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Dipole moment and polarizability differences between NH3 and ND3
CHEiMICAL
PHYSICS
LETTERS
1 (1967)
NORTH-HOLLAND
475-476.
PUBLISHING
DIPOLE MOMENT AND POLARIZABILITY BETWEEN NH3 AND NDg E. A. HALEVI, Department of Chemisfv,
22 November
of many
plot over the renge 0 - 150°C, they obtained:
6PE+A Fitting
- ~~3)
= ($P3
- fix3 E+A) -- -0.9 cm3/mole.
E+A
the same
= 0.03
D;
= (~‘~~3
experimental
results
6P
EcA
to the
= -0.71 cm3/mole.
thirty years ago. Analysis of the data by means of the Van Vleck equation yields:
B,u = 0.0U14 D;
6PE+A = -0.49 cm3/AoLe.
At our higher temperatures, excitation of the bending mode of NHQ, and particularly ND3, is
= -0.3 cm3/mole.
appreciable * [9]. A correction for population of vibrational levels above the lowest was applied, which, to be tractable, had to incorporate a fairly large number of assumptions. ALL of these can t-e justified as approximations, but none is rigorously true. They are: a) The bending and stretching modes are separable, the same one-dimensional potential functions applying to both isotopic species; b) PA, the “atomic polarization” is isotopictiy invariant * * ; c) PE depends predominantly on boncf stretching, its angular dependence being negligible [ll]; d) the dipole moment difference arises predominantly from changes in bond angle rather than bond length (61; * We are grateful to Dr. H. Friedman for suggesting to us that neglect of this factor migM lead to serious error. ** The isotopic independence of PA follows
from the classical considerations of Coop and Sutton [IOI. It also follows from a quantum mechanical anaIysis for which we are deeply indebted to Professor A. D. Buckingham (personal communication, 20 April 1965).
t Performed under Grant No. N.B.S. (G) 22, from the U. S. Department of Commerce, National Bureau of Standards, administered by the Technion Research and Development Foundation. 1967
WE+A
These results axe in remarkably good agreement with those obtained by De Bruyne and Smyth over
The isotope effect on electrical polarizability (6PE+A) is in the same direction as, but considerably larger than, that derived from refractivity data (APE) of similar molecules [5]. Bell and Coop showed, however, that even when 6PE+A was arbitrarily constrained to be zero, 6~ was only reduced to 0.012 D. Several years ago, one of us [6] justified semi-quantitatively De Bruyne and Smyth’s suggestion that the dipole moment difference arises largely from the anharmonicity of the symmetric bending mode. The admittedly crude assumptions of this treatment have since been challenged, as has the reliability of the old experimental result PIHaving constructed an instrument based on the determination of frequency ratios, which is specifically designed to measure directly small di-
December
1967
61.r= 0.0276 D ;
Van Vleck equation [2,3], which in effect corrects the classical treatment for quantization of the rotational levels, Bell and Coop [4] recalculated the values: 6~ = 0.015 D;
DIFFERENCES
electric constant differences between clcsely similar molecules [8], we have re-determined the dipole moment and polarizability differences between NH3 and ND3. Eight independent differential measurements were performed, each taken over ;he range 40 - 205OC. From a classical Debye pIot we obtain:
years ago by De Bruyne and Smyth [l]. Plotting the total molar polarization of each gas against reciprocal temperature in a conventional Debye
6~
AMSTERDAM
E. N. HARAN and B. RA-QID . Technion - Israel Institute of Technology, Haifa, IsraeE
Received The dipole moments and polarizabilities NH3 and ND3 were determined separately
COMPANY,
475
416
E. A. HALEVI.
E. N. HARAN and B. RAVID
e) the average dipole moment in a given vibrational state depends linearly on the vibrational energy *; f) the population distribution can be calculated with adequate accuracy using the partition function for the harmonic oscillator. The corrected results for the “zeroth” vibrational levels of NH3 and ND3 are: 6~ = 0.0145 sz 0.001 D; bPEtA = 0.17 f 0.03 Clll 3/mole. The errors quoted are the standard deviations from the respective mean values. The absolute accuracy of our figures is limited by the reliabiiity of our population correction. Evidently, this can affect the dipole moment difference by no more than 0.001 D or so. Taken at face value, 6PB+A is in much better agreement with the vtiue of &PE (-0.14
cm
3/mole)
calculated
from
Yoshino
and Bernstein’s polarizability derivatives [ll] and Bartell’s average bond lenoth than with the smalbased on HaIeler Va.hte (6PB = -0.05 cmg/mole) .vi’s earlier estimate [S] of 6~. However, ~PE+A is much more sensitive than is 6y to the * This dependence is obeyed extremely erage dipole moments of isotopic served by L. Wharton et al [12].
well by the avLiH molecules ob-
population correction, and consequently its value’ is more subject to the cumulative uncertainty of the assumptions underlying it. Experimental details and a discussion results will be publish&d in due course.
of the
References [I] J. M.A. De Bruyne and C.P. Smyth, J. Am. Chen. sot. 57 (1935) 1203. [Z] J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, 1932) p. 198. [3] C. P. SmJ.th. Dielectric Behaviour and Structure (McGraw Hill, 1955) p. 12. [4] R. P. Bell and I. E. Coop, Trans. Faraday Sot. 34 (1938) 1209. 1.51R.P.Bell. Trans. Faradav Sot. 38 (1942) 422. [61
E.
A_HaI&i,
Trans.
Fzu&&’
Sot.
52
(19&S)
1441;
see also E.A.Halevi, in: Cohen et al. eds. Proz-ress in Ph.vsical Organic Chemistry, Vol. 1 (Tn-
~erscience,-1963) pp.-118-9. [7] L.S. Bartell, J. Chem. Phys. 38 (1963) 1827. [8] E. A. Halevi, E. N. Haran and B. Ravid, in preparation. (9J see e.g. ref. [Z] p. 200. [lo] 1. E. Coop and Sutton, J. Chem. Sot. (1938) 1269; see also-ref. ]3] p. 417. Ill] T. Yoshino and H. J. Bernstein, J. Mol. Spectry. 2 (1958) 213. [12J L. Wharton, L. P. Gold and W.Klemperer. J. Chem. Phys. 37 (1962) 2149.
PHYSICS
LETTERS
1 (1967)
NORTH-HOLLAND
475-476.
PUBLISHING
DIPOLE MOMENT AND POLARIZABILITY BETWEEN NH3 AND NDg E. A. HALEVI, Department of Chemisfv,
22 November
of many
plot over the renge 0 - 150°C, they obtained:
6PE+A Fitting
- ~~3)
= ($P3
- fix3 E+A) -- -0.9 cm3/mole.
E+A
the same
= 0.03
D;
= (~‘~~3
experimental
results
6P
EcA
to the
= -0.71 cm3/mole.
thirty years ago. Analysis of the data by means of the Van Vleck equation yields:
B,u = 0.0U14 D;
6PE+A = -0.49 cm3/AoLe.
At our higher temperatures, excitation of the bending mode of NHQ, and particularly ND3, is
= -0.3 cm3/mole.
appreciable * [9]. A correction for population of vibrational levels above the lowest was applied, which, to be tractable, had to incorporate a fairly large number of assumptions. ALL of these can t-e justified as approximations, but none is rigorously true. They are: a) The bending and stretching modes are separable, the same one-dimensional potential functions applying to both isotopic species; b) PA, the “atomic polarization” is isotopictiy invariant * * ; c) PE depends predominantly on boncf stretching, its angular dependence being negligible [ll]; d) the dipole moment difference arises predominantly from changes in bond angle rather than bond length (61; * We are grateful to Dr. H. Friedman for suggesting to us that neglect of this factor migM lead to serious error. ** The isotopic independence of PA follows
from the classical considerations of Coop and Sutton [IOI. It also follows from a quantum mechanical anaIysis for which we are deeply indebted to Professor A. D. Buckingham (personal communication, 20 April 1965).
t Performed under Grant No. N.B.S. (G) 22, from the U. S. Department of Commerce, National Bureau of Standards, administered by the Technion Research and Development Foundation. 1967
WE+A
These results axe in remarkably good agreement with those obtained by De Bruyne and Smyth over
The isotope effect on electrical polarizability (6PE+A) is in the same direction as, but considerably larger than, that derived from refractivity data (APE) of similar molecules [5]. Bell and Coop showed, however, that even when 6PE+A was arbitrarily constrained to be zero, 6~ was only reduced to 0.012 D. Several years ago, one of us [6] justified semi-quantitatively De Bruyne and Smyth’s suggestion that the dipole moment difference arises largely from the anharmonicity of the symmetric bending mode. The admittedly crude assumptions of this treatment have since been challenged, as has the reliability of the old experimental result PIHaving constructed an instrument based on the determination of frequency ratios, which is specifically designed to measure directly small di-
December
1967
61.r= 0.0276 D ;
Van Vleck equation [2,3], which in effect corrects the classical treatment for quantization of the rotational levels, Bell and Coop [4] recalculated the values: 6~ = 0.015 D;
DIFFERENCES
electric constant differences between clcsely similar molecules [8], we have re-determined the dipole moment and polarizability differences between NH3 and ND3. Eight independent differential measurements were performed, each taken over ;he range 40 - 205OC. From a classical Debye pIot we obtain:
years ago by De Bruyne and Smyth [l]. Plotting the total molar polarization of each gas against reciprocal temperature in a conventional Debye
6~
AMSTERDAM
E. N. HARAN and B. RA-QID . Technion - Israel Institute of Technology, Haifa, IsraeE
Received The dipole moments and polarizabilities NH3 and ND3 were determined separately
COMPANY,
475
416
E. A. HALEVI.
E. N. HARAN and B. RAVID
e) the average dipole moment in a given vibrational state depends linearly on the vibrational energy *; f) the population distribution can be calculated with adequate accuracy using the partition function for the harmonic oscillator. The corrected results for the “zeroth” vibrational levels of NH3 and ND3 are: 6~ = 0.0145 sz 0.001 D; bPEtA = 0.17 f 0.03 Clll 3/mole. The errors quoted are the standard deviations from the respective mean values. The absolute accuracy of our figures is limited by the reliabiiity of our population correction. Evidently, this can affect the dipole moment difference by no more than 0.001 D or so. Taken at face value, 6PB+A is in much better agreement with the vtiue of &PE (-0.14
cm
3/mole)
calculated
from
Yoshino
and Bernstein’s polarizability derivatives [ll] and Bartell’s average bond lenoth than with the smalbased on HaIeler Va.hte (6PB = -0.05 cmg/mole) .vi’s earlier estimate [S] of 6~. However, ~PE+A is much more sensitive than is 6y to the * This dependence is obeyed extremely erage dipole moments of isotopic served by L. Wharton et al [12].
well by the avLiH molecules ob-
population correction, and consequently its value’ is more subject to the cumulative uncertainty of the assumptions underlying it. Experimental details and a discussion results will be publish&d in due course.
of the
References [I] J. M.A. De Bruyne and C.P. Smyth, J. Am. Chen. sot. 57 (1935) 1203. [Z] J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, 1932) p. 198. [3] C. P. SmJ.th. Dielectric Behaviour and Structure (McGraw Hill, 1955) p. 12. [4] R. P. Bell and I. E. Coop, Trans. Faraday Sot. 34 (1938) 1209. 1.51R.P.Bell. Trans. Faradav Sot. 38 (1942) 422. [61
E.
A_HaI&i,
Trans.
Fzu&&’
Sot.
52
(19&S)
1441;
see also E.A.Halevi, in: Cohen et al. eds. Proz-ress in Ph.vsical Organic Chemistry, Vol. 1 (Tn-
~erscience,-1963) pp.-118-9. [7] L.S. Bartell, J. Chem. Phys. 38 (1963) 1827. [8] E. A. Halevi, E. N. Haran and B. Ravid, in preparation. (9J see e.g. ref. [Z] p. 200. [lo] 1. E. Coop and Sutton, J. Chem. Sot. (1938) 1269; see also-ref. ]3] p. 417. Ill] T. Yoshino and H. J. Bernstein, J. Mol. Spectry. 2 (1958) 213. [12J L. Wharton, L. P. Gold and W.Klemperer. J. Chem. Phys. 37 (1962) 2149.