J . Phys. Chem. 1991, 95, 9716-9720
9716
-
of the binding energies as in Table I11 and the actual values differed by no more than 1 kcal/mol. In the trialkylammonium series, the binding energy of the first acetone is high because it hydrogen bonds to the hydrogen attached to the nitrogen atom. The binding energy then drops sharply and then begins to rise (with n-butyl, this happens after addition of the second acetone). This matches the pattern for trimethylamine clusters with trimethylammonium observed by Wei et al.23 In the tetraalkylammonium series, the binding energy of the second acetone is lower in the case of methyl, approximately the same with ethyl, and higher with propyl and butyl. For the large majority of hydrogen-bonded clusters the attachment energy of the second ligand molecule is usually lower by 25-30% than the first.I0 I t was considered therefore that Me4N+.nMe2C0clusters behave in the usual way. The multiple solvation of Me4N+ by two H 2 0 or MeOH molecules was considered unusuallo in that the attachment energy of the second ligand molecule is comparable in both cases to the energy of the first step. The unusual behavior of Me4N+-2H20and Me4N+.2MeOH was explained by the attachment of the second H 2 0 molecule to the first H 2 0 molecule (or C H 3 0 H to C H 3 0 H ) to form a strong hydrogen bond rather than to Me4N+ to form a second weak one-a conclusion confirmed by a b initio calculations.10 There are no a b initio calculations available for the acetone clusters, but the behavior of Et4N+-2Ac,Pr4N+.2Ac, and Bu4N+.2Ac is comparable to that of Me4N+.2H20 and Me4N+.2MeOH. Contrary to H 2 0 and MeOH, acetone cannot hydrogen bond, and it is hard to visualize a situation in which the second acetone would preferentially bind to the first one rather than to R4N+. The binding energies with the larger ions are perhaps higher than one might intuitively expect on the basis that the large ions have more diffuse charge and henceinteract more weakly with dipoles. The reason probably is that
the acetones are able to insert themselves between the alkyl chains of the ions and interact with them as well as with the central nitrogen atom. If the acetone plugs into the umbrella formed by three alkyl groups, the oxygen is attracted by the nitrogen and the methyls undergo van der Waals interactions with the alkyls. For the homologous ROH and R N H 2 series, discontinuities exist at R = n-butyl in the gas-phase acidities and proton affinities. This has been attributed to secondary (polarization) interactions of the chain with the charged site achieved by coiling of the longer chain.25 This process could also play a role in the present alkyl ammonium ions; however, recent a b initio calculation^^^ on tetrabutylammonium thiocyanate do not support the idea of coiling of the longer chains. The process of acetone insertion cannot continue indefinitely, in that in the limit the binding energy of the nth acetone must equal the latent heat of vaporization of acetone (7.22 kcal/mol). We suggest that all the cases described here correspond to the building up of the first solvation shell of the amines. After the addition of (say) four acetones; the binding energy probably drops sharply. The point is that this very drop makes it difficult to observe the species under our experimental conditions.
Acknowledgment. This research was supported by a grant from the United States/Israel Binational Science Foundation (BSF), Jerusalem. Professor A. W. Castleman, Jr. serves as the American thanks South Bank Cooperative Investigator for this grant. B.G.R. Polytechnic for sabbatical leave and the Royal Society for a study visit award. We thank the referees for very valuable suggestions. (25) Taft, R. W.; Koppel, I. A.; Topsom, R. D.; Anvia, F. J . Am. Chem. Sac. 1990, 112, 2047.
(26) Dunne, L. A.; Reuben, B. G., to be published.
Principal Component Analysis of the Polar Tensors of CH,F, and CD,F, Elisabete Suto, Roy E. Bruns,* Instituto de Quimica. Universidade Estadual de Campinas, CP 61 54, I3081 Campinas, SP, Brazil
and B. de Barros Net0 Departamento de Quimica Fundamental, Universidade Federal de Pernambuco, 50739 Recife, PE, Brazil (Received: May 20, 1991)
Polar tensors calculated from the fundamental vibrational intensities of CH2F2and CD2Fzfor all possible sign combinations of the dipole moment derivatives with respect to normal coordinates have been subjected to a principal component analysis. Comparison of the principal component scores for these sign combinations with those for tensors calculated using molecular orbital wave functions indicate that the B1symmetry dipole moment derivatives have identical signs. The CH antisymmetric stretching distortion induces a dipole moment with its negative pole in the direction of the stretched hydrogen atom. The sign combination selected as the correct one in this study leads to polar tensor invariant values in excellent agreement with those predicted by a recently proposed electronegativity model.
( I ) Kondo, S.; Nakanaga, T.; Saeki, S . J . Chem. Phys. 1980, 73, 5409. (2) Mizuno, M.; Saeki, S.Specfrochim. Acta, Parr A 1976, 32, 1077. (3) Morcillo, J.; Zamorano, L. J.; Heredia, J. M. V.Spectrochim. Acta. Part A 1966, 22, 1969.
0022-3654/9l/2095-9716$02.50/0
(4) Bruns, R. E. In Vibrational Inrensiries in Infrared and Ramon Spectroscopy; Person, W. B.. Zerbi, G . , Us.Elsevier: ; Amsterdam, 1982; Chapter 7
Q 1991 American Chemical Society
The Journal of Physical Chemiswy, Vol. 95, No. 24, 1991 9717
Polar Tensors of CH2F2and CD2F2 has been calculated only for the stretching distortions of the CH bonds adjacent to the triple bonds in HCN,’ C2H2,4and HC,N.5 For these molecules the calculated derivative signs are consistent with those determined experimentally. The alternative solution, favored by chemical valency arguments and semiempirical molecular orbital results, implies that the changes in the electronic configuration of CH2F2 result in the same polarity as the one deduced for the other fluoromethanes, Le., as the CH bonds stretch, their hydrogen atoms are pointed in the same direction as the negative poles of the dipole moments induced for either the symmetric or antisymmetric distortions. If this latter polarity is correct, one might expect to find that the hydrogen polar tensor of CH2F2is reasonably transferable to the other fluoromethane molecules. Furthermore the polar tensor invariant values corresponding to this polarity can be expected to be in better agreement with the values predicted by the electronegativity model6 constructed using the intensity data for other halomethanes, including CH3F, CHF3, and CF4. In an attempt to resolve this sign uncertainty, extensive ab initio molecular orbital calculations for the vibrational distortions of methylene fluoride have been undertaken. The theoretical polar tensor values obtained from these results are compared with the experimental tensor values obtained assuming all possible djj/dQj sign alternatives using principal component analyses.’ The dimensionality reduction in multivariate problems naturally resulting from principal component analysis has permitted low-dimensional graphical studies of the polar tensor values for all the d j / d Q j sign alternatives of chloroform.8 For methylene fluoride principalcomponent graphs are also found to be quite useful in deciding between the polar tensor values corresponding to alternative sign sets. This will be seen to be especially true for the polar tensor data corresponding to the B I symmetry species. The values of the experimental fundamental vibrational intensities, normal coordinates, and equilibrium geometry and the definitions of the signs of the dipole moment and symmetry coordinates were taken from ref 1. The orientations of the CH2F2 and CD2F, molecules in the space-fixed Cartesian coordinate system of this reference were also used in our calculations. The polar tensor of methylene fluoride is obtained by the juxtaposition of all atomic polar tensors: px = {pf)ip&H ~)ipLHdip&F~)i plfd) Each atomic polar tensor, PPI, is defined by
[
A
pi;!, = p:)
J p d J x a aPdaVa JPdaZa apjaxa
aPj+a
JPJaXa JPzIaYa
apjdza] = JPJaZa
[
Pk) P y PE P u Pxy
Pi
PAl (a)
P (a) g) Pzz
1
where a represents the specific atom. The polar tensors were calculated from the experimental intensity data for all possible sign alternatives using the TPOLAR programa9 Molecular orbital calculations were carried out using the GAUSSIANIM computer programi0on a VAX 1 1 /750 computer at the Universidade Federal de Pernambuco. The M P 2/6-31 1 G (d, p) results were kindly furnished by Prof. H. Schlegel as
+
( 5 ) Neto, B. B.; Ramos, M. N.; Bruns, R. E. J . Chem. Phys. 1986, 85, 4515. ( 6 ) (a) Neto, B. B.; Scarminio, 1. S.; Bruns, R. E. J . Chem. Phys. 1988, 89, 1887. (b) Neto, B. B.: Bruns, R. E. J . fhys. Chem. 1990, 90, 1764. ( 7 ) Mardia, K. V.; Kent, J. T.: Bibby, J. M. Multioariate Analysis; Academic Press: New York, 1979; pp 213-254. ( 8 ) Suto, E.; Ferreira, M. M. C.; Bruns, R. E. J . Compur. Chem. 1991, 12, 885. ( 9 ) Bassi, A. B. M.S.Ph.D. Thesis, Universidade Estadual de Campinas, Campinas, SP. Brazil, 1975. (IO) Frisch, M. J.; Binkley, H . B.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, W. A.; Fox, D. J.; Fleuder, E. M.;Pople, J. A. GAUSSIAN 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984.
+ a=EflabtJv + el;!, I
(1)
where (u,v) = (x,y,z), and i represents the ith set of signs of the d p / d Q j and &) is the average value of the uvth polar tensor element of the ath atom for all possible djj/dQ, sign choices. The be:” elements are called loadings and are the direction cosines relating the rotated coordinate system to the original one. The f , , values are the scores giving the new coordinate values of the ith set of signs for the ath principal component. These values are used to construct the low-dimensional projections of the information contained in higher order space. The e$ are residual values expressing the differences between the actual experimental values of pi$, and those predicted by the principal-component model. These residuals contain both experimental and modeling errors. If the el$, values are larger than the experimental errors and a single bidimensional projection is not sufficient to give an accurate representation of the sign dependence of the polar tensor element values, additional projections involving the third, fourth, etc., principal components can be investigated. The principal-component score used in the graphical representation for the ith sign combination and the ath principal component is given by ti,
Calculations
pi) =
supplementary material of a recently published article.” The principal components of the CH2F2and CD2F2polar tensor data were calculated using a microcomputer version of the ART H U R program ~ for mainframe computers.I2 Other standard multivariate statistical packages such as SAS and STATGRAPH could just as well have been used. The principal component equationa applied to polar tensor elements can be expressed as
= Epip,?bk!a = P C ~ av
(2)
where the sum is taken over all nonzero polar tensor elements in the symmetry species being treated. In these equations the modeling error is assumed to be zero, i.e., all the el;: elements are zero, and the origin of the graph corresponds to the averages of the polar tensor elements taken over all the sign combinations. Individual calculation of the principal component equations for each of the symmetry species of methylene fluoride is discussed below. The B, symmetry species, for which the sign choice is controversial, has two infrared-active fundamentals and nonzero p::), p::), pi:), and pit) polar tensor elements, which define a fourdimensional BI polar tensor space that can be reduced to twodimensional principal component space. A bidimensional principal component projection of the BI polar tensor elements as a function of the d@/dQ, signs contains 100%of the data variance; this means that there is no loss of statistical information for the polar tensor data in this bidimensional projection. The data matrix containing the pi;; elements is 8 X 4 for this symmetry species. Each line of this matrix contains polar tensor results for a possible sign set of the a@/aQ’s Le., (++), (+-), (-+), and (--), for both CH2F2 and CD2F2. L c h column contains the values of one of the nonzero polar tensor elements, pi:), pi:), pi:), and pi?. The orderings of the lines and columns are not important. In practice, the principal-component loadings and scores are obtained by diagonalizing the covariance matrix of this data matrix. The 4 X 4 covariance matrix, obtained by premultiplying the data matrix by its transpose, has two nonzero eigenvalues, each one specifying the variance explained by its associated eigenvector. The B2symmetry s ies has two infrared-active fundamentals and nonzero pi;), piy ,puu and pi:) polar tensor elements. As for the BI symmetry species, an exact twc-dimensional projection of the four-dimensional polar tensor data is obtained using principal components extracted from an 8 X 4 data matrix. The nonzero A symmetry species polar tensor elements are pi:), p!!), p$‘), p$, and &), calculated from four infrared-active
r(F),
( 1 1) Fox, G. L.; Schlegel, H. B. J . Chem. Phys. 1990, 92,4351. ( 1 2 ) Scarminio, 1. S.; Bruns, R. E. Trends Anal. Chem. 1989, 8, 326.
9718
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
TABLE I: Principal-Component Equations for the Polar Tensor Elements of CH,F, and CD,F,’
Suto et al. TABLE 11: Experimental and Molecular Orbital Values of the Polar Tensor Elements of CH2F2and CD2F2’
B,. Symmetry . . Species . CH,F, (+ +)
CD;F; (+ av (+ +)
+)
CHlF2 (-+) CD2F2 (-+) av (-+)
error MP2/6-3 1 1 +G(d,p)b 6-31 I IC** 6-31‘3’ 6-3 ICC 4-31C
(F’
P x(c) x
Pxx
P x(H’ r
0.262 0.209 0.236 f0.037 0.732 0.659 0.700 f0.052 0.786 0.924 0.936 0.980 0.924
0.141 0.159 0.150 f0.013 -0.094 -0.058 -0.076 f0.025 -0.087 -0.1 I 1 -0. I32 -0.1 I O -0.078
0.105 0.1 10 0.108 f0.005 -0.048 -0.024 -0.036 f0.017 -0.035 -0.027 -0.040 -0.050 -0.033
-0.272 -0.263 -0.268 f0.006 -0.272 -0.272 -0.272 fO.OOO -0.306 -0.352 -0.336 -0.380 -0.383
-0.746 -0.708 -0.727 f0.027 -0.821 -0.838 -0.800 -0.740 -0.734
0.363 0.332 0.348 f0.022 0.384 0.383 0.359 0.270 0.258
P I X
B, Svmmetrv Soecies 0 80
C CHZFZ
X CDzFZ
CH2F2 (+-) CD2F2 (+-) average error MP2/6-31 I+G(D,p)* 6-31 I IC** 6-31G* 6-31G‘ 4-31G
AB I N I T I O I - MP2/6-311+Gid,pi 2 - 6-3111G**
3 - 6-31G’ 4 - 6- 31G 5 - 4-31G
040 -
Pcz
xo -0 4 0
I
0 00
0.018 0.013 0.0 16 f0.004 -0.009 -0.014 -0.03 1 -0.020 -0.0 I7
A ,.~Symmetry . Species . P:F’ P y(H) y PK’
!++iliti
_”...(” r
1.458 1.391 1.425 f0.047 1.658 1.706 1.661 1.520 1.502
040
0 80
I20
PCI
Figure 1. Graph of the scores of the first two principal components for the B, symmetry species polar tensor elements of methylene fluoride.
fundamentals. Thus the information contained in the five-dimensional A , polar tensor space can be totally projected into a four-dimensional principal-component space. Since one symmetry-allowed vibrational transition for CH2F2is too weak to be measured, CH2F2and CD2F2have 8 ( P )and 16 (24) possible sign sets, respectively. Each line of the data matrix used to calculate principal components represents a aj/aQj sign set and each column a nonzero polar tensor element. Therefore the A, data matrix for CH2F2and CD2F, has dimensions of 24 X 5 . Molecular orbital values of the tensor elements are not used to calculate the principal-component equations. Instead these values are substituted into the principal-component equations (eq 2 ) determined from polar tensor values obtained from experimental intensities. The theoretically derived principal-component scores calculated in this way can then be compared with the scores calculated using the experimental intensities for the different sign combinations. Results
B, Symmetry Species. The principal-component equations (eq 2 ) calculated for the B, symmetry species polar tensor elements are listed in Table I. The principal-component representations of the polar tensor elements as a function of signs of the @/dQj are shown in Figure 1 . The eight experimental points there lie in a plane in the original four-dimensional polar tensor space. The smaller the distance between the members of a pair of isotopically related points, the more isotopically invariant are the polar tensor elements for the sign combinations of the a$/&), associated with these points. It is clearly seen that the (+ +) sign choice for both CH,F, and CD2F2,with aj/aQ, and dC/dQ, positive, corresponds to the most isotopically invariant pair of polar tensor element values. Principal-component score error limit values calculated as explained in ref 8 using the estimated intensity errors of KNS are indicated by the sizes of the symbols shown in this figure.
CH,F, ( - O w - ) 0.946 CD;F; (- + - -) 0.896 av 0.921 error f0.035 MP2/6-3I l+G(d,p)b 0.741 6-31 IIG** 1.287 6-31G* 1.279 6-31GC 1.240 4-31G 1.181
PK’
-0.086 0.010 0.233 -0.124 -0.001 0.202 -0.106 0.005 0.218 f0.026 f0.008 f0.022 -0.030 0.018 0.082 -0.105 -0.027 0.293 -0.092 -0.047 0.284 -0.090 -0.020 0.200 -0.071 -0.011 0.171
Pg’ -0.483 -0.447 -0.465 f0.025 -0.388 -0.6 18 -0.592 -0.600 -0.579
” U n i t s of electrons. bThe MP2/6-31 I+G(d,p) M O results were obtained from ref 1 I . CThe6-31G polar tensor elements were obtained from ref 6a.
Although the (+ +) sign combinations have polar tensor elements which best satisfy the isotopic invariance criterion, other comalternative, could be considered binations, such as the (-+)H(-+)D invariant, if the errors in the polar tensor elements were approximately 2-3 times the values estimated by K N S 6 Using statistical terminology, only the (+ +) sign set may be considered to have isotopically invariant polar tensor values if error values at the 9 5 8 confidence level are assumed, whereas both the (+ +) and (- +) sign sets may be considered to have isotopically invariant values, using errors at the 99% confidence level. On the other hand, ab initio molecular orbital calculations with a several different basis sets yield polar tensor values in close proximity to the values of the (- +) sign choices for CH2F2and CD2F2. This can be seen in Figure 1 and in Table 11, where the B symmetry experimental and molecular orbital tensor element values are listed. The principal-component representation of the theoretical polar tensor element values also illustrates that these values are not very sensitive to the basis set used to calculate the molecular orbitals and are only moderately sensitive to the inclusion of effects describing electron correlation in the wave functions. It seems clear that the (- +) sign choice is preferable to the (+ +) one, in spite of the isotopic invariance evidence to the contrary. B2 Symmetry Species. Figure 2 shows the principal-component representation of the B, polar tensor elements as a function of the signs of a$/aQ, and aC/aQ,. This graph of the first two principal components (see Table I) explains 100% of the polar tensor variance for the different B, ajj/8Qj sign alternatives. The preferred sign combination (+ -) (aF/3/aQ8> 0 and aj5/aQ9 < 0)
,
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9719
Polar Tensors of CHzF2 and CD2Fz 2 00
0 CHZFZ
X
ChFn
* A B INITIO
-
I YP2 /e311 2- 6-3111 OH 3 - 6 - 3 1 0" 4-6-310 5-4-31G
IO0
+ G(d,pl
1-4
TABLE 111: Mean Dipole Moment Derivative and Effective Charge Values of the CHzF, Sign Alternatives and Those Predicted Using the Electronegativity Model' preferredb alternative* electronegativity signs signs models PC
X
xc
PF XF PH XH X
I50
X COIFL
* A B INITIO
I -MP2/6-3lltG1d,pl 1
2-6-3111 G"* 3 - 6 - 3 1 0"
00
0.860 0.989 -0.487 0.573 0.057 0.123
0.992c 1.123d -0.5 1 7e 0.605d -0.044c 0.079d
"Units of electrons. *Averaged values for preferred ap/aQ, signs, (-0--) (-+) (+-)H and (-+--) (-+) (+-)D. Averaged values for alternative aj/aQ, signs, (-0--) (++) (+-)" and (-+--) (++) (+-)D. 'Calculated using eq 5 of ref 6a. dCalculated using eqs 2 and 3 of ref 6b. 'Calculated using p , = 0.6337 - 0.0945EU,where E, are the Mulliken-Jaffe electronegativitie~,'~ a = H, F.
Ittl
0 CH2FZ
1.015 1.060 -0.488 0.573 -0.018 0.078
0.50
pc2 0 00
fluoromethanes. On the other hand, the alternative sign combinations (-0--) (++) (+-)Hand (-+--) (++) (+-)D have api/az' = 0.108e. This positive value leads to the interpretation that the hydrogen end attains more positive polarity for the C H stretching distortion. Considering that the former sign combinations have polar tensor values indicating charge distortions similar to those of the other fluoromethanes, it can be expected that the mean dipole moment derivatives, p,, and atomic effective charges, xu,for these combinations have values consistent with those that can be calculated using the equations of the recently proposed electronegativity model6 for substituted methanes. Conversely, the values of these invariant quantities for the alternative (-0--) (++) (+-)Hand (-+--) (++) (+-)Dcombinations are not expected to be in as good agreement. The electronegativity model6 was developed based on the polar tensor values of the CH4, CH31, CHsBr, CH,CI, CH,F, CHCI,, CHF,, and CF4 molecules. Data for CH2Fzwere purposely left out of the modeling equations due to the sign ambiguity problem discussed here. Mean dipole moment derivative and effective charge values can be estimated for the carbon, hydrogen, and fluorine atoms using four electronegativity modeling equations: eq 5 of ref 6a, eqs 2 and 3 of ref 6b, and the equation described below. The mean dipole moment derivative values p, with a = H, F, C1, Br, and I can be regressed on the Mulliken-Jaffe electronegativitie~,'~E,, using data for the above-mentioned halomethanes except for CHzF2. The regression equation p, = 0.634 - 0.0945EU
1 ,
- I 00 -I50
- I 00
-050
000
050
100
I50
PC I
Figure 3. Graph of the scores of the first two principal components for the A , symmetry species polar tensor elements of methylene fluoride.
is clearly isotopically invariant within the estimated experimental error and in excellent agreement with the molecular orbital results. Both the experimental values for this sign selection and the molecular orbital values of the polar tensor elements have been included in Table IT. A, Symmetry Species. The four principal components are given as a function of the A! symmetry polar tensor elements in Table I. The first two principal components account for 92.2% of the total A, polar tensor variance for all the possible sign combinations of the ajj/aQ,'s for C H z F 2and CDzFz. Hence a bidimensional projection using these two principal components, shown in Figure 3, is an approximate but useful representation of the five-dimensional A , polar tensor space, allowing examination of the dependence of the element values as a function of the signs of the ajJ/aQ,'s (j = 1-4). It is easily seen that the (-O--)H and (-+--)D sign sets are isotopically invariant and in very good agreement with the molecular orbital results for the polar tensor values. The experimental polar tensor element values for this preferred sign combination and their molecular orbital counterparts are listed in Table 11.
Discussion The C H stretching distortion is more conveniently analyzed if the coordinate system of ref 1 is rotated so that the z axis is coincident with the CH bond and the H atom is pointed in the +z direction. Then the polar tensor element api/azrH is a direct measure of the change in polarity upon dislocation of the H atom. The (-0--) (-+) (+-)H and (-+--) (-+) (+-)d sign combinations, preferred here on the basis of the molecular orbital results, have an average value of apf/az'H of -0.1 17e. This implies that the hydrogen atom becomes more negative as the CH bond length increases. This same direction of change in the electronic charge density upon stretching has been found for the other
has a correlation coefficient of 0.982 and a standard F test value of 349, attesting to its statistical validity. Values of p, and xa (a = C, H, F) for CH2Fzestimated using the electronegativity modeling equations are presented in column three of Table 111. Values of these invariant quantities for the two alternative sign sets are given in the first two columns of this table. The values predicted by the electronegativity equations are in much better agreement with mean dipole moment derivative and effective charge values of the preferred (-0--) (-+) (+-)Hand (-+--) (-+) ( + - ) D sets than with those of the alternative ones. This is especially true for the p,-, xc, pH,and xHvalues.
Conclusions Principal-component analyses of the polar tensors of CHCl, and CDC13*led to the conclusion that the errors propagated into the polar tensor results due to the experimental errors in the vibrational intensities are 2-3 times smaller than the errors estimated using assumed replicate determinations for sign sets with indeterminate signs. The replicate error values can be considered to be upper bound estimates, since they include contributions from normal-coordinate uncertainty due to anharmonicity and force field approximations, as well as other sources of systematic error. These contributions are extremely difficult to assess and were not included in the error estimates reported in ref 1. Hence it is not (13) Huheey, J. E. J. Phys. Chem. 1965,69, 3284.
9720
J . Phys. Chem. 1991, 95, 9720-9727
unreasonable to expect that the polar tensor errors for CH2F2and CD,F, are also somewhat larger than those used here, in which case both alternative sign sets considered in this study will satisfy the isotopic invariance criterion. The principal component analyses then strongly indicate that the (-0--) (-+) (+-)" and (-+--) (-+) (+-)D alternative pair is to be preferred, in light of the molecular orbital results. It is encouraging that the polar tensor invariant quantities for methylene fluoride for this preferred sign set are in excellent agreement with those predicted from the
equations of the electronegativity model. Acknowledgment. We gratefully acknowledge partial financial support from CNPq, FAPESP, and FJNEP. E.S. is supported by a CNPq graduate student fellowship. GAUSSIAN 86 cakulations were carried out on a V A X 11/750 computer of the Departamento de Quimica Fundamental of the Universidade Federal de Pernambuco. Registry Yo CH2F2. 75-10-5; CD,F,, 594-24-1
Resonance Raman Characterization of the Radical Anion and Triplet States of Zinc Tetraphenylporphine Robert A. Reed, Roberto Purrello,+Kristine Prendergast, and Thomas C. Spiro* Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (Received: May 7 , 19911
Resonance Raman (RR) spectra are reported for the anion radical and for the photoexcited triplet state of ZnTPP. The anion radical was prepared by controlled-potential electrolysis in dry dimethylformamide, and care was taken to avoid phlorin contamination. RR spectra were obtained by excitation at 457.9 nm, at the anion absorption band maximum. Bands were assigned with the aid of pyrrole-d8 and phenyl-dzoisotopomers. The pattern of isotope shifts and polarizations was found , to be quite similar to that of the neutral parent, ZnTPP, and meaningful mode correlations are possible: u2, v I o ,~ 2 7 and uZ9 shift down 15-20 cm-I upon reduction, while u I r u4. and the phenyl mode & are essentially unaffected. This frequency shift pattern is discussed in terms of the expectations for placing an electron in the e** orbital, including the anticipated Jahn-Teller (J-T) effect. Although band overlaps make depolarization ratios difficult to quantitate, the v I oband is found to be essentially depolarized, indicating that the J-T effect is dynamic, rather than static in character, at least with respect to stretching of the C,C, bonds. The v 2 and u I o downshifts are attributable to porphyrin core expansion upon reduction, 9 are probably manifestations of the J-T effect. Triplet-state RR spectra were produced with but the u2, and ~ 2 reductions 416-nm photolysis and 459-nm probe pulses (7 ns) from electronically timed Q-switched Nd:YAG lasers equipped with H2/D2 Raman shifters. The RR peaks were assigned via their polarizations and the d8 and d,, isotopomer shifts. The spectrum contains three strong bands of predominantly phenyl character. Their frequencies are unshifted relative to the ground state, implying negligible electronic involvement of the phenyl groups in the T I state, but their enhancements indicate substantial involvement in the resonant T, state. This state is suggested to be produced by charge transfer from the porphyrin e** to the phenyl T * orbitals. There are also four weak bands, which are assigned to the porphyrin skeletal modes u2, u l o , u l l r and u,,, The first three of these are at frequencies which are 40-50 cm-I lower than in the ground state. For u2 the shift is comparable to the sum of the shifts seen upon forming the ZnTPP cation radical and anion radical, but for u I o the shift is much larger than this sum, indicating that the J-T effect is more pronounced in the triplet state than in the radical anion. Consistent with this conclusion, the u i 0 band of 3ZnTPP is partially polarized, suggesting a static J-T distortion along the C,C, bonds. However, the u l l band is depolarized, implying that the C,C, bonds remain equivalent. The ~ 2 band 7 shifts up 15 cm-I and broadens significantly, suggesting a dynamic B,, J-T effect along the C,-phenyl bonds.
Introduction
The photophysical properties of metalloporphyrins are important to a range of current research areas, ranging from solar energy conversion to photodynamic therapy. Our view of porphyrin excited states has evolved from the concurrent development of theoretical calculations] and of static and time-resolved electronic (emissive and absorptive)'-5 and magnetic6,' spectroscopy. The structures of these excited states can be elucidated by vibrational spectroscopies, especially resonance R a m a d (RR) and resonance coherent anti-Stokes Raman9 (RCAR) spectroscopy. These techniques have been used to characterize the triplet excited states of Ni"P ( P = octaethylporphyrin, uroporphyrin, or protoporphyrin IX dimethyl ester), in which the antibonding metal orbital in dXz+ is populated.8-10 I n this paper, we explore the character of the excited states produced by the population of porphyrin orbitals, using a closed-shell metal ion, Zn(JI), in tetraphenylporphine (TPP).Is2 A structural diagram of the molecule is shown in Figure 1, while the energy levels of the valence orbitals and states are shown 'To whom correspondence should be addressed. 'Permanent address: Dipartimento Di Scienze Chimiche Dell'UniversitL di Catania. Viale A . Doria. 8, 95125 Catania, Italy.
schematically in Figure 2. The highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) are the ( I ) Gouterman, M. In The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1978; Vol. 111, Chapter 1 and references therein. (2) Darwent, J. R.; Douglas, P.; Harriman, A,; Porter, G.; Richoux, M. Coord. Chem. Rer;. 1982, 44, 83. (3) Holten, D.; Gouterman, M. In Optical Properties and Structure of Tetrapyrroles; Blauer, G., Sund, H., Eds.; Walter D. Gruyter: New York, 1985; pp 63-88. (4) Dzhagarov, B. M.; Chirvonyi, V. S.; Gurinovich, G. P. In Laser Picosecond Spectroscopy and Photochemistry 01Biomolecules; Letokhov, V. S., Ed.; Adam Hilger: Philadelphia, 1987; Chapter 3. ( 5 ) Petrich, J. W.; Martin, J. L. Chem. Phys. 1989, 131, 31. (6) van der Waals, J. H.; van Dorp, W. G.; Schaafsma, T. J. In The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1979; Vol. IV, Chapter 5. (7) Connors, R. E.; Leenstra, W. R. In Triplet State ODMR Spectroscopy: Techniques and Applications to Biophysical Systems; Clarke, R. H., Ed.; Wiley: New York, 1982; Chapter 7. (8) Findsen, E. W.; Shelnutt, J. A.; Ondrias, M. R. J . Phys. Chem. 1988, 92, 307. (9) (a) Apanasevich, P. A. J . Mol. Struc. 1984, 1 1 5 , 233. (b) Chikishev, A. Y.; Kamalov, V. F.; Koroteev, N. I.; Kvach, V. V.; Shkurinov, A. P.; Toleutaev, B. N. Chem. Phys. Lett. 1988, 144, 90. (c) Kamalov, V. F.; Koroteev, N. 1.; Toleutaev, B. N. In Time Resolued Spectroscopy; Clarke, R. H.. Hester. R . E., Eds.; Wiley: New York, 1989; pp 288-94.
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