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Dipole moment of the v2 = 1 state of ND3 by saturation laser stark spectroscopy
Volume 84, number 2
CHJZMICAL PHYSKS
LETTERS
DIPOLE MOMENT OF THEu, = 1 STATE OF ND, BY SATURATION LASER STARK SPECTROSCOPY G. DI LONARDO and A. TROMBEFI Istiruro
di Spt?Cff~~coprh
MolecoLve
and Is?ituro di chimicn F&h
de2 CNR.
e Spettroscopfa.
40126
Bologna,
Irnly
40136 Bologna. Italy
Received 4 May 1981
XnverseLamb dips of fGUXtransitions of the ND3 PJ baud at 11.4 pm have been measured in a Stark cell @aced inside the cavity of a 13C02 laser. The electric dipole moment of the u2 = 1, (J,K) = (14,ll) and (14.13) states and of the (J,K) = (13.11) and (13.13) states of the vibrational ground state have been obtained.
1. Introduction
Ammonia and NH, D have been where laser Stark nance techniques tric dipole
~1~ =~i,,J,I(l~ll_,J,K~for(~,li:)=(i4,13)and(14, 1 I), by laser Stark saturation spectroscopy. its isotopic modifications lsNH3 and the object of several investigations, and infrared-infrared double resohave been used to determine the elec-
moment
of the ground
and u2 = 1 state
[l--4]
2. Experimental The laser Stark spectrometer
has been described
Takami et al. [5] have pointed out that the anomalousiy large vibrational dependence of the dipole moment of NH, on the inversion coordinate v2 (a decrease
previously f6]. ND3 from C. Roth OHG, 98% isotopic enric~ent was flown through the intracavity Stark cell at pressures between 1 and 10 mTorr. 13C02 99%
of 15% being observed for the u2 = 1 state) is simply explained if one considers that the measured ~1is really the transition moment < l&t1 1-1 between adjacent inversion levels of the u2 = 1 state. It was recently shown [6] that for PH,, where the energy separation between the inversion levels in the u2 = 1 state is expected to be very small (lower than 150 MHz for u2 = 4 state [7f
isotopic enrichment was obtained from Prochem. The absolute accuracy of the determination of electric fields for the Stark resonances corresponds to =3 MHz in frequency, while the relative accuracy of closed spaced resonances, like those employed in determining ( l,lpl I_) is one order of magnitude better.
and thus still lower for the v2 = 1 state),
the dipole
moment of the ground and u2 = I states are the same,
3. Results and discussion
within the experimental error. From these examples it is clear that ihere is a correlation between the change of the dipole moment in going from the ground to the u2 = 1 state in pyramidal XH3 molecules, and the energy separation of the inversion levels in the latter state. ND3 cam provide further evidence for this behaviour, because in this mobcule the inversion doubling of the u2 = 1 state is 3.458 cm-l 183 I ten times lower than in NH3 191. Ln this paper we report the determination of the moment
The Ci,,Jfc’Icr I i-J&> moments for the @SC) = (14,I i) and (14,13) states were obtained from the eiectric fields which give resonances between t3C02 laser lines P(32) and P(36) at 11.4 m and transitions (I_, 14,11&51)~(0,,13,11~),(1,,14,13~f f I)+ (0_,13,13JW) respectively. Fig_ l-shows an example of these transitions, where m = F 1 components are separated by less than the Doppler width. The derivation of pl is based on the equation
0 009-2614/Sl/OOOO-0000/$02.75
0 1981 North-Holland
327
Volume
84. number
CHEMICAL
2
PHYSICS
1 December
LETTERS
1981
To obtain higher accuracy, the transitions (I_, 14, 13) + (O-,13,13) and (1+,14,11) + (O-,13,1 1) were considered, because they provide a larger I+ - wDs 1
and consequently
give a more accurate value for po.
Av” and Pv’ in eqs. (1) and (2) were computed
by
adding the second-order contribution to the two-level expression for the Stark shift [ 1 I] . The inversion doublet separations for the ground state were taken from ref. [ 121, while for the u2 = 1 state the data of ref. [8] have been employed. Av’ of eq. (2) was first obtained by assigning to ccl an approximate value, and then computed again with the value from eq. (1). In table
1 are reported
all the results relevant
to the pres-
ent analysis. In addition to those reported in table 1,. the following resonances were observed: (1_,14,12,M + 1) + (0_,13,12,M), (1_,14,lO,M * 1) + (0+,13,1O,M),
1550
1560
Fig. 1. Laser Stark resonances
1) + (0+,13,11,8)
(1-,14,9&I f 1) + (0+,.13,9,M) with P(32); (1+,14,12, M+ 1)+(0_,13,12,M),(1+,14,10,M~ 1)+(0_,13,10, M) with P(36), all of ND,. With the latter laser line four more resonances were observed, which seem to belong to a different molecule, probably ND2H: two of them have the lower state J = 5 and the others J = 9
V
of the transitions
(l-.14,1
1.8 5
of ND, with P(32), 13C02 laser line at 1 I .4
pm. In order to observe both (M = 8 k 1) - (M = 8) transitions with siguk of the same order, the CM = 7) - (M = 8) resonance
recorded with an amplification 50 times larger than the (M = 9) + (M = 8). The resonance at 1560.5 V ti the center dip. ND3 pressure 7.0 mTorr, field modulation 7 V cm-’ at 10 kHz.
was
lAv;l
- lAv;l
= IA+
where the subscripts
- IA+ 1 and 2 refer respectively
tions (M + 1) + (M) and (M -
t‘ne same
for both
(I)
transitions.
1) + (M), J Av”
and
Av’
to transi-
and K being are the
ground-state and u2 = 1 state Stark shifts respectively. Once Au; and AUS are known, the only unknown in eq. (1) is pl. In order to calculate Avy and Av; first we derived the ground-state moment p. =
from the equation
where Au” and Au’ are the ground-state
and u2 = 1 state
of frequency ANDY [8] brought in resonance with laser line of frequency v,_ [IO] . The minus sign in eq. (2) applies when VND3 is a forbidden transition of the type (I_, J’s”, M’) + (O_,J”,K”,M”) or (I+,J’,K’,M’) + (O+,J”,K”, lw). 328
values are given in table 1 ‘for c(~ of each rotational state: the first was obtained as indicated above,
while the second was derived following the procedure used by Shimizu [I] for NH3. For comparison in table 1 are also reported the ~1values of NH, as derived from the equations of the work of Shimoda et al. [3] : the present results show that p1 is significantly closer to I_I~ in ND, than in NH,. The isotopic dependence of cc has been previously determined by Halevi et al. [ 131, who found &NDs) - p(NH3) = 0.028 D, by studying
the temperature dependence of the molar polarization in the range 40-205°C; according to the empirical corrections applied by these authors the difference is reduced to 0.014 D for the lowest vibrational level. By applying the simplified molecular model, which was employed by Freund et al. [ 141, to predict the isotopic dependence
(3 Stark shifts of the molecular
mdJ=8. Two
transition
obtain
of p of CH3F (eq. (13) of ref. [ 14]),
PO(ND~) - h(NH3)
= 0.023 D for (J,K)
we =
(13,11),and0.027Dfor(J,K)=(13,13),tobecom-
pared with the experimental values 0.029 f 0.008 D, and 0.05 1 f 0.011 D respectively. F;~ally it may be of interest to recall that the best theoretical value for the equilibrium dipole moment pe of NH3, which is isotopically invariant in the Born-Oppenheimer approximation, is 1.512 D [15].
Volume 84. number 2
1 December 1981
CHEMICAL PHYSICS LETTERS
Table 1 Observed stark resonancesof ND3 R(13.13) (l++O_I. R(13,13) (l-+03. R(13,ll) (l-+0+), R(13.11) (1,+0_1 with P(32) and P(36) 11.4 pm 13C02 laser lines and dipole moments of the ground ~0 and u2 = I states pl ND3
transition
ND3 transition
‘3co; 11.4
mn
laser
line
13co* lIA.um laser
R(13,1t)
R(13.13)
(l--O_)
M
M”
va)
M’
M”
va)
14
13
4080.0
14
13
6040.6
m b) =
l-496(10)
PO b)
=
W32)
1.495(14)
he
W36)
1.485<14)
l-499(17)
Ea b) =
l-497(11)
i;o b) =
l-492(8)
D’o C) =
1.446(l)
fro c) =
1.463(l)
R(13.13)
(l++O_)
M’
M”
va)
8
7
1009.10
6
7
1014.07
R(13.11)
(l-+0+)
PI 0) b,
M’
M”
v”)
1.386(30)
9
8
1555.40
P(36)
7
6
1176.90
5
6
1183.70
6
5
1411.44
4
5
1420.83
5
4
1761.95
3
4
1776.28
4
3
2345.36
2
3
2371.15
3
2
3505.93
1
2
3563.87
ii1 =1.355(s)
transitions
.ul ‘)=
7 1.391(24)
1.360(16)
l-345(12)
l-353(9)
1.355(8)
l-216(27)
.8
P(32)
l-368(1 7)
1565.62
8
7
1776.93
6
7
1789.93
7
6
2071.34
5
6
2089.16
6
5
2482.94
4
5
250850
5
4
3099.10
3
4
3138.96
4
3
4119.73
2
3
4190.28
3
2
6144.04
1
2
6301.73
ji, = 1.352(3)
PI @Ib)
1.350<12)
l-35.5(9)
l-353(7)
l-352(6)
1.352(S)
1.351(4)
pl =) = l-258(25)
a) This is the applied voltage in V. The plate spacing is d = 0.29386 f 0.00005 an. b) Numbers in parentheses are e xperimental errors in units of the last digit. For cc0 the error corresponds to in the IR measurements [8]. For fiI three sources of error have been considered: (i) the voltage readings: and (iii) the u2 = 1 state inversion frequency uncertainty. ji indicates the weighted mean. ‘) NH3 values Qlculated from Shimoda et al. 131.
a 0.003
cm-’
urtOemtity
cu3 the p,, uncertainty:
329
Volume 84, number 2
CHEMICAL PHYSICt
References [1 ] F. Shimizu, J. Chem. Phys. 51 (1969) 2754; 52 (1970) 3572; 53 (1970) 1149. 121 R.G. Brewer and J.D. Swalen, J. Chem. Phys. 52 (1979) 2774; E.W. van Stryland and R.L. Shoemaker, J. Chem. Phys. 64 (1976) 4968; J. Orr and T. Oka, Appl. Phys. 21 (1980) 293; J. Mol. Spectry. 66 (1977) 302. [31 K. Shimoda, Y. Ueda and J. lwahori, Appl. Phys. 21 (1980) 181. 14] G. di Lonardo, A. Trombetti and B. Velino, Chem. Phys. Letters 80 (1981) 352. [5 ] M. Takami, I1. Jones and T. Oka, J. Chem. Phys. 70 (1979) 3557. 161 G. di Lonardo and A. Trombetti, Chem. Phys. Letters 76 (1980) 307. 17] P. Bernard and T. Oka. J. Mol. Speetry. 75 (1979) 181.
330
t l YOU) ~ 0 ~ o
[10] C. Freed, L.C. Bradley and R.G. O'Donnell, IEEE J. Quantum Electron. QE-16 (1980) 1193. [11 ] W. Gordy and R.L. Cook, Microwave molecular spectra (lnterseience, New York, 1970). I12] R.G. Nuckolls, LJ. Rueger and H. Lyons, Phys. Rev. 89 (1953) l l 0 ! ; G. Hermann, J. Chem. Phys. 29 (1958) 875: [l 3] E.A. Halevi, E.N. Haran and B. Ravid, Chem. Phys. Letters l (1967) 475. [14] S.M. Freund, G. Duxbury, M. R~mheld, J.T. Tiedje and T. Oka, J. Mol. Spectry. 52 (1974) 38. [15] H.-J. Werner and W. Meyer, Mol. Phys. 31 (1976) 855.
CHJZMICAL PHYSKS
LETTERS
DIPOLE MOMENT OF THEu, = 1 STATE OF ND, BY SATURATION LASER STARK SPECTROSCOPY G. DI LONARDO and A. TROMBEFI Istiruro
di Spt?Cff~~coprh
MolecoLve
and Is?ituro di chimicn F&h
de2 CNR.
e Spettroscopfa.
40126
Bologna,
Irnly
40136 Bologna. Italy
Received 4 May 1981
XnverseLamb dips of fGUXtransitions of the ND3 PJ baud at 11.4 pm have been measured in a Stark cell @aced inside the cavity of a 13C02 laser. The electric dipole moment of the u2 = 1, (J,K) = (14,ll) and (14.13) states and of the (J,K) = (13.11) and (13.13) states of the vibrational ground state have been obtained.
1. Introduction
Ammonia and NH, D have been where laser Stark nance techniques tric dipole
~1~ =~i,,J,I(l~ll_,J,K~for(~,li:)=(i4,13)and(14, 1 I), by laser Stark saturation spectroscopy. its isotopic modifications lsNH3 and the object of several investigations, and infrared-infrared double resohave been used to determine the elec-
moment
of the ground
and u2 = 1 state
[l--4]
2. Experimental The laser Stark spectrometer
has been described
Takami et al. [5] have pointed out that the anomalousiy large vibrational dependence of the dipole moment of NH, on the inversion coordinate v2 (a decrease
previously f6]. ND3 from C. Roth OHG, 98% isotopic enric~ent was flown through the intracavity Stark cell at pressures between 1 and 10 mTorr. 13C02 99%
of 15% being observed for the u2 = 1 state) is simply explained if one considers that the measured ~1is really the transition moment < l&t1 1-1 between adjacent inversion levels of the u2 = 1 state. It was recently shown [6] that for PH,, where the energy separation between the inversion levels in the u2 = 1 state is expected to be very small (lower than 150 MHz for u2 = 4 state [7f
isotopic enrichment was obtained from Prochem. The absolute accuracy of the determination of electric fields for the Stark resonances corresponds to =3 MHz in frequency, while the relative accuracy of closed spaced resonances, like those employed in determining ( l,lpl I_) is one order of magnitude better.
and thus still lower for the v2 = 1 state),
the dipole
moment of the ground and u2 = I states are the same,
3. Results and discussion
within the experimental error. From these examples it is clear that ihere is a correlation between the change of the dipole moment in going from the ground to the u2 = 1 state in pyramidal XH3 molecules, and the energy separation of the inversion levels in the latter state. ND3 cam provide further evidence for this behaviour, because in this mobcule the inversion doubling of the u2 = 1 state is 3.458 cm-l 183 I ten times lower than in NH3 191. Ln this paper we report the determination of the moment
The Ci,,Jfc’Icr I i-J&> moments for the @SC) = (14,I i) and (14,13) states were obtained from the eiectric fields which give resonances between t3C02 laser lines P(32) and P(36) at 11.4 m and transitions (I_, 14,11&51)~(0,,13,11~),(1,,14,13~f f I)+ (0_,13,13JW) respectively. Fig_ l-shows an example of these transitions, where m = F 1 components are separated by less than the Doppler width. The derivation of pl is based on the equation
0 009-2614/Sl/OOOO-0000/$02.75
0 1981 North-Holland
327
Volume
84. number
CHEMICAL
2
PHYSICS
1 December
LETTERS
1981
To obtain higher accuracy, the transitions (I_, 14, 13) + (O-,13,13) and (1+,14,11) + (O-,13,1 1) were considered, because they provide a larger I+ - wDs 1
and consequently
give a more accurate value for po.
Av” and Pv’ in eqs. (1) and (2) were computed
by
adding the second-order contribution to the two-level expression for the Stark shift [ 1 I] . The inversion doublet separations for the ground state were taken from ref. [ 121, while for the u2 = 1 state the data of ref. [8] have been employed. Av’ of eq. (2) was first obtained by assigning to ccl an approximate value, and then computed again with the value from eq. (1). In table
1 are reported
all the results relevant
to the pres-
ent analysis. In addition to those reported in table 1,. the following resonances were observed: (1_,14,12,M + 1) + (0_,13,12,M), (1_,14,lO,M * 1) + (0+,13,1O,M),
1550
1560
Fig. 1. Laser Stark resonances
1) + (0+,13,11,8)
(1-,14,9&I f 1) + (0+,.13,9,M) with P(32); (1+,14,12, M+ 1)+(0_,13,12,M),(1+,14,10,M~ 1)+(0_,13,10, M) with P(36), all of ND,. With the latter laser line four more resonances were observed, which seem to belong to a different molecule, probably ND2H: two of them have the lower state J = 5 and the others J = 9
V
of the transitions
(l-.14,1
1.8 5
of ND, with P(32), 13C02 laser line at 1 I .4
pm. In order to observe both (M = 8 k 1) - (M = 8) transitions with siguk of the same order, the CM = 7) - (M = 8) resonance
recorded with an amplification 50 times larger than the (M = 9) + (M = 8). The resonance at 1560.5 V ti the center dip. ND3 pressure 7.0 mTorr, field modulation 7 V cm-’ at 10 kHz.
was
lAv;l
- lAv;l
= IA+
where the subscripts
- IA+ 1 and 2 refer respectively
tions (M + 1) + (M) and (M -
t‘ne same
for both
(I)
transitions.
1) + (M), J Av”
and
Av’
to transi-
and K being are the
ground-state and u2 = 1 state Stark shifts respectively. Once Au; and AUS are known, the only unknown in eq. (1) is pl. In order to calculate Avy and Av; first we derived the ground-state moment p. =
from the equation
where Au” and Au’ are the ground-state
and u2 = 1 state
of frequency ANDY [8] brought in resonance with laser line of frequency v,_ [IO] . The minus sign in eq. (2) applies when VND3 is a forbidden transition of the type (I_, J’s”, M’) + (O_,J”,K”,M”) or (I+,J’,K’,M’) + (O+,J”,K”, lw). 328
values are given in table 1 ‘for c(~ of each rotational state: the first was obtained as indicated above,
while the second was derived following the procedure used by Shimizu [I] for NH3. For comparison in table 1 are also reported the ~1values of NH, as derived from the equations of the work of Shimoda et al. [3] : the present results show that p1 is significantly closer to I_I~ in ND, than in NH,. The isotopic dependence of cc has been previously determined by Halevi et al. [ 131, who found &NDs) - p(NH3) = 0.028 D, by studying
the temperature dependence of the molar polarization in the range 40-205°C; according to the empirical corrections applied by these authors the difference is reduced to 0.014 D for the lowest vibrational level. By applying the simplified molecular model, which was employed by Freund et al. [ 141, to predict the isotopic dependence
(3 Stark shifts of the molecular
mdJ=8. Two
transition
obtain
of p of CH3F (eq. (13) of ref. [ 14]),
PO(ND~) - h(NH3)
= 0.023 D for (J,K)
we =
(13,11),and0.027Dfor(J,K)=(13,13),tobecom-
pared with the experimental values 0.029 f 0.008 D, and 0.05 1 f 0.011 D respectively. F;~ally it may be of interest to recall that the best theoretical value for the equilibrium dipole moment pe of NH3, which is isotopically invariant in the Born-Oppenheimer approximation, is 1.512 D [15].
Volume 84. number 2
1 December 1981
CHEMICAL PHYSICS LETTERS
Table 1 Observed stark resonancesof ND3 R(13.13) (l++O_I. R(13,13) (l-+03. R(13,ll) (l-+0+), R(13.11) (1,+0_1 with P(32) and P(36) 11.4 pm 13C02 laser lines and dipole moments of the ground ~0 and u2 = I states pl ND3
transition
ND3 transition
‘3co; 11.4
mn
laser
line
13co* lIA.um laser
R(13,1t)
R(13.13)
(l--O_)
M
M”
va)
M’
M”
va)
14
13
4080.0
14
13
6040.6
m b) =
l-496(10)
PO b)
=
W32)
1.495(14)
he
W36)
1.485<14)
l-499(17)
Ea b) =
l-497(11)
i;o b) =
l-492(8)
D’o C) =
1.446(l)
fro c) =
1.463(l)
R(13.13)
(l++O_)
M’
M”
va)
8
7
1009.10
6
7
1014.07
R(13.11)
(l-+0+)
PI 0) b,
M’
M”
v”)
1.386(30)
9
8
1555.40
P(36)
7
6
1176.90
5
6
1183.70
6
5
1411.44
4
5
1420.83
5
4
1761.95
3
4
1776.28
4
3
2345.36
2
3
2371.15
3
2
3505.93
1
2
3563.87
ii1 =1.355(s)
transitions
.ul ‘)=
7 1.391(24)
1.360(16)
l-345(12)
l-353(9)
1.355(8)
l-216(27)
.8
P(32)
l-368(1 7)
1565.62
8
7
1776.93
6
7
1789.93
7
6
2071.34
5
6
2089.16
6
5
2482.94
4
5
250850
5
4
3099.10
3
4
3138.96
4
3
4119.73
2
3
4190.28
3
2
6144.04
1
2
6301.73
ji, = 1.352(3)
PI @Ib)
1.350<12)
l-35.5(9)
l-353(7)
l-352(6)
1.352(S)
1.351(4)
pl =) = l-258(25)
a) This is the applied voltage in V. The plate spacing is d = 0.29386 f 0.00005 an. b) Numbers in parentheses are e xperimental errors in units of the last digit. For cc0 the error corresponds to in the IR measurements [8]. For fiI three sources of error have been considered: (i) the voltage readings: and (iii) the u2 = 1 state inversion frequency uncertainty. ji indicates the weighted mean. ‘) NH3 values Qlculated from Shimoda et al. 131.
a 0.003
cm-’
urtOemtity
cu3 the p,, uncertainty:
329
Volume 84, number 2
CHEMICAL PHYSICt
References [1 ] F. Shimizu, J. Chem. Phys. 51 (1969) 2754; 52 (1970) 3572; 53 (1970) 1149. 121 R.G. Brewer and J.D. Swalen, J. Chem. Phys. 52 (1979) 2774; E.W. van Stryland and R.L. Shoemaker, J. Chem. Phys. 64 (1976) 4968; J. Orr and T. Oka, Appl. Phys. 21 (1980) 293; J. Mol. Spectry. 66 (1977) 302. [31 K. Shimoda, Y. Ueda and J. lwahori, Appl. Phys. 21 (1980) 181. 14] G. di Lonardo, A. Trombetti and B. Velino, Chem. Phys. Letters 80 (1981) 352. [5 ] M. Takami, I1. Jones and T. Oka, J. Chem. Phys. 70 (1979) 3557. 161 G. di Lonardo and A. Trombetti, Chem. Phys. Letters 76 (1980) 307. 17] P. Bernard and T. Oka. J. Mol. Speetry. 75 (1979) 181.
330
t l YOU) ~ 0 ~ o
[10] C. Freed, L.C. Bradley and R.G. O'Donnell, IEEE J. Quantum Electron. QE-16 (1980) 1193. [11 ] W. Gordy and R.L. Cook, Microwave molecular spectra (lnterseience, New York, 1970). I12] R.G. Nuckolls, LJ. Rueger and H. Lyons, Phys. Rev. 89 (1953) l l 0 ! ; G. Hermann, J. Chem. Phys. 29 (1958) 875: [l 3] E.A. Halevi, E.N. Haran and B. Ravid, Chem. Phys. Letters l (1967) 475. [14] S.M. Freund, G. Duxbury, M. R~mheld, J.T. Tiedje and T. Oka, J. Mol. Spectry. 52 (1974) 38. [15] H.-J. Werner and W. Meyer, Mol. Phys. 31 (1976) 855.