2498
J. Phys. Chem. 1984, 88, 2498-2504
Cesium Pentacyanopropenide. Crystal Structure, Vibrational Spectra and Assignments, and Vibronic Structure In the Visible Emission Spectrum K. W. Hipps,*+Urs Geiser, Ursula Mazur, and Roger D. Willett Department of Chemistry and Chemical Physics Program, Washington State University, Pullman, Washington 991 64-4630 (Received: August 30, 1983)
The structure of the free pentacyanopropenide ion (CsN5-),a closed-shell ion, is determined by minimization of the ab initio energy at the STO-5Glevel. The crystal structure of the cesium salt is also determined and compared with the SCF results. The experimentally determined symmetric and asymmetric part of the Raman scattering of the pentacyanopropenide (PCP) anion is reported, as is the IR spectrum. The Raman spectrum of PCP is resonance enhanced and some variations in relative intensity with excitation wavelength are observed. The vibrational results are analyzed in terms of a semiempirically scaled ab initio forced field. The resulting normal coordinates, and the changes in bond order with electronic excitation calculated from Hiickel molecular orbital theory, are used to predict the vibronic structure observed in the visible emission spectrum of PCP. This latter procedure works quite well considering the level of approximation used.
Introduction
SIAN-76,l6 will be used to calculate the equilibrium geometry and
The structural and spectroscopic characterization of percyanocarbanions is an area which has received increasing attention. The early synthetic work of Middleton and his colleagues at Du Pont during the middle and late 1 9 5 0 ~ 'was - ~ followed by an accelerating interest in the characterization of these materials by physical method^.^-'^ The range of cyanocarbanions available for study is tremendous. It extends from the smallest, tricyanomethanide, to very large anions such as azotetracyanocyclopentadienide. All of these are closedshell ions which form stable salts and metal complexes. Until very recently, however, the visible and near-UV fluorescences (originally observed by Middleton) of many of the percyanocarbanions had not been studied to any degree. To date, the most detailed studies have concerned the pentacyanopropenide anion (PCP), CsN5-. Thus, it serves as a model for the properties and bonding of the entire series. Pentacyanopropenide is an intense Raman scatterer; both preresonance and direct-resonanceenhancement are observed. The intensity of the Raman scattering process and the stability of the ion are such that the Raman spectrum of a monolayer of the ion can be observed on an aluminum mirror.14 Alkali-metal salts of ' ~ low PCP fluoresce strongly under blue or UV e ~ c i t a t i o n . ' ~At temperature, the cesium salt exhibits a remarkably structured fluorescence in which both electronic-lattice and electronic-vibrational interaction play a r01e.l~ While crystal structures for simple metal salts of PCP have not been previously reported, structures of metal complexes containing PCP have appeared.s-10 These structural studies indicate that PCP may be incorporated into solids either as an N-bonded metal complexs or as a count e r i ~ n . ~When . ' ~ PCP acts as a counterion, it is very nearly planar. The deviations from planarity are primarily due to crystal packing forces. Carbon-13 N M R data support the assumption of planar geometry in so1ution.l2 The planarity of the ion is usually attributed to the very strong R orbital resonance stabilization. The goal of the present article is to (1) provide structural and vibrational data about the PCP ion, (2) analyze the vibrational data in terms of a simple molecular force field in order to provide insights into the bonding in ions of this type, and (3) utilize this information to clarify the nature of the strong electronic-vibrational coupling observed in the fluorescence of the PCP ion. In order to fully achieve this goal, we will combine experimental data with two theoretical devices. The experimental data utilized will be the IR and polarized Raman vibrational spectra, X-ray structural data, and the electronic emission spectrum. The theoretical devices will be Hiickel MO and SCF calculations. Hiickel molecular orbital theory will be used to determine bond orders in the ground and first excited electronic states of the ion. Self-consistent field theory, in the form of the program GAUS-
the ab initio force constants required for a single valence force type potential. These ab initio values are larger, and in the case of the STO-SG basis used here they are significantly larger, than the actual force constants. A scaling m e t h ~ d , ' ~ Jhowever, ~ - ~ ~ will allow their use while maintaining the number of adjustable parameters at a satisfactory level. Thus, the present paper is a synthesis of experimental and theoretical methods which yields, we believe, a whole which is greater than the sum of its parts. The primary goal of this work is to assign and interpret experimental data. The course that we follow is not the conventional one. We propose neither to make state-of-the-art calculations nor to completely specify the problem by empirical methods. Thus, Hiickel MO theory is used whenever experience dictates that its results are reliable. Thus, only the in-plane motions of the PCP ion are considered in detail because only for these are the experimental data sufficiently accurate to justify consideration. In a perfect universe where all parameters could be exactly determined by either experimental or theoretical methods only, the present treatment would be inappropriate. For the present, however, neither purely theoretical nor purely experimental methods can be successfully used to completely understand a molecule of the size of PCP without a prohibitive investment in
12914
Alfred P. Sloan Fellow.
0022-3654/84/2088-2498$01.50/0
(1) W.J. Middleton, U S . Patents 2 766243 and 2 766 246, 1976. (2) W. J. Middleton, E. L. Little, D. D. Coffman, and V. A. Engelhart, J. Am. Chem. SOC.,80, 2795 (1958); see also other papers in this issue. (3) D.A. Long, R. H. G. Carrington, and R. B. Gravenor, Nature (London), 196,371 (1962). (4) M.S. Khatkale and J. P. Devlin, J . Phys. Chem., 83, 1636 (1979). (5) J. J. Hinkel and J. P. Devlin, J. Chem. Phys., 58,4750 (1973). (6)F. A. Miller and W. K. Baer, Spectrochim. Acta, 19, 73 (1963). (7) R. H.Boyd, J. Phys. Chem., 67,737 (1963). (8) M.I. Bruce and R. C. Wallis, J. Chem. Soc., Dalton Trans., 2205 (1981). (9)G.A. Sim and D. 1. Woodhouse, J. Chem. SOC.,Dalfon Trans., 629 (1979). (10)W.P. Jensen and R. A. Jacobson, Inorg. Chim. Acta., 50,189 (1981). (11) C. E. Looney and J. R. Downing, J. Am. Chem. SOC.,80, 2840 (1958). (12) U. Mazur and K. W. Hipps, J. Phys. Chem., 86,2854 (1982). (13) K.W.Hipps and R. D. Poshusta, J . Phys. Chem., 86,4112(1982). (14) K. W. Hipps and J. W. Keder, J . Phys. Chem., 87, 3186 (1983). (15) U. Mazur and K. W. Hipps, J. Phys. Chem., 87,4641 (1983). (16) QCPE program no. 391,Indiana University, Department of Chemistry.
(17)C.E. Blom and C. Altona, Mol. Phys., 31, 1377 (1976). (18) C. E. Blom and C . Altona, Mol. Phys., 33, 875 (1977). (19) B. I. Swanson, T. H. Arnold, and Y. Yamagouchi, J . Mol. Strucr., 78, 125 (1979). (20)B. I. Swanson, T. H. Arnold, M. J. S . Dewar, J. J. Rafalko, H. S. Rzepa, and Y. Yamagouchi, J. Am. Chem. SOC.,100,771 (1978). (21) P. Pullay, G.Fogarasi, and J. E. Boggs, J . Chem. Phys., 74, 3999 (1981). (22)S.Von Carlowitz, W. Zeil, P. Pullay, and J. E. Boggs, J . Mol. Struct., 87, 113 (1982).
0 1984 American Chemical Society
Cesium Pentacyanopropenide
The Journal of Physical Chemistry, Vol. 88, No. 12, 1984 2499
TABLE I: Selected Bond Lengths and Angles of the Pentacyanopropenide Anion bond length, 8, cor for bond exptl thermal motion calcd' 1.142 (7) 1.167 (7) 1.159 1.152 (7) 1.180 (7) 1.159 1.128 (7) 1.167 (7) 1.157 1.134 (6) 1.165 (7) 1.159 1.134 (7) 1.157 (7) 1.159 1.411 (7) 1.414 (8) 1.439 1.432 (8) 1.426 (7) 1.441 1.465 (7) 1.454 (7) 1.480 1.416 (8) 1.418 (7) 1.439 1.441 (8) I .44l 1.434 (7) 1.401 (7) I .396 1.395 (7) 1.397 (7) 1.396 1.398 (7)
bond angle, deg exvtl calcd' 178.5 (6) 176.5 179.7 (6) 178.9 179.6 (6) 180.0 176.7 (5) 176.5 179.6 (7) 178.9 124.0 (4) 123.8 119.3 (5) 120.7 116.7 (4) 115.6 1 1 5.2 (4) 115.0 115.1 (4) 115.0 129.7 (4) 130.0 123.0 (4) 123.8 120.5 (5) 120.7 116.5 (4) 115.6
angle N(l)-C(l)-C(6) N(2)-C(2)-C(6) N ( 3)-C( 3)-C( 7) N(4)-C( 4)-C( 8) N (5)-C (5)-C( 8) C(l)-C(6)-C(7) C(2)-C(6)-C(7) C(l)-C(6)-C(2) C(3)-C(7)-C(6) C( 3)-C(7)-C( 8) C(6)-C(7)-C(8) C(4)-C(8)-C(7) C( 5)-C( 8)-C( 7) C(4)-C( 8)-C( 5)
RSCF. N [31
time and money. Thus, in the context of optimum allocation of finite resources, the present synthesis of experimental and theoretical methods is of value. The semiempirical procedure used here has been extensively tested and proven in assigning vibrational s p e ~ t r a . ' ~ The , ~ ~development -~~ used here for the prediction of the vibronic structure is also well d o c ~ m e n t e d . ~Our ~ - ~purpose, ~ therefore, is not to prove new theoretical methods but to use a selection of successful techniques to analyze the data presented. Experimental Section Raman. Raman spectra were measured with an ISA Ramanor spectrometer (1-m double monochromator having a dispersion of 2.5 A/mm). The 5145- and 4880-A lines of a Spectra-Physics argon ion laser were used for excitation. The polarization of the laser was rotated with a device provided by Lexel Corp. The scattered radiation was collected at 90° to the excitation and passed through a polarization scrambler prior to entry into the monochromator. Solid samples were measured as powders in capillary tubes. Solid PCP will photolyze in a sufficiently intense laser beam; thus, 4880-A radiation power should be maintained below 30 mW. Polarized solution spectra were obtained in a rectangular 0.5-mL cell made from strain-free quartz. The solutions were approximately 40 mg of cesium pentacyanopropenide per mL of acetone. Slit widths varied from 0.2 to 0.4 mm. Spectral scans were controlled and stored by a Cromemco microcomputer. These data were then transmitted to an LSI-1 l MINC computer where they were transformed to yield the symmetric and asymmetric components (in the case of polarized solution data) and plotted (in all cases). IR. Infrared spectra of CsPCP pressed into KBr pellets and in petroleum jelly mulls were measured on a Perkin-Elmer 283B spectrometer. N o cation-exchange effects were observed in the KBr pellets. Spectral resolution was 5 cm-' or less throughout the region. A far-IR spectrum was also measured in the 40030-cm-' region by using a petroleum jelly mull of CsPCP on a polyethylene window. A Perkin-Elmer FIS-3 was used to make these FIR measurements. Emission. Visible emission spectra were measured on a previously described instrument15 using broad-band UV excitation. The spectrum reported here is that of a microcrystalline powder at 3 K. For an extensive discussion of the experimental parameters the reader should consult ref 15. (23) J. D. Roberts, "Molecular Orbital Theory", W. A. Benjamin, New
York, 1962. (24) 9. W. Cooper, "Spectroscopic Techniques for Organic Chemistry", Wiley, New York, 1980. (25) K. W. Hipps, G . A. Merrell, and G . A. Crosby, J . Phys. Chem., 80, 223 (1976). (26) Subsequent to submission of this paper, a similar treatment of the vibronic structure in the electronic absorption spectrum of the TCNQ radical anion was presented by I. Zanon and C. Pacile, J . Phys. Chem., 87, 3657 (1983).
' 'Ye Figure 1. ' Atomic labeling used in characterizing the pentacyanopropenide ion.
X-ray Crystallography. A canary-yellow rhomboidal platelet of 0.29 X 0.40 X 0.04 mm was studied at 292 K by the Weissenberg film method and on an automated Picker 4-circle diffractometer usin a 8-28 scan. Zirconium filtered Mo Ka radiation (0.7107 ) was used and the intensities were corrected for absorption, and Lorentz and polarization factors. A total of 2372 reflections were collected with 28 I54.0°; all values of h and all positive values of k and 1 (including zero) in this range were viewed. After removal of systematic absences, 2258 reflections were retained for analysis. The programs used are part of a local libraryeZ7 Cesium coordinates were found from a Patterson synthesis and by direct methods. Carbon and nitrogen atoms were located from subsequent difference Fourier maps. Scattering factors from standard sources were used.z8~29The cesium atom scattering factors were corrected for the real part of the anomalous scattering. Three scale factors, coordinates, and anisotropic temperature factors were refined by using the full-matrix least-squares technique. The R values were calculated omitting reflections with F < 2a(F). The final conventional R values was 0.047 and the weighted R value was 0.040. The 200, -200,202, and -202 peaks are obviously affected by secondary extinction, but their omission from the refinement caused changes in all coordinates and thermal parameters of no more than half of a standard deviation. Materials. CsPCP was prepared and purified by previously published method^.^^*^^ Reagent-grade acetone was stored over zeolite beads to remove water, but was otherwise used as furnished by Baker Chemical Co. Single crystals were grown from acetone solution.
i
(27) D. R. Bloomquist and R. D. Willett, J . Am. Chem. SOC.,103, 2615 (1982). (28) "International Tables for X-Ray Crystallography", Vol. 111, Knycch Press, Birmingham, England, 1962. (29) D. T. Cromer and J. T. Waber, Acta Crystallogr. 18, 104 (1965).
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The Journal of Physical Chemistry, Vol. 88, No. 12, 1984
Hipps et al. TABLE III: Calculated Bond Order and Bond Displacement Changes for the ‘A, to ‘BzTransition of the Pentacyanopropenide Ion bond order change in coordinatea difference coordinateb -0.0151 0.0008 -0.01 5 1 0.0008 -0.1074 0.0060 0.0026 -0.0005 0.0026 -0.0005 0.1423 -0.0270 -0.1579 0.0300 -0.50‘
+0.25 The calculation assumes C,, symmetry and only inequivalent coordinates are shown. Distances are in angstroms and angles in degrees. ‘The use of a bending displacement is discussed in the text. Figure 2. Segment of a sheet parallel to the (0,1,0) and (l,O,l) directions in cesium pentacyanopropenide. Out-of-plane cesium atoms are indicated by a dot. TABLE 11: Least-Squares Plane Fitted to the Anion in CsPCP atom“ distance. %, atom“ distance, %, N(1) 0.1825 (57) C(3) 0.0066 (53) N(2) -0.1231 (57) C(4) -0.0955 (54) 0.0012 (56) C(5) 0.0488 (58) N(3) N(4) -0.2017 (51) C(6) 0.0228 (52) N(5) 0.0835 (52) C(7) 0.0193 (42) CU) 0.1008 (56) C(8) 0.0098 (52) C(2) -0.0550 (57) In-plane. All atoms of the anion were fitted to the plane 0.7960~ X b).
- 0.0081y - 0.60522 - 1.9218 = 0.0, where xlla, yllb, zll(a
Crystallographic Results The crystals studied formed in rhomboidal platelets having limiting faces (-1,2,1), (1,2,-1), (O,O,l), and their inverses. They are monoclinic, belonging to space group P2, c, with unit-cell parameters, a = 8.285 (9) A, b = 13.050 (6) , c = 9.000 (11) A, and ,f3 = 95.44 (9)’. There are four formula units per unit cell and the calculated density (2.05 g/cm3) agrees with the measured value (2.2 (2) g/cm3). The final atomic positional and thermal parameters, the structure factors, and a drawing of the unit cell are available as supplementary material (see paragraph at end of text regarding supplementary material). Relevant bond lengths and angles are collected in Table I, and the atomic labels used are identified in Figure 1. The structure of cesium pentacyanopropenide consists of sheets parallel to the b axis and the (l,O,l) crystallographic direction. A segment of one such sheet is shown in Figure 2. The distance between sheets has an average value of 3.19 A. The structure seems to be predominantly ionic, with eight nearest neighbors of opposite charge. The cation has nine nearest-neighbor nitrogen atoms (at an average distance of 3.39 A), since one of the eight PCP ions ‘‘coordinates” in a bidentate fashion. The anion has four cesium nearest neighbors within a sheet, and two each above and below the plane in adjacent sheets. The anion is essentially planar; the deviations from a least-squares plane are given in Table 11. The sums of the angles at C(7), C(8), and C(8) are each 360.0° within their errors; the angles at C ( l ) through C(5) are close to 180’. The largest deviations from planarity are at N ( l ) and N(4), and in these cases the angles about C ( l ) and C(4) are 178.5’ and 176.7’, respectively. This slight loss of planarity is due to the interactions of the nitrogens with their out-of-plane cesium nearest neighbors. Although all the atoms of the anion are crystallographically inequivalent, corresponding bond lengths and angles in both halves of the ion are the same within experimental error. The exceptions to this observation are the C(2)-N(2) and C(5)-N(5) bond lengths which are within about three experimental standard deviations. Thus, one would reasonably assume that the ion has C,, symmetry in the gas or solution phase.
‘l
The thermal parameters obtained are fairly large, corresponding to isotropic B values of 4.5-6.0. Some correction of the bond lengths for thermal motion is therefore indicated. The values presented in Table I were calculated with the assumption that the second atom is “riding” on the first.30 This correction is quite large for the C-N bonds, smaller for the C-CN bonds, and irrelevant for the central C-C bonds. Purely Theoretical Results o-Hiickel Calculations. One of the goals of this work was to correlate the vibrational and electronic properties to a sufficient degree so that the vibronic structure observed on the visible emission spectrum of PCP could be explained. In order to accomplish this task, we adopted the following simple model. The known correlation between ground-state bond orders and bond lengths23was generalized to include the first excited state. That is, we assumed that the change in bond lengths with electronic excitation could be correlated with the corresponding change in bond orders. Since it has been shown that Hiickel calculations yield qualitatively correct estimates of absorption intensity and transition energy for the first allowed transition in PCP,15 we selected the o-Huckel technique for the calculation of bond order changes. The program used was a modified version of that given by Cooper,24with the following parameter values: h(N) = 1.0, k(C-CN) = 0.9, and k(C-N) = 2.0. The calculated bond order changes for the excitation process ‘Al to ‘B2 are given in Table 111. In order to convert these to bond lengths, the calculated ground-state bond orders were compared to the calculated (SCF) bond lengths. Differences in C-C bond length and bond orders between the C(7)-C(8) bond and the other C-C bonds were divided and averaged to yield a value of -0.19 A/BO. Similarly, the difference in C(3)-N(3) and C(5)-N(5) bond lengths was divided by the difference in their bond orders to yield a value of -0.057 A/BO for the C-N bonds. These bond lengthjbond order ratios were then used to compute the changes in bond length with excitation given in Table 111. Changes in bond angle with excitation are much more difficult to estimate. It is clear from the changes in charge density at carbons 6 and 8, however, that there should be a significant contraction of the central C-C-C angle. In order to reflect this observation, we have arbitrarily reduced this angle by 0.5’. This value (and the associated change in the adjacent angles) is also given in Table 111. Thus, we have utilized the Huckel and S C F calculations to estimate the change in ionic geometry with electronic excitation. In a later section we will project these changes onto the ground-state normal coordinates in order to estimate the electronic-vibrational coupling and to predict the structure of the electronic emission spectrum. SCF Calculations. A linear combination of atomic orbitals self-consistent field (LCAO-SCF) method utilizing a single electronic configuration was used to determine geometry and force (30) W. R. Busing and H. A. Levy, Acta Crystallogr., 17, 142 (1964).
Cesium Pentacyanopropenide
The Journal of Physical Chemistry, Vol. 88, No. 12, 1984 2501
constants for the PCP anion. This method is described extensively in a series of papers by Pople et al.31332and was implemented as the program GAUSSIAN-76.16The internal STO-5G basis set was the largest basis available which could be used in the C M S environment of our University’s Amdahl computer. The results reported here were obtained with the STO-SG basis. We carried out the geometry optimization by varying one internal coordinate (IC) at a time using a specified uniform grid and fitting three successive points to a parabola. This procedure was repeated in two or more sequences with each IC varied in each sequence. The initial sequence utilized a 0.05-A or 5’ grid, while the final sequence utilized a 0.01-A or l o grid. The calculated geometry was found to be planar and of C2, symmetry. The calculated equilibrium bond lengths and angles are given in Table I. In-plane potential constants were determined subsequent to geometry optimization. Diagonal stretching and bending constants are provided by the program and were computed over the following intervals: 0.01-A step size for all stretches, 2.0° for the C-C-C bends, and 3.0° for the C-C-N bends. Off-diagonal force constants were computed with similar increments. The present method of force-constant determination is rather inelegant, but more advanced methods such as are available in GAUSSIAN-80, require more computer core than is presently available to use. The potential function evaluated by these methods was a valence force potential equivalent to the following form: 2U(IC) =
K(i,j) Ar(i,j)2 all
+
bonds
C
all adja&nt bonds
TABLE IV: In-Plane Force Constants for the Pentacyanopropenide Anion“
2F(i,Jj,k) Ar(i,j) Ar6,k)
+ Eall
H(i,j,k) AO(i,j,k)2 (1)
bond angles
where i, j, and k designate the atomic labels shown in Figure 1; Le., i = C(1), N ( l ) , etc. In order to perform the actual determination of the angular force constants, and later to utilize nonredundant coordinates, the LCCC bending part of the in-plane force field actually used was
+
2U(LCCC) = H’(C(6),C(7),C(8)) A L ~ ( C ( ~ ) , C ( ~ ) , C ( ~ ) ) ~ H’(C(3),C(7),C(8)) AO(C(3),c(7),C(8))2 + H’(W),W),CW) X AO(C(3),C(7),C(8)) W C ( 6 ) , C ( 7 ) , C W ) + H’(C(7),C(8),C(5)) AO(C(7),C(8),C(5))2 +
t
>
t H
II)
I1
Z W
b
I-
Z
H
Thus, a total of 24 in-plane force constants (unrelated by symmetry) were evaluated. The results are given in Table IV. Experimental Results and Discussion Figure 3 shows Raman and I R spectra of the PCP anion. Figure 3 a and b, was obtained from an acetone solution of CsPCP, and the band marked * in the figure is the strongest band in the spectrum of pure acetone. Spectrum 3a is the symmetric part of the Raman spectrum; Le., it contains only those bands for which the trace of the (derivative) polarizability tensor is nonvanishing. In the group C, only fundamentals, overtones, or combinations having a, (totally symmetric) symmetry can contribute to the symmetric part of the Raman spectrum. Spectrum 3b is the asymmetric part of the Raman spectrum. In C,, all modes may formally contribute to this spectrum. Figure 3c depicts the I R (31) M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys., 52, 4064 (1970). ( 3 2 ) W. J. Hehre, R.F.Stewart, and J. A. Pople, J. Chem. Phys., 51,2657 (1969).
m
6mIzI
lZBB
18DD
24DB
1> Figure 3. Symmetric (a) and asymmetric (b) parts of the 5145-A Raman spectrum of the pentacyanopropenide ion in acetone solution. Also shown (c) are the IR and FIR of the cesium salt in KBr and petroleum jelly, ENERGY
C c m -
respectively. and FIR spectra of CsPCP pressed in a KBr pellet and in petroleum jelly, respectively. While all but the five a2 fundamentals are formally IR active, all of the bands seen in the symmetric Raman spectrum are either relatively weak or unobserved in the I R spectrum. With two exceptions, we assign the bands in the symmetric spectrum as a l fundamentals. The band near 1708 cm-’ is assigned as a combination of the 1390- and 331-cm-’ a l fundamentals. The second exception is the 124-cm-I band and requires some discussion. Figure 4 shows the low-frequency region of the acetone solution Raman spectra of PCP a t two different excitation wavelengths.
2502
Hipps et al.
The Journal of Physical Chemistry, Vol. 88, No. 12, 1984
CsPCP
_ .
_ -
t
CsPCP - 5145A
ACETONE
in
4880A 5145A
t
II
>
t H cn
t F
---
-a
-771 I
M
N
H
cn
I
Z
Z
w
w
t
t Z
Z
H
H
J
0
I
I
I
100
200
300
ENERGY
m
400
200
ENERGY
(crn-1)
400
600
Corn-l>
Figure 4. Low-frequency Raman spectra of PCP in acetone as a function of laser excitation wavelength.
Figure 5. Comparison of Raman spectra obtained from PCP in solution and solid state in the 50-7OO-cm-' region.
The 331- and 126-cm-I bands clearly increase in intensity relative to the asymmetric 214-cm-' band. This behavior is similar to that of several other bands in the Raman spectrum. If one considers the changes in intensities with excitation seen throughout the Raman spectrum, it appears that the totally symmetric bands are more enhanced by the approach to resonance than the asymmetric ones. Thus, it is tempting to assign the 126-cm-' band as an a l mode. However, the excitation-dependent polarization spectra indicate that both the 147- and 126-cm-' bands are polarized and there cannot be two fundamentals of a l symmetry this close in energy (vide infra). Also, Figure 5 shows that the 126-cm-' band is absent in the solid-state spectrum while the 147-cm-' band is clearly present. Thus, we assign the 147-cm-' band as an a, fundamental and the 126-cm-' band as an overtone of a lowfrequency mode. The assignments of the in-plane asymmetric (b,) modes are based on three factors. First, bands present in the asymmetric Raman but absent in the symmetric Raman spectrum are potentially b2 modes. The asymmetric bands located above about 900 cm-l are clearly in-plane modes and are easily assigned. These bands are all of strong or medium intensity in the IR and/or weak or medium intensity in the Raman. Thus, the second criterion used for assigning the b2 modes was that they be of strong or medium intensity in the IR and weak in the Raman spectrum. The third criterion for assigning the b2 modes was to select bands which were located in regions predicted by the scaled SCF force field (vide infra). The assignments of the in-plane modes of PCP are presented in Table V. Of the 10 out-of-plane fundamentals, all are formally Raman active and 6 are also formally IR active. Once the assigned a i and b2 fundamentals and their combinations are removed, however, only six bands in the 70-2300-cmi region remain unassigned; these are located at 820,456, 345,225,97, and 83 cm-'. Some of these are probably lattice modes in combination with in-plane fundamentals since they appear in solid-state spectra but not in solution spectra. Thus, we note their presence but do not assign them.
TABLE V Experimental Assignments (cm-I) and Calculated Positions of In-Plane Fundamentals for the Pentacyanopropenide Ion 6P 7P 9P expt# fit fit fit descriptionb ai Modes 2241 2228 2228 2228 2217 2217 2217 u(CN) 2218 2207 2207 2207 (2200) 1390 1422 1415 1396 45% v(C=C) + 28% v(C-C) 1240 1253 1248 1246 58% v(C-C) + 24% S(CCC) 1022 1048 1042 73% v(C-C) 1029 616 616 633 625 31% v(C-C) + 43% G(CCN) 521 574 533 531 90% G(CCN) 485 493 489 487 28% v(C=C) + 38% v(C-C) 331 326 320 318 72% S(CCC) 147 127 150 145 50% S(CCC) + 33% G(CCN) 44 C-(CN)2 rocking 69 40 ( t-
H
l(i
Z W k
Z H
2 m 5 m m
22mmm
ENERGY
C C M -
19mmm 1
>
Figure 6. Observed emission spectrum of microcrystallineCsPCP at 3 K, and the calculated spectrum resulting from the projection of the normal modes onto the change in geometry with excitation predicted by
the w-Huckel method. where d, is the size of the displacement along internal coordinate q1(taken from Table 111), and C(Q,) is the coefficient of the same overall displacement projected on the ground-state normal coordinates This procedure maps the displacements d,, onto seven totally symmetric modes. These modes have energies 2241, 1390, 1240, 1029, 485, 331, and 147 cm-'. All other modes contribute less than 1% of the intensity of the 1390-cm-' mode. Assuming that there is no change in the force constants with excitation, that emission at 3 K occurs from the lowest vibrational state of the excited electronic state, and that the displacements are so small that no mode mixing occurs, these projection coefficients, C(Q,), determine the intensities of the vibronic bands observed in emission through the relationz5 X(QJ = (1.483 X 10-2)ij(Q,) C(QJZ
(3)
I(O.0 ....,010,...,ni,O,...,nj,O. . . ) ~ * /O,O ~ ( ,...,OIO,O ,...,O ) I 2 = (X(Qi)"i X(Qj)"i)/ni!nj! (4)
where the Q, have units of (amu)'I2 A, ij has units of cm-I, and the quantity on the left in eq 4, a scaled Frank-Condon factor, is the intensity of a given fundamental, combination, or overtone vibronic band relative to the 0-0 transition. The intensities computed by eq 4, the observed fundamental frequencies, the observed location of the 0-0 transition, and an arbitrarily chosen 35-cm-I full width at 1/ e height Gaussian line shape were used to predict the emission spectrum of PCP. The unknown overall intensity factor (the electronic matrix element) was chosen such that the relative intensities of the calculated and observed 1390-cm-' vibronic bands agreed. The results of this calculation are contrasted with the experimental emission spectrum of CsPCP microcrystalline powder (at 3 K) in Figure 6. The full amplitude of the calculated 0-0 transition (about 7 times that of the 1390-cm-' vibronic band) is not shown. It has been demonstrated that significant reabsorption of the 0-0 emission line occurs in the solid.15 Thus, the experimental value for the 0-0 transition intensity is incorrect. The calculated and observed vibronic structures of the PCP emission spectrum are in remarkably good agreement considering the pastiche of theoretical and empirical treatments used to obtain them. These results are qualitatively the same, although closer inspection indicates that the calculated spectrum does not completely reproduce the observed one. The most obvious flaw in the calculation is the prediction of a single C N stretching band, while a doublet is observed near 20000 c d . Also, the bands marked a and b in Figure 6 have additional structure in the observed spectrum that is not present in the calculation. One must recall, however, that the calculations relate to a gas-phase ion of C2,
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J . Phys. Chem. 1984, 88, 2504-2515
symmetry, while the experimental data relate to the cesium salt which is not C, and which has out-of-plane interactions via cesium ions. It should also be noted that band a in Figure 6 corresponds to the 147-cm-I vibrational band discussed earlier. There is no indication in the emission spectrum of a band corresponding to the 126-cm-' transition seen in the solution-phase Raman spectrum (the structure near band a in Figure 6 occurs 97 cm-' below the 0-0 transition). This serves as further confirmation of our assignment of the 147-cm-' band as a fundamental.
bond orders and the S C F calculated geometries were used to estimate the slope of the bond length/bond order curve. These values and the change in bond order with excitation gave an estimate of the excited-state geometry of the PCP ion. This excited-state geometry was projected onto the normal coordinates of the PCP ion and the vibronic structure of the electronic emission was calculated. The theoretically generated emission spectrum is quite similar to the experimental one. Thus, both the normal-coordinate calculation and the excited-state geometry estimate are consistent with the vibronic structures seen in emission. The primary changes in geometry (with electronic excitation to the 'B, term) occur in the bonds formed by the central carbon atom; backbone C-C distances increase while the C-CN distances decrease. A decrease in the central CCC angle of roughly 0.5' also occurs. The only significant change in C N distance involves the group directly attached to the central carbon atom.
Conclusions The pentacyanopropenide ion is nearly planar in the CsPCP crystalline environment and has approximately C,, symmetry. S C F calculations utilizing an STO-5G basis indicated that the free ion is planar and has C,, symmetry. The calculated bond distances and bond angles are in reasonable agreement with those determined by X-ray crystallography. Polarized solution Raman spectra and IR spectra were measured and the in-plane fundamentals were assigned. A valence force type potential was determined for the ion by least-squares fitting of the calculated frequencies (determined by a small set of parameters which scaled the S C F calculated force constants) to the observed values. A seven-parameter set gave a mean percentage error of 1.7%. Force constants calculated by using S C F theory and the 5G basis were generally too large, but the CCN bending force constants and one of the CCC bending terms were exceptions. w-Hiickel calculations were used to determine the bond orders for the ground and first electronic excited states. The ground-state
Acknowledgment. We express our appreciation to the National Science Foundation for supporting a portion of this research under grant number DMR 81 15978 and to the Department of Chemistry at Washington State University for its continued support. K.W.H. also thanks the Alfred P. Sloan Foundation for providing a Sloan Fellowship. Registry No. PCP, 45078-37-3; CsPCP, 82085-20-9.
Supplementary Material Available: A table listing positional and thermal parameters of CsPCP, a table listing observed and calculated structure factors for CsPCP, and a drawing of the unit cell of a CsPCP single crystal (9 pages). Ordering information is given on any current masthead page.
A Model for Electron Transfer at the Illuminated p-Type Semiconductor-Solution Interface Shahed U. M. Khan and John O'M. Bockris* Department of Chemistry, Texas A&M University, College Station, Texas 77843 (Received: September 12, 1983)
An analytical expression for the photocurrent as a function of the physical properties of a semiconductor electrode and the neighboring electrolyte solution has been derived. The expression is independent of implicit assumptions concerning the rate-determiningstep. The charge transfer across the double layer has been treated explicitly. The model used for the surface states includes their energy distribution and their concentration dependence on the electrode potential. Recombination of photoexcited carriers in the field-free and surface regions has been taken into account. Energies of acceptor ions in solution and their distribution are calculated. The predicted photocurrents have been integrated over the solar spectrum. Numerical comparisons with experiment are made.
I. Introduction Photoemissi~n'-~ involves the excitation of electrons from the valence band of the semiconductor to the conduction band, the diffusion of the excited electrons toward the surface, and their emission into a vacuum. Photoelectrochemical transfer (emission) of electrons at the semiconductor (p type)-solution interface involves similar processes except that the photoelectrons undergo transition through the interfacial barrier to acceptor states in solution. The surface through which this transfer is made contains (1) F. G. Allen and G. W. Gobeli, Phys. Rev., 127, 50 (1962).
(2) A. Many, T. Goldstein, and N. B. Grover, "Semiconductor Surfaces", North-Holland Publishing Co., Amsterdam, 1971. (3) S. M. Sze, "Physics of Semiconductor Devices", Wiley, New York, 1969. (4) J. I. Pankov, "Optical Processes in Semiconductors", Prentice-Hall, Englewood Cliffs, NJ, 1971. ( 5 ) C. B. Duke, "Tunneling in Solids", Academic Press, New York, 1969.
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much structure, which will change with potential, nature of the anions present, and solvent. Losses discussed in addition to those usually considered in the semiconductor-solution situation include those due to the lack of availability of acceptor states of suitable energy in solution, tunneling probability across the barrier in the double layer, and the effect of charge-transfer adsorption in forming surface states and the resultant potential-dependent influence of these on recombination. An early treatment of photoelectrochemical kinetics was given by Butler: utilizing Gartner's' model and assuming charge transport within the semiconductor to be the ratedetermining step. Recent theoretical treatments614 (cf. Wilson: Reichman: Albery (6) (7) (8) (9)
B. A. Butler, J. Appl. Phys., 48, 1914 (1977). W. W. Gartner, Phys. Rev., 116, 84 (1959). R. Wilson, J . Appl. Phys., 48, 4297 (1977). J. Reichmann, Appl. Phys. Lett., 35, 251 (1981).
0 1984 American Chemical Society
