Pure rotational spectra of LuF and LuCl

Stephen A. Cooke,* Christine Krumrey and Michael C. L. Gerry*

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

Received 22nd February 2005, Accepted 20th April 2005First published as an Advance Article on the web 31st May 2005

The pure rotational spectra of two isotopic species of LuF and three of LuCl have been measured in thefrequency range 5–17 GHz using a cavity pulsed jet Fourier transform microwave spectrometer. The sampleswere prepared by laser ablation of Lu metal in the presence of SF6 or Cl2, and stabilized in supersonic jets of Ar.Spectra of molecules in states having v ¼ 0, 1, and 2 have been measured, to produce rotational constants andcentrifugal distortion constants, along with hyperfine constants for all the nuclei. Dunham-type fits for LuClproduced a Born–Oppenheimer breakdown parameter for Cl. Although a theoretical calculation showed that Luin LuCl should have a significant field shift effect parameter, it could not be determined from the spectrum.Equilibrium internuclear distances, re, and dissociation energies have been evaluated for both molecules. Thenuclear quadrupole coupling constants are discussed in terms of the molecular electronic structure.

1. Introduction

Although the lutetium monohalides, LuX (X ¼ F, Cl, Br, I),are rare, there are nonetheless reports in the literature ofelectronic spectra of all four. For the last three (LuCl, LuBr,LuI) two electronic transitions have been observed for each,but only at vibrational resolution;1 no rotationally resolvedspectra have thus far been reported.

The electronic spectrum of LuF, however, has been studiedat high resolution in considerable detail. Around 150 bandshave been observed, comprising nine systems, in the wave-length range 3000–8000 A.2–5 Each band is remarkably regular,with a dearth of perturbations.

The ground electronic state is X 1S1, with most observedexcited states being 1S or 1P. No 3S or 3P states in Hund’s case(a) could be identified. From rotationally resolved spectra itwas possible to do global fits3,4 to produce quite accuratespectroscopic constants for several states, and particularly forthe ground vibronic state. Values for the equilibrium inter-nuclear distance re were obtained.3 Subsequently hyperfinestructure in the B 1P–X 1S band has yielded several hyperfineparameters,6 including an estimate of the 175Lu nuclear quad-rupole coupling constant eQq(175Lu) as �2918(600) MHz.From the contributions of F to the hyperfine structure, theionic character of LuF was deduced to be 495%.

In spite of all these results there is still much more informa-tion to be obtained from the spectra of these molecules. For allof them except the fluoride there are no high resolution dataand the bond lengths are unknown. Lutetium has two isotopes,and spectra of isotopomers containing only one have beenobserved. The rare isotope 176Lu (2.59% abundant) has nucle-ar spin I¼ 7, one of the largest known. Both isotopes have verylarge nuclear quadrupole moments, so that eQq(Lu) valueslarger than the rotational constants are entirely possible.

The Lu-containing molecules are also of astrophysical inter-est. Some of the lanthanide ions were detected in the opticalspectrum of Arcturus7 and in Przybylski’s holmium star8 aswell as in HR6958, a star with a peculiar chemical composi-tion.9 Sneden et al.10 have recently found spectroscopic evi-dence of Lu along with some other heavy metals in theatmosphere of the extremely metal-poor galactic halo giantCS 22892-052. Lu was also observed by Johnson and Bolte11

very recently in CS 31062-050. This search was performed with

three different terrestrial telescopes and the Hubble SpaceTelescope, mostly with high-resolution spectrometers. Accord-ing to astro- and elementary physical theories Lu is formed inneutron capture processes within long-lived low- and inter-mediate-mass stars. From there the nucleosynthetic material isinjected into the interstellar medium,12,13 where it is availablefor the synthesis of corresponding molecular compounds.In this paper we report the high resolution rotational spectra

of LuF and LuCl in their electronic ground states. Themeasurements were made using a cavity pulsed jet Fouriertransform microwave (FTMW) spectrometer of the Balle–Flygare type.14,15 The samples were prepared via a laser abla-tion technique we have now used for many studies.16–19 Spectrahave been recorded for two isotopomers of LuF and three ofLuCl in their ground vibrational states; for the isotopomerscontaining 175Lu, spectra of vibrationally excited moleculeshave also been measured. Rotational constants, hyperfineconstants and internuclear distances have been determined.The results are supported by theoretical calculations with thedensity functional theory method.

2. Experimental methods

Because a detailed description of the spectrometer used in theseexperiments has been given earlier,15,16 only essential featuresare presented here.The instrument15 contains a Fabry–Perot cavity consisting

of two spherical mirrors, 38.4 cm radius of curvature and 24 cmin diameter, approximately 30 cm apart. One mirror is fixedand the other can be moved to tune the cavity. A pulsed nozzle(General Valve, Series 9) is mounted in the fixed mirror, fromwhich samples entrained in a noble gas (usually Ar or Ne) areinjected into the cavity. This arrangement gives optimumsensitivity and resolution. However, because the jet travelsparallel to the axis of propagation of the microwaves, all linesare doubled by the Doppler effect. The microwave synthesizeris referenced to a Loran C frequency standard accurate to onepart in 1010. The frequency range of the experiments was 5–17GHz. Observed line widths were B7–10 kHz fwhm, and theestimated measurement accuracy of the lines is �1 kHz.Details of the laser ablation system are in ref. 16. A 5 mm

diameter lutetium rod (HEFA Rare Earth Canada) was held ina stainless steel nozzle cap B5 mm from the outlet of the

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

PC

CP

ww

w.rsc.o

rg/p

ccp

DO

I:1

0.1

03

9/b

50

26

83

k

2570 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online / Journal Homepage / Table of Contents for this issue

pulsed nozzle. It was ablated with the fundamental (1064 nm)of a Nd:YAG laser. LuF and LuCl were prepared by thereaction of the resulting plasma with 0.1% SF6 or Cl2, respec-tively, in Ar at backing pressures of B5–7 atm. The resultingmixture was injected into the microwave cavity as a supersonicjet, which had the effects of stabilizing the LuF and LuClmolecules in a collision free environment and of reducing theirrotational temperatures to a few degrees Kelvin.

3. Theoretical calculations

Calculations have been performed using the Amsterdam Den-sity Functional (ADF) routine.20–23 The method, based ondensity functional theory (DFT), employs an all electron basisset (QZ4P) of Slater-type orbitals (STO’s). For both compo-nents of the diatomic species the statistical average of orbitalpotentials (SAOP)24 model was also applied. A method veryrecently developed by Cooke et al.25 provides single pointcalculations presenting the electron density at the Lu nucleusin LuF and LuCl, at different internuclear distances in therange of 1–4 A. Single point calculations were also used togenerate potential functions for the molecules, predict theirequilibrium internuclear distances and provide electron densi-ties needed to determine nuclear shift effects. In addition thevibrational frequencies were calculated by applying theVIBROT program using the potential energy provided by theDFT computations.

4. Observed transitions, assignments and

preliminary analysis

4.1. LuF

The initial search for pure rotational transitions of LuF usedthe rotational constant of 175LuF in ref. 3. The strongest Luhyperfine component of the J ¼ 1–0 transition near 16256MHz was found within 65 kHz of the prediction. Using apredicted eQq(175Lu) value from the DFT calculations, theremaining two components were easily found. The lines werestrong, and visible within 5 pulses. Their assignments wereconfirmed by the extra splittings due to nuclear spin–rotationcoupling of 19F. The central 175Lu hyperfine component is inFig. 1. Lines of molecules in the v ¼ 1 and v ¼ 2 excitedvibrational states were similarly easily assigned and measured.

To assign lines of 176LuF (2.59% abundant) an r0 geometry,plus a scaled value of eQq(176Lu), both from the 175LuF results,provided an excellent prediction. Lines of this isotopomerrequired B1800 pulses for a usable signal-to-noise ratio. Over-all, only the J ¼ 1–0 transition was available in the frequency

range of our spectrometer. For 176LuF, lines of molecules onlyin the state v ¼ 0 were found.The measured line frequencies and assigned quantum num-

bers for both isotopomers are in Table 1. The quantum numberassignments follow the coupling scheme J þ ILu ¼ F1 andF1 þ IF ¼ F.Preliminary to the Dunham-type fits described below, state-

by-state analyses were carried out for each isotopomer in eachvibrational state. The program used was Pickett’s global leastsquares program SPFIT,26 and the Hamiltonian was:

H ¼ Hrot þ Hquad þ Hspin–rot (1)

with

Hr ¼ BvJ2 � DvJ

4 (2)

Hquad ¼ V(2)LuQ(2)

Lu þ V(2)halQ

(2)hal (3)

Hspin–rot ¼ CI(Lu)ILu � J þ CI(X)IX � J (4)

Fig. 1 Section of power spectrum of the J ¼ 1–0, v ¼ 0 transition of175LuF obtained using 150 averaging cycles. 4k data points wererecorded and the power spectrum is shown as a 4k transformation.

Table 1 Measured transition frequencies (in MHz) of LuF

J0 � J00 F10 � F1

00 F0 � F00 v ¼ 0 Obs. � calc.a v ¼ 1 Obs. � calc.a v ¼ 2 Obs. � calc.a

175Lu19F

1 – 0 7/2–7/2 3–3 15 300.7307 0.7 15 212.6081 �0.3 15 124.6638 0.9

7/2–7/2 4–4 15 300.7383 �0.7 15 212.6175 0.3 15 124.6711 �0.99/2–7/2 4–3 16 256.0931 �1.6 16 160.6626 �1.7 16 065.4542 �2.39/2–7/2 5–4 16 256.1358 1.6 16 160.7047 1.7 16 065.4978 2.3

5/2–7/2 3–4 16 543.5898 1.9 16 445.9238 2.2 16 348.5631 2.7

5/2–7/2 2–3 16 543.5898 �1.9 16 445.9493 �2.2 16 348.5487 �2.7

176Lu19F

1–0 7–7 13/2–13/2 15 153.2464 2.3

7–7 15/2–15/2 15 153.2464 �2.38–7 15/2–13/2 16 353.2600 �1.58–7 17/2–15/2 16 353.3002 1.5

6–7 13/2–15/2 16 529.2830 1.8

6–7 11/2–13/2 16 529.3120 �1.8a Observed frequency � frequency calculated using the constants of Table 2 (values in kHz).

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 2571T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

In eqn. (2) Bv and Dv are the rotational and centrifugaldistortion constants for the vibrational state v. The parametersto be determined in eqn. (3) are the nuclear quadrupolecoupling constants eQq(Lu) and eQq(X) for lutetium and thehalogen X, respectively (eQq(F) ¼ 0, since I(F) ¼ 1/2), forvibrational state v. The nuclear spin–rotation constants CI(Lu)and CI(X) in eqn. (4) are also vibrational state-dependent. Fitswere carried out for each isotopomer and vibrational state; theresults are in Table 2. For 175LuF Dv was held fixed at its valuein ref. 4; for 176LuF it was scaled from its 175LuF value by1/m2,with m being the reduced mass of the molecule.

4.2. LuCl

Because the only previously reported spectrum of LuCl showedno rotational structure, the DFT calclulation was first used topredict re and ae, and hence a value for the rotational constantof 175Lu35Cl in the ground vibrational state. A value ofeQq(175Lu) from the DFT calculation was scaled by the ratioof the experimental and predicted values for LuF to predict thebasic 175Lu hyperfine patterns. The initial search for transitionsproduced signals for J ¼ 2–1 within 80 MHz of the prediction.Again the lines were strong, and visible this time after B20cycles. An example is in Fig. 2. Mass scaling, plus use of a DFTae value, produced excellent predictions of lines of less abun-dant isotopomers and of vibrationally excited molecules.

Lines of the J ¼ 1–0 and 2–1 transitions of 175Lu35Cl (statesv ¼ 0, 1, 2), and 175Lu37Cl (states v ¼ 0, 1), and of J ¼ 2–1 of176Lu35Cl (state v ¼ 0) were measured and assigned. Thecoupling scheme used was J þ ILu ¼ F1 and F1 þ ICl ¼ F.The measured frequencies and their assignments are in Tables3 and 4.

As with LuF, preliminary state-by-state analyses were car-ried out for each observed isotopomer and vibrational state ofLuCl. The program was again SPFIT. The fitted constantswere the rotational and centrifugal distortion constants, plusnuclear quadrupole and nuclear spin–rotation coupling con-stants of both Lu and Cl. The results are in Table 5.

5. Dunham-type fits

It is possible to use the rotational constants in Tables 2 and 5 todetermine values of the equilibrium internuclear distance re.However, such a procedure ignores the possibility of Born–Oppenheimer breakdown (BOB), which recently has beenfound to be significant for a large number of metal-containingdiatomic molecules. These have included ZrO and ZrS,27

HfO,28 HfS,29 BiN,30 PtSi,31 SbN and SbP,18 and PtS.17 It

thus seemed appropriate to check whether BOB has an effecton the spectra of LuF and LuCl.Accordingly, for both molecules, were carried out using the

energy expression32–34 for isotopomer a of diatomic moleculeAB in a 1S electronic state:

Eav;J ¼

Xkl

Yakl vþ 1

2

� �k

½JðJ þ 1Þ�l ð5Þ

with

Yakl ¼ Uklm

�k2�l

a 1þmeDAkl

MAþ DB

kl

MB

� �� �; ð6Þ

where Ukl is a mass-independent Dunham-type parameter, me

is the electron mass, ma the reduced mass of isotopomer a, andMA, MB are the atomic masses of A and B. Dkl

A and DklB are

isotopically independent BOB parameters, with only D01A and

D01B being of significance here.Eqns. (5) and (6) do not consider hyperfine structure.

Accordingly, to apply them to LuF and LuCl it was necessaryto calculate unsplit line frequencies, with hyperfine structureremoved, for each observed rotational transition. This wasdone using the rotational constants and centrifugal distortionconstants of Tables 2 and 5, retaining enough significantfigures to reproduce the experimental accuracies.

5.1. LuF

Unfortunately, because of lack of data BOB could not bedetected for LuF. With four measured transitions, a fit couldbe obtained only for U01, U11, and U21, with U02 fixed at itsvalue derived from the distortion constant De found in theliterature.4 The results are given in Table 6, which shows well-determined values for the parameters. Values are also pre-sented for Y01, Y02, Y11, and Y21, plus re (discussed in Section6(a)), for the two isotopomers.

5.2. LuCl

The situation was more favourable for LuCl. In this case thereare nine available measured transitions. Their frequenciescould be used only cautiously, because they had to be calcu-lated from the rotational and distortion constants derivedusing SPFIT as discussed in Section 4 above. There was noproblem for 175Lu35Cl in the states v ¼ 0 and 1, or for175Lu37Cl in the state v ¼ 0; for each of these situations two

Table 2 State-by-state spectroscopic constants (in MHz) of LuF

Parameter v ¼ 0 v ¼ 1 v ¼ 2

175Lu19F

Bv 8000.334 524(42)a 7953.603 293(42) 7906.977 672(42)

103Dv 6.03b 6.06b 6.18b

eQqv(Lu) �4957.538 64(77) �4919.599 25(77) �4881.907 95(77)

103CI(Lu) 8.763(25) 8.864(25) 8.752(25)

CI(F) 0.035 56(19) 0.034 95(19) 0.035 25(19)

176Lu19F

Bv 7995.878 582(48)

103Dv 6.1c

eQqv(Lu) �6994.1495(12)103CI(Lu) 6.203(14)

CI(F) 0.035 03(20)

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

least significant figures. b Value from ref. 4. c Value from ref. 4, scaled

by m�2 (m ¼ reduced mass of the molecule).

Fig. 2 Section of power spectrum of the J ¼ 1–0, v ¼ 0 transition of175Lu35Cl obtained using 1776 averaging cycles. 4k data points wererecorded and the power spectrum is shown as a 4k transformation.

2572 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

rotational transitions were measured and a full set of constantswas derived. For 175Lu35Cl (v ¼ 2), 176Lu35Cl (v ¼ 0) and175Lu37Cl (v¼ 1) only one transition was found. Accordingly, avalue for the distortion constant had to be assumed, but thiswas not a problem in obtaining the unsplit line frequency,because any error would be absorbed by the rotational con-stant. However, for the first two isotopomers, a value forCI(Cl) also had to be assumed. Although its value was esti-mated by scaling from known values with the rotationalconstants and nuclear g-factors, and was hence reasonable,its contribution was B1�2 kHz to the transition frequencies.These data were accordingly weighted down by a factor of B4in the Dunham-type fit. For 175Lu37Cl (v ¼ 1) every parameterexcept the rotational constant had to be assumed, making thesemeasurements useless in the Dunham-type fit; they wereomitted.

Even then, the small data set meant that a fairly complexprocedure had to be carried out. An initial fit to eqns. (5) and(6) including U01, U11, U02, and U21 was performed, butomitting all BOB parameters; an unacceptable rms deviationof B10 kHz was obtained. A second fit released in additionDLu01 and DCl

01. This drastically reduced the rms deviation to lessthan 1 kHz, and produced two seemingly good BOB para-meters. However, DLu

01 was strongly correlated with U01, so twonew fits were done, in which only one of DLu

01 or DCl01 was

released, with the other set to zero. The value for DLu01 changed

drastically, and was still correlated with U01. The value of DCl01

held firm and was well determined. The rms value wasB2 kHz,which was acceptable. The result with DLu

01 ¼ 0 is presented inTable 7 as Method A.

However, DLu01 is unlikely to be zero. Accordingly a new fit

was carried out assuming DLu01 C DCl

01.17,32 The results are in

Table 7, (Method B), which also contains values for Y01, Y02,Y11,and Y21, plus equilibrium internuclear distances evaluatedfrom Y01 for each isotopomer. The isotopic variation of re iscomparable to that found in other molecules, such as ZrO,27

HfS29 and PtSi.31

There is an additional concern. Because Lu is a heavy atom,it is possible that the spectrum may be significantly affected bynuclear field shift effects. These arise because the Lu nucleuscan no longer be considered a point charge, but to have avolume. To account for this possibility eqn. (6) for Y01

a wasmodified to:34

Ya01 ¼ �U01m�1a 1þme

DLu01

MLuþ DCl

01

MCl

� �þ VLu

01 dhr2iLuLu0� �

: ð7Þ

(Field shift effects of Cl, having a much smaller nucleus, canreasonably be ignored.34) VLu

01 is the nuclear shift parameter ofLu given by:

VLu01 ¼

ZLue2

3e0kere

drLueldr

� �re

ð8Þ

where ZLu denotes the atomic number, ke is the harmonicstretching constant of LuCl, e0 is the permittivity of a vacuum,and (drLuel /dr)re represents the derivative of the electron densityat the Lu nucleus with respect to internuclear separation,evaluated at r ¼ re �U01 is given by

�U01 ¼ U01(1 þ VLu01 hr2iLu). (9)

Here, hr2iLu is the mean square nuclear charge radius ofLu available from the literature;35 it is specific to a givenisotope, so that �U01 is isotope-dependent. (U01 is isotope-independent.)

Table 3 Measured transition frequencies (in MHz) for 175Lu35Cl

J0–J00 F10–F1

00 F0–F00 v ¼ 0 Obs. � calc.a v ¼ 1 Obs. � calc.a v ¼ 2 Obs. � calc.a

1–0 7/2–7/2 5–5 5548.6994 �0.53–3 5548.7688 0.3

4–4 5548.8152 �0.59/2–7/2 5–4 6374.4979 1.2 6348.4542 0.0

4–3 6374.5240 �0.7 6348.4896 �1.06–5 6374.5941 0.4 6348.5791 �0.63–2 6374.6173 0.3 6348.6126 2.0

5/2–7/2 3–4 6628.0479 �0.2 6600.5705 �0.04–5 6628.0905 �0.3 6600.6258 �0.4

2–1 9/2–9/2 3–3 11 663.3913 1.3

6–6 11 663.4167 �0.9 11 617.5186 0.6 11 571.6791 1.5

4–4 11 663.4726 2.1 11 617.5879 1.0

5–5 11 663.4955 �0.7 11 617.6198 �0.3 11 571.7629 �1.57/2–9/2 2–3 11 759.0501 �0.1

5–6 11 759.0986 �0.1 11 712.6029 0.0

3–4 11 759.1960 1.5

4–5 11 759.2454 1.1 11 712.7918 0.2

5/2–5/2 1–1 11 941.3773 �0.94–4 11 941.4521 �1.1 11 893.9875 �0.33–3 11 941.5748 �2.2 11 894.1477 �0.8

11/2–9/2 6–5 12 387.3144 0.0 12 337.3351 �1.5 12 287.4381 �3.67–6 12 387.3481 �2.2 12 337.38100 �1.8 12 287.4855 3.6

9/2–7/2 5–4 12 489.1772 �0.1 12 438.6109 0.2

4–3 12 489.2271 0.4 12 438.6760 1.0

6–5 12 489.3132 1.8 12 438.7860 1.7

3–2 12 489.3556 0.2 12 438.8413 �0.93/2–5/2 3–4 12 490.6881 �1.8 12 440.1338 �2.5 12 389.6583 0.0

7/2–7/2 4–4 12 584.9270 1.7 12 533.7838 1.6

3–3 12 584.9517 1.1

5–5 12 584.9926 0.1 12 533.8707 1.6

2–2 12 584.0143 �1.3a Observed frequency � frequency calculated with the constants of Table 5 (values in kHz).

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 2573T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

A new fit was then carried out, using eqns. (5) and (7). Thisrequired that a reference isotopomer be chosen;34 this was175Lu35Cl. In this case dhr2iLuLu0 in eqn. (7) is the change inmean square nuclear charge radius of Lu on isotopic substitu-tion (here from 175Lu to 176Lu); it is also available fromtables.36 �U01 is that of the reference isotopomer 175Lu35Cl.Because of insufficient data, VLu

01 was fixed at a value estimatedusing eqn. (8), with (drLuel /dr)re evaluated from the results of theDFT calculations25 described in section 3 above.

The final fit was thus to �U01, U11,U02, U21, and DCl01, with DLu

01

constrained to DCl01, and VLu

01 fixed at 2.4 � 10�6 fm�2 from theDFT calculation. The result is in Table 7 (Method C).

In Table 7 the constants from Methods A and B show thatU01 varies as D

Lu01 is varied, in keeping with the high correlation

between these constants found in the initial fits. Thus fixing DLu01

at a reasonable value should produce an improved U01. Itappears from the result of Method C that the data areinsensitive to field shift effects, even though VLu

01 is not insig-nificant (see below). This leads to the conclusion that becausethe fitting parameter of Method C is �U01, then the value of U01

from Method B (which is numerically the same) is simply aneffective value, without a specific physical meaning.

Table 8 gives a comparison of the results of the Dunham-type fits with those of several related molecules. Clearly onlylimited results could be obtained for LuF. The situation wasbetter for LuCl, for which DCl

01 could be determined, thusconfirming the presence of Born–Oppenheimer breakdown.However, neither DLu

01 nor VLu01 could be obtained directly from

the spectrum, and both were fixed in the fits. The former wasassumed to be DCl

01 � 1, and the latter was the theoretical value.Comparison with the other results in Table 8 indicates thatboth fixed values are reasonable, and gives confidence that themost physically reasonable values available for �U01 and U01

have been obtained.It was initially surprising that theVLu

01 -dependence is so slight.Table 8 shows that although VLu

01 is one of the smallest examplesknown, it is not much smaller than V01

Pb in PbS or V01Tl in TlCl,

which have significant effects on the apparent values of D01Pb or

D01Tl, respectively. For both of these molecules (and also for PtSi

and PtS) there are significant differences between the two D01i

values when V01i is omitted from the fit, which can be accounted

for if V01i is included. Since determinations of both DLu

01 and VLu01

in LuCl depend on the isotopic substitution 175Lu to 176Lu theinsensitivity of the spectrum to these parameters is likely due tothe weak observed spectrum of 176Lu35Cl. (It should be addedparenthetically that a fit to VLu

01 with DLu01 fixed does give a fit.

However, the value obtained, VLu01 ¼ �2.6 � 10�5 fm2, is of the

wrong order of magnitude and has the wrong sign.)

6. Discussion

6.1. Internuclear distances

Equilibrium internuclear distances re have been evaluated forboth molecules. Several possible methods were available, all ofwhich give precise, but slightly differing values. Accordingly itis necessary to be clear on how the values were obtained, andwhat they mean.One approach is to use the Y01 values in Tables 6 and 7 to

calculate re of each isotopomer from

re ¼C2ffiffiffiffiffiffiffiffiffiffiffiffiYa

01map ð10Þ

where ma is the reduced mass of isotopomer a in atomic massunits (u). The atomic masses used were the recent values ofref. 37. C2 is given by

C2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1017�hNA

8p2:

rð11Þ

With the 1998 fundamental constants recommended by CO-DATA38 C2 has the value 710.900 1379(25) A MHz1/2 u1/2. Theresults are the traditional re values, which are isotopomerdependent because of BOB. The resulting re values for LuFand LuCl are in Tables 6 and 7, respectively.

Table 4 Measured transition frequencies (in MHz) for 175Lu37Cl and 176Lu35Cl

J0–J00 F10–F1

00 F0–F00 v ¼ 0 Obs. � calc.a v ¼ 1 Obs. � calc.a

175Lu37Cl

1–0 9/2–7/2 5–4 6098.8361 1.7

4–3 6098.8555 �0.86–5 6098.9121 2.7

3–2 6098.9271 �1.05/2–7/2 3–4 6352.8041 �0.7

2–3 6352.8214 �3.04–5 6352.8394 1.1

2–1 9/2–9/2 4–4 11 110.8369 2.8

11/2–9/2 6–5 11 834.7735 �3.0 11 788.1075 �0.27–6 11 834.8017 �2.4 11 788.1430 0.2

9/2–7/2 5–4 11 936.4994 �0.24–3 11 936.5406 2.6

3/2–5/2 3–4 11 938.0727 �5.37/2–7/2 5–5 12 033.7404 1.0

5/2–7/2 3–4 12 468.4457 3.6

1–2 12 468.4715 0.8

176Lu35Cl

2–1 8–8 19/2–19/2 11 577.4157 1.3

9–8 19/2–17/2 12 415.4210 �1.521/2–19/2 12 415.4531 �2.7

5–6 13/2–15/2 12 478.4696 �1.47–7 17/2–17/2 12 561.0464 �0.88–7 17/2–15/2 12 616.8306 1.4

13/2–11/2 12 616.9563 3.0

6–7 13/2–11/2 12 942.6297 0.8

a Observed frequency � frequency calculated with the constants of Table 5 (values in kHz).

2574 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

For LuF, two values of re, one for each isotopomer, aregiven in Table 6. They must be viewed with caution. Theyignore the possibility of Born–Oppenheimer breakdown, be-cause the breakdown terms could not be determined from thespectrum. Furthermore, this means the two values of re must bethe same, as they are. In the absence of BOB or field shiftparameters, this is as far as one can go for LuF.

For LuCl (see Table 7), the values for the three isotopomersseem reasonable; their variations ofB10�6 A give a measure ofhow well the Born–Oppenheimer approximation holds for thismolecule. In addition, an isotope-independent Born–Oppen-heimer bond length can be obtained. It is given by39

rBOe ¼ C2ffiffiffiffiffiffiffiffiU01

p ð12Þ

In this case �U01 from Method C is first converted to U01

using eqn. (9) with VLu01 derived from the DFT calculations,

and hriLurms ¼ 5.3777(301) fm.35 The resulting value is given inTable 9.

To estimate an uncertainty in reBO, separate fits of the data

were carried out varying DLu01 by � 1.32 The uncertainty in re

BO

in Table 9 reflects the variation obtained.

6.2. Vibrational constants and dissociation energy

For both LuF and LuCl the vibrational frequency, anharmo-nicity constant and dissociation energy De have been estimated

using the following equations40,41 which assume a Morsepotential:

Y10 ’ oe ’

ffiffiffiffiffiffiffiffiffiffiffi4Y3

01

�Y02

sð13Þ

Y20 ’ oexe ’ Y01�Y11Y10

6Y201

þ 1

� �2

ð14Þ

D e �Y2

10

4Y20: ð15Þ

The results for 175Lu19F and 175Lu35Cl are in Table 10, incomparison with available values from the literature and theresults of the DFT calculations. The larger uncertainties forLuF arise through use (of necessity) of the distortion constantY02 B �De from the electronic spectrum.4

For LuF there is excellent agreement between the presentand literature values of both oe and oexe. Since the literaturevalues were obtained directly from the vibrational energies2 itappears that the Morse potential applies well to the molecule.In turn this inspires confidence in the calculated dissociationenergy. The agreement with literature values for LuCl is poorerbecause the literature values are uncertain. However, it is notunreasonable to assume that the Morse potential applies in thiscase as well, making the present values reliable. For both

Table 5 State-by-state spectroscopic constants (in MHz) of LuCl

Parameter v ¼ 0 v ¼ 1 v ¼ 2

175Lu35Cl

Bv 3072.566 310(45)a 3060.212 367(64) 3047.875 316(246)

103Dv 1.0709(60) 1.1071(84) 1.108b

eQqv(Lu) �4290.655 60(42) �4266.473 00(61) �4242.452(11)103CI(Lu) 5.563(12) 5.627(13) 6.04(29)

eQqv(Cl) �0.647 27(63) �0.83942(56) �0.716(21)103CI(Cl) 2.141(42) 2.547(46) 2.9b

175Lu37Cl

Bv 2934.369 668(69) 2922.844 251(35)

103Dv 1.2327(85) 1.23b

eQqv(Lu) �4290.853 27(86) �4266.5b103CI(Lu) 4.597(16) 4.60b

eQqv(Cl) �0.500 29(92) �0.648b103CI(Cl) 1.471(56) 1.5b

176Lu35Cl

Bv 3069.6538(10)

103Dv 1.108b

eQqv(Lu) �6053.794(60)103CI(Lu) 3.26(57)

eQqv(Cl) �0.611(61)103CI(Cl) 2.2b

a Numbers in parentheses are one standard deviation in units of the least significant figures. b Fixed value.

Table 6 Dunham-type parameters for LuF

U01/u MHz U02/u2 MHz U11/u

3/2 MHz U21/u2 MHz DLu

01 D01F

LuF 137 505.300(15) �1.771a �3322.784(122) 15.49(17) 0a 0a

Y01/MHz 103Y02/MHz Y11/MHz 103Y21/MHz

Be �103De �ae 103ge re/A175LuF 8023.7399 �6.03 �46.836 91 52.75 1.917 118 15176LuF 8019.2640 �6.02 �46.797 72 52.69 1.917 118 14

a Fixed value.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 2575T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

molecules the DFT values of oe agree well with experiment.The agreement for oexe is poorer.

The implication appears to be that although the DFTpotential functions are reasonable overall, they are not sogood in detail. This appears also to be reflected in the DFTvalues of re (Table 9).

6.3. Nuclear quadrupole coupling constants

Nuclear quadrupole coupling constants have been evaluatedfor both isotopes of Lu and Cl. The latter are presented inTable 11 in comparison with values for other diatomic metalhalides. The eQq(Cl) values for LuCl are among the smallest

known. They have been used to evaluate the ionic character icof LuCl using42

ic ¼ 1þ eQqðClÞeQq310ðClÞ

ð16Þ

with eQq310(Cl) ¼ 109.7 MHz.42 This gives ic B 99.4%,indicating that LuCl is essentially fully ionic. It is notable fromTable 11 that this value is considerably higher than that ofNaCl, usually considered the benchmark ionic molecule. Also,the ionic character of LuCl is consistent with that reportedearlier for LuF.6

Table 7 Dunham-type parameters for LuCl

U01/u MHz U02/u2 MHz U11/u

3/2 MHz U21/u2 MHz DLu

01 DCl01

Method A (VLu01 ¼ 0)a

89 729.38(16)b �1.008(47) �1946.30(15) 7.20(30) 0c �2.96(12)Method B (VLu

01 ¼ 0)a

89 730.22(16) �1.010(47) �1946.29(15) 7.19(30) �2.97d �2.97(12)

Y01/MHz 103Y02/MHz Y11/MHz 103Y21/MHz

Be �103De �ae 103ge re/A175Lu35Cl 3078.7500 �1.191 �12.370 73 8.45 2.373 2930175Lu37Cl 2940.1391 �1.086 �11.544 74 7.70 2.373 2900176Lu35Cl 3075.8296 �1.189 �12.353 14 8.43 2.373 2929

Method C (VLu01 ¼ 2.4 � 10�6 fm2)e

�U01 ¼ 89 730.24(16)f �1.011(47) �1946.28(15) 7.18(30) �2.98d �2.98(12)a VLu

01 was fixed at this value in the fit. b Numbers in parentheses are one standard deviation in units of the least significant figures. c DLu01 was fixed at

zero in Method A. d DLu01 was held fixed at DCl

01 in Methods B and C. e This VLu01 value, obtained from the DFT calculations, was fixed in the fit. f This

value is �U01, related to U01 by eqn. (9).

Table 8 Born–Oppenheimer breakdown and field shift and mass-independent parameters of transition metal- and lutetium compounds

AB D01A D01

B 107VA01/fm

�2 U01/u MHz Ref.

LuF — — 137 505.300(15)a This work

LuCl �2.96b �2.96(12) 89 730.23(16) This workb

LuCl �3(1)c �2.98(12) 24d 89 724.02(36)ce This workf

�U01 ¼ 89 730.25(29)cf

ZrO �4.872(39) �6.1888(25) 172 480.086(98) 27

ZrS �5.325(82) �6.523(39) 108 670.07(19) 27

HfO �3.40(57) �5.656(23) 170 239.68(18)g 28

HfS �4.18(53) �5.820(49) 108 708.38(27) 29

PtSi 10.75(68) �2.99(4) 118 923.32(33)h 31

PtSi �3(1)c �2.99(4) �72(12) 118 952.7(47)e

�U01 ¼ 118 927.94(54)

�110d 25

PtS �42.60(74) �62.466(49) 121 604.07(30)h 17

PtS �62.5(10)c �62.46(5) �104(9) 121 647.1(20)e

�U01 ¼ 121 610.91(50)

�84d 25

TlCl �18.96(200) �1.243(49) 81 857.0(1)gh 45

TlCl �0.5i �1.257(73) 40.9(55) 46

88.0d 25

PbS �12.94(141) �1.997(71) 96 642.20(50)gh 45

PbSh �1.333i �1.988(70) 26.38(51) 46

34.5d 25

BiN — �2.788(19) 135 003.18(10)h 30

BiN �2.8(10)c �2.788(19) 32d 134 991.08(45)e

�U01 ¼ 135 004.17(10)

a The numbers in parentheses are one standard deviation in units of the least signficant figures. b Values obtained using Method B (see text). c This

is an estimated value and uncertainty based on the assumption that DA01 ¼ DB

01 � 1. The uncertainties in �U01 and U01 reflect this assumption. d Value

obtained using DFT following the method outlined in ref. 25. For LuCl and BiN the calculated value was used directly to obtain �U01 and

U01.e Value obtained from �U01 using eqn. (9). f Value obtained using Method C (see text). g This value for U01 has been calculated from the data

given in the corresponding reference. h In this fit nuclear field shift effects were neglected. i This value was held fixed in the fitting procedure. See

ref. 34 for details of the fitting procedure used.

2576 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

The magnitudes of the Lu nuclear quadrupole couplingconstants for both isotopes are, as predicted, very large, beingcomparable to (in LuF) or larger than (in LuCl) the rotationalconstants. For LuF the value is much larger in magnitude thanthe approximate value obtained from the electronic spectrum.6

Tables 2 and 5 show a clear vibrational state dependence ineQq(175Lu) for both LuF and LuCl. The constants have beenfitted to the expression

eQqv ¼ eQqe � eQq0 vþ 1

2

� �þ eQq00 vþ 1

2

� �2

ð17Þ

where eQqv is the coupling constant for vibrational state v,eQqe is the equilibrium value, and eQq00 and eQq00 give thevibrational state dependence. The results for 175LuF and175Lu35Cl are in Table 12.

The electron configuration of free Lu1 is [Xe]4f146s2 (1S0),predicting a spherical electron density distribution and a Lunuclear quadrupole coupling constant of zero. The nonzeroeQq(Lu) values suggest that the anion (F�, Cl�) causes con-siderable distortion of the Lu1electron cloud. This distortionwas recognized by Gotkis43 in his electronic structure modelfor rare earth monohalides. He depicted Lu1 in its monoha-lides as containing a [Xe]4f14 core plus a s-orbital localized onLu and polarized away from the halide. (Gotkis calls thisorbital s6s). Our own calculations confirm this and indicatethat this orbital is B95% 6s plus B5% 5dz2.

7. Conclusions

LuF and LuCl comprise only the second set of rare earthhalides whose rotational spectra have been reported (after theytterbium halides44). The laser ablation technique has beenproven to be an ideal method to prepare them, and the spectrawere generally strong. The rotational constants of 175LuF areconsiderably more precise than the literature values; those for176LuF are the first reported. New, precise values of hyperfineconstants of Lu and F have also been obtained. The experi-mental re value for 175LuF is a major improvement over theliterature value.For LuCl this is the first high resolution spectrum ever

reported, and a large set of precise spectroscopic constantshas been obtained, including hyperfine constants for all nuclei.Experimental evidence for Born–Oppenheimer breakdown hasbeen obtained. Although a significant Lu nuclear shift effectwas predicted theoretically, it was found to have no influenceon the observed spectrum. Equilibrium bond lengths re havebeen evaluated for each isotopomer, along with a Born–Oppenheimer bond length. The Cl nuclear quadrupole cou-pling constant shows LuCl to be highly ionic. The very largeLu quadrupole coupling constants are consistent with strongpolarization of the Lu1 electron distribution by the anions.

Table 9 Equilibrium bond lengths of LuF and LuCl

Molecule re/A Comment

LuF 1.917 118 15(11)a Experimental re for175Lu19F

1.9165(2) Ref. 3

1.9237 DFT calculation; this work

LuCl 2.373 2930(21) Experimental re for175Lu35Cl

2.373 3088(47)b rBOe2.3825 DFT calculation; this work

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

least significant figures. b Obtained from U01 derived using Method

C (Table 7). The uncertainty reflects the range of assumed values of

DLu01 ¼ �3 � 1.

Table 10 Vibrational parameters and dissociation energies of175Lu19F and 175Lu35Cl

Parameter LuF LuCl

oe/cm�1 This work 618(12)a 337(1)

Literature 611b 350–387c

DFT 623 329

oexe/cm�1 This work 2.82(8) 1.048(4)

Literature 2.68b 0.78–1.76c

DFT 4.02 3.01

De/kJ mol�1 This work 405(19) 324(2)

De/eV This work 4.19(20) 3.35(2)

De/eV Literature 3.451(16)d —

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

least significant figures. b Calculated from Table 2 of ref. 2. c Ref. 1.d Ref. 47.

Table 11 Halogen nuclear quadrupole coupling constants, ionic characters of lutetium halides and related species, the corresponding bond lengths

and related constants

Species eQq0/MHz Ionicity ic (%) Bond length/A Dipole moment m/D Electronegativity difference48 Ref.a

175LuF 495b 1.9175 2.71 Present study175Lu35Cl �0.647 99.4 2.3733 1.89 Present study174YbF 2.0165 3.91 2.88 44174Yb35Cl �2.16 98.5 2.4883 2.06 44

LaCl �0.950 99.1 2.4980 2.06 49

LaBr 13.624 98.2 2.6521 1.86 49

LaI �81.197 96.5 2.8788 1.56 49

MgCl �11.62 89.4 2.1991c 1.85 50

CaCl �1.002 99.1 2.4390 4.27d 2.16 51

NaCl �5.642 94.8e 2.3609f 9.002g 2.23 52

KCl 0.04 100 2.6668f 10.269h 2.34 42

a Or as stated otherwise. b See ref. 6. c See ref. 53. d See ref. 54. e See ref. 51. f See ref. 55. g See ref. 42. h See ref. 56.

Table 12 Vibrational state dependence of 175Lu nuclear quadrupole

coupling constants of 175LuF and 175Lu35Cl

Constanta 175LuF 175Lu35Cl

eQqe �4976.6014(18)b �4302.8074(43)eQq0 �38.1875(36) �24.344(13)eQq00 �0.1240(16) �0.0807(88)a The parameters are defined in eqn. (17). The equilibrium value is

eQqeb Numbers in parentheses are one standard deviation in units of

the least significant figures.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 2577T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online

Acknowledgements

This research has been supported by grants from the NaturalSciences and Engineering Research Council of Canada(NSERC) and the Berliner Programm zur Forderung derChancengleichheit fur Frauen in Forschung und Lehre.

References

1 J. Kramer, J. Chem. Phys., 1978, 69, 2601.2 J. d’Incan, C. Effantin and R. Bacis, J. Phys. B, 1972, 5, L189.3 C. Effantin, G. Wannous, J. d’Incan and C. Athenourt, Can.

J. Phys., 1976, 54, 279.4 C. Athenourt, J. L. Femenias and C. Effantin, J. Phys. B, 1976, 9,

2893.5 C. Effantin, G.Wannous and J. d’Incan,Can. J. Phys., 1977, 55, 64.6 C. Effantin, R. Bacis and J. d’Incan, Phys. Rev. A, 1977, 15, 1053.7 S. G. Hacker, Astrophys. J., 1936, 83, 140.8 C. R. Cowley, A. P. Cowley, G. C. L. Aikman and H. M.

Crosswhite, Astrophys. J., 1977, 216, 37.9 K.-I. Kato, Publ. Astron. Soc. Jpn., 2003, 55, 1133.10 C. Sneden, J. J. Cowan, J. E. Lawler, I. I. Ivans, S. Burles, T. C.

Beers, F. Primas, V. Hill, J. W. Truran, G. M. Fuller, B. Pfeifferand K.-L. Kratz, Astrophys. J., 2003, 591, 936.

11 J. Johnson and M. Bolte, Astrophys. J., 2004, 605, 462.12 M. Busso, R. Galliano and G. J. Wasserburg, Annu. Rev. Astron.

Astrophys., 1999, 37, 239.13 D. L. Burris, C. A. Pilachowski, T. A. Armandroff, C. Sneden,

J. J. Cowan and H. Roe, Astrophys. J., 2000, 544, 302.14 T. Balle and W. Flygare, Rev. Sci. Instrum., 1981, 52, 33.15 Y. Xu, W. Jager and M. Gerry, J. Mol. Spectrosc., 1992, 151, 206.16 K. A.Walker andM. C. L. Gerry, J. Mol. Spectrosc., 1997, 182, 178.17 S. A. Cooke and M. C. L. Gerry, J. Chem. Phys., 2004, 121, 3486,

and references therein.18 S. A. Cooke and M. C. L. Gerry, Phys. Chem. Chem. Phys., 2004,

6, 4579.19 S. A. Cooke and M. C. L. Gerry, J. Am. Chem. Soc., 2004, 126,

17000.20 E. J. Baerends, D. E. Ellis and P. Ros, Chem. Phys., 1973, 2, 41.21 E. J. Baerends and P. Ros, Chem. Phys., 1973, 2, 52.22 E. J. Baerends and P. Ros, Int. J. Quantum Chem. Symp., 1978, 12,

87.23 SCM, ADF Program System, Release 2002.03, Scientific Comput-

ing and Modelling NV, Amsterdam, 2000.24 P. R. T. Schipper, O. V. Gritsenko, S. J. A. van Gisbergen and E.

J. Baerends, J. Chem. Phys., 2000, 112, 1344.25 S. A. Cooke, M. C. L. Gerry and D. P. Chong, Chem. Phys., 2004,

298, 205.26 H. M. Pickett, J. Mol. Spectrosc., 1991, 148, 371.

27 S. A. Beaton and M. C. L. Gerry, J. Chem. Phys., 1999, 110,10715.

28 A. Lesarri, D. J. Brugh and R. Suenram, J. Chem. Phys., 2002,117, 9651.

29 S. A. Cooke and M. C. L. Gerry, J. Mol. Spectrosc., 2002, 216,122.

30 S. A. Cooke, J. M. Michaud and M. C. L. Gerry, J. Mol. Struct.,2004, 695, 13.

31 S. A. Cooke, M. C. L. Gerry, D. J. Brugh and R. D. Suenram, J.Mol. Spectrosc., 2004, 223, 185.

32 J. K. G. Watson, J. Mol. Spectrosc., 1973, 45, 99.33 J. K. G. Watson, J. Mol. Spectrosc., 1980, 80, 411.34 J. Schlembach and E. Tiemann, Chem. Phys., 1982, 68, 21.35 E. G. Nadjakov, K. P. Marinova and Yu. P. Gangrsky, At. Data

Nucl. Data Tables, 1994, 56, 133.36 P. Aufmuth, K. Heilig and A. Steudel, At. Data Nucl. Data Tables,

1987, 37, 455.37 G. Audi, A. H. Wapstra and C. Thibault, Nucl. Phys. A, 2003,

729, 337.38 P. J. Mohr and B. N. Taylor, Rev. Mod. Phys., 1998, 72, 351.39 P. R. Bunker, J. Mol. Spectrosc., 1977, 68, 367.40 A. Kratzer, Z. Phys., 1920, 3, 289.41 C. L. Pekeris, Phys. Rev., 1934, 45, 98.42 W. Gordy and R. L. Cook, Microwave Molecular Spectra; Tech-

niques of Chemistry, Wiley & Sons, New York, 1984, vol. XVIII.43 I. Gotkis, J. Phys. Chem., 1991, 95, 6086.44 C. S. Dickinson, J. A. Coxon, N. R. Walker and M. C. L. Gerry,

J. Chem. Phys., 2001, 115, 6979.45 E. Tiemann, H. Arnst, W. U. Steida, T. Toerring and J. Hoeft,

Chem. Phys., 1982, 67, 133.46 H. Knoeckel, T. Kroeckertskothen and E. Tiemann, Chem. Phys.,

1985, 93, 349.47 R. R. Reddy, A. S. R. Reddy and T. V. R. Rao, Indian J. Pure

Appl. Phys., 1985, 23, 424.48 L. Pauling, The Nature of the Chemical Bond, Cornell University

Press, Ithaca, NY, 2nd edn., 1948.49 D. S. Rubinoff, C. J. Evans and M. C. L. Gerry, J. Mol.

Spectrosc., 2003, 218, 169.50 Y. Ohshima and Y. Endo, Chem. Phys. Lett., 1993, 213, 95.51 W. J. Childs, D. R. Cok and L. S. Goodman, J. Chem. Phys.,

1982, 76, 3993.52 J. W. Cederberg and C. E. Miller, J. Chem. Phys., 1969, 50, 3547.53 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular

Structure, van Nostrand Reinhold, New York, 1979.54 T. Torring, W. E. Ernst and S. Kindt, J. Chem. Phys., 1984, 81,

4614.55 R. J. Mawhorter, M. Fink and J. G. Hartley, J. Chem. Phys., 1985,

83, 4418.56 A. J. Herbert, F. J. Lovas, C. A. Melendres, C. D. Hollowell, T. L.

Story, Jr. and K. Street, Jr., J. Chem. Phys., 1968, 48, 2824.

2578 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 5 7 0 – 2 5 7 8 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

Publ

ishe

d on

31

May

200

5. D

ownl

oade

d by

Uni

vers

ity o

f Pr

ince

Edw

ard

Isla

nd o

n 30

/10/

2014

08:

40:5

0.

View Article Online