Infrared vibrational intensities and polar tensors of CF3Br and CF3I

THEOCH 5998

Journal of Molecular Structure (Theochem) 464 (1999) 171–182

Infrared vibrational intensities and polar tensors of CF3Br and CF3I Harley P. Martins Filho a,*, Paulo H. Guadagnini b a

Departamento de Quı´mica, Universidade Federal do Parana´, CP 19081, CEP 81531-990, Curitiba, PR, Brazil b Instituto de Quı´mica, Universidade Estadual de Campinas, CP 6154, CEP 13081-970, Campinas, SP, Brazil

Abstract The polar tensors of CF3Br and CF3I determined from experimental intensities are reported. The sign ambiguities in the dipole moment derivatives derived from the intensities give rise to several polar tensor solutions, the most physically significant of which being chosen upon comparison with the results of ab initio molecular orbital calculations. The comparison is made more efficient by projecting the polar tensor space in bidimensional principal component graphs. The carbon mean dipole moment derivatives and effective charges in both molecules are in good agreement with estimates from electronegativity model equations obtained from fluoro- and chloromethane polar tensor data. The sum intensities of the two molecules are in good agreement with values estimated from the G sum rule in which electronegativity model estimations for the effective charges are used. Moreover, the carbon mean dipole moment derivatives of these molecules can be taken as atomic charges in a simple model recently proposed for estimation of atomic 1s core electron energies in molecular environments in which a linear relationship is expected to exist between the charge of the atom and its 1s core electron energy corrected for the electrostatic potential from neighboring atoms. The carbon mean dipole moment derivatives of CF3Br and CF3I fit very well a previous model regression of the relationship based on values of mean dipole moment derivatives for several halomethanes containing sp 3 carbon atoms. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: Vibrational intensities; Polar tensors; Electronegativity models; Atomic charges

1. Introduction In recent studies on the interpretation of infrared intensities through polar tensor theory the atomic tensor invariants (mean dipole moment derivative and effective charge) of halomethanes have been related to electronegativity parameters in models built to allow invariant estimation [1,2] and molecular intensity sum estimation [2]. According to the G intensity sum rule [3], the intensity sums are partitioned into additive contributions from each of the atoms in the molecules. These contributions are related to the electronegativities of the neutral isolated * Corresponding author. Fax: ⫹55 41 3613186. E-mail address: [email protected] (H.P. Martins Filho)

atoms. The carbon atom contributions are related to the mean electronegativity values of their substituent atoms. The terminal substituent atom contributions are related to their own electronegativity values. This simple intensity–electronegativity model was parametrized using a training set of eight halomethanes intensity sums. The model predicts the experimental intensity sums of a test set of 24 molecules with an average absolute deviation of 56 Km mol ⫺1. The deviation can be compared with a total intensity sum variation of about 1300 Km mol ⫺1 for the halomethanes. Considering the model’s simplicity, its predictions are very accurate. The basis of the invariant-electronegativity relationships is analyzed in a latter work [4] in which

0166-1280/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(98)00549-1

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CCFO contributions [5] to the carbon atom mean dipole moment derivative are calculated through molecular orbital results at Moller–Plesset (MP2) level using extensive basis sets. According to the CCFO partitioning, changes in dipole moment caused by atomic movement may be provoked by point charge movement, intramolecular charge transfer or changes in a non-classical overlap contribution. The results suggest that the linear dependence of the carbon mean dipole moment derivatives of fluoromethanes on the mean electronegativity values of substituent atoms could be explained by a point charge electrostatic model, while for the chloromethanes a similar existing linear dependence should be explained mainly by intramolecular charge transfer. As a result of the different electronic behaviors for the two groups of molecules, the slope of the model equations are significantly different in each case, although the CH4 data are common to both linear relationships. A recent determination of the CFCl3, CF2Cl2 and CF3Cl polar tensors [6] allowed a further testing of the models with molecules that are both fluoro- and chloromethanes. Correspondingly, the carbon mean dipole moment derivatives of these molecules showed to be intermediate to those expected on the basis of separate fluoro- and chloromethane models. Both point charge movement and charge transfer should be important in explaining the changes in dipole moment for these molecules, thus. In addition, the mean dipole moment derivatives of the fluorine/chlorine atoms are found to vary with the degree of fluorine/chlorine substitution, which is in contrast with the almost constant values of these quantities already reported for the separate fluoro- and chloromethanes. More recently, the electronic structure of halomethanes and several other kinds of molecules as reflected in the carbon mean dipole moment derivative values have been related to carbon 1s electron binding energies through data obtained from X-ray photoelectron spectroscopy [7]. The basic relation is established by taking the carbon mean dipole moment derivative as the carbon atomic charge in a simple potential model proposed by Siegbahn et al. [8] for estimating carbon 1s binding energies through a direct linear relationship to the carbon atomic charge. One finds that the 1s experimental ionization energies corrected for electrostatic potentials from neighboring

atoms (the 1s binding energies) are linearly related to the carbon mean dipole moment derivatives. The model regressions present different slopes according to the carbon atom hybridization, but the slopes are shown to be proportional to the inverse atomic radii of sp 3, sp 2 and sp carbon atoms. According to the simple potential model the slopes can be interpreted as estimates of Coulomb repulsion integrals involving these hybridized orbitals and the 1s core electron orbitals. This last feature of the model is particularly interesting, for it allows a unified interpretation of the model for different kinds of molecules. So far the electronegativity models for band intensities interpretation [1,2] have been restricted (and have been succesful) to the analysis of data from halomethanes containing sp 3 carbon atoms only. The calculations and analysis of the atomic mean dipole moment derivatives seem to yield electronic structure models in accordance with both infrared and X-ray photoelectron spectroscopy data. For the consolidation of the models it is highly desirable to determine the atomic polar tensors and their invariant quantities for all the molecules for which experimental infrared intensities have been measured, but the quantity of these data available is still limited. The infrared intensities of the halomethanes CF3Br and CF3I have been measured some time ago but their polar tensors have not been reported previously, most probably because of problems in resolving the sign ambiguities in the dipole moment derivatives with respect to the normal coordinates, the 2p~=2Qi . Their intensity sums are accurately predicted using the electronegativity model [2] (suggesting that their atomic invariants may fit all the models cited earlier in the text), and their 1s carbon atom experimental ionization energies have long been available [9]. Molecular orbital estimates of their polar tensors, necessary to resolve the sign ambiguities in dipole moment derivatives, are nowadays easily and rapidly done, though the presence of Br and I atoms make convenient the use of effective core potential basis sets. The polar tensors of CF3Br and CF3I may provide valuable testing of the models for tensor invariants and 1s binding energies estimation, though systematic trends in molecules containing Br and I atoms cannot be analyzed owing to lack of more experimental intensity data for other molecules.

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Table 1 ˚ rad ⫺1) and equilibrium geometry Experimental infrared fundamental frequencies (cm ⫺1), intensities (Km mol ⫺1), L ⫺1 matrices (u 1/2 and u 1/2 A parameters for CF3Br and CF3I CF3Br

CF3I

Frequencies and intensities Sym. i A1 1 2 3 E 4 5 6

ni 1085 761 350 1209 550 305

Ai 463.6 29.4 0 464.5 2.4 0

L ⫺1 matrices A1 0.2204 1.1660 ⫺5.9683 E 2.1647 2.5751 1.7179

⫺2.2709 3.5914 ⫺0.3683 ⫺0.1249 0.4240 4.1854

0.7760 1.3862 2.9149 0.3070 ⫺2.8501 0.8873

Error 14.8 2.9 0 9.3 0.15 0

Geometrical parameters and equilibrium dipole moments ˚ r (CF) ˆ 1.326 A ˚ r (CBr) ˆ 1.933 A ⬔FCF ˆ 109.47 o p o ˆ 0.65 D

I 1 2 3 4 5 6

ni 1074 743 284 1185 539 260

Ai 573.3 43.0 0.15 445.2 2.1 0.04

0.0667 0.9018 ⫺6.6243 2.2498 2.4887 1.7149

⫺2.4328 3.4751 ⫺0.6239 ⫺0.0168 0.3246 4.4043

0.7639 1.5535 3.0637 0.2795 ⫺2.8825 0.7454

˚ r (CF) ˆ 1.326 A ˚( r (CBr) ˆ 2.162 A ⬔FCF ˆ 109.47 o p o ˆ 1.0 D

1.1. Calculations

The polar tensors are calculated using

The polar tensors of the halomethanes are the juxtapositions of their five atomic polar tensors (APTs) [10],

PX ˆ PQ L⫺1 UB ⫹ P6 b

!

.. …Y† .. …X1 † .. …X2 † .. …X3 † : PX ˆ P…C† X .P X .P X .P X .P X

…1†

Each APT, PX…a† , is defined as 0

2px =2xa

B P…Xa† ˆ B @ 2py =2xa

2px =2ya 2py =2ys

2px =2za

1

C 2py =2za C A

2pz = 2x a 0

p…xxa† B B ˆ B p…yxa† @ p…zxa†

2pz =2ya 2pz =2za 1 p…xya† p…xza† C C p…yya† p…yza† C A …a † …a † pzy pzz

Error 16.9 1.4 0.03 29.2 0.3 0.01

…2†

where a represents the specific atom, C, F, Br and I.

…3†

where PQ is a matrix containing the 2p~ =2Qi elements, which are directly related to the experimentally measured intensities associated with the i ˆ 1; 2; …; …3N ⫺ 6† normal modes. The L ⫺1UB product transforms the dipole moment derivatives from normal to atomic Cartesian coordinates [11] whereas P6 b represents a rotational contribution to the polar tensor for molecules with non-zero permanent dipole moments [10]. As the signs of the 2p~ =2Qi derivatives cannot be assessed through the relation to band intensities, arbitrary attributions of signs result in polar tensor sets that are mathematically equivalent. The most physically significant set must be chosen through additional criteria. As the values of the polar tensor elements depend on the molecular orientation of the molecule in a space-fixed Cartesian coordinate system, invariant quantities defined using the polar tensor elements

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Fig. 1. Molecular orientation of halomethanes of C3v symmetry relative to a space field Cartesian coordinate system and internal and symmetry coordinate definitions.

are used to compare results of different molecules. The atomic mean dipole moment derivative is defined using the trace of the atomic polar tensor p a ˆ

1  …a †  Tr PX : 3

…4†

The sum of all the atomic mean dipole moment derivatives of a neutral molecule is zero. This and other useful properties of this invariant quantity have resulted in a proposal to interpret it as an atomic charge [12]. A second invariant polar tensor quantity is called effective charge and is defined by

x2a ˆ

1  …a † …a † 0  Tr PX PX ; 3 0

…5†

where P…Xa† stands for the transpose of the a atom polar tensor. The atomic effective charges are important because their reciprocal atomic mass-weighted values provide

contributions to the fundamental intensity sum via the G sum rule [3] (to be analyzed in detail later). The values of the experimental fundamental vibrational frequencies, the infrared intensities and their errors, the L ⫺1 matrices, the equilibrium geometry parameters and the permanent dipole moment values of CF3Br and CF3I are reproduced in Table 1. The intensity and frequency values were obtained from the works of Person and Polo [13] for CF3Br and Person et al. [14] for CF3I. Both the A1 and E symmetry species normal modes for both molecules have one intensity that is very close to zero although these bands are not inactive because of symmetry. In this case, the sign of the corresponding dipole moment derivatives cannot be resolved. The L ⫺1 matrices used in the calculation of the polar tensor elements were obtained from the complete quadratic force field in terms of internal coordinates of McGee et al. [15]. The molecular geometry parameters [16] were also taken from this reference, whereas the permanent dipole moment value is from Ref. [17]. The molecular orientation of these molecules relative to a space-fixed Cartesian coordinate system is given in Fig. 1, along with internal and symmetry coordinate definitions necessary to calculate both L ⫺1 matrices and polar tensor elements. The coordinate definitions are the same as those used in Ref. [15]. The polar tensors were calculated from each set of experimental intensity values for all possible sign alternatives using the TPOLAR program [18], which performs the calculations of Eq. (3). Molecular orbital calculations were carried out using the GAUSSIAN 92 computer program [19] on an IBM RISC 6000 workstation. For Br and I atoms basis functions are not defined in most of the standard basis sets. For CF3Br we used the basis set of Morgon et al. [20], derived from the uncontracted 14s11p5d basis set described by Dunning [21]. This basis set was used in conjunction with pseudo-potentials of Hay and Wadt [22]. For CF3I we used the standard basis sets 3-21G** [23] and LANL2DZ [24], besides the SBKJC VDZ ECP basis set defined by Stevens et al. [25] where the pseudo-potentials include relativistic effects. As the halomethanes treated here do not contain hydrogen atoms, the signs of the dipole moment derivatives with respect to the normal coordinates, 2p~=2Qi cannot be determined using isotopic invariance

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criterion. For this reason these signs are determined using only the results of the molecular orbital calculations. As such all the sets of polar tensor element values for the various 2p~=2Qi sign alternatives should be compared with all the results of the molecular orbital calculations performed. This comparison can simply be made by inspection of a table of values containing all the results determined from the experimental intensities and all those calculated using the molecular orbital wave functions. This analysis becomes more efficient if graphical methods capable of dimensionality reduction such as principal component analysis [26] are used. In this way all the mathematical solutions obtained from the experimental intensity values for the different 2p~ =2Qi sign alternatives can be visually compared with the theoretical estimates [27]. The score of the ath principal component used in the graphical representation for the jth sign combination of the 2p~=2Qi is given by [27] ÿ
X X … a † ÿ
…a † ÿ
psn j bsn;a ˆ PCa j …6† ta j ˆ a

sn

where the sum is taken over all non-zero and nonequivalent polar tensor elements in the symmetry species being treated. The coordinate axis for the ath principal component is represented by PCa. The s n th (s ,n ˆ x, y, z) element of the atomic polar tensorÿof
the ath atom for the jth sign set is designated a† j . The ath principal component loading for the byp…sn s n th polar tensor element of atom a is represented a† byb…sn ;a . The modelling error is assumed to be zero in this analysis, because all or almost all the data variance is explained by the first two principal components. Exact distances between points representing experimentally and theoretically derived polar tensor sets of values can always be calculated to check possible distortions that can occur upon projecting higher order spaces onto two-dimensional spaces. The A1 symmetry species for CF3Br and CF3I has three infrared-active bands. However, the CF3Br molecule has only two bands with non-zero intensities, simplifying the analysis for obtaining the correct mathematical solution of the polar tensor elements for the experimental intensities. Each molecule has non…Y† …F1 † …F1 † zero, p…C† zz ; pzz ; pzx , and pzz (Y ˆ Br or I) elements for this symmetry species. Although the molecules have multiple fluorine atoms, their polar tensors

175

elements are related by unitary rotational transformations, and only the elements of one of these atoms need be considered in comparing tensors obtained from the experimental intensities with those calculated from molecular orbital wave functions. As such the polar tensor space for the A1 symmetry species of these molecules is formally four-dimensional, corresponding to the four unique polar tensor elements of A1 symmetry, whereas the intrinsic dimensionality is two for the CF3Br molecule, corresponding to the number of non-zero fundamental intensities. The E symmetry species for these molecules has five non-zero and unique polar tensor elements, …Y† …F1 † …F1 † …F1 † p…C† xx ; pxx ; pxx ; pyy and pxz . These five polar tensor elements completely describe the variations in the molecular polar tensor values for all the possible 2p~ =2Qi (i ˆ 4–6) sign combinations. The E symmetry species polar tensor space is formally five-dimensional. However, each of the CF3Br and CF3I molecules has one band too weak to be measured. As such the intrinsic dimensionality of this space is twofold. As a consequence the bidimensional principal component representations of these spaces are exact. The principal component scores and loadings can be calculated separately for each symmetry species of each molecule. A data matrix is formed, for which each row corresponds to an alternative combination of signs for the 2p~=2Qi and each column corresponds to one of the unique non-zero polar tensor elements for the symmetry species being considered. The covariance matrix, which is formed by premultiplying this data matrix by its transpose, is then diagonalized to obtain the scores and loadings [26]. Molecular orbital values of the tensor elements are not used to calculate the principal component equations (Eq. (6)). Instead these values are substituted into the principal a† component equations with loadings, b…sn ;a; , determined from the alternative polar tensor values obtained from the experimental intensities. The principal component scores calculated using the molecular orbital values can then be compared with the alternative score values calculated for the different sign combinations of the2p~=2Qi . In other words, the polar tensor values obtained from the molecular orbital calculations are projected onto the principal component space formed using all possible polar tensor element values obtained from the experimental intensities.

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Fig. 2. Bidimensional principal component representation of the A1 symmetry species polar tensor elements of CF3Br (hf ˆ HF/Morgan et al. Basis set [20] and mp2 ˆ MP2/Morgon et al. Basis set [20]).

2. Results 2.1. CF3Br The bidimensional principal component representation of the A1 symmetry species polar tensor elements of this molecule is shown in Fig. 2. The first two principal component score equations are listed in Table 2. These principal components explain all of the total data variance in the polar tensor element values as a result of the possible sign attributions of the 2p~=2Qi values. Hence the bidimensional representation is an exact projection from the four-dimensional A1 polar tensor space. As the intensity for the Table 2 Principal component equations for CF3Br and CF3I and their associated percentage variance values PC equation CF3Br A1

E

CF3I A1

E

…C† PC1 ˆ 0:90pzz ⫺ 0:07p…Br† zz ⫹ …F1 † …F1 † 0:32pzx ⫺ 0:28pzz …C† PC2 ˆ 0:29pzz ⫺ 0:39p…Br† zz ⫺ …F1 † …F1 † ⫹ 0:03pzz 0:87pzx …C† PC1 ˆ 0:85pxx ⫺ 0:02p…Br† xx ⫺ …F1 † …F1 † …F1 † 0:47pxx ⫺ 0:08pyy ⫹ 0:17pxz …C† PC2 ˆ ⫺0:27pxx ⫹ 0:07p…Br† xx ⫺ …F1 † …F1 † …F1 † ⫹ 0:74pyy ⫹ 0:03pxz 0:61pxx

…C† …I† PC1 ˆ 0:89pzz ⫺ 0:02pzz ⫹ …F1 † …F1 † 0:35pzx ⫺ 0:29pzz …C† …I† PC2 ˆ 0:34pzz ⫺ 0:32pzz ⫺ …F1 † …F1 † 0:88pzx ⫺ 0:01pzz …C† …I† PC1 ˆ 0:85pxx ⫺ 0:03pxx ⫺ …F1 † …F1 † …F1 † 0:49pxx ⫺ 0:07pyy ⫹ 0:20pxz …C† …I† PC2 ˆ 0:28pxx ⫹ 0:05pxx ⫺ …F1 † …F1 † …F1 † 0:60pxx ⫹ 0:75pyy ⫹ 0:01pxz

%Variance

95.3 4.7 99.5 0.5

94.4 5.5 99.5 0.5

third normal mode is zero, only four different sign attributions exist for the A1 symmetry 2p~ =2Qi . The principal component scores for the polar tensor element values for the four alternative sign choices are represented by the open squares in the figure. The first principal component explains 95.5% of the total data variance and has a predominant positive contribution fromp…C† zz . In other words the horizontal separation in Fig. 2 corresponds to 2pz =2zC positive and negative values. As the carbon atom is undoubtedtly positively charged in CF3Br, only the (⫺⫺0) and (⫺ ⫹ 0) sign combinations on the right-hand side of this figure need be considered as possible ÿcorrect solutions. Of these only the (⫺⫺0)
alternative 2p~=2Q1 ⬍ 0; 2p~=2Q2 ⬍ 0; and 2p~ =2Q ˆ 0 is in excellent agreement with the polar tensor values obtained from the molecular orbital calculations. It is interesting to note that both the theoretical estimates obtained from the HF/ and MP2/Morgon et al. basis set [20] wave functions and represented by triangles in Fig. 2, are in close agreement with this sign alternative. The polar tensor elements calculated from the experimental intensities using these signs for the 2p~=2Qi are in much better agreement with the theoretical values than are those of the (⫺ ⫹ 0) sign combination. The tensor elements for the sign choices (⫺⫺0) and (⫺ ⫹ 0), as well as the theoretical values, are presented in Table 3. For the E symmetry species, the first two principal components define an exact projection of the fivedimensional tensor space. This is a consequence of the fact that only two fundamental intensities of E symmetry bands have non-zero intensities, just as in the case of the A1 symmetry vibrations of this molecule. The graph of the scores for the first two principal components is shown in Fig. 3. The sign of the scores

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Table 3 Preferred polar tensor element values calculated from the experimental infrared intensities of CF3Br and CF3I and their molecular orbital estimates CF3Br AI (⫺ ⫺ 0) (⫺ ⫹ 0) Errors a HF/Morgon basis set MP2/ Morgon basis set E (⫺ ⫹ 0) (⫺ ⫺ 0) Errors a HF/ Morgon basis set MP2/ Morgon basis set

p…C† xx 1.490 1.424 0.016 1.807 1.710

CF3I A1 (⫺ ⫺ ^) b Std deviation (⫺ ⫺ ^) b Errors a HF/SBKJC MP2/Lanl2dz MP2/3-21G** E (⫺ ⫹ ^) b (⫺ ⫺ ^) b Std deviation b Errors a HF/SBKJC MP2/Lanl2dz MP2/3-21G** a b

P…C† xx 1.435 1.373 0.006 0.050 1.576 1.612 1.318

…C† Pzz 2.251 1.727 0.045 2.633 2.407

P…Br† zz ⫺0.355 0.050 0.013 ⫺0.424 ⫺0.456

…F1 † Pzx 0.354 1.132 0.031 0.383 0.345

1† P…F zz ⫺0.632 ⫺0.593 0.011 ⫺0.736 ⫺0.650

P…Br† xx 0 0.018 0.001 ⫺0.039 ⫺0.014

1† P…F xx ⫺0.748 ⫺0.902 0.011 ⫺0.866 ⫺0.851

…F1 † Pyy ⫺0.245 ⫺0.060 0.004 ⫺0.312 ⫺0.279

1† P…F xz 0.278 0.287 0.003 0.320 0.314

…C† Pzz 2.486 0.016 0.038 2.221 2.242 2.593

P…I† zz ⫺0.241 0.116 0.012 ⫺0.199 ⫺0.202 ⫺0.421

…F1 † Pzx 0.431 0.005 0.021 0.265 0.275 0.295

1† P…F zz ⫺0.748 0.033 0.013 ⫺0.674 ⫺0.680 ⫺0.724

P…I† xx 0.060 0.072 0.016 0.009 0.097 0.082 ⫺0.003

1† P…F xx ⫺0.766 ⫺0.907 0.002 0.034 ⫺0.778 ⫺0.799 ⫺0.589

…F1 † Pyy ⫺0.231 ⫺0.056 0.004 0.013 ⫺0.338 ⫺0.330 ⫺0.287

1† P…F xz 0.311 0.313 0.021 0.014 0.266 0.268 0.232

Errors propagated from the estimated errors in the intensity values. Average and standard deviation values of all the indicated sign set alternatives.

Fig. 3. Bidimensional principal component representation of the E symmetry species polar tensor elements of CF3Br (hf ˆ HF/Morgon et al. Basis set [20] and mp2 ˆ MP2/Morgon et al.basis set [20]).

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Fig. 4. Bidimensional principal component representation of the A1 symmetry species polar tensor elements of CF3I (sbk ˆ MPs/SBKJc VDZ ECP, lan ˆ MP1/LANL2DZ and 321 ˆ MP2/3-21G**).

for the first principal component is mostly determined by the contribution from p…C† xx (second PC equation in Table 2) and this tensor element must be positive for the same reasons explained in the A1 symmetry analysis. This corresponds to choosing a negative sign for the first 2p~ =2Qi derivative, in accordance with the closeness of the theoretical points to the experimental points labeled (⫺⫺0) and (⫺ ⫹ 0) in Fig. 3. The choice of the sign for the second 2p~=2Qi derivative is much more difficult, as it represents little variance of the tensor element data, and so the experimental points are vertically close. The scores of the molecular orbital results are in much better agreement (considering vertical distances) with that of experimental point (⫺ ⫹ 0), and so we choose these last signs for the derivatives of this symmetry species. The tensor elements for this choice are presented in Table 3, as well as those corresponding to the choice (⫺⫺0) and the theoretical ones.

2.2. CF3I The A1 symmetry species of CF3I has three bands with non-zero intensities. For this reason three principal components are necessary to provide an exact description of the four-dimensional polar tensor space. However the first two principal components describe 99.9% of the total data variance and provide an almost perfect projection of the polar tensor element values. Their principal component score equations are listed in Table 2, and the bidimensional principal component projection of the A1 symmetry polar tensor elements is shown in Fig. 4. The polar tensor values, calculated from the experimental intensities and represented by the open squares in this figure, only vary significantly with the different sign attributions for 2p~ =2Q1 and 2p~ =2Q2 , mostly because the A3 intensity value is very small. For this reason the polar tensor values for the (⫺⫺⫹) and (⫺⫺⫺)

Fig. 5. Bidimensional principal component representation of the E symmetry species polar tensor elements of CF3I (sbk ˆ MP2/SBKJc VDZ ECP, lan ˆ MP2/LANL2DZ and 321 ˆ MP2/3-21G**).

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sign alternatives are almost the same and are represented by only one symbol in Fig. 4, identified as (⫺⫺^). The molecular orbital results, indicated by the blackened triangles, cluster about the (⫺ ⫺ ^) sign alternatives. The only other plausible set of sign alternatives, (⫺ ⫹ ^), has polar tensor values very similar to those corresponding to the (⫺ ⫺ ^) selection. However, the principal component projection shows that the polar tensor values of the (⫺ ⫺ ^) sign alternatives are in better agreement with the molecular orbital results, they correspond to a positively charged carbon atom, and should be preferred. The polar tensor values of the (⫺ ⫺ ^) alternative, taken to be an average of the (⫺ ⫺ ⫹ ) and (⫺ ⫺ ⫺) polar tensor values, are presented in Table 3 along with the theoretical polar tensor results. Though the third band of E symmetry species has non-zero value according to Person et al. [14], its value is so low that just two principal components for this symmetry species account for 100% of the total variance in the tensor elements. We will thus limit ourselves to choosing signs for the first two 2p~ =2Qi derivatives and take the average of the polar tensor element values corresponding to both signs for the third one. The first two principal component score equations are listed in Table 2 and the bidimensional principal component score projection of the E symmetry polar tensor elements is shown in Fig. 5. The signs for the first derivative discriminates the points to the right and to the left in the graph. The first ones are much more closer to the theoretical ones, besides being in accordance with a positively charged carbon atom. The first derivative sign is chosen as negative. The second derivative sign causes very little variance in the vertical positions of the points in Fig. 5. The closeness of the points corresponding to the sign choices (⫺ ⫺ ^) or (⫺ ⫹ ^) to the theoretical ones is difficult to evaluate. Though the difference in tensor element values for each sign choice is very small, the point corresponding to the sign choice (⫺ ⫹ ^) is a little closer to the theoretical ones, and we choose the corresponding tensor element values as the most physically significant. Tensor element values for the (⫺ ⫹ ^) and (⫺ ⫺ ^) sign choices as well as theoretical values are presented in Table 3.

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3. Discussion The intensity sum-electronegativity model [2] proposes that the atomic effective charges of the halomethanes carbon atoms are linearly related to the mean electronegativity values of the substituent ÿ
atoms E a . Using a training set of eight halomethanes, a model regression was obtained for the relation:

xC ˆ ⫺2:65 ⫹ 0:39E a :

…7†

For the substituent atoms the effective charges are related to their own electronegativity values. The corresponding model regression was

xa ˆ ⫺0:67 ⫹ 0:11Ea

…8†

where Ea stands for the electronegativity of these atoms. The intensity sum of a molecule is related to the effective charges of its atoms through the G sum rule [3] 3N ⫺6 X L

Ai 2924:7

N X

x2i =mi ⫺ 0974:9V

…9†

i

where Ai are the individual band intensities (Km mol ⫺1), x i the effective charges (e), mi the atomic unit masses and V is a rotational contribution to the intensities related to the molecular equilibrium dipole moment and the moments of inertia. By substituting model estimates of x i from Eqs. (7) and (8) for the x i in Eq. (9), the intensity sum can be estimated just from atomic electronegativity values. Each term in the right-hand summation of Eq. (9) is an atomic contribution (A) to the intensity sum, and the electronegativity model predicts that the carbon contribution will be variable while those of the substituent atoms will be constant. The rotational contribution is null for molecules having zero equilibrium dipole moment and is generally very small for symmetric molecules. For CF3Br and CF3I, its values are negligible (0.18 Km mol ⫺1 and 0.29 Km mol ⫺1, respectively). The model equations were tested for a test set of 24 molecules yielding an average absolute deviation of 56.9 Km mol ⫺1 from the experimental values for the sum intensities. This is very accurate for such a simple model as compared to a total intensity sum variation of about 1300 Km mol ⫺1 for the halomethanes. The carbon atom contribution to the intensities, though

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Table 4 Polar tensor invariant parameters (e), intensity sums and their atomic contributions (Km mol ⫺1), calculated from the experimental infrared intensities and from the electronegativity models

pC xC pBr or I x Br or I pE xF AC ABr or I A PF Ai

CF3Br Exp.

Elect. model a

CF3I Exp.

Elect. model a

1.743 1.780 ⫺0.118 0.205 ⫺0.542 0.638 771.50 1.54 62.66 959.83

1.738 1.734 ⫺0.168 0.254 ⫺0.527 0.670 731.76 2.36 69.05 941.09

1.786 1.853 ⫺0.040 0.147 ⫺0.582 0.703 836.08 0.50 76.08 1063.79

1.706 1.702 ⫺0.139 0.221 ⫺0.527 0.670 705.73 1.13 69.05 913.72

a

Tensor invariant quantities were determined using Eqs. (7), (8), (10) and (11). Intensity sums and their atomic contributions were determined using Eq. (9).

varying, is found to be the largest in most of the molecules. Similar model regressions were also found for the mean dipole moment derivative. For carbon atoms, the p C vary according to [6] p C ˆ ⫺2:87 ⫹ 0:41E a

…10†

while for the substituent atoms p C should be constant according to [28] p C ˆ 0:63 ⫺ 0:095Ea :

…11†

It is interesting to note that the regression equations for the carbon effective charges (Eq. (7)) and for the carbon mean dipole moment derivative (Eq. (10)) are almost identical. This is also true for the analogous equations for the terminal atom mean dipole moment derivatives and effective charge values except that opposite signs are involved in Eqs. (8) and (11). This occurs because the x a values have indeterminant signs and a positive sign has been arbitrarily assigned to all the x a values. If the x F and x Cl values for the molecules of the training set were attributed negative signs, which is reasonable because their Mulliken charge values are always negative for the halomethanes, the signs in Eq. (8) would be identical to those in Eq. (11). The values of the mean dipole moment derivatives, atomic effective charges, intensity sums and its atomic contributions calculated from the infrared

fundamental intensities of CF3Br and CF3I are presented in Table 4 along with the values obtained from the electronegativity model equations. The agreement between all quantities and their model estimates is very good, considering the model’s simplicity. Larger deviations occur for the intensity sum of CF3I and invariant quantity values for Br and I atoms, mainly for the last one. For the CF3I intensity sum the experimental value is underestimated by 14%, which comes from an underestimation of the carbon atomic contribution of the same order. In any case the deviation is not out of the average reported in Ref. [2]. The values of the mean dipole moment derivatives and effective charges for iodine atoms are the lowest among the halogen atoms, and as such we should expect larger percent deviations for its estimates. The absolute deviations are comparable to those for Cl invariants in CF3Cl and CFCl3 molecules [6]. The assumption of constant values for tensor invariant quantities of halogen atoms appears to be correct for the fluoromethanes, for which an electrostatic model is consistent with infrared intensity data, as stressed in Ref. [6]. A CCFO analysis of the polar tensors for fluorochloromethanes [4] showed that intramolecular charge transfer must be important for molecules that mix fluorine and other halogen substituent atoms. Thus we should expect deviations in the estimates for invariant quantities of Cl, Br and I atoms, depending on the molecular environment. The variation in invariant quantities for these atoms, however, is much smaller than the predicted variations in carbon atom invariant quantities, in accordance with the model’s basic assumptions. Very recently it has been reported that the mean dipole moment derivatives obtained from infrared intensity measurements of a wide variety of molecules can be related to the carbon 1s electron binding energies obtained from ESCA or photoelectron X-ray spectroscopy [7]. As such, infrared results may be useful in predicting ESCA results and vice versa. Using the simple potential model proposed by Siegbahn et al. [8] X qB =RAB …12† ECORE;A ˆ kqA ⫹ B苷A

the core electron energy on atom A, after discounting the intramolecular potential because of the neighboring atoms (summation in the right-hand side of

H.P. Martins Filho, P.H. Guadagnini / Journal of Molecular Structure (Theochem) 464 (1999) 171–182 Table 5 Experimental 1s carbon binding energies (eV) and their estimates from the simple potential model regression equation for CF3Br and CF3I CF3Br

EC 1s Vb a b

181

systematic trends that may occur upon varying substitution of halogen atoms, as done for the fluorochloromethane molecules in Ref. [6].

CF3I

Exp. a

Estimate

Exp. a

Estimate

299.33 —

299.00 ⫺18.53

299.00 —

298.95 ⫺19.22

Experimental values from Ref. [9]. V (eV) stands for the second term in Eq. (12).

Eq. (12)), is proportional to the charge on this atom. In Ref. [7], atomic mean dipole moment derivatives were used in Eq. (12) instead of atomic charge values that are almost always obtained from theoretical quantum chemical calculations. Excellent model regressions of the relation were obtained separately for molecules containing sp 3, sp 2 and sp carbon atoms, using 1s experimental ionization energy values as the experimental data corresponding to the carbon atom core electron energies. Actually the 1s experimental ionization energies are conceptually comparable with core electron energies only if a correction is allowed for relaxation energies. On doing the corrections, the model regressions are improved even further. For molecules containing sp 3 carbon atoms the model regression of Eq. (12) in Ref. [7] corresponds to the equation ECORE;A ⫺ V ˆ 15:52p C ⫹ 299:46

…13†

for energies in eV and pC in e. V stands for the second term in Eq. (12). The values of experimental carbon atom 1s ionization energies and their estimates from Eq. (13) for CF3Br and CF3I are presented in Table 5, along with the potential owing to neighboring atoms (V) needed for the estimation which are evaluated with p values for the substituent atoms. The agreement between experimental values and estimates is almost perfect, which confirms the accuracy of the simple potential model for the data of these molecules. Although more calculations are needed for further analysis of all the models mentioned here (relaxation energies, CCFO contributions), the CF3Br and CF3I results give more evidence in their favor. The lack of intensity data for more molecules containing Br and I atoms will prevent, however, the analysis of

Acknowledgements The authors thank CNPq and FAPESP for partial financial support. P. H. G. thanks CNPq for graduate student fellowships. Computer time was generously furnished by the Centro Nacional de Processamento de Alto Desempenho de Sa˜o Paulo (CENAPAD-SP).

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