lems in a three-ligand model of the Fe(Acac)3 complex, we could precisely assign the bands in IR spectrum of this compound. CALCULATION PROCEDURE.
Russian Journal of Coordination Chemistry, Vol. 29, No. 7, 2003, pp. 484–488. Translated from Koordinatsionnaya Khimiya, Vol. 29, No. 7, 2003, pp. 519–524. Original Russian Text Copyright © 2003 by Slabzhennikov, Ryabchenko, Kuarton.
Normal Vibration Calculations for Iron Tris(acetylacetonate) S. N. Slabzhennikov, O. B. Ryabchenko, and L. A. Kuarton Far East State University, ul. Sukhanova 8, Vladivostok, 690600 Russia Received June 25, 2002
Abstract—The frequencies, shapes, and intensities of the absorption bands in IR spectrum of Fe(Acac)3 complex are calculated. The experimental data are adequately described using the force constants suggested for the complex. The spectral bands are unambiguously assigned on the basis of the theoretical analysis. In particular, the positions of the bands due to the FeO bond vibrations are determined.
IR spectrum of the Fe(Acac)3 complex was interpreted many times [1–7]. However, this interpretation was performed either on the basis of calculations in the one-ligand approximation or a direct vibrational problem was solved only [1, 3, 4], which is inadequate for the accurate band assignment. A comparative analysis used in [2, 5, 6] made it possible to refine IR spectra, but the results obtained differed in some cases. A generalized assignment was carried out for several bands, i.e., for vibrations of the atoms in a chelate ring. The authors mainly were engaged in determining the positions of the bands from the FeO, CO, CC, and ëëç3 bond vibrations, since they could not analyze the spectrum in more details. By making use of the results obtained in [1–7] and having solved the direct and inverse vibrational problems in a three-ligand model of the Fe(Acac)3 complex, we could precisely assign the bands in IR spectrum of this compound. CALCULATION PROCEDURE IR spectrum of Fe(Acac)3 was calculated in the classical harmonic approximation with account of the D3 symmetry group using the method described in [8]. The geometrical parameters of the complex were calculated by ab initio Hartree–Fock–Rutan method with the GAMESS version [9] from the GAMESS (US) QC program package [10]. The optimization of the geometrical parameters of the complex was carried out in the valence-splitted 3-21GF* basis (* means that the basis set to be calculated was supplemented with the polarization d-functions of the Fe atom). The calculated set of the geometrical parameters agrees with the experimental data (Table 1) and is used in the calculations of IR spectrum, since it is more complete as compared with the experimental set. The following natural vibrational coordinates (NVC) were used also in IR calculations: the changes in the bond lengths, in the bond angles, in the angle between the bond and the plane formed by the other two bonds (R), and in the torsion angle (X). The total
number of NVC chosen was 174, which exceeded the number of normal modes equal to 123. The vibrational representation has the form Γ = 20A1 + 21A2 + 82E. The force constants for the Cr(ÄÒaÒ)3 complex [8] were taken as the initial force constants. The bond numbering in a fragment of the Fe(Acac)3 complex used for designation of the force constants are as follows: H 6
H
5 H Cm 4 3 8
7
2
C O 1
Hγ C γ 15 Fe 9 C 14 O H 13 Cm10 H 12 11 H
16 30
The data of the preliminary calculation of the Fe(Acac)3 spectrum were used to match up the theoretical frequencies of the normal vibrations and the experTable 1. The calculated (3-21GF*) and experimental [3] bond lengths (d) and angles (w) for Fe(Acac)3 Bond Fe–O C–O C–C C–CH3 C–Hγ Angle OFeO FeOC OCC CCC CCCH3 OCCH3
dexp, Å
dcalcd, Å
1.95 1.28 1.423 1.53 1.086
1.98 1.27 1.39 1.51 1.07
ωexp, deg
ωcalcd, deg
90 131 119 130 120 121
84 133 124 122 120 116
1070-3284/03/2907-0484$25.00 © 2003 åÄIä “Nauka /Interperiodica”
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Table 2. Force constants (×106, cm–2) for Fe(Acac)3 complex (with optimal values in parentheses) Parameter*
Value
Parameter
Value
Parameter*
K3
6.191(5.911)
3, 7 2, 3 2ϕ7
–0.277(–0.280)
l 2, 7
K3, 4
1.139(1.134)
2, 7 2, 3 3ϕ7
–0.115(–0.115)
K4, 5
0.655(0.678)
2, 3 10, 14 7ϕ9
K5, 6
0.334(0.321)
χ 2, 3
0.695(0.625)
7, 9
Value
Parameter 14
Value
–0.298(–0.490)
H1
l 7, 8
0.355(0.544)
A1
–0.003(–0.033)
K2, 3
1.005(0.939)
A1
0.114(0.097)
K3, 7
1.789(1.899)
A1
χ 2, 7
0.09(0.093)
H2
3
1.286(1.675)
A1
2, 7 14, 15 1, 2ϕ9, 14
0.001(0.007)
H3
7
–0.215(–0.237)
A2
–0.043(–0.037) K1
3.309(3.259)
A2
1.009(1.002)
l 1, 2
l 4, 5
–0.122(–0.115) K1, 15
1.550(1.527)
A3
0.512(0.375)
l 1, 2
K2
13.257(13.039)
K1, 16
1.171(0.552)
A3
0.012(0.090)
l 1, 2
0.021(0.011)
K7
10.322(9.737)
K1, 30
0.398(0.017)
A3
–0.422(–0.468)
K8
8.7
15
0.472(0.627)
A7
–0.607(–0.666)
H7
8
0.1
16
0.452(0.281)
A7
0.515(0.201)
A8
30
0.344(0.218)
l 2, 3
0.135(0.129)
A8
–0.02
0.972(0.987)
l 2, 3
0.458(0.490)
K4
8.12
0.499(0.464)
H4
5
0.05
0.465(0.454)
H5
6
0.05
0.772(0.759)
A4
0.507(0.508)
A4
0.627(0.626)
A5
–0.12(–0.120)
A5
3, 4
A3
3, 5
l 3, 4 4, 5
l 3, 4 5, 6
–0.029(–0.027)
3, 4 7, 9
7, 9
2, 3 2, 3 2, 7 3, 7 2, 3
K2, 7
2.057(1.707)
H1
K7, 8
0.853(0.816)
H1
K7, 9
0.863(1.077)
H1
7
0.539(0.318)
A1
9
–0.624(–0.675)
A1
0.223(0.099)
l 2, 7
9
0.341(0.652)
K1, 2
1.514(1.590)
ρ8
0.384(0.515)
χ 1, 2
0.064(0.045)
ρ2
0.467(0.458)
χ 1, 2
0.263(0.273)
ρ3
0.526(0.550)
H1
2
1.180(1.021)
ρ7
0.299(0.366)
H1
7
–0.859(–1.168)
–0.363(–0.380)
H1
9
0.301(0.403)
H2 H2 H7 2, 7
A2
2, 7
A7
7, 8
A7
7, 9
A7
8, 9
A7
1, 15 1, 16
2, 3 2, 7
3, 7
2, 7 3, 7 3, 7 7, 9 3, 7 2, 7 2, 3
3, 7 2, 7 2ϕ3
1, 2 2, 3 2, 7 14, 15 1, 2
1, 15 2, 3 2, 7
7, 8 7, 9
3, 4 4, 5 5, 6 4, 5
0.875(1.144) 0.759(0.742) –0.090(–0.119) –0.227(–0.288) –0.246(–0.243) –0.323(–0.608) 0.457(0.441) –0.095(–0.080)
0.173
0.35 0.35 0.35 0.35
* Designation of force constants and their indices corresponds to [8].
imental frequencies given in [5, 7]. As follows from [5], the replacement of the 54Fe isotope by the 57Fe isotope does not change the position of the band at 669 cm–1. This band cannot be assigned to the normal vibrations with participation of the Fe atom, although the preliminary calculations of IR spectrum revealed that this theoretical band corresponds to the normal vibration with prevailing contributions of the FeO bonds in its shape. At the same time, the Fe isotope replacement results in a shift of the band at 656 cm–1, which, according to the calculations, belongs to the vibrations of the CγHγ RUSSIAN JOURNAL OF COORDINATION CHEMISTRY
bonds relative to a ring plane. Hence, the inverse assignment of the normal vibrations should correspond to the bands at 669 and 656 cm–1. In order to eliminate the discrepancy, the force constant K1 was scanned until the shapes of the normal vibrations showed a satisfactory agreement with the data on the Fe isotope replacement [5]. The obtained value of the force constant of the Fe–O bond was 3.309 × 106 cm–2. The resulting force constants used as a zero approximation in calculation of IR spectrum of Fe(AÒaÒ)3 are given in Table 2. Vol. 29
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Table 3. The experimental frequencies (νexp, cm–1) and isotopical shifts (δexp and δtheor, cm–1) for Fe(Acac)3 during replacement of 54Fe by 57Fe νexp (54Fe) [5]
δexp [5]
δtheor
772.8 668.0 654.5 562.0 551.3 436.0 415.5 408.0 300.5 202.0
0 0 1 1 0 2 0 0 5 0
0 0 0 1 0 2 0 4 0
OPTIMIZATION OF FORCE CONSTANTS The optimization of the force constants was performed as described in [8]. In the course of optimization of the force constants, the band at 1445 cm–1 in the experimental spectrum was related to the normal vibrations, which could not be performed at the beginning of the optimization. According to the data in [3], IR spectrum of Fe(Acac)3 contains three separate bands at –801, 771, and 780 cm–1. However, the author of [7] believes that the band at 780 cm–1 should be considered as a shoulder of the band at 771 cm–1. A thorough analysis of the band shapes in the lowfrequency region of IR spectrum suggests that the normal vibrations with frequencies at 238 cm–1 can be attributed to the low-frequency shoulder of the band at 298 cm–1. That is why these normal vibrations were not considered during optimization. The optimization was finished when the root-meansquare deviation of the experimental frequencies from the theoretical values was 1.4 cm–1, the modulus of the greatest deviation being 4.2 cm–1. The calculations of the isotopical band shifts in the case of 54Fe replacement by 57Fe (Table 3) revealed a satisfactory agreement of these data with the corresponding experimental data and thus, the reliability of the force constants found. The authors of [5] measured the isotopical shift with an accuracy of ±0.3 cm–1, whereas the isotopical shifts given in Table 3 contain significant digits only. RESULTS AND DISCUSSION The bands of the experimental IR spectrum of Fe(Acac)3 were assigned as described in [8] using the distribution of the normal vibration energies over NVC (∆NVC), integrated intensities of the normal vibrations (I), and their symmetry types (ST) (Table 4).
As follows from the calculations, the band at 1570 cm–1 consists of three bands, two of which are due to the doubly degenerate normal vibrations. All these three bands are, most likely, due to the change of the CO bonds. The band at 1525 cm–1 corresponds to the characteristic vibrations of the çëmç bond angles in the methyl groups (84% contribution).The band at 1445 cm–1 is due to the vibrations of the ëγë bonds of the chelate rings and the çëmë and çëmç bond angles of the methyl groups, while the band at 1425 cm–1 is produced by the doubly degenerate normal vibration with almost equal participation of the çëmç and çëmë bond angles of the methyl groups. The band at 1370 cm–1 is due to the change in the bond angles çëmç in the methyl groups and to a small contribution of the ëγë bonds. One can see that the band at 1274 cm–1 is a composite band that corresponds to the normal vibrations with different shapes. The main contribution to the shapes of the normal vibrations assigned to the band at 1274 cm–1 is made by the changes in the HCmC and HγCγC bond angles and by the changes in the ëëm bonds. However, the comparison of the intensities shows that only the bands from the vibrations of the HCmC and HγCγC bond angles are active in IR spectrum. The band under consideration is the only one IR band produced by the vibrations of the atoms in the HγCγC bond angles. The bands at 1188 and 1022 cm–1 are mainly due to the vibrations of the HCmC and HCmç bond angles in the methyl groups. However, the band at 1022 cm–1 is partially due to the vibration of the CγHγ bonds (R879) relative to the chelate ring plane. The band at 930 cm–1 should be assigned to the doubly degenerate vibration with the participation of the CγC bonds of the chelate ring. We assigned the band at 801 cm–1 to the degenerate normal vibration caused by the changes of the CγCOFe torsion angles (X17) and deviations of the CO and CmC bonds from the chelate ring planes. According to our calculations, the shoulder at 780 cm–1 and the band at 771 cm–1 are due to the normal vibrations of the A1 symmetry type that are inactive in IR spectrum. Such a discrepancy between the experimental and theoretical data can be explained by the fact that the Fe(Acac)3 complex in a solution has the symmetry group lower than D3, whereas the considered normal vibrations have the symmetry type other than A1. The vibrations corresponding to the band at 669 cm–1 are suggested to be characteristic vibrations with respect to the vibrations of the Cγçγ bonds (R879) relative to the chelate ring plane. This suggestion is confirmed by the 52% contribution of NVC R879 to the energy of the normal vibrations, while the contribution of each of the remaining NVC does not exceed 12%. The frequencies of the stretching and deformation vibrations of the coordination core lie in the range of 298–656 cm–1. In this range, we shall consider only the
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Table 4. The experimental and normal vibration frequencies, their integrated intensities, symmetry types for Fe(Acac)3, and energy distribution over NVC νexp, νtheor, I, cm–1 [3] cm–1 % 1570
1525
1445
1425 1370 1274
1188
1022
1572 1571 1570 1570
ST
1 40 0 24
A2 E A1 E
1527 128 1527 49 1526 0 1526 0 1447 20 1446
8
νexp, νtheor, cm–1 [3] cm–1
I, %
ST
1023
15
A2
1022 1020 1018
4 E 0 A1 40 E
HCmC(51), HCmH(42) HCmC(46), HCmH(35), CO(11) HCmC(48), HCmH(36), CO(11)
0 0 84 0 0
CCm(52), CγC(26) CγC(46), CO(24) CγC(45), CO(25) CCm(52), CγC(28) X17(26), R273(22), R327(20), HCmC(16) X17(26), R273(22), R327(20), HCmC(16) FeO(37), CCm(25), OCCγ(12) R879(52), X17(12) R879(53), X17(13) CCm(29), FeO(26), OCCm(14) FeOC(29), OCCm(22), OCCγ(21) FeOC(30), OCγC(24), OCCm(23) CγCCm(35), FeO(33), CCm(22) FeO(51), CCm(25), CγCCm(12) FeO(35), CγCCm(32), CCm(12) CγCCm(41), FeO(26), CCm(18) CγCCm(30), FeO(29), OFeO(24) OFeO(43), FeO(15) CγCCm(35), FeOC(24) CγCCm(48), OCCm(11) X13(35), X17(15), OFeO(13) X17(22), OFeO(17), X13(12), CγCCm(11) X13(28), X17(21), OFeO(12) X13(62)
A2 E E A1 A2
CO(51), HγCγC(23), CγC(14) CO(55), CγC(18), HCmC(11) CO(58), CγC(20), HCmC(12) CO(54), CγC(16), HγCγC(13), HCmC(11) HCmH(84), HCmC(14) HCmH(84), HCmC(14) HCmH(84), HCmC(13) HCmH(84), HCmC(13) CγC(27), HCmC(24), HCmH(22)
801
933 932 930 929 771
E
CγC(27), HCmC(24), HCmH(22)
780
771
HCmH(46), HCmC(42) HCmH(46), HCmC(42) HCmH(36), CγC(31), HCmC(18) HCmH(35), CγC(32), HCmC(17) CCm(36), OCCγ (17), HCmH(16), CγC(16) CCm(36), OCCγ (17), HCmH(16), CγC(16) HγCγC(57), HCmC(19), CO(13) HγCγC(59), HCmC(19), CO(13) HCmC(34), R879(15) HCmC(33), R879(14) HCmC(68), HCmH(21) HCmC(68), HCmH(21) HCmC(70) HCmC(70) HCmC(54), CO(23), HCmH(17) HCmC(53), CO(23), HCmH(17)
771 669 656 559
694 669 668 656 557
0 4 0 62 99
A1 E A2 E A2
548
549
40
E
433
436 0 A2 433 12 E 432 0 A1 410 2 E 299 19 A2 298 48 E 243 0 A1 238 4 E 204 112 E 204 0 A1
1421 0 A1 1421 60 E 1370 100 A2 1369 38 E 1280 0 E 1280
0
A1
1275 1274 1274 1274 1192 1192 1187 1187 1184 1183
15 12 80 24 0 10 0 0 1 0
A2 E E A2 A1 E E A1 A2 E
1023 1023
NVC (∆NVC, %)
930
412 298
202
6 E HCmC(47), R879(31) 0 A2 HCmC(47), R879(26), HCmH(11)
bands due to the vibrations of the FeO bonds and the OFeO bond angles. On the basis of the calculations, the band at 433 cm–1 can be reliably assigned to the FeO bond vibrations. This is also supported by the experimental and theoretical data on the isotopical shifts during the replacement of 54Fe by 57Fe (Table 3). The band at 298 cm–1 shows a particularly essential isotopical shift in this case. A comparison of the integrated intensities of the normal vibrations attributed to the band at 298 cm–1 shows that the main contribution to this band is made by the doubly degenerate vibration of the OFeO bond angles. However, the values of ∆NVC indiRUSSIAN JOURNAL OF COORDINATION CHEMISTRY
201 200
A1 A2 E E E
0 A1
20 E 30 A2
NVC (∆NVC, %) HCmC(50), HCmH(37)
cate that this band is produced also by the vibrations CγCCm bond angles. IR spectrum contains the separate band at 412 cm–1, which is assigned also to the vibrations of the CγCCm bond angles with a significant contribution to the energy. The low-frequency band at 202 cm–1 made by three active components is mainly due to the vibrations of the torsion CmCOFe angles (X13). REFERENCES 1. Nakamoto, K., McCarthy, P., Ruby, A., and Martell, A.E., J. Am. Chem. Soc., 1961, vol. 83, no. 5, p. 1066. Vol. 29
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2. Gillard, R.D., Silver, H.G., and Wood, J.L., Spectrochim. Acta, Part B, 1964, vol. 20, no. 1, p. 63. 3. Mikami, M., Nakagawa, I., and Shimanouchi, T., Spectrochim. Acta, Part A, 1967, vol. 23, no. 4, p. 1037. 4. Gribov, L.A., Zolotov, Yu.A., and Noskova, M.P., Zh. Strukt. Khim., 1968, vol. 9, no. 3, p. 448. 5. Nakamoto, K., Udovich, C., and Takemoto, J., J. Am. Chem. Soc., 1970, vol. 92, no. 13, p. 3973. 6. Nekhoroshkov, V.P., Kamalov, G.L., Zheltvai, I.I., et al., Koord. Khim., 1984, vol. 10, no. 4, p. 459.
7. Thornton, D.A., Coord. Chem. Rev., 1990, vol. 104, no. 2, p. 173. 8. Slabzhennikov, S.N., Denisenko, L.A., Litvinova, O.B., and Vovna, V.I., Koord. Khim., 2000, vol. 26, no. 2, p. 105. 9. Granovsky, A.A., gamess/index.html.
www.classic.chem.msu.su/gran/
10. Schmidt, M.W., Baldzidge, K.K., Boatz, J.A., et al., J. Comput. Chem., 1993, vol. 14, no. 11, p. 1347.
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