J . Phys. Chem. 1986, 90, 2340-2346
2340
can suffer several fates. Either 8 can fragment to N 0 2 + / C H 3 or N02/CH3+or it can decay or cross to two lower states. Decay to a 2A’ (7) state is expected to be rapid since the two states are of the same symmetry 22A’ 12A’. This state may be the precursor of NO+/OCH3 which is known to produce behavior predicted by QET. Crossing to the 2A” state (9) may be slower since an electronic state of different symmetry is involved. This state may be the precursor of NO/H2COH+ which is known not to display QET behavior. In the process 22A’ LI, 2A’’ N O / H2COH+,the rate of fragmentation may depend on the rate of crossing between surfaces, k , . In conclusion, although quantitative agreement is not obtained, many experimental results can be consistently explained in terms of the described potential energy diagrams. It is also demonstrated that with caution single configuration results can be used, provided correlation is accounted for through fourth-order MP perturbation
-
correction although ideally an MCSCF treatment would be preferable. Finally, higher electronic states can be investigated provided symmetry can be adjusted to allow the desired state to be the lowest of a given symmetry while two adiabatic ground states differing in the dominant configuration can be calculated if an avoided crossing between the ground-state and excited-state surfaces occurs.
Acknowledgment. I would like to thank Andreas Illies for helpful discussions. Computer time for this study was donated by the Auburn University Computer Center. Peter Pulay is acknowledged for point out the possibility of a broken symmetry solution for nitromethane and other useful suggestions. Tomas Baer has kindly provided a preprint of his work and has suggested a number of corrections and improvements to the present manuscript.
Solvent Effects on the Absorption and Raman Spectra of Aromatic Nitro Compounds. 1. Calculation of Preresonance Raman Intensities E. D. Schmid, M. Moschallski, and W. L. Peticolas* Institut f u r Physikalische Chemie, Uniuersitat Freiburg, 0 - 7 8 Freiburg i. Br., Hebelstrarse 38, F.R.G. (Received: October 28, 1985)
The absorption and preresonance Raman spectra (taken with 514.5-nm incident light) of a series of aromatic nitro compounds are examined in solvents of varying dielectric @-nitroaniline, p-nitrophenol, p-nitroanisole, and N,N-diethyl-p-nitroaniline) constants and index of refraction. The observed absorption maxima are found to vary between 24000 and 40000 cm-’ while the preresonant Raman intensity varies over 3 orders of magnitude. A plot of the Raman intensities for the NOz symmetric stretching vibrations vs. the absorption maxima for this series of compounds in the various solvents has been made. The points fall on a single curve in which the Raman intensity increases monotonically as the absorption maximum shifts closer toward the laser excitation frequency. We have been able to fit this curve with a theoretical equation derived by assuming that (1) in every case the preresonance Raman enhancement is obtained from the lowest observed absorption band; (2) the vibrational frequencies and the electronic transition moments are the same for each of these molecules independent of the solvent; (3) both the nonresonant and the resonant terms of the Kramers-Heisenberg equation are included in the calculation of the Raman intensity; (4) the exciting line is sufficiently far off resonance that the damping term is negligible; (5) the shift in the excited-state geometry of the NO2 group is small and independent of solvent so that the small shift approximation is adequate. The resulting equation has no adjustable parameters and fits the data to within their measurable precision.
Introduction The study of resonance Raman spectroscopy has received much attention in recent years (for reviews see ref 1-3). However, the phenomenon of preresonance Raman spectroscopy has been considered only by relatively few workers mostly in the field of nucleic acid bases3-’ In spite of this latter work it is still not exactly clear under which conditions one can have a quantitative theory of the preresonance Raman effect. If one uses an incident laser light which is lower in frequency than the first absorption band, then in principle the intensity of the Raman scattered light is obtained from an infinity of states of increasing electronic energy. This has been known since the early work of Kramers and Heisenberg and Dirac.*s9 More recent work however has emphasized that for Raman scattering from totally symmetric molecular vibrations the intensity is governed to a large extent by the Franck-Condon (FC) factors and these in turn are related to the displacement of the molecular geometry along the normal coordinates in the excited electronic state.I0 This fact tends to limit the origin of vibrational Raman intensity to low-lying electronic states. Indeed in the higher electronic state the change in the electronic bonding of the molecule may be so great that the normal mode structure in these higher electronic states is * Present address: Department of Chemistry, University of Oregon, Eugene, OR 97403. 0022-3654/86/2090-2340.$01.50/0
completely different from the lowest excited state or the ground state. Under these conditions the magnitude of the FC factors between the ground and highly excited state vibrations may be very weak. This is due to a Dushinsky effect in which the excited-state vibrations are related to the ground-state vibrations by a matrix of rotation. Instead of preserving the Raman intensity in a single vibration it is spread over all 3N-6 vibrations so that the measured resonance Raman intensity in any one band is negligible. This may be the origin of the recent observation that (1) Johnson, B. B.; Peticolas, W. L. Annu. Rev. Phys. Chem. 1976, 27, 465-91. (2) Spiro, T.; Stein, P. Annu. Rev. Phys. Chem. 1977, 28, 465-91. (3) Tsuboi, M.; Nishimura, Y.; Hirakawa, A. Y.; Peticolas, W. L. In Raman Spectroscopy of Biological Molecules; Spiro, T., Ed.; Wiley: New York, 1986; Vol. 1:. (4) Tomlinson, B. L.; Peticolas, W. L. J . Chem. Phys. 1970, 52, 2154. (5) Tsuboi, M.; Takadahashi, S.; Muraishi, S.: Kaiiura, T. Bull. Chem. SOC.Jpn. 1971, 44, 2921. (6) Pezolet, M.; Yu, T. J.; Peticolas, W. L. J . Raman Spectrosc. 1975, 3, 55. (7) Nishimura, Y.; Hirakawa, A. Y.; Tsuboi, M. “Resonance Raman Spectroscopy of Nucleic Acids”. In Advances in Infrared and Raman Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Heyden: London, 1978; Vol. 5 , p 217. ( 8 ) Kramers, H. A.; Heisenberg, W. Z . Phys. 1925, 31, 681. (9) Dirac, P. A. M. Quantum Mechanics; Oxford, University Press: London, 1930. (10) Champion, P. M.; Albrecht, A. C. Annu. Rec. Phys. Chem. 1983, 33, 353.
0 1986 American Chemical Society
Spectra of Aromatic Nitro Compounds resonance with higher electronic excited states gives much weaker resonance enhancement than that obtained with lower lying excited states." It may be that for certain molecular vibrations, the lowest lying allowed excited electronic state may be the only one in which there is a substantial displacement along the vibrational normal coordinate. This means that this low-lying excited electronic state will be the only one from which the preresonance Raman effect will obtain a measurable Raman intensity. As we will show in this work, the NO2 symmetric stretching vibration at 133d cm-' which occurs in a series of chemically related p-nitro-substituted aniline and phenol derivatives appears to fall into this category. This has permitted us to derive an equation to quantitatively fit a plot of the experimental points for the measured value of the preresonance Raman intensity against the absorption maxima for a wide range of solvent-induced changes.
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986 2341 resonant and nonresonant terms, we can obtain a closed expression for the Raman tensor and its absolute square and so obtain the intensity of the Raman scattering as a function of absorption maximum which is assumed to be close to the 0transition. With these assumptions eq 2 may be written explicitly as 1
1
wI - w
+ir
-
1
w1
+ w + ir
If we use a common denominator we may write explicitly for the Raman tensor a = 21/2AQMe: X
+
wlw0 + wZ - r2 i q w 0 + w l )
Theory The Raman scattering intensity from a vibrating molecule is proportional to the absolute square of the Raman tensor which for a single vibration in the single-mode approximation may be written as
+
+
(wOz- w2 - rz 2irwO)(wl2- w2 - r2 2 i r w , )
+
where w, wo uQ. Now let us turn our attention to the summation over u, the vibrational levels of the excited electronic state. Some time ago, Blazej and one of the present authors12showed that if the products of Franck-Condon factors ( l l u ) ( u l O ) which are found in this equation are evaluated specifically in terms of A, the shift parameter in the excited state along the normal coordinate, this factor is proportional to f A / 2 ' t 2 for u = 0,l but goes as higher powers of A for u > 1. Thus if A is small then the infinite summation over u may be truncated to u = 0,l and this results in a great mathematical simplification. It furthermore means that it is not necessary to use the multimode theory of Raman scattering. In this earlier work and in similar work by Warshel" it was customary to leave out the nonresonance part of the Raman tensor. However, leaving out this part of the tensor will result in a measurable error for the preresonance Raman effect. By including only the first two terms in the sum over u and by considering only one excited electronic state (the lowest) but including both the (11) Rava, R. P.; Spiro, T. G. J . Phys. Chem. 1985, 89, 2089. (12) Blazej, D. C.; Peticolas, W. L. Proc. Natl. Acad. Sci. U.S.A. 1977, 74, 2639. (13) Warshel, A.; Dauber, P. J . Chem. Phys. 1977, 66, 5477.
(4)
W e observe that this equation is of the form
( A + iB) ( C + iD)(E iF')
+
where Meg is the electronic transition moment between the ground-state g and excited electronic state e, wo is the 0-0 electronic transition frequency, u is the vibrational quantum number of the excited state, 52 is the frequency of the vibrational quantum, w is the laser frequency, r is the damping, 10) is the wave function for the 0th vibrational level of the ground state, (11 is the wave function for the first excited vibrational level of the ground state, and Iu) (ul is a product of ket and bra vectors for the uth vibrational level of the excited intermediate electronic state. N R is the nonresonant part of the Raman scattering tensor. It is the complex conjugate to the resonant part with -w substituted for w. The nonresonance term has the significance of resonance with a negative frequency. Since this is physically impossible it only contributes to the preresonance measurements. The summation ever e goes over an infinity of excited states. The single-mode approximation may be justified if a small shift in the potential energy minimum along each of the normal coordinates in the excited state is present. If we assume preresonance only with the lowest excited electronic state then we may drop the sum over e; if we take the value of Meg evaluated a t the position of the normal coordinate, Q = 0, then eq 1 may be rewritten as
]
1
where K = 21/2A52M,,2. Hence the Raman intensity can be obtained from the absolute square, i.e.
I
=:
Id1 = @{(A2 + B2)/[(C? + D2)(E2+ @ ) I )
(6)
In the above equation, the damping was included as is customary in this type of treatment. However, as we will discuss below for our preresonance Raman measurements, the damping is small compared to the frequency difference wo - w and so considerable simplification results in eq 6 if the damping is set equal to zero. In this approximation the Raman scattering tensor and Raman intensity become
In the above equations, the dependence of the Raman intensity on the fourth power of the incident laser frequency is not included. Since all of our measurements are made with the same laser frequency, this fourth power term does not need to be included. Quite some time ago a preresonance-resonance theory was derived by Shorygin.I4J5 This theory calculates the Raman tensor in terms of the electronic states without considering either the vibrational (i.e., harmonic oscillator) wave functions or the Franck-Condon factors. Shorygin derived his vibrational theory by taking the derivative of the Raman tensor, a,expressed solely in terms of the electronic transition with respect to the normal coordinate. He kept both the resonant and nonresonant portions and was able to obtain an equation for the intensity as a function of the 0-0 absorption maximum and the incident frequency. His theory has two parts, an A and a B part. The only part we will consider in this paper is the A part which has been shown to be the most important part.I5 This quantity is usually designated by FA and is given by (9)
A comparison of eq 9 with 8 shows that if wo + 52 = wo, the two
equations are identical in frequency dependence. (14) Shorygin, P. P. J . Phys. Chem. (Moscow) 1947, 21, 1125. (15) For a derivation of the Shorygin equation see: Koningstein, J. A. Introduction to the Theory of the Raman Effect; D. Reidel: Dordrecht, Holland, 1972; p 146. But note that the nonresonant term must be added to equation V, 4-5 in order to obtain the Shorygin equation V, 4-6.
2342 The Journal of Physical Chemistry, Vol. 90, No. I I , 1986
840 800 760 7 20 Figure 1. Raman spectrum of 0.2 M cyclohexane in carbon tetrachloride: (a) the difference spectrum showing the spectrum of cyclohexane; (b) the solution spectrum; and (c) the spectrum of the pure solvent
Materials and Methods In obtaining the compounds studied, p-nitrophenol, p nitroanaline, etc. and the solvents, we followed the same procedures as Taft and co-workers16-z0who have made a detailed study of the absorption spectra of these solute-solvent systems. We have also followed their solvent numbering. The experimental measurements of the Raman intensities were carried out by using an apparatus described previously.z1 With this apparatus the spectra are obtained on a Princeton Applied Research OMA I1 image intensifier and recorded on a PDP-8 data collection system. The data were collected over a long period of time-first on the purified solvent and then on the dilute solution of the appropriate solute. A different spectrum was obtained by the subtraction of the solvent spectrum from the solution spectrum so that only the substrate bands were obtained. Details of the experimental setup have been described elsewhere.2z However. Figures 1 and 2 show two examples of the technique we used to obtain the solute Raman spectra and suppress the solvent spectra. In the first case, the solute (in this experiment cyclohexane) has a Raman band which is well distinguished from that of the solvent. In the second the Raman band of the solute is buried in that of the solvent but may be obtained by subtraction of the Raman spectrum of the solvent. This latter example illustrates the worst case we encountered. To obtain the preresonance Raman intensities (or relative scattering coefficients), S, the method developed by Bernstein and Allen23was used. This method uses the 458-cm-I band of carbon tetrachloride as a standard. It was possible to obtain the relative intensity for the NO, symmetric stretching vibration and for each of a series of paranitroaromatic compounds which will be discussed on the following pages. Results and Discussion A systematic study of the Raman and absorption spectra was made of the following compounds: p-nitroaniline, N,N-diethylp-nitroaniline, p-nitrophenol, and p-nitroanisole. For these four (16) Kamlet, M. J.; Taft, R. W. J . A m . Chem. SOC.1976, 98, 377. (17) Taft, R. W.; Kamlet, M. J. J . Am. Chem. SOC.1976, 98, 2886. (18) Yokoyama. T.; Taft. R. W.; Kamlet, M. J. J . A m . Chem. SOC.1976. 98,3233. (19) Kamlet, M. J.; Kayser, E. G.; Jones, M. E.; Abboud, J.-L.; Eastes, J. W.; Taft, R. W. J . Phys. Chem. 1978.82, 2477. (20) Kamlet, M. J.; Solomonovici, A,; Taft, R. W. J . Am. Chem. SOC. 1979, 101, 3734. (21) Schmid, E. D.; Berthold, G.; Berthold, H.; Brosa, B. Ber. Bunsenges, Phys. Chem. 1971, 7 5 , 149. (22) Moschallski, M. Thesis Universitat Freiburg, F.R.G., 1984. (23) Bernstein. H. F.: Allen. G.J . Opt. SOC.A m . 1955, 45. 237.
Schmid et al.
1600 1500 1400 I300 Figure 2. Raman spectrum of 0.1 M nitrophenol in heptane: (a) the difference spectrum showing the Raman spectrum of the nitrophenol; (b) the solution spectrum; and (c) the spectrum of the pure solvent. This was the worst case we encountered and represents the limit of our difference
capability.
I/
i
1400
I
1360
1320
1280
1240
S/cm-'
Figure 3. Raman difference spectra of p-nitroaniline in 13 different solvents. The numbering system follows that of Taft and co-workers.'6-20 See Tables I-IV for the solvent name corresponding to its number.
compounds we have measured the Raman intensities of two vibrations, the NO, symmetric stretching vibration and the pair of ring breathing modes which are usually designated as v8a and v8b, respectively. In this, the first of two papers, we will only discuss the NOz symmetric stretching vibration. In order to study the effect of solvents on the Raman intensities a wide variety of solvents were used. In selecting these solvents we were motivated by the work of Taft and co-workers16-z0who have made a detailed study of the absorption spectra of these same p-nitro compounds in the same solvents. In a subsequent paper we will use this work in detail to explain the effect of H bonding and ethyl group shielding on the relative Raman intensities of these compounds in various solvents. However, in this first paper we
The Journal of Physical Chemistry, Vol. 90, No. 1 1 , 1986 2343
Spectra of Aromatic Nitro Compounds
29 29 I
1400
1360
I
I
1320
1280
1400
1240
G/cm-'
Figure 4. Raman difference spectra of p-nitroaniline in 12 solvents
different from those in Figure 3. See Tables I-IV for meaning of numbers.
I
1360
1320
1280
I240
Gfcrn'
Figure 6. Raman difference spectra of N,N-diethyl-p-nitroanilinein
another 13 different solvents.
2jg A
43 3
_ _ I4L-
y3kO
13h0
I
1280
-1 1240
1400
__ 1360
-
~~~
1320
T 1280
1 1240
i/cm-l
iVcrn-1
Figure 7. Raman difference spectra of p-nitrophenol in 12 different
Figure 5. Raman difference spectra of N,N-diethyl-p-nitroanilinein 13 different solvents.
solvents.
will only deal with the Raman intensities of the NOz symmetric ring breathing vibrations which as we will demonstrate may be expressed as a single-valued, monotonic function of the absorption maxima when measured in the same solvent. Figures 3 and 4 show the solvent subtracted Raman spectra of the NO2 symmetric stretching vibrations of p-nitroaniline in a variety of solvents. Figures 5-10 show the same spectra for N,N-dieth yl-p-nitroaniline, p-nitrophenol, and pnitroanisole. The NO2 symmetric stretching vibration is sometimes a doublet in certain solvents. This effect will be discussed in a later paper but in this work we have taken the entire area under the curve as the
intensity. The numbers are the solvent numbers given originally by Taft and co-workers1620 and they are defined in Tables I-IV in which the data are presented in a tabular, quantitative manner. Tables I-IV give the following data for p-nitroanaline, N,Ndiethyl-p-nitroaniline, p-nitrophenol, and p-nitroanisole: column 1, solvent; column 2, the solvent number given by Taft and Kamlet;I6I9 column 3, the Raman intensity coefficient of the NO2 symmetric stretching bond relative to the carbon tetrachloride line at 459 cm-' (we estimate the uncertainty of these values to be less than 20% based on reproducibility of values obtained on the same sample at different times); column 4,the Raman frequency
2344
The Journal of Physical Chemistry, Vol. 90, No. 1 I, 1986
Schmid et al.
I
'I
39
-t 0 VI
i27
w I
126_ 26 1
1
1400
1360
1320
1280
I 1240
G/cm-'
Vcm'
Figure 8. Raman difference spectra of p-nitrophenol in 13 solvents different from those in Figure 7.
Figure 10. Raman difference spectra of p-nitroanisole in another 13
different solvents. TABLE I: Raman and Absorption Spectral Data for p-Nitroaniline in Various Solvents'
hexane, heptane cyclohexane triethylamine butyl ether CCI, dioxane ethyl acetate tetrahydrofuran benzene 2-butanone ethyl chloroacetate acetone CI,C=CHCI triethyl phosphate anisole trichloroacetone
I
1400
1360
1320
1280
I 1240
i+m'
Figure 9. Raman difference spectra of p-nitroanisole in 12 different
solvents. of the intensity maximum of the NO, symmetric stretching vibration; columns 5 and 6, molar absorption coefficient and frequency of the absorption maximum in the ultraviolet absorption spectrum. Figure 11 shows a plot of the relative Raman intensities of the NO, symmetric stretch vibrations against the absorption maxima for the four p-nitro compounds in a large number of different solvents. These data are taken from Tables I-IV. It is at first remarkable that these data taken on four different compounds in a wide variety of solvents should fall on a single monotonic
11
13 14 16 39 18 IO 19 17 50 30 ClCHzCHlCl 20 CH2C12 21 pyridine 24 hexamethylphosphoramide 26 but yrolactone 27 dimethylformamide 25 dimethylacetamide 23 dimethyl sulfoxide 29
'AAbL I39
1
2 3 5 43 6 9
104 94 239 208 94 122 229 263 310 198 361 297 343 156 470 245 340 212 242 253 530 715 454 607 586 721
1340 1338 1334 1334 1345 1337 1313 1333 1320 1334 1316 1333 1315 1337 1317 1333 1315 1335 1334 1334 1313 131 1 1313 1311 1310
1310
14469
31.25
15674
28.90
14427 15665 16493 17215 14050 16519 15729 16800 14005 19150 14485 16192 14218 14861 14652 17828 23 100 17312 18692 19610 19875
30.80 28.25 28.01 27.47 29.07 27.32 27.55 27.32 29.45 26.46 28.23 27.40 28.65 28.37 28.57 26.52 25.57 26.81 26.18 26.01 25.59
"Columns 1-6 list respectively the solvent, the solvent number, the Raman intensity of the NO2 symmetric stretching vibration, the frequency of this vibration in cm-', the molar absorptivity (extinction coefficient), and the frequency (in 1000 cm-') of the maximum absorption of the first allowed absorption band. function of Raman frequency vs. absorption maximum. In order to explain these results we use the theory presented above. In that theory it is assumed that in each of these molecules there is a symmetric displacement (probably an elongation) of the nitrogen-oxygen bonds when the molecule absorbs a photon and goes into the first excited electronic state. It is this displacement which gives intensity to the resonant Raman band of
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986 2345
Spectra of Aromatic Nitro Compounds
TABLE IV: Raman and Absorption Data for p-Nitroanisole"
I 1 Raman and Absorption Spectral Data for N,N-Dimethyl-p-nitroaniline in Various Solvents"
TABLE
430 367 429 470 460 473 805 750 91 1 680 1060 91 1 1012 778 1050 840 1470 1120 1180 1270 1126 1310
vNoz/cm-l 1332 1330 1329 1327 1330 1324 1320 1319 1319 1320 1314 1313 1313 1320 1313 1315 1312 1315 1314 1313 1312 1312
(cm-cm) 22 493
5e/103 cm-' 27.65
22 430 21 699 22 160 23 124 23 672 24 145 22 239 24 098 23 501 23 940 22 523 23 895 22 663 23 768 24035 24085 24035 23 688 24 250
26.93 26.80 26.75 25.77 25.74 25.54 25.70 25.35 25.20 25.25 25.75 25.19 25.32 24.90 24.95 25.06 24.95 24.70 24.77
1459 1370 1450 1850
1309 1310 1310 1306
24 070 23951 23 422 23 566
24.51 24.60 24.70 24.33
CrnaxILI
solvent hexane. heptane cyclohexane triethylamine butyl ether
no. 1 2 3 5 43 6 CCI, 9 dioxane 11 ethyl acetate 13 tetrahydrofuran 14 benzene 16 2-butanone 39 ethyl chloroacetate 18 acetone 10 Cl,C=CHCl 19 triethyl phosphate 17 anisole 50 trichloroacetone 30 20 CICH2CH2C1 21 CH2C12 24 pyridine hexamethylphosphor- 26 amide 27 butyrolactone 25 dimethylformamide 23 dimethylacetamide 29 dimethyl sulfoxide
sNO2
solvent hexane, heptane triethylamine butyl ether ethyl ether CC14 ethyl ether ethyl acetate tetrahydrofuran benzene 2- butanone ethyl chloroacetate acetone CI,C=CHCl triethyl phosphate anisole trichloroacetone CICH2CH2C1 CH2CI2 pyridine hexamethylphosphoramide but yrolactone dimeth ylformamide dimethylacetamide dimethyl sulfoxide
2000
TABLE III: Raman and Absorption Spectral Data for p-Nitrophenol'
no. 1 3 5 7 43 6 CCl, 9 dioxane 11 ethyl acetate 13 tetrahydrofuran 14 benzene 16 2-butanone 39 ethyl chloroacetate 18 acetone 10 CI,C=CHCI 19 triethyl phosphate 17 anisole 50 trichloroacetone 30 20 CICH2CH2Cl 21 CH2C12 24 pyridine hexamethylphosphoramide 26 27 butyrolactone 25 dimethylformamide 23 dimethylacetamide 58 29 dimethyl sulfoxide
solvent hexane. heDtane triethylamine butyl ether ethyl ether
sNo2 vN02/cm-' 32.0 1346 60.7 1338 41.1 1338 49.3 1340 54.0 1344 35.0 1344 40.0 1340 1341 49.6 1339 54.8 1342 35.0 59.3 1338 1340 47.7 48.7 1338 1340 51.7 1340 71.6 1340 46.9 56.5 1340 1340 48.9 43.0 1342 43.3 1342 76.4 1335 61.6 1334 80.0 1338 1335 80.7 77.2 1334 55.5 1337 1335 94.0
~ 0 (mol-cm) cm-l 9975 35.09 11616 32.35 11 370 33.17 11 377 33.11 9 836 34.25 10 207 34.48 10851 32.89 11 000 32.62 32.47 11 268 33.67 9 55 10788
32.68
9813 11 266 9 670 10582 10510 10 342 IO 290 11 323 9714 10770 10903 11 237
32.57 31.70 32.73 32.57 32.36 33.22 33.33 31.25 30.67 32.00 31.35 31.30
10927
31.01
'See the text or Table I for an explanation of the data listed in the six columns. t h e symmetric nitrogen-oxygen stretching vibration. Furthermore it is assumed t h a t this excited-state displacement is t h e s a m e for all of these molecules i n every solvent. A l t h o u g h this latter assumption may a t first seem unlikely, the fact that all of the d a t a i n Figure 11 fall o n a single monotonic curve is strong evidence t h a t this assumption is correct. T h e r e a p p e a r s to b e no o t h e r explanation for t h e superposition of these points f r o m different p-substituted nitrophenyl compounds taken in different solvents on t h e same curve. If t h e displacement of t h e nitrogen-oxygen
sNo, vN0,/cm-I 29.8 1344 39.3 1342 37.7 1342 47.5 1341 35.8 1341 43.0 1342 47.5 1341 49.0 1341 49.7 1341 52.5 1341 1340 55.1 56.3 1341 46.9 1340 42.2 1341 68.8 1337 44.3 1340 1341 62.7 1342 61.8 60.8 1341 57.0 1341 60.0 1339 67.8 1338
27 25 23 58 29
82.7 63.5 63.9 54.6 70.0
1340 1339 1338 1340 1338
cmax/LI
)e/1o3
(mol-cm) 11 892 11 409 11 556 11 712 11 194 11 820 11 712 11 348 11 666 10985
cm-I 34.31 33.90 33.56 33.45 33.45 33.56 33.45 32.84 32.79 32.79
11 276
32.57
11 112 11 225 10 279 11 436 11 435 11 375 11 498 10922 11 141
32.89 32.41 32.41 32.47 32.15 32.36 32.28 32.00 31.90
11 134 10 863 10936
32.00 32.05 32.05
10949
31.70
'See the text or Table I for an explanation of the data listed in the six columns.
'See Table 1 or the text for an explanation of the data listed in the six columns.
~,,,ILJ
no. 1 3 5 7 43 6 7 11 13 14 16 39 18 10 19 17 50 30 20 21 24 26
I I
!\
3
0
L,,
25
30
35
0
"e
Figure 11. Plot of the integrated Raman intensities of the spectra shown in Figures 3-10 vs. the frequency of the absorption maximum in units of 1000 cm-I. The solid circles are the values for p-nitroaniline, the open the open triangles are for pcircles are for N,N-diethyl-p-nitroaniline, nitrophenol, the small spherical points are for p-nitroanisole, and the open squares are for p-nitrophenyl ethyl ether.
bonds differed for t h e same molecule in going f r o m solvent t o solvent or differed f r o m molecule t o molecule then t h e r e should be decidedly m o r e scatter i n t h e results t h a n w e observe. The observation of equal excited-state displacements for t h e symmetric nitrogen-oxygen stretching vibrations has a n interesting corollary. The origin of this displacement almost certainly resides in t h e involvement of t h e electrons in t h e N-0 bonds in t h e II t o lI* electronic tranistion of t h e lowest excited state. T h i s involvement causes a c h a n g e (probably a reduction) i n t h e bond order of the N-0 bonds, resulting in a c h a n g e in t h e N-0 bond lengths i n going f r o m t h e ground t o t h e excited electronic state.
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The Journal of Physical Chemistry, Vol. 90, No. 11, 1986
It seems that in each of these compounds this change in bond order is the same so that the involvement of the N-O bonding electrons in the II to II* transition remains constant for this series of chemically related compounds. The single monotonic curve is also evidence for our assumption that taking the integral over the entire Raman band when it occurs as a doublet in certain solvents is justified. The origin of this doublet probably lies in an interaction with the solvent which does not involve all of the molecules so that a fraction of them are in different environments in the same solvent. The assumption of a small shift in the excited-state geometry is discussed in the derivation of eq 3 where the infinite sum over vibrational levels is truncated after the first two (0-0 and 0-1) terms. The range of validity of this approximation has been examined in detail by BlazejZ4who found that for values of displacement of the excited-state potential curve from 0 to 0.5 the small shift approximation gives values for the calculated Raman intensity which are identical with those calculated from the complete sum over all of the vibrational levels of the excited state (usually truncated after 5-10 terms). In our calculations displacement of the excited-state potential curve is taken to be the dimensionless value of the normal-mode displacement, Q, as defined by Messiah in his quantum mechanical treatment of the harmonic o s c i l l a t ~ r . ~ ~ The observation that the preresonance enhanced Raman intensity is dominated by a single excited state (in this case the lowest excited state) is very similar in form and impact to the observation of Birge and co-workers that a single intermediate-state approximation can be used to accurately describe the two-photon absorptivities of forbidden states in conjugated molecules with low-lying allowed singlet state^.^^.^^ The fact that preresonance Raman intensities and two-photon absorptivities are both dominated by contributions from a single low-lying allowed state is of course not a coincidence. Geoppert-Mayer pointed out the essentially identical quantum mechanical origin of these two spectroscopic phenomena many years ago.28 However, this appears to be the first time that preresonance Raman behavior has been dealt with in such experimental and theoretical detail. The solid curve in Figure 11 is that calculated from the eq 9 of Shorygin using a scaling constant of 0.449 X 10’. Similarly the dashed curve is obtained from eq 8 by multiplying the quantity in brackets by the scaling factor 0.657 X 10’. These scaling factors were obtained by a least-squares fit of the observed and calculated values for the Raman intensity as a function of the absorption maximum. Since there are no adjustable parameters which govern the shape of these curves, only the scaling factor which shifts the calculated curve vertically is subject to adjustment. It is evident from Figure 11 that the equation derived here fits the data to within their measurable precision and appears to be superior to the equation of Shorygin. This is borne out by statistical analysis. (24) Blazej, D. C. Ph. D. Dissertation, University of Oregon, 1978. (25) Messiah, A. Quantum Mechanics; Wiley: New York, 1965; Vol. I, p 433. (26) Biree. R. R.: Pierce. B. M. J . Chem. Phvs. 1979. 70. 165. (27) Birge; R. R.:Bennett, J. A,; Pierce, B. M.;Thomas,’T. M . J . A m . Chem. SOC.1978, ZOO, 1533; 1982, 104, 2519. ( 2 8 ) Geoppert-Mayer, M. Ann. Phys. 1931, 9, 273.
Schmid et al. The variance for each of the calculated curves gave interesting results. The variance was calculated as the sum of the squares of the differences between calculated and observed Raman intensities divided by the number of data points. This gave a value of 17.1 for eq 8 and 871 for eq 9. This large difference is due to the fact that the Shorygin equation is consistently displaced from the observed intensities throughout the region of 26 00033 000 wavenumbers. This leads to a large value for the variance. If the Shorygin curve is displaced vertically then the calculated curve is displaced above the observed data points in the upper part of the curve and the squares of the differences in observed and calculated values of the intensity become very large. Vertical displacement also displaces the Shorygin equation from the lower values so that if one minimizes the least squares of the percentage differences (i.e., the square of the differences in the observed and calculated intensities divided by their mean) then the error caused by mismatch in the high-intensity region is not so great but a large percentage error is now found in the low-intensity values. Thus we are lead to the conclusion that although the difference between the Shorygin eq 9 and eq 8 derived here is not great, the Shorygin equation does not give the correct curvature of the measured excitation profile. Furthermore the derivation of eq 8 gives a coherent theory of the origin of the remarkable monotonic curve of Figure 11 for preresonance Raman behavior. An analysis of the experimental curve using the equation derived previously by using only the resonant part of eq 8 (see ref 12 and 13) gave a poor fit. The error gets worse as the difference between the absorption maximum and the laser line widens. It can be shown that the percentage error goes between 5% at 25000 wavenumbers and almost 40% at 40 000 wavenumbers. Finally it should be pointed out that we have not made an attempt to measure and calculate the absolute scattering cross sections. In principle this information coupled with measurement of the absolute transition moment from molar absorption data could be used to determine the excited-state displacement of the nitrogen-oxygen bonds in angstroms. However, the relative intensity curve given here is sufficient to demonstrate rather conclusively that the symmetric nitrogen-oxygen stretching vibration in p-nitro aromatic compounds obey the assumptions of the theory outlined above. It certainly appears that the contribution of excited states other than the first excited state to the preresonance Raman intensity is too weak to be measured by our technique. Hence one may conclude that there does exist a quantitative theory (eq 8) for the preresonance Raman effect which may be applicable to certain types of vibrations. This relation is probably valid only for certain types of very localized vibrations which are coupled to the ground and first electronic state of a series of similar molecules.
Acknowledgment. We acknowledge the inspiration and guidance of Professor J. Brandmuller on the occasion of his 65th birthday. W.L.P. thanks the Alexander von Humboldt Foundation for a Senior von Humboldt Award. We also thank the U S . National Science Foundation and the U S . Public Health Service for partial financial support of this work. Registry No. p-Nitroaniline, 100-01-6; p-nitrophenol, 100-02-7; pnitroanisole, 100-17-4; N,N-diethyl-p-nitroaniline, 221 6-1 5-1.
