2957
Raman Spectra of Liquid Ammonia
Liquid Ammonia. A Comparative Study ob Models via Raman Spectroscopy James W. Lundeen and William H. Koehler* Department of Chemistry, Texas Christian University, Fort Worth, Texas 76 129 (Received July 23, 1975) Publication costs assisted by the Robert A. Welch Foundation
High-density digital Raman spectra of pure ammonia in the 3000-3500-~m-~region have been collected as a function of temperature. The data were used to critically evaluate two previously suggested models. One model interprets the spectrum in terms of associated and unassociated species. Resolution of the N-H region into four bands, three attributed to the unassociated (C3") species and one attributed to the associated (C,) species, forms the basis for interpretation of the Raman spectrum of pure ammonia and ammonia solutions. This interpretation raises questions concerning line shapes due to the C, species, variation of line shapes with temperature, relative intensities of V I and VI', and coincidences necessary to explain the absence of other C, bands. The second model, the damped, coupled oscillator model, attempts to interpret the spectrum in terms of coupling of vibrational states. Correction of a sign error in the original formulation and the use of only the isotropic Raman scattering resulted in a satisfactory explanation of the changes observed in the spectrum as temperature is varied. The band at ca. 3290 cm-I (at high temperatures) is assigned to V I , the totally symmetric N-H stretching mode, and the same band is assigned to 2u4 a t low temperatures (below 240 K). The change in assignments is due to a lowering in frequency of the nonresonating symmetric stretch with increased hydrogen bonding. Fermi resonance between V I and 2u4 gives rise to an observed spectrum in which observed peak positions do not change appreciably.
This band is reported to increase in intensity as the temperature is decreased, and such an intensity change acThe Raman spectrum of liquid ammonia is characterized counts for the observed intensity reversals with temperaby weak scattering around 1060 and 1640 cm-I and strong ture. The four-band model has been used to explain the scattering around 3300 cm-l. The 1060- and 1640-cm-l bands observed in the N-H stretching region in salt solubands have been unambiguously assigned as U Z , symmetric tions,6-8 in NDzH,j and most recently in solutions of ambending mode, and v4, asymmetric bending mode, respecmonia in deuteri~benzene.~ tively. The 3300-cm-l region is characterized by an enveInspection of the results presented by the aforemenlope which appears to be three overlapping bands. Little tioned investigatorss raises certain questions. Although doubt exists concerning the assignment of the highest enercomplete band parameter data are not given, the shape of gy band (ca. 3380 cm-l) to v3, asymmetric stretching mode; the band assigned to VI' appears significantly different than however, controversy exists concerning the assignment of the shape of the band assigned to VI. If these are both due the two lower energy bands. It is not the purpose of this to totally symmetric vibrations, their band shapes might be paper to review comprehensively all band assignments. expected to be more similar. The fact that the C, species Suffice it to say that various investigatorslJ have assigned could have six Raman active modes yet only one is obthe bands at ca. 3220 and 3305 cm-l to 2u4 and V I , symmetserved necessitates fortuitous coincidences. Finally, the inric stretching mode, respectively, whereas other investigators3 have reversed these assignments. The problem o f , tensity of YI' is always less than that of V I . One of two conclusions must be drawn: either the vibration giving rise to band assignments is complicated by the existence of Fermi VI' is not as efficient a scattering center as the vibration resonance4 between 2Vq and V I , and the intensity reversals which occur with increasing (decreasing) t e m p e r a t ~ r e . ~ giving rise to VI, and/or the concentration of associated molecules is less than that of the unassociated molecules. The importance of the correct interpretation of the N-H An alternative model based on coupling of vibrational stretching region cannot be minimized if meaningful conmodes has been proposed.1° This model is an extension of clusions concerning solute-solute and solute-solvent interthe model used to explain the low-frequency photon couactions in liquid ammonia solutions are to be forthcoming. pling in solids.ll While a complete derivation will not be Recently, two models have been proposed to explain the given here, the basic equations are presented for reference spectral features observed in the 3300-cm-l region. One purposes: model, henceforth referred to as the four-band model, suggests that there are two types of ammonia molecules present in liquid ammonia.6p7 One type of ammonia molecule is unassociated and has Csu symmetry, whereas the second type is associated with another ammonia molecule via hydrogen bonding and has C, symmetry. Resolution of the 3300-cm-l envelope into three, four, and five bands rewhere vealed that a four-band fit was statistically more meaningA = Q12Q22 - w(Q12 n22) w4 - w2rlr2 - b2 (2) ful than either a three- or five-band fit.s The fourth band and at ca. 3265 cm-l is polarized and has been assigned as vl', the totally symmetric stretching mode of the C, species. B = w ( Q 2 2 r l + Q12r2) - w3(rlr2) (3)
Introduction
+
+
+
The Journal of Physical Chemistry, Voi. 79, No. 26, 1975
2958
James W. Lundeen and William H. Koehler
I
n ,31034 A RCA PM ( - 3 3 ' C )
interface
Spex 1 4 0 3
------i
Xerox Sigma 9
magnetic t a p e
Figure 1. Laser Raman spectrometer.
In the above formulation Zzz(w) is the isotropic Raman intensity. ~ ( w is) the Bose-Einstein population factor, b is the interaction energy or coupling parameter, C1 and C2 are the relative scattering strengths of the uncoupled oscillators, l71 and rz are the damping constants and are equivalent to the line widths normally observed for vibrations which are not in Fermi resonance, w1 and w2 are the observed frequencies, and 91 and are the frequencies of the uncoupled vibrations. 91 and i l 2 are calculated as follows: Q i 2= '/Z(W,'
+ ~ 2 ' ) + t/,[(~,' - 0 2 ' ) ~
- 4b'11''
(4)
and where w1 and w2 are the observed peak frequencies. Although the results of this model appear promising, it too raises questions. Some of the data are reportedlo a t 182 K but ammonia solidifies a t 193 K. In the original publication, the sign preceding the term 2C1C2[bB/(A2 B2)] in eq 1 was reported as negative; however, an analysis of the deviation yields a positive sign.12 Close examination of the curve fitting reveals a deficiency in intensity in the valley between the peaks. This is the same region where the fourband model suggests VI' should be. Regardless of band assignments CZ/C1 = 0.3 appears too large; such a ratio suggests that either the intrinsic scattering of 2 4 is greater than that of u1 or that it is 30% of u1. Certainly the intensity of the overtone would not be greater than the fundamental, and it is doubtful that it would be as large as 30%. Finally, the anisotropic scattering, although small, should be removed from the isotropic scattering since the model is applicable only to isotropic scattering. The four-band model results in assignment of the bands in the 3300-cm-l region as 3214 (2U4), 3271 (VI'), 3300 ( V I ) , and 3385 cm-I ( u s ) at 25OC. The assignments based on the coupled oscillator model are 3220 (VI), 3305 (2~41,and 3388 cm-I ( u g ) at 25°C. Unfortunately the assignment dilemma remains unresolved. Because of the questions which have been raised, a review of both models seemed in order. Highdensity Raman scattering data obtained under carefully
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The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
controlled experimental conditions are necessary to critically evaluate the proposed models. Only when the two models are subjected to analyses using the same data can meaningful conclusions be drawn. The acquisition of Raman scattering data, treatment of the data using the four-band model and a corrected version of the coupled oscillator model, and assignment of the bands in the Raman spectrum of liquid ammonia form the subject of this work. Experimental Section A laser Raman spectrometer was constructed using five primary components: (1) control Laser-Orlando 1-W Ar+ ion laser fitted with an optical feedback loop for power stabilization; (2) Spex 1493 double monochromator; (3) SSRI photon counting detection system with buffered binary scaler; (4) RCA 31034A photomultiplier tube housed in a Products for Research thermoelectric cooler (dark count -50 Hz a t -3OOC); and (5) PDP-11/80 minicomputer with magnetic tape drive. The instrument geometry is shown schematically in Figure 1. The laser beam (4880 A, maximum power 400 mW) was focused on the sample after deflection into a vertical plane parallel to the monochromator entrance slit. The scattered light was focused on the entrance slit by a 75 mm fll.0 lens. Prior to reaching the slit, the light passed through an analyzer followed by a calcite wedge scrambler. The analyzer permitted accurate depolarization measurements. Measured depolarization values for carbon tetrachloride were 0.0092, 0.740, and 0.752 for the 459-, 314-, and 218-cm-l bands, respectively, using the same slit width as for the ammonia spectra (10.7-cm-' band-pass). Comparison to literature valued3 of 0.0039, 0.751, and 0.758, which were obtained using narrower slits, demonstrated that the analyzer was satisfactory. The monochromator drive motor was controlled by the minicomputer with spectral data accumulated only when the drive was stationary. Since the scaler input did not involve an RC time constant the effective time constant was zero, and there was no time constant distortion of the band contours. The Raman spectral data were written on magnetic tape by the PDP-11 minicomputer for off-line pro-
2959
Raman Spectra of Liquid Ammonia
1.00 1
PI
i
.80 E
.60
1
.oo
I
3044
3188
3332
8
3476 vlbiEh
W N E \ W E RS
Figure 2. N-H
‘,
Figure 3. N-H
stretching region (polarized)(22OC).
cessing on a Xerox Sigma 9 computer. Samples were prepared by condensing ammonia (Matheson, 99.99%), which had been distilled twice from sodium metal, into glass Raman sample tubes on a vacuum line. The samples were frozen in liquid nitrogen and sealed off under vacuum. The samples were held in a vertical orientation in a metal block which was cooled by recirculating cold methanol. A plexiglass cube filled with dry nitrogen surrounded the sample block preventing condensation on the sample. Temperatures were monitored with a thermistor and are accurate to f3OC.
” 3332 ” ’ 3476
”BiRC
stretching region (depolarized)(22OC).
each parameter were approximated by relations of the type shown in eq 11,where A = O.O05(I’l). af(I’l)/aI’l = [f(T’l
+ A) - f(I’1 - A)]/2A
(11)
The computer used, a Xerox Sigma 9, was capable of only six significant figures in floating point notation, and therefore all computations were performed in double precision mode since significant figures were lost in the subtraction step as well as during the solution of the matrix equation in the least-squares iteration. It was found that the best results were obtained by constraining the observed peak maxima (which were found quite accurately using program RES0Llg) and allowing only five parameters to be Data Treatment adjusted. If all seven parameters were varied, oscillation Any slit distortion was removed by d e c o n ~ o l u t i n g l ~ - ~around ~ the final solution occurred. A “manual regression” using an observed slit function for this instrument. This was performed on the observed peak maxima by making function was derived from a mercury emission line contour small adjustments in these parameters. The values which measured as a function of slit width. The Raman scattering gave the smallest weighted sum of squares of residuals were polarized in the z direction is given17J8 by accepted as the final solution in all cases. The weighting scheme w = (number of counts)-l, which is appropriate for Z, = k(45(&’)2 4(7’)2)Ey2 (6) counting experiments, was applied during all computawhich corresponds to the matrix equation tions. azz= (jS)(Tr(a)) + (1h)(3azz- T r ( a ) ) (7) Results and Discussion
+
of Schwartz and Wang.l0 Since these authors formulated a model in which only scattering due to the first term is considered, it was necessary to isolate the Raman scattering due to the h’ term in eq 6. This was accomplished by utilizing the scattering polarized in the y direction17J8 given by:
Zy = k(37’)2Ey2
(8)
and applying the relation shown by eq 9 a t each frequency. 6’= k ( I z
- (4/3)IY)
(9)
The resulting isotropic spectrum was resolved by a nonlinear damped least-squares programlg into symmetrical bands described as a sum of a Gaussian and a Lorentzian having the same band centers and half-widths. The function used is given by eq 10, where 00 is the band center, h is the band half-width, and G and L are the Gaussian and Lorentzian intensities, respectively. This analysis was done using the same computer program used in references 8 and 9. I ( w ) Geb4In
2((w-woh)z
+ L / ( 1 + 4[(0 - w0)/hI2)(IO)
The coupled oscillator model was programmed so that all seven parameters ( b , I’l, I’z, C1, Cz/C1, 01, and 02) could be refined simultaneously. Due to the complexity of the model, the partial derivatives of intensity with respect to
Raman scattering data in liquid ammonia as a function of temperature were collected. Polarized and depolarized spectra in the 3300-cm-” region are shown in Figures 2 and 3. Prior to any analysis, the data were deconvoluted with a slit function. The data in the 3300-cm-’ region were subjected to a curve fitting procedure using program RESOL.” Using Hamilton’s R factors30 as a criteria of “goodness” of fit, these analyses confirmed‘ that a fourband fit was statistically better than either a three- or fiveband fit. Results of the curve fitting for both the polarized and depolarized spectra are presented in Tables I and 11, and representative plots of the data are shown in Figures 4 and 5. The error curve shown at the bottom is on the same scale as the ordinate. Inspection of Table I reveals several interesting and unexpected results. The bands a t ca. 3205 and 3290 cm-l, assigneds as 2u4 and VI, respectively, exhibit a high percentage of Lorentzian character. This is not unexpected because a Lorentzian or Voigt function is generally regarded as a satisfactory description of most Raman bands.20-22 The lower percentage of Lorentzian character observed in the 3380-cm-l band, assigned to ug, seems reasonable, since s t ~ d i e s have ~ ~ - shown ~ ~ that line widths corresponding to non-totally symmetric vibrations are considerably greater than those corresponding to totally symmetric vibrations. The Journal of Physical Che-mistry, Vol. 79, No. 28, 1975
2960
James W. Lundeen and William H. Koehler
TABLE I: Four-Band Model Parameters (Polarized) Halfwidth, cm-'
Intensity. Hz Temp, K
u,
295
cm-'
3209 3258 3294 3383 3207 3256 3293 3376 3204 3249 3291 3374 3203 3252 3291 3375
258
243
228
Gaussian
Lorentzian
2650 3950 2680 1350 3370 5820 3850 1240 4370 6150 3250 1700 180 400 40
12720
28 67 29 66 35 77 35 57 32 92 41 51 32 80 42 19
0
22150 790 15290 0
15490 1720 13050 0
11590 3080 1190 0 1080 350
0
Area, Hz X cm-I x
%
lo5
6.4 2.8 10.9 1.8 8.5 4.7 9.9 2.2
Lorentzian 83 0
89 37 82 0
80 58 75
8.1 6.0
0
8.9 3.4 0.7
78 64 87
0.3
0
0.7 0.3
96 100
Table 11: Four Band Model Parameters (Depolarized) Halfwidth, cm-I 50 43 44 77 42 65 42 59 46 31 63 52 43 45 44 49
Intensity, Hz Temp, K 295
cm-' 3213 3254 3294 3381 3207 3254 3296 3377 3208 3246 3287 3375 3207 3256 3292 3374
Gaussian 170 10
u,
258
243
228
10 0 100
380 210 0
380 34 0 720 690 40 30 40 60
.99 7
.79
Lorentzian 140 2 60 470 1920 470 170 390 3220 500 0
160 3090 40 1
40 110
2.0 1.8
3.3 23 3.5 4.3 3.5 30 5.5 1.2 6.4 29 0.04 0.01
0.04 0.11
%
los
Lorentzian 44 97 98 100
82 31 65 100
57 0
18 82 49 4 46 64
.87
n
n
i
Area, Hz x cm-I x
II
.70 >
t
.52
r v-
z
.35 .17
-. 00
1
WAVENUMBERS '
'
'
.-4--
WAVENUWERS '
'
j
Figure 4. Resolution of polarized N-H stretching region into four bands (22'C).
Flgure 5. Resolution bands (22OC).
The unexpected result is the total Gaussian character of the band a t 3255 cm-l. This band is assigned as V I ' , the totally symmetric stretching mode of the associated species. That the band parameters describing this totally symmetric vibration should differ so markedly from the parameters describing the totally symmetric vibration of the unassociated species is difficult to rationalize.
Although the parameters (Table I) describing the bands a t 3205, 3290, and 3380 cm-' vary with temperature in a not unreasonable manner, the band parameters set forth in Table I1 seem to vary in a nonsystematic way with temperature. This variation may be due to the greater uncertainty caused by the lower intensities. Examination of the spectra a t various temperatures did
The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
of depolarized N-H stretching region into four
2961
Raman Spectra of Liquid Ammonia
1.00
.80 .60 t
.40
r
: .20 5
-. 00
m
20.00
f,
m
Y
m Figure 6. Isotropic component of N-H stretching region fit with coupled oscillator model (22OC).
‘“1
-20.00
220.0
I
1
I
I
240.0
280.0
280.0
300.0
Figure 6. Damping factors, 3.000
-
0 2.300
-
c, c
1
x
T [K)
i 320.0
and r2, as a function of temperature.
I
Y 6 2.800 I
2.700
2. eo0 no.0
240.0
zso.0
T
IK)
ao,o
m,o
3
0
Flgure 7. Coupling constant, b, as a function of temperature.
not reveal any new bands; changes in spectral features were limited to a sharpening of the band a t 3380 cm-’ with decreasing temperature and an intensity reversal involving the bands a t 3205 and 3290 cm-’. These results are perplexing if the four-band model is used to interpret the spectrum, since the associated species has C, symmetry and could have six Raman active fundamental modes. Furthermore, the symmetry of the modes is such that Fermi resonance is allowed between any overtone and any A‘ fundamental. In light of the fact that a t -3OOC the band (~1’) attributed to the associated species accounts for -23% of the area under the computed envelope, the absence of other bands attributable to the C,9species seems somewhat astonishing. To explain the apparent absence of these bands a great many fortuitous coincidences must be invoked. The possibility of such coincidences raises questions involving the quality of the band parameters ascribed to the v i , 2 ~ 4and , us of the unassociated species. The coupled oscillator modello was investigated using the same Raman scattering data as was used to evaluate the four-band model. Prior to fitting the data, a sign error in the second term of eq 11 in the original publicationlo was
Flgure 0, Observed frequencies, w , and w 2 , and uncoupled frequencies, ‘21 and ‘22, as a functlon of temperature. changed.I2 The data were deconvoluted with a slit function, and the anisotropic contribution to the spectrum was removed (vide supra). Although Schwartz and Wang held the ratio C2/C1 constant after establishing a “best” value of 0.3 via a manual regression technique, C2IC1 and C1 were treated as adjustable parameters during the present study. As a consequence five parameters were refined simultaneously. A representative result of the curve fitting procedure is shown in Figure 6. Variation of the parameters b , rl and r2, and w1, u p , Q l , and Q2 with temperature is shown in Figures 7, 8, and 9. In these figures, the line(s) shown are the result of a linear least-squares analysis. The data are presented in tabular form in Table 111. Comparison of these results with those presented by Schwartz and Wang reveals certain similarities and some distinct differences. In general, the computed curve in this study fits the experimental data better in the region between the peaks than does the The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
2962
James W. Lundeen and William H. Koehler
TABLE 111: Coupled Oscillator Model Parameters Temp, K 295
r ', cm-'
rz,cm-' b, cm-2 c 2
IC,
o ' , em-' Lj2,
SI
z,
cm-' cm-' cm-'
15.8 43.7 2.78 X 105 7 x 10-3
258 9.6 58.8 3.03 X 105 4 x 10-3
-
243 18.5 59.0 2.97 X 105
1x
1700.
10-2
228 ---
105 7
x
10-3 3296 3208 3262 3243
3297 3204 3254 3247
3293 3202 3248 3248
1680.
14.3 57.6 2.98 x
3293 3201 3245 3250
1660. c
z
CJ 1
1 I
1640.
{A
3
0
."
!
Y
28
curve reported in the original publication;1° however, there is still some problem with the fit a t the top of the peaks and on the wings. The values of b reported in this study are of similar magnitude to those previously reported, but b increases rather than decreases with decreasing temperature. Values of rl and r2 agree quite well with those reported. The variation of 91 and 9 2 with temperature is very significant in that they cross around 240 K. 91 decreases with decreasing temperature whereas Q2 appears to increase. Whether a variation of 5 cm-' in the value of 9 2 over 50°C can be considered a significant change is dubious. The variation of 9 2 with temperature is very similar to the variation of the corresponding fundamental v4 with temperature (Figure 10). An unexpected but satisfying result concerns the ratio C2/C1 (Table 111).Although treated as an adjustable parameter, C2/CI always converged to a value of -0.01. This value lends support to the conclusions which follow. The results of this study indicate that the Raman spectrum of liquid ammonia can be interpreted as follows. There is little question that the bands at ca. 1060, 1640, and 3380 cm-' can be assigned to v2, v4, and v3, respectively. The controversy has centered around the bands a t 3205 and 3290 cm-1. The two modes are coupled via Fermi resonance as indicated by a nonzero value of b , and as a result of this resonance, both bands are combinations of V I and 2~4.At high temperatures (300 K) the band at 3290 cm-' has more v1 character than 2Vq character and likewise the 3205-cm-l band has more 2v4 character than V I character. As the temperature is decreased the ammonia molecules are subjected to environmental changes, probably through increased hydrogen bonding, which perturb the molecules and shift ill, the frequency of the uncoupled oscillator, to lower frequency with decreasing temperature. Such frequency shifts are expected as a result of increased hydrogen bonding. The coupling between the two energy levels increases because they are now closer together. As a result of increased coupling the observed frequencies (w1 and w2) appear relatively constant. The fact that 91 decreases and n2 remains constant or increases supports the supposition that at 300 K the band at 3290 cm-l is primarily of v1 character and the band at 3205 cm-l is primarily of 2Vq character because a symmetric stretching mode should be more affected by hydrogen bonding than a bending mode. As coupling increases, the 3290-cm-' band increases in 2 ~ 4 character and the 3205-cm-I band increases in v1 character. As a consequence of the increasing 2v4 character of the 3290-cm-l band, the intensity decreases, whereas the intensity of the 3205-cm-l band increases because of increasing v 1 character. Around 240 K, Ql has shifted such that it is equal to 9 2 and, therefore, each band is of equal v1 and The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
1 1*1 I
1830. m.0
a 0 29 2
10
111
I
I
I
I
no.0
240.0
260.0
280.0
Flgure 10. Position of v4
r [Io
4
3m.0
as a function of temperature.
2v4 character. This result confirms those previously re-
p ~ r t e d Below .~ 240 K, the band a t 3290 cm-' has more 2v4 character, whereas the 3205-cm-l band has more v 1 character. In other words, if definite labels must be placed on these bands, above 240 K, the higher energy band is v l and the lower energy band is 2u4; below 240 K the higher energy band is 2v4 and the lower energy band is VI. Such labels should be summarily rejected because the resonance phenomenon requires that both bands be combinations of states (modes) and only the degree of mixing holds any significance. The value of C2IC1 = 0.01 lends support to the aforementioned assignments. Intuitively an overtone is expected to scatter much less than a fundamental, and a ratio of 0.01, C2,,/C,,, is more plausible than the reported ratio of 0.30. In summary, the results of this study suggest that until questions involving band shapes and frequency coincidences are resolved, interpreting the N-H stretching region in terms of two species of ammonia should be viewed with a great deal of skepticism. In addition to these questions, the four-band model requires 12 adjustable parameters (for the isotropic spectrum) whereas the coupled oscillator model requires only 7. Application of the coupled oscillator model permits a reasonable interpretation of the observed spectrum. This model also fits the spectrum of ammonia in carbon tetrachloride, benzene, and pentane26 as well as the spectrum of alkali halide-liquid ammonia solutions.27 Further refinement of the model is possible but in the present form it seems'to offer a satisfying solution to the controversy involving band assignments in the N-H stretching region. Acknowledgments. We wish to thank the Robert A. Welch Foundation and the Research Corporation for their financial support.
References and Notes (1) C. A. Plint. R. M. B. Small, and H. L. Welsh, Can. J. Phys., 32, 653 (1954). ( 2 ) S.Kinumaki and K. Aida, Sci. Rep. Res. lnst. Tohoku Univ., Ser. A, 8, 186 (1954). (3) T. Birchall and I. Drummond, J. Chern. SOC.A, 1859 (1970). (4) G. Herzberg, "Infrared and Raman Spectra", D. Van Nostrand Co.. Princeton, N.J., 1966.
Optical and Magnetic Data for Na-NHS
2963
Solutions
(5)8. De Bettignies and F. Wallert, C. R. Hebd. Seances Acad. Sci., Ser. 6, 640 (1970). (6)D. J. Gardiner, R. E. Hester, and W. E. L. Grossman, J. Chem. Phys., 59, 175 (1973). (7)J. H. Roberts, A. T. Lemiey, and J. J. Lagowski, Spectrosc. Lett., 5, 271 (1972). (8)A. T. Lemley, J. H. Roberts, K. R. Plowman, and J. J. Lagowski, J. Phys. Chem., 77, 2185 (1973). (9)J. H. Roberts and B. De Bettlgnies, J. Phys. Chem., 78, 2106 (1974). (IO) M. Schwartz and C. H. Wang, J. Chem. Phys., 59,5258 (1973). (1 1) J. F. Scott, “Light Scattering In Solids”, M. Balkanski, Ed., Flammarion, Paris, 1972. (12)M. Schwartz, North Texas State University, Denton, Tex., private communication.
(13)W. F. Murphy, M. E. Evans, and P. Bender, J. Chem Phys., 47, 1836 119871 \.-I -
(14) K. S. Seshadri and R. N. Jones, Spectrochim. Acta, 19, 1013 (1963). (15)R. N. Jones, R. Venkataraghavan, and J. W. Hopkins, Spectrochim.
Acta, Part A, 23,925 (1967). (16) R. N. Jones, T. E. Bach, H. Fuhrer, V. B. Kartha, J. Pitha, K. S. Seshadri,
R. Venkataraghavan, and R. P. Young, NRC Bull., No. 11 (1968). (17) T. C. Damen, S. P. S. Porto, and B. Tell, Phys. Rev. (Ser. 2),142, 570 (1966).
(18) T. R. Giison and P. J. Hendra, “Laser Raman Spectroscopy”, Wiiey-lnterscience, New York, N.Y., 1970. (19)P. F. Rusch, Ph.D. Dissertation, University of Texas, Austin, Tex., 1971. (20)H. S.Goldberg and P. S. Pershan, J. Chem. Phys., 58,3816 (1973). (21)M. McClintock, D. A. Jennings, and M. Mizushima, Phys. Rev. Left., 21,
276 (1968). (22)W. L. Greer, S. A. Rice, and G. Morris, J. Chem. Phys., 52, 5622 (1970). (23)W. R. L. Clements and 6. P. Stoicheff, Appl. Phys. Left., 12, 246 (1968). (24)J. D. Masso, Y. D. Harker, and D. F. Edwards, J. Chem. Phys., 50, 5420 (1969). (25)M. Scotto, J. Chem. Phys., 49, 5362 (1968). (26)J. W. Lundeen and W. H. Koehler, to be submitted for publication. (27)J. W. Lundeen and W. H. Koehler, to be submitted for publication. (28)B. L. Smith, Masters Thesis, Texas Christian University, Fort Worth, Tex., 1973. (29)Present work. (30)W. C. Hamilton, Acta Crystallogr., 18, 502 (1965).
Correlation of Optical and Magnetic Data for Sodium-Ammonia Solutions Gabrlel Rubinstefn School of Theoreticaland Applied Science, Ramapo College, Mahwah, New Jersey 07430 (Received July 25, 1975)
The resolution of the optical spectra of Na-NHS solutions into two b a n d ~ , l -one ~ of which may be associated with a species incorporating two electrons, permits the correlation of the optical data with the magnetic data of Huster4 and of Freed and Sugarman5, without reference to any particular model for the solutions. With the aid of the redox model: the optical data are shown also to correlate with the spin susceptibility data of Hutchinson and Pastor.’ The latter correlation requires identification of the diamagnetic species as one of stoichiometry M-. The resolution of the broad infrared spectra of dilute (10-5-10-3 M ) solutions of Na-NH3 at -75, -65, and -55OC reveals the presence of two distinct, yet similar bands separated by about 600 cm-l. At -65OC their maxima occur a t 7067 and 6494 cm-‘, respectively. The shape function fl(v) for the band occurring at the higher frequencies was obtained by extrapolation to infinite dilution and was assigned to a species composed of two electrons in some form. Since the optical analysis revealed the presence of two bands and that f&) is due to a species containing two electrons, it is natural to suppose that this species is diamagnetic. Figure 1 compares Huster’s4 static susceptibility data for Na-NHS solutions with optical data at -75OC. As can be seen, a good correlation is obtained at the overlapping metal concentrations (about and the trend established at low sodium concentrations (optical data) is carried over to the more concentrated metal solutions (magnetic data). The fraction of unpaired spins, Y , derived from the magnetic data is obtained from the ratio of the measured, net molar static susceptibility (xm)to the theoretical magnetic susceptibility of a mole of free electrons (XT = NOP/kT). The reported xm values have been corrected for the solvent’s diamagnetism, while the relative diamagnetic-paramagnetic contributions from the other species is expected to be small for the more dilute solutions. Since xm for 0.105
and 7.63 X lov3 M solutions were -19.0 X and 202 X 10-6 erg/(mol G 2 ) ,the diamagnetic contributions are expected to be less than 10% for the solutions more dilute than the latter concentration. It is assumed that the minimum negative Y values were characteristic of essentially 100% diamagnetic solutions and that the molar diamagnetic susceptibility decreases with decreasing metal concentrations. Since the sodium metal concentrations were not experimentally determined, the Y values obtained from the optical data were calculated from
Y = Cl/[Na] where [Nal = Alm/tlmL + A2m/~rnL
A I , and Azm are the absorbances a t the maximum for each band determined in this work, while the extinction coefficients at the maxima are those calculated by other investigat or^^,^ (elrn = 5.0 X lo4 and tzrn = 4.5 X lo4 M-1 cm-1 ) and were both based on total metal concentrations. It is reasonable to assume that both q m and qmwere determined for solutions characterized mainly by either species 1 or species 2, respectively. C1 represents the concentration of all paramagnetic species and is equal to A ~ ~ l t l where ~L, L is the path length (cm). Figure 2 correlates Freed and Sugarman’s5 static suscepThe Journal of Physical Chemistry, Vol. 79, No. 26. 1975
