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Force constant calculations for ferrocene
1.5 July 1972
CHEMICAL PHYSICS LETTERS
Volume 1.5, number 1
FORCE CONSTANT
CALCULATIONS
FOR FERROCENE
I.J. HYAMS Deportment
of Chemistry, Bowdoin
College. Brunswick, Main 01011. USA
Recei\vd il April
1972
This represents the fist attempt to determine it force field for ferrocrne which does not either assume the cyclepentidiene rings are free or that the rings can be approximated to point masses.
Force constant calculations for sandwich type molecules are hampered by the problem ofdefining the internal coordinates without introducing a large number of redundant coordinates. To avoid these difEculties those calculations that have been.carried out [l-4] have approximated the rings as point masses and assumed a triatomic molecule as a basis for determining metal-ring force constants; the force constants for the ring were found by assuming the ring to be free of the rest of the molecule. Calculations carried out in this way, however, ignore the very important interactions expected between the metal-carbon and carbon-carbon bonds which could be considered if such vibrations as the metal-carbon stretch and the tilting of the ring were included. If all internal coordinates are used to calculate the force field for ferrocene matrices larger than 100 by 100 would have to be handled. Even with modem computers the problem can be unwieldly, especially in those areas where human participation is required. The basic model assumed for the present calculations, a cyclopentadiene ring bonded to a metal atom, is a step towards the complete solution and is exact for those molecules where oniy one ring is involved, e.g., alkali-metal and thallium complexes. Interactions between the rings in ferrocene are small but the present assumption does ignore the important interactions between one ring-metal bond and the other and between the tilting motion of one ring and the other, Th; force constant calculations were carried out, using the frequencies of ungerade vibraticns because during these the metal atom move&
If the carbon
atoms of a ring are numbered
cycli-
cally C, -C,, then the tilting motions of the ring can be defined in terms of linear combinations of angles such as Fe-C, -C2. Three ways of defining the ring-. metal stretch were used. (i) All 5 Fe-C b on d s were used as internal coordinates and an Fe-C (symmetrised) force constant determined. (ii) One interna! coordinate was defined which was the sum of the changes in 5 Fe-C bonds. A ‘pseudo’ ring-Fe force constant was thereby obtained. (iii) One internal coordinate was defied in which ati the C atoms moved parallel to the principal axis of the molecule and the Fe atom moved anti-parallel, Again a ‘pseudo’ ring-Fe force constant was obtained. The remaining coordinates were defied in the normal way [5] . In table 1 the calculated and observed [l-4] azu frequencies are compared. !n each case on going from
one molecule to the next, the force field remained constant. The best fit appears to be given by definition (i) though (ii) is almost as good. A symmetrised Fe-C force constant of approximately 1.4 X lo5 dyne cm-l was found*- (i), (ii) and (iii) suggest that the aZU C-D stretching
mode lies closer to 2320 cm-l,
i.e., near
the corresponding
alg mode [7].. In all the calcula-
tions the interaction
force constant between the ringwith the C-C bonds was important.
metal or C-metal
*This MIIbe mmpared with a Mlue [6] of 1.48 x 10’ dyne cm-l symmetriti axxtvlt for the CT-C bond found iaa recent calculation for dibenzene chromium.
voiunle
IS, number
CHEitfICAL PWSfCS
1
Tabb 1 qU modes of C5HjFe-h5 and ifs and Cuff,-Ru. Calculated and observed [ 11 tiequakes (latter only shown once) in cm-’
15 July 1972
LETTERS Table 2 elu modes of G~H$&~ and 4s.
CsD.$=c
Cgfi5Fe CSHsFe Gilt. obs. (i) 3098 1107 818 477 (ii)
(iii)
2098 1107 818 417
C5DsFc catc. obs.
UIC.
abs.
2319 1050 630 448
3098 1103 817 418
3100 1104 806 446
2354 1044 637 457
CsHsRu
3098 1106 823 477
2320 10% 630 451
3098 1103 822 416
3104 I.109 812
2325 1051 647
a)
481
429
a) Not calculated the ferrocencs.
because the agreement
was not so good for
The results for the elu modes are shown in table 2. In comparing the calcuiated and observed values, it should be recalled that in the actual molecules this symmetry species also contains the ring-metal-ring bending mode. The assignment [l] for deutcroferrocene is also tentative. Agreement here is therefore not expected to be so good. The caIcuIations have been extended to nickefocene using defiition (ii}. That the bond between the
Units cm-’
ulc.
obs.
CJlc.
abs.
3105 1385 1047 824 503
3098 1414 1006 840 490
2318 1302 781 692 441
2354 1260 771 679 48-F
ring and Ni atom is weaker than its anaiogue in ferrocene is apparent from a drop of 34% in the ‘pseudo’ ring-metal force constant.
References
E.R. Lippincott and R.D. Nelson, Spectrochim. Acta 10 (19.58) 30:. t1.P. Fritz, Adran. Ckganometailic Chcm. 1 61964) 239, L.S. Mayants, B.V. Lokshin and G.B. Shaltupr, Opt. Spectry. 13 (1962) 317. D. Hartley and Xf.J. Ware, J. Chem. Sot. A (1969) 138. E.B. Wilson Jr., J.C. Dccius and P.C. Cross, hfoltcuiar vibrations (McGraw-Hill, New York, 1955). S.3. C‘yvin and J. Brunvol~, J. Chem. Phys. 54 (1971) 1517. R.T. Bailey, Spectrochim. Acta 27A (i971j 199.
CHEMICAL PHYSICS LETTERS
Volume 1.5, number 1
FORCE CONSTANT
CALCULATIONS
FOR FERROCENE
I.J. HYAMS Deportment
of Chemistry, Bowdoin
College. Brunswick, Main 01011. USA
Recei\vd il April
1972
This represents the fist attempt to determine it force field for ferrocrne which does not either assume the cyclepentidiene rings are free or that the rings can be approximated to point masses.
Force constant calculations for sandwich type molecules are hampered by the problem ofdefining the internal coordinates without introducing a large number of redundant coordinates. To avoid these difEculties those calculations that have been.carried out [l-4] have approximated the rings as point masses and assumed a triatomic molecule as a basis for determining metal-ring force constants; the force constants for the ring were found by assuming the ring to be free of the rest of the molecule. Calculations carried out in this way, however, ignore the very important interactions expected between the metal-carbon and carbon-carbon bonds which could be considered if such vibrations as the metal-carbon stretch and the tilting of the ring were included. If all internal coordinates are used to calculate the force field for ferrocene matrices larger than 100 by 100 would have to be handled. Even with modem computers the problem can be unwieldly, especially in those areas where human participation is required. The basic model assumed for the present calculations, a cyclopentadiene ring bonded to a metal atom, is a step towards the complete solution and is exact for those molecules where oniy one ring is involved, e.g., alkali-metal and thallium complexes. Interactions between the rings in ferrocene are small but the present assumption does ignore the important interactions between one ring-metal bond and the other and between the tilting motion of one ring and the other, Th; force constant calculations were carried out, using the frequencies of ungerade vibraticns because during these the metal atom move&
If the carbon
atoms of a ring are numbered
cycli-
cally C, -C,, then the tilting motions of the ring can be defined in terms of linear combinations of angles such as Fe-C, -C2. Three ways of defining the ring-. metal stretch were used. (i) All 5 Fe-C b on d s were used as internal coordinates and an Fe-C (symmetrised) force constant determined. (ii) One interna! coordinate was defined which was the sum of the changes in 5 Fe-C bonds. A ‘pseudo’ ring-Fe force constant was thereby obtained. (iii) One internal coordinate was defied in which ati the C atoms moved parallel to the principal axis of the molecule and the Fe atom moved anti-parallel, Again a ‘pseudo’ ring-Fe force constant was obtained. The remaining coordinates were defied in the normal way [5] . In table 1 the calculated and observed [l-4] azu frequencies are compared. !n each case on going from
one molecule to the next, the force field remained constant. The best fit appears to be given by definition (i) though (ii) is almost as good. A symmetrised Fe-C force constant of approximately 1.4 X lo5 dyne cm-l was found*- (i), (ii) and (iii) suggest that the aZU C-D stretching
mode lies closer to 2320 cm-l,
i.e., near
the corresponding
alg mode [7].. In all the calcula-
tions the interaction
force constant between the ringwith the C-C bonds was important.
metal or C-metal
*This MIIbe mmpared with a Mlue [6] of 1.48 x 10’ dyne cm-l symmetriti axxtvlt for the CT-C bond found iaa recent calculation for dibenzene chromium.
voiunle
IS, number
CHEitfICAL PWSfCS
1
Tabb 1 qU modes of C5HjFe-h5 and ifs and Cuff,-Ru. Calculated and observed [ 11 tiequakes (latter only shown once) in cm-’
15 July 1972
LETTERS Table 2 elu modes of G~H$&~ and 4s.
CsD.$=c
Cgfi5Fe CSHsFe Gilt. obs. (i) 3098 1107 818 477 (ii)
(iii)
2098 1107 818 417
C5DsFc catc. obs.
UIC.
abs.
2319 1050 630 448
3098 1103 817 418
3100 1104 806 446
2354 1044 637 457
CsHsRu
3098 1106 823 477
2320 10% 630 451
3098 1103 822 416
3104 I.109 812
2325 1051 647
a)
481
429
a) Not calculated the ferrocencs.
because the agreement
was not so good for
The results for the elu modes are shown in table 2. In comparing the calcuiated and observed values, it should be recalled that in the actual molecules this symmetry species also contains the ring-metal-ring bending mode. The assignment [l] for deutcroferrocene is also tentative. Agreement here is therefore not expected to be so good. The caIcuIations have been extended to nickefocene using defiition (ii}. That the bond between the
Units cm-’
ulc.
obs.
CJlc.
abs.
3105 1385 1047 824 503
3098 1414 1006 840 490
2318 1302 781 692 441
2354 1260 771 679 48-F
ring and Ni atom is weaker than its anaiogue in ferrocene is apparent from a drop of 34% in the ‘pseudo’ ring-metal force constant.
References
E.R. Lippincott and R.D. Nelson, Spectrochim. Acta 10 (19.58) 30:. t1.P. Fritz, Adran. Ckganometailic Chcm. 1 61964) 239, L.S. Mayants, B.V. Lokshin and G.B. Shaltupr, Opt. Spectry. 13 (1962) 317. D. Hartley and Xf.J. Ware, J. Chem. Sot. A (1969) 138. E.B. Wilson Jr., J.C. Dccius and P.C. Cross, hfoltcuiar vibrations (McGraw-Hill, New York, 1955). S.3. C‘yvin and J. Brunvol~, J. Chem. Phys. 54 (1971) 1517. R.T. Bailey, Spectrochim. Acta 27A (i971j 199.