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Vibrational spectra and force constants of the hexacarbonyls of chromium, molybdenum and tungsten
Spectrochimica Aeta, 1963,Vol. 19, pp. 329 to 335. PergamonPressLtd. Printedin Northern Ireland
Vibrational spectra and force constants of the hexacarbonyls of chromium, molybdenum and tungsten* LLEWELLYN
H.
JONES
Los Alamos Scientific Laboratory, University New Mexico
of California, Los Alamos,
(Received 18 June 1962) Ab&&-The infrared absorption spectra of the hexacarbonyls of Cr, MO, and W have been observed in the gaseous and solid states. Eleven of the thirteen fundamental frequencies of each have been assigned. Force constants were calculated using a resonance interaction potential function. The order of metal carbon force constants is Fwc > FQC > FM&. For these three hexacarbonyls it is found that a higher metal-carbon force constant is accompanied by a lower CO force constant, indicating a decrease in metal-ligand rr bonding in the same order as the metal-carbon force constants. The various calculated interaction constants are discussed. They all have reasonable values except the non-coplanar MCO, MC0 bending interaction constants, which are unexpectedly large. The results of this work support the use of the resonance interaction valence force field for molecules of this sort. INTRODUCTION
articles [l-4] have appeared on the vibrational spectra and force constants There has been very little work of the hexacarbonyls of chromium and molybdenum. Recently the author published [5] a treatment on W(CO), reported in the literature. of molybdenum hexacarbonyl applying a resonance interaction valence force field [6] to calculate meaningful force constants. Since that time we have obtained similar data on Cr(CO), and W(CO), which we wish to report. The results for Mo(CO), are included for a critical comparison with the chromium and tungsten species. The resonance interaction valence force field [6] has been applied to these three hexacarb,onyls in order that force constants of the three species can be compared and related to the bonding properties. The crystal structures of the solid M(CO), compounds, the vibrational selection rules in the solid and gaseous states, and the Raman spectrum of Mo(CO), in chloroform as determined by DANTI and COTTON[3] are given in Ref. [5]. The Raman spectra of Cr(CO), and W(CO), in chloroform are also given in Ref. [3]. SEVERAL
* This work was sponsored by the U.S. Atomic Energy Commission. N. J. HAWKINS, H. C. MATTRAW, W. W. SABOL and D. R. CARPENTER, J. Chem. Phys. 23, 2422 (1955). [2] H. MURATA and K. KAWAI, J. Chem. Phys. 27, 605 (1957); BUZZ.Chem. Xoc. Japan 33, 1008 (1960). [3] A. DANTI and F. A. COTTON, J. Chem. Phys. 28, 736 (1958). [4] C. W. F. T. PISTORIUS and P. C. HAARHOFF, J. Mol. Spectrosc. 3, 621 (1959). [!?I] L. H. JONES, J. Chem. Phys. 36, 2375 (1962). [6] L. H. JONES, J. Mol. Spectrosc. 8, 105 (1962). [l]
329
330
LLEWELLYN H. JONES EXPERIMENTAL
The tungsten and molybdenum hexacarbonyls were donated by the Climax Molybdenum Company. Chromium hexacarbonyl was purchased from the Bram Metallurgical Company. We recorded the infrared spectra of 3 cm, 10 cm, 1 m and 10 m path lengths of the vapor. Because of the low vapor pressure (about 0.1 mm at 20°C) it was necessary to heat the 10 m cell with a heat lamp to record some of the weaker combination bands. The infrared absorption spectrum of the solids was observed also. The vapor was allowed to impinge upon a CsBr window at -120” K forming a thin film of desired thickness. The spectra of Cr(CO), and W(CO), are similar to that of Mo(CO), which is shown in Refs. [l] and [5]. Therefore, the spectra are not reproduced here. The frequencies and approximate peak intensities are reported in Table 1. In order to determine the absorption coeficients it is necessary to know the gas pressure. LANDER and GERMER [7] give the vapor pressures of Mo(CO), and CORDES and SCHREINER [8] give similar W(CO), as a function of temperature. information for Cr(CO),. Our spectra were recorded at a sample temperature of about 26.5°C at which temperature Refs. [S] and [9] yield pressures of O-25, 0.13 and Our sample contained 0.04 mm Hg for Cr(CO),, Mo(CO), and W(CO),, respectively. an excess of solid in the cell and thus the vapor should be saturated. Using these pressures we obtain the approximate absorption coefficients, cc, given in Table 1. The difference in u of the CO stretching frequency, v6, for the three compounds is somewhat surprising; however, more accurate intensity measurements should precede any detailed discussion of these values of u. Slit width and pressure effects on the apparent intensity are not considered here. The values of a are intended only as a guide to the approximate relative intensities of the various transitions. The observed peaks for solid M(CO), at 80°K below 700 cm-l are given in Table 2. The intensities are relative, based on 100 for the most intense band in the region (v,). ASSIGNMENT OF FREQUENCIES CO stretching and CMC bending vibrations
These frequencies are assigned on the basis of the observed CO stretching fundamental of F,, symmetry and the various combination frequencies of a CO stretching vibration with a CMC bending vibration. The arguments for the Cr and W compounds run the same as those presented [5] for Mo(CO),. The results are given in Table 3. The F,, CMC bending frequency, v13,is not observed in combination with a CO stretching frequency. The fundamental, vg, of Cr(CO), vapor was observed in the far infrared at 98 cm-l by MCDOWELL and JONES [9]. [7] J. J. LANDER and L. H. GERMER, Am. Inst. Mining Met. Engra. Inst. Metals Technol. 14, No. 6, Tech. Pub. No. 2259 (1947). [8] J.F. CORDES and S. SCRREINER, Z.anorg.u.allgem.Chem. 299,87 (1959). [9] R. R. MCDOWELL and L. H. JONES, J. Chem. Phys. N&3321 (1962)
Div.,
Metala
Vibrational
spectra and force constants of the hexacarbonyls
of chromium
331
MC stretching and MC0 bending vibrations v7 and vs. For each of the three hexacarbonyls a pair of intense absorption peaks is observed in the 700-300 cm-l region. These occur at 668 and 441 cm-l for Cr(CO),, Table 1. Observed infrared absorption frequencies for M(CO),
Cr(Co)6
V3 + V6 Vl + V7 V3 + V? VI + VQ V3 +
V6
Vz + VI3 Vl +
Ve
V3 + VQ V.5+
Vll
Vl - VQ V&S '6 VClS V3 - VQ '6 - '11 '6 - '4 '6 - '2 V5 + V7 V2 + V7 VP + V7 V5 + V6 V4 + V12 V2 + VQ VP + V6 V7 + Vll V7 V5 +
VQ
V5 + V13 V2 + VQ VP + VQ V4 + V13 V6
w(co)6 _______~~._
a x 104*
v (cm-l)
4109.5 4007
20 20
4118 4010
40 30
4113 4002
2785 2691 2555 2467 2390 2215 2122 2089 2020
1 2 2 5 5 4 10 40
2717 2622 2488 (2394 (2394 2204 2109 2084 2044
1 1 4 20)
2602 2496
20) 7 30 80 3
2409 2204 2101 2080 2043
15 8 13 80 5
1998 1965
12,000 220
V (cm-l)
Yl + yl3
MOW),
202ot 2000 1967.5 1927 1909
20 8000 200 1 4
1615 1199 1047 1031 974 876 820 796 754 668 638 600 480 458
1.5 6 4 24 3 15 8 1 1 1100 10 2 10 3
441
250
2020t 2004 1971 1945 1922 1662 1608 1074 985 937 (850 850 745 708 675 593 562
a Y 104
30 20,000 500 6 8 2 4 40 35 48 48) 48 18 5 13 1280 32
473
3
400 368
4 800
v (cm-‘)
a X 104 20 20
0.2 5
1915
5
1069 1005 948
8 7 20
883
15
585 564
320 100
443 424 374
12
’
12 250
* The absorption coefficients, CL,are measured at the maximum of intensity. They are approximate, varying with path length, effective slit width and pressure. As recorded in this table they are measured on the Cary Model 14 (4000 cm-’ region), Perk&Elmer Model 221 with prism-grating interchange (3000-700 cm-l) and Perkir-Elmer Model 221 with CsBr prism (700-300 cm-r). The units of a are P’t-1 where P is pressure in mmHg, t is path length in cm. t There is an unexplained band at about 2020 cm-l for Cr(CO), and Mo(CO),. It may arise from M(C0)5(C130) as discussed in Ref. [5].
332
LLEWELLYN H. JONES Table 2. Frequencies for solid M(CO), Cr(CO), V7 VI0 v5 V12
Vi3 % VP
656 562 534 512 489
(100) (0.8) (0.6) (1) (0.3)
448 400 385 368
(84) (0.9) (0.5) (1)
Mo(CO),
Table 3. Fundamental Representation and designation
Al,
Vl
01 -%l
v2 v3
FlF,,
v4 v5
F 1U
V%
V? Vs vD F2,
F 2u
VlO
VI1 92 y13
from 700 to 300 cm-l WCO),
587 (100)
585 (100)
474 (0.8) 512 (1)
482 (0.6) 526 (1)
367 407 i 394 346
373 (80)
(80) (.5) (2) (1)
418 (1) 365 (0.4)
frequencies of M(CO),
Cr(CO), 2118 cm-l 2172* 390 2026 2103* 363 534 2000 2078* 668 441 98 562 90 512 cwt
WCO),
W(CO),
2124 2186* 392 2027 2112* 344 481 2004 2092* 593 368
2124 2174* 420 2019 2084* 363 484 1998 2066* 585 374
(5&t 81 512
(5::) 83 520
(Wt
t
(67) t
* WI, W3’ and os are the approximate zero-point vibrational frequencies of the CO stretching vibrations, determined in the same manner as those of Mo(CO), in Ref. [5]. t Calculated values.
593 and 368 for Mo(CO),, and 585 and 374 for W(CO),. By analogy with Ni(CO), [lo] the lower frequency of each pair is no doubt primarily the F,, metal-carbon stretching frequency, the higher then being the Flu MC0 bending frequency. Ye. The several fairly intense combination peaks in the region 850-1200 cm-1 are valuable in making further assignments. For example, the peaks at 1199, 1074 and 1069 for the Cr, MO and W compounds respectively, must arise from Y, plus a “g” frequency at 531, 481 and 484 respectively. Further evidence for this frequency is the solid-state spectrum given in Table 2, in which are observed peaks at 534,474 and [lo]
L. H. JONES, J. Chem. Phys. 28, 1215 (1958).
Vibrational
spectra and force constants of the hexacarbonyls
of chromium
333
482 for the Cr, MO and W compounds respectively. Because this frequency is quite a bit lower than v,, we assign it as the F,, bending frequency, vg, as discussed in Ref. [5]. Ref. [6] indicates that the F,, force constant should be the lowest of the MC0 bending symmetry force constants. v2 and vq. Arguments based on observed combination bands and the solid state spectrum, similar to those presented for Mo(CO), in Ref. [5], show that v2 is about 390, 392 and 420 and vq at 363, 344 and 363 for the Cr, MO and W compounds respectively. These assignments are supported by the appearance of peaks near these values in the solid-state spectrum of Table 2. There is some disagreement for the value of v2 of Cr(CO), as derived Gem the various combination bands. For example we find v2 = 390 from v2 + vs, 383 from v2 + v7, 379 from v2 + vs, 382 from v2 + vg, 385 from vs - v2 and 385 and 400 from the solid state. The value derived from vg - v2 would be accurate except that location of the band center is uncertain. We shall assign the higher value of 390 for vp of Cr(CO), realizing that it may be as low as 380 cm-l. v10and v12. Let us first discuss W(CO),. A fairly intense combination is observed at 883 cm-l. Because of its intensity we feel obliged to call it a binary combination. It must have F,, symmetry and therefore must involve either an F,, fundamental or an F,, fundamental. If it involves an F,, fundamental, the other component, necessarily a “g” vibration, is either 298 cm-l, 509 cm-l or 803 cm-l. The frequency 298 is too low and 803 is too high for one of the remaining fundamentals. 509 could arise from v10 of F,, symmetry, however it does not correspond to an observed frequency in the solid state. There are observed in the solid two frequencies at 526 and 365 which add up to 891, and thus most probably the combination at 883 cm-1 in the vapor arises from the same two vibrations. The peak in the solid at 365 arises from V~ (~363 in the vapor). The other component must then be a “u” frequency. Thus, the most reasonable explanation for the absorption at 883 is vq + v12, which , is infrared active, placing v12 M 520 cm-l. The calculation of-potential constants indicates that vrOmay be at about 509 cm-l for W(CO), and thus 883 could arise from vs + vrO_However, for Cr(CO), an analogous binary combination appears at 876 cm-l which cannot arise from vs + vrO (441 + 562 = 1003) and thus must arise from vq + v12 (363 + 512) as there is no reasonable binary combination involving an F,, frequency to give 876 cm-l. By analogy we must then assign the tungsten band at 883 as v4 + v12, An analogous peak appears for Mo(CO), at 850 cm-l. This could arise from vg + vS (481 + 368); however, it no doubt arises primarily from vp + vr2 (344 + 512) by analogy with the chromium and tungsten compounds. There is no indication of the value of v10of F,, symmetry except for the peak at 562 cm-l in solid Cr(CO),. The assignments are compiled in Table 3. Anharmonic
corrections
For all but the CO stretching frequencies the anharmonic corrections appear to be small and we neglect them. For the CO stretching frequencies, vl, va and vs,we make approximate corrections for anharmonicity as discussed in Ref. [5]. That is, from vl, vQ, vs, v1 + vg and vQ + vg we calculate, for Cr(CO),, Mo(CO), and W(CO),
334
LLEWELLYNH. JONES
respectively, X,, = -8.5, -10 and -9 cm-l and X,, = -19, -21 and -15 cm-l. For XII, Xa3, X,, and X,, we use the average of X,, and X,,*. The resulting zeropoint vibrational frequencies are included in Table 3 as con oar and o,,. POTENTIAL FUNCTION AND FORCE CONSTANTS The F and G matrices for a General Quadratic Valence Force Field are given in Reference 6 for octahedral M(CO),. The “resonance interaction”[b] simplification is used for the interaction constants (see Table 6 of Ref. [5]), with the exception of the pi, /Ij interaction constants (the pi and #?jare the MC,O, and MC,O, angles). For the B frequencies the simplified potential function apparently does not fit [5]. Therefore for Fpy we shall use the general expression of Ref. [6]. This leads to the F matrix given in Table 4. As in Ref. [5] we let 4 = 1, K = H = T = 0. The arguments for these assignments are given in Ref. [5] for Mo(CO), and apply also to Cr(CO), and
W(CO),. Table 4. F matrix of M(CO), Al,
Fll
=
+ 3qB FM, + qD2/3B (1 - q)D
F,,
F,,
=
E"l2
=
F 33 F 44
=
Fco
+
3qB(Z
=
FMC
+
kD2/3B1[(z - 2)/(2 + 4)l
F34
=
[l
PI,
F,,
=
F. - Fpp’ - 2F,$
F 1U
Fl36
=
F77 F80 Fe, F.s7 F,, F,, F,;8 F,, FM
= = = = = = = = =
F 10,lO
=
EC2
F2s
F 11.11 F 10911 F 2v
F 12.12 F 13.13 F 12,x3
-
q(z
-
-
2)/(2
2)/(2
+
+
4)]D
- 3qBZ/(Z + 4) + 4)l FMO- W2/3Bl[Wz Fp + Fpa’ + 2 (F&” + Fob”“) [8A/(3A -t l)]Fa + 4Fa,’ [l + qz/(z + 4)lD 0 0 -22/(2) K 2H 2/(2) T Fco
=
Fg - Fpp’ + 2 Fpa” [4(1 - A)/(1 + 3A)lE”,
=
T
= =
=
4)
Fp + Fpp’ - 2(F,$” + F,g$“‘) [8A/(3A -+- l)]Fg - 4F,,’ d(VT
Since we do not observe yIo for the MO and W compounds we cannot calculate all the Fpp constants. For Cr(CO), Fpp” is about zero so we shall let it equal zero for the other two hexacarbonyls. The resulting force constants are given in Table 5. * Though this is a crude approximation correction.
it certainly is better than making
no anharmonic
Vibrational
spectra and force constants of the hexacarbonyls
of chromium
335
Table 5. Force constants of the hexacarbonyls
17.873 2.034 0.825 0.218
F CO F MC F/i E’z
Fco,oo’ (opposite) Pco,co” (adjacent) li6ac.Mc’(opposite) F IIIC.MC” (adjacent) B’Co,ar,’(neighbours) F CO,HC”(opposite) F co,yc”’ (adjacent,)
FOP’ FM” E;$.J”’ + F&J””
B D
A z
_~
18.122 1.806 0.759 O*lQO
17.695 2,148 0.762 0.213
0,180 O-039
0‘120 0.040
0.137 0.053
0.340 0.074
0.364 0.121
0.366 0*141
0.462 - 0.247 - 0.054
0.487 - 0.209 - 0,070
0.568 - 0.224 -0.OR6
0.022 0 0.079
0.073 0 0.048
0.073 0 0.043
0.112 0.462 0.38 4.6
0.093 0.487 0.37 3.0
0,116 0.568 0.39 2.6
With the exception of the E, frequencies these force constants yield the observed frequencies reported in Table 3. For the E, frequencies the differences are reported in Table 6. It is seen in Table 6 that the observed and calculated values for Y.,are in reasonable agreement. They can be made to agree exactly by slight adjustments of the force constants. To bring observed and calculated mginto agreement would require making 4 of Table 4 greater than 1. As discussed in Ref. [5] it is unreasonable that p be greater than 1. The anharmonicity corrections are approximate and mrty account for the discrepancy. DISCUSSIONOF FORCE CONSTANTS F MC The strengths of the metal--carbon bonds apparently do not follow fhe order of the periodio table; thus P,, > F,,, > F,,,. This result, however, is to be expected from the observed bond distances. BROCKWAY, et al. [ll] from electrondiffraction experiments found R,,, = 1.92 f 0.04 A, R,,,= 2.08 f 0.04 d, and R,, = 2.06 f O-04 A. R@DORFFand HOFMANN[12] determined the crystal structure and found that solid Cr(CO}~ has the smallest unit cell while Mom has the [ll] L. 0. BBOCKWAY,R. V. G. EVANS and M. W. LISTEB, TTCWM. Fcwu&zySoc. &4,1350 (1938). [12] IV. RODORFFand U. HOFMANN, 2. physik. Chem. (Leipzig) B28, 351 (1935).
336
LLEWELLYN H. JONES Table 6. Observed and calculated E, frequencies for M(CO), w3
Cr(CO), Mo(CO), W(CO),
VP
Obs.
Calc.
Obs.
Calc.
2103 2112 2084
2131 2130 2104
363 344 363
363 340 365
largest and they are roughly in proportion to the electron diffraction distances. If we then use the distances of BROCKWAY et al. along with BADGER’S rule [ 131 we find p,, > F,,, > Fnroc,in the same order as the observed force constants. F co From Table 5 we see that the CO stretching force constants are in the reverse order of the MC force constants; thus, the higher the metal-carbon force constant the lower the carbon-oxygen force constant. This fact suggests that there are significant differences in the amount of metal-carbon pi-bonding. Such metal-carbon pibonding should increase the metal-carbon force constant and decrease the carbonoxygen force constant [14]. Thus it appears that the extent of metal-carbon pibonding decreases slightly in the order WC > CrC > MoC.
The angle a is a CMC angle. Its force constant should increase slightly as the metal-carbon distance decreases since the C-C distance becomes smaller resulting in increased C-C repulsion. This is seen in Table 5 to be true, though we might expect F, for W(CO), to be closer to FX for Mo(CO),. A decrease of three wave numbers in the frequency assignments for the CWC bending frequencies will bring F’, for W(CO), very close to F, for Mo(CO),.
The MC0 bending force constants are very large for these hexacarbonyls, much larger than the corresponding force constants of Ni(CO), [15]. As has been discussed in reference [5], this implies strong interaction of the metal d, electrons with the CO groups. The constant D This constant represents the interaction of C,Oi with C,M. It is about the same for Cr and MO but somewhat higher for W. The increased metal-carbon m-bonding in W(CO), over that in Mo(CO), is in agreement with the larger value of D. Cr(CO), apparently does not fall in line. It should be recalled that there is some uncertainty in the assignment for vp of Cr(CO),. We have defined [6] D as equal to dF,, where That is, a unit positive displacement of C,O, leads to a contraction d = -(&Jd)c,o,. [13] R. M. BADOER, J. Chem. Phys. [14] L. H. JONES, J. Mol. Spectrosc. [15] L. H. JONES, J. Mol. Spectrosc.
3, 710 (1935). 9, 130 (1962). 5, 133 (1960).
Vibrational spectra and force constants of the hexacarbonyls
of chromium
337
of C&M equal to d. From D and FMc we calculate d to be 0.227, 0.270 and 0.264 respectively for Cr(CO),, Mo(CO), and W(CO),. Thus, for the tungsten and molybdenum compounds d is essentially the same. From this it is apparent that chromium behaves differently from MO and W while the latter two behave similarly. Actually we would expect d to be less for Mo(CO), than for W(CO), as it arises partially from the metal-carbon r-bonding which is apparently greater in W(CO),. The constant B B was defined [6] as equal to K,dF,,/S
where K, is a constant equal to
Thus it was hypothesized [6] that a unit displacement of CrO, causes proportionate changes in C,O, and C,M (i # 1). Substituting for d and F,, we find K, = 0.084, O-057 and 0.075 for Cr(CO),, Mo(CO), and W(CO),. We would feel better if the magnitude of K, followed the order of n-bonding: MO < Cr < W. However, it is apparent that here again chromium does not fall in line, whereas MO and W are in the order of degree of n-bonding. The constant 2 2 was defined [6] as (S C,~&J(XC,M)C,O1 which is the ratio of the change in opposite (180’) CM bond length to the change in adjacent (90”) CM bond length arising from unit displacement of C,O,. In order to discuss this quantity it will be convenient to study a schematic diagram as in Fig. 1. This figure represents the d,,
Fig. 1. Schematic represent,at,ion of d,, orbital for M(CO),.
orbital of M(CO),. As C,M is stretched the d orbital will 7~bond less strongly with C,O,. A discussion of this is given elsewhere [14]. This will cause the d,, electrons to spend more time in the 23 and 24 lobes and less in the 13 and 14 lobes, leading to a distorted d orbital similar to Fig. l(b). The resulting overlap of d,, (lobes 23 and 24) with C, is considerably increased, whereas the overlap of d,, with C, is increased in lobe 23 but decreased in lobe 13. Thus we expect a much greater effect on C,M (the opposite CM bond) than on C&M (an adjacent CM bond). Furthermore, the opposite CM bond (C&M) is also affected by similar accompanying changes in d,, when C,M is 22
LLEWELLYN 33..JONES
338
stretched. Therefore we expect the quantity Z to be greater than 2. Indeed it is close to 3 for Mo(CO), and W(CO),. It appears to be considerably higher for Cr(CO),. The Cretan
A
A was defined [S] as -(Xb114)E1Bf that is, the change in ~1~~accompanying a unit positive change in the adjacent, coplanar angle, a16. It is shown in Ref [S] that it should be between +Q and +&. Thus, the observed value of 0.37-0.39 is quite reasonable.
In Ref. 6 it was concluded that the important ,!-fi interactions were among coplanar MC0 angle changes and we could neglect the non-coplanar 6 interactions. However, from the results of Table 5 it is apparent that this is not so. In fact, for Cr(CO), the non-coplanar interactions (P @@“’+ FPB”“) are greater than the coplanar interacti constants FPP’ and FPbf’. These results rest primarily on the assignment for the combination band Y* i_ 7x2 appearing at 876, 850 and 883 for CrfCO),, MO (CO), and W(CO), respectively. The solid-state spectrum also verifies this assignment as discussed in the section on assignment of frequencies. In order to check the assignment of the 883 cm-l band for W(CO), as v4 + v12we made a study of the intensity of this band in solid W(CO)~as a function of temperature in the range 148°K to 215’K. According to the theoretical work of LISITSA and STRIZHEVSKII [ 161 the ratio of integrated absorbances, At, should be R = .4,&4,,, = 1.09 for vq + v12. For the possible ternary combinations R - 1.45. The observed value is 1.12, confirming our assignment as a binary combination. Thus we are left in the rather unfortunate position of being unable to present an explanation for the observed interactions among the MC0 angles. Further theoretical studies of the orbital interactions are required. CONCLUSIONS The vibrational spectra of Cr(CO),, Mo(CO), and W(CO), have been studied and eleven of the thirteen fundamental frequencies of each have been assigned. The force constants for a ~~resonan~e interaction valence force field” [6] have been calculated. They show that the metal-carbon T-bonding increases in the order MoC < CrC < WC. The interaction constants for the Mo(CO), and W(CO), fall in line with this order of n bonding ; however, Cr(CO), shows anomalous behavior in this respect. The non-coplanar MC0 bending interactions are unexpectedly large and remain unexplained.
[16] Bi. P. LISITSAand V. L. STBIZHEVSHII,O@&.Z i ~pek~ro5ko~i~a 10, 48 (1961).
Vibrational spectra and force constants of the hexacarbonyls of chromium, molybdenum and tungsten* LLEWELLYN
H.
JONES
Los Alamos Scientific Laboratory, University New Mexico
of California, Los Alamos,
(Received 18 June 1962) Ab&&-The infrared absorption spectra of the hexacarbonyls of Cr, MO, and W have been observed in the gaseous and solid states. Eleven of the thirteen fundamental frequencies of each have been assigned. Force constants were calculated using a resonance interaction potential function. The order of metal carbon force constants is Fwc > FQC > FM&. For these three hexacarbonyls it is found that a higher metal-carbon force constant is accompanied by a lower CO force constant, indicating a decrease in metal-ligand rr bonding in the same order as the metal-carbon force constants. The various calculated interaction constants are discussed. They all have reasonable values except the non-coplanar MCO, MC0 bending interaction constants, which are unexpectedly large. The results of this work support the use of the resonance interaction valence force field for molecules of this sort. INTRODUCTION
articles [l-4] have appeared on the vibrational spectra and force constants There has been very little work of the hexacarbonyls of chromium and molybdenum. Recently the author published [5] a treatment on W(CO), reported in the literature. of molybdenum hexacarbonyl applying a resonance interaction valence force field [6] to calculate meaningful force constants. Since that time we have obtained similar data on Cr(CO), and W(CO), which we wish to report. The results for Mo(CO), are included for a critical comparison with the chromium and tungsten species. The resonance interaction valence force field [6] has been applied to these three hexacarb,onyls in order that force constants of the three species can be compared and related to the bonding properties. The crystal structures of the solid M(CO), compounds, the vibrational selection rules in the solid and gaseous states, and the Raman spectrum of Mo(CO), in chloroform as determined by DANTI and COTTON[3] are given in Ref. [5]. The Raman spectra of Cr(CO), and W(CO), in chloroform are also given in Ref. [3]. SEVERAL
* This work was sponsored by the U.S. Atomic Energy Commission. N. J. HAWKINS, H. C. MATTRAW, W. W. SABOL and D. R. CARPENTER, J. Chem. Phys. 23, 2422 (1955). [2] H. MURATA and K. KAWAI, J. Chem. Phys. 27, 605 (1957); BUZZ.Chem. Xoc. Japan 33, 1008 (1960). [3] A. DANTI and F. A. COTTON, J. Chem. Phys. 28, 736 (1958). [4] C. W. F. T. PISTORIUS and P. C. HAARHOFF, J. Mol. Spectrosc. 3, 621 (1959). [!?I] L. H. JONES, J. Chem. Phys. 36, 2375 (1962). [6] L. H. JONES, J. Mol. Spectrosc. 8, 105 (1962). [l]
329
330
LLEWELLYN H. JONES EXPERIMENTAL
The tungsten and molybdenum hexacarbonyls were donated by the Climax Molybdenum Company. Chromium hexacarbonyl was purchased from the Bram Metallurgical Company. We recorded the infrared spectra of 3 cm, 10 cm, 1 m and 10 m path lengths of the vapor. Because of the low vapor pressure (about 0.1 mm at 20°C) it was necessary to heat the 10 m cell with a heat lamp to record some of the weaker combination bands. The infrared absorption spectrum of the solids was observed also. The vapor was allowed to impinge upon a CsBr window at -120” K forming a thin film of desired thickness. The spectra of Cr(CO), and W(CO), are similar to that of Mo(CO), which is shown in Refs. [l] and [5]. Therefore, the spectra are not reproduced here. The frequencies and approximate peak intensities are reported in Table 1. In order to determine the absorption coeficients it is necessary to know the gas pressure. LANDER and GERMER [7] give the vapor pressures of Mo(CO), and CORDES and SCHREINER [8] give similar W(CO), as a function of temperature. information for Cr(CO),. Our spectra were recorded at a sample temperature of about 26.5°C at which temperature Refs. [S] and [9] yield pressures of O-25, 0.13 and Our sample contained 0.04 mm Hg for Cr(CO),, Mo(CO), and W(CO),, respectively. an excess of solid in the cell and thus the vapor should be saturated. Using these pressures we obtain the approximate absorption coefficients, cc, given in Table 1. The difference in u of the CO stretching frequency, v6, for the three compounds is somewhat surprising; however, more accurate intensity measurements should precede any detailed discussion of these values of u. Slit width and pressure effects on the apparent intensity are not considered here. The values of a are intended only as a guide to the approximate relative intensities of the various transitions. The observed peaks for solid M(CO), at 80°K below 700 cm-l are given in Table 2. The intensities are relative, based on 100 for the most intense band in the region (v,). ASSIGNMENT OF FREQUENCIES CO stretching and CMC bending vibrations
These frequencies are assigned on the basis of the observed CO stretching fundamental of F,, symmetry and the various combination frequencies of a CO stretching vibration with a CMC bending vibration. The arguments for the Cr and W compounds run the same as those presented [5] for Mo(CO),. The results are given in Table 3. The F,, CMC bending frequency, v13,is not observed in combination with a CO stretching frequency. The fundamental, vg, of Cr(CO), vapor was observed in the far infrared at 98 cm-l by MCDOWELL and JONES [9]. [7] J. J. LANDER and L. H. GERMER, Am. Inst. Mining Met. Engra. Inst. Metals Technol. 14, No. 6, Tech. Pub. No. 2259 (1947). [8] J.F. CORDES and S. SCRREINER, Z.anorg.u.allgem.Chem. 299,87 (1959). [9] R. R. MCDOWELL and L. H. JONES, J. Chem. Phys. N&3321 (1962)
Div.,
Metala
Vibrational
spectra and force constants of the hexacarbonyls
of chromium
331
MC stretching and MC0 bending vibrations v7 and vs. For each of the three hexacarbonyls a pair of intense absorption peaks is observed in the 700-300 cm-l region. These occur at 668 and 441 cm-l for Cr(CO),, Table 1. Observed infrared absorption frequencies for M(CO),
Cr(Co)6
V3 + V6 Vl + V7 V3 + V? VI + VQ V3 +
V6
Vz + VI3 Vl +
Ve
V3 + VQ V.5+
Vll
Vl - VQ V&S '6 VClS V3 - VQ '6 - '11 '6 - '4 '6 - '2 V5 + V7 V2 + V7 VP + V7 V5 + V6 V4 + V12 V2 + VQ VP + V6 V7 + Vll V7 V5 +
VQ
V5 + V13 V2 + VQ VP + VQ V4 + V13 V6
w(co)6 _______~~._
a x 104*
v (cm-l)
4109.5 4007
20 20
4118 4010
40 30
4113 4002
2785 2691 2555 2467 2390 2215 2122 2089 2020
1 2 2 5 5 4 10 40
2717 2622 2488 (2394 (2394 2204 2109 2084 2044
1 1 4 20)
2602 2496
20) 7 30 80 3
2409 2204 2101 2080 2043
15 8 13 80 5
1998 1965
12,000 220
V (cm-l)
Yl + yl3
MOW),
202ot 2000 1967.5 1927 1909
20 8000 200 1 4
1615 1199 1047 1031 974 876 820 796 754 668 638 600 480 458
1.5 6 4 24 3 15 8 1 1 1100 10 2 10 3
441
250
2020t 2004 1971 1945 1922 1662 1608 1074 985 937 (850 850 745 708 675 593 562
a Y 104
30 20,000 500 6 8 2 4 40 35 48 48) 48 18 5 13 1280 32
473
3
400 368
4 800
v (cm-‘)
a X 104 20 20
0.2 5
1915
5
1069 1005 948
8 7 20
883
15
585 564
320 100
443 424 374
12
’
12 250
* The absorption coefficients, CL,are measured at the maximum of intensity. They are approximate, varying with path length, effective slit width and pressure. As recorded in this table they are measured on the Cary Model 14 (4000 cm-’ region), Perk&Elmer Model 221 with prism-grating interchange (3000-700 cm-l) and Perkir-Elmer Model 221 with CsBr prism (700-300 cm-r). The units of a are P’t-1 where P is pressure in mmHg, t is path length in cm. t There is an unexplained band at about 2020 cm-l for Cr(CO), and Mo(CO),. It may arise from M(C0)5(C130) as discussed in Ref. [5].
332
LLEWELLYN H. JONES Table 2. Frequencies for solid M(CO), Cr(CO), V7 VI0 v5 V12
Vi3 % VP
656 562 534 512 489
(100) (0.8) (0.6) (1) (0.3)
448 400 385 368
(84) (0.9) (0.5) (1)
Mo(CO),
Table 3. Fundamental Representation and designation
Al,
Vl
01 -%l
v2 v3
FlF,,
v4 v5
F 1U
V%
V? Vs vD F2,
F 2u
VlO
VI1 92 y13
from 700 to 300 cm-l WCO),
587 (100)
585 (100)
474 (0.8) 512 (1)
482 (0.6) 526 (1)
367 407 i 394 346
373 (80)
(80) (.5) (2) (1)
418 (1) 365 (0.4)
frequencies of M(CO),
Cr(CO), 2118 cm-l 2172* 390 2026 2103* 363 534 2000 2078* 668 441 98 562 90 512 cwt
WCO),
W(CO),
2124 2186* 392 2027 2112* 344 481 2004 2092* 593 368
2124 2174* 420 2019 2084* 363 484 1998 2066* 585 374
(5&t 81 512
(5::) 83 520
(Wt
t
(67) t
* WI, W3’ and os are the approximate zero-point vibrational frequencies of the CO stretching vibrations, determined in the same manner as those of Mo(CO), in Ref. [5]. t Calculated values.
593 and 368 for Mo(CO),, and 585 and 374 for W(CO),. By analogy with Ni(CO), [lo] the lower frequency of each pair is no doubt primarily the F,, metal-carbon stretching frequency, the higher then being the Flu MC0 bending frequency. Ye. The several fairly intense combination peaks in the region 850-1200 cm-1 are valuable in making further assignments. For example, the peaks at 1199, 1074 and 1069 for the Cr, MO and W compounds respectively, must arise from Y, plus a “g” frequency at 531, 481 and 484 respectively. Further evidence for this frequency is the solid-state spectrum given in Table 2, in which are observed peaks at 534,474 and [lo]
L. H. JONES, J. Chem. Phys. 28, 1215 (1958).
Vibrational
spectra and force constants of the hexacarbonyls
of chromium
333
482 for the Cr, MO and W compounds respectively. Because this frequency is quite a bit lower than v,, we assign it as the F,, bending frequency, vg, as discussed in Ref. [5]. Ref. [6] indicates that the F,, force constant should be the lowest of the MC0 bending symmetry force constants. v2 and vq. Arguments based on observed combination bands and the solid state spectrum, similar to those presented for Mo(CO), in Ref. [5], show that v2 is about 390, 392 and 420 and vq at 363, 344 and 363 for the Cr, MO and W compounds respectively. These assignments are supported by the appearance of peaks near these values in the solid-state spectrum of Table 2. There is some disagreement for the value of v2 of Cr(CO), as derived Gem the various combination bands. For example we find v2 = 390 from v2 + vs, 383 from v2 + v7, 379 from v2 + vs, 382 from v2 + vg, 385 from vs - v2 and 385 and 400 from the solid state. The value derived from vg - v2 would be accurate except that location of the band center is uncertain. We shall assign the higher value of 390 for vp of Cr(CO), realizing that it may be as low as 380 cm-l. v10and v12. Let us first discuss W(CO),. A fairly intense combination is observed at 883 cm-l. Because of its intensity we feel obliged to call it a binary combination. It must have F,, symmetry and therefore must involve either an F,, fundamental or an F,, fundamental. If it involves an F,, fundamental, the other component, necessarily a “g” vibration, is either 298 cm-l, 509 cm-l or 803 cm-l. The frequency 298 is too low and 803 is too high for one of the remaining fundamentals. 509 could arise from v10 of F,, symmetry, however it does not correspond to an observed frequency in the solid state. There are observed in the solid two frequencies at 526 and 365 which add up to 891, and thus most probably the combination at 883 cm-1 in the vapor arises from the same two vibrations. The peak in the solid at 365 arises from V~ (~363 in the vapor). The other component must then be a “u” frequency. Thus, the most reasonable explanation for the absorption at 883 is vq + v12, which , is infrared active, placing v12 M 520 cm-l. The calculation of-potential constants indicates that vrOmay be at about 509 cm-l for W(CO), and thus 883 could arise from vs + vrO_However, for Cr(CO), an analogous binary combination appears at 876 cm-l which cannot arise from vs + vrO (441 + 562 = 1003) and thus must arise from vq + v12 (363 + 512) as there is no reasonable binary combination involving an F,, frequency to give 876 cm-l. By analogy we must then assign the tungsten band at 883 as v4 + v12, An analogous peak appears for Mo(CO), at 850 cm-l. This could arise from vg + vS (481 + 368); however, it no doubt arises primarily from vp + vr2 (344 + 512) by analogy with the chromium and tungsten compounds. There is no indication of the value of v10of F,, symmetry except for the peak at 562 cm-l in solid Cr(CO),. The assignments are compiled in Table 3. Anharmonic
corrections
For all but the CO stretching frequencies the anharmonic corrections appear to be small and we neglect them. For the CO stretching frequencies, vl, va and vs,we make approximate corrections for anharmonicity as discussed in Ref. [5]. That is, from vl, vQ, vs, v1 + vg and vQ + vg we calculate, for Cr(CO),, Mo(CO), and W(CO),
334
LLEWELLYNH. JONES
respectively, X,, = -8.5, -10 and -9 cm-l and X,, = -19, -21 and -15 cm-l. For XII, Xa3, X,, and X,, we use the average of X,, and X,,*. The resulting zeropoint vibrational frequencies are included in Table 3 as con oar and o,,. POTENTIAL FUNCTION AND FORCE CONSTANTS The F and G matrices for a General Quadratic Valence Force Field are given in Reference 6 for octahedral M(CO),. The “resonance interaction”[b] simplification is used for the interaction constants (see Table 6 of Ref. [5]), with the exception of the pi, /Ij interaction constants (the pi and #?jare the MC,O, and MC,O, angles). For the B frequencies the simplified potential function apparently does not fit [5]. Therefore for Fpy we shall use the general expression of Ref. [6]. This leads to the F matrix given in Table 4. As in Ref. [5] we let 4 = 1, K = H = T = 0. The arguments for these assignments are given in Ref. [5] for Mo(CO), and apply also to Cr(CO), and
W(CO),. Table 4. F matrix of M(CO), Al,
Fll
=
+ 3qB FM, + qD2/3B (1 - q)D
F,,
F,,
=
E"l2
=
F 33 F 44
=
Fco
+
3qB(Z
=
FMC
+
kD2/3B1[(z - 2)/(2 + 4)l
F34
=
[l
PI,
F,,
=
F. - Fpp’ - 2F,$
F 1U
Fl36
=
F77 F80 Fe, F.s7 F,, F,, F,;8 F,, FM
= = = = = = = = =
F 10,lO
=
EC2
F2s
F 11.11 F 10911 F 2v
F 12.12 F 13.13 F 12,x3
-
q(z
-
-
2)/(2
2)/(2
+
+
4)]D
- 3qBZ/(Z + 4) + 4)l FMO- W2/3Bl[Wz Fp + Fpa’ + 2 (F&” + Fob”“) [8A/(3A -t l)]Fa + 4Fa,’ [l + qz/(z + 4)lD 0 0 -22/(2) K 2H 2/(2) T Fco
=
Fg - Fpp’ + 2 Fpa” [4(1 - A)/(1 + 3A)lE”,
=
T
= =
=
4)
Fp + Fpp’ - 2(F,$” + F,g$“‘) [8A/(3A -+- l)]Fg - 4F,,’ d(VT
Since we do not observe yIo for the MO and W compounds we cannot calculate all the Fpp constants. For Cr(CO), Fpp” is about zero so we shall let it equal zero for the other two hexacarbonyls. The resulting force constants are given in Table 5. * Though this is a crude approximation correction.
it certainly is better than making
no anharmonic
Vibrational
spectra and force constants of the hexacarbonyls
of chromium
335
Table 5. Force constants of the hexacarbonyls
17.873 2.034 0.825 0.218
F CO F MC F/i E’z
Fco,oo’ (opposite) Pco,co” (adjacent) li6ac.Mc’(opposite) F IIIC.MC” (adjacent) B’Co,ar,’(neighbours) F CO,HC”(opposite) F co,yc”’ (adjacent,)
FOP’ FM” E;$.J”’ + F&J””
B D
A z
_~
18.122 1.806 0.759 O*lQO
17.695 2,148 0.762 0.213
0,180 O-039
0‘120 0.040
0.137 0.053
0.340 0.074
0.364 0.121
0.366 0*141
0.462 - 0.247 - 0.054
0.487 - 0.209 - 0,070
0.568 - 0.224 -0.OR6
0.022 0 0.079
0.073 0 0.048
0.073 0 0.043
0.112 0.462 0.38 4.6
0.093 0.487 0.37 3.0
0,116 0.568 0.39 2.6
With the exception of the E, frequencies these force constants yield the observed frequencies reported in Table 3. For the E, frequencies the differences are reported in Table 6. It is seen in Table 6 that the observed and calculated values for Y.,are in reasonable agreement. They can be made to agree exactly by slight adjustments of the force constants. To bring observed and calculated mginto agreement would require making 4 of Table 4 greater than 1. As discussed in Ref. [5] it is unreasonable that p be greater than 1. The anharmonicity corrections are approximate and mrty account for the discrepancy. DISCUSSIONOF FORCE CONSTANTS F MC The strengths of the metal--carbon bonds apparently do not follow fhe order of the periodio table; thus P,, > F,,, > F,,,. This result, however, is to be expected from the observed bond distances. BROCKWAY, et al. [ll] from electrondiffraction experiments found R,,, = 1.92 f 0.04 A, R,,,= 2.08 f 0.04 d, and R,, = 2.06 f O-04 A. R@DORFFand HOFMANN[12] determined the crystal structure and found that solid Cr(CO}~ has the smallest unit cell while Mom has the [ll] L. 0. BBOCKWAY,R. V. G. EVANS and M. W. LISTEB, TTCWM. Fcwu&zySoc. &4,1350 (1938). [12] IV. RODORFFand U. HOFMANN, 2. physik. Chem. (Leipzig) B28, 351 (1935).
336
LLEWELLYN H. JONES Table 6. Observed and calculated E, frequencies for M(CO), w3
Cr(CO), Mo(CO), W(CO),
VP
Obs.
Calc.
Obs.
Calc.
2103 2112 2084
2131 2130 2104
363 344 363
363 340 365
largest and they are roughly in proportion to the electron diffraction distances. If we then use the distances of BROCKWAY et al. along with BADGER’S rule [ 131 we find p,, > F,,, > Fnroc,in the same order as the observed force constants. F co From Table 5 we see that the CO stretching force constants are in the reverse order of the MC force constants; thus, the higher the metal-carbon force constant the lower the carbon-oxygen force constant. This fact suggests that there are significant differences in the amount of metal-carbon pi-bonding. Such metal-carbon pibonding should increase the metal-carbon force constant and decrease the carbonoxygen force constant [14]. Thus it appears that the extent of metal-carbon pibonding decreases slightly in the order WC > CrC > MoC.
The angle a is a CMC angle. Its force constant should increase slightly as the metal-carbon distance decreases since the C-C distance becomes smaller resulting in increased C-C repulsion. This is seen in Table 5 to be true, though we might expect F, for W(CO), to be closer to FX for Mo(CO),. A decrease of three wave numbers in the frequency assignments for the CWC bending frequencies will bring F’, for W(CO), very close to F, for Mo(CO),.
The MC0 bending force constants are very large for these hexacarbonyls, much larger than the corresponding force constants of Ni(CO), [15]. As has been discussed in reference [5], this implies strong interaction of the metal d, electrons with the CO groups. The constant D This constant represents the interaction of C,Oi with C,M. It is about the same for Cr and MO but somewhat higher for W. The increased metal-carbon m-bonding in W(CO), over that in Mo(CO), is in agreement with the larger value of D. Cr(CO), apparently does not fall in line. It should be recalled that there is some uncertainty in the assignment for vp of Cr(CO),. We have defined [6] D as equal to dF,, where That is, a unit positive displacement of C,O, leads to a contraction d = -(&Jd)c,o,. [13] R. M. BADOER, J. Chem. Phys. [14] L. H. JONES, J. Mol. Spectrosc. [15] L. H. JONES, J. Mol. Spectrosc.
3, 710 (1935). 9, 130 (1962). 5, 133 (1960).
Vibrational spectra and force constants of the hexacarbonyls
of chromium
337
of C&M equal to d. From D and FMc we calculate d to be 0.227, 0.270 and 0.264 respectively for Cr(CO),, Mo(CO), and W(CO),. Thus, for the tungsten and molybdenum compounds d is essentially the same. From this it is apparent that chromium behaves differently from MO and W while the latter two behave similarly. Actually we would expect d to be less for Mo(CO), than for W(CO), as it arises partially from the metal-carbon r-bonding which is apparently greater in W(CO),. The constant B B was defined [6] as equal to K,dF,,/S
where K, is a constant equal to
Thus it was hypothesized [6] that a unit displacement of CrO, causes proportionate changes in C,O, and C,M (i # 1). Substituting for d and F,, we find K, = 0.084, O-057 and 0.075 for Cr(CO),, Mo(CO), and W(CO),. We would feel better if the magnitude of K, followed the order of n-bonding: MO < Cr < W. However, it is apparent that here again chromium does not fall in line, whereas MO and W are in the order of degree of n-bonding. The constant 2 2 was defined [6] as (S C,~&J(XC,M)C,O1 which is the ratio of the change in opposite (180’) CM bond length to the change in adjacent (90”) CM bond length arising from unit displacement of C,O,. In order to discuss this quantity it will be convenient to study a schematic diagram as in Fig. 1. This figure represents the d,,
Fig. 1. Schematic represent,at,ion of d,, orbital for M(CO),.
orbital of M(CO),. As C,M is stretched the d orbital will 7~bond less strongly with C,O,. A discussion of this is given elsewhere [14]. This will cause the d,, electrons to spend more time in the 23 and 24 lobes and less in the 13 and 14 lobes, leading to a distorted d orbital similar to Fig. l(b). The resulting overlap of d,, (lobes 23 and 24) with C, is considerably increased, whereas the overlap of d,, with C, is increased in lobe 23 but decreased in lobe 13. Thus we expect a much greater effect on C,M (the opposite CM bond) than on C&M (an adjacent CM bond). Furthermore, the opposite CM bond (C&M) is also affected by similar accompanying changes in d,, when C,M is 22
LLEWELLYN 33..JONES
338
stretched. Therefore we expect the quantity Z to be greater than 2. Indeed it is close to 3 for Mo(CO), and W(CO),. It appears to be considerably higher for Cr(CO),. The Cretan
A
A was defined [S] as -(Xb114)E1Bf that is, the change in ~1~~accompanying a unit positive change in the adjacent, coplanar angle, a16. It is shown in Ref [S] that it should be between +Q and +&. Thus, the observed value of 0.37-0.39 is quite reasonable.
In Ref. 6 it was concluded that the important ,!-fi interactions were among coplanar MC0 angle changes and we could neglect the non-coplanar 6 interactions. However, from the results of Table 5 it is apparent that this is not so. In fact, for Cr(CO), the non-coplanar interactions (P @@“’+ FPB”“) are greater than the coplanar interacti constants FPP’ and FPbf’. These results rest primarily on the assignment for the combination band Y* i_ 7x2 appearing at 876, 850 and 883 for CrfCO),, MO (CO), and W(CO), respectively. The solid-state spectrum also verifies this assignment as discussed in the section on assignment of frequencies. In order to check the assignment of the 883 cm-l band for W(CO), as v4 + v12we made a study of the intensity of this band in solid W(CO)~as a function of temperature in the range 148°K to 215’K. According to the theoretical work of LISITSA and STRIZHEVSKII [ 161 the ratio of integrated absorbances, At, should be R = .4,&4,,, = 1.09 for vq + v12. For the possible ternary combinations R - 1.45. The observed value is 1.12, confirming our assignment as a binary combination. Thus we are left in the rather unfortunate position of being unable to present an explanation for the observed interactions among the MC0 angles. Further theoretical studies of the orbital interactions are required. CONCLUSIONS The vibrational spectra of Cr(CO),, Mo(CO), and W(CO), have been studied and eleven of the thirteen fundamental frequencies of each have been assigned. The force constants for a ~~resonan~e interaction valence force field” [6] have been calculated. They show that the metal-carbon T-bonding increases in the order MoC < CrC < WC. The interaction constants for the Mo(CO), and W(CO), fall in line with this order of n bonding ; however, Cr(CO), shows anomalous behavior in this respect. The non-coplanar MC0 bending interactions are unexpectedly large and remain unexplained.
[16] Bi. P. LISITSAand V. L. STBIZHEVSHII,O@&.Z i ~pek~ro5ko~i~a 10, 48 (1961).