Asundi, R K

Padhye, M R

English

IACS Institutional Repository

31THE NEAR ULTRA-VIOLET SPECTRA OF BENZENE PART III. FERMI RESONANCE IN THE EMISSION SPECTRUM OF BENZENEB v R. K. A SU N D l ANn M. R. P A D H Y E 'ABSTRACT. A large iinniber of b'emii doublets have been di.scovered in the emission .spectrimi of benzene. These are due to accidental degeneracy in the vibrations 1596 cj and 1598 (combination of 606 cj+gga «,„) further superposed by .several quanta ofggzoi,, vibration and involving also (j;>3 a ,,, excited frequency in addition to series of 160 difference frequency. The magnitude of doublet interval with increasing excitation of the vibrations is w'cll represented by an expression deriv'nble from considerations of the first order perturba­tion in the potential function of the molecule.i ;N T ]{ O D U C T 1 O N A N D R E vS U L T SFenui resonance in the case of benzene seems to have been first discovered by Wilson (1934). The Raman spcctnim of benzene shows two strong lines at a frequency difference of 1584 and 1606 instead of one cal­culated at 1596.* These have been explained as Fermi doublets due to ie.souance between (1506) clj and (606 c'l/ + Qg2 ci,, = 1.598) <-’J.In the Raman S])ectrum, lines involvmg higher vibrational quanta are usually too weak to observe and these vibrations are inactive in the infrared spectrum. Hence Fermi doublets involving overtones or combination tones have not been recorded. In the absorption spectrum similarly only the fundamental Fermi doublet is observed but since absorption can go to different vibrational levels in the excited electronic state, two more doublets have been recorded both of which, however, involve the same fundamental Fermi doublet. In the high pressure fluorescence spectrum (Ingold and Wilson, 1936), there is evidence of not only the fundamental Fermi doublet but also two more doublets involving one and two quanta of 992 superposed on the Fermi doublet.In the case of the emission spectrum, in addition to the fundamental doublet, four more Fermi doublets are found involving one to four quanta of 99a successively added to both components of the doublet. Each of these Is further developed into series involving the 160 difference frequency. Some of them also develop into progressions involving the 923 frequency in the excited state overlapped by the 160 difference frequency. The wavenumbers on these doublets ovserved in the course of an investigation on the emission* All frequencies are given in wavenvunhers in cm” ' units.282 R . K , Asundi and M. R , Padhyespectrum of benzene? are collected together in Table I, in which also the bands observed in absorption and fluorescence are suitably indicated.The Table shows two parallel series of bands termed * and ^ which involve these doublets. The fundamental doublet frequencies obtained from the value for the mean of the five bands that occur in the 160 series superposed over the fundamental doublet is 1585 and 1603. .Similarly the positions from the ground slate of the doublets involving i  to 4 quanta of 992 are obtained as mean values from the corresponding 160 progressions. These data on observed mean frequencies are given in Table 111. They enable us to study the Fermi interaction with increasing quanta of vibrations as in COa or H2O. It must, however, be remembered that the differences in the present case are obtained from the band head data which are themselves subject to an error of about ±3 cm~’ , fID I S C U S S I O N OF R E S U L T SThe case of accidental degeneracy here met with falls to a certain extent in the same class as of CO2, w'hich has been fully worked out by Dennison (1932; 1940) and Adel and Dennison (1933). The interaction is treated as a perturbation brought about by anharmonicity. The first order perturbed energies are obtained by solving the secular determinant | — AIFi 8, J = o.The roots of this determinant A IF, furnish the required perturbed energies. The quantity/I j is the matrix element of the perturbing function Ti +Ar/ i .  The first order perturbation should give the magnitude of the interaction correctly. This is nearly but not wholly borne out by experiment. The agreement between theory and experiment becomes, however, more complete if the second order perturbation is also employed. A complete theory of Fermi resonance for CO  ^ is hence given by Dennison and Adel and Dennison, which is further extended by Darling and Dennison (1940) with suitable alterations to H2O. The accuracy of experimental data available in both these molecules is superior to that in our experiments on benzene. Here we do not observe the band origins as in CO2 or H2O particularly in their infrared data but only band heads. It is, therefore, thought that the first order pertur­bation alone need be considered. The case of methyl halides which is analogous to CQn is in this respect particularly interesting and has been worked out by Adel and Barker (1934). Using only the first order perturba­tion, they obtain expressions for Wa and IFiS which are separations from theunperturbed levels including the constant shift — due to the ground level.2Thus,IFb= A - i- -4 .“ H- Ib^§ For details of eKperimental procedure, etc., refer to the paperon the Emission Spectrum of Benzene in the near ultraviolet Port I of this series.Ultra-violet Spectra of Benzene 283and A * ^ wb®where A  is the displacemeut of the calculated £ requeucy from the meau of the(A 2 _ a 2 \.... where A  is the doublet sepa­ration aud n takes values I, 2.-.etc., b is a measure of the auharraonicity appearing in the cubic part of the potential function.In benzene, the fundamental perturbation occurs between the singly excited e'^ , vibration and the single excited coinj>osite vibration 1598 c'l, (formed by 992 niff+ 606 c'ff). In otlrer words* the degeneracy is between two doubly degenerate vibrations. For single excitation, the degeneracy is not removed both and vibrations have the same / value namely i. In this respect the funda­mental degeneracy in benzene differs from that in CO. or the methyl halides whex'e the fundamental degeneracy is between a singly excited non-degenerate vibration and a doubly excited degenerate vibration. The I value for the non-degenerate vibration being always o, only the component having /=o of the doubly excited non-degenerate vibratit)n enters into interaction whereas the component having / = 3 is unaffected.The observed excited Fermi doublets in benzene arise on account of superposition of a non-degenerate totally symmetrical vibration which has no influence on the I value. The vibration quantum numbers of the frequencies giving rise to the doublets are shown in Table II. Among such doublets found in COs, there are similarly those which arise by suiJerposition of a non-degenerate vibration. These considerations lead us to adopt expi'essions for Wa^ndWa  similar to those used by Adel and Barker. The value for the component vibrations thus calculated arc given iu Table III along with the observed values. The agreement is considered satisfactory.Note added on January 1 2 ,1949.—in  a recent paper which reached us last month, Garforth and Ingold (1948) have made a detailed analysis of the fluorescence bands of benzene. From a re-exainination of the spectrograms and micro-photograms of the bands previously reported by Ingold and Wilson (1936), they have recast the data on band maxima and recorded similar resonance doublets. Although there is some discrepancy in the wavelength data it is satisfactory to find that the doublet separations are exactly identical with those recorded here.284 R. K. Asundi and M. R. PadhyeT ahi.k ISeries*rvao,Int .SeriesI'vueInl.8 36486^  ’ ! 1 8V  3634 3 ■'■’1 ! AS 0^' 36325''"-11 536182 I I /Sq* 36166^  ' i ! 3Oo* 36023II I 36006 M 1*5“0^ 35871 L V  3584811 0“-i" 3 5 5 i7 t+ 5 /J-.® 3 5 4 9 2 1 1 1«-i^  35356II 3 1’ 35330H 4,5“-I* 35193II 1  ^ 1® 35J69II 4 l.“-1^  3503HII - -^1® 35007'“-1'' 34877II ■ 3 \«-2® 34530! 1 3 8-2® 3 4 5" HI 4.5 \“-2’ 3437M1 3 fl-2' 34338 It 3“.-2® 34208 li 1 3 -2® 34176! 1 30.2* 34046 34111R! 1 0»-3® 3 3 5 4 9  ^ S 8-3® 33512! + 3«-s’ . 3384 2.3 8-3^  3 3 3 4 7 * 0«-3* 33189 c-^4“ 32524-^4’ 32351 132210 0“i-t® 36442 2 <>i-i® 3 6 -I2 1 '’ 3-5«i-i* 36276 I fli- i’ 3625736097 2“1-2“ 3 5 4 5 5 3-5 1^-2" 35425 • 4i?)“iV  3 5 3 9 3 1 1^-2’ 35264 2(?;“>® 37427 0 ■ — '“2® 38353+ 2 (f)t These are also present in the absorption spectrum Radle and Becb, (19^ 0).I I these are.also present in the fluorescence spectrum Ingold and Wilson (i936\ ^ The notation followed is the one given in Tart T of the scries, namely, negative subscripts for superposition of 992 quanta in the ground state and the superscript denoting the quanta of the dilference frequency lOo superposed** The intensities are those visually estimated relative to the intensity of the strongest band h(P as 10.The complete table given in Tart 1 of the series gives some more bands as belonging to a and  ^ series but since the assignment is not unique, they are not included iniiiivs table.Vitra-‘Viotet Spectra of BenzeneTABtli IIDoublet Vt(1596)No. 6o6 993f-J- a 1 j,— ’ --- -  ^ ■ --- -1 (I T 0( 0 O 111'.1 0111 i( * 3 nHI >( o T11 0IV 3 1V 1„ 5 04 TT abi.k IIIA  = i^-(w. + i'„)==i5Q3.5 - i 5y S -  -,].5  curT A " /r = J34-4( 4 2285^S6 IR. K . Asuhdi atid M , H .  Padhyer r i ^k r e n c e sAdd and i^orker, 193-I, ./• P h y s . ,  2, 627.A d d  and P e iiu iso n , I933» ^D a rlin g  an d  D e n n iso n . 19^10, P h y s ,  R e v , ,  87 , i28, D enn ison, 1932, P h y s ,  R e v , ,  41 , 30-i.,, 19^0, R e v s .  Mod^ P h y s . ,  12, 175*O a rfo rth  an d  In g o ld , 1948, /, C. S . ,  p. 427*In g o ld  and W ils o n , 1936, J. C. S . ,  i^p. 94^ an d  1210, R a d le  and H eck, ic4n , /. Ch.  P h y s . ,  8, 507,W ilso n , 1934, P h y s .  Re v. ,  46 , 146.

The Near Ultra-Violet Spectra of Benzene Part III. Fermi Resonance in the Emission Spectrum of Benzene

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The Near Ultra-Violet Spectra of Benzene Part III. Fermi Resonance in the Emission Spectrum of Benzene

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