J. Phys. Chem. 1995,99, 15387-15395
15387
Density Functional Computations of the Dipole Moment Derivatives for Halogenated Methanes Dulan PapouSek and Zlata Papoulkovh Institute of Atomic and Molecular Sciences, Academia Sinica, P. 0. Box 23-166, Taipei, Taiwan
Delano P. Chong* Deparmtent of Chemistry, 2036 Main Hall, University of British Columbia, Vancouver, B. C.,Canada V6T IZ1 Received: February 22, 1995; In Final Form: May 23, 1995@
Electric dipole moments for the equilibrium molecular structures and their derivatives along the symmetry coordinates of vibration were computed for CH2F2, CDzF2, CH2C12, CD2C12, CSClz, CH3F, CD3F, CH3C1, CD3C1, CHF3, CDF3, CHCl3, CDC13, CFCl3, CF3C1, CF4, and C C 4 by means of the deMon density functional program (St-Amant, A,; Salahub, D. R. Chem. Phys. Lett. 1990, 169, 387). A satisfactory agreement was found between the experimental and computed dipole moments for the equilibrium molecular structures. Perfect agreement was found between the rotational corrections to the dipole moment derivatives calculated by deMon and those obtained independently from the permanent dipole moment and the orthogonality relations between the symmetry coordinates and the rotational coordinates. Using force constants which are available from the literature, derivatives of the dipole moments were transformed into the representation of the normal coordinates of vibration, and the results were compared with the experimental data on the infrared intensities. Density functional computations provide reliable information on the relations between the signs of the dipole moment derivatives and in most cases also on their absolute values in the series of investigated molecules.
Introduction Vibration-rotational transitions are very useful for identifying trace components in planetary atmospheres or in combustion processes. Although precise frequencies of these transitions are invaluable for their identification, infrared intensities are often used to determine the concentration of a species. For a number of highly reactive species, such as radicals and transient molecules, it is difficult to determine the absolute intensities of their vibration-rotational bands experimentally. On the other hand, a reliable prediction of these intensities might be useful for deciding how to set up an often difficult experiment. In general, determination of reliable dipole moment functions even for stable molecules is a problem which requires further work and analyses of high-quality experimental data on infrared intensities which are not easily obtained. It would be therefore useful to be able to predict reliable infrared intensities computationally. Ab initio methods using rather larger basis sets have not been so far quite successful for molecules with a larger number of electrons as in halogenated methanes and silanes. The computed band intensities often differed by a factor of 2 or 3 from experiment. Relatively recently, density functional theory offered an attractive alternative to expensive ab initio methods with promising results in the computation of the dipole moment functions. In our previous papers'-2 we used the density functional program deMon3s4(cf. refs 5 , 6 for the general discussion of the density functional theory) to compute electric dipole moments for a series of diatomic and small polyatomic molecules at their average or equilibrium structures. We used this technique also to compute the derivatives of the dipole moments along the symmetry coordinates of vibration for a series of molecules with C3, and Td ~ y m m e t r y ~and - ~ for some small linear molecu1es.l0
* To whom correspondence @
should be addressed. Abstract published in Advance ACS Abstracts, October 1, 1995.
0022-365419512099-15387$09.00/0
Comparison of the computed values of these quantities with the experimental values was encouraging and indicates that the density functional method could give reliable predictions for the infrared band intensities even for larger molecules. Especially the determination of the signs of the derivatives for polyatomic molecules is an important problem in infrared intensity studies. At present, the relative signs of the dipole moment derivatives can be obtained from experimental data, either by a simultaneous analysis of the infrared intensities of isotopically substituted molecules"-'4 or by analyzing the intensity perturbations of the vibration-rotational bands due to vibration-rotational interactions.l5 These analyses require high-quality experimental data on the infrared intensities of vibration-rotational bands which are not easily obtained. In the present paper, we extend the density functional computations of the dipole moment derivatives to the halogenated methanes CH2Y2 (CDZYZ),CH3Y (CD3Y), CHY3 (CDY3), and CY4 where Y = F or C1, and to CFCl3, CF3C1, and CF2C12. Emphasis will be put on the verification of the relations which follow from symmetry between the computed dipole moment derivatives and on the accuracy with which the density functional method computes the rotational c o ~ ~ e c t i o n s 'to~ .the '~ dipole moment derivatives. Using the force fields parameters which are available in the literature, the derivatives of the dipole moment functions along the symmetry coordinates will be converted to the derivatives along the normal coordinates of vibration in order to compare the computational results with experimental data (including the signs of the dipole moment derivatives).
Theory The orientation of the molecule-fixed axes x , y , and z with respect to the reference configuration of the atomic nuclei and the numbering conventions for the atomic nuclei are given in Figures 1 and 2. 0 1995 American Chemical Society
15388 J. Pkys. Ckem., Vol. 99, No. 42, 1995
where
a = sin(a/2)cos@/2)/N
(IN
b = sin@/2)cos(a/2)/N
(11)
c = sin(y/2)cos(y/2)/N
(1m)
Y
Figure 1. Orientation of the molecule-fixed axes x , y , and z and the definition of the valence force coordinates in molecules XCY3 (X = F or CI). A/3, is the bending coordinate corresponding to the valence angle XCY,.
x
where a, @, and y are the equilibrium valence angles and N is a normalization factor. It should be noted that in ref 18, c differs by a factor of 2 from the correct expression lm. Then, the values of the coefficients d, e, J g, and k in eqs IC and Id can be easily found by the condition that each coordinate is normalized and orthogonal to each other. Sometimes a different set of symmetry coordinates S3 and S, is used for this type of molecule (see, e.g., ref 19) defined as
S,(Al) =
yz
12-”*(2Aa
:I I, ,-j X?
\i
Figure 2. Orientation of the molecule-fixed axes x , y , and z and the numbering conventions for the X and Y atoms in molecules X2CY2 (X = H in CHzFz and CHf& and X = F in CF2C12). For CF? and CCld molecules, the axis system should be rotated anticlockwise around the axis z by n/4; Aa,, corresponds to the valence angle subtended by the bonds r, and r, where r3 is understood to be CY1 and rd is CY?.
For the X2CY2 molecules, Arl is the vibrational coordinate corresponding to CXI, Ar2 to CX2, Ar3 to CYI, Ar4 to CY?; A a corresponds to the valence angle X I C X ~AB , to Y I C Y ~ ; Ayl corresponds to the valence angle XICYI,Ay2 to X I C Y ~ , Ay3 to X ~ C Y Iand , Ay4 to X2CY2. For the X2CY2 molecules, the symmetry coordinates of vibration are then defined:
+ Ar,) &(A1) = 2-”2(Ar3 + Ar,) S , ( A , )= 2-”*(Ar,
(14 (1b)
S,(A,) = 2-’l2(Aa - Ap)
(In)
+ 2Ap - Ay, - Ay, - Ay, - Ay,)
(lp)
Although these coordinates are orthogonal to each other and to all the other symmetry coordinates in eqs la-i, they are orthogonal to the redundancy coordinate S, only in the limiting case of XzZYz molecules with all six valence angles equal. Davis ef defined their symmetry coordinates S’3 and S’4
where the coefficients p , q, r, and s are obtained easily from the condition that these coordinates are orthogonal to the coordinate S, and normalized. Their advantage is that for example S’3 is defined as a pure HCH or HSiH bending coordinate, with no change in ClCCl or ClSiCl. However, S’3 and S’, are not mutually orthogonal, and one has to be careful in GF matrix computations to take this into account when transforming the force constant and kinematic matrices from the valence force coordinate representation to the symmetry coordinate representation. There is of course a simple relation between S3, S, and S‘3,
The symmetry coordinates for XCY3 molecules are defined as (cf. Figure 1 for the definition of the valence coordinates)
S,(A,)= 3-”’(Ar1
We used symmetry coordinates which are obtained by an orthonormal transformation of the valence-force coordinates and are orthogonal to the redundant coordinate S, describing the linear dependence of the six valence angle coordinates Aa,AB, and A y . The redundancy condition for these coordinates for the X2CY2 molecules of Cz, symmetry was for the first time obtained by Shimanouchi and S ~ z u k i : ~ ~
+ Ar2 + Ar3)
(2a)
Dipole Moment Derivatives for Halogenated Methanes
J. Phys. Chem., Vol. 99, No. 42, 1995 15389
S,,(E) = 2-'I2(Ar3 - Ar2)
(2e)
S,,(E) = 6 - ' / 2 ( 2 A ~ 1- A% - Aa,)
(2f)
S,,(E) = 2-'"(Aa3
- A%)
&(E) = 6-'/2(2Ap, - AB2 - Ab,)
(2g)
(2h)
The redundancy of the angle deformation coordinates has been removed according to Aldous and Mills;21thus in eq 2b, P = (1 I442 21?)1/2,Q = (1 - I442 2I?)'I2 with K = - 3 sin @ cos @/sin 0 (0is the equilibrium angle YCY and @ the equilibrium angle XCY). For CXq molecules, the symmetry coordinates are defined as (cf. Figure 2 for the definition of the valence coordinates)
+
+
+
&(A,) = 2-'(Arl
+ Ar2 + Ar3 + Ar,)
+ Ar, - Ar,) S3,(FJ = 2-'(Ar1 - Ar, - Ar, + Ar,) S3,(Fz) = 2-'(Ar1 + Ar2 - Ar, - Ar,) S3,(F2) = 2-'(Arl - Ar,
S4z(F2)= 2-'"(Aa3,
Arot. = pe(Ag
&uT*
(74
In this equation, A,, is the (3N - 6) x 3 matrix of the elements
(3a)
(3d) (3e) (30
- Aa,,)
We used the same procedure for calculating the derivatives apa/aSi of the dipole moment function along the symmetry
coordinates of vibration as described in detail in our previous paper.7 We use a relation between the 3N Cartesian displacement coordinates of the N atomic nuclei and the vibrational symmetry coordinates in the form
(4) in which X is the column matrix of the 3N Cartesian vibrational displacements and Sextis the column matrix of the 3N - 6 symmetry coordinates defined by eqs 1-3, extended by the three coordinates of translation T,, T,, and T, and three coordinates of rotation R,, R,, and R,. Translation and rotation coordinates are orthogonal to each other and orthogonal to the 3N - 6 genuine vibrational symmetry coordinates Si (but Si need not be orthogonal to each other). Thus an inverse transformation exists.
where
Thus for each value of the symmetry coordinate Si, an instantaneous configuration of the atomic nuclei in terms of the 3N Cartesian coordinates is obtained from eq 5 for which the dipole moment is calculated by using deMon. As discussed for the first time by Crawford,I6 @,/asiare isotopically invariant only for the totally symmetric vibrational coordinates. For vibrations perpendicular to the symmetry axis and for molecules with a permanent dipole moment, these derivatives are different because of the mass dependent rotational contributions to apa/aSi. A useful recipe for calculating these differences can be found in ref 17. We used the following formula to calculate the differences between the rotational corrections to the derivatives of the dipole moment along the symmetry coordinates:
pe x ea is the component of the permanent dipole moment in the direction of the axis a;AHis the submatrix of the dimension 3N x (3N - 6) of the transformation defined by eq 5 (it is understood that the last six rows of Be,, correspond to the coordinates Ta and Ra). Furthermore in eq 7a, /3~, is the 3 x N submatrix of Be,, which corresponds to the rotational coordinates R,, R,, and R,. We use the same definition of the sense of rotation as discussed in ref 17, where the explicit definition can be found of the elements of this matrix and of the normalization factors. Finally, U denotes a row matrix which for molecules with the permanent dipole moments in the direction of the z-axis has the elements
where e, and e, are the unit vectors in the direction of axes x and y , respectively. Note that the subscripts H and D denote the isotopomer to which the particular quantity belongs. Thus we can obtain the differences of the rotational corrections either by subtracting values of the dipole moment derivatives computed in the present paper by the program deMon or calculate them independently by using eq 7a with the experimental value of pe or that computed by deMon for the equilibrium structure. Calculations were done with the deMon density functional with the following options. The deMon program uses two kinds of basis functions. We used the deMon density functional program with an adequate atomic orbital basis set H [43], C and F [543] and C1 [653]. For the auxiliary fitting functions, we followed the recommendation of the authors and selected (3,1;3,1)for hydrogen, (4,4;4,4)for carbon and fluorine, and (5,4;5,4) for chlorine. The meaning of (ij;k,l) has been given elsewhere.1a,10.2zIn comparison with our previous c~mputation,~ the auxiliary fitting functions for hydrogen are slightly modified (see footnote 1 in our papefl), and we have therefore recalculated the dipole moments and their derivatives for CH3F and CH3C1. On the other hand, the orbital basis used in this work is identical to that used in other studies in this ~ e r i e s , ~namely, -~ the efficient atomic natural orbitals of A M o f and Taylor.23 The exchange-correlation functional used in the present study is a nonlocal one, which included Perdew's correctionz4to the local functional of Vosko, Wilk, and N ~ s a i r . ~ ~ This choice of using a nonlocal density functional theory is labeled NLDFT in the tables later on.
15390 J. Phys. Chem., Vol. 99, No. 42, 1995
PapouSek et al.
TABLE 1: Experimental Molecular Structures and Experimental and Computed Dipole Moments of Halogenated Methanee .Pe
molecule
C-H
CHzFz CH2C12 CFzClz CH,F CH3C1 CHF, CHC13 CF3C1 CFCIj CFJ CC14
1.084 1.080 1.0947 1.086 1.09I 1.100
C-F 1.3508 1.347 1.3890
C-C1
1.766 1.745 1.778
HCH, FCFf
XCX,b ClCCV
expt'
112.8 112.10 106.2 110.32 110.67
108.49 1 1 1.96 112.7
1.97 1.60 0.55 1.857 1.869 1.6526 1.04 0.50 0.46
1.3284 1.3248 1.343 1.3151
1.758 1.7522 1.7634 1.765
108.58 111.3 108.57 I10.5 109.471 109.471
NLDFTd 1.811 1.606 -0.558 -1.713 - 1.880 1.469 0.990 0.302 -0.377
ref' 26,27 28,29 30,31 32,33 34.35 36,37 38,39 40,41 42,41 43 44
'! Bond lengths in angstroms; dipole moments in debyes; angles in degrees. X = F or CI. ' Absolute value of the dipole moment. Sign convention explained in the text. First reference number pertains to molecular geometry, the second one to the measured dipole moment. 'For CF2C12.
For each symmetry coordinate, the dipole moment vector was computed for five values of the symmetry coordinate S = 0, f O . l , and h 0 . 2 A. The five values of each component of the dipole moment vector were then fitted to a cubic equation. Our convention is that a component of the dipole moment is negative if the direction from the positive charge to the negative charge coincides with the positive direction of the corresponding axis. Note that this is an opposite convention in comparison with that which we used p r e v i o ~ s l y . ~The - ~ reason for this change is that the present convention is consistent with that which is used by deMon.
Results and Discussion There are several ways of checking the reliability of the density functional computations of the dipole moments with experimental data: (i) comparing the computed dipole moments with the experimental dipole moments for the equilibrium structure; (ii) checking the results of the computations with those which follow from symmetry considerations; (iii) comparing the differences between the rotational corrections to the dipole moment derivatives as computed by NLDFT and computed according to eq 7a; (iv) comparing the results of the computations with the experimental infrared band intensities. Dipole Moments for the Equilibrium Molecular Structures. The equilibrium structures of the halogenated methanes which were studied are given in Table 1 together with their experimental and computed dipole moments. The computed derivatives of the dipole moment functions ap,/aS, and the differences between the rotational contributions to these derivatives for the corresponding isotopomers are given in Tables 2-17. It is obvious from Table 1 that we have a satisfactory agreement between the experimental and computed dipole moments for equilibrium structures. The largest difference was found for CF3C1, where perhaps the experimental value of the dipole moment should be remeasured. In molecules with so many electrons the computed dipole moment is quite sensitive to the experimental equilibrium structure, which might have also contributed to this difference. In general, dipole moments computed by NLDFT in this study are all within 0.2 D of the observed values. Relations Which Follow from Symmetry Considerations. The computed values of ap,/as, can be checked by comparing them with relations which follow from symmetry. For molecules of C3t symmetry (Tables 7-16)
For molecules of CzV symmetry, the only nonzero components a,u,/aS, are those for which S, belongs to the A I symmetry species, while ap,/aS, are nonzero for symmetry B I and zero otherwise; apx/aS, are nonzero for symmetry species B? and zero otherwise (Tables 2-6). For the symmetry coordinate of species A2, the vibration is infrared inactive and all the components of the dipole moment derivative apa/aS5(A2)= 0. For molecules of symmetry T d , we have calculated all the dipole moment derivatives along the symmetry coordinates of a C3u molecule (eqs 2 ) and transformed them to the derivatives along the Td symmetry coordinates (eqs 3). The resulting dipole moment derivatives should satisfy the following relations which follow from symmetry for the nonvanishing dipole moment derivatives of molecules of Td symmetry:
Note that in molecules of symmetry C3L.,the z-axis coincides with the C3 symmetry axis (Figure 2 ) , while in CF4 or CCl4 it coincides with the S4 axis. We found that our computed values of the dipole moment derivatives satisfy well these relations as discussed in our previous paper.' The small nonzero values which were obtained for dipole moment derivatives which should be zero by symmetry reasons come from numerical inaccuracy in the integration. The errors could be reduced by using a nonrandom grid (rather than random) and could be further reduced by choosing extra fine grid (rather than fine). The latter would require of course more computing time, and we feel that it may have little effect on the dipoles and the dipole moment derivatives. Rotational Corrections to the Dipole Moment Functions. We computed the dipole moment derivatives for all the symmetry coordinates of the corresponding isotopomers. We found that their values are isotopically invariant for all the totally symmetric coordinates of vibration. For the symmetry coordinates of vibrations perpendicular to the symmetry axis, the rotational corrections computed by NLDFT are compared in Tables 3, 5, 8, 10, 12, and 14 with those obtained by eq 7a using the computed values of pe from Table 1. The agreement between both sets of results was excellent in all cases, the largest deviation being only 7%. Infrared Band Intensities. We transformed the derivatives of the dipole moments along the symmetry coordinates into the normal coordinate representation according to the relation
in which L,k are the elements of the eigenvectors of the GF
J. Phys. Chem., Vol. 99, No. 42, 1995 15391
Dipole Moment Derivatives for Halogenated Methanes matrix4s corresponding to the kth eigenvalue and q is a dimensionless normal coordinate of vibration. We used the force constants available in the literature to obtain the eigenvectors of the GF matrix. There are of course uncertainties related to the fact that exact corrections for anharmonicities are not known and only approximate harmonic frequencies or even directly the observed wavenumbers of the fundamental bands have been used by individual authors in their force constant determinations. If the derivatives of the dipole moment along the normal coordinates are obtained as the difference between terms which are large and of approximately the same magnitude (cf. CH3F in Table 7 or CF4 in Table 17), the uncertainties in the force field may become more important. Nevertheless we believe that the transformation to normal coordinates is not the main source of uncertainties in comparing the computed and experimental dipole moment derivatives (see further). An exact comparison of the theoretical and experimental data on the dipole moment functions would of course require a determination of an anharmonic potential function of the molecule from the experimental vibration-rotational transition frequencies and the determination of an anharmonic dipole moment function of the molecule by analyzing the effect of vibration-rotational and anharmonic interactions on the absolute line intensities of vibration-rotational transitions. For the series of molecules studied in the present paper, such complete information is not available. As for the infrared intensities, it is still the integrated band intensity A which is the main source of information on the "experimental" dipole moment derivatives. We use the following expression relating the dipole moment derivative and the integrated band intensity (see e.g. ref 46)
where ap/aq is in debye and A in kilometers per mole, and vi is the experimental transition wavenumber of a fundamental band in cm-' units. For molecules of Td symmetry and transition to a triply degenerate level of symmetry Fz, the derivatives is apz/ aq, and C = 0.515 72; for a transition to a nondegenerate level in C3" or C2, molecules, the derivative is apz/aqi for C3, and apa/aq,(a = x , y , z ) for C2,, and C = 0.893 26 for C2, and C3"; for a transition to a doubly degenerate vibrational level in C3, molecules, the derivative is ap&3qtXand C = 0.631 63. It is well-known that integrated band intensities may be spoiled by hot bands overlapping the fundamental band and of course also by intensity perturbations due to anharmonic and vibration-rotational interactions. The interference of the hot bands can be removed by measuring the absolute line intensities of vibration-rotational transitions of the fundamental band and determining the integrated band strength (see, e.g., ref 47). The dipole moment derivatives are related to S: according to eq 12 if A is replaced by and C by 0.85235(ZZJ273.15) for a transition to a nondegenerate vibrational level or by 0.60270(ZJ273.15) for a transition to a degenerate level (T is temperature, and Z, is the vibrational partition function). Integrated band strength $ provides reliable information on the dipole moment function for isolated bands, but neither A nor alone make it possible to determine the relative signs of the dipole moment derivatives. The most reliable determination of these signs requires measurement of the absolute line intensities for transitions to interacting vibrational states and the analysis of the intensity data by taking into account mixing of the rovibrational wavefunctions (see, e.g., refs 15 and 48). Signs of the dipole moment derivatives along the normal coordinates are of course arbitrary because only the relative signs
TABLE 2: Computed and Experimental Values of apa/aSi and apa/aqi for CH2F2"b
4
2948.0 (SI) -0.7761 1508.0 (S3) 3.2037 1113.2 (Sz) -0.2046 528.2 (S4) -1.3933
a=z -0.1 175 0.0898 0.0650 0.0988 0.0159 0.0077 0.2422 0.199 0.2533 0.2649 -0.0881 0.0843 0.0851 0.0846
6 7
3014.3 (S6) -0.7889 1177.9 (S,) 0.6393
-0.0980 0.1042 0.1057 0.0796 0.0966 0.0779 0.0988 0.1070
8 9
1435.0 (S9) -6.1056 1090.1 (Ss) -0.0465
1
2
3
a=y a=x
0.0827 -0.4181
0.0757 0.422
0.0757 0.0859 0.4107 0.4316
a apa/aS, in D/A; a,,&, in D;v,in cm-. I . Force field, see Hirota.26 References 49 and 50. Reference 5 1. e Reference 52.
can be determined of the coefficients Lik of the eigenvector of the GF matrix. In the present paper, we define the signs of the derivatives apa/aq by relating them to the individual symmetry coordinates. Thus a symbol for the symmetry coordinate Si in the brackets in Tables 2-17 indicates that the sign of the corresponding coefficient Lik in the transformation described by eq 11 was chosen to be positive. The symmetry coordinate S, was of course chosen such that it is the most characteristic coordinate for the particular mode of normal vibration (in molecules with strongly interacting vibrational modes this does not necessarily mean that the corresponding coefficient L i k is the largest in its absolute value). As was discussed for the first time by diLauro and Mills,Is a physical (and thus nonarbitrary) meaning has the product of the Coriolis coupling coefficient connecting two interacting vibrational states and the two corresponding dipole moment derivatives. For example, for symmetric top molecules, the sense of the observed intensity perturbations in the infrared spectrum depends only on the sign of the product of the Coriolis coupling coefficient and the dipole moment derivatives ap,/aq,, apx/aqtx,
c:,fx
The sign of this product is invariant with respect to the sign conventions used in defining the normal coordinates of vibration, and it is quite important in analyzing the intensity perturbations in symmetric tops. Individual Molecules. CHzF2, CDzF2. The results for CH2F2 and CDzF2 are given in Tables 2 and 3. For the infrared inactive mode V S , the derivatives computed by NLDFT are apx/ as5 = -0.0037 D,apjas5 = 0.0088 D, and ap,/as5 = 0.0102 D. Similar results were obtained for the infrared inactive modes in other X2CY2 molecules, and they will not therefore be given in the following tables. We have in general very good agreement between the computation and experiment for CH2F2. There is an excellent agreement for the v4, V6, and vg bands and especially for the most intense vg band. For example, the experimental integrated band intensity9 for the vg band is 244 kmmol-I, computed 238 h m o l - I . The v2 band is predicted by NLDFT to have extremely small intensity in agreement with e ~ p e r i m e n t . 4The ~-~~ ab initio computation of Kim and Parks0 on the 6-31G level failed to predict it (they obtained lapZ/aq2(= 0.040 D), and they obtained apz/aq3= 0.305 D. D i ~ o used n ~ ~ab initio molecular orbital theory with a large basis set to compute the infrared intensities for CHzF2 which agreed with the experiment within a factor of 2 (for example, he obtained apz/aq3= 0.451 D and
15392 J. Phys. Chem., Vol. 99, No. 42, 1995
PapouSek et al.
TABLE 3: Computed and Experimental Values of apa/aSi and ap,/aui for CD2FZab 1
V,
NLDFT au,ias, a~,ia9,
expt
expt'
i
0.0 0.0 0.0 0.0
0.0757 0.0866
0.0 0.0 0.0 0.0
a=y 6 2283.9 (S6) -0.8229 -0.1020 0.1086 7 962.1 (S7) 0.8348
0.0798 0.0802
a =x 0.3423 -0.2529
8 1158.3 (Ss) -6.0601 9 1002.4 (Sa) -0.0073
0.0346 0.0340 -0.1955 -0.1994 -0.0455 -0.0392
-0.0471 -0.0401
ap,/aS, in DIA; ap,laq, in D: v, in cm-I. Force field see Hirota.26 References 49-51. d A is the difference in rotational corrections of the isotopomers computed as (ap,/aS,)~- (i3pa/X,)o;B is computed according to eq 7a using pe obtained by NLDFT (see Table 1); a = : for vibrations parallel with the z-axis: a = x or y for vibrations perpendicular to the z-axis.
I a,u,iaq, I
NLDFT
B"
ia~,/a9~l
a=z 1 2128.9 (SI) -0.7761 -0.1345 2 1165.0 (S?) 3.2037 0.1436 3 1026.5 (S2) -0.2046 0.1753 4 521.7 (S4) -1.3933 -0.0916
TABLE 5: Computed and Experimental Values of apa/aSi and ap,/aqi for CD2Cl2"b
V~
ap,/as,
ap,/aq,
~e
B'
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
d
c
a=z 1 2206 (Si) -0.2324 -0.0367 0.1 11 0.048 2 1434 (S3) 1.1648 -0.0011 0.015 3 683 (Sz) -0.1359 0.0996 0.0776 0.169 4 279 (5'4) -0.6680 -0.0302 0.0047
a=y 6 231 1 (S6) 0.0025 0.0021 0.0 7 713 ( S 7 ) -0.0811 -0.0106
0.042
0.0401 0.0408 -0.1651 -0.1603
a=x 8 9
961 (S9) -4.7768 0.2636 0.204 729 (S8) 0.3978 -0.3088 0.271
0.21 1 -0.0211 0.246 -0.0167
Force field, see refs 5 1 'I ap,/aS, in D/A; apalaq,in D, v, in cm-' . and 52. Reference 54. Reference 55. See footnote d in Table 3.
TABLE 6: Computed and Experimental Values of apa/aSi and apalaqi for CFZCIZ"~ NLDFT
TABLE 4: Computed and Experimental Values of apa/aSi and apa/aqifor CHzClzab expt
Iapa/aq,1
NLDFT 1
V!
aP,ias,
aPa/aq,
C
d
e
0.030 0.036 0.0942
0.043 0.018 0.0947 0.041
0.021 0.039 0.091 0.009
0.031 0.032
0.0 0.032
0.030 0.033
0.144 0.354
0.129 0.316
0.118 0.332
i
Vf
ap,ias,
1 2 3 4
1102.4 (SI) 666.8 (S?) 468.5 (Si) 261.6 (5'4)
-4.6297 2.2449 1.4563 -0.6207
2998 (Si) 1434(S?) 712.9 (Sz) 281.5 (Sd)
-0.2324 1.1648 -0.1359 -0.6680
-0.0330 -0.0194 0.1024 -0.0292
6 7
1161.1 (S6) 46 1.8 (S7)
-4.8414 0.5358
3055 (S6) 897.7 (S7)
0.0426 -0.2462
8 9
1268 ( S g ) 758 (SR)
-4.7979 0.3811
0.0082 -0.0363
iap,/a9,1
-0.4520 0.0424 -0.0310 0.0 122
0.45 1
-0.3598 -0.0029
0.350
-0.5798 -0.0040
0.550
a=y
a=y 6 7
expt' a,uaiaqt
a=:
a=z 1 2 3 4
-0.0205 -0.0156
a=x 8 9
908.0 (Sx) 437.0 (S9)
-4.6162 2.6655
apa/aS,in D/A: ap,/aq, in D; v, in cm-I. Force field, see ref 30. Reference 56.
a=x 0.1549 -0.3763
fl a,u,/aS, in D/A: ap,/aqi in D; v, in cm-I. Force field, see refs 5 1 and 52. Reference 53. Reference 54. e Reference 55.
apJaqg = 0.313 D). Amos et ~ l . used ~ * second-order MoellerPlesset perturbation theory to compute the dipole moment derivatives of CH2F2. Their results are in very good agreement with our NLDFT computations (Table 2 ) . In the last two columns of Table 2, we give the absolute values of the dipole moment derivatives. Kondo et uL5' determined experimentally the relative signs of the dipole moment derivatives for the pairs of bands perturbed by Coriolis interactions (v3/vg, v3Iv7, and v7/v9 in CH2F2 and v2/vg in CD2F2). Our computed sign relations in Tables 2 and 3 are in agreement with these results if it is taken into account that our q 3 is defined with opposite sign in comparison with that in ref 51. Because of the strongly overlapping bands v2, vg and v3, v g in CD2F2, it is not possible to compare directly the computed results with experimental values unless the absolute line intensities of the overlapping bands will be measured. The computed value of ap:/aql is considerably larger than the experimental value. Kim and Parks0computed I = 0.120 D and noticed that there is an inconsistency between the experimental values of CH2F2 and CD2F2. CH2Cl2, CD2C12. Theoretical and experimental dipole moment derivatives for CH2Cl2 and CD2C12 are compared in Tables 4 and 5. There is a considerable discrepancy between experimental band intensities of several a ~ t h o r s . ~For ~ - example, ~~ Saeki and TanabeS4claimed that the intensity of the symmetric CH2 stretching band V I of CH2C12 reported by Morcillo el should be corrected, but our value of ap,/aq, is in excellent
agreement with the value of Morcillo et aLs3 On the other hand, our computed value of &/a92 is in agreement with the experimental value of Saeki and Tanabe54 but not with those values given in refs 53 and 55. Our computed dipole moment derivatives are in a very good agreement with the experimental data for the v3 and v7 bands (Table 4) for which the data of the a ~ t h o r s are ~ ~ consistent. -~~ They are in a reasonable agreement with the experiment for the most intense bands vg and vg, where however the published experimental band i n t e n s i t i e ~ ~are ~-~~ not so consistent. A similar situation occurs for CDzC12 (Table 5) in the A I block. CF2Cl2. NLDFT predicts correctly that this important molecule ("Freon-1 2") is transparent to infrared radiation except in the spectral region between 8p and 12p (Table 6). The agreement between the computed and experimental infrared band intensities is excellent for all three fundamental bands V I , V 6 , and vg. CHjF, CDjF. The infrared intensities of fluoromethane vibrational bands have been studied p r e v i o ~ s l y ' ~by, ' ~means of the isotopic invariance rule, with special emphasis on the determination of the signs of the dipole moment derivatives. We have measured4*the absolute line intensities in the infrared spectrum of the v2 and v5 bands whose intensities are perturbed by the Coriolis interaction for rotation around the x , y axes. This made it possible to determine the "unperturbed" vibrational transition moments and the relative signs of the dipole moment derivatives ap:/aq2 and apJaq5. Law et al.57 have recently determined a more reliable force field of CH3F, which was important especially for a more accurate determination of the theoretical value of ap&2 (cf. ref 7).
J. Phys. Chem., Vol. 99, No. 42, 1995 15393
Dipole Moment Derivatives for Halogenated Methanes
TABLE 7: Computed and Experimental Values of apalaSi and a@qi for CH3Pb
TABLE 10: Computed and Experimental Values of ap,/aSi and apa/aqi for CD3CW
a=z
a=z 2160.2 (SI) 0.6202 0.0759 0.074 1028.7 (Sz) -0.1557 -0.0863 -0.0912 701.4(S3) -2.1614 -0.1385 -0.1302
2 3
2919.6 (SI) 1459.4 ( S 2 ) 1048.6 (S3)
0.7072 0.1785 -4.2850
0.0910 -0.0119 -0.2687
0.084 -0.016 -0.271
1 2 3
4~ 5~ 6~
2999.0 (S4) 1467.8 (S5) 1182.7 (&)
a=x 0.7687 -0.2131 -0.2314
0.0847 -0.0547 -0.0278
0.090 -0.049 -0.030
a=x 4~ 2283.3 (S4) 0.3545 0.0254 0.030 5~ 1059.9 (S5) -0.2709 -0.0510 -0.051 6~ 767.6 (&) 0.0909 0.0189 0.025
1
* apa/aS,in DIA; apa/aq,in D; v, in cm-l. Force field, see ref 57. aprlaqz and apJaq5, see ref 48; other values see ref 14.
TABLE 8: Computed and Experimental Values of ap,/aSi and ap,laqi for C D p b NLDFT i
apalaS,
V,
expt'
apa/aq, lapalaq,l
Ad
Bd
a=z 2112.0 (SI) 0.7072 0.0947 1134.6 (S2) 0.1785 -0.1564 992.3 (S3) -4.2850 -0.2129
1 2 3
a=x 4~ 2999.0 (S4) 0.7991 0.0780 5~ 1467.8 (S5) -0.1751 -0.0369 6~ 1182.7 ( $ 6 ) -0.3291 -0.0437
0.097 0.167 0.237 0.085 0.042 0.049
0.0 0.0 0.0
0.0 0.0 0.0
-0.0304 -0.0307 -0.0380 -0.0396 0.1071 0.1028
apa/aS,in DIA; apa/aq,in D; v , in cm-'. Force field, see ref 57. Reference 14. See footnote d in Table 3.
TABLE 9: Computed and Experimental Values of ap,/aSi and ap,laqi for CH3CW NLDFT i
1 2 3
2967.8 (SI) 1354.9 (S2) 732.8 (S3)
apalaSl a=z 0.6202 -0.1557 -2.1614
3039.3 (S4) 1452.1 (S5) 1017.3 (&)
a=x 0.3171 -0.3080 0.1678
VI
exptc apa/aq,
0.0769 -0.0619 -0.1543
apa/aq,
0.0 0.0 0.0
0.0 0.0 0.0
-0.0373 -0.0365 -0.0371 -0.0365 0.0768 0.0762
a ap,/aS, in D/A; apa/aq,in D; v, in cm-l. Force field, see ref 57. Reference 11 except apz/aq2and apz/aq3which were taken from ref 62 (in reference 11 apz/aq2= -0.091 D, apz/aq3= -0.133 D). See footnote d in Table 3.
TABLE 11: Computed and Experimental Values of dp,/aSi and apalaqi for CHF3"b expt NLDFT lapa/%tI i V, apalaS, awa/aa C d 1 2 3 4X 5~ 6~
3035.4 (S3) 1141.3 (SI) 700.1 (S2)
a=z 1.9678 -0.0989 -2.0728 0.2430 -0.5359 -0.1031
1377.7 ( s 6 ) 1157.5 (S4) 507.8 (S5)
a=x -0.1620 5.8545 1.3643 0.4329 0.0315 0.0463
0.0804 0.300 0.123 0.159 0.425 0.061
0.0793 0.117 0.154 0.0575
a +,/as, in DIA; apa/aq,in D; Y,in cm-'. Force field, see reference 63. Reference 64. Reference 65.
TABLE 12: Computed and Experimental Values of apalaSi and au,laai for CDF@
0.075 -0.067 0.166
a=z -0.1231 0.2287 -0.1063
0.102 0.233 0.121
0.0 0.0 0.0
0.0 0.0 0.0
0.436 0.139 0.0596
0.0229 0.0100 0.0356
0.0229 0.0098 0.0351
1 2 3
2261.2 (S3) 1.9677 1111.2 (Si) -2.0727 694.2(&) -0.5359
apa/aS,in DIA; apa/aq,in D; v, in cm-]. Force field, see ref 58. c iapz/aqli,iap,iaq3i, iapdaq4~i. see ref 59; ap,iaqz and a p ~ a qsee ~ ~ref , 60; lapdaq6xlrsee ref 61.
4~ 5X 6~
1210.6 (S4) 975.5 ( s 6 ) 502.7 (Ss)
Results for CH3F are given in Table 7; for CDF3, in Table 8. We have quite satisfactory agreement with the experiment. It should be noted that, with the improved force field,57the sign of the computed derivative ap,/aq2 for CH3F was reversed in comparison with our previous deMon comp~tation.~This is now in agreement with the experimental results according to which there is a negative intensity perturbation of the v2 and v5 bands of CH3F (see refs 15 and 48). CH3C1, CD3Cl. We have excellent agreement between theory and experiment for CH3C1 (Table 9) as well as for CD3C1 (Table 10). The average percentage deviation from experiment for the 12 cases is only 10%. CHF3, CDF3. There is in general good agreement between computed and experimental value^^.^^ for CHF3 (Table 11) if we take into account the large error of the experimental integrated band intensities for the v2 and v5 bands due to their overlap. Less satisfactory is the agreement with the value of lapI/aq4x1 = 0.113 D obtained by Sofue et a1.66by measuring absolute line intensities of two vibration-rotation lines of the v4 band [P(J=K=35) and P(J=K=36)] which cannot be perturbed by the x-y Coriolis interaction. Perhaps one should not rely on the results of measurement of the intensities of just
a apa/aS,in D/A; apa/aqiin D; vi in cm-'. Force field, see reference 63. Reference 65. See footnote d in Table 3.
4~ 5~ 6~
0.0291 -0.0611 0.0402
0.033 -0.053 0.0388
a
5.8316 1.3544 -0.0042
a=x 0.4411 0.1357 0.0471
two lines and extend instead of it the measurement and analysis on the perturbed as well as unperturbed spectrum lines of the v4 band and other interacting bands (vz, 2v3, ?). On the other hand, Kim and Park5" computed integrated band intensities on the 6-31G level and obtained 18pd8q4xl= 0.129 D (but lapx/ = 0.113 D). The agreement between computed and experimental values for CDF3 is excellent (Table 12), the average percentage deviation being 11%. This may be related to the fact that the fundamental bands are not overlapping in CDF3 to such an extent as that in CHF3, which indicates that the quality of the density functional computation is very good for fluoroform. The ab initio computation of the infrared intensities for CDF3 by Kim and Park50 is in reasonable agreement with the v4 band (lapI/aq4xl= 0.467 D but much worse for the other bands (e.g., lapx/aq21 = 0.321 D). CHCl3, CDCl3. Agreement between theory and experiment is satisfactory for CHC13 (Table 13) as well as for CDCl3 (Table 14), although not as good as that for fluoroform.
PapouSek et al.
15394 J. Phys. Chem., Vol. 99, No. 42, 1995 TABLE 13: Computed and Experimental Values of apa/aSi and au,lao; for CHCl@
1 2 3
3033.1 (S?) 675.5 (SI) 366.8 (Sz)
a=z 0.0080 0.5150 -0.4762 0.0587 0.1451 -0.0155
4X 5x 6x
1219.7 (s6) 773.7 (SA,) 259.9 (S5)
a=x 4.6021 -0.1 153 0.7687 0.3968 -0.2257 0.0470
a apa/aS,in D l k a,u,/aq, in D; v, in cm-'. 67. Reference 68. Reference 69.
0.0092 0.0721 0.033 0.995 0.336
0.0
Force field, see reference
TABLE 14: Computed and Experimental Values of ap,/aSi and a,ua/aqifor CDC13aa expt NLDFT laPu/aq!l V, ap,ias, apdaq, c d A' a=z 2264.8 (S3) 0.5150 0.0006 0.0 0.0 657.6 (SI) -0.4762 0.0574 0.0773 0.0 364.2 (S:) 0.1451 -0.0162 0.0 0.0
i
1 2 3
a=x 914.5 (S6) 4.5967 -0.2505 0.208 0.7647 0.3283 0.280 747.0 (SJ) 0.0466 0.0 258.8 (Ss) -0.2345
4x 5x 6x
2 3
a=z 1.3679 -0.3062 -4.6811
0.0 0.0 0.0
844.3 (SA,) 395.3 (S6) 242.8 (S5)
4.5409 0.8692 - 1.5680
5~ 6x
a=i 0.5880 1108.2 (SI) 4.0013 783.3 (S?) -2.9732 -0.1708 -0.0323 476.7 (Si) -3.4799
1216.8 (SA,) 562.4 (Ss) 347.6 (Sb)
a =x 5.0038 0.4237 1.1871 0.0314 -0.6231 -0.0168
0.0054 0.0054 0.0039 0.0038 0.0088 0.0087
-0.3456 0.0954 0.0779
0.339
0.4839 -0.01 17 0.0414
0.445
a 8p,laS, in DIA; ap,/aq, in D; v,in cm-]. Force field, see reference 42. Reference 70.
CFClj. NLDFT correctly predicts that this important molecule ("Freon-l l") is transparent to infrared radiation except for two extremely strong bands V I of the symmetric CF stretching vibration and especially v2 of the antisymmetric CCI stretching vibration (Table 15). Theoretical values of the band intensities are in excellent agreement with experiment. CFjCZ. Theoretical and experimental values of the infrared band intensities are in very good agreement (Table 16). CF4, CC14. There are only two infrared active fundamental bands in molecules with Td symmetry corresponding to transitions to vibrational levels of symmetry Fz. For CF4, the agreement between the computed value of apZ/aq3:and experiment is excellent; it is slightly worse for apJaq4z (Table 17). In the latter case, the value of the derivative is obtained from apJ and 8pt/aS4; as a difference of two large quantities, and it is therefore sensitive to the force field of the molecule. The relative signs of the computed dipole moment derivatives apJi3q3zand apz/aq4;are the same in CF4, but they are opposite in CC14 (Table 17).
0.554 0.168 '0.0041
0.635 0.189
0.410 0.0496
