THE RAlLf AN E F F E C T O F D E U T E R I O A ~ l ~ I O ~ I A ' ~ GEO. GLOCKLER
ASD
F.
'r. WALL
School of Chemistry, Unicersity of Winnesola, Jfinneapolis, Minnesota
Received July 29, 1956 INTRODTJCTIOK
The apparatus developed in this laboratory (3) has been used to study the Ranian spectrum of gaseous heavy XD3. An improvemeiit introduced by us consisted of a cylindrical aluminum reflector surroundiiig the eight mercury-neon lanipr. To the e n d of the reflector was attached a 3-in. pipe leading to an air blower which permitted fair control of the temperature. EXPERIJIESTAL RESULTS
The sample of heavy ammonia n-as contained in a Raniaii tube of 230-CC. capacity a t n preswre of about 900 mm. of mercury. Because of the limited amount of the saniple only two Raman frequencies of the four expected could be obtained in spite of the very long exposure times used. One of the frequencies found could be photographed in five days, and a tea-day exposure yielded the other line. Our results are in agreeinelit with the findings of Silverman a d Saiiderson (8) in the infra-red, as seen in table 1. The value of the S - D vibration (vl) given in table 1 is the nieaii of ten observations (see table 2). The frequency shift (vg) corresponding to the doublet obtained by hmaldi and Placzek (1) for light ammonia a t 933.8 and 964.3 cni.-l n-as much inore difficult to measure. The mean poqition was determined on one plate Tyhich requlted from a ten-day expowre. I t is ceen that the valuei: of the fundamental frequency vi found in the infra-red and in the Raniaii ywctriiiii are in good agreement. It seeinecl impractical t o nialie further effort t o obtain the other b o lines, since tlicir intensity x-a? likely t o be extremely low, because the change in polarizability during the motion of the atoms iiivolwd in these tn-o de1 Presented a t the Symposium on 3lolecular Structure, held a t Princeton University, Princeton, Kew Jersey, December 31, 1936 to January 2 , 1937, under the auspices of the Division of Physical and Inorganic Cheiiiisti> of the ,Imerican Chemical Society. 2 This article is based upon part of a thesis to he presented to the Faculty of the Graduate School of the University of Minnesota by F T. Wall in partial fulfillment of the requirements for the degree of Doctor of Philosophy. We wish to thank Professor H. S. Taylor of Princeton Uriiversity for a saniple of SDI 143
144
GEO. GLOCKLER AND F. T. WALL
generate frequencies is very small. This situation is similar to the case of methane studied by 1lacWood and Urey ( 5 ) . T H E THEORY O F SMALL VIBRATIONS APPLIED TO
NDs
By means of the method of small vibrations, it is possible to obtain expressions for the fundamental frequencies of a molecule (for example, TABLE 1 Fzindatnental FREQUEXCY
ISIP.4-RED
I v3
Y4 V1
I
V?
EXPERIMEhT N O
(7
equeiicies
(6)
R i I I LX L I S E S
786 (1)
__
THEORETICU
I
c 171
74s 1191 2420 2556
--I
cm.-1
722 1190 2377 ?
I
2420 0
H g - E K C l T l \ G LI\E
i I
I
FREQUEVCY SEIrT
cni
I
4358 4047
I
4358 4047
I
4358 4017
4(b)
4047
;(a)
'
4358 4338
~
-1
2419 2418 2420 2419 2419 2420 2420 2420 2120 2419
1047
4(a)
j(h)
NDI
cnL,-l
i l
1 (a) 1(b) 2(a) 2(h) 3(a) 303)
OJ
I
I
3 7 1 5 3 9 8 4 8 9
~~
i
Average
2420 0
XD3) in terms of the force con*tants, niasseb, and geometric properties (2, 4, 7). Assuming a potential function of the form
v = ax.KD(5; + x :
+ .ti) + 3kD,(1/& + +
the equations of niotion can be written
1/:3
1/:11
(1)
145
RAMAN EFFECT OF DEUTERIOAMMONIA
where xi is the displacement of the distance N-Di from equilibrium and y i j is the displacement for the distance D;-Di. The constants have the values
where mo = mass of the nitrogen atom, ml= mass of the deuterium atom, = angle between two valence bonds, and 4 = angle IC'-D-D = x / 2 D ~ D are D the force constants. - 0/2. ~ N and Assuming simple harmonic vibrations, i.e.,
e
where nl2x = frequency, then one arrives a t a determinantal equation which reduces to [n4
+ ( a + 26 + 6g)n2+ (6ag + 12bg + 4cf)l.
+ ( a - b + 3g)n2+ (3ag - 3bg - cf)]'
[n4
= 0
(4)
There will be six roots for n?,two single roots and two double roots, the double roots corresponding to degenerate vibrations. ASSIGNMENT O F TYPE OF VIBRATIONS TO THE FREQUENCIES
Introducing the values of the above frequencies back into equations 2 and taking into accouiit equations 3, it is possible to find the types of vibrations associated with the different frequencies, This is done by finding the ratios of the displacements by making use of the substituted equations (2). For the non-degenerate frequencies it is seen that x1
and that
=
5 2
=
z3; YlZ =
Y23
= y31
(5)
146
GEO. GLOCKLER A S D F. T. WALL
From equation 5 it is seen that the non-degenerate vibrations are totally symmetrical, \vith the nitrogen atom moving along the axis of symmetry. From equation 6 we find that the ratio of displacements is positive for a value of n? greater than -6g, since f is negative. The higher frequency has such a value that the ratio is positive and for the lower frequency the ratio is negative. Hence for the higher frequency the motion i- such that the deuterium atoms inoT e nearly along the valency bond direction., and for the lower frequency they move in a dirrction +omewhat perpendicular to the valency bonds. *r
93
*I
24 2 0 sm-l
"a
zss6
1191 cm"
7+8 cm-'
FIG.1. rundamental frequencies of deuterioammoiiia. vi and v 8 a r e non-d(>ytnerate, totally symmetrical vibrations; v 2 and v4 are degenerate vibrations.
For the degenerate vibrations it 1- not possible to find all of t h e ratio, of displacements, but the follon ing information i, available :
xl
+ + .z3 = 0 and y12 + + x2
y23
u31
=
0
A130 Sg
- SL -
n.1
yl2
y31
Y23
-
7z2
+ 3q f
For the lon-er degenerate frequcncy, a3 thc diqtancc betn ecn the nitrogen atoin and one deuterium atom le--en+, the distance hctwmi the other t n o dcuteriuni atonis les-cnq dqo, but for the higher degenerate frequency, the signs of these displacement- arc oppoqitc In the clegeneratc viliration?, the nitrogen atom n i o rs ~ tr&ii\\er-ely to the axis of symmetry, TI hilc the dcutcriuni atonis mol-e uiicyinmrtrically along or tranqversely to the 1-alencr l ~ o n t ldirection-, depending upon P whether t h r frecluciicy i\ high or 1cm .
RAMAN EFFECT OF DEUTERIOAMMONIA
147
Using the expression for the frequencies of the KD3 type molecule we have recalculated three of the four frequencies for heavy ammonia, making use of the observed values for light ammonia (8) and the ratio of the force constants given by Howarcl (4). The calculated values are found in table 1. The agreement b e t m e n the experimental and calculated values of the frequencies is about as good as can be expected, taking into account the approximations involT-ed. SUMM.4RT
The Raman spectrum of deuterioamnionia, ND3, has been studied. The results check satisfactorily 11-ith the infra-red spectrum. A method of allocating types of motions of atoms to the fundamental frequencies has been illustrated in some detail. This is done by finding the ratios of the displacements of the atom from equilibrium for a given vibrational frequency. REFERESCES
PLACZEK, G.: z. Physik 81, 259 (1933). DESNISON,D. 31.: Phil. Mag. 1, 195 (1926). GLOCKLER, GEO.,A N D MORRELL, C. E.: J. Chem. Physics 4, 15 (1936). HOWARD, J. B.: J. Chem. Physics 3, 207 (1935). AIAc\T’ooD,G. E., AND TJREY, H. C.: J. Chem. Physics 4,402 (1936). (6) ~ I I G E O T T 31. E v., , A I D BARKER, E. F.: P h p . Rev. 60,418 (1936) ( 7 ) ROSESTHAL, J. E.: Phi-s. Rev. 46, 730 (1934) (8) SILVERXIN, S , ASD SASDERSOX, J. 4.:Phys Rev. 44, 1032 (1933). (1) (2) (3) (4) (5)
AMALDI,E . ,
AND
