Insights into the xenon–silver halide interaction from a rotational

spectroscopic study of XeAgF and XeAgCly

Stephen A. Cooke and Michael C. L. Gerry

Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, BC,Canada V6T 1Z1. E-mail: sacooke@chem.ubc.ca; mgerry@chem.ubc.ca

Received10thDecember 2003, Accepted13th April 2004F|rst published as an AdvanceArticle on theweb17thMay 2004

XeAgF and XeAgCl have been prepared by laser ablation of Ag metal in the presence of xenon and SF6 orxenon and Cl2 , respectively. Rotational spectra for 12 isotopomers of XeAgF and 16 isotopomers of XeAgClhave been recorded. Analysis of the spectra indicates that (i) both chemical systems are unusually stronglybound compared to conventional van der Waals complexes, (ii) significant charge rearrangement occurs at thexenon nucleus upon formation of both XeAgF and XeAgCl as shown by the 131Xe nuclear quadrupole couplingconstants and (iii) in both XeAgF and XeAgCl the Xe–Ag distance is small compared to the sum of the Xe vander Waals radius and the Agþ ionic radius. An ab initio study of the two species has been performed. Thecombined experimental and theoretical investigations indicate that the Xe–Ag interaction is not easilydescribed, but that there is some evidence for weak chemical bonding.

1 Introduction

Several experimental studies on NgMX type molecules (whereNg ¼ Ar or Kr, M ¼ Cu, Ag or Au and X ¼ F, Cl or Br)have now been performed in this laboratory.1–6 In all casesthe complexes have been found to be linear, with short Ng–M interatomic distances when compared to the sums of thevan der Waals radii of Ng and the ionic radii of Mþ. In eachcase the strength of the Ng–M interaction has been assessedusing both experimental data and supporting ab initio calcula-tions. For those complexes studied the Ng–M stretching fre-quencies have been approximated from experimental data tobe �120–230 cm�1 with dissociation energies calculated to bebetween �20–50 kJ mol�1. Interesting trends so far observedinclude the increased Ng–Au stretching force constant and dis-sociation energy for KrAuCl compared to ArAuCl and alsothe increasing strength of the Ar–Cu interaction in ArCuXas X is altered from Cl to F. A traditional viewpoint recognizesthese trends as being consistent with the increased atomicpolarizability of Kr over Ar and the greater electron withdraw-ing properties of F over Cl. Both of these effects are likely to beimportant when considering the nature of the Ng–M inter-action and clearly it is of interest to extend the study to includeXe-containing complexes. In this paper we report the firstmicrowave spectroscopic investigations of molecules contain-ing both Xe and a metal halide, specifically XeAgF andXeAgCl.

2 Experiments

A Balle–Flygare-type,7 pulsed-nozzle Fourier transformmicrowave (FTMW) spectrometer8 was employed to recordthe pure rotational spectra of XeAgF and XeAgCl. The nozzlehas been modified9 to allow a rotating silver metal rod (Good-fellow, 99.9% purity) to be ablated by a pulsed Nd:YAG laserat its fundamental wavelength (1064 nm). During ablation

the resulting silver plasma was entrained by a short pulse ofgas issued from a high pressure holding tank through a sole-noid nozzle (General Valve, series 9) into a Fabry-Perot cavity8

housed within an evacuated chamber. For the preparation ofXeAgF and XeAgCl the backing gases were composed of0.1% SF6 (Matheson, �99.8% purity) or 0.1% Cl2 (Matheson,�99.9% purity), plus 5% Xe (Matheson, �99.995% purity)in 6–7 atm of Ar (Matheson, �99.8% purity), respectively.Whilst collisions between atoms inevitably occur within thebarrel of the ablation nozzle the expansion from the nozzle ori-fice into the cavity ensures that no further collisions occur andtherefore has the effect of stabilizing the reaction products.Pulses of microwaves were coupled into the cavity along thesame direction as the expanding gas mixture i.e. parallel tothe central axis of the mirrors forming the cavity. With thisarrangement all transitions were observed as Doppler doub-lets. All measurements were referenced to a Loran C frequencystandard that is accurate to one part in 1010. The line widthswere �7 kHz (fwhm), and the estimated measurement accu-racy is �1 kHz.

3 Quantum chemical calculations

The Gaussian 0310 suite of programs was used to perform avariety of ab initio calculations. For Ag a relativistic effectivecore potential (RECP) was used which left 19 valence electrons(4s24p64d105s1). This RECP along with the optimized (31111s/22111p/411d) Gaussian basis set was taken from Andraeet al.11. The Ag basis set was further augmented with two ffunctions af ¼ 3.1235 and af ¼ 1.3375.12 For Cl we used the(631111s/52111p) McLean–Chandler basis set13 augmentedwith one d-polarization function (ad ¼ 0.75).12 For F we usedthe simple 6-311G** basis set.10 For Xe the ‘‘aug-cc-pVTZ-PPsmall-core relativistic PP correlation consistent basis set ’’ ofPeterson et al.14 was employed. Most of the basis sets indicatedwere obtained from the Extensible Computational Environ-ment Basis Set Database.15 The above arrangement was usedto calculate the bond lengths, vibrational frequencies and dis-sociation energies and to perform population analyses for bothXeAgF and XeAgCl. The calculations were optimized at the

y Electronic supplementary information (ESI) available: Frequenciesof all observed transitions. See http://www.rsc.org/suppdata/cp/b4/b404953p/

PCCP

www.rsc.o

rg/pccp

R E S E A R C H P A P E R

3248 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 2 4 8 – 3 2 5 6 T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4

DOI:10.1039/b404953p

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second-order Møller–Plesset (MP2)16 level of theory. Basis setsuperposition error (BSSE) was accounted for in all calcula-tions, using the counterpoise correction method of Boys andBernardi.17

The suitability of the basis sets was checked by calculatingseveral parameters. They gave 4.02 A3 for the polarizabilityof Xe (experimental value 4.04 A318) and 4.25 A for r(XeXe)in Xe2 (experimental value 4.36 A19). Predicted bond lengthsfor the monomeric silver halides were r(AgF) ¼ 1.977 A(experiment 1.983 A20) and r(AgCl) ¼ 2.280 A (experiment2.281 A21).Using MOLDEN 3.4,22 plots were prepared to display the

electron densities within the molecules as determined fromthe ab initio calculations. This package was also used to calcu-late and show plots of the Laplace concentration of the elec-tron density �H2r(r), which has been shown to be indicativeof concentration (�H2r(r) > 0) and depletion (�H2r(r)< 0)of negative charge within a molecule.23–27

4 Results and analysis

The spectra of both XeAgF and XeAgCl showed the overall‘‘picket fence-like ’’ pattern characteristic of linear molecules.The spectra were unambiguously assigned to these two mole-cules on the following basis. Firstly, observation of the transi-tions assigned to XeAgF required ablation of the Ag rod withthe presence of both Xe and SF6 in the backing gas mixture. Asimilar requirement was true for XeAgCl, but with SF6

replaced by Cl2 . Secondly, while the majority of the transitionsassigned to XeAgF comprised single lines, those of XeAgClshowed Cl nuclear quadrupole hyperfine structure. Thirdly,the known number and abundances of Xe isotopes were repro-duced in the observed spectra. Fourthly, all the assignmentswere confirmed by the presence of 131Xe(I ¼ 3

2) nuclear quad-rupole hyperfine structure in the spectra of those moleculescontaining this isotope. The frequencies of all observed transi-tions (Tables S1 and S2) may be found as electronic supple-mentary information.y For molecules with one quadrupolarnucleus the quantum numbers are those of the couplingscheme Jþ I ¼ F, where I is the nuclear spin angular momen-tum of the quadrupolar nucleus. For molecules containing twoquadrupolar nuclei the coupling scheme is Jþ IXe ¼ F1 ;F1þ ICl ¼ F. Representative transitions of XeAgF andXeAgCl are in Figs. 1 and 2 respectively.No magnetic hyperfine structure arising from the 107Ag,

109Ag or F nuclei (all possess I ¼ 12) was observed. For those

molecules where no nuclei possess I� 1, e.g. 132XeAgF, thefollowing Hamiltonian was used in the fitting procedure:

H ¼ H rotation þHcentrifugal distortion

¼ B0J2 �D0J

4: ð1Þ

For those isotopomers containing one of either 131Xe or Cl afurther term �1

6V�Q was added to eqn. (1):

Hnuclear quadrupole ¼ � 16V �Q: ð2Þ

For those isotopomers containing both 131Xe and Cl, the termdescribed in eqn. (2) was replaced by:

H two nuclear quadrupoles ¼ � 16 ðVXe �QXe þ VXe �QClÞ: ð3Þ

In eqns. (2) and (3), the parameters determined are the nuclearquadrupole coupling constants (NQCCs), designated eQq, foreach quadrupolar nucleus. Least-squares analyses using therelevant Hamiltonian were performed using Pickett’s globalleast-squares fitting program SPFIT.28 The results for each iso-topomer are given in Table 1 for XeAgF and in Table 2 forXeAgCl.

5 Internuclear distances

In determining the geometry of any molecule from spectro-scopic data it is often useful, for comparative purposes, toquote an equilibrium geometry i.e. the geometry at the globalminimum of the potential surface. However, equilibrium struc-tures can be reliably determined from rotational spectra onlywhen transitions are observed from within excited vibrationalstates, which is not the case here.Many approaches are available in the literature for approx-

imating the equilibrium structure of a molecule from the mea-surement of rotational transitions within the vibrational groundstate alone. Four approaches of this type are considered hereand all require the availability of data from several isotopomers.Firstly, we approximate the ground state effective geometry,

r0 . Here the ground state geometries are assumed to be avail-able from the familiar rigid rotor formulae with no isotopic orvibrational structural dependence. The r0 geometry is obtainedby performing a least squares fit of the bond lengths to theground state moments of inertia:

I0 ¼ I rigidðr0Þ: ð4Þ

Secondly, we may attempt to account partially for the vibra-tional dependence of the moments of inertia, I0 , with the intro-duction of an extra parameter, e, in the least-squares fit. If e isassumed to be isotopically independent then we may fit bondlengths plus e to the moments of inertia thus

I0 ¼ I rigidðrIeÞ þ e: ð5Þ

Fig. 1 A portion of the 131Xe107AgF spectrum showing two over-lapped lines from the J ¼ 7–6 transition. The experiment required2000 averaging cycles and is shown as a 4k transform (no zero filling).

T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 2 4 8 – 3 2 5 6 3249

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This gives the so-called rIe geometry.29 When there is a largenumber of isotopic data this method is equivalent to thewell-known rs procedure.

30

In the third and fourth methods, mass-dependent rð1Þm and

rð2Þm structures31 were calculated by fitting the experimental

moments of inertia to the equation

I0 ¼ Im þ c Imð Þ1=2 þ dm1m2m3

M

� �1=4

: ð6Þ

where c and d are fitting constants. In an rð1Þm fit d is set to zero;

in an rð2Þm fit both c and d are included as fitting parameters;

This procedure, when applied to triatomics, has been shownby Watson et al.31 to give bond lengths which, in many cases,are excellent approximations to the equilibrium distances re .In the case of XeAgF it was necessary to fix the Ag–F intera-tomic distance for the purpose of obtaining an r

ð2Þm geometry in

order to remove correlations between the fitted parameters.The Ag–F distance was fixed in this method to the equilibriumbond length for the AgF monomer.20

The results from all these structural determinations aresummarized in Tables 3 and 4. They, plus ab initio values,are compared to bond lengths of related molecules in Table 5.In addition, for reference purposes, Table 5 contains van derWaals, covalent and ionic radii for the various atoms/ions,along with relevant sums.From Table 5 the r(AgX) values seem smaller than the

re(AgX) values of the uncomplexed silver halides. They mightthus indicate significant bending flexibility for the complexes.However, we hesitate to draw this inference for several rea-sons: (i) In general, for all the NgMX complexes, the MX bondlength is very close to that of the MX monomer, and experi-mentally no systematic difference has been found.6 Partiallythis has arisen because neither Ar nor F can be isotopicallysubstituted, with the result that different definitions of thebond lengths (i.e. re , r

ð1Þm etc.) have been used for different com-

plexes, thus masking any small variations. (This problem alsomasks any variation of r(AgX) with noble gas.) (ii) Theobserved shortenings are paralleled by results of ab initio cal-culations, which do not consider angle bending. This trendhas been found not only from our own calculations1–6 but alsofrom some recently published calculations of Lovallo andKlobukowski.32 (iii) The ab initio bending frequencies inTable 6 (see below) are relatively high.However, systematic variations of the Ng–Ag distance are

large enough to be noticeable; i.e. r(Xe–Ag) in XeAgX clearlyincreases as X goes from F to Cl. Presumably this variationreflects the lesser ability of Cl to withdraw electrons comparedto F. Similar variations in r(Ng–M) are found for all com-plexes thus far observed.6 In addition the r(Ng–Ag) distanceincreases in the sequence Ar–Kr–Xe. This is hardly surprisinggiven the increasing atomic radii of the noble gases in this samesequence.An especially interesting trend is found when the r(Ng–Ag)

values are compared with the sums of standard radii. The bot-tom of Table 5 compares the experimental bond lengths withthe sums of the Ng van der Waals radius and Agþ ionic radius,and with the sums of the Ng and Ag(I) covalent radii. Thesecan be considered as the van der Waals and covalent limitsrespectively. In all cases the experimental values are betweenthe two limits; they are closer to the van der Waals side whenNg ¼ Ar, intermediate when Ng ¼ Kr, and closer to the cova-lent limit when Ng ¼ Xe. Similar trends (in fact, nearer to thecovalent limit) are found for the corresponding Cu and Aucomplexes.6,33

6 Flexibility and bond energies of XeAgX

We have evaluated the Xe–Ag stretching force constant, ks ,for both complexes. For a typical van der Waals-type complexthe quadratic approximation of Millen34 is often used. Here, ksis related to the centrifugal distortion constant of the complex,DJ , by

ks ¼16p2B3m

DJ

� �1� B

BAgX

� �; ð7Þ

Fig. 2 A portion of the hyperfine structure of the J ¼ 7–6 transitionof 131Xe107Ag35Cl. The experiment required 5000 averaging cycles andis shown as a 4k transform (no zero filling).

Table 1 Molecular parameters for XeAgF

B0/MHz DJ/kHz

eQq(131Xe)/

MHz

rmsa /

kHz

129Xe107AgF 812.38497(16)b 0.1397(11) 0.4129Xe109AgF 808.66730(16) 0.1397(11) 0.8130Xe107AgF 809.6127(4) 0.139(4) 0.3130Xe109AgF 805.8849(4) 0.138(4) 0.1131Xe107AgF 806.87283(12) 0.1381(8) �82.77(15) 0.5131Xe109AgF 803.13529(12) 0.1371(8) �82.93(15) 0.3132Xe107AgF 804.17922(16) 0.1369(11) 0.2132Xe109AgF 800.43204(16) 0.1360(11) 0.3134Xe107AgF 798.89883(16) 0.1358(11) 0.3134Xe109AgF 795.13272(16) 0.1347(11) 0.5136Xe107AgF 793.76488(16) 0.1333(11) 0.2136Xe109AgF 789.98043(16) 0.1330(11) 0.4

a Root mean square deviations of the fit. b Numbers in parentheses

are one standard deviation in units of the last significant figure.

3250 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 2 4 8 – 3 2 5 6 T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4

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where

m ¼ mXemAgX

mXe þmAgXð8Þ

and B and BAgX are the equilibrium rotational constants of thecomplex and of either AgF or AgCl.When Bdiatomic�Bcomplex eqn. (7) reduces to the well known

pseudodiatomic approximation35

ks ¼16p2mB3

DJ: ð9Þ

For comparative purposes the values of ks obtained for XeAgFand XeAgCl using both eqn. (7) and eqn. (9) are given in Table6. In both equations the zero-point rotational constants ofTables 1 and 2 and refs. 20 and 36 were used.The stretching wavenumbers for the complexes can easily be

calculated from ks obtained from either of the above methodsusing

ns ¼ 2pcð Þ�1 ksm

� �1=2

: ð10Þ

The values of ns calculated for XeAgF and XeAgCl along withcomparative data from XeHCl37 and XeHF38 are given inTable 6. For XeHCl and XeHF the invariance of the valuesof ks and ns to the approximation used reflects that for thesetwo complexes BHX�Bcomplex . For XeAgF and XeAgCl theratio of appropriate rotational constants is more significant.

Regardless of the approximation used the results in Table 6clearly show that in terms of the stretching force constantthe XeAgX complexes are over an order of magnitude moretightly bound than the XeHX complexes. The stretching fre-quencies calculated ab initio complement the experimentallyderived values; these are also given in Table 6, along withthe ab initio bending frequencies. For further comparison wenote that the van der Waals stretching frequency has been eval-uated for a different class of Ng–MX complex, namelyAr–NaCl,39 by using the pseudodiatomic approach and byab initio methods. In this case the pseudodiatomic approachyielded a ns value of just 21 cm

�1 which was much smaller thanan ab initio value of 76 cm�1. The investigators suggested thatArNaCl may have a quasilinear nature causing a strong cou-pling between the van der Waals stretching and van der Waalsbending mode similar to that observed in Ar–HCN.40,41

We have also calculated ab initio the Xe–Ag dissociationenergies in XeAgF and XeAgCl. These energies are given inTable 7. In both complexes the dissociation energy for the pro-cess Xe–AgX!XeþAgX is calculated to be �30–40 kJmol�1. The study by Lovallo and Klobukowski32 using a dif-ferent Xe basis set to that used in our calculations has pre-dicted the dissociation energies for XeAgF and XeAgCl tobe �40 kJ mol�1 (see Table 7). A dissociation energy of thismagnitude is large for a typical neutral van der Waals molecule(De� 10 kJ mol�1). A photoionization spectroscopic study42

has placed a lower bound of 46.6 kJ mol�1 for the dissociationenergy of the Xe–Agþ dimer. Again, this binding energyappears large but the investigators suggest that the magnitudecan likely be explained with an electrostatic model because of

Table 2 Molecular parameters for XeAgCl

B0/MHz DJ/kHz eQq(Cl)/MHz eQq(131Xe)/MHz rmsa /kHz

eQq(35Cl)129Xe107Ag35Cl 588.76441(8)b 0.0630(3) �32.29(16) 0.5129Xe109Ag35Cl 587.42066(8) 0.0630(3) �32.35(16) 0.5130Xe107Ag35Cl 586.77073(5) 0.0637(5) �32.19(27) 0.5131Xe107Ag35Cl 584.79905(10) 0.0620(7) �32.64(79) �78.05(12) 1.0131Xe109Ag35Cl 583.43974(11) 0.0626(7) �32.45(94) �78.29(14) 1.1132Xe107Ag35Cl 582.85988(8) 0.0616(3) �32.20(16) 0.4132Xe109Ag35Cl 581.49285(8) 0.0616(3) �32.35(16) 0.3134Xe107Ag35Cl 579.05561(9) 0.0611(4) �32.61(22) 0.4134Xe109Ag35Cl 577.67342(9) 0.0611(3) �32.29(22) 0.4136Xe107Ag35Cl 575.35327(11) 0.0603(5) �32.43(22) 0.5136Xe109Ag35Cl 573.95635(11) 0.0608(5) �32.22(22) 0.3

eQq(37Cl)129Xe107Ag37Cl 574.59730(10) 0.0587(5) �25.63(22) 0.5129Xe109Ag37Cl 573.37836(9) 0.0590(3) �25.38(22) 0.9132Xe107Ag37Cl 568.81525(8) 0.0581(3) �25.44(16) 0.8132Xe109Ag37Cl 567.57367(9) 0.0579(3) �25.53(22) 0.9134Xe107Ag37Cl 565.08946(10) 0.0574(5) �25.56(22) 1.1

a Root mean square deviations of the fit. b Numbers in parentheses are one standard deviation in units of the last significant figure.

Table 3 Bond lengths for XeAgF determined from experiment

r(Xe–Ag)/A r(Ag–F)/A

r0 2.66335(37)a 1.9799(11)

rIeb 2.66390(2) 1.97214(11)

rð1Þm

c 2.66235(2) 1.97099(12)

rð2Þm

d 2.66627(4) 1.98317e

re (AgF) 1.98317f

a Numbers in parentheses are one standard deviation in units of the

last significant figure. b e ¼ 0.734(9) u A2. c c ¼ 0.0585(7) u1/2 A.d c ¼ �0.232(3) u1/2 A and d ¼ 0.758(9) u1/2 A2. e Held fixed at

re(AgF) (ref. 20) to remove correlations between the fitted parameters.f Ref. 20.

Table 4 Bond lengths for XeAgCl determined from experiment

r(Xe–Ag)/A r(Ag–Cl)/A

r0 2.71064(43)a 2.27137(82)

rIeb 2.70752(17) 2.27181(15)

rð1Þm

c 2.7055(3) 2.27012(16)

rð2Þm

d 2.70456(7) 2.27011(3)

re (AgCl) 2.28079e

a Numbers in parentheses are one standard deviation in units of the

last significant figure. b e ¼ 1.301(64) u A2. c c ¼ 0.0881(44) u1/2 A.d c ¼ 0.1605(36) u1/2 A and d ¼ �0.261(13) u1/2 A2. e Ref. 21.

T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 2 4 8 – 3 2 5 6 3251

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the considerable polarizability of the Xe atom. This wasconfirmed in ref. 18.At this point it seems sensible to examine the electrostatic

interactions occurring between Xe and AgX. The majorportion of the dipole-induced dipole interaction energy,Edip–ind.dip , between neutral Xe and a diatomic AB whichhas a permanent dipole moment DAB may be qualitativelyobtained from (ref. 43, eqn. (10.16))

Edip�ind:dip ¼�aXeD

2AB 1þ 3 cos2 y

� �8pe0r6Xe;AB

: ð11Þ

Here aXe is the electric dipole polarizability of Xe (4.04 A3),18

e0 is the permittivity of a vacuum, rXe,AB is the distance

between the Xe nucleus and the center of charge of the ABbond and y is the angle between the AB axis and the line fromXe to the midpoint of AB (y ¼ 0� in the present case). Thedipole moments of AgF and AgCl have been evaluated as6.22(20) D20 and 6.076(60)D44 respectively. More rigorousexpressions for this type of interaction, i.e. using terms in r�7

and higher, may be found in ref. 45. It is our purpose hereto obtain an estimate of the magnitude of this type of inter-action in XeAgF and XeAgCl and therefore only the leadingterm given above is considered. Using the above equation weestimate Edip–ind.dip for XeAgF and XeAgCl to be ��8 kJmol�1 and �5.6 kJ mol�1 respectively. These values equateto only 19% and 14% of the calculated De (taken from ref.32) for XeAgF and XeAgCl respectively.

Table 5 A comparison of the interatomic distances and some related parameters for the noble gas–silver halides

r(Rg–M)/A r(M–X)/A

ArAgFa b 2.55813c 1.98605c

KrAgFd e 2.59415c 1.956696c

XeAgF

Experimentald f 2.66627(4)g 1.98317h

Experimentali f 2.66390(2) 1.97214(174)

ab initiof 2.737 1.961

ab initioj 2.684 1.969

AgFk l — 1.98317

ArAgClm b 2.61022c 2.26932c

KrAgCld n 2.6412354(32) 2.2675722(12)

XeAgCl

Experimentald f 2.70456(7) 2.27011(3)

ab initiof 2.780 2.268

ab initioj 2.728 2.274

AgClk o — 2.280781(16)

Atomic, ionic and covalent radii/A

rvdW(Ar) ¼ 1.88p rcov(Ar) ¼ 0.94–0.95q

rvdW(Kr) ¼ 2.00p rcov(Kr) ¼ 1.09–1.11q

rvdW(Xe) ¼ 2.18p rcov(Xe) ¼ 1.30–1.31q

rion(Agþ) ¼ 0.81r rcov(Ag(I)) ¼ 1.28s

r(Ng–AgX) rvdW(Ng)þ rion(Agþ) Experiment rcov(Ng)þ rcov(Ag(I))

Ar–AgX 2.69 2.56–2.64 2.26

Kr–AgX 2.81 2.59–2.66 2.38

Xe–AgX 2.99 2.65–2.70 2.58

a r0 bond length. b Ref. 1. c No uncertainties are quoted as the number of parameters obtained equalled the number of constants used in the cal-

culation. See reference for details. d rð2Þm bond length. e Ref. 5. f This work. g Numbers in parentheses are one standard deviation in units of the last

significant figure. h Held fixed at this value. i rIe bond length. j From Ref. 32. k re bond length. l Ref. 20. m rd bond length. n Ref. 3. o Ref. 21.p Ref. 53. q Ref. 54. r Ref. 55. s Ref. 56.

Table 7 Calculated induction energies for a series of Rg–AgXcomplexes

Edip–ind.dip/

kJ mol�1Echg–ind.dip/

kJ mol�1

De/kJ mol�1

qAga Corr. Ref. 32

XeAgFb 0.653 �8.0 �24.0 36 43

KrAgF �5.6c �16.7c 17 28

ArAgF �3.8d �11.3d 14 18

XeAgClb 0.555 �5.6 �16.3 33 39

KrAgCl �3.8e �11.0e 15 26

ArAgCl �2.6d �7.6d 13 16

a Fractional charge of the Agþ and X� ions, evaluated from the MX

dipole moment and bond lengths using eqn. (13). b This work. c Cal-

culated using the geometries given in ref. 5. d Calculated using the geo-

metries given in ref. 1. e Calculated using the geometries given in ref. 3.

Table 6 Some calculated structural and dynamic properties for theprincipal isotopomersa of XeAgCl, XeAgF, XeHCl and XeHF

XeAgCl XeAgF XeHClb XeHFc

Stretching parameters using the quadratic approximation

ks/N m�1 48.5 57.7 1.9 2.1

ns/cm�1 109.7 123.3 33.7 45.3

Stretching parameters using the pseudo-diatomic approximation

ks/N m�1 57.6 64.2 1.9 2.1

ns/cm�1 119.6 130.0 33.8 45.3

Stretching frequencies from ab initio calculations

ns/cm�1 98.8 108.3 — —

Bending frequencies from ab initio calculations

nb/cm�1 47.1 68.0 — —

a 132Xe107Ag35Cl, 132Xe107AgF, 132XeH35Cl and 129XeHF. b Ref. 37.c Ref. 38.

3252 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 2 4 8 – 3 2 5 6 T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4

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The ionic nature of the AgX compounds and the shortr(Xe–Ag) separation suggests that the charge-induced dipoleinteraction energy may be a more useful quantity in account-ing for the dissociation energies of the XeAgX complexes.This leading term may be calculated from (ref. 43 eqn. 10.14)

Echg�ind:dip ¼�aXeq

2Ag

8pe0r4Xe;Ag

: ð12Þ

Here qAg is the effective charge on Ag and rXe,Ag is the inter-nuclear distance between Xe and Ag. The effective chargeson the Ag atom in AgF and AgCl have been estimated using

qAg ¼ 0:2082DAgX

r AgXð Þ ð13Þ

where DAgX is the dipole moment in debye and r(AgX) is thesilver halide internuclear separation in angstrom. Using eqn.(12) above and neglecting the repulsive effect of the halogenwe estimate Echg–ind.dip for XeAgF and XeAgCl to be �24.0kJ mol�1, 56% of De , and �16.3 kJ mol�1, 42% of De , respec-tively (where again we have used De’s from ref. 32). The resultsalong with the values for the analogous Kr and Ar complexesare in Table 7. The disparity between the induction energiesand the dissociation energies for the XeAgX complexes sug-gests that the Xe–Ag interaction requires forces other thanthose of a purely inductive nature for proper description.For further comparison the procedures outlined above were

repeated on the XeHF complex. An MP2 calculation usingidentical basis sets as outlined above together with the6-311G** basis set for H was performed. A BSSE correcteddissociation energy for XeHF!XeþHF was calculated tobe �1.58 kJ mol�1. Nevertheless, using data from ref. 38 thecharge-induced dipole interaction energy, Echg–ind.dip , was cal-culated from eqn. (11) to be �6.8 kJ mol�1, i.e. �4De! Itshould be noted that for a purely inductive interaction thereis a significant repulsive energy and therefore the attractiveenergy should exceed the magnitude of the dissociation energyas it apparently does in XeHF. It is interesting that in this wayDe for XeHF can be more than accounted for using a longrange induction energy, whilst the same treatment provesinadequate when applied to the XeAgX complexes.

7 Nuclear quadrupole coupling

Nuclear quadrupole coupling constants (NQCCs) have beenevaluated for 131Xe in both complexes, and for 35Cl and 37Clin XeAgCl. They have provided useful information on thedistributions of electron density at the nuclei in question.Because, reasonably, the NQCCs for 35Cl and 37Cl are in the

ratio of the quadrupole moments, the discussion about Clnuclear quadrupole coupling will consider only the 35Cl values.Those of XeAgCl are compared with those of monomericAgCl, other NgAgCl complexes and the strongly boundcomplex OCAgCl46 in Table 8.For van der Waals complexes the small changes of the 35Cl

NQCCs have been historically interpreted in terms of a large

amplitude bending. The equation used is

eQq ¼ eQq03 cos2 b� 1

2

ð14Þ

where eQq and eQq0 are the halogen coupling constants in thecomplex and monomer, respectively, and b is the bendingangle. In XeAgCl, for example, this would give b ¼ 16.2�, sug-gesting a fair degree of bending flexibility. However, it is cur-ious that such flexibility should be greatest for XeAgCl, whichof the NgAgCl complexes is the most strongly bound (Table7). Given that the potentials between constituents of van derWaals complexes are often isotropic,25 an alternative rationalefor the changes in eQq(35Cl) should be sought. It should benoted as well that for Cu and Au complexes, the NQCCs ofthe metal are incompatible with an interpretation solely interms of eqn. (14).2,4,6

The changes on complex formation of the 35Cl NQCCs arenot large on an absolute scale. However, on a relative scalethey are very large. In particular the change on addition ofXe is �4.4 MHz, i.e. over 50% of the change when OC isadded. Also, these changes are more than those which occurwhen Ar or Kr is added (24% and 32%). There is increasingdistortion of the electron distribution of AgCl (even at Cl)on complexation with a noble gas in the sequence Ar–Kr–Xe. The change on addition of Xe is comparable to that onformation of a full chemical bond.The NQCCs of 131Xe also reflect significant change in elec-

tron distribution on complex formation, though this time itis on Xe. The values, which are designated eQq(131Xe) inTables 1 and 2, are rather large (��80 MHz) for both com-plexes. They are proportional to the field gradient at thenucleus Vzz . The NQCC for a free (uncomplexed) Xe atomis zero because its spherical closed shell charge distributionmakes Vzz ¼ 0. The typical weakly bound van der Waals com-plex Xe–HCl has eQq(131Xe) ¼ �4.9 MHz.37 The change inXe electron distribution is much greater on formation ofXeAgX than on formation of Xe–HCl. It suggests the possibi-lity that the natures of the bonding to Xe in XeAgX andXe–HCl are different.It is thus necessary first of all to check whether the values of

eQq(131Xe) arise simply because the Xe atom is polarized bythe nearby AgX molecule. The relation between the NQCCand Vzz is

37

ðeQqÞ ¼ eQVzz ð15Þ

where (eQq) is to be considered a single unit, and e is the(positive) elementary charge. Values of Vobs

zz from the mea-sured eQq(131Xe) are in Table 9; for both complexesVobs

zz ��3� 1022 V m�2.Our model considers a spherical atom in the presence of

external charges. In this case Vzz is predicted using47–49

Vzz ¼ ð1þ gXeÞEzz þ eXeE2z þ . . . ð16Þ

where Ez and Ezz are the field and field gradient at the Xenucleus due solely to the external charges. The electrons arepolarized by the external charges and greatly magnify the field

Table 8 35Cl Nuclear quadrupole coupling constants in AgCl and itscomplexes

Molecule eQq(35Cl)/MHz

AgCla �36.44

ArAgClb �34.49

KrAgClc �33.79

XeAgCld �32.20

OCAgCle �28.15

a Ref. 21. b Ref. 1. c Ref. 5. d This work. e Ref. 46.

Table 9 Electric field gradientsa at Xe in XeAgF and XeAgCl

XeAgF XeAgCl

Vobszz �3.00(26) �2.83(24)

Ezz(AgX) �0.0083 �0.0068

(1þ gXe)Ezzb �(1.2–1.5) �(0.9–1.2)

|eXeE2z |c <0.1 <0.1

a Given in units of 1022 V m�2. b Calculated using 138 gXe 177.c Calculated using eXe< 15 V�1.

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gradient. This is measured by g, the Sternheimer antishieldingconstant (usually �100), and e, a second constant. Both g and eare characteristics of the particular element (Xe in this case),hence the designations gXe and eXe.For XeAgX, Ez and Ezz (dEz/dr) due to AgX alone are

given by

Ez ¼eqAg

4pe0r XeAgð Þ2þ eqX

4pe0r XeXð Þ2: ð17Þ

and

Ezz ¼ � eqAg

2pe0r XeAgð Þ3� eqX

2pe0r XeXð Þ3ð18Þ

where qAg and qX are the effective charges on the Ag and Xions, as discussed earlier (see eqn. (13)) and r(XeAg) andr(XeX) are the distances between Xe and Ag or X nuclei inthe complex. For AgF and AgCl, Ezz��8� 1019 V m�2, overtwo orders of magnitude smaller than Vobs

zz .To apply eqn. (16), values of gXe and eXe are required.

Keenan et al.37 used a value of gXe ¼ 138 (note that for a p6

atom we adopt the convention of a positive sign for g and anegative sign for e48). Baiocchi et al.38 determined it to be157–159 by assuming that Vzz for XeHF and XeHCl arosesolely from the first term of eqn. (16). Feiock et al.50 havecalculated a larger value of 177. With this range of values,138 gXe 177, the first term of eqn. (16) was calculated forboth complexes; the results are all ��1.2� 1022 V m�2, andare also in Table 9. The values given indicate that this termaccounts for less than 50% of Vobs

zz for both XeAgF andXeAgCl.From the work of Keenan et al.,37 eXe has been estimated as

�11.1 V�1. With the liberal range of �5 eXe�15 the sec-ond term in eqn. (16) is at most 1021 V m�2, roughly an orderof magnitude smaller than the first term. Given the uncertaintyin gXe discussed above, the second term can be ignored in semi-quantitative discussions. The entire model represented by eqn.(16) thus accounts for less than 50% of Vobs

zz (and hence of themeasured eQq values). This result parallels that reached for theinduction energies and dissociation energies given above.The NQCC(131Xe) in both XeAgF and XeAgCl may be used

to evaluate the extent of charge transfer between Xe and AgX.A NQCC for 131Xe in a 3P2 electronic state has been measuredto be �505 MHz.51 This state corresponds to an electron con-figuration for Xe of [Kr]5p5 6s1. Because electrons in s-shellsdo not contribute to the field gradient at a nucleus this valuecan be considered the NQCC of 131Xe following removal ofone electron. Using this value we find that the ratios ofNQCC(131Xe) in XeAgF and XeAgCl to this atomic NQCCvalue are 0.16 and 0.15, respectively. Therefore in XeAgFand XeAgCl approximately 15% of the effect of electronremoval on the field gradient at the 131Xe nucleus is experi-enced upon complex formation. This should be compared toanalogous values of only 2% and 3% for XeHF and XeHClrespectively.37,38

8 Natural bond orbital populations andwavefunction topology

In the preceding sections the geometries, bond energies andNQCC’s indicate that the XeAgX complexes do not ‘‘fitcomfortably ’’ into the traditional class of van der Waals typemolecules. Accordingly, further examination of the Xe–Aginteraction in these complexes is warranted.Natural bond valence orbital populations have been calcu-

lated ab initio, and are given for both XeAgF and XeAgCl inTable 10. Aside from the absolute populations, of greaterinterest are the changes that occur in the AgX and Xe popula-tions upon formation of the complexes. With respect to xenonwe find a small depletion in electron density occurs in the 5ps

orbitals upon complexation. The extent of this depletion,�0.06 in both XeAgF and XeAgCl is greater than the corre-sponding changes for Kr (4ps) in KrAgF (0.03) and KrAgCl(0.04). For silver we calculate a noticeable increase in thepopulation of the 5ss orbital but a small decrease in that of4ds on complex formation. This trend is also observed forKrAgX, but not to the same extent. The halogen orbital popu-lations are essentially unchanged on addition of xenon. Similartrends were found using Mulliken populations not only forthese complexes, but also for all other noble gas–noble metalhalides examined previously in this laboratory.1–6 Also of noteis the overall drop in electron density on the xenon atom fol-lowing complexation. The population analysis indicates thatXe carries a charge of �0.06 in both complexes. From this ana-lysis a MOLDEN 3.422 contour plot of electron density of theoccupied 3s molecular orbital has been prepared and is shownin Fig. 3. A sharing of electron density between Xe and Ag isclearly implied.The Laplace concentration of the total electron density,

�H2r(r), can predict where electrons congregate and can there-fore give additional information on the electronic structure ofa molecule. It has been highly touted for noble gas com-plexes.25,26,52 The MOLDEN 3.4 program has been used togenerate �H2r(r) for XeAgCl and a contour plot of this quan-tity is shown in Fig. 4. Within a dative-covalently bound mole-cule electrons will be found to congregate in both bonding andnon-bonding regions. Bonding may be demonstrated by obser-vation of a deformation in the valence spheres between oneatom and another atom along what may be referred to asthe bond path. From Fig. 4 only a minor deformation isobserved between Xe and Ag suggesting a minimal covalentbond in XeAgCl; a similar result is found for XeAgF.

9 Conclusions

The microwave spectra of XeAgF and XeAgCl are the first tobe reported of the Xe–noble metal halide complexes. Theirrotational constants, centrifugal distortion constants andnuclear quadrupole coupling constants have been preciselyevaluated. The geometries of both complexes have been deter-mined. The nature of the bonding has been probed using theseresults along with those of supporting ab initio calculations.

Table 10 MP2 natural bond orbital populations and charges, q, forXe, AgF, AgCl, XeAgF and XeAgCla

XeþAgF XeAgF XeþAgCl XeAgCl

Xe

q 0.00 0.057 0.00 0.062

ns 2.00 1.99 2.00 1.99

nps 2.00 1.95 2.00 1.94

npp 4.00 4.00 4.00 4.00

Ag

q 0.877 0.803 0.856 0.763

ns 0.12 0.24 0.15 0.27

nps 0.01 0.01 0.01 0.01

npp 0.03 0.03 0.01 0.01

nds 1.96 1.93 1.97 1.95

ndp 4.00 4.00 4.00 4.00

ndd 4.00 4.00 4.00 4.00

X

F(AgF) F(XeAgF) Cl(AgCl) Cl(XeAgCl)

q �0.877 �0.860 �0.856 �0.825

ns 1.99 1.98 1.99 1.97

nps 1.91 1.90 1.87 1.86

npp 3.97 3.97 3.99 3.99

a The units of q are fractions of the elementary positive charge e.

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An accurate classification of the Xe–Ag interaction in particu-lar has been found to be elusive.On the one hand, as with all other Ng-noble metal halide

complexes, XeAgF and XeAgCl are rigid, with relatively shortXeAg bonds. The XeAg internuclear distances are closer to thesum of the covalent radii of the atoms than to the sum of theXe van der Waals radius and the Agþ ionic radius. The nuclearquadrupole coupling constants indicate significant redistribu-tion of electron density on complex formation. This is espe-cially so for Xe, whose eQq(131Xe) is much bigger than thatfound in more conventional van der Waals complexes. Ratherlarge ab initio dissociation energies approaching 40 kJ mol�1

have been obtained; charge–induced dipole calculations canaccount for only �50% of these values. The eQq(131Xe) valuescan only partially be accounted for by polarization of the Xeelectrons by a nearby polar AgX molecule. Natural bond orbi-tal populations suggest donation of �0.06 electrons from Xe toAg roughly consistent with the experimental eQq(131Xe) data,which predict a donation of �0.15 electron. A MOLDEN plot

of an occupied s valence molecular orbital suggests consider-able electron sharing between Xe and Ag.On the other hand, the Laplace concentrations from the

ab initio calculations give no indication of significant electronbuild up between the nuclei. This is consistent with van derWaals bonding, and suggests marginal covalent bonding atbest. However, as with other NgMX complexes,1–6 it is verydifficult to rationalize all the experimental parameters with asimple electrostatic interaction of a xenon resting againstAgX. Clearly the complexes are at the border between vander Waals and chemical bonding. As has recently been shown,6

chemical bonding seems less likely for NgAgX complexes thanfor NgCuX and NgAuX. The present complexes, XeAgF andXeAgCl, are consistent with this statement. The total picture isnot yet available, and work is continuing on other complexesto complete it.

Acknowledgements

This research has been supported by the Natural Sciences andEngineering Research Council (NSERC) of Canada and bythe Petroleum Research Fund, administered by the AmericanChemical Society.

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