- Email: [email protected]
Raman intensity as a function of exciting wavelength for a vibration known to mix electronic states
Voiume 17, number 3
1 December
CHEMICAL PKYSiCS LETTERS
1972
RAMAN INTENSITY AS A FUNCTION OF EXCITMG WAVELENGTH FOR A VIBRATION KNIT TO MIX ELE~R~NI~ STATESj?# A.H. KALANTARf, Department
ES. FRANZOSA and K.K. INNES
of C~iemistry, State University of hew York, Birrgltomton, New York 13901, USA Received
15 August 1972
The vs(b, ) vibration of liquid pyrazine is known to mix an eB ,u escited state with the eB3U excited state of the 3200 A (n.4z,n) electronic transition, while it is known that V4(bag) does not mix them. ‘The pre-resonance Raman intensity behaviors of v4 and vs have been compared. The intensity of us (relative to ~4) increases with the frequency of the exciting line, as required by theory. The observed increases are in close accord with two published quantum theories, for specified assumptions.
1. introduction Eleven years agot Afbrecht
developed
a quantum
74.9 /==
C,H,N; + e
mechanical theory of vibration& Raman intensities [I]. The theory predicts that the normal mode most responsible electronic
for “forbidden” transition should
intensity in an allowed show the greatest activity
Raman scattering, especially in pre-resonance Raman studies at wavelengths approaching those of the electronic transition. While many exampies of a preresonance Raman effect are known [2, 33, for lzutze has there been given independent proof of the identity of the mixing vibration and/or the location of the states being mixed, thus leaving the above quaiitative prediction as yet uncon~~ed. Vibronic anatysis of the 3200 A 1B3U- iA, system of pyrazine (fig. 1) revealed an ideal case for testing ‘he prediction, namely us (btg). It was proved that this out-of-plane, hydrogen-bending vibration mixed the intensity of a stronger transition with that of the 3200 hi transi‘B,,-IA tion [4, 51. The electronic levels and transitions of in
37.8
Fig. 1. Observed electronic states of pyrazine. The four transitions of interest are indicated by the arrows and include f-values. The ~4s choices for pyrazine are also sketched_
+ presented in part at the 27th Symposium
on Molecular Structure and Spectroscopy, The Ohio State University, Columbus, Ohio, June, 1972, paper M 11. p This work was supported by the National Science Foundation. $ On sabbnticat leave from University of Alberta, Edmonton, Alberta, Canada T6G 2G2, 1970-71.
interest [6, 7) are displayed in fig. 1. Thecries of Raman intensities have undergone further development during the past ten years [2,3, Cl-IO]. Moreover, it is only in that time that the variety of Raman exciting lines necessary for testing 335
Volu&e 17, number 3
1 December 1972
CHEMWAL PHYSICS LETTERS
the theories has been made avajkbk through the ready accessibility of gas lasers. These sources have made possible &e present report. of me~~rernen~s of the intensity of ps (924 cm-l) of liquid pyrazine, relative to u4 jbz,, 703 cm-l), which is not [4] involved in mixing this same e33U state with other eBlu efectronic states. Raman intensities have been measured for exciting fines from the red to the ultraviolet. The data have been standardized further by the more usual measurements in which the reference line is a solvent Raman.Iine whose intensity as a function of exciting frequency is known.
2. Experime&
22 938 q 22 640X
0.2
Pyrazine (99%, Aldrich Chemical Co.), purified by subl~ation and sealed off in L-shaped Pyrex tubing (7 mm o.d.), was studied as liquid?. The cells for room temperature solution spectra were sealed melting point tubes. Several commerci~ Raman spectrometers (Spex Ramalog and Ram&b, Jarrell-Ash, and Gary 81) were used to obtain the exciting lkes shown at the right of fig. 2. AI1 exciting lines were laser lines except for the two ~~est-frequency oner: which were the 4358 and 4047 A lines of the Toronto arc. In alI cases, the Raman radiation entering the dr;uble monochromator was rendered unpolarized. SIit widths employed varied from 2 to 1 I cm-l, nearly spanning the observed full widths at half maxima of the two Iines of interest for liquid pyrazine, namely 6 cm-l (v4) and 13 cm-l (v,). Repeated tracings of the u4 and vs peaks were recorded in alternate order. The ratios of the measured areas (using a planimetrr), together with the standard deviations, are shown in fig. 2 as a function of slit widths and exciting frequency (Q). A large part of the scatter is attributable to intensity fluctuations in the light sources??. Three other kinds of experimei~ts were performed,
OD 0
_: 19 429 *
2 4 6 -8 SPECTRA1 SLlf WIDTH (cm-‘)
liquid sample coot above the melting point (53*C). Consequently
the sample iemperature
was kept above 60°C to
obviate such problems, which may be related to the solid phase_transition described by Schettino et al. [ 1 L]. 336
I2
Fig. 2. hfeasured values of the ratio of integrated intensities of Raman lines of liquid pyrazine; that of v5 = 924 cm-’ to that of vq = 703 cm-‘, as a function of spectral slit width, and as a function of exciting line, ~0. All data arc corrected for spectrometer gain and photomuIt~pI~er tube responses.
Data for the two lowest vg are corrected for grating reflectivity, Each instrument correction was based on information supplied by the manufacturer. Such corrections should not be in error by ntore than 20% of the applied corrections (which ranged up to lS%). Standard deviations are indicated. u4 corrections are not included.
using the 4880 and 6471 A lines. (1) To test for interference from the nearby, strongly polarized Raman line (vl (a,) at 1016 cm-l) of liquid pyrazine, I_fI,, was detested for positions of an analyzer which maximized and minimized the possibility of interference. No significant variations in the ratio were found. (2) Dependence of the Raman intensity of v4 on ++In the case of the weak 24705 cm-’
; The ~5 peak undergoes a large frequency shift (from 924 cm-1 to IX_940. a~‘~) and becomes very small as the
K)
exciting line, the num-
ber of independent determinations was less than half those for any other exciting frequency. In addition, 24705 cm-’ is only 2000,cm-i befow the O-O band of the 3B,,-iA
electronic transition of pyrazine so that some further laca of reprqducibtiity, of absorption and re-emission in our samples may exist.
Volume 17, number 3
Wavelength
CHEhliCAL
dependence
Raman peaks (cm-r )
of fully corrected
Area ratio for 4880 A escitation (and number
Table 1 relative intensities .---
0.143(7) 1 0.091(17) 16.6f4) 0. f9(4) 1.36(6)
a) The groups of lines inc!udcd in the areas denoted the different vo.
Experimental
enhancement
Approx. std. dev. of change %
from 6471 A excitation
6471 A of data)
:1.X7(35) 14.8(3) 0.21{4) 1.47(6)
1972
of Raman lines of pyrazine at 65-70°C
Change
0.075(7)
5981 703 7031 703 9241 103 1015j 703 123011015 1575/1230a)
1 December
PHYSICS LETTERS
down l/2 -
IO
up 2.8 times -11% +iOk +8
20 13 9 I6
by 1575 and i230 also showed no changes, relative to each other, for
Table 2 of Raman intensity for excitation
Line(s) studied
Reference
cm”/molecule
cm-‘/molecule -
lines
I 924lpyraz~e 703lpyrazin~ 2 703,1016,~1200,1525,157S/pyrazine 3 1230lpyrazine 1178/benzene 4 1525,1575/pyrazine 1585,1605/benzene 5 I 178/benzene 1585,1605/benzene 6 ~016/pyr~ineb) 4.59i~cLo b) 7 IO 16lpyrazine 690&F, rcFa b) 8 459/CCl&J 690/&F 1,CF,
at 4880 A. relative to 6471 Aa)
(Studied/ReC)asan (Studied/Ref.)6471 2.8 =i 1.26 1.02 0.82 I.19 1.21 0.98
a) Fini et al. [ 121 show that refractive index corrections must be applied to our solution However, these corrections cancel (within 1%) because we have compared comparable for the same solutions at two different vo. b) These lines are totally symmetric.
exciting wavelength has been compared with those of other liquid pyrazine Raman lines, as shown in table 1 and discussed later. (3) Similarly, pyrazine solutions were studied for comfiarisons of the behavior of pyrazine lines with thoscof selected strong lines of the solvents, as listed in table 2 and discussed later.
3, Qualitative test of the theory Fig. 2 presents the ratios of the areas of the u5 and v4 lines, as a function of both slit width and exciting line, ZJ~.These data leave no doubt that the intensity
data. data
of ~5 increases markedly as v. is increased. The same conclusion follows from the less extensive data of tables 1 and 2. Table 1 shows that v8b (b,,, 152.5 cm-‘ f7], which cannut mix eB3u with any dipGle allowed state, behaves like the other strong vibrational lines and thus it is only v5 that mixes the 30 876 cm-l state with any other state in pyrazine. Earlier data are also consistent with these results [4. 131. These result: constitute a striking qualitative confirmation of Albrecht’s prediction, for o mse in which there is independent ~~~~l~dg~ of the mixing ujb~Qt~o~and ofthe states being Axed. Therefore this experimental work establishes the general validity of the theoretical approaches which have attempted to account for this 337
Volume 17, number 3
CHEhfICAL
effect. Clearly this establishment helps to justify the previous inferences that the vibrational mode(s) responsible for rnnxing electronic states can be identified if it shows a pre-resonance Raman effect. This result assures us of the complementary nature of Raman and electronic spectroscopies [2, 3, 8,5].
4. The simplest
model and quantitative
test of theories
In this model it is assumed that the knowledge of activity in the Iowest-lying singlet-singlet electronic transition of a molecule is a sufficient basis for understanding as striking a pre-resonance Raman intensity effect as is obsened here. Effects of vibronic activity (i.e., v. dependence other than in u”) between
vibronic
higher-lying states are assumed to be such that they approximately cancel when one compares vibrations of the same molecule and symmetry. That is, for pyrazine, we treat the Raman intensity of our internal standard, u,, as though it goes simply as u4, and that of vs as though fi is multiplied by only a single preresonance contribution (see expressions below). For the desired tests, it is necessary to discuss first the experimental numbers and then the available theories. Data obtained on different instruments agree within the experimental errors (standard deviations, ICI- 15%). Solution data (standard deviations =5%) are self-consistent and also agree with those for liquid pyrazine. Thus we may use clur most extensive set of
numbers, namely those of fig. 2. For each exciting frequency, vo, we use the appropriately weighted mean of the ratio, R, = Iyg/Iy~. Values taken as “observed” are therefore? (v. (cm-r), R,); 15450, 0.086; 17595, 0.137; 19429,0.192;20487, 0.246; 22640 and 22938,0.545; and 24705,0.669. Three theoretical expressions [ 1, 10, IS] will be applied to the data. Ali of the expressions are of the form: consrant (yo-
elements 2 -f( vu, ve, etc.) I ’ matrix
qJ4 22
I
PHYSICS
1 December
LETTERS
1972
and relatively. This is a strong reason to reduce each expression to a single term. Ratios of these terms, for different vo, will then allow the cancellation of the vo-independent numerator and permit a comparison with the results above. This test is therefore very restrictive, amounting, as it does, to seeing if a single
term model describes the data. In what follows, the &Afactor will be explicitly omitted. The numerical corrections will, however, be applied when appropriate. Generally speaking, the theories provide selection rules, account for Raman intensity in principle, and show how the intensity of a line may, e.g., increase faster [ 16, 171 than LJ~as v. is increased (pre-reso nance Raman effect). An early form, due to Shorygin [ 151, finds the intensity
to be proportional
to
(v2+v2)2/(v2-Y~)4 . e e 0
(1)
Clearly, as v. + v,, the intensity is predicted to rise very rapidly with vo_ Here v, amounts to an “effective” absorption frequency. This expression has been applied to correlate intensities as a function of vo, from which the “effective” absorption frequencies are calculated. Expressions having different uo-dependence are due to A!brecht [ I] and Pericolas et al. [ IOj. Both expressions display the vibronic activity of the vibrations in coupling dipole-allowed electronic states, which are located at ve and vs. (For pyrazine v, = 30 876 and v, = 50 880 or 60 700 cm-l _) Albrecht finds [ 11 the intensity to vary as (v v es
e-v;)2(vf-“;)‘. -w*)2/(v2 0
(2)
The expression due to Peticolas et al. (eq. (46) of ref. [IO] ) may be greatly theory to yield
simplified#
using group
(3) From the three equations applied to our simplest model for pyrazine, we may form table 3, in which both possible rBlu states of fig. 1 are considered in
The matrix elements are unknown, both absolutely #
In terms of the symbols used in ref. [lo], c2-p. tl$, e& and er-pkansfonn a;B,,, B,, b2g~ BI, and B,, (for tie vibronic coupling of us in pyrz;ine), (aHlaQ)~.
7 Appropriate least squares 1141 tests of the lines of fig. 2 provide no evidence that the slopes of the straight lines are both signif+ntly
-338 ._:
and systematically
different
from zero.
respectively. non-zero.
Only the first term of eq. (46),
ref. [IO] is
Volume 17, number 3
I December 1972
CHEMICAL PHYSICS LETTERS Table 3 Theoretical factors used for fig. 3 ue = 30 876 cm-’ (all entries X Ions)
Exciting line, vc (cm-’ ) vat.
vg-924‘4
(
IQ-703
15 450 17 59.5 19 429 20 487
)
5.448 9.287 16.11 23.25 56.94 65.73 176.7
0.9414
0.9481 0.9536 0.956 i 0.9603 0.9608 0.9637
22 640 22 938 24 70.5
DATA
vs = 50 880 cm-*
17
,
16
33
35
17
1
,
1.161 1.643 2.34 1 2.958 5.184 5.665 10.33
3.348 5.117 7.715 10.03 18.49 20.33 38.33
cq. (2)
eq. (31
0.7362 1.010 1.398 x.734 2.915 3.165 5.552
2.052 3.05 1 4.481 5.730 10.18 11.13 20.27
turn. In fig. 3, the ratio of the theoretical result (for vs = 50880 cm -l) to the respective experimental point is plotted. We &rd good fits (nearly horizontal fines) by our single term models of expressions (2) and (somewhat better) (31, but the fit by (1) is not
8
A,*
Kr+
us = 60 700 cm-*
I
good. Quite similar results are obtained if the theoretical results for ps = 60 700 cm-t are used.
Expressions (2) and (3) are free of adjustable parameters, and fig. 3 shows that each represents the pyrazine data quite well for these vo. Clearly, the ~mm3tion over states in the more genera! form given earher offers the possibility of introducing any number of adjustable parameters, ad hoc, to “improve” the fit. This would not be satisfying theorzticaliy and it is fortunate that it could add oniy margins lumencal improvements to the description of our case. Only time will tell whether
our example
is typical
and the
extent to which such a model can be applied. Another case which should
that of quinoxaline
be studied
in comparable
detail is
[18].
5. Further study of the reference Raman Tine, v4 + +ttt
+.
9
I
BOO EXCiTlNG
20,oDiY
FREQUENCY.
25,oc
vc (cm-‘)
Fig 3. Average values of the measured ratios of fig. 2 for each excitj,ng line, Y,J,have been divided into the values that may be pr+icted theoretical&(table 3). The resulting numbers (and one standard deviation) are plotted against ~0. *, A, and - refer to expressions (I), $31, and (21, respectively.
AU of the experimentally identified electronic states of pyrazine are included in fig. I. These probably include all of the upper states of strong, discrete absorption systems. Of these states, only the pairs lBaU and ‘B,, can be mixed by the vibrations vs and v4 fb28). However, only vs is active in such rn~~g for the known tBsu state. This is the likely reason for the apparent success of our simple model. However, one may ask whether the success is accidental. An unequivoc~ answer is probably unat: 339
Volume i 7, number 3:
ChIcmated enhancement
1 2 3 4 5 6 7
1 December
CHEMICAL PHYSICS LETTERS
of Raman intensity
“e
“S
30 876 30 876 75 000 55 560 57 000 80 000 (~10000) 124 000
so 75 75 55 92 124
expected
Table 4 for excitation at 4880 A, relative to 6471 A for single term appkation of theory
124 000
ell. (2)
eq. (1)
Molecule 880 000 (1P) 000 560 500 (IP) a) 000 UP)
1972
pyrazine
eq. (3)
C.~PIICP~
4.266 4.265 1.218 1.446 1.418 1.19?0.05
2.544 2.202 1.218 1.446 1.262 1.13”0.02
2.992 2.630 1.424 1.714 1.482 1.30r0.03
%F,rCPs
1.07
1.07
1.21
pyrazina pyra.zine
benzene cc14
a) See ref. [ZO] .
tamable even for our favorable case. All that we can do is to better define the limits of our interpretation. This requires consideration of the dependence of the Raman intensity of our reference line, v4, on uo_ We have attempted to determine this dependence in three ways. (1) Table 1 shows that all but onei_ of the other Raman lines of liquid pyrazine behave like v4 = 703 cm-l and that none of these mix the stat2 at 30 876 cm-l. It follows that our assumption that ~5 also behaves like v4 in mixing high-energy states is the best one we could make. (2) The actual change in the intensity of v4 for vovalues in the range of interest may be estimated from table 2 which contains the Raman line 459 cm-l of the solvent Ccl4 and those near 1600 cm-’ for benzene for each of which the uo-dependence of intensity has been measured [ 16, i7]. Extrapolation of the reported measurements to the region between 6471 and 4880 K gives a pre-resonance enhancement of intensity, in each case, of about a factor of 1.39% Rows 2,4 and 6 of table 2 therefore imply that pyrazine lines (including v4) show a pie-resonance enhancement t The weak line at 598 (~~a) is a 1g and decreases sh;irpIy as ~0 increases. Such an effect may be a result of irrtensity borrowing by some upper, lBSu state from the first ex-
cited singlet at 30 8715cm-‘. R Xecent work on CCk, [ 191 indicates that this may be hi& However, our measurements on the enhancement of various CC& lines, relative to one another, agree well with the sesuits-of extrapolation of the fitted data in ref. [ 16 J. 340
of very roughly a factor of 1.4. As we have emphasized this must be attributed to vibronic activity among states higher than the lE$,, state of fig. 1. In the extreme case that us did not benefit at all from the higher-level vibronic activity, the numbers plotted in fig. 3 would be wrong by about 40% It seems more reasonable
to assume
that
v4 and v5 benefit
more
nearly equally from such mixing, at least as far as any vo-dependent contribution for these u. is concerned. This would reduce such a (40%) correction$. (3) Some justification of the preceding sentence may be found in the calculations which are summarized in table 4. In particular, row 3 of table 4 shows that
?: If we allow for vibronic mixing of the upper states by both v4and v5, we mighthave1,,/1,4 = [2.992+1.424p]/1.424 a single adjustable parameter expression, using lines 1 and 3 of table 4. Experimentally this ratio is el.4 X 2.8 and so p would be ~1.8, for both (see footnote ‘) expressions (2) and (3). In fact, the reIative intensities of vs and u4 for long wavelength excitation are such (table 1) that p is expected to be < 1 if only vdependent terms contribute to these lines’ intensities. * In cases where theory must be used to determine both the vodependence of a Raman line intensity and to correct for a similar effect of some reference line, it happens that it becomes virtually impossible to distinguish between expressions (2) and (3). If we let the primes refer to the
standard compound whose resonance Raman effect will be corrected for by using theory, then for vs and v; in the range 40-70000. ue = 30 000 cm-‘, either uk or 2vk = vk, and for vo ranging from 12-30 000 (or < vk), the net resuits for the two theories are-found to be only = l/2% apart
Volume 17, number 3
CHEMICAL
PHYSICS
LETTERS
1 December 1972
one can account for the e~~ce~en~ factor 1.4 found for ~4 and g.ives no reason to expect a different factor for vibronic mixing near the ionization level by
KM. Innes. J.D. Simmons and S.G. Tilford, I. hiol. Spcctry. I.; (1963) 257. K.K. Innes and J.E. Parkin, J. hfoi. Spectry. 21 (I9661
vs*
%.
We close with words of caution. (1) Regarding the application of the single term expressions near ionization levels: rows 6 and 7 of table 4 predict that for a substance with an ionization potential as high as that of perfl~~romethylcyc~~ hexane one might find Raman lines whose intensities were essentially constant (both relative to other Raman lines in the same compound and absolutely) for such remote Q. The 690 cm-* line satisfies the first requirement, but not tile second, as shown in the last 3 rows of tabk 2. (2) Different lines of the solvent wilt have difprmt vVdependence (besides fi effects) and care must be exercised in choosing “standard” reference lines.
Acknow (edgement
We thank the following ~dividu~s for their help with experiments or useful discussions: R. Swindkburst. N.G. Elmer, and F.W. Eirss (Univ. Alberta); A.C. Albrecht, Ann T. Lemley, and R. Plane (Cornell); 5. SticWes (S.U.N.Y.); and R. Reed (Spex).
References [If A.C. Albrecht, 5. Chem. Phys. 34 (19511 1476.
{Z] P.P. Shorygin, Russian Chem. Rev. 40 (1971) 367. [31 J. Behtinger, in: Ramnn spectroscopy, Vol. 1, ed. Ii.A. Szymanski (Plenum Press, New York, 1967) p. 168.
407.
Psrkin and K.K. Innes,
J. Mol. Spectry. 15 (1965)
K.K. Innes, J.P. Byrne and I.G. Ross, J. Mot Spectry. (1967) 125. C.-H. Tin:: and K.-C. Kan, J. Chinese Chcm. Sot. I8 (1971) 9.
21
J. Tang and A.C. t\tbrecht, in: Raman spectroscopy, Vol. 2, ed. H.A. Szymanski (Pfenum Press, New York, 1970) p. 33, and references therein. W.L. Peticolas, L. N&e, P. Stein and 3. Fanconi, 3. Chem. Phys. 52 (19701 i576. ir_ Schettino, G. Sbrana and R. Righini, Chem. Phys. Letters 13 (1972) 284. G. Fir& P. Mirone and P. Patella. 3. Mol. Spect:y. 2& (1968) 144. M. Ito, R. Shimada, T. Kucaishi and W. Mizushima, 3. Chem. Phys 25 (1956) 597; R. Lord, A. hfarston and F.A. MlIIer, Spectrochim. Acta 9 (1957) 113. [I41 J.H. Williamson,Can. J. Phys. 46 (1968? 1845. [ISI P.P. Shorygin, Izv. Akad. Nauk SSSR, Ser. Fiz. 17 (1953) 581. (161 W. Hoffmann and H. Moser, Iler. Bunsenger Physik. Chem. 68 (L964) 129. f17] H. Buyken, K. Klauss and W. Moser, Ber. Bunsenges. Physik. Chem. 71 (1967) 578. [18j R.W. Glass, L.C. Robertson and J.A. Merritt, J. Chem. Pkys. 53 (1970) 3857; I. Mol. Spectry. 36 (19701316; G. Fischer, A.D. Jordan and I.G. Ross, J. Mlol. Spectry. 40 (1971) 397; to be published. 1191 K. Kaya, N. hfikami, Y. Udagaw and hl. Ito, Chem. Phys. Letters 13 (1972) 27-I. [20] J.L. Franklin, J.G. Diliar, H&l. Rosenstock, J.T. Herron. K. Draxl and F.H. Field, Ionization potentials, ap pearance potentials, and heats of formation of gaseous positive ions, NSRDS-NBS 26 (U.S. Govt. Printing Office, Washington, 1969).
1 December
CHEMICAL PKYSiCS LETTERS
1972
RAMAN INTENSITY AS A FUNCTION OF EXCITMG WAVELENGTH FOR A VIBRATION KNIT TO MIX ELE~R~NI~ STATESj?# A.H. KALANTARf, Department
ES. FRANZOSA and K.K. INNES
of C~iemistry, State University of hew York, Birrgltomton, New York 13901, USA Received
15 August 1972
The vs(b, ) vibration of liquid pyrazine is known to mix an eB ,u escited state with the eB3U excited state of the 3200 A (n.4z,n) electronic transition, while it is known that V4(bag) does not mix them. ‘The pre-resonance Raman intensity behaviors of v4 and vs have been compared. The intensity of us (relative to ~4) increases with the frequency of the exciting line, as required by theory. The observed increases are in close accord with two published quantum theories, for specified assumptions.
1. introduction Eleven years agot Afbrecht
developed
a quantum
74.9 /==
C,H,N; + e
mechanical theory of vibration& Raman intensities [I]. The theory predicts that the normal mode most responsible electronic
for “forbidden” transition should
intensity in an allowed show the greatest activity
Raman scattering, especially in pre-resonance Raman studies at wavelengths approaching those of the electronic transition. While many exampies of a preresonance Raman effect are known [2, 33, for lzutze has there been given independent proof of the identity of the mixing vibration and/or the location of the states being mixed, thus leaving the above quaiitative prediction as yet uncon~~ed. Vibronic anatysis of the 3200 A 1B3U- iA, system of pyrazine (fig. 1) revealed an ideal case for testing ‘he prediction, namely us (btg). It was proved that this out-of-plane, hydrogen-bending vibration mixed the intensity of a stronger transition with that of the 3200 hi transi‘B,,-IA tion [4, 51. The electronic levels and transitions of in
37.8
Fig. 1. Observed electronic states of pyrazine. The four transitions of interest are indicated by the arrows and include f-values. The ~4s choices for pyrazine are also sketched_
+ presented in part at the 27th Symposium
on Molecular Structure and Spectroscopy, The Ohio State University, Columbus, Ohio, June, 1972, paper M 11. p This work was supported by the National Science Foundation. $ On sabbnticat leave from University of Alberta, Edmonton, Alberta, Canada T6G 2G2, 1970-71.
interest [6, 7) are displayed in fig. 1. Thecries of Raman intensities have undergone further development during the past ten years [2,3, Cl-IO]. Moreover, it is only in that time that the variety of Raman exciting lines necessary for testing 335
Volu&e 17, number 3
1 December 1972
CHEMWAL PHYSICS LETTERS
the theories has been made avajkbk through the ready accessibility of gas lasers. These sources have made possible &e present report. of me~~rernen~s of the intensity of ps (924 cm-l) of liquid pyrazine, relative to u4 jbz,, 703 cm-l), which is not [4] involved in mixing this same e33U state with other eBlu efectronic states. Raman intensities have been measured for exciting fines from the red to the ultraviolet. The data have been standardized further by the more usual measurements in which the reference line is a solvent Raman.Iine whose intensity as a function of exciting frequency is known.
2. Experime&
22 938 q 22 640X
0.2
Pyrazine (99%, Aldrich Chemical Co.), purified by subl~ation and sealed off in L-shaped Pyrex tubing (7 mm o.d.), was studied as liquid?. The cells for room temperature solution spectra were sealed melting point tubes. Several commerci~ Raman spectrometers (Spex Ramalog and Ram&b, Jarrell-Ash, and Gary 81) were used to obtain the exciting lkes shown at the right of fig. 2. AI1 exciting lines were laser lines except for the two ~~est-frequency oner: which were the 4358 and 4047 A lines of the Toronto arc. In alI cases, the Raman radiation entering the dr;uble monochromator was rendered unpolarized. SIit widths employed varied from 2 to 1 I cm-l, nearly spanning the observed full widths at half maxima of the two Iines of interest for liquid pyrazine, namely 6 cm-l (v4) and 13 cm-l (v,). Repeated tracings of the u4 and vs peaks were recorded in alternate order. The ratios of the measured areas (using a planimetrr), together with the standard deviations, are shown in fig. 2 as a function of slit widths and exciting frequency (Q). A large part of the scatter is attributable to intensity fluctuations in the light sources??. Three other kinds of experimei~ts were performed,
OD 0
_: 19 429 *
2 4 6 -8 SPECTRA1 SLlf WIDTH (cm-‘)
liquid sample coot above the melting point (53*C). Consequently
the sample iemperature
was kept above 60°C to
obviate such problems, which may be related to the solid phase_transition described by Schettino et al. [ 1 L]. 336
I2
Fig. 2. hfeasured values of the ratio of integrated intensities of Raman lines of liquid pyrazine; that of v5 = 924 cm-’ to that of vq = 703 cm-‘, as a function of spectral slit width, and as a function of exciting line, ~0. All data arc corrected for spectrometer gain and photomuIt~pI~er tube responses.
Data for the two lowest vg are corrected for grating reflectivity, Each instrument correction was based on information supplied by the manufacturer. Such corrections should not be in error by ntore than 20% of the applied corrections (which ranged up to lS%). Standard deviations are indicated. u4 corrections are not included.
using the 4880 and 6471 A lines. (1) To test for interference from the nearby, strongly polarized Raman line (vl (a,) at 1016 cm-l) of liquid pyrazine, I_fI,, was detested for positions of an analyzer which maximized and minimized the possibility of interference. No significant variations in the ratio were found. (2) Dependence of the Raman intensity of v4 on ++In the case of the weak 24705 cm-’
; The ~5 peak undergoes a large frequency shift (from 924 cm-1 to IX_940. a~‘~) and becomes very small as the
K)
exciting line, the num-
ber of independent determinations was less than half those for any other exciting frequency. In addition, 24705 cm-’ is only 2000,cm-i befow the O-O band of the 3B,,-iA
electronic transition of pyrazine so that some further laca of reprqducibtiity, of absorption and re-emission in our samples may exist.
Volume 17, number 3
Wavelength
CHEhliCAL
dependence
Raman peaks (cm-r )
of fully corrected
Area ratio for 4880 A escitation (and number
Table 1 relative intensities .---
0.143(7) 1 0.091(17) 16.6f4) 0. f9(4) 1.36(6)
a) The groups of lines inc!udcd in the areas denoted the different vo.
Experimental
enhancement
Approx. std. dev. of change %
from 6471 A excitation
6471 A of data)
:1.X7(35) 14.8(3) 0.21{4) 1.47(6)
1972
of Raman lines of pyrazine at 65-70°C
Change
0.075(7)
5981 703 7031 703 9241 103 1015j 703 123011015 1575/1230a)
1 December
PHYSICS LETTERS
down l/2 -
IO
up 2.8 times -11% +iOk +8
20 13 9 I6
by 1575 and i230 also showed no changes, relative to each other, for
Table 2 of Raman intensity for excitation
Line(s) studied
Reference
cm”/molecule
cm-‘/molecule -
lines
I 924lpyraz~e 703lpyrazin~ 2 703,1016,~1200,1525,157S/pyrazine 3 1230lpyrazine 1178/benzene 4 1525,1575/pyrazine 1585,1605/benzene 5 I 178/benzene 1585,1605/benzene 6 ~016/pyr~ineb) 4.59i~cLo b) 7 IO 16lpyrazine 690&F, rcFa b) 8 459/CCl&J 690/&F 1,CF,
at 4880 A. relative to 6471 Aa)
(Studied/ReC)asan (Studied/Ref.)6471 2.8 =i 1.26 1.02 0.82 I.19 1.21 0.98
a) Fini et al. [ 121 show that refractive index corrections must be applied to our solution However, these corrections cancel (within 1%) because we have compared comparable for the same solutions at two different vo. b) These lines are totally symmetric.
exciting wavelength has been compared with those of other liquid pyrazine Raman lines, as shown in table 1 and discussed later. (3) Similarly, pyrazine solutions were studied for comfiarisons of the behavior of pyrazine lines with thoscof selected strong lines of the solvents, as listed in table 2 and discussed later.
3, Qualitative test of the theory Fig. 2 presents the ratios of the areas of the u5 and v4 lines, as a function of both slit width and exciting line, ZJ~.These data leave no doubt that the intensity
data. data
of ~5 increases markedly as v. is increased. The same conclusion follows from the less extensive data of tables 1 and 2. Table 1 shows that v8b (b,,, 152.5 cm-‘ f7], which cannut mix eB3u with any dipGle allowed state, behaves like the other strong vibrational lines and thus it is only v5 that mixes the 30 876 cm-l state with any other state in pyrazine. Earlier data are also consistent with these results [4. 131. These result: constitute a striking qualitative confirmation of Albrecht’s prediction, for o mse in which there is independent ~~~~l~dg~ of the mixing ujb~Qt~o~and ofthe states being Axed. Therefore this experimental work establishes the general validity of the theoretical approaches which have attempted to account for this 337
Volume 17, number 3
CHEhfICAL
effect. Clearly this establishment helps to justify the previous inferences that the vibrational mode(s) responsible for rnnxing electronic states can be identified if it shows a pre-resonance Raman effect. This result assures us of the complementary nature of Raman and electronic spectroscopies [2, 3, 8,5].
4. The simplest
model and quantitative
test of theories
In this model it is assumed that the knowledge of activity in the Iowest-lying singlet-singlet electronic transition of a molecule is a sufficient basis for understanding as striking a pre-resonance Raman intensity effect as is obsened here. Effects of vibronic activity (i.e., v. dependence other than in u”) between
vibronic
higher-lying states are assumed to be such that they approximately cancel when one compares vibrations of the same molecule and symmetry. That is, for pyrazine, we treat the Raman intensity of our internal standard, u,, as though it goes simply as u4, and that of vs as though fi is multiplied by only a single preresonance contribution (see expressions below). For the desired tests, it is necessary to discuss first the experimental numbers and then the available theories. Data obtained on different instruments agree within the experimental errors (standard deviations, ICI- 15%). Solution data (standard deviations =5%) are self-consistent and also agree with those for liquid pyrazine. Thus we may use clur most extensive set of
numbers, namely those of fig. 2. For each exciting frequency, vo, we use the appropriately weighted mean of the ratio, R, = Iyg/Iy~. Values taken as “observed” are therefore? (v. (cm-r), R,); 15450, 0.086; 17595, 0.137; 19429,0.192;20487, 0.246; 22640 and 22938,0.545; and 24705,0.669. Three theoretical expressions [ 1, 10, IS] will be applied to the data. Ali of the expressions are of the form: consrant (yo-
elements 2 -f( vu, ve, etc.) I ’ matrix
qJ4 22
I
PHYSICS
1 December
LETTERS
1972
and relatively. This is a strong reason to reduce each expression to a single term. Ratios of these terms, for different vo, will then allow the cancellation of the vo-independent numerator and permit a comparison with the results above. This test is therefore very restrictive, amounting, as it does, to seeing if a single
term model describes the data. In what follows, the &Afactor will be explicitly omitted. The numerical corrections will, however, be applied when appropriate. Generally speaking, the theories provide selection rules, account for Raman intensity in principle, and show how the intensity of a line may, e.g., increase faster [ 16, 171 than LJ~as v. is increased (pre-reso nance Raman effect). An early form, due to Shorygin [ 151, finds the intensity
to be proportional
to
(v2+v2)2/(v2-Y~)4 . e e 0
(1)
Clearly, as v. + v,, the intensity is predicted to rise very rapidly with vo_ Here v, amounts to an “effective” absorption frequency. This expression has been applied to correlate intensities as a function of vo, from which the “effective” absorption frequencies are calculated. Expressions having different uo-dependence are due to A!brecht [ I] and Pericolas et al. [ IOj. Both expressions display the vibronic activity of the vibrations in coupling dipole-allowed electronic states, which are located at ve and vs. (For pyrazine v, = 30 876 and v, = 50 880 or 60 700 cm-l _) Albrecht finds [ 11 the intensity to vary as (v v es
e-v;)2(vf-“;)‘. -w*)2/(v2 0
(2)
The expression due to Peticolas et al. (eq. (46) of ref. [IO] ) may be greatly theory to yield
simplified#
using group
(3) From the three equations applied to our simplest model for pyrazine, we may form table 3, in which both possible rBlu states of fig. 1 are considered in
The matrix elements are unknown, both absolutely #
In terms of the symbols used in ref. [lo], c2-p. tl$, e& and er-pkansfonn a;B,,, B,, b2g~ BI, and B,, (for tie vibronic coupling of us in pyrz;ine), (aHlaQ)~.
7 Appropriate least squares 1141 tests of the lines of fig. 2 provide no evidence that the slopes of the straight lines are both signif+ntly
-338 ._:
and systematically
different
from zero.
respectively. non-zero.
Only the first term of eq. (46),
ref. [IO] is
Volume 17, number 3
I December 1972
CHEMICAL PHYSICS LETTERS Table 3 Theoretical factors used for fig. 3 ue = 30 876 cm-’ (all entries X Ions)
Exciting line, vc (cm-’ ) vat.
vg-924‘4
(
IQ-703
15 450 17 59.5 19 429 20 487
)
5.448 9.287 16.11 23.25 56.94 65.73 176.7
0.9414
0.9481 0.9536 0.956 i 0.9603 0.9608 0.9637
22 640 22 938 24 70.5
DATA
vs = 50 880 cm-*
17
,
16
33
35
17
1
,
1.161 1.643 2.34 1 2.958 5.184 5.665 10.33
3.348 5.117 7.715 10.03 18.49 20.33 38.33
cq. (2)
eq. (31
0.7362 1.010 1.398 x.734 2.915 3.165 5.552
2.052 3.05 1 4.481 5.730 10.18 11.13 20.27
turn. In fig. 3, the ratio of the theoretical result (for vs = 50880 cm -l) to the respective experimental point is plotted. We &rd good fits (nearly horizontal fines) by our single term models of expressions (2) and (somewhat better) (31, but the fit by (1) is not
8
A,*
Kr+
us = 60 700 cm-*
I
good. Quite similar results are obtained if the theoretical results for ps = 60 700 cm-t are used.
Expressions (2) and (3) are free of adjustable parameters, and fig. 3 shows that each represents the pyrazine data quite well for these vo. Clearly, the ~mm3tion over states in the more genera! form given earher offers the possibility of introducing any number of adjustable parameters, ad hoc, to “improve” the fit. This would not be satisfying theorzticaliy and it is fortunate that it could add oniy margins lumencal improvements to the description of our case. Only time will tell whether
our example
is typical
and the
extent to which such a model can be applied. Another case which should
that of quinoxaline
be studied
in comparable
detail is
[18].
5. Further study of the reference Raman Tine, v4 + +ttt
+.
9
I
BOO EXCiTlNG
20,oDiY
FREQUENCY.
25,oc
vc (cm-‘)
Fig 3. Average values of the measured ratios of fig. 2 for each excitj,ng line, Y,J,have been divided into the values that may be pr+icted theoretical&(table 3). The resulting numbers (and one standard deviation) are plotted against ~0. *, A, and - refer to expressions (I), $31, and (21, respectively.
AU of the experimentally identified electronic states of pyrazine are included in fig. I. These probably include all of the upper states of strong, discrete absorption systems. Of these states, only the pairs lBaU and ‘B,, can be mixed by the vibrations vs and v4 fb28). However, only vs is active in such rn~~g for the known tBsu state. This is the likely reason for the apparent success of our simple model. However, one may ask whether the success is accidental. An unequivoc~ answer is probably unat: 339
Volume i 7, number 3:
ChIcmated enhancement
1 2 3 4 5 6 7
1 December
CHEMICAL PHYSICS LETTERS
of Raman intensity
“e
“S
30 876 30 876 75 000 55 560 57 000 80 000 (~10000) 124 000
so 75 75 55 92 124
expected
Table 4 for excitation at 4880 A, relative to 6471 A for single term appkation of theory
124 000
ell. (2)
eq. (1)
Molecule 880 000 (1P) 000 560 500 (IP) a) 000 UP)
1972
pyrazine
eq. (3)
C.~PIICP~
4.266 4.265 1.218 1.446 1.418 1.19?0.05
2.544 2.202 1.218 1.446 1.262 1.13”0.02
2.992 2.630 1.424 1.714 1.482 1.30r0.03
%F,rCPs
1.07
1.07
1.21
pyrazina pyra.zine
benzene cc14
a) See ref. [ZO] .
tamable even for our favorable case. All that we can do is to better define the limits of our interpretation. This requires consideration of the dependence of the Raman intensity of our reference line, v4, on uo_ We have attempted to determine this dependence in three ways. (1) Table 1 shows that all but onei_ of the other Raman lines of liquid pyrazine behave like v4 = 703 cm-l and that none of these mix the stat2 at 30 876 cm-l. It follows that our assumption that ~5 also behaves like v4 in mixing high-energy states is the best one we could make. (2) The actual change in the intensity of v4 for vovalues in the range of interest may be estimated from table 2 which contains the Raman line 459 cm-l of the solvent Ccl4 and those near 1600 cm-’ for benzene for each of which the uo-dependence of intensity has been measured [ 16, i7]. Extrapolation of the reported measurements to the region between 6471 and 4880 K gives a pre-resonance enhancement of intensity, in each case, of about a factor of 1.39% Rows 2,4 and 6 of table 2 therefore imply that pyrazine lines (including v4) show a pie-resonance enhancement t The weak line at 598 (~~a) is a 1g and decreases sh;irpIy as ~0 increases. Such an effect may be a result of irrtensity borrowing by some upper, lBSu state from the first ex-
cited singlet at 30 8715cm-‘. R Xecent work on CCk, [ 191 indicates that this may be hi& However, our measurements on the enhancement of various CC& lines, relative to one another, agree well with the sesuits-of extrapolation of the fitted data in ref. [ 16 J. 340
of very roughly a factor of 1.4. As we have emphasized this must be attributed to vibronic activity among states higher than the lE$,, state of fig. 1. In the extreme case that us did not benefit at all from the higher-level vibronic activity, the numbers plotted in fig. 3 would be wrong by about 40% It seems more reasonable
to assume
that
v4 and v5 benefit
more
nearly equally from such mixing, at least as far as any vo-dependent contribution for these u. is concerned. This would reduce such a (40%) correction$. (3) Some justification of the preceding sentence may be found in the calculations which are summarized in table 4. In particular, row 3 of table 4 shows that
?: If we allow for vibronic mixing of the upper states by both v4and v5, we mighthave1,,/1,4 = [2.992+1.424p]/1.424 a single adjustable parameter expression, using lines 1 and 3 of table 4. Experimentally this ratio is el.4 X 2.8 and so p would be ~1.8, for both (see footnote ‘) expressions (2) and (3). In fact, the reIative intensities of vs and u4 for long wavelength excitation are such (table 1) that p is expected to be < 1 if only vdependent terms contribute to these lines’ intensities. * In cases where theory must be used to determine both the vodependence of a Raman line intensity and to correct for a similar effect of some reference line, it happens that it becomes virtually impossible to distinguish between expressions (2) and (3). If we let the primes refer to the
standard compound whose resonance Raman effect will be corrected for by using theory, then for vs and v; in the range 40-70000. ue = 30 000 cm-‘, either uk or 2vk = vk, and for vo ranging from 12-30 000 (or < vk), the net resuits for the two theories are-found to be only = l/2% apart
Volume 17, number 3
CHEMICAL
PHYSICS
LETTERS
1 December 1972
one can account for the e~~ce~en~ factor 1.4 found for ~4 and g.ives no reason to expect a different factor for vibronic mixing near the ionization level by
KM. Innes. J.D. Simmons and S.G. Tilford, I. hiol. Spcctry. I.; (1963) 257. K.K. Innes and J.E. Parkin, J. hfoi. Spectry. 21 (I9661
vs*
%.
We close with words of caution. (1) Regarding the application of the single term expressions near ionization levels: rows 6 and 7 of table 4 predict that for a substance with an ionization potential as high as that of perfl~~romethylcyc~~ hexane one might find Raman lines whose intensities were essentially constant (both relative to other Raman lines in the same compound and absolutely) for such remote Q. The 690 cm-* line satisfies the first requirement, but not tile second, as shown in the last 3 rows of tabk 2. (2) Different lines of the solvent wilt have difprmt vVdependence (besides fi effects) and care must be exercised in choosing “standard” reference lines.
Acknow (edgement
We thank the following ~dividu~s for their help with experiments or useful discussions: R. Swindkburst. N.G. Elmer, and F.W. Eirss (Univ. Alberta); A.C. Albrecht, Ann T. Lemley, and R. Plane (Cornell); 5. SticWes (S.U.N.Y.); and R. Reed (Spex).
References [If A.C. Albrecht, 5. Chem. Phys. 34 (19511 1476.
{Z] P.P. Shorygin, Russian Chem. Rev. 40 (1971) 367. [31 J. Behtinger, in: Ramnn spectroscopy, Vol. 1, ed. Ii.A. Szymanski (Plenum Press, New York, 1967) p. 168.
407.
Psrkin and K.K. Innes,
J. Mol. Spectry. 15 (1965)
K.K. Innes, J.P. Byrne and I.G. Ross, J. Mot Spectry. (1967) 125. C.-H. Tin:: and K.-C. Kan, J. Chinese Chcm. Sot. I8 (1971) 9.
21
J. Tang and A.C. t\tbrecht, in: Raman spectroscopy, Vol. 2, ed. H.A. Szymanski (Pfenum Press, New York, 1970) p. 33, and references therein. W.L. Peticolas, L. N&e, P. Stein and 3. Fanconi, 3. Chem. Phys. 52 (19701 i576. ir_ Schettino, G. Sbrana and R. Righini, Chem. Phys. Letters 13 (1972) 284. G. Fir& P. Mirone and P. Patella. 3. Mol. Spect:y. 2& (1968) 144. M. Ito, R. Shimada, T. Kucaishi and W. Mizushima, 3. Chem. Phys 25 (1956) 597; R. Lord, A. hfarston and F.A. MlIIer, Spectrochim. Acta 9 (1957) 113. [I41 J.H. Williamson,Can. J. Phys. 46 (1968? 1845. [ISI P.P. Shorygin, Izv. Akad. Nauk SSSR, Ser. Fiz. 17 (1953) 581. (161 W. Hoffmann and H. Moser, Iler. Bunsenger Physik. Chem. 68 (L964) 129. f17] H. Buyken, K. Klauss and W. Moser, Ber. Bunsenges. Physik. Chem. 71 (1967) 578. [18j R.W. Glass, L.C. Robertson and J.A. Merritt, J. Chem. Pkys. 53 (1970) 3857; I. Mol. Spectry. 36 (19701316; G. Fischer, A.D. Jordan and I.G. Ross, J. Mlol. Spectry. 40 (1971) 397; to be published. 1191 K. Kaya, N. hfikami, Y. Udagaw and hl. Ito, Chem. Phys. Letters 13 (1972) 27-I. [20] J.L. Franklin, J.G. Diliar, H&l. Rosenstock, J.T. Herron. K. Draxl and F.H. Field, Ionization potentials, ap pearance potentials, and heats of formation of gaseous positive ions, NSRDS-NBS 26 (U.S. Govt. Printing Office, Washington, 1969).