J. Phys. Chem. 1993,97, 6161-6166
6161
Principal Component Analysis of the cis- and trans-Difluoroethylene Polar Tensors Elisabete Suto Departamento de Quimica, Universidade de Brasilia, 70910 Brasilia OF, Brasil
Mozart N. Remos Departamento de Quimica Fundamental, Universidade Federal de Pernambuco. 50000 Recife. PE. B r a d
Roy E. Bruns' Instituto de Quimica, Universidade Estadual de Campinas, CP 6154, 13081-970 Campinas, SP, Brasil Received: December 21, 1992; In Final Form: March 8, 1993
The isotopic invariance criterion, molecular orbital calculations at the HartreeFock and Moller-Plesset levels, and principal component analysis have been used to determine the in-plane atomic polar tensor (APT) elements of cis-C2HzFz and cis-CzD2F2 and the out-of-plane elements of their trans isomers. The in-plane APT elements of the cis-difluoroethylenes are shown to be transferable to their trans isomers. On the other hand, the outof-plane cis elements transferred to the trans compound lead to calculated A6 and A7 intensities of 46.9 and 3.7 km mol-' for trans-C2H2F2, significantly lower than the measured 56.7 and 12.7 km mol-' values. The differences in these intensity values stem primarily from the different p g ) APT out-of-plane elements of these isomers, -0.193e and -0.096e for the trans and cis molecules, respectively, suggesting different electronic densities for the fluorine atoms. Recent high-resolution infrared spectra indicate geometry differences for these isomers that chemical valency arguments can attribute to different fluorine atomic charges in these isomers. The transferable cis and trans in-plane APT elements appear to be predominantly determined by charge flux contributions to the APT elements, as suggested previously.
Introduction
300
Some time ago, several articles14 demonstratedthat the atomic polar tensors (APT)of cis-CzHzF2 and cis-CzHzC12 could be directly transferred to their respective trans isomers for accurate fundamental vibrational intensity predictions. This result was considered important since a simplification in the vibrational intensity studies of geometrical and rotational isomers might be possible. If the APT elements of the cis- and trans-difluoroethylene isomers are transferable, their atomiceffective chargesmust be the same. This being so, the fundamental intensity sums of the cis molecules are expected to be identical, neglecting small rotationalcontributions? to thoseof the trans isomers. In Figure 1,the bar graph illustrates the experimentalintensity sums of the cis and trans isomers of CzH2F2, CzDzF2, CzHDFz, CzH2Cl2, and CzD2Clz. As can be seen, all cis trans pairs have intensity sums agreeing within 20 km mol-' (- 10% of the intensity sums), providing strong evidence for the transferability of the APTs of cis- and trans-difluoroethylene. Although experimentalintensity data are not available for rotational isomers, recent theoretical calculations6 showed that the ethanethiol intensity sum is almost constant for the gauche and trans conformers, suggesting that their atomic effective charges are essentially the same. In spite of this, the distribution of the intensity sum into the fundamental bands of ethanethiol is calculated to be very sensitive to its rotational configuration. Recent molecular orbital results7 have indicated that although the in-plane APT elements of both cis-difluoro- and cisdichloroethyleneand the out-of-plane elements of the latter are transferable to their trans isomers, this approximation is not as accurate for the calculation of the out-of-plane vibrational intensities of trans-difluoroethylene. If the out-of-plane APT elements are not transferable for cis- and trans-difluoroethylene, their out-of-plane intensity sums should be different. Unfortunately, comparison of cis- and trans-CzHzF2 out-of-plane intensitiesis hampered because their bands overlap with in-plane bands. On the other hand, the only out-of-plane cis-CzD2Fz band is 0022-3654/93/2097-6161$04.00/0
EA 200
1oC
C
Figure 1. Fundamental vibrational intensity sums of the hydrogen and deuterium analogues of cis- and trans-difluoro- and dichloroethylene.
isolated from other bands having an intensity of 17.6 km mol-'. This value is smaller than the sum of the two out-of-plane transCzDzF2 intensities, 27.8 km mol-' for the isolated A6 band and an estimated 12.6 km mol-' for the overlapped A7 band. This experimental evidence and the molecular orbital results for the cis- and trans-difluoroethyleneMulliken and corrected charges (6-31G up to the 6-311++G** level) of ref 7 suggest that the out-of-plane cis-difluoroethylene APT elements are not as transferable to their trans isomers as are the in-plane elements for accurate intensity predictions. The B,,in-plane trans-CzD2Fz sum is 242.6 km mol-', in good agreement with the in-plane intensity sum (AI + B1 symmetry species) of 247.2 km mol-' for cis-CzDzF2, supporting the transferability of the in-plane APT elements. In other words, the 18.2 km mol-' difference between the cis- and trans-CzDzFz total intensity sums appears to be mostly attributable to the out-of-plane bands. 0 1993 American Chemical Society
6162 The Journal of Physical Chemistry, Vol. 97, No. 23, 19'93
Due to the intrinsic interest in comparing the electronic structures of geometrical isomers and their possible applications to the vibrational spectra of rotational conformers,the evidence leading to the conclusion of cis-trans transferable APT elements for the difluoroethylenes is reexamined. Molecular orbital calculationsof atomic polar tensors using a variety of basis sets, some obtained at the Moller-Plesset perturbationlevel, are carried out for both cis- and trans-C2HzFz to test the transferability of their APT elements. Furthermore, the APT values determined from experimentalinfrared intensities in previous ~tudies1.4.~ were based on dipole moment derivative sign determinations made using the isotopic invariancecriterion and semiempirical CNDO molecular orbital results for cis-difluoroethylene, These sign attributions should be verified since the isotopic invariance criterion is not sufficient to determine a unique set of APTvalues. Here, ab initio results and experimentallyderived APT elements are examined using principal component analysis.&'* This analysis provides two- and three-dimensionalgraphs illustrating the relationships of all possible a$/aQJ sign alternatives with the theoretical results. The ab initio molecular orbital results and the principal component graphs result in more secure a$/aQJ sign selections and as such more reliable APT element values. The polar tensors determined using this procedure for cisdifluoroethylene are expected to be more reliable than those reported earlier and can then be transferred to trans-difluoroethylene to predict its intensities, providing a direct test of the transferability of the cis and truns APT values.
Calculations The values of the experimental fundamental vibrational intensities, normal coordinate transformations, the molecular geometry, and the definitions of the symmetry coordinates were taken from ref 1. The orientations of c ~ s - C ~ H and ~ Fcis-CzDzF2 ~ in the space-fixed Cartesian coordinate system, the atom numbering scheme, and the internal coordinatesare identical to those in Figure 2 of ref 1. The corresponding informationfor the transC2HzFz and truns-CzD2F molecules was taken from ref 3. The polar tensor of cis-difluoroethyleneis represented by a juxtaposition of all its atomic polar tensors.11
Each atomic polar tensor, PF),is defined by
The polar tensors were calculated from the experimental intensity data for all possible sign alternatives using the TPOLAR program.12 Molecular orbital calculationswere carried out using the GAUSSIAN 88 computer program" on an IBM 3090 at the computer center of the Universidade Estadual de Campinas. All the intensity and APT molecular orbital calculationswere carried out using theoretically optimized geometries. The principal components of the difluoroethylene polar tensor data were calculated using a microcomputer version of the ARTHUR program for mainframe computers.14 The principal component equation9J0appliedto the polar tensor elements can be expressed as
where (up)= ( x g , z ) and i represents the ith set of signs of the a$/aQJ and pea) is the average value of the auth polar tensor
Suto et al. element of the ath atom over all possible a$/aQJ sign choices. The b!$ elements are called loadings and are the direction cosines relating the rotated coordinate system to the original one. The ti, values are the scores giving the transformed coordinate values of the ith set of signs for the uth principal component. These values are used to constructthe low-dimensional projections of the information contained in the higher order space. The e!z are residual values expressing the differences between the actual experimental values of pi,% and those predicted by the principal component model. The residuals contain contributions from both experimental and modeling errors. If the e!$ values are larger than the experimentalerrors and a single bidimensional projection is not sufficient to give an accurate representation of the a$/aQJ sign dependence of the polar tensor element values, additional projections involving the third, fourth, etc., principal components can be investigated. In practice, the loadings and scores in eq 1 are obtained by diagonalizing the covariancematrix,XX, whereX is a data matrix containing the polar tensor element values calculated using the experimental intensities for all possible sign set alternatives of the a$/aQJ for both the hydrogen and deuterium analogues.The eigenvectors resulting from this diagonalization contain the loadings and define the principal components relative to the original coordinate system. Their associated eigenvalues are equivalent to the variances described by the principal components. The principal component scores, which are graphed to determine preferred ajj/aQJ sign sets, are obtained from the loadings and the original data matrix, X. For the ith sign combination and the uth principal component, PC,, the score is given by
where the sum is taken over all nonzero and nonequivalent polar tensor elements in the symmetry speciesbeing treated and contains contributions from all the atoms in the molecule. Here, 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. The principal component loadings, btA, in eq 1 are determined using only the polar tensor element values obtained from the experimental intensity values, pi,%, for all the possible sign combinations, i, of the afi/aQ~for the symmetry species being treated. Theoretical values of the principal component scores, ria, in eq 2 are calculated by substituting the theoretical values of the polar tensor elementsinto this equation, whereas the loadings values, b$\, are those obtained from eq 1. Individual calculations of the principal component equations for each of the symmetry species of cis-CzH2Fz and the A, symmetry s p i e s of rrans-C2H2F2 are discussed below. The Al symmetry species has five infrared-active intensities and six nonequivalent and nonzero polar tensor elements, IC,) (Cd (Hd (Hi) (F4) and p!2). since there exist 32 Pzx Pzz Pzx P,, P z x 7 different combinations of signs for the five afi/aQ, and polar tensor data are available for both cis-CzHzF2 and cis-CzD2F2, the A1 symmetryspecies data matrix is 64 X 6. The B1 symmetry specieshas four nonzero afi/t3QJvaluesfor both isotopic analogues and hence has a data matrix with 32 rows. There are six nonequivalent and nonzero polar tensor elements pi?), p:?), p:?)., p g ) ,and pi?) giving origin to the six columns of the data matrm. The data matrix for the B2 species is of dimension 4 X 3 since there is only one infrared-active mode, two isotopic analogues, and there are three relevant polar tensor elements pic1),pi:), and p g ) . For the out-of-planeA, symmetry species o f b e trans isomer, there are two active fundamentals and three nonzero and nonequivalent APT elements. Hence its datamatrix, including the rrans-C2D2F2values, is 8 X 3. 9
9
9
9
pg),
The Journal of Physical Chemistry, Vol. 97,No. 23, 1993 6163
cis- and trans-Difluoroethylene Polar Tensors
TABLE I: Calculated' and Experimental* Fundamental Intensity Sums and Calculated Deviations for cisCfi82 (km mol-')
4-31G 6-31G 6-31G** 6-31++G** 6-311G** MP2/4-31G MP2/6-31G MP2/6-31G*e
126.0 129.8 184.7 211.8 204.6 90.4 91.9 140.3 127.6
16.7 16.2 16.1 22.1 20.5 14.5 13.9 4.9 -
165.7 169.6 229.2 256.1 258.1 101.3 102.9 151.6 129.2
13.8 14.6 33.5 42.8 44.0 13.0 12.6 7.2
36.4 40.7 29.9 52.9 39.5 33.6 37.8 33.4 39.0
291.7 299.4 413.9 467.9 462.7 191.7 194.8 291.9 256.8
328.1 340.1 443.8 520.8 502.2 225.3 232.6 325.3 295.8
experimental 0 Calculated values correspond to theoretically optimized molecular geometries and their corresponding force fields. Experimental values from ref 1. Fundamental intensity sum. Deviation of experimental andcalculated intensities,dev = [Ci(Ai,F"IIA,,+c)2/y] lI2. e Experimental and MP2/6-31G*, in parentheses, individual intensity values: A1 = 3.7 (8.3), A2 3: 42.0 (40.0), A3 29.4 (29.1), A4 50.7 (60.5), As = 1.8 (2.4), As = 3.7 ( l S ) , A9 20.0 (28.0), A10 = 84.9 (93.8), Ai1 = 20.6 (28.3), and A12 = 39.0 (33.4) km mo1-I. TABLE 11: Calculated' and Experimental*Fundamental Intensity Sums and Calculated Deviations for trsosCfi~zFt (km mol-') in-plane, B, out-of-plane, A,, level ZAf de@ EA! dev total Ai 4-31G 6-31G 6-31G** 6-31++G** 6-3 1 1G** MP2/4-31G MP2/6-31G MP2/6-31G* e
experimental
295.1 303.7 412.1 458.8 451.2 190.9 170.4 292.9 243.4
22.2 25.6 65.0 91.4 85.7 29.7 41.2 15.0
-
113.2 116.3 73.7 94.3 88.4 89.7 106.4 66.5 69.4
26.2 28.9 4.7 21.5 15.7 13.9 26.6 5.2
-
408.3 420.0 485.8 553.1 539.6 280.6 276.8 359.4 312.8
Calculated values correspond to theoretically optimized molecular geometries and their corresponding force fields. Experimental values from ref 3. C Fundamental intensity sum.d Deviation of experimental andcalculatedintensities,dw = [Z,(A,,ap- Ai,dc)2/n]1/2. e Experimental and MP2/6-31G*, in parentheses, individual intensity values: A9 = 9.5 (10.0), Ai0 14.7 (27.1), Ail = 217.7 (242.4), A12 1.5 (13.4), A6 56.7 (59.8), A7 = 6.7 (12.7) km mol-l.
Results Molecular orbital estimates, at the 4-31G, 6-31G, 6-31G**, 6-31++G**,and6-311G** Hartree-Focklevelandat the4-3 lG, 6-31G, and 6-31G* Moller-Plesset 2 level, of the fundamental vibrational intensity sums for cis- and trans-difluoroethylene are presented in Tables I and 11. These sums are also shown graphically for the different molecular orbital calculations in Figure 2. The conclusions drawn from this information are quite clear. Independent of the basis set used and at both the HartreeFock and Moiler-Plesset levels, the in-plane intensity sums of cis- and trans-CzHzF2 are almost the same. On the other hand, the trans-CzH2F2 out-of-plane theoretical intensity sums are always approximatelydoublethe correspondingc ~ s - C ~ H sums. ~F~ These theoretical results are in agreement with the experimental intensity sum values for the C2HzFz and C2D2Fz molecules. As such, the in-plane intensity APT elements may be transferable between cis- and trans-difluoroethylene. However, the out-ofplane elements are probably not transferable, at least for intensity calculations of the accuracy that appears to be possible for the in-plane values. The results in these tables and Figure 2 show that, of all the theoretical results, the MP2/6-3 lG* values are most consistent with the experimental intensities for both cis- and transdifluoroethylene. Not only are its fundamental intensity sums in best agreement with the experimental sums, but the sums of
100
I
4-36
6-31G
6-31GII
6-31++Gct
C.
CIS-
CIHsFz
W
Irons
- C2H2F2
MPZ/4-JIG
I-)IIGX*
Basis Set
YP216-31GI
YPZI6-nG
and
EXP
Level
Figure 2. Molecular orbital estimates of the in-plane and out-of-plane intensity sums of cis- and trans-CzHZF2 as a function of atomic orbital
basis sets at the HartreuFwk and Moller-Plesset levels.
the squares of the deviations of the individual intensities from their experimental values are less for the MP2/6-31G* results. In ref 7, the transferability of the in-plane cis- and transdifluoroethylene APT elements was studied by performing an equilibrium chargecharge flux (ECCF) analysis of ab initio 6-31G* results. Comparable charge flux parameters for these isomers dominate the electronic variations for the in-plane vibrations, accounting for their similar in-plane intensity sums. On the other hand, the ECCF model charge flux parameters do not exist for the out-of-plane vibrations, and different values of the equilibrium atomic charges for the isomers are expected to result in different out-of-plane sums. The 6-31G* intensity values are similar to those calculated with a 6-31G** basis set. The data in Tables I and I1 show large deviations of the 6-31G** intensity sums from the experimental values for both isomers. These deviations are just as large for the 6-3 lG* sums. The use of ECCF parameters obtained from 6-3 1G* Moller-Plesset-level wave function calculations would provide a more reliable interpretation of why the in-plane elements appear to be more transferable than the out-of-plane ones. The most direct way of investigating the transferability of the cis- and trans-difluoroethylene APTs would be to calculate their elements from the intensities and normal coordinate transformations of these isomers and compare the results, taking into account experimental errors. However, the determination of the in-plane trans-difluoroethylene tensor elements is difficult since the directions of the afi/dQ, vectors are not restricted along the symmetry axes. For this reason, transferability of the cis-trans APTs is tested by using the cis-difluoroethylene AFT values to predict the trans-difluoroethylene intensities. cis-Difluoroethylene APTs have been calculated previously' from their experimental intensities. However,only semiempirical CNDO molecular orbital estimates of the afi/aQIsigns were used in that work. Ab inirio molecular orbital results, especially those obtained with the Moller-Plesset perturbation treatment, are expected to provide much more accurate results and more reliable afi/aQ, signs. Furthermore, the earlier studies were not benefitted by principal component graphs that providevisual representations of all alternative experimental solutions together with all the theoretical results. cis-Difluoroethylene AI Symmetry Species. Two principal component equationscalculated for the A1 symmetry species polar tensor elements are presented in Table 111. These components describe 51% and 42% of the total data variance. Hence, the score graph for these two components, illustrated in Figure 3, accounts for 93%of the variance. The sizes of the symbols in this graph indicate the experimental uncertainty in the scores due to estimated errors (one standard deviation) in the measured intensities. The intensity errors were propagated into the score values as described previo~sly.~
"
6164 The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 TABLE III: Principal Com nent Equations for Polar Tensor Elements of c i s - C a E and cis-CzDzF2 AI symmetry species PC1 z -0.13&') - 0.61pi:1'- 0.42pi9) + 0.66p!?) PC2 ET 0.98p:;I) - 0.lOp;F) - O.l4p$"
51%" 42%
BIsymmetry species
PC1= -0.3 lp::) - 0.67pL:) + 0.3lpi?) - 0.60pL7) PC2 = 0.53pLc;')- 0.62p:yl) - 0.56p;" + 0.13pi7)
71% 22%
Bz symmetry species PC1= 4,82p$') a
+ 0.45pF) + 0.36~;:)
100%
Percentage variance described by the principal component.
0.60
6-31++G
o'20 6 - 3 l l G U d
PC2
[
PZX
(--+++)Hb
(--+++jD (..++.)H (..++.)D
(+-+++)H (+-+++)D (+-++-)H
std deV
prop error(' AI Symmetry Sprcler X- CzHzFz 0- C z h F z
)o( X
\
*-6-31G,-MPZ
< *6\ 6 - 3 I G H
-
-
3 1G M P 2
6- 31 G
-0.20
p:p
p!gId
(Cd
signs
avgc
. @
.
.
et ai.
TABLE IV Preferred APT Values. Derived from Experimental Intensities of cisCJItF2 and cisC&F~ and Their 6-316 Basis Set Molecular Orbital Estimates for the AI Symmetry Swcies
(+-++-)D
1
,
but0
6-31@ 6-31Gb* 6-31++G** 6-311G** MP2/6-31G MP2/6-31G*
0.447 0.481 0.447 0.482 0.495 0.546 0.496 0.546 0.493 0.038 0.022 0.201 0.314 0.426 0.347 0.174 0.490
0.578 0.566 0.517 0.506 0.515 0.507 0.454 0.447 0.511 0.046 0.027 0.667 0.779 0.806 0.813 0.564 0.673
-0.042 -0,014 -0.048 -0,027 0.002 0.026 -0.004 0.013 -0.012 0.026 0.042 -0.023 -0.037 -0.03 1 -0.040 -0.027 O.OO0
~
&4)
-0.014 -0.045 -0.015 -0.045 0.058 0.020 0.058 0.019 0.005 0.041 0.004
0.210 0.209 0.454 0.445 0.209 0.208 0.454 0.444 0.329 0.129 0.012 0.004 0.185 -0.026 0.276 -0.011 0.311 -0.018 0.301 -0.013 0.147 -0.024 0.553
-0.564 -0.521 -0.502 -0.461 -0,573 -0.527 -0.51 1 -0.467 -0,516 0.040 0.007 -0.672 -0.753 -0.795 -0.794 -0.551 -0.650
a Units of electrons, e. *The signs of afi/aQ,, j = 1,2, ...,5. C Average and standard deviation values for the above eight alternative solutions. d Polar tensor element errors propagated from the experimental intensity measurement errors. e Molecular orbital calculationsproviding the better intensity sum estimates. -100
-060
020
-020
0
eo
100
Symmetry
81
Specier
PC1
Figure 3. Principal component score graph of the A1 symmetry species polar tensor element values as a function of the signs of the afi/aQ, (j = 1-5) for c ~ s - C ~ H Thisgraphcontains9396of ~F~. the totaldatavariance.
Several pairs of symbols, each with one for cis-CzHzF2 and one for cis-C2DzF2, overlap in this figure, indicating possible isotopically invariant pairs. The theoretical scores of the MP2/631G* molecular orbital calculation as well as those for the other quantum calculationsindicate that the well-definedgroup of eight symbols, four for C2H2F2 and four for CzDzF2, circled in the upper-left-hand corner of Figure 3 most certainly contains the correct set of signs for the isotopicanalogues. These eight symbols correspond to the (&-++&) combination of signs in the order d$/dQ, (j = 1, 2, ..., 5) for both isotopically related molecules. A sign uncertainty remains for d$/dQ5 since the As intensity values (1.8 and 1.7 km mol-' for c~s-C~HZFZ, respectively) correspond to less than 1% of the total AI symmetry intensity sums. The MP2/6-31G* element values, especially the one calculated for &'), seem to indicate that a negative ajj/dQj should be preferred. Also, the C ~ H ~ and F Z CzDzF2 signs for d$/dQ1 are difficult to determine because the A1 intensity values for both isotopic analogues are very small (3.7 and 1.7 km mol-'). As such, it is not possible to choose one setxamong the four alternatives. Since the a$/dQ~ and d@/dQ5 ambiguities cannot be securely resolved, average values of the (*-++*)H.D sets are used for the cis-difluoroethyleneAPT values. The average values of the eight sign sets and their standard deviations have been included in Table IV. The standard deviation values are a bit larger than the estimated errors of ref 1 obtained from the measurement errors in the intensities, except for the pLfr'" element. It is recommended that the larger of the standard deviation or the propagated error value be used as the error estimate of each APT value. Based on CNDO calculated signs of the dipole moment derivatives, the (-+++) sign combination for both cis isotopic analogues was selected as the correct one in ref 1. However, the principal component graph clearly illustrates that this sign selection is only one possible correct result. It should be remembered that the sizes of the symbols for the alternative cisC2H2F2 and c ~ s - C ~ Dresults ~ F ~ are for errors derived from only the intensity measurement source and correspond to one standard deviation. Assuming 95% confidence level errors and all error
X
I
pc*
- ~ ,
,
,
~
~
,,
,
,
xn
,
j" ,
-0 bo -1
40
- I 00
-060
- 0 20
0.20
Ob0
100
PCI
F g v e 4. Principal component score graph of the B1 symmetry species polar tensor element values as a function of the signs of the afi/aQ, (j = 8-11) for c ~ s - C ~ H ~This F ~ .graph contains 93% of the total data variance.
sources, these symbols would occupy areas several times larger than those in Figure 3, increasing the degree of overlap among the eight symbols. cis-Difluoroethylene B1 Symmetry Species. The first two principal componentsalso describe 93% of the total data variance, and their equations are given in Table 111. The principal component graph illustrating the dependence of the polar tensor score values on the signs of the d$/aQ, is presented in Figure 4. The molecular orbital calculations have scores positioned in the second quadrant of this graph, clearly indicating that the correct experimental results also fall in this region. The C ~ H ~ F T C ~ D ~ F Z pair that clearly overlaps in this quadrant corresponds to the (++-+) sign combination. The alternative (-+-+) choice appears less likely to be correct based only on this experimental evidence since larger errors would have to be assumed to satisfy the isotopic invariance criterion. The APT values and their estimated errors for these sign combinations of c ~ s - C ~ Hand ~F~ c ~ s - C ~ Dare ~ Fpresented ~ in Table V. However, here again, not all possible experimentalerror sources have been considered in the calculation of the APT errors listed in Table V. These lower bound errors have been propagated into the score values and are indicated by the sizes of the symbols in Figure 4. If error sources other than the one arising from the intensity measurements are also important, the symbols for the (-+-+)H and (-+-+)D combinations could overlap, implying isotopic invariance. In fact, previous principal component
The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6165
cis- and trans-Difluoroethylene Polar Tensors TABLE V Preferred APT Values' Derived from Experimental Intensities of ci4CJI82 and &C&F2 and Their 6-316' Basii Set Molecular Orbital Estimates for the B1 Symmetry Species signs (++-+)Hb
(++-+jD (-+-+)I+
(.+.+)D
(-+-+)avgc std deV properror' 6-31W 6-31G** 6-31++G** 6-311G** MP2/6-31G MP2/6-31G*
(CI) Pu
Pxr
pp
0.451 0.404 0.497 0.488 0.492 0.006 0.048 0.584 0.659 0.675 0.690 0.482 0.538
0.516 0.480 0.453 0.355 0.404 0.069 0.049 0.528 0.619 0.685 0.670 0.372 0.490
0.047 0.097 0.004 0.019 0.012 0.011 0.015 0.047 0.033 0.043 0.038 0.036 0.037
(Cd
pp 0.016 0.021 -0.057 -0.109 -0.083 0.037 0.019 0.009 -0.006 0.013 0.001 0.000
~~~~
-0.499 -0.501 -0.501 -0.507 -0.504 0.004 0.042 -0.632 -0.692 -0.718 -0.728 -0.519 0.OOO -0.575
0.493 0.506 0.503 0.520 0.512 0.012 0.027 0.527 0.684 0.713 0.723 0.397 0.553
Units of electrons. The signs of the afi/aQ,, j = 8-1 1. Average and standard deviation values for the (-+-+)sign alternative. Polar tensor element errors propagated from the experimental intensity measurementerrors. e Molecular orbitalcalculationsproviding the better intensity sum estimates. a
TABLE VI: Alternative Polar Tensor and Score Values' Obtained from Experimental Intensities of us-Cfi82 and cisC2D2Fz and Their Molecular Orbital Estimates for the B2 Symmetry Species sign of ap/aQI2
p(cl)
w cis-CzHzFz -0.060 cis-CzDzFz -0.065 c ~ s - C ~ H ~-F Z 0.387 c~ss-C~D ~ F ~ 0.318 -0.063 avgb std devb 0.004 prog errofl 0.003 6-31G 0.019 6-31G** -0,013 6-3 1 ++G** -0.066 6-311G** 0.006 MP2/6-31G -0.004 MP2/6-31GL -0.043
+
+
p(H3)
YY
0.157 0.160 -0.091 -0.053 0.159 0.002 0.002 0.175 0.146 0.203 0.183 0.164 0.148
p) YY -0.097 -0.095 -0.296 -0.265 -0.096 0.001 0.003 -0.194 -0.133 -0.188 -0.189 -0.160 -0.105
TABLE W: Alternative Polar Tensor Values. Obtained from trpo4Difluoroethylene Experimental Intensities and Their Molecular Orbital Estimates for the B. Symmetry SDecies signs p(cl) p(t4) p(F3) w YY YY
score +0.085 +0.090 -0.464 -0.379
-0.007 +0.029 +0.078 +0.010 +0.020 +0.064
Units of electrons. Average and standard deviation values for the afi/aQlz > 0 sign alternative. Polar tensor errors propagated from the experimental intensity measurement errors. a
analysesgJ0 have shown that the propagated errors calculated from only intensity measurement errors are several times smaller than the errors expected based on the comparison of the APT elements of isotopic analogues. Strong evidence that the (-+-+)HsD combination is the correct one is provided by the molecular orbital results. As shown in Figure 4, all basis set Hartree-Fock and Moller-Plesset calculations lead to results in better agreement with the APTs of this sign set than with those corresponding to the (++-+)H,D sign set. As such, the (-+-+) alternative with symbols circled in Figure 4 is preferred here for both cis-CzHzFz and c ~ s - C ~ D Z FIn~ . Table V, average and standard deviation values of the APT elements for this sign combination are presented along with the pertinent theoretical values. It is worth noting that the (-+-+) combination was also preferred on the basis of CNDO-calculated derivative signs.' cis-Difluoroethylene B2 Symmetry Species. This symmetry species contains only one infrared-active fundamental. Hence, thep('I),pF), and p p ) values can be exactly represented by one YY principal component score (see Table 111). In Table VI, the BZ polar tensor element and score values are presented for the experimental alternative sets and the molecular orbital results. Clearly the molecular orbital results are in closest agreement with the polar tensor and score values for the positive sign choice for a@/aQlz. In fact, all of the signs of the AFT elementspredicted
(++F (++j"
(+-IH (+-ID
avgb std de9 6-31G 6-31G** 6-31++G*' 6-31 1G** MP2/6-31G MP2/6-31G* a
-0.390 -0.312 0.015 -0.01 0 0.003 0.018 0.032 0.005 -0.057 -0.026 0.006 -0.024
0.138 0.102 0.181 0.192 0.187 0.008 0.237 0.189 0.217 0.209 0.228 0.182
0.249 0.268 -0.200 -0.186 -0.193 0.010 -0.269 -0.194 -0.160 -0.184 -0.234 -0.157
Units of electrons. Average and standard deviation values for the
(+-) sign alternative.
by the molecular orbital calculations at the Moller-Plesset level are in agreement with the signs of these elements for dj/aQ12 > 0. trmsDifluoroethyleneB.Symmetry Species.The out-of-plane trans-difluoroethylene symmetry species contains two infraredactive fundamental bands, v6 and v7. Two alternative sets of APT element values are presented in Table VI1 along with the values calculated using the various basis sets at the H a r t r e e Fock and Moller-Plesset levels. Two other sets of APT alternatives, (--) and (-+) calculated from the experimental intensities, have equal magnitudes but oppositesigns to the values in this table for the (++) and (+-) sets. All the molecular orbital estimated APT elements are in excellent agreement with the (+-) set of experimentallyderived values. A principal component graph (an exact two-dimensional representation for this symmetry species) shows that this alternative satisfiesthe isotopic invariance criterion a little better than the (++) alternative. As such, the averages of the (+-) APT element values of rrans-C2H2Fz and trans-CzDzF2 are selected as the preferred values.
Discussion Transferenceof the cis- and trans-difluoroethyleneatomic polar tensors was tested in the followingmanner. The average preferred c~s-C~H and ~ cis-CzDzF2 F~ polar tensor element values of Tables IV-VI for the hydrogen and fluorine atoms were transferred to the trans isomer after being transformed to take into account the different relative positions of these atoms in the two isomers. The carbon polar tensor element values were obtained from the null tensor equation, Z,P$) = 0.For the four in-plane trans-C2H2Fz fundamentals, the transferred cis values result in estimates of 7.9, 6.6, 213.7, and 5.0 km mol-' for Ag, Ala, All, and ,412, respectively. These values are in excellent agreement with the experimental values of 9.5, 14.7, 217.7, and 1.5 km mol-' for trans-C2H2F2,providing strong evidence for the transferability of the cis- and trans-difluoroethylene in-plane AFT elements. The calculated 233.2 km mol-' sum is almost the same as the 243.4 km mol-' experimental fundamental intensity sum of rransCzH2F2. For the out-of-plane fundamentals, transference of the cis atomic polar tensors is not as accurate. This can be confirmed by comparing the preferred out-of-plane AFT element values for cis-and trans-difluoroethylenein Tables VI and VII. The largest discrepancy occurs for the p!? values, -0.096e and -0.1 93e, for cis- and trans-difluoroethylene. The calculated 46.9 and 3.7 km mol-' values for and A7 of trans-difluoroethylene using the averaged cis-difluoroethylene APT elements are significantly smaller than the 56.7 and 12.7 km mol-' values measured for the trans-CzHzF2 fundamental intensities. As such, the calculated 50.6 km mol-' intensity sum is significantly less than the 69.4 km mol-' experimental sum for trans-difluoroethylene.
6166 The Journal of Physical Chemistry, Vol. 97,No. 23, 19513
These results are consistent with those obtained from the molecular orbital calculations. For all basis sets at both the HartreeFock and Moller-Plesset levels, the in-plane cis and trans intensity sums are estimated to be the same although the out-of-planesum for transts-C2H2F2is always significantly larger than the one calculated for its cis isomer. It is not easy to explain why the in-plane polar tensor elements are transferable between the isomers whereas the out-of-plane elements are not. It has been suggested' that although the charge flux contributionsto the in-plane polar tensor elements are about the same for both isomers the fluorine atomic charges are somewhat different. Also, smaller differencesare calculated for the hydrogen and carbon charges. Since charge fluxes are predominant contributions for the in-plane intensities whereas the atomic charges determine the out-of-plane intensities, one might expect essentially equal in-plane intensity sums for these isomers and different out-of-plane sums. The a v e r a g e $ )value of -0.193e determined from the trunsCzHzFzand trans-C2DzF2experimentalintensities is much larger than the -0,096e average value for this element of cis-difluoroethylene. This difference is consistent with chemical valency arguments based on molecular structure. Recently, analysis of high-resolution infrared spectra of trans-difluoroethylenehas led to a proposed equilibrium geometry for which the C-F bond in the trans isomer is slightly longer than the one in the cis molecule.15 This indicates slightly more p character for the trans CF bond, confirmed by the smaller CCF angle (1 19.6') proposed for the trans isomer in comparison with the larger value of this angle (122.1') for the cis compound. An increase in p character can be expected to result in a larger negative charge on the terminal atom. As such, the negative fluorine atomic charge in transdifluoroethylene can be expected to be slightly larger than the one in cis-difluoroethylene. Of course, the small differences in the equilibrium geometries of the cis and trans isomers cannot be expected to explain all of the differencein thep(Z)polar tensor element values of these isomers or the entire diffYerence in their out-of-plane intensity sums. However, it is reassuring that the observations are consistent with electrostatic principles and the slightly greater cis isomer stability. For the basis sets studied here, all the Moller-Plesset level molecular orbital results confirm these arguments, with the trans isomer having longer C F bonds, smaller CCF angles, and more negative fluorine atoms. For example,our MP2/6-3 1G* calculations result in a CF bond length
Suto et al. of 1.353 A and a CCF angle of 119.8' for the trans isomer, whereas the corresponding values for the cis isomer are 1.348 A and 122.0'. These results are in excellent agreement with the geometries derived on the basis of experimental evidence and those calculated at the MP4/6-31G* level.16 The hydrogen equilibrium charges of the isomers also appear to contribute to the different out-of-plane intensity sums. The average value of 0.159e derived from the cis-CzHzFz and c ~ s - C ~ D ~intensities FZ is significantly less than the corresponding 0.18 1e trans value. A smaller hydrogen atom charge in the cis isomer might be expected since the repulsive H-H interaction in this isomer is absentin the trans compound. Again, the MollerPlesset level molecular orbital results confirm this, with the hydrogen atom having smaller calculated Mulliken charges for cis-C2H2Fz.
pp'
Acknowledgment. The authors thank FAPESP and CNPq for partial financial support. References and Notes (1) Kagel, R. 0.; Powell, D. L.; Overend, J.; Ramos, M. N.; Bassi, A. B. M. S.; Bruns, R. E. J. Chem. Phys. 1983, 78, 7029. (2) Hopper, M. J.; Overend,J.; Ramos, M. N.;Bassi, A. B. M. S.;Bruns, R. E. J . Chem. Phys. 1983, 79, 19. (3) Kagel, R. 0.;Powell,D. L.; Overend,J.; Hopper, M.; Ramos, M. N.; Bassi, A. B. M. S.;Bruns, R. E. 1.Phys. Chem. 1984,88, 521. (4) Ramos, M. N.; Neto, B. B.; Bruns, R. E. J. Phys. Chem. 1985,89, 4979. (5) Crawford, B. L., Jr. J. Chem. Phys. 1952,20, 977. (6) h a , C.; Bartlett, R. J.; KuBulat, K.; Person, W. B. J. Phys. Chem. 1989, 93, 517. (7) Ramos, M. N.; Fausto, R.; Teixeira-Dias, J. J. C.; Castiglioni, C.; Gussoni, M.; Zerbi, G. J . Mol. Strucr. 1991, 248, 281. (8) Mardia, K. V.; Kent, J. T.; Bibby, J. M. Mulrivuricrre Analysis; Academic Press: New York, 1979; pp 213-254. (9) Suto, E.; Fcrreira, M. M. C.; Bruns, R. E. J. Compur. Chem. 1991, 12, 885. (10) Suto, E.; Bruns, R. E.; Neto, B. B. J. Phys. Chem. 1991, 95,9716. (11) Person, W. B.; Newton, J. H. J. Chem. Phys. 1974, 61, 1040. (12) Bassi, A. B. M. S. Doctoral Thesis, Universidade Estadual de Campinas, 1975. (13) Frisch, M. J.; Head-Gordon, M.; Schlegel,H. B.;Raghavachart, K.; Binkley, J. S.; Gonutlez, C.; Defrces, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Nuder, E. M.;Topiol,S.;Pople,J. A. GAUSSIAN 88; Carncgie-Mcllon Quantum Chemistry Publishing Unit: Pittsburgh, 1988. (14) Scarminio, I. S.;BNW, R. E. Trends Anal. Chem. 1989,8, 326. (15) Craig, N. C.; Brandon, D. W.; Stone, S.C.; Lafferty, W. J. J . Phys. Chem. 1992,96, 1598. (16) Saebo, S.;Sellers, H. J. Phys. Chem. 1988, 92, 4266.
