.58 /2444 24.30/356 10.47 /3366 �28.76 /5555 70.80/346 �20.33 /2266 �101.00 /1555 �5.94/256 41.03 /2566 �73.20 /4555 23.10/246 45.27 /2466 6.80 /4455 10.24/556 �23.72 /5566 �12.84 /1145 12.02/156 70.58 /1566 �50.38 /1445 4.90/456 �7.38 /4566 10.70 /4445 21.00/146 102.99 /1166 �7.60 /1111 224.40/446 �20.18 /1466 �14.04 /1144 335.76/333 �249.54 /4466 8.00 /1444 151.74/233 43.22 /2356 �4.64 /4444 466.56/133 10.84 /3556 �4.84/223 �16.38 /2256 56.12/123 �5.00 /2246 �9.10/355 18.48 /2556 4.68/222 362.40 /2446 �14.30/122 �61.48 /5556 �45.60/255 �72.12 /1556 15.66/245 �15.04 /4556 26.60/112 �117.72 /4456 �7.28/244 �142.76 /1146 �11.96/555 224.68 /4446 �14.10/155 �72.82 /3333 88.08/455 26.60 /2333 �16.80/145 �71.78 /1333 �6.24/111 �1079.52 /2222 �34.32/144 �1116.90 /2255 21.56/444 �780.66 /1122 24.56

Constants are expressed in cm�1. Only cubic force constants over 6cm�1 and quartic constants over 4 cm�1 are reported.

Table 3Calculated harmonic vibrational frequencies (cm�1) for CH3Li and three of isotopotomers

Modes CH3Li CD3Li CH36Li 13CH3Li

Exp. [9] aug-ccpVTZ ccp-VTZ Exp. [9] ccp-VTZ Exp. [9] ccp-VTZ Exp. [34] ccp-VTZ

CCSD(T) CCSD(T) all electron B3LYP B3LYP B3LYP B3LYP B3LYP

x6 408 425 419 428(162) 435(178) 319 334(141) 411 437(186) – 432(174)x3 530 624 649 630(26) 631(23) 510 611(24) 558 666(25) � 624(22)x2 1158 1097 1103 1086(3) 1092(13) 883 839(2) 1158 1092(13) – 1085(14)x5 1387 1451 1457 1445(4) 1450(6) 1027 1052(0) 1387 1450(6) 1383 ± 2 1447(7)x1 2780 2957 2986 62964(81) 2961(77) 2030 2122(38) 2780 2961(77) – 2958(77)x4 2820 3023 3022 3021(44) 3019(46) – 2229(12) 2820 3019(46) – 3009(48)

The IR intensities (km/mol) are included in parentheses.

N. Gohaud et al. / Chemical Physics 310 (2005) 85–96 89

harmonic results are in good agreement with theCCSD(T) results.

In order to confirm this conclusion, several comple-mentary calculations have been made. First, we have ta-ken into account the electron core/valence interactions,which need to be considered when an alkali atom be-longs to the system, and we have seen that CCSD(T) cal-culations with only eight valence electrons gave the sameresults as CCSD(T) and B3LYP with all electrons (Table3). In addition, as Breidung and Thiel [10] showed,changes of the harmonic wavenumbers with the use ofcc-pVXZ (with X = T or Q) basis sets are quite small(about 3–4 cm�1 in absolute value). Moreover, we canobserve for CH3Li that increasing the basis sets withmore diffuse functions is only justified for an extensiveknowledge of the relative intensities. In this case, no ma-jor modification is noticeable (Table 3), except for theintensity of the x2 mode, which differs in a quantitativeway. However, the computed intensity of this mode isvery low. Finally, the frequency and intensity resultsfor the three 13CH3Li, CH3

6Li and CD3Li compoundsare also calculated and follow exactly the same behav-iour, i.e., a problematic assignment of both m2 and m3modes.

In conclusion, the discrepancy between theory andexperiment cannot be explained by the inability ofDFT methods to take into account the ionic characterof chemical bonds where there is a strong electropositiveatom such as lithium as suggested in [29]. The B3LYPmethod with a triple f basis set is perfectly appropriatefor this study.

3.2. Anharmonic study for CH3Li

First, calculations of harmonic frequencies are al-lowed thanks to quadratic force constants which aredetermined by a second-order linear regression of a 24points twice redundant grid calculated in the space ofthe internal coordinates of symmetry. Taking into ac-count the symmetry of the molecule and starting fromthe relations of Henri and Amat [35], the approximation[36] which consists [14] to consider only the three coor-

dinates a1 and the three components ex of the doublydegenerated modes mentioned in Fig. 1 to describe com-pletely the harmonic and anharmonic force field ofCH3Li is used in this work.

The anharmonic force constants expressed in thedimensionless normal coordinate system are reportedin Table 4. These results confirm the strong anharmonic-

Tab

le5

Calculatedharmonic,an

harmonic

andexperim

entalvibrational

frequencies

formonomeric

CH

3Lian

ditsisotopic

analogs

CH

3Li

CD

3Li

CH

36Li

13CH

3Li

***

***

***

***

***

***

***

***

m 6(c

HCLi)

435(413

){413

}43

0(40

5)40

8.5a

417b

450–

405c

334(321

){321

}33

0(31

6)31

9a33

6b43

7(415

){414

}43

2(40

7)41

1a44

6b43

2(41

1)42

8(40

3)Notassa

m 3(m

CLi)

631(609

){606

}62

8(61

4)53

0a51

4b51

9c(670

d)

611(591

){587

}60

8(58

6)51

0a43

6b66

6(640

){642

}66

3(64

7)55

8a51

7b62

4(60

3)62

1(60

8)Notassa

m 2ðd

sCH

3Þ

1092

(107

4)

{106

9}

1097(106

0)11

58a10

96–1

061b

1052

b,

1080

c

839(829

){827

}84

4(82

3)88

3a82

7–81

5b10

92(107

3)10

97(106

0)11

58a10

96–1

061b

1085

(106

7)10

90(105

3)Notassa

m 5ðd

asCH

3Þ

1450

(142

9)

{142

1}

1452(140

6)13

87a14

80–1

427b

1484–1

424c

1052

(103

6){104

2}10

53(103

3)10

27a11

00–1

043b

1450

(142

2)14

52(140

7)13

87a14

80–1

427b

1447

(141

8)14

48(140

2)Notassa

1383

2c

m 1ðm

sCH

3Þ

2961

(280

7)

{282

3}

2961(285

0)27

80a27

80b27

80c

2122

(204

3){204

7}21

23(207

6)20

30a20

27b

2961

(280

7)29

62(285

0)27

80a2780

b29

58(280

5)29

58(284

6)Notassa

m 4ðm

asCH

3Þ

3019

(285

1)

{286

1}

3031(288

6)28

20a28

40b28

20c

2229

(213

5){215

3}22

37(215

4)Notassa

2150

b30

19(285

1)30

30(288

6)28

20a2840

b30

09(284

3)30

21(287

8)Notassa

*OurB3L

YP/cc-pVTZresults:harmonic

values.Thevalues

betweenparan

theses

relate

totheuse

ofperturbationmethod;theva

lues

betweenbracesrelate

totheuse

ofvariational

method.

**Harmonic

CCSD(T)/cc-pVQZ+au

g(C)va

lues.Theva

lues

betweenparan

theses

relate

toan

harmonic

wav

enumbersobtained

byusingperturbationmethod.

***Exp

erim

entalsvalues:aRef.[9]Armatrix,

bRef.[1]mulls,

c Ref.[34]

gasphase,

dRef.[11]

(estim

ated

value).

90 N. Gohaud et al. / Chemical Physics 310 (2005) 85–96

ity of this hypersurface. Some potential constantsinvolving principally the CH3 stretching modes m1 andm4 and, in a less significant way, the m2ðds CH3

Þ modeare large. Except for the latter, the anharmonicity doesnot directly relate to the modes for which there is disa-greement between experience and theory. On the otherhand, there are strong couplings, compared to the prin-cipal terms at third- and fourth-order between these crit-ical modes and the others, i.e., couplings that couldinduce several resonances.

All the experimental and theoretical frequencies arelisted in Table 5. On one hand, we can see a satisfac-tory agreement for the m6, m5, m1 and m4 modes. On theother hand, we observe a large systematic discrepancyfor the m3(mC–Li) and m2ðds CH3

Þ modes. For the sym-metric methyl deformation m2, the IR spectroscopicstudy [9] is the only one observing a band in the1150–1200 cm�1 range. Several authors found alterna-tively 1 or 2 bands, with the average positions be-tween 1090–1080 and 1060–1050 cm�1, respectively.Andrews explains this difference by assuming thatthe monomers were the only species present in thegaseous phase with his protocol. Unfortunately, inthe same way as for m3, calculations by Breidungand Thiel predict a band near 1060 cm�1, i.e., about100 cm�1 in disagreement with the experiments. Ourcomplete perturbational anharmonic computationslead to the same conclusion as the one establishedby Breidung and Thiel. However, the phenomena ofresonance are, at this level, not totally taken into ac-count. Only a pure complete variational study makesit possible to refine the results in the spectral areaconsidered.

In the present work, we have used the pure varia-tional method in both spectroscopic windows: 300–2300 and 2700–2900 cm�1, which gives, for the firsttime, the complete spectrum of CH3Li reported in Table6. First, we notice that there is no significant modifica-tion between the variational and perturbational results,since, even if they exist, the interactions we have dis-cussed earlier are not strong enough to change thedescription of the modes (in particular the two sensitivem2 and m3 modes). Second, even if we had taken into ac-count the diagonal force constants at fifth and sixth or-ders 1 and/or second order effects (like Grenier–Bessonterms), our conclusion would have been the same: inthe IR spectroscopic study, the author did indeed ob-serve a system where monomeric methyllithium wasnot the only species present, due, in our opinion, tothe nature of this compound.

1 The maximum variation calculated on the fundamental modes byusing the method of perturbation, never exceeds more than 2 cm�1.

Table 6Calculated vibrational wavenumbers for CH3Li (C3v) in the [300–2300] and [2700–2900] cm�1 areas obtained from the B3LYP/cc-pVTZ quartic forcefields

Description Symmetry [300–2300 cm�1] Description Symmetry [2700–2900 cm�1]

m16ð�1Þ E(?) 413 2m2+m3 A1 2702m3 A1 606 m1 A1 28232m26ð�2Þ E(?) 815 2m25ð�2Þ E 28402m06ð0Þ A1(//) 812 2m05ð0Þ A1 2840m16 þ m3ð�1Þ E 1017 m2+3m3 A1 2863m2 A1 1069 m11ð�1Þ E 28612m3 A1 1200 m16 þ m2 þ m15ð�2Þ E 28983m36ð�3Þ A1,A2 1211 m16 þ m2 þ m15ð0Þ A1 28943m16ð�1Þ E 12072m06 þ m3ð0Þ A1 14202m26 þ m3ð�2Þ E 1419m15ð�1Þ E 1421m16 þ m2ð�1Þ E 1481m16 þ 2m3ð�1Þ E 1616m2+m3 A1 16703m3 A1 17903m36 þ m3ð�3Þ A1,A2 18093m16 þ m3ð�1Þ E 1811m16 þ m15ð�2Þ E 1836m16 þ m15ð0Þ A1,A2 18342m06 þ m2ð0Þ A1 19042m26 þ m2ð�2Þ E 19002m06 þ 2m3ð0Þ A1 20212m26 þ 2m3ð�2Þ E 2015m3 þ m15ð�1Þ E 2023m16 þ m2 þ m3ð�1Þ E 20832m2 A1 2120m16 þ 3m3ð�1Þ E 22002m26 þ m15ð�1Þ E 22352m06 þ m15ð�1Þ E 22502m26 þ m15ð�3Þ A1,A2 22302m3+m2 A1 2267

The vibrational angular quantum number [21] takes the values L = 0, ± 3, ± 6. . . for the symmetry A and L = ±1,±2,±4, ±5. . . for the symmetry E.

N. Gohaud et al. / Chemical Physics 310 (2005) 85–96 91

3.3. The methyllithium clusters (CH3Li)n (n = 1–6)

3.3.1. Structural study

Burczyk and Downs [37] characterized methylso-dium and methylpotassium 23 years after Andrews�experimental work. Although their chemical propertiesare extremely similar, these compounds have not beenthroughly studied. The whole conclusions and thecomplexity of the IR spectra led both Burczyk andDowns and us to think that some of the observedbands could belong to compounds that are not themonomer CH3X (X = Li, Na, K), but aggregates con-taining very polarized bonds, i.e., ðCH�

3 XþÞn. Indeed,

it is well known that those compounds have a strongtendency to aggregate. These aggregates exist in solid,liquid and gas phases [1,32]. The degree of aggrega-tion depends mainly on the temperature, the concen-tration, the solvent, and the nature of the alkylgroups. In fact, practically no experimental data existfor these aggregates except for two works, with one

from the X-ray diffraction study [38] and the other,flash vaporization mass spectroscopy [39]. On the con-trary, among the multitude of theoretical studies ofthese compounds, the majority deal only withmodestly size aggregates (up to the tetramer)[6,7,31,32,40].

Nowadays, with computational improvement, it ispossible to determine the structure of methyllithiumaggregates larger than the tetramer.

We have therefore optimized all the equilibrium geo-metrical structures at the B3LYP/cc-pVTZ level (Fig.2). Table 7 shows the energies for (CH3Li)n withn = 2,3,4 and 6. It is important to note that the bindingenergy per molecule of monomer increases significantlywith n. As mentioned in [32], three kinds of structureshave been studied, namely linear (only for the dimer),ring (Cnh, n = 2,3,4) and polyedric (n = 4,6). Whilethe results obtained mostly agree well with the literaturedata (Table 7), there are nevertheless two significantdifferences:

Fig. 2. Structure of methyllithium aggregates (CH3Li)n (n = 2,3 and 4).

92 N. Gohaud et al. / Chemical Physics 310 (2005) 85–96

• The potential energy surface for the dimer is very flatnear the equilibrium geometry, so the optimizationprocess gives a structure in which the methyl groupsare shifted (Fig. 2). This is not in agreement withthe MP2/6-31G* calculations results reported byKaufmann et al. [6]. His results led us to two imagi-nary frequencies (very small) describing the hinderedrotation movements for the methyl groups.

• (CH3Li)4 belongs to the Td symmetry group, inwhich the methyl group are linked to the triangularfaces of the central tetrahedron Li4; the carbonatoms� projection is located on each center� side. Thistime, our results are in agreement with Kaufmann�s,but disagree with the X-ray structure. These differ-ences can be rationalised by the presence of stronginteractions in the crystal between the tetramer units,interactions which are not present in gaseous phase.

Harmonic frequencies for (CH3Li)n with n = 2–4 andfor the isotopic compounds are given in Table 8. Onlythe frequencies whose IR intensities exceed 15 km/molare reported.

Although it seems that aggregates larger than thetetramer are a little more stable, it is likely that theywere not present in Andrews� experiments. Given hisprotocol, it is reasonable to think that Andrews didnot have aggregates larger than the tetramer in his Armatrix: indeed, Andrews created in situ the methyllith-ium and trapped it at very low temperature conditions.Under such conditions, Andrews� concern was not toworry about the aggregates� dissociation but to ensure

that he was not making associations between mono-meric units.

3.3.2. Frequency results

We focus on m2 and m3 modes for which there is largediscrepancy between experience and theory.

We have noticed that only the calculations on themonomer are far from IR experimental results. If wetake into account the position (although they are com-puted at the harmonic level) and the intensity of eachmode, it appears that the experimental results corre-spond to one or several aggregates, most likely the di-mer. A full calculation on the anharmonic force fieldof (CH3Li)2 has been undertaken with the same com-putational conditions as for the monomer for thesetwo special modes. Given the fact that we can con-sider the dimer as two monomers with strong intermo-lecular interactions, we can expect that vibrationalmovements of the methyl groups will be very similarin the monomer as in the dimer. It would be logicalthat the anharmonic correction for the CH3 umbrellamovement in the dimer is likely equal to the correc-tion for the monomer (i.e., about 20 cm�1). Thisexpectation is indeed confirmed by the use of the cu-bic anharmonic force field at the perturbation level.Thus, the vibrational mode estimated at 1188 cm�1

in the harmonic approximation moves to the 1170–1160 cm�1 region once anharmonicity is taken into ac-count. This value is therefore in excellent agreementwith Andrews�experimental assignment of the m2 modefor the monomer.

Table 7Structural parameters (A and �) and binding energies (kJ/mol) of methyllithium aggregates obtained at the B3LYP/cc-pVTZ level

Level of theory C–Li Li–Li C–C C–H \HCH *

(CH3Li)2B3LYP/ccpVTZ 2.095 2.145 3.602 1.104 103.8 �181.3 (�90.7)B3LYP/cc-Pvtz+aug(C) 2.099 2.149 3.606 1.100 103.0HF/3-21G (MP2/6-31G) [6] 2.149–2.364 2.173 �185.9MP2/6-311+G* [40] �178.8MP2(full) [7] 2.105, 2.128 2.147 3.649 1.104 103.7, 105.8 �179.2MP2(full)/6-31++G** [7] 2.153 3.640MP2/MP4SDTQ/6-31+G* [31] 2.142,2.152 2.186 3.696 �184.2B3LYP/6-31+G* [41] 2.114 2.170 3.629 104.4B3LYP/VDZ [32] 2.17 2.24 �178.8–179.6

(CH3Li)3B3LYP/cc-pVTZ 2.146 2.615 4.093 1.101 105.2 �344.2 (�114.7)MP2/MP4SDTQ [31] 2.116–2.090 2.672 �368.0HF/3-21G (MP2/6-31G) [6] 2.105–2.376 2.638 �330.3B3LYP/6-31+G* [41] 2.063–2.087 2.621 4.096 102.7B3LYP/VDZ [32] �319.5

(CH3Li)4B3LYP/cc-pVTZ 2.182 2.387 3.559 1.104 102.5 �528.8 (�132.3)B3LYP/cc-pVTZ+aug(C) 2.182 2.387 3.557 1.103 102.5Solid state (RX) [7,42] 2.31 2.68 3.68 0.96Experimental estimation from IR [9] 2.28MP2(full) [7] 2.188 2.363 3.582 1.107 102.9 �550.6MP2-MP4SDTQ/6-31G* [31] 2.228 2.430 �572.8HF/3-21G (MP2/6-31G) [6] 2.236-2.240 2.420 �514.1B3LYP/6-31+G* [41] 2.195 2.400 3.579 102.3B3LYP/VDZ [32] �488.2 �551.8

(CH3Li)5B3LYP/cc-pVTZ 2.152 2.507 3.699 1.104 101.5 �647.3 (�129.4)

(CH3Li)6B3LYP/cc-pVTZ 2.229 2.400 3.477 1.103 102.8 �843.2 (�140.6)HF/4-31G trans [43] 2.180–2.284 2.433–2.953B3LYP/VDZ [32] �782.5

* Values in parentheses are binding energies per molecule of monomer. Binding energies taking into account zero-point energy (ZPE) and BSSEcorrections.

N. Gohaud et al. / Chemical Physics 310 (2005) 85–96 93

About the m3 mode, a band near 530 cm�1 can be ob-served for the trimer and tetramer spectra. The associ-ated intensities are all large enough to beexperimentally detected. For the dimer, two intensebands could be observed (529 and 553 cm�1). Theanharmonicity calculated by our pertubational methodis, respectively, 27 and 6 cm�1, i.e, 502 cm�1 and 547cm�1. These results confirm the presence of only one ac-tive band near the experimental value (530 cm�1). Theband round 500 cm�1 is too far and estimated in a spec-tral area where there are a lot of bands due to differentspecies [9]. On the contrary, the monomer has no funda-mental, harmonic or combination bands between 500and 600 cm�1. A complete calculation on every(CH3Li)n deuteriated compound (n = 1–4) supports thisconclusion. These results are reported in Table 9. Basedjust on the observation of these results, the assumptionof the presence of aggregates in gas phase seems compel-ling. Several theoretical and experimental data supportthis assumption:

Andrews suggests that the existence of four separatebands for the four isotopic species Li + (CH3I,CH2-

DI,CHD2I,CD3I) confirms the presence of only themonomer. The regular separation (Dm) between the posi-tion of the observed isotopic bands for m2 and m3 are suf-ficient to conclude that there are three equivalenthydrogen atoms. We have computed the isotopic shiftsfor each of the (CH3Li)n systems (n = 1–4). These resultsare listed in Table 9. For the m2 mode, every shift is inagreement with the experimental observations. For m3,shifts for the trimer are very different. We deduce thata simple reasoning based on the observed shifts is notsufficient to infer on the nature of the observed com-pound. Indeed, it is also necessary to take the positionsand the intensities of the vibrational modes into ac-count. In this case, it is noticeable that the computedintensities for the monomer are all very weak, and thatthe positions are unusually far away from the experi-mental bands. For the trimer and the tetramer, the shiftsand intensities seem to be in agreement with the IR

Tab

le8

OurB3L

YP/cc-pVTZharmonic

vibrational

frequency

results:IR

andRam

anintensities

arein

parentheses

CH

3Li

(CH

3Li)2

(CD

3Li)2

(CH

36Li)2

(13CH

3Li)2

(CH

3Li)3

(CD

3Li)3

(CH

36Li)3

(13CH

3Li)3

(CH

3Li)4

(CD

3Li)4

(CH

36Li)4

(13CH

3Li)4

435(178

–49)

359(0–2

5)26

4(0–1

6)33

7(0–1

6)12

4(21–

0)41

6(0–1

6)29

4(3–1

8)41

8(0–1

6)41

3(0–1

7)33

6(84–

0)31

5(45–

13)

344(0–1

5)33

3(85–

14)

631(23–

241)

476(225

–0)

435(205

–0)

491(245

–0)

354(0–2

8)42

7(29–

1)38

2(61–

2)42

7(0–1

1)42

1(0–1

1)57

4(288

–0)

413(57–

0)35

3(90–

0)55

4(0–1

5)

1092

(13–

838)

529(175

–0)

446(155

–0)

538(188

–0)

471(219

–0)

444(32–

1)39

6(70–

2)44

1(53–

2)42

4(33–

1)12

41(33–

0)53

3(238

–1)

474(12–

0)56

8(278

–3)

2961

(77–

23)

553(202

–0)

538(180

–0)

583(224

–0)

524(170

–0)

466(53–

2)44

8(192

–0)

460(65–

1)44

0(35–

0)14

53(0–1

7)55

5(0–1

4)59

6(307

–18)

1234

(30–

7)

3019

(46–

254)

1188

(42–

15)

572(0–1

5)62

0(0–1

9)54

7(198

–0)

537(221

–0)

613(155

–0)

485(16–

1)46

1(38–

1)29

16(43–

715)

941(37–

12)

1242

(32–

8)29

12(45–

834)

2924

(76–

0)90

6(58–

17)

1188

(41–

15)

1181

(37–

14)

626(178

–0)

622(189

–0)

545(237

–0)

532(215

–0)

2955

(191

–261

)20

99(12–

407)

2916

(43–

833)

2945

(195–2

36)

2956

(157

–211

)21

05(22–

0)29

24(76–

365)

2919

(80–

364)

641(226

–0)

908(30–

48)

666(192

–0)

622(173

–0)

2179

(70–

129)

2955

(191

–237

)

2993

(106

–246

)21

79(56–

113)

2956

(157

–211

)29

47(161

–210

)11

90(16–

53)

2108

(16–

259)

679(240

–0)

636(219

–0)

2206

(39–

136)

2993

(107

–247

)29

84(109

–247

)29

31(44–

565)

2196

(37–

80)

1190

(16–

53)

1182

(14–

50)

2975

(112

–149

)22

02(33–

93)

2931

(44–

565)

2928

(43–

568)

2984

(103

–158

)29

75(112

–149

)29

66(116

–148

)

2984

(103

–158

)29

74(107

–154

)

Only

modes

withI>15

km/m

olareshown.

94 N. Gohaud et al. / Chemical Physics 310 (2005) 85–96

observations; however, the positions of m3 for the trimerand m2 for the tetramer are too distant.

The IR spectroscopic [9] study shows that the bandassociated with m3 splits into two parts when CH3Li isformed from an equal molar mixture of CH3I andCD3I; an assignment to association for CH3Li andCD3Li was proposed for these bands. However, a care-ful inspection of the IR spectrum reveals a shoulder onone of the bands. Our B3LYP/cc-pVTZ results for allthe isotopic compounds are compared to the experimen-tal spectra (Table 10).

By making the assumption that the dimer was pre-sent in the matrix, we can showed beyond doubt thatthese ‘‘two observed bands’’ are in fact three bandsassociated to the Li–Li balancing movement of(CH3Li)2, (CD3Li–CH3Li) and (CD3Li)2, respectively.The associated bands of the monomer are 50 cm�1 high-er than the energetic window Andrews considered [500–600 cm�1 ].

Another reason to believe that it might be difficultto observe the m3 vibration of the monomer is that theassociated intensity is extremely low (Tables 3 and 9).Whichever basis set is used (cc-pVTZ orcc-pVTZ+aug(C)), the relative intensity is predictedto be too low to be observed without ambiguity.Moreover, a band at 610 cm�1 (even in the absenceof Li) is always present in the IR spectra: thus, thisband certainly hides the m3 band in combination witha possible impurity. For similar reasons, the detec-tion of the m2 mode of the monomer is always dis-turbed by the presence of ethane (CH3 is highlyreactive). Only the band associated to the dimer, forwhich the computed intensity is high, is probablyobserved.

We have also calculated the Raman intensities for the(CH3Li)n systems (Table 8). To our knowledgment,there is only one Raman study on CH3Li [44], whichshows the presence of an intense mode at 1070 cm�1,which we associate, thanks to our calculations, to thedeformation mode (m2) of the monomer only. B3LYP/cc-pVTZ+aug(C) calculations show that there are no in-tense modes for the dimer (or other aggregate) in this re-gion. The band at 1070 cm�1 seems clearly associatedwith the monomeric compound, whereas the band at1158 cm�1 must involve a movement of vibration ofthe aggregate system.

Finally, matrix shifts for vibrations associated withionic bonds are often considerably larger than thoseassociated with uncharged molecules [10], particularlythe stretching modes for bonds in highly polar sys-tems like LiF, LiCl or LiBr. In such cases, the shiftcan be up to 40 cm�1. Even if this shift exists inmethyllithium (which can reasonably be anticipated,as the dipole moment is nearly 6 Debye), it cannot ex-plain a 100 cm�1 discrepancy between experience andtheory.

Table 9Changes in band positions for the various isotopotomers compounds of (CH3Li)n

IR [9] CH3Li (CH3Li)2 (CH3Li)3 (CH3Li)4

mi (cm�1) Dm mi (cm

�1) I Dm mi (cm�1) I Dm mi (cm

�1) I Dm mi (cm�1) I Dm

m27Li + CH3I 1158 1092 13 1188 42 1190 16 1241 337Li + CH3Br7Li + CH2DI 1068 90 1009 15 83 1094 47 94 1097 14 93 1138 29 1037Li + CHD2I 955 113 909 8 100 971 41 123 973 11 124 998 23 1407Li + CD3I 883 72 839 2 70 906 58 65 908 30 65 941 37 57

m37Li + CH3I �530 630 23 553 202 537 221 574 2887Li + CH3Br LiBr band7Li + CH2DI 523 7 628 24 2 551 197 2 492 182 45 559 291 157Li + CHD2I 518 5 622 26 6 545 189 6 465 184 27 543 253 167Li + CD3I 510 8 610 24 12 538 180 7 449 192 16 533 238 10

Table 10Analysis of the [500–600] and [600–700] cm�1 areas

Area 500–600 Area 600–700

CH36Li 666 (25)

CD36Li 657 (20)

(CH36Li)2 538 (188) 583(224) 620 (19)

(CH36Li)(CD3

6Li) 506 (172) 576 (211) 619 (17)(CD3

6Li)2 569 (200) 617 (17)

Experimental [9] 537 (with D) sh Impurity557 (with H)

Comparison between theoretical results (B3LYP/cc-pVTZ) and avail-able experimental data for the isotopotomer monomeric CH3

6Li.

N. Gohaud et al. / Chemical Physics 310 (2005) 85–96 95

4. Conclusion

Our study on CH3Li shows that some of the experi-mental assignments obtained by IR spectroscopy arein disagreement with our theoretical calculations,regardless of the specific approximations and the com-putational conditions. In a more general way, the studyof the CH3X family (X = Li, Na and also K) will enableus to show [37,45] that problems remain with the assign-ment of vibrational spectra. In the case of CH3Li, anal-ysis of both the position and intensity of bands formonomeric methyllithium in extended spectral areas(for example, the 500–630 cm�1 area to study m3) andthe study of aggregated, led us to suggest a new interpre-tation for the IR methyllithium spectrum, in which someobserved bands are assigned to the dimer.

Acknowledgements

We acknowledge the Centre Informatique Nationalde l�Enseignement Superieur (CINES) for support ofthis work. We express our sincere gratitude to Pr. DaisyZhang and to Pr. Alain Dargelos for helpful discussions.We would like to thank Pr. Colin Marsden for his inval-uable comments on the manuscript.

References

[1] R. West, W. Glaze, J. Am. Chem. Soc. 83 (1961) 3580.[2] D. Shigorin, Spectrochim. Acta 14 (1959) 198.[3] T.L. Brown, M.T. Rogers, J. Am. Chem. Soc. 79 (1957) 1859.[4] P.I. Arvidsson, Chiral Lithium Amides in Asymmetric Synthesis,

University of Goteborg, 1999.[5] K.B. Wiberg, C.M. Hadad, C.M. Breneman, K.E. Laidig, M.A.

Murcko, T.J. LePage, Sciences 252 (1991) 1266.[6] E. Kaufmann, K. Raghavachari, A.E. Reed, P. von Rague

Schleyer, Organometallics 7 (1988) 1597.[7] F.M. Bickelhaupt, N.J.R.v.E. Hommes, C.F. Guerra, E.J. Baer-

ends, Organometallics 15 (1996) 2923.[8] NIST: National Institute of Standards and Technology. Available

from: <http://www.nist.gov/srd/>.[9] L. Andrews, G.C. Pimentel, J. Chem. Phys. 47 (9) (1967) 3637;

L. Andrews, J. Chem. Phys. 47 (11) (1967) 4834.[10] J. Breidung, W. Thiel, J. Mol. Struct. 599 (2001) 239, and

references therein.[11] D.B. Grotjahn, T.C. Pesch, M.A. Brewster, L.M. Ziurys, J. Am.

Chem. Soc. 122 (2000) 4735;D.B. Grotjahn, T.C. Pesch, J. Xin, L.M. Ziurys, J. Am. Chem.Soc. 119 (1997) 12368.

[12] P. Carbonniere, D. Begue, A. Dargelos, C. Pouchan, in: T.E.Simos (Ed.), Computational Methods in Sciences and Engineering2003, World Scientific, Singapore, 2003.

[13] P. Carbonniere, D. Begue, A. Dargelos, C. Pouchan, Chem. Phys.300 (2004) 41.

[14] P. Carbonniere, D. Begue, C. Pouchan, Chem. Phys. Lett. 393(2004) 92.

[15] K. James, G. Watson, J. Mol. Spectrosc. 41 (1972) 229.[16] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007.[17] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.[18] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.[19] M.J. Frisch et al., Gaussian 98, Revision A.7, Gaussian, Inc,

Pittsburg, PA, 1998.[20] A. Willetts, N.C. Handy, Chem. Phys. Lett. 235 (1995) 286.[21] G. Herzberg, Spectra of Diatomic Molecules, Van Nostrand,

Princeton, NJ, 1945.[22] P. Barchewitz, Spectroscopie infrarouge – Vibrations molecul-

aires, Gauthier-Villars & Cie, Paris, 1961.[23] I.M. Mills, Molecular Spectroscopy: Modern Research, Academic

Press, New York, 1972.[24] J. Pliva, J. Mol. Spectrosc. 139 (1990) 278.[25] C. Pouchan, K. Zaki, J. Chem. Phys. 107 (1997) 342;

D. Begue, P. Carbonniere, C. Pouchan, J. Phys. Chem. A 105(2001) 11379;

96 N. Gohaud et al. / Chemical Physics 310 (2005) 85–96

P. Carbonniere, D. Begue, C. Pouchan, J. Phys. Chem. A 106(2002) 9290.

[26] M.H. Dupin, I. Baraille, C. Larrieu, A. Dargelos, Chem. Phys.256 (2000) 7.

[27] D. Begue, P. Carbonniere, C. Pouchan, submitted.[28] N.C. Baird, R.F. Barre, R.K. Datta, J. Org. Chem. 59 (1973) 65;

A. Streitwieser, J.E. Williams, S. Alexandratos, J.M. McKelvey,J. Am. Chem. Soc. 98 (1976) 4778;L. Herzig, J.M. Howell, A.M. Sapse, E. Singman, G. Snyder, J.Chem. Phys. 77 (1) (1982) 429.

[29] W.D. Bare, A. Citra, C. Trindle, L. Andrews, Inorg. Chem. 39(2000) 1204.

[30] S.C. Tyerman, G.K. Corlett, A.M. Ellis, T.A. Claxton, J. Mol.Struct. 364 (1996) 107.

[31] N.E. Hommes, P.R. Schleyer, Y.D. Wu, J. Am. Chem. Soc. 114(1992) 1146.

[32] P. Verstraete, A. Deffieux, A. Fritsch, J.C. Rayez, M.T. Rayez, J.Mol. Struct. (Theochem.) 631 (2003) 53.

[33] J. Gauss, J.F. Stanton, Int. J. Quantum Chem. 77 (2000) 305.

[34] J. Goubeau, K. Walter, Z. Anorg. Allg. Chem. 322 (1963) 58.[35] L. Henry, G. Amat, J. Mol. Spectrosc. 5 (1960) 319;

L. Henry, G. Amat, J. Mol. Spectrosc. 15 (1965) 168.[36] J.M.L. Martin, T.L. Lee, P.R. Taylor, J. Chem. Phys. 97 (1992)

8361.[37] K. Burczyk, A.J. Downs, J. Chem. Soc., Dalton Trans. (1990)

2351.[38] E. Weiss, G. Hencken, J. Org. Chem. 21 (1970) 265.[39] J.W. Chinn, R.J. Lagow, Organometallics 3 (1984) 75.[40] L.M. Pratt, I.M. Khan, J. Comput. Chem. 16 (9) (1995) 1067.[41] O. Kwon, F. Sevin, M.L. McKee, J. Phys. Chem. 105 (2001) 913.[42] C. Schade, P.V. Rague Schleyer, Adv. Organomet. Chem. 27

(1987) 169.[43] L.J. Kirschenbaum, J.M. Howell, E.L. Singman, Struct. Chem. 7

(1996) 79;L.J. Kirschenbaum, J.M. Howell, Struct. Chem. 5 (1998) 327.

[44] Von P. Krohmer, J. Goubeau, Z. Anorg. Allg. Chem. 369 (1969)238.

[45] N. Gohaud, D. Begue, C. Pouchan, submitted.