George H. Schenk and Peter A. Fryer

George H. Schenk and Peter A. Fryer. Department of Chemistry, Wayne State University, Detroit, Mich. 48202. The fact that many T complexes may exhibit...
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George H. Schenk and Peter A. Fryer Department of Chemistry, Wayne State University, Detroit, Mich. 48202 The fact that many T complexes may exhibit at least two charge transfer (CT) spectral absorption bands is important for analytical chemists in that such systems should be characterized by as many spectral bands as possible. Because the wavelength maxima of the lowest energy and higher energy CT bands vary and are not always easy to locate, it is useful to be able to utilize the Dewar molecufar orbital theory of CT spectra i n searching for multiple bands. It is possible to use both the HUckel molecular orbital method and the selfconsistent molecular orbital method of the Pariser, Parr, and Pople type to calculate energy levels for the aromatic hydrocarbon donors in applying the Dewar theory of CT spectra for this purpose. This approach was used to calculate approximate locations of both 6T bands of the complexes of aromatic hydrocarbons and 2,3-dichforo-5,6-dicyano-p-benzoquinone (DDQ). The approach correctly indicated the location of sewera1 of the lowest energy CT bands of these complexes to be in the near infrared region. MANYANALYTICAL STUDIES have been made of the charge transfer (CT) spectra of molecular donor-acceptor complexes. Some recent examples are the visual detection and mass spectrometric identification of some n - g complexes, involving amines and phenols (1) with acceptors such as 2,3-dichloro-5,6-dicyano-p-benzoquinone(DDQ), 2,4,7-trinitrofluorenone (TNF), and tetracyanoethylene (TCNE); and studies of the complexes of T N F (2, 3), TCNE (4), and 2,6-dichloroquinone-4-chloroimide(5). An important aspect of this field which analysts have neglected i s that a given complex may exhibit two, or more than two, CT bands (6, 7). It is obvious that this is important from a qualitative and a quantitative viewpoint, and that analytical studies should include a careful search for all CT bands. Fortunately, the Dewar molecular orbital interpretation (6, 7) of CT spectra may be used as an aid in searching for such bands. According to this interpretation, the energy of the highest filled molecular orbital (HFMO) and lower filled orbitals of the complexed donor, as well as that of the lowest unfilled molecular orbital (LUMO) of the complexed acceptor, should be little different than the corresponding energies of the orbitals of the uncomplexed molecules. In addition, the energy of a singlet-singlet CT transition should be close to the energy of a singlet-triplet CT transition. Accordingly, a one-electron energy diagram, as shown in Figure 1 for the aromatic hydrocarbon pyrene and any acceptor, can be used to calculate the energies of singletsinglet transitions that in many cases give rise to two (or more) CT bands. (I) 0.Hutzinger, ANAL.CHEM., 41, 1662 (1969). (2) H. T. Gordon and M. J. Huraux, ;bid., 31, 302 (1959). (3) 6. H. Schenk, P. W. Vance, J. Pietrandrea, and C. Mojzis, ibid., 37, 372 (1965). (4) G. H. Schenk, M. Santiago, and P. Wines, ibid., 35, 167 (1963). (5) J. H. Ross, ibid.,40, 2138 (1968). (6) M. J . S. Dewar and A. R. Lepley, J. Amer. Chern. Soc., 83, 4560 (1961). (7) A. R. Lepley and C. C. Thompson, ibid., 89, 5523 (1967). 1694

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This interpretation must be used with care because of several reasons. In many cases only one band may be observed when more are predicted from the calculations. The calculations apply to isolated molecules, but solvent shifts of the CT band maxima can be appreciable for quantitative comparisons. Finally there is the possibility of interaction between CT states with locally excited states of the donor or of the acceptor, which again could alter the energy (8) of the CT band. Nevertheless, as will be shown in the discussion of the results, the Dewar interpretation is a definite aid in helping one to decide to search for low energy bands in the 750 to 1000 nm region, or even above 1000 nm, a region inaccessible to many common spectrophotometers. It can also assist in searching for higher energy bands. Workers have utilized two different methods for calculating the energies of the HFMO and lower orbitals of the donor: the Wiickel molecular orbital (HMO) theory, and the selfconsistent molecular orbital method of Parker, Parr, and Pople (PPP). In the latter, if only ground state interactions are considered, the equation relating the energy of any charge to the energy of the LUMO of the actransfer band, AEoL, ceptor, Bj, and the energy of an occupied donor orbital, A $ ,i s simply (7) :

AEct

=

Bj

- AI

(1)

Lepley and Thompson (7) have calculated Al values for a number of aromatic hydrocarbons using the PPP method (termed the PPPl method in their paper). However, the Bj value for a given acceptor must be determined graphically after spectrophotometric measurement of the CT bands of a large number of complexes. However, one can make an estimate of it by locating the wavelength maximum of one or two complexes using a typical donor such as pyrene or naphthalene. Although the energy of B j is usually expressed in eV, it is convenient to express it in cm-1. If the more familiar H M O theory is used, it can be seen from Figure 1 that the energies of the first (lowest energy) and second (higher energy) GT bands are given by: AEotl

=

(x, - xi)@

(2)

(3) A E t , = (xj - yi)P (The coefficients and p are the usual symbols used in HMO theory and are defined in the caption of Figure 1.) Hence to calculate the energies and locations of CT bands, P and the coefficients in Equations 2 and 3 must be known. The coefficients of aromatic hydrocarbon donors are available in several standard monographs (9); three such coefficients are (8) R. S. Mulliken and W. R. Person, “Molecular Complexes,” Wiley-Interscience, New York, 1969, Chapter 14. (9) A. Streitwieser, Jr. and J. I. Braurnan, “Supplemental Tables of Molecular Orbital Calculations,” with @. A. Coulson and A. Streitwieser, Jr., “Dictionary of n-electron Calculations,” Pergamon Press, New York, 1965, and E. Heilbronner and P. A.

Straub, “Muckel Molecular-Orbitals,” Springer-Verlag, New York, 1966.

ANALYTICAL CHEMISTRY, VOL. 42, NO, 14, DECEMBER 1970

Figure 1. A one-electron energy diagram showing possible CT electronic transitions of pyrene-acceptor complexes

At the left are the HMO calculated energies of the three highest filled orbitals and the three lowest unfilled orbitals of pyrene. The 01 and p terms are, respectively, the coulomb and resonance integrals for sp2 hybridized carbon. In general, the energy of the HFMO of a donor molecule is LY f x,p (x, = 0.445 for pyrene), and the energy of the next highest filled (penultimate) molecular orbital of a donor molecule is a: y e p ( y % = 0.879 for pyrene). Similarly, the energy of the LUMO of an acceptor molecule is LY - x,p in general. The transitions indicated by arrows are: (1) The lowest energy CT transition that can occur in any donoracceptor complex, such as a pyrene-acceptor complex. For any pyrene-acceptor complex, the HMO energy of the CT transition will be ( x , - O.445)p. Both p and the (x, - 0.445) term are negative, giving a positive energy after multiplication (2) The higher energy CT transition that may occur in any donoracceptor complex, and that does appear to occur in DDQ complexes, such as DDQ-pyrene, and in TCNE complexes. For any pyreneacceptor complex, the HMO energy of this transition will be ( x , - 0.879)p. Both terms are negative, giving a positive energy after multiplication (3) The higher energy CT transition observed in TCNB complexes instead of transition 2. This transition is possible in DDQ complexes but has not been observed, probably because it occurs among the intense ultraviolet absorption bands of DDQ

+

t

E

a-l.ooop a -0.879Q a

-0.44 50

g

+0.44 5Q

a+0.8790 U+I

.ooop Pyr ene

a 6

Any c e ptor

Table I. Estimated Energies ( x @ ) of the LUMO of Various Acceptors Complexed with Naphthalene and Pyrene, Using p = -24,700 cm-1 (-3.06 eV) xip = 0.618 p (naphthalene), x i p = 0.445 p (pyrene) x j p of LUMO of acceptor Energy of CT Acceptor Donor CT band location band in p Estimated Literature value5 TCNE Naphthalene 18,200cm-1(12) 0.737/3 -0.119 p -0.05 p (7) TCNE Pyrene 13,800 cm-l(12) 0.559 /3 -0.114 /3 TNB Naphthalene 27,400(6) 1.109/3 -0.491 p -0.46 /3 (6) TNB Pyrene 22,500 (6) 0.911p -0.406 p TNF Naphthalene 23,300(9) 0.943 p -0.325 -0.30/3 (9) TNF Pyrene 19,200(9) 0.777p -0.332 p TCNBa Naphthalene 24,500(10) 0.992p -0.374 p -0.335 p (10) TCNBa Pyrene 20,100 (10) 0.814p -0.369 p a TCNB is pyromellitonitrite or 1,2,4,5-tetracyanobenzene, The number of complexes used to determine the literature value was: for TCNE, 16; for TNB. 22; for TNF, 23; and for TCNB, 12. shown for pyrene in Figure 1. However, p is essentially a least squares slope evaluation in the literature, and as such has little meaning. However, if it is understood that a value for p is to be used simply for calculations to aid in searching for CT bands, then there is some validity to assigning a value to p. For the purpose of calculating locations of CT bands, a judicious choice of the value of p must be made. This choice is best made from the more numerous /3 values found from studies of the lowest energy CT bands, even though Lepley and Thompson (7') have found the p values of the lowest energy and higher energy CT bands of TCNE complexes to be somewhat different. A logical value for p is -3.06 eV (-24,700 cm-1) which is the mean of the following reported /? values of complexes for the respective acceptors: -2.93 eV for TCNE (7), -3.00 eVfor trinitrobenzene (61, -3.11 eV for T N F (IO), and -3.21 eV for pyromellitonitrile (11). [The p value of -3.06 eV for TCNE complexes reported by Dewar and Rogers (12) was not used because it does not reflect the more recent data used in obtaining the -2.93 eV value.] Unfortunately, x j is not always readily calculated by the (10) A.R. Lepley, J. Amer. Chen?. Sac., 84, 3577 (1962). (11) A. Zweig, J. E. Lehnsen, W. G. Hodgson, and W. J. Jura, ibid.,85, 3937 (1963). (12) M. J. S.Dewar and H. Rogers, ibid.,84, 395 (1962).

HMO method and must be determined graphically after spectrophotometric measurement of the CT bands of a large number of complexes of a given acceptor. However, one can again make estimate of it by locating the wavelength maximum of the lowest energy CT band of one or two complexes, using a typical donor such as pyrene or naphthalene. By substituting the corresponding energy of the CT band in eV in Equation 2, along with the value of -3.06 eV for 8, one can obtain an estimate of xg. T o give some indication of the possible deviation that might arise from using different donors with the same acceptor I O estimate xlrsome typical calculations have been made with acceptors using both naphthalene and pyrene as donors. The location of the CT bands of TCNE were taken from the paper of Merrifield and Phillips (13). The data are shown in Table I. The deviation between xg values calculated with naphthalene and pyrene is small, and the agreement is also reasonable with literature values of xj. EXPERIMENTAL Reagents. The aromatic hydrocarbons were sublimed prior to use, except that azulene, 1,2-benzpyrene (both from Rutgerwerke A.G.) and 1,2-benzanthracene (from Eastman (13) R. E. Merrifield and W. D. Phillips, ibid., SO, 2778 (1958).

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Table 11. Comparison of the Observed and Calculated Locations of the Lowest Energy CT Band Maxima of Complexes of DDQ and Aromatic Hydrocarbons Aromatic Orbital energy of hydrocarbon HFMO of donor Theoretical dE,t(l) Calculated AE,tcl) (cm-l) (donor) WMO (p) PPP ( e ~ ) 4 HMO PPP (eV) HMOb PPPC Observed AE,tcl) Anthracene 0.414 1.576 -0.444 /3 1.38 I1,OOO 11,100 11,500 Azulene 0,477 1.562 -0.507 6 1.40 12,500 11,300 13,900 1.47 11,900 11,900 12,100 1,2-Benzanthracene 0.452 1 494 -0.482 /3 1,ZBenzpyrene 0.497 -0.527 p ... 13,000 ... 12,800 Biphenyl 0.705 0: 682 -0.735 fl 2.28 18,200 18,400 17,800 -0.S50 p 1.61 13,600 13,000 14,600 Chrysene 0.520 1.347 ... -0.648 /3 .., 16,000 16,900 Fluoranthene 0.618 Naphthalene 0.618 0.980 -0.648 fl 1.98 16,000 18,000 16,300 Perylene 0.341 1,862 -0.377 p 1.10 9,300 8,870 9,900 Phenanthrene 0.605 1.076 -0.635 /3 1.88 15,700 15,200 17,400 Pyrene 0.445 1.603 -0.475 6 1.36 11,700 11,000 11,800 g-Terpheny1 0.593 1.110 -0.623 /3 1.85 15,400 14,900 15,700 a Correspond to PPPl calculated energies of reference 7, Deviations from observed calculate the wavenumber, or wavelength. (For example, the energy 0,445 p. By referring to of the HFMO of pyrene is a Figure 1, it can be seen that the energy of transition 1 will be -0.475 p, and the location of the lowest energy CT band will be 11,700 cm-1 or 850 nm.) These calculations enabled us to make careful spectral searches in the appropriate regions to locate both the lowest energy and the higher energy CT bands o f the complexes. Lowest Energy CT Rands. Table II lists, side by side, the theoretical energies of the lowest energy CT transitions calculated by the HMO theory and by the PPP method, as well as the calculated locations o f the lowest energy CT bands of the DDQ complexes. Although three significant figures are given for the wavenumber ( ~ m - ~of) each band, only twofigures are infendedto be significant because of solvent shifts and other reasons mentioned above. The third figure is included merely to indicate that there are small differences in the locations of the bands calculated by the HMO and PPP methods. As indicated in the footnotes o f Table 11, the relative deviation of the locations calculated by either method from the observed locations is less than 6 except in certain cases. Thus the PPP method i s not superior to HM theory in the case of the low energy CT bands of DD complexes; in addition, HMO energies are available ( 9 ) for a great many more molecules at the present time. A f i n d point of major importance is just how broad (or “flat-topped”) the lowest energy C T bands are; this will give some perspective to the variation between the observed and calculated locations. This point will be discussed later with reference to both the lowest energy and higher energy CT bands. Figure 2 shows the lowest energy, and the higher energy, CT bands of four DDQ-aromatic hydrocarbons complexes. It is important to note that all of the lowest energy CT bands

ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970

+

W

0 2

U

m

P 0

-8enzan thraceno

v)

m

a

700 800 WAVELENGTH

600

900

1000

Figure 2. CT spectra of the DDQ complexes of pyrene, 1,2-benzanthracene9anthracene, and perylene. The DDQ-perylene complex exhibits only one CT band at 1010 nm (9900 ern-'), but the other three DDQ complexes each exhibit two CT bands, as follows: DDQ-pyrene at 530 (18,900 cm-I) and 847 nm (11,800 em-I), DDQ-1,2-benzanthracene at 595 (16,800 cm-I) and 830 nm (12,100 crn-I), and DDQ-anthracene at 515 (19,400 cm-I) and 870 nm (11,500 cm-')

Table 111. Comparison of the Calculated and Observed Locations of the Higher Energy CT Bands of DDQ-Aromatic Hydrocarbon Complexes Aromatic Orbital energy of hydrocarbon second HFMO of donor Theoretical hE,t:ll Calculated AEot;l) (cm-l), Observed AE,tc2) (donor) HMO ( p ) PPP (ev). HMO PPP(eV) NMOb PPPC Anthracene 1.000 0.314 -1.03Op 2.65 25,400 21,400 19,400 1,2-Benzanthracene 0.715 0.828 -0.745 p 2.13 18,400 17,200 16,800 1,ZBenzpyrene 0.718 ... -0.748 fl ... 18,500 ... 16,200 1,000 0 020 -1.030p 2.94 25,400 23,700 22,600 Biphenyl 2.22 20,300 17,900 16,500 Chrysene 0.792 0.742 -0.822 p 1.000 0.201 -1.03Op 2.76 25,400 22,300 20,600 Naphthalene Pyrene 0.879 0.584 -0.909 p 2.38 22,400 19,200 18,900 1.000 0.056 -1.03Op 2.90 25,400 23,400 19,000 p-Terpheny I a Corresponds to PPPl calculated energies of reference 7. Mean deviation from observed = 20%. Only two of the three figures for wavenumbers should be considered significant. Deviation from observed < 10 %: except pterphenyl(23 %). Only two of the three figures for wavenumbers should be considered significant. I

in Figure 2 are located beyond the range of many ultravioletvisible spectrophotometers. Indeed, the lowest energy CT band of DDQ-perylene is located above 1000 nm, beyond the range of all such spectrophotometers and accessible only to spectrophotometers, such as the Cary 14, equipped t o operate in the near infrared region. Thus it is very important to be able to calculate the location of the lowest energy bands so that the proper region of the spectrum may be scanned. A recent but limited survey (15) of the CT bands of a few D D Q complexes (using the implications of the Mulliken theory of CT) is illustrative of the consequences of not applying the Dewar MO theory a t the same time. Only one CT band (at 540 nm) was reported for the DDQ-pyrene complex, as well as for some of the other complexes studied.

It is obvious that this band is too far away from the calculated locations of 850 nm (HMO), or 910 nm (PPP), of the lowest energy CT band to be that band. Instead, the calculated locations of 450 nm (HMO), or 520 nm (PPP), of the higher energy band (Table 111) indicate that the reported 540-nm band is really the higher energy band. The spectrophotometer used i n this survey (15) unfortunately could not scan at wavelengths longer than the visible region. Higher Energy CT Bands. For acceptors like DDQ (and TCNE), a second, or higher energy CT band will arise from a transition such as transition 2 in Figure 1. All that is needed to calculate the energies in this case are the energies of the penultimate filled orbital of the aromatic hydrocarbon donor (Table III), the energy of the LUMO of DDQ used -~above, the Equation 1 for the PPP method, or Equation 3 for the HMO calculation. Table 111 lists, side by side, the (15) R. D. Strivastava and G. Prasad, Spectrochim. Acta, 22, 1869 (1966). theoretical energies of the higher energy CT transitions ~

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Table IV. Range of Absorption Maxima of CT Bands of DDQ Complexes in Terms of “Energy” Units and Wavelength Lowest Rangeazb energy (1) of maxima and higher in terms of energy (2) “energy” Rang@ of Donor CT bands (cm-1) : , , ,A nm Anthracene 1 550 870 i 20 2 1000 520 + 15 Azulene 1 200 720 i: 5 1,2-Benzanthracene 1 400 830 i 15 2 600 600 i 10 1 ,ZBenzpyrene 1 250 780 L 8 2 300 620 i: 5 Biphenyl 1 250 560 f 5 2 § 50 440 i 5 Chrysene 1 550 680 (s) i 15 2 3 50 610 & 8 Fluoranthene 1 400 590 f 8 Naphthalene 1 350 610 & 5 2 450 490 i: 5 7 50 1010 f 30 Perylene 1 Phenanthrene 1 450 580 f 8 Pyrene 1 350 850 i 12 2 550 530 f 8 p-Terphenyl 1 400 640 L 8 2 400 530 (s) i. 5 a Location of CT bands in cm-1 in Tables I1 and 111. Range is defined as the bandwidth at 0.01 absorbance unit below the absorbance at . , , ,A

calculated by HMO theory and by the PPP method, as well as the calculated locations of these bands. As for the lowest energy bands, the third significant figure is only included to indicate that there are small differences in the locations of the bands as calculated by the H M O and PPP methods. As indicated in the footnotes of Table 111, the mean relative deviation of locations calculated by the H M O method from the observed locations of the bands is about twice that of the locations calculated by the PPP method. Thus, the PPP method is superior to H M O theory in the case of the higher energy bands. Again, a good example is the reported (15)CT band of DDQ-pyrene at 540 nm: application of the PPP method gave a calculated location of 520 nm (19,200 cm-1) compared to the H M O calculated location of 450 nm (22,400 cm-l). The PPP calculations clearly indicate that this band is very likely a higher energy CT band, and certainly not the lowest energy CT band. Two other general points should also be mentioned. Although a higher energy CT band is expected and can be predicted in general, a higher energy band is not always found. For example, only one C T band was found for the D D Q complexes of azulene, fluoranthene, phenanthrene, and perylene (Table 111). It can be seen in Figure 1 that the lowest energy CT band of perylene is quite broad, with no definable higher energy band apparent. Lepley and Thompson (7) also found no higher energy band for the TCNE complexes of azulene and perylene, but did report a higher energy band for phenanthrene. Second, one should verify that the higher energy band does not arise from a transition involving the HFMO of the donor and a higher energy unoccupied orbital of the acceptor (transition 3 in Figure 1). Such a possibility has been ruled out for TCNE complexes (16) A. Zweig, Tetrahedron Lett., 2, 89 (1964). (17) S . Iwata, J. Tanaka, and S . Nagakura, J. Amer. Chem. Soc., 88, 894 (1966). 1698

(16), but has been demonstrated (27) for complexes of 1,2,4,5tetracyanobenzene (TCNB), or pyromellitonitrile. In evaluating the possibility of a transition from the HFMO of the donor to a higher energy unoccupied orbital of TCNB as acceptor, Iwata, Tanaka, and Nagakura (17) found that the frequency difference (Act) between the lowest energy and higher energy bands for a series of aromatic donors complexed with TCNB was almost constant, ranging from a Act of 6300 cm-l to 6700 cm-l. (This frequency difference should roughly be proportional to the energy difference between the two unoccupied orbitals of the acceptor shown in Figure 1.) In contrast, they calculated a range of from 5200 cm-1 to 13,100 cm-l for Act for TCNE complexes. We find a range of Act values of from 1900 cm-1 for the DDQ-chrysene complex to 7900 cm-1 for the DDQ-anthracene complex. It appears very likely that DDQ is like TCNE in that the higher energy CT transition does not involve a higher energy unoccupied orbital of DDQ, but instead involves the penultimate occupied orbital of the aromatic hydrocarbon donor. This does not imply that for DDQ, transition 3 in Figure 1 could not occur, but only that it is of much higher energy than transition 2 and would therefore occur in the ultraviolet region where intense DDQ absorption would make it almost impossible to observe. Bandwidth at CT Maxima. C T bands are normally rather broad; it is thus important to have a measure of just how broad the observed bands are at the maxima to give some perspective to the deviation between the observed and calculated locations. In Table IV we have first listed the range of each C T maxima in terms of wavenumbers (“energy”). The range is arbitrarily defined as the length of a line (“bandwidth”) drawn at 0.01 absorbance unit below the absorbance at the band maxima. Most of the ranges fall in a span of 350-600 cm-l, but both anthracene and perylene exhibit much broader bands. Because most spectrophotometers utilize wavelength instead of wavenumbers, we have also translated the wavenumber range into a slightly different type of wavelength range in Table IV. This is stated in terms of the wavelength of the C T maxima =t half the bandwidth (in wavelength). For example, for the higher energy CT band of pyrene, which we obierved at 530 nm, the range about the maxima is from 522 to 538 nm. In this case, the range happens to include the PPP calculated C T maxima of 530 nm, and thus describes in a more quantitative way the deviation between the observed and calculated CT maxima. Results of Dewar MO Treatment. When the H M O COefficient, X ~ of , the donor is plotted against the energy (A&) of the donor-DDQ CT band, according to Equation 1, a fair straight line results. The correlation coefficient, an indication of the variation from linearity, is 0.971. (A perfect linear correlation would give a correlation coefficient of 1.OOO.) The slope of the plot yields a value of ,8 = -3.20 eV, which agrees favorably with the values of -2.93 eV, -3.00 eV, -3.11 eV, and -3.21 eV found in the similar treatment of different acceptor-donor complexes. The intercept on the xi-axis yields a value of -0.026 p for x j which is in excellent agreement with the value of x j = -0.030 ,8 used as an estimate in making predictions of the wavelength maxima of different DDQ complexes. The values of /? and x1 were determined by a least squares treatment. RECEIVED for review April 20, 1970. Accepted August 31, 1970.

ANALYTICAL CHEMISTRY, VOL. 42, NO. 14, DECEMBER 1970