D-nuclear quadrupole and H(D),19F nuclear-spin—nuclear-spin hyperfine coupling constants from rotational spectra of H2O…DF and H2O…HF

Volume92., numkr

4

CHEMICAL

29 October 1982

PHYSICS LETTERS

D-NUCLEAR QUADRUPOLE AND H(D),‘gF NUCLEAR-SPIN-NUCLEAR-SPIN WERFINE

COUPLING CONSTANTS FROM ROTATIONAL SPECTRA OF H,O...DF AND H20..,HF

A.C. LECON and L.C. WILLOUGHBY Chmropher

Jngold Lzborarones.

20 Gordon Sweet, Londorl

WClH

Recewed 9 September 1982;ln

Depvrmenr

OAJ,

of Chemlsrrj.

Umrersrry

College

London.

UK

timal form 22 September 1982

The hyperfme struc~u~z UI the lo, .- Ooo trxmt~ons of H20.. DT and H*O...HF arlsmg from D-nuclearquadrupoleAnd H@).t9F nuckarspin-nuclwipm coupl~~~ng effectshare been resolwd and measured by the rcc~q_uc oipulscd-noulc I-ouner-transfon mlcroware spectroscopy IO gw the followng hypcrfie couphg constmts Xllll - 263 3(X) LHr,D$

= 12 7(25) kHz2nd DfaF: _z.j~(5) kH7.

1. Introduction

We report the detection in the gas phase of the

speciesH,O...DF and HDO...DF of the hydrogenbonded complex formed by water with hydrogen fluoride. Each species has been identified through its *01+%0

rotational

transition for which, in the case

of H,O...DF, the characteristic hyperfiie structure arising from D-nuclear quadrupole and D,t9F nuclear-

Point motion, the electric field gradient at the D nucleus and the H(D)F internuclear distance. Consequently, such coupling constants are important sources of reformation about the dimer. We discuss here the magnitude of the reported coupling constants in relation to those of several other B...H(D)Fspecies and identify a systemattc behavlour as the strength of the intermolecular binding increases.

spin-nuclear-spin couplinghas been completely resolved and assigned. We also discuss here the complete resolution of the H,I9F nuclear-spin-nuclear-spin hyperfme pattern in the previously reported [I] lo, + Ooo transition of the species H,O...HF. A detailed analysisof these transitions for H,O..DFand H,O...HF leads to the II components, &t, $f,’ and D!oF, of the D-nuclear quadrupole, D,tgF spin-spin and H,lgF spin-spin coupling tensors, respectively. These results have been achieved by taking advantage of the high resolution and high sensitivity for weakly bound WITIplexes of a pulsed-nozzle, Fourier-transform microwave spectrometer. ‘Ihe hyperfiie coupling Constants x0:, DForand DtaF of a hydrogen-bonded dimer B...H@)F in which the H(D)F molecule lies along the a axis of the dimer can differ from the corresponding quantities $, DtF, DtF of free H(D)F by virtue of three properties of H(D)F that change on dimer formation: the zero0 009.2614/82/0000-0000/S

02.75 0 1982 North-Holland

2. Experimental

rotational transnion in the vtbraThe lo, ~0, tional ground state of each of H,O...DF, H20...HF and HDO...DF wasobserved by using the pulsed-nozzle, Fourier-transform rmcrowave spectrometer recently constructed at University College London. The spectrometer is of the type developed by Flygareand coworkers [2,3] and wti be described in detail elsewhere. Gas mixtures of water at its vapour pressure

and hydrogen fluoride at a partral pressure of -25 Torr in argon at total pressure of ti.5 atm and room temperature were pulsed into an evacuated Fabry-Wrot cavity through a nozzle of 0.7 mm diameter. Rotational transitions with frequency falling withm the cavity bandwidth (~1 MHz) were polarized by a delayed microwave pulse 333

Volume

92. number

CHEhUCAL

4

I.

0

I28

61

IO2

PHYSICS

-

320

256

29 October

LE7TERS

1982

--

Time Ips

Fig. 1 Tnns~r cm~won from the I,,, -0oo transnmn Hz0 DF chgrtlzcd at a rate of 0 5 w/pomt

oi

and the subsequent coherent molecular emission was detected and digitized at the rate of 0.5 ~.lsper pomt for 512 points. The result of averagmg several such emissions from the lo1 +Ooo transition IS shown in fig. 1 for H,O...DF. The Founer transform of the tLmedomam recording in fig. 1 and that of the corre-

0

FIN 3. Power specrrum resultmg from the I,,, - Ooo emw slon sgnal oi HZ0 .HT. Frequenciesare ofiset 81 a rate of 3 90625 kHz/pomt from the polanlzmg irequcncy 14103 0791 MHz. The calculated hyperrme sphtumgof the 101 t 000 rranuflon of H20...HF is mdlcared by the stick dhgram.

spending transition of H,O...HF are displayed in figs. 2 and 3, in which the high resolution of the technique is clearly evident. Each of the D-nuclear quadrupole or H, I9Fspin-spin hyperfmecomponentsappearsin

r

fact as a doublet as a result of a well-understood

Doppler sphttmg [4] characteristic of this type of spectrometer.

3 Results 3.1. Determirtation of the hyperjine coupling constants x,t,

I.

0

.

100

Tlg Z Pouer

I. 200

300

I

I

400

spectrum irom Fourier tnnsiormarion

of the

signal shown m fig I _rrcquencles are oiisct at 3 nte 3 9067-S kHr;pomt from Ihe polvizmg frequency 14396.1983 MHz. The calcularcd hyprfine sphrrmg of the 10, .- 0~ Lranwon oiH20..

334

DF IS mdnxtrd

by the suck

dupm.

DEF and DiF

Observed frequencies (estimated accuracy 1 kHz) of the hyperfiie components in the 1o1 + Ooo transittons of H,O...DF and HzO...HF are recorded in table 1. The hyperfme pattern in the H,O..DF complex (see fig. 2) IScharacteristic of the presence of D nuclear quadrupole coupling and D,lgF nuclear-spinnuclear-spin coupling while that for HzO...HF arises from H,tgF spm-spin coupling alone (see fig. 3). There E no evidence of further line sphtting or

Volume 92, number 3

CHEhllCALPHYSICSLET'l-ERS

29October 1982

Table I Observed and calculated frcqucncia of hyprrfimr components m the lo1 - OW transrtrons of H20. ill- and Hz0 ..DT Transrtron /‘I’F

H20. DF

I;+Of: 1:&-o;:

II W

I

14396.5100

-1.5

-0 6

l~f-0~~ 33

33

14396 4825

19

01

l~~‘O~? 35

33

14396.4185

3.4

I.5

I fT’O?S 31

HF

I a)

.- J”I”F”

11396 5035

1 ig_o;; I;;+()+;

Hz0

U,,bs - “~31~(kHz)

vubs(h!tf@

-4.1

-1.3

-1 33

111-011 IOI-000 I lz-oI1 IIO-011

14396 1918

0’

-0 1

15302.7898 l-I402 8172 14402.8656 14402.9710

0.1 -3 0 3.3 03

I6 -3.5 13 0.7

a) Sptn-rotst~on cifects not mcludcd b) Obserred frequcnacs fist corrccred for spm-ror~lon efirctj (see IN).

broadening resulting from coupling of the proton nuclear spins in the H20 molecule among themselves or with those of rhe H@)F molecule and the molecular rotation. This observation is consistenr with pr+vlous concIusions [I 1 about the potential energy function

of H?O...HF. Ithasbeen established unambiguously [l] that the ground state of H20...HF is symmetric with respect to exchange of the H,O protons. It has also been shown that the equihbrium configuration at the oxygen atom is pyranudal (C, symmetry) but with a barrier to inverslon through the planar form sufficiently low that the ground-state wavefunction has Czv symmetry. If I, and I2 are the nuclear spm vectors of the Hz0 protons, the Pauli principle then requires that of the allowed spin states If, t f21 = land I, +I2 = 0, only the latter can occur in combmatlon with the rotational levels I o1 and Ooo in the zero-point state of the dimer 151. Consequently, only the couplmg of the H(D)F nuclear spins can contribute to the observed hyperfme structure in the I,, * Ooo transitions. The form of the hamiltonian appropriate to the analysis is

H=H, tHa +Hss +HSR

(1)

m which HR and HQ are the well-known rotational and nuclear quadrupole interactron terms. Hss describes the spin-spin interactions and has the form HSS =

(3)

IF +‘IH( D)

in whxh D is the nuclear-spin-nuclear-spin

coupling

tensor with elements D,, = oO/4rrlgFgHcD,P~(R’s,l

- 3R&)1R5 1

(5)

where POis the permeabdity of free space,& and gH are the nuclear g values and the R, arc components of rhe VeCfOr JObUng the F and H(D)nuclei. The magnrlK coupling of the nuclear spin angular momenta IF and IH(D) to the framework rotation/ is described by the spin-rotation term HSR = -I,*M”d,

(4)

where M* is the spin-rotation tensor of nucleus A. The matrix elements of HQ, kiss and HSR m the coupled basis IF +&)=I,

I +J=F,

335

Volume 92, number 4

CHEMICAL

29 October 198’

PHYSICS LEnERS

Table 2 Spcctroscoplc quantltlcs dcwrmuicd from 10, + 000 trzm~u~onsof various notopic spec~csof water-hydrogen Qu.mtrty 1120. .Dt-

II,~ Hi-

I a) 263 O(7.0)

?63_5(2 5)

0;“

-41.1(7

-12 7(2 5)

‘) b, ‘) d,

or

0)

voWHz)

14396.4111(19)

$A\&, + MC_) (LHz)

-

o&p (IiHZ)

-X2.1(5

Y,, V.fHz)

HDO

II b)

x0” (liW Wz)

MC;, (kHz)

-

+(M$

M$

-

(hHz)

uu(AIHz)

14396 4X3(7) (-3

3) c)

-MJA(S

8)

14403 8501(16)

;(M&,+

fluonde

4)

l-1102 8507( IS) (-3.1)

c)

(0.8) e)

13694.-M(3)

d)

-

Spm rowon eiiccls rgnorcd m dcrwmg qumrws III ttus column. @LIJ~IIII~~ dewed irom observed ircqucncwr fiist corrcctcd for spm-rolarlan (see tc\t for dlscusgon). Calculad MJCS (SW tc\[ ior drscussron). Lstml3wd iron! parlrJlly wsolwd h)pcrfinc strucwrc.

have been given [6,7] and allow the matrur of H to be set up and disgonahzed m blocks of F. Initiallp, irequencms d the hyperfiie components + Oootransitions were fitted usmg least-squares procedures to gwe unperturbed tnnskon frequencies v. and the appropnate coupling constants but with of I,,

the spin-rotxlon terms set to Zero. The quantttles so derrrnuned are recorded in column I of table 2. The dliferences bcrween observed and calculated transItton frzquencles are correspondmgly gnen m column I of table I.. InspectIon of table 1 reveals that the residuals in rhc least-squares fit are a little m excess of the error of frequency measurement, which suggests that spinrotation Interactions are just significantandshould be taken into account. Oi the elements of the tensor MA, only the diagonal

term 4(ilfbt +Af,$) can contribute to the lo, + Ooo tranntlons. Moreover, in the absence of electronic and nuclear contributions from the H,O molecule, these termsare related [6] to the spin-rotation constants ,$(A = H, D or F) of free hydrogen fluoride by

where b. ISthe rotational constant of H@)F, 19is the instantaneous angle between the a inertial axis and the H(D)F internuclear a.Gs in the complex, and the 336

average is taken over the zero-point motion. Using the appropriate constants of H@)F + values of $lfh tJr”,>, as recorded m table 2, have been calculated from eq. (5) with the ald of the angle 0 = 18.8” denved from the imtialD~~ value as described below. The irutial molecular constants of table 2, column I were then used with the spm-rotation constants to calculate corrections to observed frequencies that arise from the inclusion of spin-rotation coupling. The corrected frequencies were then fitted as described above to gtve the refmed constants shown in column II of table 2. A glance at the corresponding residuals of the fit (m column II of table 1) demonstrates that this correction significantly improves the fit for HjO...DF and slightly improves it for H,O...HF. Unfortunately, only the 1,,I + 0, transitions of water-hydrogen fluoride are accesnble with our spectrometer and rotational constants are not directly available from the u. values here presented. Nevertheless, If D, = 56(l) kHz is assumed unchanged from H,O...HF [S], the v. values of table 2 lead to the following values of f(fQ + Co):

* Sec. for eNample, table 5 of ref. [6 J for a conrement rabulatmn.

Volume 92. number 1

CHEMICAL

PHYSICS LEITERS

29 October 1981

Values of the angle 0 (m deg) defermmed from the hyperlime muplmng mnslanls oiH20. .DFand Hz0 . HI-

Table 4 DCcrcnccs UI the 3n&sBD snd OH ior dlmcrs of Ihc lspc B .DF and B .HT

Hypcrtinc mnstant used

H20.. DF

Hz0 ..Hi-

B

0 H (dq)

flD (dc&

BD - 611 (dCL!)

D WD)F aa DF

9W

18.3(1.3)

-

k I91 Kr [lOI

31.1

XA(0 4)

32.1 30 8 22 2 229

-9 3 -8 3 0.3 as

71.5 X.0 2-t 1

I7 22

Table 3

xaa

7198324(l),

7201.537(l),

ygen atom. 3.2. hterpretation of the D-mclear quadmpole aud H(D].lgF spin-spin cotcphg cotrstattts

The observed hyperfmr coupling constants are the components of the appropriate second-rank tensors along the u inertial axis of the dimer. Consequently, if the electic field gradient at D and the H@)F distances were to survive dimer formatton, an observed constant C, would be given by

= iCo(3 co&% - I),

HC=CH

19.8

[6]

H2C=CH2 [ 131 Hz0 (rlus aork)

6847.35(l)hlHz

for H,O...DF, H,O...HF and HDO...DF, respectively. For the last-named species vu has been estunated from the partially resolved hyperfiie srructure that arues from coupling of the two D and the F nuclear spins With the overall rotation. We note that :(Bo t Co) for H20...DF differs only slightly from the value for H,O...HF, thus fflustratmg that the substttuted atom’fi close to the dimer mass centre and confirming the earher conclusions [1,8] that the intermolecular bindmg is via a hydrogen bond to the oh-

c,

OC[lll PHI 1121

39 2 7-1.9 20 I

(f-J

where Co values refer to free H(D)F. The operationally defmed values of 0 detemuned by usmg the various C, values in eq. (6) under the above assumptions are given m table 3. We note that 0 obtained from x,“, is stgnificantly larger than that resulting from fl: , which is the reverse of the order expected on the basis of attenuated excursions of the D atom from the a axis. The value of gUF IS not sufficiently well determined to be useful in this context.

I9 8 I8 3

61

..HF and XE III H,O...DF, n series of smlilerly denved values is avatlable for the species B...HF and B...DF, where B = AI [9], Kr [IO], OC [ll], PH3 [12], HCXH [6], H,C=CH, [I31 and H?O. The results are summartzed m table 4 A striking ieaturc of table 4 is that the difference 8, - 6, changes irom the expected negattrc value when the complex ISvery weakly bound (B = Xr and Kr) to a posittve value when the binding ts relatrvely strong (B = H20) As fIH is hkely to be larger the more weakly bound is the dimer, it can be used as an approxtmate criterion of bmding strength. Thus, when the B...HF are arranged, as In table 4, in order of decreasing e HI we note th 0, - 0, incrcascs along this series, presumably because the assumpttons inherent m the us2 of cq. (6) (that the electrrc field gradient 82 V/i& at the D nucleus and H(D)F dtstances survive dtmcr formatton) become progresstvrly poorer. Ahhough we cannot deconvolute the two factors that cause 0 D -tit, to mcrease from the weak bmding hmtt, we ten note the result of asstgning all the observed effect to one of the factors. It has been pointed out [ 1I!] that xt and Djir vary with bond distance r accordmg to d$/dr = -33 kHzlO.01 A and dDHmF/dr= 9.3 kHz/O.Ol A in H(D)F. If we rcqulre that the proper value of BD - 0,, is -1’ (as determined for example, in HCTH,HCI and HeCH, DC1from the nuclear quadrupole couplmg constants of the remote 35Cl nucleus [ Id]). it is necessary to invoke a lengthening of ti.02 A in r when HzO...H(D)F IS formed. in Hz0

4. Discussion Now that angles 0 have

been determined from DE 337

Volume 92. number -t

29 October 1982

CHEMICAL PHYSfCS LETTERS

161WG. Resd tmd W-H Fly&are, J Chem. Phys. 76 (1982) A research grant from SERC is gratefutiy acknowledged. The authors thank Dr. E.J. Campbell for the timely loan of a ~~~dlode switch. References [I

1 2. Ewl, AC. Lqon md DJ. hllcn, Proc.Roy Sot. X381

(1981)419

EJ. Campbell, hf R Kccnsn2ndW.H. Fl)garc. J Chem. Phjs 72 (1980) 922. [3] T J Bailc and W H. I-1)gare. Rev. !%I instrum 52 (1981) 33 ]a] EJ Ctunpbcli. L WY.Bu\ron,T J. BaUe. hi R. Kct?n~n and W.H. Fi~g~n~.J Chem Phys 74 (1981) 829. ]S 1 R Vwvsn3rh3n 2nd T R Dykc. J Chem. Phys. 77 (1982) 1166 [?I

338

TJ.

Wk.

2283. ]7] M-R Kccnan, D B. Wozmak ZII~ W H. Flygare, J Chem. Phys. 75 (1981) 631. [8] J.W Bew~, 2 Klstel. A.C. Legon, DJ. hftien sod SC Rogers, Froc. Roy. Sot. A372 (1980) 441. [9] M R Kcenan, L.W. Buxton, EJ. Campbell. A.C. Legon and W.H. Flygac. J Chcm Phys. 74 (1981) 2133; T.A. Dixon, C.H. Joyncr, F.A Baiocchi und W. Temperer. J. Chem. Phys 74 (1981) 6539.

[lo] L W Buxton, EJ. Campbell,M.R Keenzi, T I. Balk and U H. fI>pxe.Chcm. [ 11 I

Phrs.

S-t (1981)

173.

AX! Legon, P D. Saper and W H Flypare, J. Chem. Phys. 74 (1981) 4944. [ 121 A C. Legon and L C WdIoughby , Chcm. Phys.. to be pub~hed [ 131 J A. Shea and W.H rlygare, J. Chem. Phys. 76 (1982) 4857. [ 14 ] A C. Legon. P.D. Aldwh and W.H. Flygtua. J. Chem. Phys. 75 (1981)625