2323
J. Phys. Chem. 1083,87,2323-2329
Ab Initio Molecular Orbital Calculations on Clusters of Methyl Fluoride' Takao 01, Ellen Sekreta,+ and Takanobu Ishlda' Department of Chemishy, State University of New York at Stony Brook, Stony Brook, New York 11794 (Received August 19, 1982; In Final Form: December 16, 1982)
Various two-, and three-, and four-membered clusters of methyl fluoride have been studied by means of the Gaussian-70 program using the minimal STO-3G and the 4-31G basis sets. Results obtained by using the STO-3G set are more consistent with experimental results than those obtained by using the 4-31G set. The optimum C-F- .H-C configuration in all clusters investigated is as follows: RHF= 2.1 A, FHC angle = MOO, CFH angle = 120-125'. The optimum STO-3G stabilization energies obtained for the three cluster sizes correspond to the following: -0.78,-0.82, and -0.83, in kcal/mol of F--.H-C interaction,for the two-, three-, and four-membered clusters, respectively; and -0.39, -0.82, and -0.83, in kcal/mol of monomer, for the two-,three-, and four-membered systems, respectively. The optimum angles are in reasonable agreement with crystallographic data for solid methyl chloride. An explanation is given for the preferred angles of 120-125'.
-
Introduction There has been significant evidence of more than a casual molecular association in the condensed phases of methyl fluoride. Barnes, Hallam, Howells and Scrimshaw: in their matrix isolation study at 20 K, identified IR peaks with C-F stretching frequencies of dimer, trimer, and tetramer of CH3F. A microwave and far-infrared study of liquid methyl fluoride by Gerschel et ala3led to a conclusion which is consistent with local clustering. The differences in the vapor pressures of liquid methyl fluorides, 12CH3F,13CH3F,and 12CD3F,evidently suggest a strongly directional association of methyl fluoride molecules in the l i q ~ i d .We ~ had found a similar directionality in isotopic liquid fluor~forms,~ and an ab initio molecular orbital calculation6on the two-membered clusters of CHF3 confirmed it. In this paper we report on the ab initio MO calculations on various clusters of CH3F up to four-membered systems. Using a modified Gaussian-70 program we performed the majority of our calculations on the basis of the STO-3G set, and the results were compared to experiments and, in some cases, with results obtained by using the 4-31G basis set. The structure of the CH3F monomer was optimized for each basis set (Table I), and the respective internal geometry was assumed rigid in all cluster calculations. Some definitions follow. An n-numbered cluster is one which consists of n molecules of CH3F, which are often called n-mers. The member molecules in an n-mer are designated M1, M2, ...,Mn. The i-th member consists of Ci, Fi, Hi2, Hi3, Hi4. An m-membered ring is a cyclic configuration in which each of m molecules contributes its C, F, and one H atom. The stabilization energy of a given n-mer is AE, = &-mer) - nE(1-mer) where E(n-mer) and E(1-mer) are the energies of the n- and 1-mers, respectively. To minimize the number of calculations involving large clusters the following manual optimization scheme was employed. First, using the STO-3G basis set, we mapped the energy surfaces of four basic dimeric configurations, and a temporary conclusion was drawn about the relationship between the stabilization energy and the geometrical parameters. This conclusion was then applied to select the number of basic configurations and variables considered for the three-membered systems. A further temporary conclusion obtained from the trimer study was t Present address: Department of Chemistry, Indiana University, Bloomington, IN 47405.
0022-3654/83/2087-2323$0 1.50/0
TABLE I: Geometry of CH,F Monomer optimized parameters
exptl"
STO-3G
4-31G
C-F distance C-H distance FCH angle HCH angle
1.386 A 1.095 A 108.60' 110.33'
1.384 A 1.097 A 110.6" 108.3'
1.409 A 1.076 A 108.3' 110.6'
a Reference
7,
applied in choosing viable four-membered cluster configurations. After the study of the various tetramers, general conclusions were deduced. We preferred this procedure over an automated optimization not only for the sake of CPU time economy but also for the ease of physical interpretation of the results. For n-mers up to n = 3 the cluster geometry optimized by the STO-3G calculations was further varied by using the 4-31G set and the 4-31Goptimized internal geometry.
Two-Membered Clusters For two-membered systems four basic configurations were studied, two of which, the 2A and 2B configurations, are shown in Figures 1 and 2. Two other configurations are8 2C (CZhsymmetry), obtained rotating M1 of the 2B configuration around its C-F axis by 60°, and 2D (C3" symmetry), an eclipsed tandem rocket geometry. In the 2A configuration, four parameters were varied from their respective values of the basic configuration as shown in Figure 1: (i) Rm, which is the H--.F distance between molecule 1 (Ml) and molecule 2 (M2), (ii) a,the molecular rotation around the z axis, which is zero at the basic geometry and increases when M2 rotates clockwise as seen from M1 in the +z direction, (iii) @, the tilting angle of M2 around F1 in the yz plane, which is 180' at the basic (1) Research supported by the Office of Basic Energy Sciences, U.S. Department of Energy, Contract No. DE-AC02-80ER10612. (2) Barnes, A. J.; Hallam, H. E.; Howells, J. D. R.; Scrimshaw, G. F. J. Chem. SOC.,Faraday Trans. 2 1973,69, 738. (3) Gerschel, A,; Dimicoli, I.; Jaffre, J.; Riou, A. Mol. Phys. 1976, 32, 679. (4) Oi, T.; Shulman, J.; Popowicz, A.; Ishida, T. J. Phys. Chem., in press. (5) Popowicz, A.; Oi, T.; Shulman, J.; Ishida, T. J. Chem. Phys. 1982, 76, 3732. (6) Popowicz, A.; Ishida, T. Chem. Phys. Lett. 1981, 83, 520. (7) Andersen, F. A.; Bak, B.; Broderson, S. J. Chem. Phys. 1956, 24, 989. (8) Diagrams of the basic configurations have been deposited as s u p plementary material. See paragraph at end of text regarding supplementary material.
0 1983 American Chemical Society
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The Journal of Physical Chemistry, Vol. 87, No. 13, 1983
Oi et al.
0.2
2
0.1
0.0
7-
H24
-0.1
f
-0.2
0
.
L
E ?- - O m 3
Q
RHF
-0
U
Y
-0.4
?Ap
Hmy -0.0
X
Flgure 1. Dimer type 2A: In the basic configuration (C,symmetry) this may be called a staggered linear geometry. The atoms C,, H,,, F,, and C, are collinear with the z axis, and the atoms Fz,Cz, H ,,, F,, C,,and Hi, are coplanar with the yz plane.
e
H12
Figure 2. Dimer type 28: I n the basic configuration (C,symmetry) this is an antiparallel geometry. The atoms F,, C,,H12,F,, C,, and HZ2 are coplanar with the yz plane, the atoms F,, H2,, H,,, and H,, and the atoms Fp, H,,, H13, and H, form two planes parallel to each other and perpendicular to the z axis, and the bonds CIF, and CpF, are parallel to the z axis.
geometry and decreases when M2 tilts clockwise around F1as seen from the +x side into the -x direction, and (iv) y, the tilting angle of M2 around HN in the yz plane, which is 180' in the basic configuration and decreases when M2 tilts clockwise around HZ4as seen from the +x side into the -x direction. The stabilization energies obtained by the STO-3G calculations for the 2A configuration are presented in Figures 3-5. It is seen that (1)the most stable geometry derived from this configuration is that of RHF = 2.1, A, cy = 0, @ = 120', and y = 180°,(2) the force responsible for the linearity around the interacting hydrogen atom is one of the strongest (Figure 5, curve b) we found in the present study, (3) the rotation around the FHC axis is almost free when /3 = 0, while it is mildly hindered when the tilting angle is 120'. The last effect is attributable to the proximity of the (Hz2,H23) pair and the (Hlz,H13) pair caused by the combined rotations of /3 = 120' and a = 180'. The additional stability obtained by the tilting at F1 (Figure
0
2
4
I
RHF
I
6
8
1
0
(A)
Flgure 3. A€, vs. Rw for the 2A configuration by STO-3G: (a) a = Oo, p = y = 180'; (b) a = ,'O p = 120', y = 180'. -0.3 I
.-'
s Y #
I
I
I
I
I
I
I
1
1
20
40
60
80
100
120
140
160
180
-0.5
-0.6
I
0
(L
(degrees
)
Flgure 4. A€* vs. a for the 2A configuration by STO-3G: (a) RHF= 2.3 A, @ = y = 180°, (b) R,, = 2.1 A, p = 120', y = 180'.
5, curves a and c) is due to the attraction between F, and the (H12,H13)pair. The configuration becomes less stable as /3 decreases beyond 120°, due mainly to the repulsive interaction between C1 and H24and, less extensively but significantly, to the interactions between the (H12,H13) pair and H24. For both 2B and 2C configurations the most stable geometry is that of RCFqF = 3.8 A, with M2 translated in the +z direction by 0.6 A. For the 2D conformation the optimum geometry occurs at Rcc = 4.8 A and with the two molecules staggered. Table I1 is a summary of the optimum parameter values of the dimeric configurations. The H.-.F interaction I1 plays an important role in affecting the HFC angles of type I interactions. It is seen that, according to the STO-3G basis set, the best stability among the two-molecule clusters is the one derived from the 2A conformation, which has a linear structure around the interacting hydrogen, R H F = 2.1 A, cy = 0, and @ = 120'. The 4-31G basis set also yields the linear FHC geometry and similar HFC angles (112.5') but a far larger stabilization energy than the
The Journal of Physical Chemistry, Voi. 87, No. 13, 1983
MO Calculations on Clusters of Methyl Fluoride
2325
TABLE 11: Most Stable Geometries of Two-Membered Clusters
H. . .F interaction IIb
H. . .F interaction Ia type
RHF, A
basis set
deg
YC
RHF, A
YC
A E , kcal/mol
deg
of 1-mer
2A STO-3G 2.1 1 180.0e 4.3 2 89.5 - 0.39 2A 4-31G 2.3 1 180.0f 4.2 2 94.9 - 1.45 2B STO-3G 2.8 1 147.2 3.5 2 106.1 - 0.20 2c STO-3G 3.5 4 106.1 0 -0.15 2D STO-3G 3.2 3 91.9 0 -0.13 a The shortest of all H. . .F distances contained in the most stable geometry of the given configuration type. The H. . .F interactions of secondary importance containing the fluorine atom that is not involved in the type I interaction. Thus, if F, is involved in the shortest H. . .F interaction, those listed under interaction I1 may involve F, when applicable, and vice versa. Number of interactions. The FHC angle associated with the interaction type (I or 11) being considered. e The optimum HFC angle is 120.0". The optimum HFC angle is 112.5'. TABLE 111: Most Stable Geometries of Three-Membered Clusters
type
basis set
wa
3A 3B 3C 3D 3D
STO-3G STO-3G STO-3G STO-3G 4-31G
2 2 2 3 3
parameters fixed LFHC = LFHC = LFHC = LFHC = iFHC =
180", iHFC = 120" 180" 180", iHFC = 120" 180" 180"
optimum values of varied parameters
best A E , kcalimol of 1-mer
R H F =2 . 1 A , CY = 0" R H F= 2.2 A , CY = 180°,b p = 120"' R H F= 2.2 A R H F= 2 . 1 A , a i '= 30",d other a m n ' s = 0 R H F= 2.3 A , all a ' s = 0", LHFC = 131.7"
-0.53 - 0.48 - 0.46 -0.82 - 3.00
a Number of F. .H-C interactions. CY is the angle formed by the C,F,H,, plane and the C,F,H,, plane. p is the angle H,F,C, ( m = 2, 3). For definition of a m n , see the legend of Figure 7. The optimum angles are iH,,F,C, = 122.3", iH,,F,C, = 126.4", iH,,F,C, = 129.4",or the equivalent sets obtained by permutations of these angles.
23
-0.1
-0
-0.2
E
2
Q
A
-0.3
Y
.-E -0.4 1 0
-
3
-0.5
Figure 6. Trimer type 3A: The atoms Hs, C,, F,, H, C1, F,, H,,, C,, and F, are coplanar with the yz plane. The angles C3F3H14 and C,F1H, are fixed at 120', and the angles F3H,,C, and F1H2,C2are kept at 180'. cy = 0 in the basic configuration.
PI
u
4 -0.6 -0.7
- 0.8
80
100
120
140
B or Y
160
180
200
(degrees)
Figure 5. A€, vs. @ and y for the 2A configuration by STO-30: (a) = 2.3 A, a = ,'O y = 180'; (b) y varied at R , = @ = 120'; (c) @ varied at RHF= 2.1 A, a = ,'O y = 180'.
6 varied at R , 2.1 A, a = ,'o
minimal set. This trend persists in three-membered clusters, which will be discussed further in a later section.
Three-Membered Clusters On the basis of the results obtained on the two-membered clusters, we chose four basic configurations for three-membered clusters which were expected to yield either better stabilities or new situations. One of them, type 3A, illustrated in Figure 6 is a chain configuration with a C, symmetry. T h e central molecule, M1, is a hydrogen acceptor against M2 and a donor in the Ml-M3 coupling. Each of the M3-M1 and Ml-M2 pairs forms the most stable 2A geometry. In type 3B,8 another chain configuration with C, symmetry, the central molecule M1
uses its F atom for both interactions, Ml-M2 and Ml-M3, in which the terminal members M2 and M3 are hydrogen donors. The atoms F1, C1, and H14 lie on the plane of symmetry, the atoms F1, H24, and C2 are collinear, the atoms F1, H,, and C3 are collinear, the atoms C1, F1,H24, C2, and Fzare coplanar, and the atoms C1, F,, H34,C3, and F3are coplanar. In type 3C,8 still another chain configuration with a C, symmetry, the central molecule M1 is a hydrogen donor against each terminal member. Each of the Ml-M2 and Ml-M3 pairs forms the most stable 2A configuration. The atoms F1, C,,and H14 lie on the plane of symmetry. The atoms F,, C,, H12,F3,C3, H34are coplanar, and the atoms F1, C1, H13, F2, C2, and H24 are coplanar. The angles H12F3C3and Hl3F2CZare kept a t 120'. T h e type 3D, illustrated in Figure 7, is a threemembered ring configuration. In its basic geometry (C3,J, all atoms other than H,, and Hm3,m = 1, 2, and 3, are coplanar with the plane of cluster symmetry. Three FHC angles are kept a t 180'. This ring configuration contains three F. ..H-C structures, the maximum such number for a 3-mer. Figure 8 illustrates the effects of H-F distances in the four configurations. In each conformation, all equivalent H-F distances were varied simultaneously. In 3A the rotation of M3 around the C3-F3 axis is completely free
2326
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The Journal of Physical Chemistry, Vol. 87, No. 13, 1983
2
Figure 7. Trimer type 3D: a , is an out-of-plane tilting angle of a member molecule Mm in which the rigid structure consisting of Mm and the F, H, axis rotates around the F, F, axis. It is defined as the angle between the plane of F,F2F3and that of F,C,H,,F,. All a , = 0 at the basic C3,,symmetry.
,
0.0
126.4'. The slight improvement associated with the tilting may be viewed as evidence of relieved HFC-angle strain: All HFC angles are 129.4' at am, = 0 while, when one of the am,ls is increased to 30°, two of the HFC angles are decreased to 123.3' and 126.4'. The similarly small effects of tilting angles were observed on the basis of the 4-31G set. We thus feel reasonably secure in concluding that the most stable geometry derived from the 3D configuration is not far from the one described by Rm = 2.1 A and a,, = 0' (all mn combinations). The large difference in the energy levels between the two basis sets (Table 111) will be discussed later. Although the 3D geometry is most stable even in terms of energy per mole of monomer (Table 111), the energies per Fa -H-C interaction in all trimer configurations are comparable. The enhanced stability of the ring structure is thus attributable to the fact that it contains the largest number of F...H-C interactions possible for a trimer.
-0.5
0
-1.0 L
0
.-E
-
L
5
-
Y
-1.5
0
Lu
a
Figure 9. Tetramer type 4C: Besides the in-plane atoms of the 3D configuration, the atoms , H C,, and F, are also coplanar with the plane of cluster symmetry, the yz plane. All H-F distances are fixed at 2.1 A, and the H,,FIC, angle is set at 123'.
-2.0
-2.5 1
2
3'4
5
6
R H F (AI Figure 8. A,E3 vs. R, for the three-membered clusters: (a) 3A, CY = 180'; (b) 3B, a = @ = 120' (see footnotes band c of Table 111 for definitions of a and @I; (c) 3C; (d) 3D, a12= a 2 3 = a s l = . ' 0
within f O . O 1 kcal/mol of 3-mer. As shown in Table 111, the configurations 3B and 3C yield similar stabilization energies. We note that a variation of the HFC angle in type 3B led to confirmation of our earlier observation that the optimum HFC angle is, according to the STO-3G basis set, somewhere near 120'. The type 3D configuration, even in its basic C3,, symmetry, yields by far the largest AE3 among all 3-mers tested (Figure 8). The stability of the 3D configuration is improved slightly (Am3 0.01 kcal/mol of 3-mer) by increasing one of the a,)s from 0' to 30'. A further increase in the tilting angle or a simultaneous tilting of all member molecules generally makes the system less stable due to the repulsions among the out-of-plane hydrogens. Associated with the change in one of a,,'s from ' 0 to 30°, two of the HFC angles decrease from 129.4' to 122.3O and
-
Four-Membered Clusters Four basic configurations were considered. The first, type 4A,8 is a chain conformation (C,symmetry) with the number ( u ) of linear F...H-C structures being three, obtained by adding the fourth member to the 3A configuration. All HFC angles were kept at 120O. The second, type 4B,8 is a four-membered ring (C4hsymmetry) with u = 4, obtained by inserting the fourth member in the three-membered ring of 3D structure. In its "planar", Ca, symmetry, all HFC angles in the plane are 159.4'. The out-of-plane tilting angles am, were defined in a manner similar to the one used in the 3D configuration. The third configuration, 4C (Figure 9), is a three-membered ring with one spur molecule ( u = 4), and the fourth, 4D (Figure lo), is a ring structure with a bridge ( u = 5). The best geometries of these configurations have been summarized in Table IV. In the 4B conformation the stabilization energy per mole of monomer improves from -0.57 kcal at a, = 0 (all CY,,) to -0.83 kcal when the tilting angles are changed by an equal magnitude, a (=lamnl)= 70.3', but in alternating opposite directions. This manner of tilting avoids the intermolecular C-H and H-H repulsions, while reducing the HFC angle to 122.7O. The 4C configuration is less stable than the best 4B geometry. The H44F1C1angle of 123' for the 4C was chosen somewhat arbitrarily on the basis of the previous observation that the HFC angles in the most stable dimer and trimer geometries were somewhat greater than 120° according to the STO-3G basis. The changes in the H,FICI angle and tilting of the ring members did not significantly change
The Journal of Physical Chemistry, Vol. 87, No. 13, 1983 2327
MO Calculations on Clusters of Methyl Fluoride
TABLE IV: Most Stable Geometries of Four-Membered Clusters for STO-3G
type ua 4A
3
4B
4
4C
4D
4 5
best AE, kcall optimum values of mol of parameters fixed varied parameters 1-mer LFHC= 180" LHFC = 120" LFHC= 180"
R H F= 2.1 A
- 0.61
R H F =2 . 1 8 , 01 = 70.3°,b iHFC = 122.7'
-0.83
i F H C = 180", R H F= 2.1 A LH,,F,C, = 123" i F H C = 180" R H F =2.2Ac
a Number of F . . .H-C interactions. --a4, and a = Iamnl. The most stable
TABLE V: Total Gross Populations and Charge Redistributiona in CH,F Monomer and the 2A Configurationsb for STO-3G Basis Set ~~
2A atoms
F, C, HI, HI,
HI, - 0.78
monomer 9.1460 6.0462 0.9359 0.9359 0.9359
F2
c2
H2 2
-0.71
23
€4 7.4
a l2 = - a z 3 = a 3 4= 4B geometry has S4
symmetry. The corresponding HFC angles are H,,F,C2 = 97.9", H3,F1C,= H,F,Cl = 106.0", H,,F3C3 = H,,F,C, = 115.7".
the stability (AAE 5 0.01 kcal/mol of l-mer). In the 4D conformation the single variable RHFuniquely determines the geometry of the cluster due to the requirements of intramolecular rigidity, the FHC linearity, and the maintenance of the C, symmetry. The HFC angles in the best 4D geometry are significantly smaller than the generally preferred values of 120-125O. The straining of the HFC angles accounts for the distinctly smaller energy per H. .F-C in comparison with other tetramer configurations: for each mole of H.. .F-C, the energies are in the order 4B (0.83 kcal) > 4A (0.81 kcal) > 4C (0.78 kcal) > 4D (0.57 kcal). Stretching of the four H..-F distances in the "wing" and an independent shortening of H14-F2 somewhat increase the HFC angles and the stability, but the latter increase is hardly sufficient to make the 4D structure comparable to the other three configurations. We are aware of the fact that the four four-membered configurations that we have investigated represent only a small sample of numerous other viable structures. However, we feel that we not only have confirmed most of the tentative conclusions drawn from the STO-3G study of three-membered clusters but also have found a need for a modification of them: Although the number of He .F-C interactions is the most important factor, it should not be sought at an expense of straining of the HFC angles. The latter prefers to be maintained near its optimum value in the range between 120' and 125'.
-
p = 120"
P= 112.5"
P= 127.5"
9.1466 (- 0.6) 6.0458 (+0.5) 0.9329 (+3.0) 0.9329 ( + 3.0) 0.9338 (+2.1) [+8.21 9.1511 (-5.1) 6.0557 (-9.5) 0.9396 (- 3.7) 0.9396 (-3.7) 0.9220 (+13.9) [-8.21
(- 0.4) (+O.l) (+3.2) ( + 3.2) (+2.1) [+8.21 (-5.2) (-9.5) (- 3.5) (- 3.5) (+13.5) [-8.21
(+0.7) (+2.9) ( + 2.9) (+2.1) [+7.81 (-5.0) (-9.3) (- 3.9) (- 3.9) (+14.2) [-7.81
(- 0.8)
a All values of total gross atomic populations are in units of number of electrons. The numbers in parentheses show the shift relative to the population in the monomer, in units of electron. A positive value means that the atom becomes more positively charged or less negatively charged in comparison to the atom in the monomer. RHF = 2.1 A , 01 = 0 , y = 180". The numbers in brackets are molecular charge transfer, in units of number of electron.
TABLE VI: Total Gross Populations and Charge Redistributiona in CH3FMonomer and the 2A Configurationb for 4-31G Basis Set 2A ( p = 112.5') atoms monomer ~~~
9.4611 (+3.0) 6.0410 (-6.7) 0.8259 ( + 8.0) HI2 13 0.8259 (+8.0) 0.8294 (+4.5) 14 [ + 16.7Ia 9.4735 (-9.4) 6.0591 (-24.8) 0.8401 (- 6.2) 0.8401 (-6.2) 0.8039 ( + 29.9) [- 16.71 a See footnotes a and c of Table V . R H F= 2.4 A , 0, y = 180". F,
c,
9.4641 6.0343 0.8339 0.8339 0.8339
01
=
is to be compared against the 4-31G values of E = 1.45 and 3.00 kcal at n = 2 and 3, respectively. Obviously, the 4-31G set grossly overestimates the work necessary for the liberation of a liquid molecule from its neighbors in that it would lead to a heat of vaporization which is greater than Discussion 6 kcal/mol despite the fact that the ab inito calculation We will first address ourselves to the question of the does not account for the dispersion forces. large discrepancy in the stabilization energies of the most It is interesting to note further that the normal boiling stable dimers and trimers between the two basis sets that points of fluoromethanes CH4.+Fk(k = 0-4) are, in the we have used. The heat of vaporization at the normal order of increasing k from CHI to CF4, 112,'O 195,4222," boiling point (194.95 K) is 4.196 kcal/mol of m ~ n o m e r . ~ 191,5and 145 K.12 The fact that CH3F and CHF, have If one assumes that, in liquid methyl fluoride, no more almost identical boiling points in spite of the significant than three linear H. .H-C interactions per molecule are differences in the number of electrons in these molecules meaningfully possible, it can be shown that the number, implies that the electrostatic force is the primary force in m,of such H...F-C interactions contained in an n-memliquid CHF, and most probably in liquid CH,F as well. bered cluster is given by m = 2 (n- 2) for n L 5. Thus, Thus, while the 4-31G set definitely overestimates the if t is the average stabilization energy per mole of such interaction energy, the minimal set probably underestiH. .F-C interations, the total stabilization energy for the mates it. n-mer is hE, = 2t (n- 2). It follows then that the average The charge redistribution pattern on the STO-3G basis energy per mole of monomer as n tends to infinity is 2t. shown in Table V is typical of hydrogen-bonded dimer According to the present STO-3G calculations, t is 0.78, 0.82, and 0.83 kcal for n = 2, 3, and 4, respectively. This (10) Bigeleisen, J.; Cragg, C. B.; Jeevanadam, M. J.Chem. Phys. 1967, 9
(9)Grosse, A, V.;Wackher, R. C.; Linn, C. B. J.Phys. Chem. 1940,44, 275.
47,4335. (11) "Engineering Sciences Data, Item No. 75010"; Institution of Chemical Engineers: London, 1975. (12)Lobo, L. Q.;Staveley, L. A. K. J. Chem. Eng. Data 1981,26,404.
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The Journal of Physical Chemistry, Vol. 87, No. 13, 1983
Oi et al.
TABLE VII: Interatomic Overlap Populationsa and Interatomic Distancesb between Molecules in the 2A ConfigurationC molecule 2 molecule 1 [p = 127.5'1 CI
c2
F,
H2,
H 23
0.07 (4.19) (3.20)
- 1.07
-(4.53) +(3.90)
- ( 4.76) 0.02 (3.69)
- (4.76)
F,
c,
0.07 (4.07) - 1 . 0 9 (3.20)
-(4.38) + ( 3.90)
-(4.66) 0.02 (3.69)
- (4.66)
FI
c,
0.05 (3.94)
- (4.21)
-(4.55)
-(4.55)
0.02 (3.69)
H 24 - 0.41
(3.14) 2.96 (2.10)
[p = 120.0"] 0.02 (3.69)
- 0.52
(3.04) 3.06 (2.10)
[ p = 112.5"]
a
-0.70 (2.92)
-1.11 (3.20) + (3.90) 0.02 (3.69) 0.02 (3.69) 3.10 (2.10) F, The overlap populations are in units of electron. Only the signs are indicated for those which are less than 0.5 x electron. Numbers in the parentheses are interatomic distances in angstroms. R H F= 2.1 a , = 0 , = 180".
Figure 10. Tetramer type 4D: This configuration (C, symmetry) contains two "wing" planes (one consisting of F,, HW, C3, F3, H23, and C, and another made up with F,, H , C, F, H ,,, and C,) and one vertical plane (the plane of symmetry) on which lie the atoms F,, C,, H, F, C1, and H .,, M3 and M4 are equivalent. M1 and M2 are not. All FHC angles are fixed at 180'.
systems,13J4although the energy involved is too small to be called a hydrogen bond. While the usual pattern of alternating signs of electron redistribution is evident along the C1-F1-H24-C2 chain on the STO-3G basis, the same is apparently not true according to the 4-31G set (Table VI): The latter set gives the unusual pattern of (-, +, +, -) along the chain of these atoms. The fluorine atom using the 4-31G set is more electronegative as compared to the minimal set, which explains the smaller FCH angle in the monomer (Table I) for the former set. The more extensive tilting of M2 in the dimer (i.e., the smaller @; @ = 112.5' for the 4-31G and 120.0' for the STO-3G) and the higher stabilization energy given by the 4-31G set are attributable to the high fluorine electronegativity and the high electronic polarizability (Table VI). Dill, Allen, Topp, and Pople15 found that, for the hydrogen-bonded dimers such as (NH3)2, (H20),, and (HF),, the 6-31G basis set yields consistently reliable results, to which the STO-3G results are closer than the 4-31G calculations. The remaining discussion will be on the basis of the STO-3G calculations only. The most persistent tendency in the STO-3G calculations is the apparent preference for 120-125' by the HFC angle. However, the atomic orbital overlap populations do not support the possibility of the sp2 hybridization around the fluorine atoms. Although M ~ r o k u m a ' found ~,~~ (13) Kollman, P. A.;Allen, L. C. Chem. Reu. 1972, 72, 283.
(14) Del Bene, J. J. Chem. Phys. 1971, 55, 4633.
(15) Dill, J. D.;Allen, L. C.; Topp, W. C.; Pople, J. A. J. Am. Chem.
SOC.1975, 97, 7220.
(16) Morokuma, K.;Winick, J. J. Chem. Phys. 1970,52, 1301.
an sp3hybridization on an oxygen in a H20 dimer and sp2 orbitals around the carbonyl oxygen in a H2CO-H20 interaction, such a hybridization is apparently not warranted for the weak interactions such as those in our present systems. The causes responsible for the relatively narrow range in the preferred HFC angle would be a composite effect of several long-range interactions rather than a single localized force. Table VI1 has been prepared to illustrate the source of such interactions for the best (STO-3G) dimer geometry. The overlap integrals involving hydrogen atoms are less than 5 X lo* electron except for those involving the overlaps with HU, the magnitude of which is on the order of electron. Although the most extensive intermolecular overlaps occur between F1 and H24 and between F1 and C2, they are not the factor for the determination of the equilibrium HFC angle, simply because the torque due to these interactions around F, in the yz plane is zero. The strongest torque-generating overlap is a repulsive (angleopening) one between C1 and HZ4,and the repulsion increases rapidly as @ decreases below 120° (Table VII). The counteracting force is provided by the attractive Coulombic interaction between the (H12,H13) pair and F2. If one assumes, admittedly crudely, that the net point charge on an atom is given by the difference between the total gross population (Table V) and the atomic number, then all F and C are negatively charged and all H's are positively charged. Such a charge on F2 is the largest of all. It can be shown that the attractive (angle-closing) torque caused by the Coulombic F2-(H12,H13)interactions is at least 3 times larger than the next largest torque in the same direction, i.e., the one between C2and (H12,H13). Furthermore, this largest attractive torque increases rapidly as @ decreases below 120'. We thus conclude that the relatively narrow range of preferred HFC angle is established on a balance between these opposing torque-generating interactions. Similar arguments also hold for the larger clusters.18 The overlap populations in the longer chains and larger cyclic structures are quite similar to those in the two-membered cluster.18 To the best of our knowledge, there are no crystallographic data available for solid methyl fluoride. The closest thing which we were able to compare our calculations to is the X-ray diffraction data of methyl chloride crystal: Burbank,lg who considered several space-group symmetry-allowed orientations of the methyl group to best explain the diffraction data, concluded that each molecule makes the closest contacts at 3.00 or 3.01 A with six neighbor molecules, three via the three hydrogens and the (17) Morokuma, K. J . Chem. Phys. 1971,55, 1236. (18) Tabulations of total gross populations and interatomic overlap populations of the trimers and tetramers have been placed in the supplementary material. (19) Burbank, R.D. J. Am. Chem. SOC. 1953, 75, 1211.
J. Phys. Chem. 1983, 87. 2329-2336
other three via the chlorine atom. These distances are exactly the sum of the van der Waals radii of H (1.20 A) and C1 (1.80 A). One of the three Cl.-.H-C angles is 171'46', and the remaining two are 172'32'. He also reported three H. .C1. .-H angles, one of which is 103'50' and the remaining two are 100'36'. If one approximates this geometry around the chlorine atom by a right triangular pyramid having an average HClH angle of 172.15', the corresponding CClH angle would be 116.45'. These data on the CHBClcrystal, i.e., the XHC and CXH angles, are comfortably consistent with our present results. The optimum RHFvalue that we have obtained, which is smaller than the sum of the van der Waals radii, is an indication of the fact that the H...F interaction in methyl fluoride is stronger than that for methyl chloride. To summarize we make the following statements: (1) Methyl fluoride is more stable as a cluster than a monomer. (2) Among the clusters of a given size, the one with ring structures tends to be more stable than the one without any. (3) The stabilization energy per linear F.. .H-C interaction increases with the cluster size: The best values on the basis of the STO-3G set are as follows: -0.78, -0.82, and -0.83, all in kcal/mol of FHC interaction, for the two-, three-, and four-membered configurations, respectively. This is because a larger cluster has more degrees of freedom by which to relieve possible HFC-angle strains. However, these numerical values are probably lower than the true values. The 4-31G set grossly overestimates the interaction energies. (4) The large the cluster, the more stable it is on the bdis of stabilization energy per mol of monomer: Among the configurations tested, the best stabilization energies per mol of monomer on the basis of the STO-3G set are
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AE4/4 = -0.83 kcal/mol of monomer, AE,/3 = -0.82 kcal/mol of monomer, AE2/2 = -0.39 kcal/mol of monomer. This is not only because the energy per F...H-C interaction increases with the cluster size, but also because the number of such linear F a . .H-C interactions increases faster than the cluster size. However, the latter tendency should level off as the cluster continues to grow since, even if six F...H-C interactions are possible around each molecule as in the CH3C1crystal, the maximum number of such interactions per molecule is three. (5) In any cluster, the optimum C-F. .H-C configuration is as follows: RHF = 2.1 A, FHC angle = 180', CFH angle N 120-125'. (6) The optimum CFH angle is determined by a balance of the repulsive and attractive interactions between the atoms in the electron-donor molecule and the electronacceptor molecule. The repulsive overlap is cause mainly between the H involved in the F...H-C interaction and the C (and, to a lesser extent, H's) of the donor molecule. The Coulombic attraction is most significant between the F of the acceptor molecule and the H's in the donor molecule.
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Acknowledgment. We acknowledge use of computer time at the State University of New York at Stony Brook. We are also grateful to Mrs. Michiko Ishida for her beautiful drafting. Registry No. Methyl fluoride, 593-53-3.
Supplementary Material Available: Figures of various basic configurations and AE's as functions of geometrical parameters for 2-, 3- and 4-mers, and tables of population analysis results for 3- and 4-mers (14 pages). Ordering information is given on any current masthead page.
Mossbauer and Infrared Studies of Matrix-Isolated Iron-Carbonyl Complexes' Charles H. F. Peden,t Stewart F. Parkertt Paul H. Barrett,t and Ralph G. Pearson't Departments of Chemistry and Physlcs, University of California, Santa Barbara, Santa Barbara, California 93 107 (Received: October 14, 1982; In Final Form: January 3, 1983)
The matrix-isolated binary'carbonyls, Fe(CO),, x I5, and Fe2(CO),,y = 8, 9, formed upon cocondensation of iron atoms with noble gas/CO gas mixtures have been investigated by infrared and Mossbauer spectroscopies. Assignments for the Mossbauer absorptions of these species are made. New information on the C-0 stretching frequencies of Fe(C0) and Fe(C0)2has been obtained. The very low infrared stretching frequency (1898 cm-l) and the negative Mossbauer isomer shift (-0.60 mm/s) of Fe(C0) are evidence for a large da K* interaction for this fragment.
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Introduction There has been much interest in coordinativelv unsaturated transition-metal complexes formed in matrix isolation experiments. This interest is due to their proposed role as intermediates in homogeneous catalytic2 and photochemical r e a ~ t i o n sand , ~ as models for heterogeneous bulk metal catalyst^.^ Further, the simplest of these complexes can be used to test the utility of various theoretical calculations.&1° +Department of Chemistry. Department of Physics.
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0022-3654/83/2087-2329$01.50/0
The binary carbonyls M(CO), where M = Co, Rh, Ir, Ni, Pd, Pt (x = 1,4)," Au (x = 1,2), CU,Ag ( x = 1-3), Cr (x (1) A preliminary report of this work was presented at the Third International Meeting on Matrix Isolation in Nottingham, England, July 23, 1981.
(2) Parshall, G. W. "HomogeneousCatalysis";Wiley: New York, 1980. (3) Wrighton, M. Chem. Rev. 1974, 74, 401. (4) Muetterties, E. L.; Rhodii, T. N.;Band, E.; Brucker, C. F.;Pretzer, w. R. Chem. Reu. 1979, 79,91, (5) Walch, S.P.; Goddard, W. A. I11 J.Am. Chem. SOC.1976,98,7908. (6) Ozin, G. A.; Power, W. J.; Upton, T. H.; Goddard, W. A. I11 J.Am. Chem. SOC.1978, 100, 4750. (7) McIntosh, D. F.; Ozin, G. A.; Messmer, R. P. Inorg. Chem. 1981, 20,3640.
0 1983 American Chemical Society
