J. Phys. Chem. 1983, 8 7 , 2085-2090
2085
Rotational Spectrum and Structure of a Hydrogen-Bonded Dimer of Phosphine with Hydrogen Bromide L. C. Wllloughby and A. C. Legon' Christopher IngoM Laboratories, Department of Chemlstry, University Coiiege London, London WC 1H OAJ, United Kingdom (Received: November 0, 1982)
The rotational spectra of five isotopic species of a weakly bound dimer formed by phosphine with hydrogen bromide have been observed and measured by using pulsed-nozzle,Fourier-transform microwave spectroscopy. Rotational constants Bo (MHz), centrifugal distortion constants DJ (kHz) and DjK (kHz), and Br-nuclear quadrupole coupling constants xoa(MHz) determined for the three symmetric rotor species identified are as follows: PH3.H7gBr,1237.8651 (21, 2.318 (31, 179.6 (41, 427.956 (5); PH3.HB1Br,1228.7638 (2), 2.283 (4), 177.1 (3), 357.521 (6); PH3.D7%r,1239.8565 (4), 2.223 (7), 162.9 (5), 444.68 (25). The observed spectroscopicconstants have been interpreted in terms of a dimer of Cb symmetry, with the HBr subunit lying along the C3 axis of PH3 at equilibrium and oriented so as to form a hydrogen bond to the P atom. Some details of the strength of the intermolecular binding and the zero-point motion of the dimer are considered.
Introduction The existence of the phosphonium halides in the solid phase is well established. On the other hand, at normal temperatures and pressures, the vapor phase of the phosphonium halides is usually considered to be completely dissociated into phosphine and the corresponding hydrogen halide. Evidence for the existence of phosphonium halides as discrete entities in the vapor phase or for weakly bound dimers formed between phosphine and hydrogen halide molecules is accordingly a matter of interest in chemistry. Moreover, a knowledge of the properties of any intermolecular species PH3.HX in the vapor will enhance our understanding of the nature of the interaction. Rotational spectroscopy is a rich source of the properties of weakly bound dimers in the gas phase. In particular, the technique of pulse-nozzle, Fourier-transform microwave spectroscopy recently developed by Flygare and coworked3 has proven a powerful tool for investigating even the most weakly bound species. We now report the rotational spectrum of a dimer formed by phosphine with hydrogen bromide. The spectra of the five isotopic species PH3.H79Br, PH3.HB1Br,PH3.D79Br, PH2D.H79Br, and PH2D.D79Brobserved by the pulsed-nozzle, FT method have been analyzed to give rotational constants, centrifugal distortion constants, and Br-nuclear quadrupole and spin-rotation coupling constants. We establish from the nature of the observed spectra and the derived spectroscopic constants not only the existence of this weakly bound species but also that it has C3"symmetry, with the HBr molecule lying along the C3 axis of the PH3 molecule at equilibrium and oriented so as to form a hydrogen bond to the phosphorus atom. Other details of the molecular geometry and the intermolecular interaction are reported. Experimental Section The microwave spectrometefl used in this investigation is of the pulsed-nozzle, Fourier-transform type in which the radiation-molecule interactions occur in a Fabry-Perot cavity. Details of its theory and practice have been given by Flygare and c o - w ~ r k e r s . ~ ~ ~ (1)T.J. Balle, E. J. Campbell, M. R. Keenan, and W. H. Flygare, J. Chem. Phys., 72,992 (1980). (2) T. J. Balle and W. H. Flygare, Rev. Sci. Instrum., 52, 33 (1981). (3)Details to be published. For a preliminary description, see A. C. Legon and L. C. Willoughby, Chem. Phys., 74, 127 (1983). (4) E. J. Campbell, L. W. Buxton, T. J. Balle, M. R. Keenan, and W. H.Flygare, J. Chem. Phys., 74,829 (1981). 0022-3654/83/2087-2085$01.50/0
A gas mixture composed of - 4 % each of phosphine and hydrogen bromide in argon, held at room temperature and -2.5-atm pressure, is expanded as a short pulse through a 0.7-mm-diameter orifice into an evacuated Fabry-Perot cavity. When the weakly bound PH3.HBr species so created are in collisionless expansion between the FabryPerot mirrors, they are polarized by a suitably delayed, 1-l.cs pulse of microwave radiation formed from a phase-locked, monochromatic oscillator by means of a pin-diode switch. Because the half-life (TJof the macroscopic polarization so induced is much greater than that ( 7 c ) for dissipation of the microwave pulse between the mirrors, the original radiation has decayed when the polarized dimers begin to emit at some rotational transition frequency .,v A pindiode switch is then opened to allow the weak emission at v, to be observed, unencumbered by intense background radiation, in the detection system. Detection employs a double superheterodyne method. In the first stage, the emission at v, is mixed down with a phase-coherent signal at (v - 30) MHz while in the second stage the resultant is further mixed down to Iv - v,I with phase-coherent 30-MHz radiation. The emergent beat signal at Iv - v,l is then digitized at a rate of 0.5 ps per point for 512 points. Signal averaging is employed as necessary until a suitable signal-to-noise ratio is achieved. As an example of the Iv - v,I transient signal, Figure 1 shows the emission that results from the F = 5/2 and 5/2 3/2 components of the J = 4 3, K = 0 transition in PH3. H79Br. Figure 2 shows the power spectrum that results when Fourier transformation to the frequency domain is carried out. We note that each of the two components consists of a doublet. The origin of the doubling lies in the nature of the gas distribution as the pulse emerges from the nozzle and has been discussed in detail.4 The true molecular frequencies are located at the doublet centers. Frequencies in Figure 2 are offset at a rate of 3.906 25 kHz per point from the polarizing frequency v. Measurements of v were made with an HP 5342A frequency counter whose calibration (together with that of the entire spectrometer) was occasionally checked by measuring the frequency5 of the J = 1 0 transition of 16012C32S.Our measurements of this transition, which occurs at 12 162.9790 (1) MHz, had a precision of better than 0.5 kHz. Observed transition widths at half-height in PH3-HBr were about 10 kHz and
-
-
-
-
(5) A. Dubrelle, J. Demaison, J. Burie, and D. Boucher, 2. Naturforsch. A , 35, 471 (1980).
0 1983 American Chemical Society
2086
The Journal of Physical Chemistry, Vol. 87, No. 12, 1983
Wiiloughby and Legon
TABLE I: Observed and Calculated Rotational Transition Frequencies for K = 0 States of PH3.HBr PH,.H 79Br PH,.H8'Br uobsd - Ycalcdra
J'K'F' t J , K " F " 4o
51,
3
o
51,
kHz
"obsd - ucalcd,a
A
B
9 803.9461 9 862.4571 9 899.1244 9 899.1194 9 911.2174 9 911.4841 10 006.2128
-1.7 -1.4 -5.3 4.7 1.6 -0.7 -4.1
0.2 1.0 2.1 0.2 -0.1 -1.1 -0.6
9 747.4015 9 796.0974 9 826.8484 9 826.8831 9 836.9887 9 837.1743 9 916.3343
12 275.2727 12 345.1700 12 375.2161 12375.3135 12 382.4377 12 382.5458 12482.3727
-5.2 -5.1 1.5 6.4 1.9 -0.1 -4.7
-1.9 -1.2 -1.5 2.0 0.3 -0.4 0.2
14 826.0269 14 850.7548 14 850.1806 14 855.5322 14 855.5790
-1.8 -0.6 5.1 4.0 -4.7
4.0 -3.0 1.5 3.0 -4.5
uobsd,
MHz
Yobsdr
MHz
A
kHz B
1.1 -1.3 8.8 4.3 1.2 -2.7 -8.8
1.1 1.4 5.1 -1.2 -0.2 -2.3 0.2
12 201.1382 1 2 259.9010 12 284.6371 12 284.6690 12 290.6468 12 290.7204 (12314.0939)
-3.7 -3.5 -2.4 7.0 1.4 -2.7
-1.7 1.6 -5.7 1.9 0.1 -2.1
14 656.3664
-5.4
-0.5
14 741.8359 14 741.8530 14 745.8350 14 145.8756
2.4 5.4 -1.1 0.3
-0.3 1.5 -1.2 2.0
a Difference between observed and calculated frequencies when all K = 0 transitions of the indicated isotopic species are fitted by a least-squaresprocedure. Differences in column A and B refer to analyses when Br spin-rotation effects are omitted and included, respectively.
0
16
32
- -
48
64 Time 1 ps
80
96
112
128
-
Flgure 1. The transient emission signal arising from the F = ' I 2 5/, and F = 5/2 3/2 79Br-nuclearquadrupole components in the J =4 3, K = 0 transition of P H , O H ~ ~digitized B~ at a rate of 0.5 @point. The polarizing frequency was 99 11.67 15 MHr.
I
,
0
100
1
200
300
400
Frequency offset
500
600
7 IO
I kHz
Flgure 2. The power spectrum obtained as a result of Fourier transformation of the PH,.H7'Br emission signal shown in Figure 1. The labels (a) and (b) refer to the F = 1 ', 5/2 and F = 5/2 components, respectively, of the J = 4 3, K = 0 transitlon. Frequencies are offset at a rate of 3.906 25 kHz/point from 991 1.6715 MHz. +-
+-
+-
frequencies are reported here with an estimated accuracy of -1 kHz. Phosphine (Matheson Inc.) and hydrogen bromide (B.D.H. Chemicals Ltd.) were used without further purification. The rotational spectra of the various D-substituted species of PH,-HBr were observed in a gas mixture prepared from PH, and DBr. Gaseous DBr was prepared by dropping 45% DBr in DzO solution onto Pz06and subsequently drying the evolved gas over Pz05.
Results Rotational Spectra and Spectroscopic Constants. The rotational spectra exhibited by the isotopic species PH3.H79Br16PH3.H81Br, and PH3.D79Brhave been ob(6) For a preliminary account, see A. C. Legon and L.C. Willoughby, Chem. Commun., 997 (1982).
served and measured in the frequency range 9-15 GHz. All observed spectra are characteristically those of the vibrational ground state of a symmetric rotor species in which a Br nucleus (I = ,/*) is present on the symmetry axis. The frequencies of Br-nuclear quadrupole hyperfine components that occur in the J = 4 3 , 5 4, and 6 5 transitions of the first two species as a result of the presence of the Br nucleus are recorded in Tables I and 11, respectively, while those correspondingly assigned to the J = 5 4 and 6 5 transitions of PH3.D79Brare given in Table 111. We note from Tables 1-111 that transitions involving both the K = 0 and the K = 1 states have been observed in all three species. Since the rotational constant A , i= 100 GHz in such species, we estimate from the observed intensity of K = 1 transitions that the molecules
- -
- -
-
PH,.HX Dimers
The Journal of Physical Chemistty, Vol. 87, No. 12, 1983 2007
TABLE 11: Observed and Calculated Rotational Transition Frequencies for K = 1 States of PH,.HBr PH,sH'~B~
JK'F'
J"K"F"
4 1 'I2
3 1
7/2
51
'I1 'I2
9/2
7/2
7/2
'I2
9/2
9/2
912
4 1
911
1312
11 I2
?I2
'I2 'I2
I I I2
9h 61
512
%
7/2
MHz
A
9 819.8681 9 873.7353 9 894.7106 9 899.8083 9 905.1508 9 910.7433 9 986.0254
-2.8 -9.7 6.2 2.7 3.4 2.2 -6.6
1 2 350.3419 1 2 371.8194 1 2 376.3172 1 2 377.0446 1 2 381.7498
-4.0 4.9 0.5 3.9 1.5
uobsd - "calcd?
kHz B
9 760.4156 9 805.3776 9 822.9283 9 827.2471 9 831.6840 9 836.3507
A 0.3 -3.7 4.1 -0.5 0.4 -1.3
-0.2 0.4 -0.1 1.6 -0.9 -0.2
1 2 281.4764 1 2 285.2624 1 2 285.8563 1 2 289.7905
3.8 -2.3 0.7 -1.2
0.1 0.1 -0.6 -0.2
"obsdr MHz
14 847.5801 1.1 -0.7 14 738.8545 3.6 0.6 14 850.5693 0.3 -0.3 14 741.3595 1.5 0.6 9i2 7/2 14 851.1166 -3.3 -1.0 14 741.8227 -4.9 -1.9 1112 9/2 14 854.2083 -0.7 -0.1 14 744.4037 -0.5 0.9 Differences between observed and calculated frequencies when all K = 1transitions of the indicated isotopic species are fitted in the least-squares procedure. Differences in columns A and B refer to analyses when Br spin-rotation effects are omitted and included, respectively. I%
5 1
kHz B 0.7 -4.7 1.2 0.8 -0.8 -1.0 0.4 3.4 0.8 0.2 0.9 -0.2
"obsd - "calcd? Vobsds
7/2
"12
PH ,.H 81 Br
l3I2
l3I2
"I2
TABLE 111: Observed and Calculated Rotational Transition Frequencies in K = 0 and K = 1 States of PH,.D79BP K=O K=l
-
"obsd -
JF'
511/2 4
"//z 9/2
7h
6
"calcdt
tJ"F"
12395.1565 1.8 l1I2 1 2 395.1910 -0.8 12402.5839 -1.5 'I2 12402.7019 0.6
kHz
12397.2205 12391.7974 12402.1083 12396.4609
0.1 -0.1 -0.1 0.0
14 874.6729 -1.7 14 874.7568 -8.4 14 874.6992 0.2 14 871.6555 0.3 14 879.6297 3.1 14 878.5357 0.2 l1l2 9/1 0.0 'I2 TIz 14 879.6822 -1.6 14 875.3235 Br spin-rotation effects included in each separate analysis of K = 0 and K = 1 transitions. 1312
'%
5
"calcdr
kHz
9/2
transitions of these asymmetric rotor species are given in Table IV. Components associated with the K-l = 1 transitions could just be discerned in the 6 5 transitions of the first species but were extremely weak and not measured. This inordinate weakness in such species made asymmetric by off-axis D substitution has been noted previ~usly.~ In analyzing the observed frequencies in Tables I-IV to give spectroscopic constants, only the coupling of the Br-nuclear spin angular momentum (I) to that (J) of the molecular rotation need be considered. Although molecules PH3.HBr have six nuclear spins that can be coupled together and to J through either magnetic or electric interactions, the observed hyperfine pattern of transitions was exactly that expected from the presence of the Br nucleus only, except for a tiny splitting of -10 kHz in some A F = 0 components, which arises no doubt from other spin couplings but which is negligible. Justification for this neglect lies in the excellent agreement between observed and calculated frequencies in the treatment described below. Observed frequencies were fitted by a nonlinear leastsquares procedure that employed complete diagonalization of the Hamiltonian matrix. The inadequacy of the usual first-order approximation for PH3.HBr is graphically illustrated by Figure 2, for the two transitions shown would be degenerate in first order. The matrix of the Hamiltonian
"/2
l3I2
have an effective rotational temperature T R 6 K. Even with averaging, however, the strongest K = 2 component, whose frequency could be accurately predicted, was not observed. Given that a transition having -0.2 of the intensity of the stronger K = 1components could be observed, we estimate that T S 13 K. When mixtures of PH3 and DBr were used, the rotational spectra of the species PH2D.H79Brand PH2D-D79Br were also observed, thus indicating that a rapid scrambling of the D label had occurred. Frequencies of 7BBr-nur$ear quadrupole components in the 505 404 and 6%
-
-
H =HR
+ HQ + H S R
(1)
TABLE IV: Observed and Calculated Rotational Transition Frequencies for K = 0 States of PH2D.H79Brand PH2D.DwBf PH,DsH~~B~
J'KPFt + J , K T ! F ! , 5 0 l1l2 4 0
"12
9i2
7/2
7/2
'I2 5 0
60
11985.1399 11985.1746 11992.3026 11992.4144
14 382.6362 14 382.6618 'I2 14 387.4127 "12 711 14 387.4638 9/2 Br spin-rotation effects included in the analyses.
'I2
a
912
l3l2
"ob& - "calcd,
Vobsd, MHz
1112 13/2
kHz 1.1 -1.0 -0.8 0.7 -0.7 0.4 1.5 -1.3
PH2D.D79Br vobsdr MHz
12006.2020 12006.2368 1 2 013.6275 1 2 013.7482 14 407.9674 14 407.9972 14 412.9233 14 412.9802
"obsd - "calcd?
kHz 2.3 -1.2 -1.0 0.0 -3.1 1.5 1.9 -0.2
2088
The Journal of
Willoughby and Legon
Physical Chemistry, Vol. 87, No. 12, 1983
was set up in the coupled basis I + J = F. In eq 1,HR is appropriate to the semirigid symmetric rotor and has only diagonal elements ER = B d ( J + 1) + ( A , - Bo)@ - D#(J + 1)' D j d ( J + 1)@- DKK4 (2) where Bo, A. and the D's have their usual meaning. The term HQaccounts for the nuclear quadrupole coupling of I and J according to7 HQ = -'/,Q:VE (3) where Q and V E are the Br-nuclear electric quadrupole tensor and the electric field gradient tensor at the Br nucleus, respectively. For a symmetric top molecule, the quadrupole interaction is characterized by the single term xaa = -eQ(a2V/da2).The final term in (1)describes the magnetic coupling of I and J and has the form H S R = -1.M.J (4) where M is the Br spin-rotation tensor. For a prolate symmetric rotor (4) becomess HSR= [(Ma, - Mbb)(@/J(J + 1)) - Mbb1I-J (5) Initially, the term HSRwas neglected. The resulting differences of observed and calculated frequencies in separate fits of K = 0 and K = 1 transitions for both PH3.H79Br and PH,.H*'Br are shown in columns A of Tables I and 11,as appropriate. The corresponding set of spectroscopic constants so derived are recorded in column A of Table V. Subsequent inclusion of the spin-rotation term in (1)led to significant improvement in the fits, as illustrated by columns B in Tables I and I1 and in the constants given in column B of Table V. For the D-substituted species the fits included in Tables 111and IV result from the full analysis, with the corresponding spectroscopic constants displayed in Table VI. The spin-rotation constants and xaa are less well-determined for the D species because AF = 0 transitions were too weak to observe. The species PH2D.H7gBr and PHzD.D79Br are sufficiently close to the prolate symmetric rotor limit that (Bo + C0)/2 and the remaining constants for K-' = 0 transitions could be fitted with acceptable accuracy with the above procedure. We draw attention to a point of interest about the coupling constants Although both Ar-HBr and KPHBr show an effect due to centrifugal distortion D, of the Br-nuclear quadrupole coupling constant: no dependence of xoaon J was observed here. Since this effect is proportional to 66,where 6 is the average angle between the H-Br and symmetry axes, and 6 = 20° in PH3.HBr (see below), D, is estimated to be too small to detect. We do note, however, that xaaincreases significantly from K = 0 to K = 1 transitions for each of the H79Br,HBIBr,and D79Brspecies. Dimer Geometry and the Nature of the Weak Binding. The form of the observed spectra for the various isotopic species of PH3.HBr and the magnitude of the spectroscopic constants lead directly to the molecular symmetry, the nature of the intermolecular binding, and some quantitative knowledge of the dimer geometry. The fact that the species P H , S H ~ ~PH,*HslBr, B~, and PH3.D79Brare proper symmetric rotor molecules is immediately evident from the above analysis for spectroscopic constants. The only chemically reasonable model for (7) C. H. T o m e s and A. L. Schawlow, "Microwave Spectroscopy", McGraw-Hill, New York, 1955. (8)See ref 7, p 220. (9) M. R. Keenan, E. J. Campbell, T. J. Balle, L. W. Buxton, T. K. Minton, P. D. Soper, and W. H. Flygare, J. Chem. Phys., 72,3070 (1980).
I
9
-
I3
h
P-
a
a m
2
N N rl
I
9
%
h
0 rl
w
0
d
: ua
m
h
IN
-
m
PH3 > CO > Ar. A similar conclusion follows from the operationally defined angles 0 determined from the nuclear quadrupole coupling constants xaa(Br) when the latter are interpreted in terms of a model in which their decrease from the free HBr values is attributed to zero point averaging effects. The values of the Br spin-rotation constants Mbbhave also been shown to be consistent with this model in PH3.HBr. Finally, we note that the order of strength of binding based on k, as a criterion in the series B.HFl3 is B=HCN > PH3 > OC > Ar, as concluded above for the corresponding series BaHBr. Acknowledgment. A research grant from the Science and Engineering Research Council is gratefully acknowledged. Registry No. PH3.H7%r,84944-36-5;PH3.Hs1Br,84944-37-6; P H , D S H ~ ~84944-38-7; B~, PH2D.D7gBr,84944-39-8. (13) A. C. Legon and L. C. Willoughby, Chem. Phys., 74, 127 (1983).
