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Microwave spectra of nitrogen trifluoride in the excited vibrational states
JOURNAL
OF MOLECULAR
Microwave
SPECTROSCOPY
Spectra
28, 316-324 (1968)
of Nitrogen Trifluoride Vibrational States Equilibrium
~\/IASAYUKI OTAKE,~ Department
of Chemistry,
Faculty
in the Excited
Structure
CHI
R~ATSUMURA,'
of Science,
The University
AND
YONEZO
MORINO
of Tokyo, Hongo, Tokyo, Japan
The microwave spectra of two isotopic species of the NF3 molecule were investigated in the excited vibrational states. The vibration-rotation interaction constants 0l-B for the ~1 , ~2, v3and vq states were found to be -43.45, +38.65, +78.81, and +4.48 MHz for 14NF, and -38.41, +40.14, +75.67, and +4.64 MHz for lSNF3 , respectively. The equilibrium rotational constant, B. , was then derived to be 10761.91 f 0.2 MHz for “NFa and 10710.63 f 0.2 MHz for 16NF3 , from which the equilibrium structure was determined to be r,(N-F) = 1.365 f 0.002 A and LY~( LFNF) = 102”22 ZIZ2’. A set of linear relations was derived between cubic potential constants from the observed aDB and P-type doubling constants. INTRODUCTION
Microwave spectrum of nitrogen trifluoride in its ground vibrational state has been observed by Gordy and his co-workers (1-S). They measured J = 2 +- 1 transitions for two isot’opic species, 14NF3 and 15NF,, and determined the r. structure of the molecule by using the ground-state rotational constants, Bo (1) . The most straightforward way of eliminating the effect of zero-point vibrations from the T-O structure is to correct the ground-state rot,at#ional constants for the vibration-rotation interaction constants o(~. It should be mentioned that the observation of the vibrational satellites is import’ant not only for the determination of the equilibrium struct,ure, but also for the study of the intramolecular potential function. The e-type doubling constant’ is also available for the latter purpose. EXPERIMENTAL
METHODS
The sample of the normal species of nitrogen trifluoride used in the present experiment was contaminated with about 10 %# of CF4 but it was pure enough for 1Present address: The Central Research Laboratories, Ltd., Mizonokuchi, Kanagawa, Japan. 2 Pressent address: Government Chemical Industrial Tokyo, Japan. 316
Mitsubishi Research
Chemical Institute,
Industries Hatagaya,
EQUII,IBRIUM
STRUCTURE
OF NP,
:
t,he microwave studies. The 15N species of nitrogen trifluoride was prepared 1~~ modifying the electrolytic method reported by Watanabe (,$ ). An iron cell, 20 mm in diameter and 30 cm in length, with a gas inlet’ and outlet on the side wall was used as a cathode, and a graphite anode. 1 cm in diameter, n’a,s fixed on the bottom with a Teflon insulator and connected to a copper terminal supported by a F’crflon rubber stopper. Dehydrated ammonium bifluoride containing ‘“S isotope in 97 ‘: atomic concentration was used as electrolyte. It was diluted t80 5 7: by adding a large amount of KH$, (mp 76°C ), which 1va.s prepared b> condensing calculat’ed amount of anhydrous hydrogen fluoride on potassium hydrogen fluoride (6). The electrolysis was carried out at 110 f S’C’, keeping the cell in an oil-bath, \cith the anodic potential of k-5 V and tbe current densit,) of 0.01 A/cm’. The product was let to a liquid-oxygen trap by means of A carrier g:ls of NT . It \vas purified by a simple bulb-to-bulb dist,illat’ion at liquid-nitrogen tcmpcrature. The purity of the sample was checked by t,he infrared spcckun. The rotational spectrum n-as recorded wit,h a conventional microwave spectromet,er a-ith 110 kHz sinusoidal-wave Stark modulation. An S-band waveguidt ccl1 u-as used. The J = 1 +- 0 transitions were observed \vit,h a crystal harmonic gcnerntor drivel] by a Varian X-13 klystron. The measurement was carried out at room temperature. The sweep rate was reduced to 03-0.2 ,\IHz/min in order to observe u-e:& lines in the excited vibrational states. The assignment8 was confirmed, if necessary, by observing the spectra for t,he tsansit’ions J = 2 +- 1 :ud ,I = 3 +- 2: the details of the spectra for t#hese transitiow are in Ref. c6”). RESULTS T\vo
fairly strong vibrational sat,ellites \vere observed, bot#h for “^\jI’, :ultl ‘5SIi3 1 tit the frequencies slightly lower than the ground-state line, M-hile tu-o ot,her exkemely weak lines were observed, one at, much lower and the ot,her at much higher frequencies. The stronger lines were assigned to the satellit,es of th(J bending modes, v2 and ark, nherens t.he weaker ones were assigned to t.hose of t,hra stretching modes, v1 and t+, in accordance with the calculated absorpt,ion coefficients, ylllDx, given in Table I. The sntellit,e due to the vq excited stat)e is 1’11~: TABLE
Mode ground state u1 Y:! YZl Y( 2b, :I CMculated
Symmetry
Vibrational energy (cm-‘)
91 dl 11 % E
0 1032 647 907 493
‘4, + E
(986)
with M = 0.234 L), AV = 5MHz,
I
Boltzmann factor 1.0 0.00765 0.0481 0.0137 0.0954 0.00911
and T = 300°K
YNlnr” cm-’ 1.08 8.27 5.20 1.49 1.03 9.85
X X x X x X
1OP lo-“’ 10-y 10-y 10-x lo-“’
318
OTAKE,
MATSUMURA,
AND
MORINO
strongest. For the assignment of the transitions to those in the ~1 and v3 states, the transition due to 2~4 state was of some help, because the line of the latter state should be slightly more intense than the corresponding line in the V~state and less than that in the v3 state. The line in the v3 state was definitely distinguished from that in the v1 state by the existence of the &type doublet in the corresponding J = 2 + 1 and J = 3 +- 2 transitions. The J = 1 +- 0 transition of 14NF3 was split into three hyperfine components, F = 0 +- 1, F = 2 +-- 1 and F = 1 +- 1 (intensity ratio = 1: 5:3) due to the quadrupole moment of the 14N nucleus. All three lines were observed for the ground, the va and the v2 excited states and the values of B, and e&q were determined by least-squares method by taking into consideration the first- and the second-order quadrupole effects. The F = 0 +-- 1 lines were not observed for the v3, the 2v4, and the VI states because of their weak intensities. The B, and e&q values were determined by the observed frequencies of the two transitions. A small correction was made for t’he centrifugal distortion by the use of DJ in TABLE
-
OBSERVED FREQUENCIES FOR THK
-
State
Assignment
GS
F = 1 + 1 21 360.34
v,bs
II
TR.ANSITION
J =
1 + 0 OF 14NFa (MHz)
-
yuB(by
eQq
B,
-7.01
f
21351.37 2 + 1 21 353.46 0 +- 1 21 356.64
10 676.54 zt 0.01
-7.02
zt 0.04
21283.46 2 +- 1 21 285.09 0 +- 1 21 288.30
10 642.38 f
0.02
-6.99
f
0.12
10 602.22 f
0.03
-6.87
i
0.2
10 724.47 zt 0.03
-G.Q2
f
0.2
10 671.90 f: 0.05
-7.01
f
0.2
1 21 362.60
_.
I0.01
2+
infrared)”
/
10 681.02 f
0.06
0 + 1 21 365.60 F=l+l
F=l+l
4.48 zk 0.0 ‘2
I
(16.5)
38.65 & 0.0
F = 1 + 1 21 202.80 2 + Otl
1 21 204.82 -
F = 1+-l
21 447.27 2 +- 1 21 449.33 0+-l -
-42
F = 1 + 1 21 342.09 2 t 1 21 344.18 O+l
a Ref.
(8).
9.12 f
0.0
the ground st,ate obtained are tabulated in Table II.
by Cowan and Gordy (3). The results for “Nky’a The constants (Y,,’ were simply calculat,ed hi B cy,, = RI, -
R,. .
(11
due t,o the No yuadrupole effect appears in the case of ‘“W3 : five transitions excited vibrational states were observed and analyzed in a similar way. Th(b transition frequencies and the H,, values are listed in Table III. The schematic diagram of the J = 1 +- 0 spectra of ‘“NFa is sho\\n in Fig. 1.
So\\, that all t.he cy,“Y have c:kxl:tted by the relat#ion
been
H, = Ho + +/
obtained,
the 13, of “Sl(‘3 and
“SIC, ;Lw
+ J+YzB + CyaH+ cqH.
(“I
Thr r,.-structure derived from t,he H p’s is sholvn in Table IV. The r,,-_;tructuw is also given in Ta.ble IV for comparison. It, is seen t,hat t.he r,( N-k’) distttnce is shorter t#han the ~~~-vnlue by about 0.006 w and the equilibrium angle a’,( L FKIC ) is greater than (Y,,(L IWF) by about 12’. The rOt~&Jlld constnntj C, calculated from the equilibrium st’ruct.ure is also shown in Table IV, where the 6” constant (desigwted by C,) corresponding to t,he r&ructure is given for comparison.
State
_~ c;:,
Y,,llh
..._~__
“4 Y:!
21 258.92 21 249.65 21 178.64
ua VI 2v,
21 107.58 21 335.74 21 240.28
B,
___._~~ 10 629.44 f 10 624.80 i 10 589.30 f 10 553.77 * 10 667.85 * 10 620.12 i
.~ __~~
~~
H (Yii
0.03 0.02 0.02
4.64 f 0.05 40.14 k 0.05
0.02 0.04 0.03
75.67 * 0.05 -38.41 + 0.07 9.32 f 0.06
GS.
FIG.
1.
Vibrational
satellites
in the J = 1 + 0 traIlsi t iota for IjNF:, (Y, = 21258.9’2 nf HZ 1
OTAKE,
320
MATSUMURA, TABLE
AND
MORINO
IV
MOLECULAR STRUCTURE OF NFI %Fg 10 681.02 f
16NF3 0.01
I$j
47.32983”
10 629.44 f 0.03 47.559518
MHz amu IL2
B,
10 761.91f 0.2
Z($
46.97411*
10 710.63zt 0.2 47.198998
MHz amu Rz
Bo
= 1.3648 & 0.002 4, cx,(LFNF) = I.3710 zt 0.002 A, (YQ(LFNF)
r,(N-F) ro(N-F)
5880 xt 20 MHz 5844 zk 20 MHz
C, co * Conversion
f 2' = 102"22' = 102"10 i 2'
factor
50 5531 (MHz)
(amu.iz)
is used.
B. Vibration-rotation interaction constants The vibration-rotation interaction constant, 01, j consists of the harmonic and anharmonic parts, and the former is further divided in the terms depending on the change of the moment of inertia, ab,“” and Afr.$),,l , and the Coriolis terms. In the case of an XY, pyramidal molecule, the vibrational modes are grouped into A1 and E symmetry species, two for each species. It follows that each anharmonic term of 01, involves only two cubic constants, and if both LYE,’ and o(,’ were experimentally determined, these two of t#he cubic constants would be uniquely determined, as was the case of NH3 (7). Anharmonic part of a, ’ , is obtained by subtracting from the observed value the harmonic part of a,’ which is calculated by using the harmonic potential constants shown in Table V.3 The results are given in Table VI. They offer linear relations between t#he cubic constants (cm-‘) ; for instance for 14NF, , OllH: W :
w
W ff3 : W 011
:
2.9992. k,,, -
1.S33S.kllz
= 124.15,
(3)
+ 9.9974’lcrn
= 990.02,
(4)
4.9987. I?,,, -
9.1691.&32
= 1830.6,
(5)
4.9987.kul
9.1691.k244 = 719.8.
-55.015.k,,,
-
The P-type doubling constants, whose determination also provide relations between the cubic potential appear in the above expressions. q3 :
5.2527 k333- 18.278 i&s4 = -557.7
q4 : -54.832
3The potential
constants
i&
-
were determined
1.7509 k344 = 431.3 by the analysis
(6)
is described in Ref. (6)) constants which do not
given in Ref. (6).
(7) (8)
EQUILIBRIUM
STRUCTURE TABLE
OF
NF,
V
HARMONIC POTENTIAL CONSTANTS OF NF2
F11
6.14 f 0.15 0.844 k 0.04 2.41 f 0.05
F,2 F??
F33 F31 F44
md/K md md.8
TABLE
3.39 -0.45 l.(j7
md/.\ md md.,i
=t 0.05 & 0.03 f 0.02
VI
Harmonic -
Observed a,$a’B)and A (a01 ffP c@
_____--_
Anharmonic”
Total
f f
0.04 0.03
-2.04 -4.74
-78.63b 13.71
-80.67 8.97
37.23 29.68
78.81 f 4.48 f 121.38” 51.41”
0.04 0.02
3.07 -19.33 -1.03 0.00
20.86h 2.23 -53.47 -0.32
23.93 -17.10 -54.50 -0.32
54.88 21.58 -tiG.88 51 .i3
-43.45 38.65
WE ffP Qa u4
Coriolis
- cz,B(harm). contribution comes are not, determined
3 cz,.fl(obs) h Main ‘. Signs
from the Coriolis experimentally.
interaction
het.ween
V, and Y$.
DISCUSSION
The two sublevels, t, = 0 (A1 symmetry) and P4 = f2 (E symmetr!. 1 of the 2v4 stat.e should have different rotational constants, t~he difference being 4ye,(, . We carefully searched but 110 line was found except a single line almost at, the position of 2(& - k,‘), predicted from t’he value of wB for the first excited state of the v4 vibrat’ion. This result, must be attributed to one of t’he following t#\vo possibilities: (i) the observed line is to be assigned to the A, symmetry as usual, whereas the I3 line is not detected by some reason or other; (ii ) the value of the y~,l, is too small to make the two lines separable. Since the observed intensity of the 2~~ line is a little stronger than that of the v3 line, it seems likely that the 2~~ line is not split into two components. Ver! recently Popplewell et al. (8) reported the rotational constants in the first excited vibrational stat’es, by the analysis of the infrared bands. Their values of CX,,~’ quoted in Table II agree with the present, resu1t.s except for CQ”.We have observed t’he rotational co&ant in the first overtone state of t.he v4 vibration and made sure that the change of R from B, was close to 2aaB. It gives us a confirmation ot the value of a4B obtained for the microwave spectra in the v4 state. The values of CY~’and (~8~were found large and opposite in sign. It is interesting to not’e that the reversed signs were reported for 133’3 (9). As shown in Table VI, the large negative value of (ylB comes from bhe large Coriolis inter&ion betneen the v1 and Q states.
OTAHE,
322
bfATSUMUI1A,
AND
MORINO
As showy in Table VII, the anB value of 15N1c3is larger than that of 14SF3 , a-hereas al’ and OLAF values of the former species are smaller than t’hose of the latter. This is well understood by the calculation of the harmonic contribution to & which are found to be larger for the former species, whereas t’he oppo&e is the case for cqB and a::. The six linear relations (3)-(S) obtained above are useful for the estimation of t,he cubic potential constants. Anharmonic potential function for pyramidal molecules were considered for NH, and XD3 by Kuchitsu and Rlorino (7). Their conclusion was that the valence force model (VF) and the Van der Waals (VdW) model reproduced the experimentsal values of CX,~and qt constants fairly well, and hence it would be interesting t’o see \vhether t’hese simple potential models are also valid to estimate the anharmonic constants of NF, . The most general expression for the third-order potential function must involve 14 parameters listed in Table VIII, where J”TTT, etc., are t’he coefficients in the expaw TABLE HARMONIC
CoNTftIfsuTfON
-43.45 38.65 78.81 4.48
TO
~l,.~
\:I1 FOR
14NFs
-38.41 40.14 75.ti7 4.G4
TABLE CUfSIc
POTfCNTIAL
VF model
XNI)
15NF, (MHz)
-80.67 8.97 23 .93 -17.10
-77.38 12.07 21.24 -17.35
VIII
CONST.4NTS
OF
‘%E’s
VdW model
Tentative model
-4.824 0 0
-4.824 -0.283 -1.15 -0.577
u - 8.75 md/A2 0.50 md/.b -1.2 -1.6 md/;i md/.T
0
-1.175 -0.780
-0.75 -1.0 md md
f W’+-” i,,..
0 0
0 0
0.2 md/L\z -0.1 0.1 rnd..q rnd,i
;;;“:* I1cx’cT’ f
0 0
0 0
-0.2 0.5 md m:l/P\ 0.1 md
;::::..
0
0
-0.6 0.0 md/K md
it For the definition,
see Ref.
(7).
EQUILIBRIUhf
STRUCTURE
:-I2:<
OF NF,
Aon of the potential function in terms of the internal coordinat.es Ar and Aa. The VF model assumes a single termf,,, , neglecting all the others. The value of from the corresponding diatomic radical NF: t’hat is, /‘rT7.\\-a~ j?TI is transferred estimated to he -4.524 md/,&’ from the value of u3 = 2.24 ;I-’ of t’he SF radical are listed in t,he third column (at’ ( IO). The calculated al,n and qt constants Table IX. On the ot,her hand, t,he VdW model assumes a nonbonded repulsion betwen the fluorine atoms, in addition to the bonding terms frrr of the VF model. The t,hird-order k-1’ repulsion constant, F3 , was estimated to be -3.654 md .I’. using the Buckingham type potential of argon and the five t,hird-order COII&ants of the triatomic type, i.e., f+ , frr4 , f+, , fTaclmd jaamwere cnlculatccl. :IS shown in the t,hird column of Table VIII. The resulting ~y,~ and qt con~t:wts MC listed in the fourt,h column of Table IX. It is seen t,hat rough estimates of (Ye” :III~ qr are given fairly well by t’hese tn-o simple models, especially for thcw primarily concerned nit,h the stretching mode, such as cqB and wiR. .\ preliminary fit, of all t,he constants is given in t,he last column of Table 1’1 Il. in which remaining eight parameters are all introduced Cth :t reasoning simil:w to t.hat used by Kuchitsu and JIorino (7 ). The calculat,ed values come C~OSPttr the observed onw though t’he sign of a ,” cannot, be reproduced.
Calc
ObS VF model
VtlLV model
__~. ._~
Tentative
model
OTAKE,
3’4 .a
MATSUMURA,
AND
RIORINO
In the above computation, the third model has eight adjustable parameters ;ihown in the lower half of Table VIII, but it would be worthwhile noticing that the observed aB are reproduced by a set of small values of t’hese paramet#ers, as was found for NH, and ND, (7). The (Y’ are calculated with the cubic constants of the last model and are listed in Table X. These values, t.ogether with the value of G, in Table IV, gives Cu to be 5810 MHz, while the value calculated with the ‘q)structure is 5844 MHz. ACKNOWLEDGMENT The authors are greatly indebt.ed to Dr. N. Watanabe for valuable suggestions concerning the preparation of the 15NF, sample. They would like also to express their gratitude to Toyo Rayon Foundation for the Promotion of Science and Technology for the financial support of this research. RECEIVED:
April 22,1968 REFERENCES
1. 2. 8. 4. 5.
J. SHERIDANANDW. GORDY, Phys. Rev. 79,513 (1950). C.M. JOHNSON,R. TRAMBARULO,AND W. GORDY, Phys. Rev. 84,1178 (1951). 11. COWAN AND W. GORDY, Bull. Am. Phy,u. Sot. 6, Ser. II, 241 (1960). N. WATANABE, Denki Kagaku, 32, G74 (1964). J. I). FORRESTEI~,M. E. SENKO, A. ZALKIN, AND D. H. TEMPLETON,Acla Crysf. 16, 58
(1963). 6. &I. OTAKE, E. HIKOTA, AND Y. MERINO, J. IMoE.Spectry. 28, 325 (1968). 7. K. K~CHITSU AND Y. MOKINO, Spectrochim. Acta, to be published. 8. R. J. L. POPPLEWELL,F. N. MASRI, AND H. W. THOMPSON,Spectrochim.
Acta, 23A, 2797
(1967). 9. P. KBLIUK AND C. H. TOWNES, Satl. Bur. Std. Circ. 618, (1952). cf. C. H. TO%-NESAND A. L. SCHAWLOLV, “Microwave Spectroscopy,” p. 638. McGraw-Hill, New York, 1955. 10. A. E. DOUGLASANDW. E. JONES, Can. J. Phvs. 44,225l (1966).
OF MOLECULAR
Microwave
SPECTROSCOPY
Spectra
28, 316-324 (1968)
of Nitrogen Trifluoride Vibrational States Equilibrium
~\/IASAYUKI OTAKE,~ Department
of Chemistry,
Faculty
in the Excited
Structure
CHI
R~ATSUMURA,'
of Science,
The University
AND
YONEZO
MORINO
of Tokyo, Hongo, Tokyo, Japan
The microwave spectra of two isotopic species of the NF3 molecule were investigated in the excited vibrational states. The vibration-rotation interaction constants 0l-B for the ~1 , ~2, v3and vq states were found to be -43.45, +38.65, +78.81, and +4.48 MHz for 14NF, and -38.41, +40.14, +75.67, and +4.64 MHz for lSNF3 , respectively. The equilibrium rotational constant, B. , was then derived to be 10761.91 f 0.2 MHz for “NFa and 10710.63 f 0.2 MHz for 16NF3 , from which the equilibrium structure was determined to be r,(N-F) = 1.365 f 0.002 A and LY~( LFNF) = 102”22 ZIZ2’. A set of linear relations was derived between cubic potential constants from the observed aDB and P-type doubling constants. INTRODUCTION
Microwave spectrum of nitrogen trifluoride in its ground vibrational state has been observed by Gordy and his co-workers (1-S). They measured J = 2 +- 1 transitions for two isot’opic species, 14NF3 and 15NF,, and determined the r. structure of the molecule by using the ground-state rotational constants, Bo (1) . The most straightforward way of eliminating the effect of zero-point vibrations from the T-O structure is to correct the ground-state rot,at#ional constants for the vibration-rotation interaction constants o(~. It should be mentioned that the observation of the vibrational satellites is import’ant not only for the determination of the equilibrium struct,ure, but also for the study of the intramolecular potential function. The e-type doubling constant’ is also available for the latter purpose. EXPERIMENTAL
METHODS
The sample of the normal species of nitrogen trifluoride used in the present experiment was contaminated with about 10 %# of CF4 but it was pure enough for 1Present address: The Central Research Laboratories, Ltd., Mizonokuchi, Kanagawa, Japan. 2 Pressent address: Government Chemical Industrial Tokyo, Japan. 316
Mitsubishi Research
Chemical Institute,
Industries Hatagaya,
EQUII,IBRIUM
STRUCTURE
OF NP,
:
t,he microwave studies. The 15N species of nitrogen trifluoride was prepared 1~~ modifying the electrolytic method reported by Watanabe (,$ ). An iron cell, 20 mm in diameter and 30 cm in length, with a gas inlet’ and outlet on the side wall was used as a cathode, and a graphite anode. 1 cm in diameter, n’a,s fixed on the bottom with a Teflon insulator and connected to a copper terminal supported by a F’crflon rubber stopper. Dehydrated ammonium bifluoride containing ‘“S isotope in 97 ‘: atomic concentration was used as electrolyte. It was diluted t80 5 7: by adding a large amount of KH$, (mp 76°C ), which 1va.s prepared b> condensing calculat’ed amount of anhydrous hydrogen fluoride on potassium hydrogen fluoride (6). The electrolysis was carried out at 110 f S’C’, keeping the cell in an oil-bath, \cith the anodic potential of k-5 V and tbe current densit,) of 0.01 A/cm’. The product was let to a liquid-oxygen trap by means of A carrier g:ls of NT . It \vas purified by a simple bulb-to-bulb dist,illat’ion at liquid-nitrogen tcmpcrature. The purity of the sample was checked by t,he infrared spcckun. The rotational spectrum n-as recorded wit,h a conventional microwave spectromet,er a-ith 110 kHz sinusoidal-wave Stark modulation. An S-band waveguidt ccl1 u-as used. The J = 1 +- 0 transitions were observed \vit,h a crystal harmonic gcnerntor drivel] by a Varian X-13 klystron. The measurement was carried out at room temperature. The sweep rate was reduced to 03-0.2 ,\IHz/min in order to observe u-e:& lines in the excited vibrational states. The assignment8 was confirmed, if necessary, by observing the spectra for t,he tsansit’ions J = 2 +- 1 :ud ,I = 3 +- 2: the details of the spectra for t#hese transitiow are in Ref. c6”). RESULTS T\vo
fairly strong vibrational sat,ellites \vere observed, bot#h for “^\jI’, :ultl ‘5SIi3 1 tit the frequencies slightly lower than the ground-state line, M-hile tu-o ot,her exkemely weak lines were observed, one at, much lower and the ot,her at much higher frequencies. The stronger lines were assigned to the satellit,es of th(J bending modes, v2 and ark, nherens t.he weaker ones were assigned to t.hose of t,hra stretching modes, v1 and t+, in accordance with the calculated absorpt,ion coefficients, ylllDx, given in Table I. The sntellit,e due to the vq excited stat)e is 1’11~: TABLE
Mode ground state u1 Y:! YZl Y( 2b, :I CMculated
Symmetry
Vibrational energy (cm-‘)
91 dl 11 % E
0 1032 647 907 493
‘4, + E
(986)
with M = 0.234 L), AV = 5MHz,
I
Boltzmann factor 1.0 0.00765 0.0481 0.0137 0.0954 0.00911
and T = 300°K
YNlnr” cm-’ 1.08 8.27 5.20 1.49 1.03 9.85
X X x X x X
1OP lo-“’ 10-y 10-y 10-x lo-“’
318
OTAKE,
MATSUMURA,
AND
MORINO
strongest. For the assignment of the transitions to those in the ~1 and v3 states, the transition due to 2~4 state was of some help, because the line of the latter state should be slightly more intense than the corresponding line in the V~state and less than that in the v3 state. The line in the v3 state was definitely distinguished from that in the v1 state by the existence of the &type doublet in the corresponding J = 2 + 1 and J = 3 +- 2 transitions. The J = 1 +- 0 transition of 14NF3 was split into three hyperfine components, F = 0 +- 1, F = 2 +-- 1 and F = 1 +- 1 (intensity ratio = 1: 5:3) due to the quadrupole moment of the 14N nucleus. All three lines were observed for the ground, the va and the v2 excited states and the values of B, and e&q were determined by least-squares method by taking into consideration the first- and the second-order quadrupole effects. The F = 0 +-- 1 lines were not observed for the v3, the 2v4, and the VI states because of their weak intensities. The B, and e&q values were determined by the observed frequencies of the two transitions. A small correction was made for t’he centrifugal distortion by the use of DJ in TABLE
-
OBSERVED FREQUENCIES FOR THK
-
State
Assignment
GS
F = 1 + 1 21 360.34
v,bs
II
TR.ANSITION
J =
1 + 0 OF 14NFa (MHz)
-
yuB(by
eQq
B,
-7.01
f
21351.37 2 + 1 21 353.46 0 +- 1 21 356.64
10 676.54 zt 0.01
-7.02
zt 0.04
21283.46 2 +- 1 21 285.09 0 +- 1 21 288.30
10 642.38 f
0.02
-6.99
f
0.12
10 602.22 f
0.03
-6.87
i
0.2
10 724.47 zt 0.03
-G.Q2
f
0.2
10 671.90 f: 0.05
-7.01
f
0.2
1 21 362.60
_.
I0.01
2+
infrared)”
/
10 681.02 f
0.06
0 + 1 21 365.60 F=l+l
F=l+l
4.48 zk 0.0 ‘2
I
(16.5)
38.65 & 0.0
F = 1 + 1 21 202.80 2 + Otl
1 21 204.82 -
F = 1+-l
21 447.27 2 +- 1 21 449.33 0+-l -
-42
F = 1 + 1 21 342.09 2 t 1 21 344.18 O+l
a Ref.
(8).
9.12 f
0.0
the ground st,ate obtained are tabulated in Table II.
by Cowan and Gordy (3). The results for “Nky’a The constants (Y,,’ were simply calculat,ed hi B cy,, = RI, -
R,. .
(11
due t,o the No yuadrupole effect appears in the case of ‘“W3 : five transitions excited vibrational states were observed and analyzed in a similar way. Th(b transition frequencies and the H,, values are listed in Table III. The schematic diagram of the J = 1 +- 0 spectra of ‘“NFa is sho\\n in Fig. 1.
So\\, that all t.he cy,“Y have c:kxl:tted by the relat#ion
been
H, = Ho + +/
obtained,
the 13, of “Sl(‘3 and
“SIC, ;Lw
+ J+YzB + CyaH+ cqH.
(“I
Thr r,.-structure derived from t,he H p’s is sholvn in Table IV. The r,,-_;tructuw is also given in Ta.ble IV for comparison. It, is seen t,hat t.he r,( N-k’) distttnce is shorter t#han the ~~~-vnlue by about 0.006 w and the equilibrium angle a’,( L FKIC ) is greater than (Y,,(L IWF) by about 12’. The rOt~&Jlld constnntj C, calculated from the equilibrium st’ruct.ure is also shown in Table IV, where the 6” constant (desigwted by C,) corresponding to t,he r&ructure is given for comparison.
State
_~ c;:,
Y,,llh
..._~__
“4 Y:!
21 258.92 21 249.65 21 178.64
ua VI 2v,
21 107.58 21 335.74 21 240.28
B,
___._~~ 10 629.44 f 10 624.80 i 10 589.30 f 10 553.77 * 10 667.85 * 10 620.12 i
.~ __~~
~~
H (Yii
0.03 0.02 0.02
4.64 f 0.05 40.14 k 0.05
0.02 0.04 0.03
75.67 * 0.05 -38.41 + 0.07 9.32 f 0.06
GS.
FIG.
1.
Vibrational
satellites
in the J = 1 + 0 traIlsi t iota for IjNF:, (Y, = 21258.9’2 nf HZ 1
OTAKE,
320
MATSUMURA, TABLE
AND
MORINO
IV
MOLECULAR STRUCTURE OF NFI %Fg 10 681.02 f
16NF3 0.01
I$j
47.32983”
10 629.44 f 0.03 47.559518
MHz amu IL2
B,
10 761.91f 0.2
Z($
46.97411*
10 710.63zt 0.2 47.198998
MHz amu Rz
Bo
= 1.3648 & 0.002 4, cx,(LFNF) = I.3710 zt 0.002 A, (YQ(LFNF)
r,(N-F) ro(N-F)
5880 xt 20 MHz 5844 zk 20 MHz
C, co * Conversion
f 2' = 102"22' = 102"10 i 2'
factor
50 5531 (MHz)
(amu.iz)
is used.
B. Vibration-rotation interaction constants The vibration-rotation interaction constant, 01, j consists of the harmonic and anharmonic parts, and the former is further divided in the terms depending on the change of the moment of inertia, ab,“” and Afr.$),,l , and the Coriolis terms. In the case of an XY, pyramidal molecule, the vibrational modes are grouped into A1 and E symmetry species, two for each species. It follows that each anharmonic term of 01, involves only two cubic constants, and if both LYE,’ and o(,’ were experimentally determined, these two of t#he cubic constants would be uniquely determined, as was the case of NH3 (7). Anharmonic part of a, ’ , is obtained by subtracting from the observed value the harmonic part of a,’ which is calculated by using the harmonic potential constants shown in Table V.3 The results are given in Table VI. They offer linear relations between t#he cubic constants (cm-‘) ; for instance for 14NF, , OllH: W :
w
W ff3 : W 011
:
2.9992. k,,, -
1.S33S.kllz
= 124.15,
(3)
+ 9.9974’lcrn
= 990.02,
(4)
4.9987. I?,,, -
9.1691.&32
= 1830.6,
(5)
4.9987.kul
9.1691.k244 = 719.8.
-55.015.k,,,
-
The P-type doubling constants, whose determination also provide relations between the cubic potential appear in the above expressions. q3 :
5.2527 k333- 18.278 i&s4 = -557.7
q4 : -54.832
3The potential
constants
i&
-
were determined
1.7509 k344 = 431.3 by the analysis
(6)
is described in Ref. (6)) constants which do not
given in Ref. (6).
(7) (8)
EQUILIBRIUM
STRUCTURE TABLE
OF
NF,
V
HARMONIC POTENTIAL CONSTANTS OF NF2
F11
6.14 f 0.15 0.844 k 0.04 2.41 f 0.05
F,2 F??
F33 F31 F44
md/K md md.8
TABLE
3.39 -0.45 l.(j7
md/.\ md md.,i
=t 0.05 & 0.03 f 0.02
VI
Harmonic -
Observed a,$a’B)and A (a01 ffP c@
_____--_
Anharmonic”
Total
f f
0.04 0.03
-2.04 -4.74
-78.63b 13.71
-80.67 8.97
37.23 29.68
78.81 f 4.48 f 121.38” 51.41”
0.04 0.02
3.07 -19.33 -1.03 0.00
20.86h 2.23 -53.47 -0.32
23.93 -17.10 -54.50 -0.32
54.88 21.58 -tiG.88 51 .i3
-43.45 38.65
WE ffP Qa u4
Coriolis
- cz,B(harm). contribution comes are not, determined
3 cz,.fl(obs) h Main ‘. Signs
from the Coriolis experimentally.
interaction
het.ween
V, and Y$.
DISCUSSION
The two sublevels, t, = 0 (A1 symmetry) and P4 = f2 (E symmetr!. 1 of the 2v4 stat.e should have different rotational constants, t~he difference being 4ye,(, . We carefully searched but 110 line was found except a single line almost at, the position of 2(& - k,‘), predicted from t’he value of wB for the first excited state of the v4 vibrat’ion. This result, must be attributed to one of t’he following t#\vo possibilities: (i) the observed line is to be assigned to the A, symmetry as usual, whereas the I3 line is not detected by some reason or other; (ii ) the value of the y~,l, is too small to make the two lines separable. Since the observed intensity of the 2~~ line is a little stronger than that of the v3 line, it seems likely that the 2~~ line is not split into two components. Ver! recently Popplewell et al. (8) reported the rotational constants in the first excited vibrational stat’es, by the analysis of the infrared bands. Their values of CX,,~’ quoted in Table II agree with the present, resu1t.s except for CQ”.We have observed t’he rotational co&ant in the first overtone state of t.he v4 vibration and made sure that the change of R from B, was close to 2aaB. It gives us a confirmation ot the value of a4B obtained for the microwave spectra in the v4 state. The values of CY~’and (~8~were found large and opposite in sign. It is interesting to not’e that the reversed signs were reported for 133’3 (9). As shown in Table VI, the large negative value of (ylB comes from bhe large Coriolis inter&ion betneen the v1 and Q states.
OTAHE,
322
bfATSUMUI1A,
AND
MORINO
As showy in Table VII, the anB value of 15N1c3is larger than that of 14SF3 , a-hereas al’ and OLAF values of the former species are smaller than t’hose of the latter. This is well understood by the calculation of the harmonic contribution to & which are found to be larger for the former species, whereas t’he oppo&e is the case for cqB and a::. The six linear relations (3)-(S) obtained above are useful for the estimation of t,he cubic potential constants. Anharmonic potential function for pyramidal molecules were considered for NH, and XD3 by Kuchitsu and Rlorino (7). Their conclusion was that the valence force model (VF) and the Van der Waals (VdW) model reproduced the experimentsal values of CX,~and qt constants fairly well, and hence it would be interesting t’o see \vhether t’hese simple potential models are also valid to estimate the anharmonic constants of NF, . The most general expression for the third-order potential function must involve 14 parameters listed in Table VIII, where J”TTT, etc., are t’he coefficients in the expaw TABLE HARMONIC
CoNTftIfsuTfON
-43.45 38.65 78.81 4.48
TO
~l,.~
\:I1 FOR
14NFs
-38.41 40.14 75.ti7 4.G4
TABLE CUfSIc
POTfCNTIAL
VF model
XNI)
15NF, (MHz)
-80.67 8.97 23 .93 -17.10
-77.38 12.07 21.24 -17.35
VIII
CONST.4NTS
OF
‘%E’s
VdW model
Tentative model
-4.824 0 0
-4.824 -0.283 -1.15 -0.577
u - 8.75 md/A2 0.50 md/.b -1.2 -1.6 md/;i md/.T
0
-1.175 -0.780
-0.75 -1.0 md md
f W’+-” i,,..
0 0
0 0
0.2 md/L\z -0.1 0.1 rnd..q rnd,i
;;;“:* I1cx’cT’ f
0 0
0 0
-0.2 0.5 md m:l/P\ 0.1 md
;::::..
0
0
-0.6 0.0 md/K md
it For the definition,
see Ref.
(7).
EQUILIBRIUhf
STRUCTURE
:-I2:<
OF NF,
Aon of the potential function in terms of the internal coordinat.es Ar and Aa. The VF model assumes a single termf,,, , neglecting all the others. The value of from the corresponding diatomic radical NF: t’hat is, /‘rT7.\\-a~ j?TI is transferred estimated to he -4.524 md/,&’ from the value of u3 = 2.24 ;I-’ of t’he SF radical are listed in t,he third column (at’ ( IO). The calculated al,n and qt constants Table IX. On the ot,her hand, t,he VdW model assumes a nonbonded repulsion betwen the fluorine atoms, in addition to the bonding terms frrr of the VF model. The t,hird-order k-1’ repulsion constant, F3 , was estimated to be -3.654 md .I’. using the Buckingham type potential of argon and the five t,hird-order COII&ants of the triatomic type, i.e., f+ , frr4 , f+, , fTaclmd jaamwere cnlculatccl. :IS shown in the t,hird column of Table VIII. The resulting ~y,~ and qt con~t:wts MC listed in the fourt,h column of Table IX. It is seen t,hat rough estimates of (Ye” :III~ qr are given fairly well by t’hese tn-o simple models, especially for thcw primarily concerned nit,h the stretching mode, such as cqB and wiR. .\ preliminary fit, of all t,he constants is given in t,he last column of Table 1’1 Il. in which remaining eight parameters are all introduced Cth :t reasoning simil:w to t.hat used by Kuchitsu and JIorino (7 ). The calculat,ed values come C~OSPttr the observed onw though t’he sign of a ,” cannot, be reproduced.
Calc
ObS VF model
VtlLV model
__~. ._~
Tentative
model
OTAKE,
3’4 .a
MATSUMURA,
AND
RIORINO
In the above computation, the third model has eight adjustable parameters ;ihown in the lower half of Table VIII, but it would be worthwhile noticing that the observed aB are reproduced by a set of small values of t’hese paramet#ers, as was found for NH, and ND, (7). The (Y’ are calculated with the cubic constants of the last model and are listed in Table X. These values, t.ogether with the value of G, in Table IV, gives Cu to be 5810 MHz, while the value calculated with the ‘q)structure is 5844 MHz. ACKNOWLEDGMENT The authors are greatly indebt.ed to Dr. N. Watanabe for valuable suggestions concerning the preparation of the 15NF, sample. They would like also to express their gratitude to Toyo Rayon Foundation for the Promotion of Science and Technology for the financial support of this research. RECEIVED:
April 22,1968 REFERENCES
1. 2. 8. 4. 5.
J. SHERIDANANDW. GORDY, Phys. Rev. 79,513 (1950). C.M. JOHNSON,R. TRAMBARULO,AND W. GORDY, Phys. Rev. 84,1178 (1951). 11. COWAN AND W. GORDY, Bull. Am. Phy,u. Sot. 6, Ser. II, 241 (1960). N. WATANABE, Denki Kagaku, 32, G74 (1964). J. I). FORRESTEI~,M. E. SENKO, A. ZALKIN, AND D. H. TEMPLETON,Acla Crysf. 16, 58
(1963). 6. &I. OTAKE, E. HIKOTA, AND Y. MERINO, J. IMoE.Spectry. 28, 325 (1968). 7. K. K~CHITSU AND Y. MOKINO, Spectrochim. Acta, to be published. 8. R. J. L. POPPLEWELL,F. N. MASRI, AND H. W. THOMPSON,Spectrochim.
Acta, 23A, 2797
(1967). 9. P. KBLIUK AND C. H. TOWNES, Satl. Bur. Std. Circ. 618, (1952). cf. C. H. TO%-NESAND A. L. SCHAWLOLV, “Microwave Spectroscopy,” p. 638. McGraw-Hill, New York, 1955. 10. A. E. DOUGLASANDW. E. JONES, Can. J. Phvs. 44,225l (1966).