Corremondence CO Force Constants and CO-CO Interaction Constants of Metal C a r b o n y l s 1
MnX-MnC interaction constants in the generous range +0.3 to -0.3 mdyn/A has negligible effect on the calculated CO force constants. In order to make the calculations tractable, the following reasonable assumptions were adopted: (1) the cis-interaction constants for CO-CO interaction are the same for radial CO with radial CO as they are for radial CO with axial CO (Cotton’sz kc = k c ’ ) ; ( 2 ) the cis MC-C’O’ interaction is the same for radial-radial and radial-axial groups ; (3) the MC-CO interaction involving the same carbon is the same for radial as for axial MCO groups. The results of these calculations can be summarized by
Sir:
Recently Cotton, et ~ 1 .published ) ~ another in a series of papers which present calculation of CO stretching force constants and CO-CO interaction constants with neglect of all other force constants and all frequencies but those from CO stretching vibrations. They claim that these calculations2 on BrMn(CO)s, HMn(CO)5, CH3Mn(C0)5, and especially CFaMn(C0)6show that . .highly simplified (Cotton-Kraihanzel) force the field is not only practical but satisfactory in comparison ki (kilo - 0.34Fxa 1 . 2 F ~ c - c of XI (1) to more elaborate schemes and that it comes fairly kz (kzh - 0 . 3 4 F ~ c 1 . 2 F ~ c - c o+;us (2) close to being literally correct in its assumptions, a t kc = ko‘ = ( k o h - 0 . 3 4 P ~ c - i 1 ~ ’ 1. 2 F C ~ ~ c - c r 0 ’ x o least for XMn(CO)5 molecules.” As evidence for the (3) validity of this force field, they showed that correct kt (kt)o - 0.34Ftarc-~1c’ 12F‘~c-c’o’ Xt (4) frequencies were calculated for the m ~ n o - ~ ~ C - s u b The force constants are defined as follows: k1, the stituted species and that the ratio k t / k , was found to be harmonic axial CO stretching force constant; ka, the close to 2, as hypothesized in the Cotton-Kraihanzel harmonic radial CO stretching force constant; k,, the force field.3 harmonic constant for interaction of axial CO with a The use of this simplified force field is an enticing radial CO; kc’, the harmonic constant for interaction procedure. However, it is important to know how of two cis radial CO groups (assumed equal to k,) ; kt, much these approximate results may deviate from the the harmonic constant for interaction of two trans radial true quadratic force constants. The author has CO groups. The same symbols with a subscript zero shown4 that for Mo(C0)G inclusion of M C stretching are the zero approximation values calculated in the COvibrations, MC-CO interactions, and anharmonicity factored force field (neglecting all force constants but corrections leads to quite different results than obCO stretch and CO-CO interactions and all vibrational tained by the approximate method of Cotton and frequencies except those arising from CO stretching). K r a i h a n ~ e l . ~Inasmuch as Cotton, et U Z . , ~ present their The superscripts c and t are for cis and trans interaction, results on CF3Mn(C0j5, BrMn(CO)5, etc., as strong respectively. The xi are correction terms to allow for evidence that k t / k , = 2 as assumed in their approximate anharmonicity. As pointed out above, the general treatment, it seems that comparison with a more quadratic force constants not appearing in eq 1-4, if rigorous approach for these compounds is especially in held within a reasonable range of values, have negligible order. Therefore a series of calculations has been effect on k1, kt, k,, and k t . made to show what values the CO force constants, and I n order to evaluate the various anharmonicity corespecially the CO-CO interaction constants, may have rection terms (xi)in eq 1-4, the author has measured in a more general force field for Mn(CO)5Br. CO fundamentals and binary and ternary combinaA complete general quadratic force field was used. tions of CO vibrations for Mn(CO)6Brin CCI, solution. The MCO and CMC bending frequencies were assumed These are listed in Table I along with the CO stretchto be about the same as for M(C0)e5 (575 f 100 and ing fundamentals. These frequencies have been ob80 f 20 cm-l, respectively). The MnBr stretching served before2m8 but different solvents were used for frequency was chosenG$’as 218 cm-l. The CMnBr fundamentals and combinations. bending frequencies were chosen7 as 50 cm-I. From The frequencies of Table I were treated in the same a large number of calculations it was found that changes manner as those of M(CO)2 to arrive a t the anharof greater than 50% in the frequencies mentioned in this monicity constants and harmonic fundamental freparagraph have negligible effect on the calculated CO quencies given in Table 11. force constants. Furthermore, it was found that inUsing the data of Table I1 the following values are clusion of the stretch-bend, bend-bend, MnX-CO, and calculated for the x i in eq 1-4: XI = 0.44 m d y n / k ; (1) Work performed under the auspices of the U.S. Atomic Energy Comxz = 0.43 mdyn/A; xo = 0.06 mdyn/A; and xt = mission. (2) F. A. Cotton, A. Musco, and G . Yagupsky, I n o v g . Chem., 6, 1357 -0.18 mdyn/A. These correspond to xco = 0.54, (1967 j . xo = 0.02, and Xt = -0.19 mdyn/A for M O ( C O ) ~ ; ~ (3) F. A. Cotton and C. S. Kraihanzel, J . Am. Chcm. Soc., 84, 4432 (1962). ‘ I .
+ + + +
(4) (5) (6) (7)
L. H. Jones, I n w g . C h m t . , 6, 1269 (1967). L. H. Jones, Spectrochim. Acta, 19, 329 (1963). M . A. Bennett and R . J. H. Clark, Chem. I n d . (London), 861 (1963). J. A. Cengel, Ph.D. Thesis, Purdue University, 1865.
+
+
(8) H. D. Kaesz, R . Bau, D. Hendrickson, and J. M. Smith, J. A m . Chem. Soc., 89, 2844 (1967). (9) J. 19. Smith and L. H. Jones, J. Mol. S p e c l r y . , 20, 248 (1966).
1081
1682 CORRESPONDENCE
Inorganic Chemistry
TABLE 1 OBSERVEDCO FUSDAMESTALS ASD COXRINATIONS C h l - l ) FOR Mn(C0)sBr (Cdv SYMhIETRY) I S cc14 S O L U T I O S 2135.2 v1 VI5 4053.2 2001, 5 v9 VIS 4120.4
foundlo that Fllc-cfOl = -0.1 mdyn,la, Unfortunately we cannot expect that this value would neces(IN sarily apply to k, and kt of hexacarbonyls and pentacarbonyl halides, as the interactions are a t 90 and 180' rather than the 109.5' for Ni(CO)*. Nevertheless, it is 20833 apparent from eq 7 and 8 that it would be completely 2052.1 2 v j + Y:! 62555 if k,, k t , and k t / k , were approximately equal to fortuitous 4265.0 2Vl -t VIP\ 6300 3982.2 Y1 2vJ ( k , ) ~ (kt)o, , and (kt)o/(k,)o, respectively. The correction 4089.7 VI VP v,s\ terms to (kc)"and (kt)o are of the same order of magniGli6 4132.1 vp + 2ve 1 tude as (k,)o and ( k J 0 themselves. If k , = ( k & and 4179.1 3u,s 6108 kt = (k& it would mean that P,\lcGto, = -0.05 This frequency of B1 symmetry was observed in the Raniati while F t ~ ~ c - c ~=o ,+0.3 mdyn/A,. The latter value is spectrum. All others were observed in absorption. too large and of the wrong sign to be TABLE I1 Inspection of eq 7 and 8 shows also that the less ANHARMONICITY CONSTANTS AKD HARMONIC FUNUAMESTAL CO stringent restriction that k t / k , = ( k t ) o / ( k , ) o = 2 would STRETCHING FREQUENCIES ( I N C M - ~ ) FOR Mn(C0);Br require quite unreasonableio~'lvalues for one or both of IN CC14 SOLUTIOX Ft\1c-c~o, and F % Y C - ~ , O ) . [The resulting relation is XI1 -2.7 X29 [OIb Ft,\lC-cfo, = 2FhIC--C/O' 0.41. Xsz -10.4 X m -0.4 The two points mentioned by Cotton, et al.,2in supx 9 9 [+7Ia Xw; -14.7 port of their simplified approach may now be taken up. 'YIS,l5 -7.3 Wl 2156,l Xi2 -4.6 W% 2025.0 First. the frequencies of the monosubstituted XI 9 [ -lO]Q WB 2088.7 species are just not very sensitive to the force constants. XlJ5 --8.2 Wl6 8085.7 The solutions arrived a t by the approximations used in Xot determinable from observed data. The vibration v 8 the calculations discussed in this paper (including involves motion similar t o that of the E, CO stretching vibration Ftllc-cfo, = F " ' ~ I ~ - c ~ O=~ -0.1 mdyn/k) yield CO of M(C0)6j therefore, X99 is chosen as +7 cm-1 and X , Q as - 10 cm-' by analogy with M(CO)6.9 b This value was chosen stretching frequencies for the equatorial and axial as zero because it involves vibrations which are perpendicular t o m0110-~~C species of XIn(CO)5Br within 1 cm-1 of the each other, as for Xt,ls. observed values. Furthermore, any number of solutions can be chosen to fit all of the observed isotope thus, the anharmonic corrections appear to be someshifts exactly by inclusion of various interaction conwhat transferable from M(CO)ato pII(CO)5X. stants. I t is not profitable to do so unless all of the Now it is possible to estimate the various correction isotope shifts are known to better than 0.3 cm-l. terms in eq 1-4. For ll(CO)e, calculations based on From these observations one can conclude that the the frequency assignments of ref 9 show t h a t F > I ~= agreement of calculated and observed isotopic fre2 mdyn/a, = 0, and F t h l c - l r c l = 0.5 mdyn/A, quency shifts shown in ref 1 is not a proof of the validity regardless of values chosen for the other interaction of the Cotton-Kraihanzel force field. constants. Furthermore, for Ni(CO)I it was foundlo Second, the results presented above indicate that that F$IC-CO= 0.5 mdyn/'a. for reasonable approximations concerning the MC--CO If we transfer these force constants to Mn(CO)SBr,we interactions kt,'kc # 2. The hypothesis that k t l k , = 2 find was made by the author12 and by Cotton and Kraik , 0 (kl),, 0.36 (5) hanze13 on the basis of vbonding arguments. Howki (&)a 0.35 (6) ever, such arguments are not very compelling and the available evidence gives them no support. The fact k , z (&)a + 1. ~F"DIc-c'o/+ 0 .OB (7) (k,)o/(k,)o is close to 2.0 is remarkably fortuitous, that kt (kt)" 1.2F'nrc-c'o' - 0.36 (8) but it by no means indicates that k t / k , = 2. Thus it The corrections to the CO force constants arise prishould be realized that the CO-CO interactions calmarily from anharmonicity terms as the terms involvculated with a CO-factored force field have no JundaO cancel each other. It aping F X C and F M ~ - C nearly mental significance, either in their relative or absolute pears that it may be appropriate to evaluate relative values.l 3 CO bond strengths by comparing CO force constants, (11) I,. H. Jones, J . Mol. S p e c l v r . , 8 , 105 (1862). (12) L. H. Jones, "Advances in t h e Chemistry
