- Email: [email protected]
Isotope effect in resonant vibrational excitation of H2O (D2O), NH3 (ND3), CH4 (CD4)
Volume 167, number 6
CHEMICALPHYSICSLElTERS
13 April 1990
ISOTOPE EFFECT IN RESONANT VIBRATIONAL EXCITATION OE Hz0 (DzO), NH3 WD3h 0-b (CD,) Mondher BEN ARFA, Florence EDARD and Michel TRONC Laboratoirede ChimiePhysiqueI, Universitt! Pierreet Marie Curie, I1 Rue Pierreet Marie Curie, 75231 ParisCedpx 05, France
Received 8 December 1989;in final form 29 January 1990
Isotope effectshave been measured fordifferential vibration&excitation cross sections of X-H (D) stretching motion (X=0, N, C) through broad electron scattering shape resonances in H20 (DzO), NH3 (NDa) and CH, (CD,) around 8 eV impact energy.In the adiabatic nuclei approximation, a simple harmonic+cillator formula can account for the experimental results.
1. Introduction Isotope effects have been observed in low energy electron-resonance phenomena, both in dissociative attachment (DA) and in vibrational-excitation (VE ) cross sections. In dissociative attachment, a spectacular isotope effect ( > 200) was observed around 4 eV for H- and D- cross sections in Hz and D2 respectively [ 11. Such a large effect results from the very small survival probability of the intermediate anion state [ 2,3 ] and from the greater time to dissociate for the heavy molecule Dz compared to the light Hz. As the potential energy curves are similar for the two isotope molecules, the dissociating atoms (ions ) experience the same forces and their separation velocity is proportional to p-i/’ (where fl is the reduced mass). Heavy molecular anions dissociate more slowly and can reject their extra electron for a longer time to give VB, so that their DA cross sections are smaller. Similar large direct isotope effects were observed in H2S [4] around 2.2 eV (a(HS-)/a(DS-)>ZS), in CLHz [4] around 2.5 eV (u(&H-)/a(C,D-)> 11) and in CH, [5] around 11 eV (o(CHi)/ a(CD,-) > 100). In polyatomic molecules, small direct isotope effects [4,6,7 ] have been observed for H/D- production through Feshbach resonance states. These small effects (a(H-)/a(D-)a 1.2fO.l) were under’ AssocitauCNRSURA 176.
602
stood either as the competition between dissociation and auto-detachment [ 41 in the core-excited resonances which are narrower (r, ,2 s 0.1 eV ) by an order of magnitude than single particle shape resonance states, or without invoking autodetachment, but in connection with the kinetic energy operator [ 71 coupling electronic and nuclear motion to give a(H-)/a(D-)=(/~x_~/~x_,#“” 1.2. A small inverse isotope effect [8] has been observed in CH,,(CD,) around 9 eV with u(H-)/ a( D- ) = 0.8. It is related to the normalisation of the initial vibrational wave function appearing as a preexponential term in the DA cross section [9].
Moreover, in molecules having equivalent H and D atoms, such as HDO, HDS, CzHD and HDCO, an intramolecular isotope effect has been observed for (H-)/(D-) cross sections (a(H-)/a(D-)= 2.5 & 1) [4]. This non-diatomic effect [4] has been connected to the HXD- dissociation on a saddlepoint repulsive potential surface, and results from the competition between the spreading of the HXD’ wave packet and its preferential dissociation toward the H- + DX valley [ 4]_ Isotope effects in various electron scattering cross sections were predicted by using the fi-ame-transformation theory [ 10 1. They were first observed in rotational and vibrational cross sections in H2 and Dz through the very broad 2E,’ shape resonance state around 4 eV .[lo]. In the harmonic-oscillator approximation, isotopic substitution has two distinctive effects on cross sections: the first one is con-
0009-2614/90/S 03.50 Q Elsevier Science Publishers B.V. (Nor&Holland)
Volume167,number6
13 April 1990
CHEMICAL PHYSICS LETTERS
netted to rotational population and affects only elastic and purely vibrational cross sections. In our limited energy resolution experimental conditions, this effect cannot be observed because cross sections are summed and averaged over final and initial rotational states respectively. The second effect is related to the reduced mass of the vibrating atoms and makes cross sections behave [ IO] as ,u”/* (where fl is the reduced mass, and n the vibrational quantum number). Cross sections for excitation of H (D) atoms along the C-H (C-D) bond through broad O* shape resonances in CPH, (C,D,) around 7.5 eV ( I 1 ), in CzH2 ( CzD2) around 6.2 eV ( 12 ) and in CH,CN (CD&N) around 6 eV [ 131 have been shown to agree with such a simple diatomic picture. In this paper we present for the second-period hydride series Hz0 (D,O), NH3 (ND,) and CH4 (CD,), absolute differential elastic and vibrational cross sections, together with isotope effects, around 7-8 eV impact energy, centre of a broad ( > 3 eV) dwave dominated shape resonance.
2. Experimental Elastic and vibrational inelastic cross sections of the title compounds have been obtained with a crossed-beam electron impact spectrometer using hemispherical electrostatic filters and described in detail elsewhere [ 141. The apparatus was used in the energy loss mode with an overall ( fwhm ) resolution of 30-35 meV, not good enoughto resolve the symmetric wI from the degenerate cu, stretching mode (see table 1). The absolute differential cross sections
for the light isotopes were obtained by using the relative mass-flow techtique [ 15 ] and comparison with the absolute differential cross sections in N1. The accuracy is estimated to be about 15% for the more strongly excited vitiational modes. The spectra of the heavy isotopes have been normalised to the light ones on the elastic v= 0 energy-loss peak, and isotope effects were simply obtained by measuring the ratio of corresponding inelastic peak areas in the hydrogenated and deuteiated molecules. Isotope effects have been found to be constant within experimental errors in the 30-90” scattering angular range where measurements have been performed. All deuterated co,mpounds were obtained from CEA-IRIS with high stated isotope enrichment (D20>99.8%, NHS)99.7% and CH&99%).
3. Results and discussion 3.1. Impulsive approximation cross section For a broad resonance (impulse approximation), where the nuclei can be considered as fixed (adiabatic approximation) the excitation cross section from the v= 0 vibrational ground state up to the level n is given by Dubt and Henenberg [ 161: (da/dWo-.n
where x0 and xn are the initial and final vibrational wave functions, v. and v, the incident and scattered electron velocity and F(R) is the potential between
Table 1 Normal mode vibrational energies 60 (meV) for H20, NH,, C&and their fully deuterated
isotopes
w, (sym. sm.)
w, (sym.defor.)
0) a)
D20
453.4 331
197.7 146
465.1 345.7
NQ ND3
413.7 300
117.8 92.7
427 317.9
201.7 147.7
CH, CD.
361.6 261.5
190 135.4
314 280
161.9 123.5
MOkClllCS H20
w4(deg.defor.)
*)wj is asymmetricstretchin H20,anddegeneratestretchin NH3andCH,. 603
Volume 167, numk
6
CHEMICAL PHYSICS LETTERS
the outgoing electron and the rest of the molecule; m is the mass of the electron, F(R) is connected to the internuclear distance R through the energy separation between the groundstate molecule and the resonance-state potential curves, but it does not contain any dynamical term (no derivative d/M term). Thus, F(R) is the same for the light and the heavy molecules. As F(R) varies slowly in the FC region of the ground-state molecule around &, it can be developed in a Taylor series about R,: F(R) = f a”(&,) (R-R,)“. m-0 For a short-lived resonance, the first vibrational levels only are excited, and the harmonic-oscillator approximation seems to be justified. Then all terms (x,,] (R-&)“~x~) vanish except for m=n-O=n, and the cross section (da/dL&,, is proportional to (w)-“, where fro the vibrational energy quantum varies as cc-‘/2. The differential cross section (da/d& for the u=O+n excitation in the hydrogenated molecule is then related to the (da/d&, cross section in the deuterated one through
0.0
1.0
ENERGY
13 April 1990
This formula is similar to the isotope effects predicted by Chang and Wong [lo] when using the frame-transformation theory. 3.2. Isotope effe Figs. 1, 2 and 3 show absolute differential elastic and vibrational cross sections for H20, NH3 and CH4 respectively and their fully deuterated isotopes, at 8 eV impact energy and a scattering angle of 40 ’ (H,O, CH4) and of 30” ( NHJ). The energy-loss spectra are dominated by two series: the strongest series corresponds to the X-H stretching motion (X = 0, N, C ) . . which wtll be denoted nw,,, because symmetric stretch and degenerate stretch (or asymmetric stretch in HzO) are not energy resolved. A second series, excited to a lesser extent, corresponds to the stretching X-H motion together with one quantum of angular deformation (figs. 1, 2, 3 and table 2). This last scries becomes relatively more and more excited in passing from H20 to NH. and to CH+ Note that in NH, the N-H stretching-motion series ~0,,~ together with one quantum of symmetric 012or with one quantum of degenerate w4 angular deformation are resolved [ 14 1. Isotope effects are obtained from the ratio of cor-
OfJ LOSS
OS
1.0
bv)
Fig.1. Absolute cross sections for elastic and vibrational excitation for HZ0 and 90 at 8 eV impact energy and 40” scattering angle, 604
.ro-‘8 5
Ei = 7.5 eV
0
1
r
13 April 1990
CHEMICAL PHYSICS LETTERS
Volume 167, number 6
8=30’
I
Ei.6
x10-’
2 I
3 I
av
8-40'
7 “93 6
I:.,
..:is
‘. .__.,. D
0.1
,.,... 0.2
., ‘i_2”’
‘,._ :’ r,
0.4
0.5
0.3 ENERGY
ENERGY
LOSS
\ ~~_~_,,“~.“.~,.~_~,~,~ .._. .__ _0.7 08 0.6
0.6
LOSS
1.0
(eV,v)
Fig. 3. Absolute cross sections for elastic and vibrational exeitation for CI-I, and CD, at 8 eV impact energy and 40’ scattering angle.
ceV)
Fig. 2. Absolute cross sections for elastic and vibrational excitation for NH1 and NDs at 7.5 eV impact energy and 30” scattering angle.
effects (table 3) enables one to generalize the diatomic theory to potential and broad resonance scattering in polyatomic molecules when the empty antibonding MO, where the extra electron is trapped, is local&d enough to induce selective excitation up to a few quanta of vibration between two atoms. At the resonance energy, the direct-excitation cross sections of the IR active modes 43 in Hz0 and NH3 and v3 in CH4 are smaller by an order of magnitude
responding inelastic peak areas in the two isotope molecules. They are reported in table 3 for the stretching-motion series ~KLI~,~ where they are compared with theoretical isotope effects calculated in the fixed nuclei (adiabatic) approximation for a harmonic oscillator (see section 3.1). The good agreement between measured and calculated isotope
Table 2 Neutral ground state and shape resonance state characteristics for second period hydrides H20, NH3 and CA, Neutral ground state & (pm)
Shape resonance state
DO(eV)
P (D)
a ~49
E (eV
symmetry
partial waves
levels WJ*+W,.’ nW,+O~+O,
Hz0
95.8
5.11
1.84
1.46
m6.5
*B2
1=2+1
NH3
101.5
4.38
I.47
2.22
w7.3
2E
/=2+1
CH,
109.2
4.40
0
2.59
a8
2T2
1=2+1
fw.3 nwl,,+~z nw1,3+a
‘I Although w, and w1 are not resolved, the nw, +w~ assignment in Hz0 is deduced from the angular distribution
nwl.3 nw1.3+%4 (ref.
[ 201).
605
Volume 167, number 6
CHEMICAL PHYSICS LETTERS
13Aprill990
Table 3 Measured isotope effects du[no,,,(X-H)]/da[ nw,,,(X-D)] for stretching vibrational-excitation cross sections and calculated for an harmonic oscillator in the impulse approximation with the formula [ q3( X-H)/w,,,( X-D) 1”.The calculated isotope effect is the mean of the values for o, and w, nfJh.3
n=l ?I=2 n=3
HzO/D20 exP-
talc.
exp.
talc.
exp.
CdC.
1.47 1.81 2.6
1.36 1.84 2.50
1.40(0.1) 1.86(0.3) 2.86(0.5)
1.36 1.85 2.52
1.3 1.75 2.5
1.36 1.84 2.50
than the resonant ones and hence they cannot affect the isotope effect at our precision level. For the combination band series ~co,,~+w~,~isotope effects exist, but no values are reported because the energy-loss spectra of the deuterated molecules can be polluted by the light ones (by exchange of D with adsorbed H atoms for example) and because the strong no1,3 series of the light molecules overlap with the weak nw,,,t 0.12,4 of the deuterated ones. This is particularly clear in the ND3 spectrum between the 0.4 and 0.5 eV energy loss, where the separation between the o,,~ t o2 (0.402 eV) and the w,,4twI (0.457 eV) peaks is blurred by the o1,3 (0,420 eV) energy-loss peak corresponding to a small amount of NH3 impurity. No isotope effect is observed for the first quantum of angular deformation c&s in CH4, w2 in NH3 and w2 in H20 probably because the direct process is dominant, as shown by the angular distribution [ 17,14,18] and because the vibrational motion involves more than two atoms, so that the formula based on diatomic molecules does not apply.
4. Conclusion We have measured isotope effects, which vary as 0(1,.J~,,)~for X-H stretching vibrational differential cross sections around 8 eV in the second-period hydrides H,O, NH3, CH4 and their deuterated homologues. As these effects are characteristic of broadshape resonances it will be of interest to look at VE through long-lived &, resonances, but no such resonances have yet been observed. Work is in progress on VE in third-row hydrides (PH3, SiH4) where the @&, resonances are lowered from 7-8 eV for the second period to around 2 eV, but are still short lived 606
CH,/CDd
NHx/ND3
1 eV) [ 191, and on the fourth-period hy(r,/z= dride GeH,.
Acknowledgement We acknowledge fruitful discussions with D. Teillet-Billy.
References [ 1 ] G.J. Schulz and R.K. Asundi, Phys. Rev. 158 ( 1967) 25. [Z] Yu.N. Demkov, Phys. Letters 15 (1968) 235. [3] T.F. O’Malley, Phys. Rev. 150 (1966) 14. [4] M. Tronc, Thtse, Universitk Paris-Sud, Orsay ( 1973) NO. 1104. [ 51 T.E. Sharp and J.T. Dowell, .J.Chem. Phys. 50 ( 1969) 3024. [a] R.N. Compton, J.A. Stockdale and P.W. Reinhardt, Phys. Rev. 180 (1969) 111. [7] R.N. Compton and L.G. Christophorou, Phys. Rev. 154 (1967) ! 10. [8] T.E. Sharp and J.T. Dowell, J. Chem. Phys. 46 (1967) 1530. [9] T.F. O’Malley, J. Chem. Phys. 47 (1967) 5457. [lo] E.S. Chang and S.F. Wong, Phys. Rev. Letters 38 (1977) 1327. [ 111 LC. Walker, A. Stamatovic and S.F. Wong, J. Chem. Phys. 69 (1978) 5532. [ 121 M. Tronc, unpublished results. [ 131 F. Edard, A.P. Hitchcock and M. Tronc, J. Phys. Chem., in press. [ 141 M. Ben Arfa and M. Tronc, J. Chim. Phys. 85 (1988) 889. [ 15 ] SK. Srivastava, A. Chutjian and S. Trajmar, J. Chem. Phys. 63 (1975) 2659. [16]LDub&andA.Herzenberg,Phys.Rev.A11 (1975) 1314. [ 171 H. Tanaka, M. Kubo, N. Onodera and A. Suzuki, J. Phys. B 16 (1983) 2861. [ 181 G. Seng and F. Linder, J. Phys. B 9 (1976) 2539. [ 191 M. Tronc and F. Edard, Proc. XVI and ICPEAC ( 1989) p. 334; to be published. [ 20 ] D. Cvejanovic, A. Huetz, J. Mazeau and R.I. Hall, in: Physics of ion&d gas IX SPIG, bd. R.K. Janev (Dubrovnik, 1978) p. 23.
CHEMICALPHYSICSLElTERS
13 April 1990
ISOTOPE EFFECT IN RESONANT VIBRATIONAL EXCITATION OE Hz0 (DzO), NH3 WD3h 0-b (CD,) Mondher BEN ARFA, Florence EDARD and Michel TRONC Laboratoirede ChimiePhysiqueI, Universitt! Pierreet Marie Curie, I1 Rue Pierreet Marie Curie, 75231 ParisCedpx 05, France
Received 8 December 1989;in final form 29 January 1990
Isotope effectshave been measured fordifferential vibration&excitation cross sections of X-H (D) stretching motion (X=0, N, C) through broad electron scattering shape resonances in H20 (DzO), NH3 (NDa) and CH, (CD,) around 8 eV impact energy.In the adiabatic nuclei approximation, a simple harmonic+cillator formula can account for the experimental results.
1. Introduction Isotope effects have been observed in low energy electron-resonance phenomena, both in dissociative attachment (DA) and in vibrational-excitation (VE ) cross sections. In dissociative attachment, a spectacular isotope effect ( > 200) was observed around 4 eV for H- and D- cross sections in Hz and D2 respectively [ 11. Such a large effect results from the very small survival probability of the intermediate anion state [ 2,3 ] and from the greater time to dissociate for the heavy molecule Dz compared to the light Hz. As the potential energy curves are similar for the two isotope molecules, the dissociating atoms (ions ) experience the same forces and their separation velocity is proportional to p-i/’ (where fl is the reduced mass). Heavy molecular anions dissociate more slowly and can reject their extra electron for a longer time to give VB, so that their DA cross sections are smaller. Similar large direct isotope effects were observed in H2S [4] around 2.2 eV (a(HS-)/a(DS-)>ZS), in CLHz [4] around 2.5 eV (u(&H-)/a(C,D-)> 11) and in CH, [5] around 11 eV (o(CHi)/ a(CD,-) > 100). In polyatomic molecules, small direct isotope effects [4,6,7 ] have been observed for H/D- production through Feshbach resonance states. These small effects (a(H-)/a(D-)a 1.2fO.l) were under’ AssocitauCNRSURA 176.
602
stood either as the competition between dissociation and auto-detachment [ 41 in the core-excited resonances which are narrower (r, ,2 s 0.1 eV ) by an order of magnitude than single particle shape resonance states, or without invoking autodetachment, but in connection with the kinetic energy operator [ 71 coupling electronic and nuclear motion to give a(H-)/a(D-)=(/~x_~/~x_,#“” 1.2. A small inverse isotope effect [8] has been observed in CH,,(CD,) around 9 eV with u(H-)/ a( D- ) = 0.8. It is related to the normalisation of the initial vibrational wave function appearing as a preexponential term in the DA cross section [9].
Moreover, in molecules having equivalent H and D atoms, such as HDO, HDS, CzHD and HDCO, an intramolecular isotope effect has been observed for (H-)/(D-) cross sections (a(H-)/a(D-)= 2.5 & 1) [4]. This non-diatomic effect [4] has been connected to the HXD- dissociation on a saddlepoint repulsive potential surface, and results from the competition between the spreading of the HXD’ wave packet and its preferential dissociation toward the H- + DX valley [ 4]_ Isotope effects in various electron scattering cross sections were predicted by using the fi-ame-transformation theory [ 10 1. They were first observed in rotational and vibrational cross sections in H2 and Dz through the very broad 2E,’ shape resonance state around 4 eV .[lo]. In the harmonic-oscillator approximation, isotopic substitution has two distinctive effects on cross sections: the first one is con-
0009-2614/90/S 03.50 Q Elsevier Science Publishers B.V. (Nor&Holland)
Volume167,number6
13 April 1990
CHEMICAL PHYSICS LETTERS
netted to rotational population and affects only elastic and purely vibrational cross sections. In our limited energy resolution experimental conditions, this effect cannot be observed because cross sections are summed and averaged over final and initial rotational states respectively. The second effect is related to the reduced mass of the vibrating atoms and makes cross sections behave [ IO] as ,u”/* (where fl is the reduced mass, and n the vibrational quantum number). Cross sections for excitation of H (D) atoms along the C-H (C-D) bond through broad O* shape resonances in CPH, (C,D,) around 7.5 eV ( I 1 ), in CzH2 ( CzD2) around 6.2 eV ( 12 ) and in CH,CN (CD&N) around 6 eV [ 131 have been shown to agree with such a simple diatomic picture. In this paper we present for the second-period hydride series Hz0 (D,O), NH3 (ND,) and CH4 (CD,), absolute differential elastic and vibrational cross sections, together with isotope effects, around 7-8 eV impact energy, centre of a broad ( > 3 eV) dwave dominated shape resonance.
2. Experimental Elastic and vibrational inelastic cross sections of the title compounds have been obtained with a crossed-beam electron impact spectrometer using hemispherical electrostatic filters and described in detail elsewhere [ 141. The apparatus was used in the energy loss mode with an overall ( fwhm ) resolution of 30-35 meV, not good enoughto resolve the symmetric wI from the degenerate cu, stretching mode (see table 1). The absolute differential cross sections
for the light isotopes were obtained by using the relative mass-flow techtique [ 15 ] and comparison with the absolute differential cross sections in N1. The accuracy is estimated to be about 15% for the more strongly excited vitiational modes. The spectra of the heavy isotopes have been normalised to the light ones on the elastic v= 0 energy-loss peak, and isotope effects were simply obtained by measuring the ratio of corresponding inelastic peak areas in the hydrogenated and deuteiated molecules. Isotope effects have been found to be constant within experimental errors in the 30-90” scattering angular range where measurements have been performed. All deuterated co,mpounds were obtained from CEA-IRIS with high stated isotope enrichment (D20>99.8%, NHS)99.7% and CH&99%).
3. Results and discussion 3.1. Impulsive approximation cross section For a broad resonance (impulse approximation), where the nuclei can be considered as fixed (adiabatic approximation) the excitation cross section from the v= 0 vibrational ground state up to the level n is given by Dubt and Henenberg [ 161: (da/dWo-.n
where x0 and xn are the initial and final vibrational wave functions, v. and v, the incident and scattered electron velocity and F(R) is the potential between
Table 1 Normal mode vibrational energies 60 (meV) for H20, NH,, C&and their fully deuterated
isotopes
w, (sym. sm.)
w, (sym.defor.)
0) a)
D20
453.4 331
197.7 146
465.1 345.7
NQ ND3
413.7 300
117.8 92.7
427 317.9
201.7 147.7
CH, CD.
361.6 261.5
190 135.4
314 280
161.9 123.5
MOkClllCS H20
w4(deg.defor.)
*)wj is asymmetricstretchin H20,anddegeneratestretchin NH3andCH,. 603
Volume 167, numk
6
CHEMICAL PHYSICS LETTERS
the outgoing electron and the rest of the molecule; m is the mass of the electron, F(R) is connected to the internuclear distance R through the energy separation between the groundstate molecule and the resonance-state potential curves, but it does not contain any dynamical term (no derivative d/M term). Thus, F(R) is the same for the light and the heavy molecules. As F(R) varies slowly in the FC region of the ground-state molecule around &, it can be developed in a Taylor series about R,: F(R) = f a”(&,) (R-R,)“. m-0 For a short-lived resonance, the first vibrational levels only are excited, and the harmonic-oscillator approximation seems to be justified. Then all terms (x,,] (R-&)“~x~) vanish except for m=n-O=n, and the cross section (da/dL&,, is proportional to (w)-“, where fro the vibrational energy quantum varies as cc-‘/2. The differential cross section (da/d& for the u=O+n excitation in the hydrogenated molecule is then related to the (da/d&, cross section in the deuterated one through
0.0
1.0
ENERGY
13 April 1990
This formula is similar to the isotope effects predicted by Chang and Wong [lo] when using the frame-transformation theory. 3.2. Isotope effe Figs. 1, 2 and 3 show absolute differential elastic and vibrational cross sections for H20, NH3 and CH4 respectively and their fully deuterated isotopes, at 8 eV impact energy and a scattering angle of 40 ’ (H,O, CH4) and of 30” ( NHJ). The energy-loss spectra are dominated by two series: the strongest series corresponds to the X-H stretching motion (X = 0, N, C ) . . which wtll be denoted nw,,, because symmetric stretch and degenerate stretch (or asymmetric stretch in HzO) are not energy resolved. A second series, excited to a lesser extent, corresponds to the stretching X-H motion together with one quantum of angular deformation (figs. 1, 2, 3 and table 2). This last scries becomes relatively more and more excited in passing from H20 to NH. and to CH+ Note that in NH, the N-H stretching-motion series ~0,,~ together with one quantum of symmetric 012or with one quantum of degenerate w4 angular deformation are resolved [ 14 1. Isotope effects are obtained from the ratio of cor-
OfJ LOSS
OS
1.0
bv)
Fig.1. Absolute cross sections for elastic and vibrational excitation for HZ0 and 90 at 8 eV impact energy and 40” scattering angle, 604
.ro-‘8 5
Ei = 7.5 eV
0
1
r
13 April 1990
CHEMICAL PHYSICS LETTERS
Volume 167, number 6
8=30’
I
Ei.6
x10-’
2 I
3 I
av
8-40'
7 “93 6
I:.,
..:is
‘. .__.,. D
0.1
,.,... 0.2
., ‘i_2”’
‘,._ :’ r,
0.4
0.5
0.3 ENERGY
ENERGY
LOSS
\ ~~_~_,,“~.“.~,.~_~,~,~ .._. .__ _0.7 08 0.6
0.6
LOSS
1.0
(eV,v)
Fig. 3. Absolute cross sections for elastic and vibrational exeitation for CI-I, and CD, at 8 eV impact energy and 40’ scattering angle.
ceV)
Fig. 2. Absolute cross sections for elastic and vibrational excitation for NH1 and NDs at 7.5 eV impact energy and 30” scattering angle.
effects (table 3) enables one to generalize the diatomic theory to potential and broad resonance scattering in polyatomic molecules when the empty antibonding MO, where the extra electron is trapped, is local&d enough to induce selective excitation up to a few quanta of vibration between two atoms. At the resonance energy, the direct-excitation cross sections of the IR active modes 43 in Hz0 and NH3 and v3 in CH4 are smaller by an order of magnitude
responding inelastic peak areas in the two isotope molecules. They are reported in table 3 for the stretching-motion series ~KLI~,~ where they are compared with theoretical isotope effects calculated in the fixed nuclei (adiabatic) approximation for a harmonic oscillator (see section 3.1). The good agreement between measured and calculated isotope
Table 2 Neutral ground state and shape resonance state characteristics for second period hydrides H20, NH3 and CA, Neutral ground state & (pm)
Shape resonance state
DO(eV)
P (D)
a ~49
E (eV
symmetry
partial waves
levels WJ*+W,.’ nW,+O~+O,
Hz0
95.8
5.11
1.84
1.46
m6.5
*B2
1=2+1
NH3
101.5
4.38
I.47
2.22
w7.3
2E
/=2+1
CH,
109.2
4.40
0
2.59
a8
2T2
1=2+1
fw.3 nwl,,+~z nw1,3+a
‘I Although w, and w1 are not resolved, the nw, +w~ assignment in Hz0 is deduced from the angular distribution
nwl.3 nw1.3+%4 (ref.
[ 201).
605
Volume 167, number 6
CHEMICAL PHYSICS LETTERS
13Aprill990
Table 3 Measured isotope effects du[no,,,(X-H)]/da[ nw,,,(X-D)] for stretching vibrational-excitation cross sections and calculated for an harmonic oscillator in the impulse approximation with the formula [ q3( X-H)/w,,,( X-D) 1”.The calculated isotope effect is the mean of the values for o, and w, nfJh.3
n=l ?I=2 n=3
HzO/D20 exP-
talc.
exp.
talc.
exp.
CdC.
1.47 1.81 2.6
1.36 1.84 2.50
1.40(0.1) 1.86(0.3) 2.86(0.5)
1.36 1.85 2.52
1.3 1.75 2.5
1.36 1.84 2.50
than the resonant ones and hence they cannot affect the isotope effect at our precision level. For the combination band series ~co,,~+w~,~isotope effects exist, but no values are reported because the energy-loss spectra of the deuterated molecules can be polluted by the light ones (by exchange of D with adsorbed H atoms for example) and because the strong no1,3 series of the light molecules overlap with the weak nw,,,t 0.12,4 of the deuterated ones. This is particularly clear in the ND3 spectrum between the 0.4 and 0.5 eV energy loss, where the separation between the o,,~ t o2 (0.402 eV) and the w,,4twI (0.457 eV) peaks is blurred by the o1,3 (0,420 eV) energy-loss peak corresponding to a small amount of NH3 impurity. No isotope effect is observed for the first quantum of angular deformation c&s in CH4, w2 in NH3 and w2 in H20 probably because the direct process is dominant, as shown by the angular distribution [ 17,14,18] and because the vibrational motion involves more than two atoms, so that the formula based on diatomic molecules does not apply.
4. Conclusion We have measured isotope effects, which vary as 0(1,.J~,,)~for X-H stretching vibrational differential cross sections around 8 eV in the second-period hydrides H,O, NH3, CH4 and their deuterated homologues. As these effects are characteristic of broadshape resonances it will be of interest to look at VE through long-lived &, resonances, but no such resonances have yet been observed. Work is in progress on VE in third-row hydrides (PH3, SiH4) where the @&, resonances are lowered from 7-8 eV for the second period to around 2 eV, but are still short lived 606
CH,/CDd
NHx/ND3
1 eV) [ 191, and on the fourth-period hy(r,/z= dride GeH,.
Acknowledgement We acknowledge fruitful discussions with D. Teillet-Billy.
References [ 1 ] G.J. Schulz and R.K. Asundi, Phys. Rev. 158 ( 1967) 25. [Z] Yu.N. Demkov, Phys. Letters 15 (1968) 235. [3] T.F. O’Malley, Phys. Rev. 150 (1966) 14. [4] M. Tronc, Thtse, Universitk Paris-Sud, Orsay ( 1973) NO. 1104. [ 51 T.E. Sharp and J.T. Dowell, .J.Chem. Phys. 50 ( 1969) 3024. [a] R.N. Compton, J.A. Stockdale and P.W. Reinhardt, Phys. Rev. 180 (1969) 111. [7] R.N. Compton and L.G. Christophorou, Phys. Rev. 154 (1967) ! 10. [8] T.E. Sharp and J.T. Dowell, J. Chem. Phys. 46 (1967) 1530. [9] T.F. O’Malley, J. Chem. Phys. 47 (1967) 5457. [lo] E.S. Chang and S.F. Wong, Phys. Rev. Letters 38 (1977) 1327. [ 111 LC. Walker, A. Stamatovic and S.F. Wong, J. Chem. Phys. 69 (1978) 5532. [ 121 M. Tronc, unpublished results. [ 131 F. Edard, A.P. Hitchcock and M. Tronc, J. Phys. Chem., in press. [ 141 M. Ben Arfa and M. Tronc, J. Chim. Phys. 85 (1988) 889. [ 15 ] SK. Srivastava, A. Chutjian and S. Trajmar, J. Chem. Phys. 63 (1975) 2659. [16]LDub&andA.Herzenberg,Phys.Rev.A11 (1975) 1314. [ 171 H. Tanaka, M. Kubo, N. Onodera and A. Suzuki, J. Phys. B 16 (1983) 2861. [ 181 G. Seng and F. Linder, J. Phys. B 9 (1976) 2539. [ 191 M. Tronc and F. Edard, Proc. XVI and ICPEAC ( 1989) p. 334; to be published. [ 20 ] D. Cvejanovic, A. Huetz, J. Mazeau and R.I. Hall, in: Physics of ion&d gas IX SPIG, bd. R.K. Janev (Dubrovnik, 1978) p. 23.