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Band intensities in the infrared spectra of metal carbonyl complexes: Chromium, molybdenum and tungsten hexacarbonyls
JOURNAL OF MOLECULARSPECTROSCOPY48,47-56 (1973)
Band Intensities in the Infrared Spectra of Metal Carbonyl Complexes: Chromium, Molybdenum and Tungsten Hexacarbonyls S. KH.
V. T. ALEKSANYA~T,
SAMYELYAN,
Institute of Organo-Element
Compounds,
AND B.
V.
LOKSHIK
Academy of Sciences, AIOSGOTL~, USSR
The absolute integrated intensities for IR absorption bands of M(C0)6 (M = Cr, MO, W) were measured. The calculations of dipole moment derivatives of the molecules were performed using a procedure suggested by L. S. Mayants and R. S. Averbukh. The effective atomic charges of n!f(CO), are estimated and discussed.
INTRODUCTION
In recent years many studies have been carried out on the vibrational spectra of Cr, MO, and W hexacarbonyls (1-18). Most of them deal with band assignments and caiculations of the force constants. As for the IR band intensities they are investigated only within the range of the CO stretching vibrations (19-21). No information is available on the intensities of the other three active IR modes although they are of great interest. The present paper is concerned with the measurements of absolute integrated intensities
for all IR active absorption
with the calculations method
of L. S. Mayants
appendix
bands of M(COs)
of dipole moment
derivatives
and B. S. Averbukh.
the effective atomic
and charges are compared
(M = Cr, MO, W) as well as
of these molecules,
Using the procedure
charges were determined.
in the series of investigated
employing suggested
the
in the
The values of the derivatives compounds.
EXPERIMENT.iL
Spectra were recorded on an UR-20 Zeiss prism spectrometer cm-l),
a Perkin-Elmer
grating
spectrometer
model 4.57 gratin g spectrometer (140-75 cm-‘). Measurements
formed in CC14 solutions, made in n-hexane
solution.
Method
(750-250
of integrated
cm-l)
intensities
and FIS-1 were per-
except in the range 75-140 cm-‘, where measurements The absolute
integrated
method of Wilson and Wells (24). It was assumed mum, the absorption
(prism LiF, 2150-1900
curve has Lorentz
II of Ref. (25). The obtained
intensities
were calculated
that in the range far from the masi-
form. The wing corrections
intensities
were using
were made using
are listed in Table I. It was difficult to
measure the intensities of the bands vg because of the low sensitivity of the instrument within this frequency range and also the low intensities of these absorption bands. Thus the error of these intensities is large. 47 Copyright 0 1973 by Academic Press. Inc. All rights of reproduction in any form reserved.
SAMVELYAN,
48
ALERSANYAN, TABLE
AND LOKSHIN
I
ABSOLLTTE INTEGRATED INTENSITIES OF IR ABSORPTION BANDSOF Cz, MO, ANDW HEXACARRONYLS (IN 1.mol-1cm-2. 104)ANDSIGNCOMBINATIONS OF (&,/%&)o ((Y= X,Y,Z) IN CALCULATION OFdi Sign combination Cr(CO)G Mo(CO)G W(CO)e 1 V6 v’7 ei P9
79.0
64.0 5.9 1.7 0.15
82.0 4.0 2.5 0.16
4.6 2.5 0.09
+ + + +
3
2 + + +
+ + +
4 + + + -
5
6
+ +
+ + -
7 + + -
8 + -
CALCULATIONS (a)
Normal
Coordinate
Treatment
To evaluate dipole moment derivatives of the molecule, both the absolute integrated intensity values and the modes of the normal vibrations must be known. The calculation was performed using the El’yashevich-Stepanov method (26). The molecules investigated belong to the symmetry group Oh. The M-C and C-O bond distances used were 1.916 and 1.171 A for Cr(CO)G (27), 2.063 and 1.145pi for Mo(CO)E and 2.059 and 1.148 A for W(CO)6 (28). The force field evaluated by Jones (9) was taken as an initial approximation. To make force constants more precise the data on the frequencies of three types of the isotopically substituted molecules M(12C160)6, M(12C180) 6, and M(%160)6 (29) have been employed. Calculations were performed on a BESM-3M digital computer using the programs of Dr. D. S. Bystrov. The calculated and experimental frequencies for the IR-active F1, modes are listed in Table II. Table III shows the force constants in terms of the symmetry coordinates and Table IV represents the normalized modes for 1M(12C160)6 molecules. The symmetry coordinates used are as follows : I = 2$/2(Z1 - Z3), P = 1/2(P,=J - PP t = 21/2(t1 -
(Y = 2*/4(~, (b) Dipole Moment The procedure
dipole moment
- PC= + W),
t3), -
cfz3 - a34 + al1 + al5 + al6 - (y3s - 4.
Derivatives
of Mayants
and Averbukh
~1 with respect
allows one to determine
to bond vectors
According to (22, 23) the dipole moment normal coordinate) are given by
the derivatives
R(O (i = 1, 2, 3. ., N -
derivatives
(ap/aQ,)o
of
1) (Fig. 1).
(where Qk is the k-th
IR INTEXSITIES
FOR Cr, MO, W CARBONYLS TABLE
49
II
EXPERIMENTAL ANDCALCULATED FREQUENCIES OF NORMAL MODES FOR F1, S~ETRP SPECIES Frequency (cm-‘)
Isotope
Cr(CO)e
MO(C0)6
W(CO)6
C
0
12
16
12
18
13
16
12
16
12
18
13
16
12
16
12
18
13
16
V6
V7
VS
&l
exp cal exp cal exp cal
2043.7 2043.5 1994.7 1995.1 1997.5 1997.4
668.1 670.2 665.8 664.2 654.8 654.3
440.5 439.2 429.7 430.9 433.5 433.1
97.2 96.7 93.6 93.0 96.2
exp cal exp cal exp cal
2043.1 2042.9 1993.4 1994.1 1997.5 1997.1
595.6 597.2 592.7 590.6 580.0 580.5
367.2 367.2 359.7 359.2 362.3 362.8
81.6 81.5 78.2 78.5 81.3 81.1
exp cal exp cal exp cal
2037.6 2037.5 1988.8 1989.2 1991.8 1991.6
586.6 587.6 583.3 580.9 568.8 570.2
374.4 374.1 364.5 364.2 368.4 369.0
82.0 82.6 79.4
where I(“’ is the column matrix [(&.~~/@k)~, ($A,,I’@~)~, (&A/LQ)~]. values are determined from the expression
82.1
The (&JI~QL.)~
with an ambiguity of sign. EC,,, in the block form is Ecp) = jjE3 El . . . Esj[ where Es is the three-dimensional unitary matrix. Cj is the submatrix of orthonormalized matrix C corresponding to the jth symmetry species. C expresses the column matrix gs of symmetry coordinates in terms of the changes of vector R(O projection, x6, on the TABLE
III
FORCE CONSTANTS FOR FI, SYMMETRYSPECIES(IN 10scm-2) ; FI,, Fig, Ft,, FtB, FuB ARE FOUND TO BE LESS THAN O.Ola
ck(CO)6 Mo(CO)e W(CO)s
FL1
Ftt
F&3
FW
F,t
26.75 26.82 26.68
2.64 2.25 2.79
1.35 1.22 1.21
0.40 0.35 0.42
1.14 1.10 1.25
-. 8 The values of force constants obtained in our work do not differ significantly from those in (29). The units used here are defined in (26): F~~(105cm-2) = l..56F+’ (mdyn/.%) (a,j = 1~); F&10Bcm-2) = 1.31 Fk,‘(mdyn.A) (k = a,@); F;k(lO%m-*) = 1.43Fik’(mdyn).(i = 1~; k = a~?).
50
SAMVELYAN,
ALEKSANYAN, TABLE
AND LOKSHIN
IV
NORMALIZED MODES OF VIBRATION OF F,,
“6
w(co)s
“7
us v9
SWYETRY
SPECIES
1
P
t
a
0.39834 0.00198 0.00373 0.00013
-0.00139 0.52212 -0.12995 0.02130
-0.23061 0.12612 0.25167 0.00932
-0.00184 -0.29949 -0.04281 0.14601
0.39835 0.00046 0.00179 0.00004
-0.00034 0.51923 -0.05618 0.01626
-0.22875 0.05827 0.23998 0.00592
0.00046 -0.23673 -0.04526 0.13365
0.39835 0.00047 0.00302 0.00005
-0.00033 0.51438 -0.03679 0.01813
-0.22933 0.03277 0.22098 0.00347
0.00044 -0.21961 -0.02567 0.12335
molecular Cartesian coordinate system XI’2 (Fig. 1) : g” = Cxa. S is the matrix relating the Cartesian coordinates of the atomic displacements x and x6 ; thus x6 = Sx. e is the diagonal matrix of reciprocal atomic masses. Bi is the submatrix of B corresponding to the jth symmetry species. B expresses the symmetry coordinates pa in terms of x, thus (I” = Bx. Tjj is the block of the jth symmetry species of the kinetic energy matrix T written in terms of q8 coordinates. qojSCk) _ is a normalized Rth normal mode.
FIG. 1. M(CO)B molecule (M = Cr, MO, W). l-6 and 7-12 are. the atoms C and 0 respectively; R, the bond vector; XYZ, the common coordinate system, xg&, the “own” coordinate systems of bonds.
IR INTENSITIES
FOR Cr, MO, W CARBONYLS
51
Djs = HiDOHj-’ where Do is the matrix of derivatives of v with respect to the projections ~80of vectors R(” on the axes of “own” (for each bond) coordinate system x+zi (Fig. 1). H, = CjA ; A determines the transformation x6 = AxsO. The matrices H and Do are respectively H = CA, Do = iiDA. The symmetry class FI, contains 4 modes. There are four independent dipole moment derivatives :
The derivatives tli are obtained by the solution of the system equations (1). But the solusigns of (a~~/@ k) 0 are not defined and the problem has therefore 2” independent tions corresponding to various sign combinations of ($.&/a&)0 k being the number of IR active modes. In the case of M(CO)G there are eight solutions (with an ambiguity of the relative signs). The derivatives di are given in Tables V. A11 calculations of cii were preformed on an electronic digital computer. DISCGSSIOS
Analysis of the vibration modes (Table IV) shows that ve and va are practically purely stretching vibrations. But in v6 along with coordinate 2 (stretching of CO bond) there is an essential contribution of the coordinate t (the MC bond stretching) ; VTis determined generally by the change of the /3 angle; vg is practically a purely bending vibration determined by 01,the MC0 groups bending approximately as the rigid pivots fixed at the metal atom. Before discussing the derivatives obtained we note that hexacarbonyls have close geometries, force constants, and modes of vibrations. Thus it can be assumed that in the series Cr(CO)G, Mo(CO)e, and W(C0) 6 one may compare the ni values for solutions with the same sign combination. As it is seen from Table V for all the compounds there exist two groups of four solutions (solutions 1, 3, 4, 7 and 2, 5, 6, 8) which differ in the relative signs of derivatives tl, and dq. The dh values are large due to an exclusively high intensity of IQ,. From the data presented it can be seen that for all sets of the solutions the dz derivatives alway-s increase from Cr(CO)d to Mo(C0) 6 and W(CO)6. The same order is retained for the (14.We also note that the derivatives (11and & always have the opposite signs. Moreover, with respect to these derivatives the solutions can be divided into 4 pairs the derivatives dl (d3) being equal within each pair of l-2, 3-5, 446, and 7-8. These pairs of solutions differ by relative signs of the derivatives ($~,/a@)~ and the equality of dl (d3) is due to a negligibly small contribution of bending terms in ZQ (Table IV). The choice of the true solution is a rather complex task. The effective atomic charges in hesacarbonyls might be of aid. Besides, the knowledge of these charges is certainly of interest in itself. Depending upon definition the term “effective charge” may have different meaning [see, e.g., (30)]. It is essential that a comparison of effective charges is meaningful only in terms of the same definition.
SAMVELYAN,
52
ALEKSANYAN, TABLE
AND LOKSHIN
V
DERIVATIVESd; (IN D/A) FORIM(CO)s MOLECULES(OTHEREIGHT SOLUTIONS ARE OBTAINED CHANGING THESIGNSOFdi FOREACHSOLUTION) 1
4 Mo(COh
“,: da
dl W(COh
;: da
2
3
4
5
6
7
8
BY
0.44 4.57 -1.55 15.80
4.96 - 1.55 - 10.28
1.62 3.29 -0.59 15.07
-2.19 2.28 1.53 14.46
1.62 3.68 -0.59 -11.01
-2.19 2.67 1.53 -11.63
-1.02 1.01 2.50 13.73
-1.02 1.40 2.49 - 12.36
0.47 4.96 - 1.73 17.46
0.47 5.18 -1.73 -11.64
1.49 4.17 -0.94 17.01
-1.76 3.92 1.65 16.86
1.49 4.39 -0.94 - 12.09
-1.76 4.13 1.65 - 12.24
-0.73 3.13 2.44 16.41
-0.73 3.34 2.44 -12.70
0.25 5.10 - 1.93 17.83
0.25 5.50 - 1.93 -11.72
1.74 4.37 -0.82 17.41
- 1.90 4.40 1.26 17.42
1.74 4.77 -0.82 -12.14
- 1.90 4.80 1.26 -12.13
-0.41 3.67 2.37 16.70
-0.41
0.44
4.07 2.37 - 12.55
Using the method presented in the appendix we estimated the effective atomic charges in compounds investigated (Table VI). Like the derivatives, the values ei are known with an ambiguity of sign, e.g., one cannot unequivocally determine the signs of charges from the intensities alone. Some indirect information should be used for such purpose. It is known that the electron-deficient systems of Lewis acid type produce metal carbonyl complexes via oxygen (31). On the contrary a nucleophilic attack at the M(CO)e carbonyl group by the organolithium reagents (CHaLi, CeH,Li) is carried out through the carbon atom (32). Taking into account this information along with high oxygen electronegativity, in our opinion it seems reasonable to assume the effective charge at the carbonyl oxygen atom to be negative. One may choose eight solutions for which TABLE
VI
EFFECTIVE ATOMICCHARGES (IN UNITSOF ELECTRON CHARGE, 1 ELECTRON CHARGE= 0.208 D/A)
0 Cr(CO)G
C Cr
Mo(CO)c
C MO
W(CO)e
c
0
0 W
1
2
3
4
5
6
7
8
-0.32 0.41 -0.55
-0.32 0.41 -0.55
-0.12 0.46 -2.02
0.32 -0.77 2.73
-0.12 0.46 -2.02
0.32 -0.77 2.73
0.52 -0.73 1.27
0.52 -0.73 1.27
-0.36 0.46 -0.59
-0.36 0.46 -0.59
-0.18 0.51 - 1.86
0.34 -0.71 2.20
-0.18 0.51 - 1.86
0.34 -0.71 2.20
0.51 -0.66 0.91
0.51 -0.66 0.91
-0.40 0.45 -0.31
-0.40 0.45 -0.31
-0.17 0.53 -2.17
0.26 -0.66 2.37
-0.17 0.53 -2.17
0.26 -0.66 2.37
0.49 -0.58 0.51
0.49 -0.58 0.51
IR INTESSITIES
FOR Cr, MO, W CARBOKYLS
53
this is the case. We also note that the signs of effective charges at oxygen and metal are always the same and opposite to that at carbon. Thus in the view of these assumptions the metal charge is negative while the carbon one is positive. From these eight solutions, Kos. 1-2, ‘i-8 seem to be more preferable since metal charges in such cases are lower in the absolute values. Thus we choose solutions l&2, 7-8 which are pairwise equivalent in terms of the effective charges. Tndependently of the solution choice it can be seen that the effective oxygen charge is of about 0.2.-0.5 electron charge. In all the solutions chosen, metal charge decreases in (roing from Cr to W. _4t the MO atom it is either close to that at Cr or is an intermediate Between Cr and W. In the literature it is commonly adopted that the changes in properties of transition metal carbonyl complexes are discussed in terms of the changes in character of is obviously rather simpli(I,(M) - P,(C) conjugation. However, such representation fied. u-interaction may also effect essentially the properties of bonds. Thus from measuring the Raman intensities it has been shown that the a-interaction enhances in the order 110 < W < Cr (18). But this result is in disagreement with a decrease of metal charge when passing to W without account of u-interaction. A pathway of changes of the charges is inconsistent with the change of force constants of M-C bond as well MO < (‘r < W. On the other hand our results agree with MO calculations of M(C0)6 (33). Although in these two methods of computation the effective charges are defined in a different way and it is incorrect to compare the absolute values of charges, the authors of (33) revealed the same tendency in a decrease of charge in going from (‘r to \2;. APPENDIX
Let *I*atoms of the molecule bear some charges pi (i = 1, 2, 1. . , A’) varying vibrations. Then dipole moment of the molecule can be written in the form
tr =
:
under
eiRi
i=l
where Ri is the radius vector of the ith atom with respect to an arbitrary panding Eq. (2) into a series of small changes of Ri we have:
Ap = E eo
i=l
(aei,/‘aRj),ARi
j=l
point.
Ex-
(3)
where eo; is the charge of the ith atom at its equilibrium point, Roi is the equilibrium radius vector of this atom. Equation (3) can be written in certain Cartesian coordinate systems in the matrix form pk = E’(,,[J
+ R’H’]X’k = E’c,,lD’_yk.
(4
Here p,Qis the column (Apz, AFT, Apz)k, E’c,,) = /IES . . - Ez/j, J and D’ in the block form are respectively J = l/JiBijl\, D’ = IlDi’bijl[ 7where Ji = eoiEa and the elements of D,’ have the same meaning as derivatives of ~1 in the computation scheme of Morcillo
SAMVELYAN,
54 (34). Matrix
=
/1fI:S,ll
AND LOKSHIN
R' = [lRi'S;jlj, Ri being Ri’
EZ’
ALEKSANYAN,
=
x01,
x02,
* - -,
XON
J’ol,
yoz,
* * *,
YON
ZOl,
202,
* - *,
ZON
where the block Hi is
Finally Xk = (AXI, Ayl, AZI, . . . , AXN, Ayx, AzN)~ where Ac~i are the atomic displacements (~7= 2, y, z). The matrices Jiare scalar and consequently are invariant under the orthogonal coordinate transformation, e.g., eoi are determined only by the electronic shell of the molecule. Obviously, mathematically one can determine only the elements of matrices D'.However, if one could find the conditions when the diagonal elements of matrix R'H'vanish (or are close to zero) then eoi might be computed by virtue of (33). Let us introduce the “own” coordinate systems of the atoms analogously to (2, 23). Transition from the common molecular coordinate system K to the “own” ones Ki is given by means of the orthogonal transformation A. Expression (4) in the Iii systems takes the form /.JK = E’(,,A”[I + R,,'H~']AXK = E'&~D,'XKO (5) where Ro'= AR',Ho'= H'A,DO'= AD'A. Let us discuss physical elements of Ro'Ho'. The I-th block of the matrix Ro'Ho' corresponding can be written in system K1 as
C (&/axll)OxOil,
C (dei/f.W)OxOil,
C (dei/W)OxOil
C (Wdxl')OyOil,
C (deil$Q)0y0il,
IL
C (%/dyl')OzOil, ,
C (dei/W)OzOil
*
(Ro’Ho,)l
=
sense of matrix to the I-th atom
z
IL
C (aei/an,l)0z0il,
z
i
i
1
(%/~z?)oyoi’
/I
The derivative (aei/&& in this matrix is a partial derivative of the i-th atoms charge in displacement Aal’ of the I-th atom with respect to Kl. aoi1 is equal to projection of Ro, onto the a! axis of Kl-th system. The following relation gives physical meaning of sums in (Ro'HO')l AP,G = [eel -I- c
1
(dei/8cu?)ocuoi’]AaI’
(6)
where Ap,l1 is the change of cr-th component of ~1in the system k’l under displacement of the I-th atom over A&. Then the sum in Eq. (5) is the partial derivative of pal1 accounting for only the changes in electron cloud of the molecule during the above displacement. Let us consider this sum for some molecules. To begin with we take the planar molecule, ethylene for example. All its atoms lie in the symmetry plane of the molecule.
IR INTENSITIES
I:IG. 2. Ethylene tems of atoms.
molecule.
FOR Cr, MO, W CARBONYLS
XYZ is the common
s: axes are perpendicular
coordinate
system;
n_Viai, the “own”
55
coordinate
sys-
to the plane of figure.
Let us make one of the axes of systems K1, for example z, perpendicular to this plane (Fig. 2). When some atom shifts along the z axis then on the basis of molecular symmetry one may ascertain that the change of any atomic charge is an even function with respect (&i/&l’)o at an equilibrium point would to the s coordinate. Then the derivatives vanish and consequently, the diagonal elements of matrix Do’ corresponding to the displacements Az,l are equal to ~1. We define such charges as the effective atomic charges of the molecule. For the hesacarbonyls when atom 1 shifts along yl (see Fig. 1) the contributions of atoms l-3, T-10 into the sum xi (aei/y 1l) ,, are equal to zero as in the previous case. But for atoms S-6 and 11-12 this is not the case. Thus the computed diagonal elements of Do’ corresponding to the bending vibrations are not exactly the effective charges. One may assume, however, that a comparison of these values within the series Cr(CO)G, MOM, W(CO)6 may rather accurately correspond to the changes of effective charges in going from one to the other molecules investigated. In terms of this approsimation the obtained atomic charges in hexacarbonyls are given in the main text. Tn order to determine the elements of matrix Do’ one should use the computation scheme described in (34). However, such computation could be made as well in following the steps: (1) computation by the Mayants-Averbukh method; (2) transition to ?vforcillo’s derivatives by means of transformation reported in (35). ACKNOWLEDGMENTS The authors are grateful to Dr. B. S. Averbukh for stimulating discussions, Dr. E. R. Razumova for assistance in computer work, Dr. N. S. Kolobova for providing chromium, molybdenum and tungsten hexacarbonyls, Dr. B. S. Bystrov for providing his computer programs of the vibrational problem, and Dr. S. L. Zimont for assistance in computer programming. RE(:EIVED:
August
25, 1972 REFERENCES
1. N. J. HAWKINS, N. C. MATTRAW, W. W. SABOL AND D. K. CARPENTER,J. Chz. (1958).
Plrys. 23, 2422
56 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 13. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
SAMVELYAN,
ALEKSANYAN,
AND LOKSHIN
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Band Intensities in the Infrared Spectra of Metal Carbonyl Complexes: Chromium, Molybdenum and Tungsten Hexacarbonyls S. KH.
V. T. ALEKSANYA~T,
SAMYELYAN,
Institute of Organo-Element
Compounds,
AND B.
V.
LOKSHIK
Academy of Sciences, AIOSGOTL~, USSR
The absolute integrated intensities for IR absorption bands of M(C0)6 (M = Cr, MO, W) were measured. The calculations of dipole moment derivatives of the molecules were performed using a procedure suggested by L. S. Mayants and R. S. Averbukh. The effective atomic charges of n!f(CO), are estimated and discussed.
INTRODUCTION
In recent years many studies have been carried out on the vibrational spectra of Cr, MO, and W hexacarbonyls (1-18). Most of them deal with band assignments and caiculations of the force constants. As for the IR band intensities they are investigated only within the range of the CO stretching vibrations (19-21). No information is available on the intensities of the other three active IR modes although they are of great interest. The present paper is concerned with the measurements of absolute integrated intensities
for all IR active absorption
with the calculations method
of L. S. Mayants
appendix
bands of M(COs)
of dipole moment
derivatives
and B. S. Averbukh.
the effective atomic
and charges are compared
(M = Cr, MO, W) as well as
of these molecules,
Using the procedure
charges were determined.
in the series of investigated
employing suggested
the
in the
The values of the derivatives compounds.
EXPERIMENT.iL
Spectra were recorded on an UR-20 Zeiss prism spectrometer cm-l),
a Perkin-Elmer
grating
spectrometer
model 4.57 gratin g spectrometer (140-75 cm-‘). Measurements
formed in CC14 solutions, made in n-hexane
solution.
Method
(750-250
of integrated
cm-l)
intensities
and FIS-1 were per-
except in the range 75-140 cm-‘, where measurements The absolute
integrated
method of Wilson and Wells (24). It was assumed mum, the absorption
(prism LiF, 2150-1900
curve has Lorentz
II of Ref. (25). The obtained
intensities
were calculated
that in the range far from the masi-
form. The wing corrections
intensities
were using
were made using
are listed in Table I. It was difficult to
measure the intensities of the bands vg because of the low sensitivity of the instrument within this frequency range and also the low intensities of these absorption bands. Thus the error of these intensities is large. 47 Copyright 0 1973 by Academic Press. Inc. All rights of reproduction in any form reserved.
SAMVELYAN,
48
ALERSANYAN, TABLE
AND LOKSHIN
I
ABSOLLTTE INTEGRATED INTENSITIES OF IR ABSORPTION BANDSOF Cz, MO, ANDW HEXACARRONYLS (IN 1.mol-1cm-2. 104)ANDSIGNCOMBINATIONS OF (&,/%&)o ((Y= X,Y,Z) IN CALCULATION OFdi Sign combination Cr(CO)G Mo(CO)G W(CO)e 1 V6 v’7 ei P9
79.0
64.0 5.9 1.7 0.15
82.0 4.0 2.5 0.16
4.6 2.5 0.09
+ + + +
3
2 + + +
+ + +
4 + + + -
5
6
+ +
+ + -
7 + + -
8 + -
CALCULATIONS (a)
Normal
Coordinate
Treatment
To evaluate dipole moment derivatives of the molecule, both the absolute integrated intensity values and the modes of the normal vibrations must be known. The calculation was performed using the El’yashevich-Stepanov method (26). The molecules investigated belong to the symmetry group Oh. The M-C and C-O bond distances used were 1.916 and 1.171 A for Cr(CO)G (27), 2.063 and 1.145pi for Mo(CO)E and 2.059 and 1.148 A for W(CO)6 (28). The force field evaluated by Jones (9) was taken as an initial approximation. To make force constants more precise the data on the frequencies of three types of the isotopically substituted molecules M(12C160)6, M(12C180) 6, and M(%160)6 (29) have been employed. Calculations were performed on a BESM-3M digital computer using the programs of Dr. D. S. Bystrov. The calculated and experimental frequencies for the IR-active F1, modes are listed in Table II. Table III shows the force constants in terms of the symmetry coordinates and Table IV represents the normalized modes for 1M(12C160)6 molecules. The symmetry coordinates used are as follows : I = 2$/2(Z1 - Z3), P = 1/2(P,=J - PP t = 21/2(t1 -
(Y = 2*/4(~, (b) Dipole Moment The procedure
dipole moment
- PC= + W),
t3), -
cfz3 - a34 + al1 + al5 + al6 - (y3s - 4.
Derivatives
of Mayants
and Averbukh
~1 with respect
allows one to determine
to bond vectors
According to (22, 23) the dipole moment normal coordinate) are given by
the derivatives
R(O (i = 1, 2, 3. ., N -
derivatives
(ap/aQ,)o
of
1) (Fig. 1).
(where Qk is the k-th
IR INTEXSITIES
FOR Cr, MO, W CARBONYLS TABLE
49
II
EXPERIMENTAL ANDCALCULATED FREQUENCIES OF NORMAL MODES FOR F1, S~ETRP SPECIES Frequency (cm-‘)
Isotope
Cr(CO)e
MO(C0)6
W(CO)6
C
0
12
16
12
18
13
16
12
16
12
18
13
16
12
16
12
18
13
16
V6
V7
VS
&l
exp cal exp cal exp cal
2043.7 2043.5 1994.7 1995.1 1997.5 1997.4
668.1 670.2 665.8 664.2 654.8 654.3
440.5 439.2 429.7 430.9 433.5 433.1
97.2 96.7 93.6 93.0 96.2
exp cal exp cal exp cal
2043.1 2042.9 1993.4 1994.1 1997.5 1997.1
595.6 597.2 592.7 590.6 580.0 580.5
367.2 367.2 359.7 359.2 362.3 362.8
81.6 81.5 78.2 78.5 81.3 81.1
exp cal exp cal exp cal
2037.6 2037.5 1988.8 1989.2 1991.8 1991.6
586.6 587.6 583.3 580.9 568.8 570.2
374.4 374.1 364.5 364.2 368.4 369.0
82.0 82.6 79.4
where I(“’ is the column matrix [(&.~~/@k)~, ($A,,I’@~)~, (&A/LQ)~]. values are determined from the expression
82.1
The (&JI~QL.)~
with an ambiguity of sign. EC,,, in the block form is Ecp) = jjE3 El . . . Esj[ where Es is the three-dimensional unitary matrix. Cj is the submatrix of orthonormalized matrix C corresponding to the jth symmetry species. C expresses the column matrix gs of symmetry coordinates in terms of the changes of vector R(O projection, x6, on the TABLE
III
FORCE CONSTANTS FOR FI, SYMMETRYSPECIES(IN 10scm-2) ; FI,, Fig, Ft,, FtB, FuB ARE FOUND TO BE LESS THAN O.Ola
ck(CO)6 Mo(CO)e W(CO)s
FL1
Ftt
F&3
FW
F,t
26.75 26.82 26.68
2.64 2.25 2.79
1.35 1.22 1.21
0.40 0.35 0.42
1.14 1.10 1.25
-. 8 The values of force constants obtained in our work do not differ significantly from those in (29). The units used here are defined in (26): F~~(105cm-2) = l..56F+’ (mdyn/.%) (a,j = 1~); F&10Bcm-2) = 1.31 Fk,‘(mdyn.A) (k = a,@); F;k(lO%m-*) = 1.43Fik’(mdyn).(i = 1~; k = a~?).
50
SAMVELYAN,
ALEKSANYAN, TABLE
AND LOKSHIN
IV
NORMALIZED MODES OF VIBRATION OF F,,
“6
w(co)s
“7
us v9
SWYETRY
SPECIES
1
P
t
a
0.39834 0.00198 0.00373 0.00013
-0.00139 0.52212 -0.12995 0.02130
-0.23061 0.12612 0.25167 0.00932
-0.00184 -0.29949 -0.04281 0.14601
0.39835 0.00046 0.00179 0.00004
-0.00034 0.51923 -0.05618 0.01626
-0.22875 0.05827 0.23998 0.00592
0.00046 -0.23673 -0.04526 0.13365
0.39835 0.00047 0.00302 0.00005
-0.00033 0.51438 -0.03679 0.01813
-0.22933 0.03277 0.22098 0.00347
0.00044 -0.21961 -0.02567 0.12335
molecular Cartesian coordinate system XI’2 (Fig. 1) : g” = Cxa. S is the matrix relating the Cartesian coordinates of the atomic displacements x and x6 ; thus x6 = Sx. e is the diagonal matrix of reciprocal atomic masses. Bi is the submatrix of B corresponding to the jth symmetry species. B expresses the symmetry coordinates pa in terms of x, thus (I” = Bx. Tjj is the block of the jth symmetry species of the kinetic energy matrix T written in terms of q8 coordinates. qojSCk) _ is a normalized Rth normal mode.
FIG. 1. M(CO)B molecule (M = Cr, MO, W). l-6 and 7-12 are. the atoms C and 0 respectively; R, the bond vector; XYZ, the common coordinate system, xg&, the “own” coordinate systems of bonds.
IR INTENSITIES
FOR Cr, MO, W CARBONYLS
51
Djs = HiDOHj-’ where Do is the matrix of derivatives of v with respect to the projections ~80of vectors R(” on the axes of “own” (for each bond) coordinate system x+zi (Fig. 1). H, = CjA ; A determines the transformation x6 = AxsO. The matrices H and Do are respectively H = CA, Do = iiDA. The symmetry class FI, contains 4 modes. There are four independent dipole moment derivatives :
The derivatives tli are obtained by the solution of the system equations (1). But the solusigns of (a~~/@ k) 0 are not defined and the problem has therefore 2” independent tions corresponding to various sign combinations of ($.&/a&)0 k being the number of IR active modes. In the case of M(CO)G there are eight solutions (with an ambiguity of the relative signs). The derivatives di are given in Tables V. A11 calculations of cii were preformed on an electronic digital computer. DISCGSSIOS
Analysis of the vibration modes (Table IV) shows that ve and va are practically purely stretching vibrations. But in v6 along with coordinate 2 (stretching of CO bond) there is an essential contribution of the coordinate t (the MC bond stretching) ; VTis determined generally by the change of the /3 angle; vg is practically a purely bending vibration determined by 01,the MC0 groups bending approximately as the rigid pivots fixed at the metal atom. Before discussing the derivatives obtained we note that hexacarbonyls have close geometries, force constants, and modes of vibrations. Thus it can be assumed that in the series Cr(CO)G, Mo(CO)e, and W(C0) 6 one may compare the ni values for solutions with the same sign combination. As it is seen from Table V for all the compounds there exist two groups of four solutions (solutions 1, 3, 4, 7 and 2, 5, 6, 8) which differ in the relative signs of derivatives tl, and dq. The dh values are large due to an exclusively high intensity of IQ,. From the data presented it can be seen that for all sets of the solutions the dz derivatives alway-s increase from Cr(CO)d to Mo(C0) 6 and W(CO)6. The same order is retained for the (14.We also note that the derivatives (11and & always have the opposite signs. Moreover, with respect to these derivatives the solutions can be divided into 4 pairs the derivatives dl (d3) being equal within each pair of l-2, 3-5, 446, and 7-8. These pairs of solutions differ by relative signs of the derivatives ($~,/a@)~ and the equality of dl (d3) is due to a negligibly small contribution of bending terms in ZQ (Table IV). The choice of the true solution is a rather complex task. The effective atomic charges in hesacarbonyls might be of aid. Besides, the knowledge of these charges is certainly of interest in itself. Depending upon definition the term “effective charge” may have different meaning [see, e.g., (30)]. It is essential that a comparison of effective charges is meaningful only in terms of the same definition.
SAMVELYAN,
52
ALEKSANYAN, TABLE
AND LOKSHIN
V
DERIVATIVESd; (IN D/A) FORIM(CO)s MOLECULES(OTHEREIGHT SOLUTIONS ARE OBTAINED CHANGING THESIGNSOFdi FOREACHSOLUTION) 1
4 Mo(COh
“,: da
dl W(COh
;: da
2
3
4
5
6
7
8
BY
0.44 4.57 -1.55 15.80
4.96 - 1.55 - 10.28
1.62 3.29 -0.59 15.07
-2.19 2.28 1.53 14.46
1.62 3.68 -0.59 -11.01
-2.19 2.67 1.53 -11.63
-1.02 1.01 2.50 13.73
-1.02 1.40 2.49 - 12.36
0.47 4.96 - 1.73 17.46
0.47 5.18 -1.73 -11.64
1.49 4.17 -0.94 17.01
-1.76 3.92 1.65 16.86
1.49 4.39 -0.94 - 12.09
-1.76 4.13 1.65 - 12.24
-0.73 3.13 2.44 16.41
-0.73 3.34 2.44 -12.70
0.25 5.10 - 1.93 17.83
0.25 5.50 - 1.93 -11.72
1.74 4.37 -0.82 17.41
- 1.90 4.40 1.26 17.42
1.74 4.77 -0.82 -12.14
- 1.90 4.80 1.26 -12.13
-0.41 3.67 2.37 16.70
-0.41
0.44
4.07 2.37 - 12.55
Using the method presented in the appendix we estimated the effective atomic charges in compounds investigated (Table VI). Like the derivatives, the values ei are known with an ambiguity of sign, e.g., one cannot unequivocally determine the signs of charges from the intensities alone. Some indirect information should be used for such purpose. It is known that the electron-deficient systems of Lewis acid type produce metal carbonyl complexes via oxygen (31). On the contrary a nucleophilic attack at the M(CO)e carbonyl group by the organolithium reagents (CHaLi, CeH,Li) is carried out through the carbon atom (32). Taking into account this information along with high oxygen electronegativity, in our opinion it seems reasonable to assume the effective charge at the carbonyl oxygen atom to be negative. One may choose eight solutions for which TABLE
VI
EFFECTIVE ATOMICCHARGES (IN UNITSOF ELECTRON CHARGE, 1 ELECTRON CHARGE= 0.208 D/A)
0 Cr(CO)G
C Cr
Mo(CO)c
C MO
W(CO)e
c
0
0 W
1
2
3
4
5
6
7
8
-0.32 0.41 -0.55
-0.32 0.41 -0.55
-0.12 0.46 -2.02
0.32 -0.77 2.73
-0.12 0.46 -2.02
0.32 -0.77 2.73
0.52 -0.73 1.27
0.52 -0.73 1.27
-0.36 0.46 -0.59
-0.36 0.46 -0.59
-0.18 0.51 - 1.86
0.34 -0.71 2.20
-0.18 0.51 - 1.86
0.34 -0.71 2.20
0.51 -0.66 0.91
0.51 -0.66 0.91
-0.40 0.45 -0.31
-0.40 0.45 -0.31
-0.17 0.53 -2.17
0.26 -0.66 2.37
-0.17 0.53 -2.17
0.26 -0.66 2.37
0.49 -0.58 0.51
0.49 -0.58 0.51
IR INTESSITIES
FOR Cr, MO, W CARBOKYLS
53
this is the case. We also note that the signs of effective charges at oxygen and metal are always the same and opposite to that at carbon. Thus in the view of these assumptions the metal charge is negative while the carbon one is positive. From these eight solutions, Kos. 1-2, ‘i-8 seem to be more preferable since metal charges in such cases are lower in the absolute values. Thus we choose solutions l&2, 7-8 which are pairwise equivalent in terms of the effective charges. Tndependently of the solution choice it can be seen that the effective oxygen charge is of about 0.2.-0.5 electron charge. In all the solutions chosen, metal charge decreases in (roing from Cr to W. _4t the MO atom it is either close to that at Cr or is an intermediate Between Cr and W. In the literature it is commonly adopted that the changes in properties of transition metal carbonyl complexes are discussed in terms of the changes in character of is obviously rather simpli(I,(M) - P,(C) conjugation. However, such representation fied. u-interaction may also effect essentially the properties of bonds. Thus from measuring the Raman intensities it has been shown that the a-interaction enhances in the order 110 < W < Cr (18). But this result is in disagreement with a decrease of metal charge when passing to W without account of u-interaction. A pathway of changes of the charges is inconsistent with the change of force constants of M-C bond as well MO < (‘r < W. On the other hand our results agree with MO calculations of M(C0)6 (33). Although in these two methods of computation the effective charges are defined in a different way and it is incorrect to compare the absolute values of charges, the authors of (33) revealed the same tendency in a decrease of charge in going from (‘r to \2;. APPENDIX
Let *I*atoms of the molecule bear some charges pi (i = 1, 2, 1. . , A’) varying vibrations. Then dipole moment of the molecule can be written in the form
tr =
:
under
eiRi
i=l
where Ri is the radius vector of the ith atom with respect to an arbitrary panding Eq. (2) into a series of small changes of Ri we have:
Ap = E eo
i=l
(aei,/‘aRj),ARi
j=l
point.
Ex-
(3)
where eo; is the charge of the ith atom at its equilibrium point, Roi is the equilibrium radius vector of this atom. Equation (3) can be written in certain Cartesian coordinate systems in the matrix form pk = E’(,,[J
+ R’H’]X’k = E’c,,lD’_yk.
(4
Here p,Qis the column (Apz, AFT, Apz)k, E’c,,) = /IES . . - Ez/j, J and D’ in the block form are respectively J = l/JiBijl\, D’ = IlDi’bijl[ 7where Ji = eoiEa and the elements of D,’ have the same meaning as derivatives of ~1 in the computation scheme of Morcillo
SAMVELYAN,
54 (34). Matrix
=
/1fI:S,ll
AND LOKSHIN
R' = [lRi'S;jlj, Ri being Ri’
EZ’
ALEKSANYAN,
=
x01,
x02,
* - -,
XON
J’ol,
yoz,
* * *,
YON
ZOl,
202,
* - *,
ZON
where the block Hi is
Finally Xk = (AXI, Ayl, AZI, . . . , AXN, Ayx, AzN)~ where Ac~i are the atomic displacements (~7= 2, y, z). The matrices Jiare scalar and consequently are invariant under the orthogonal coordinate transformation, e.g., eoi are determined only by the electronic shell of the molecule. Obviously, mathematically one can determine only the elements of matrices D'.However, if one could find the conditions when the diagonal elements of matrix R'H'vanish (or are close to zero) then eoi might be computed by virtue of (33). Let us introduce the “own” coordinate systems of the atoms analogously to (2, 23). Transition from the common molecular coordinate system K to the “own” ones Ki is given by means of the orthogonal transformation A. Expression (4) in the Iii systems takes the form /.JK = E’(,,A”[I + R,,'H~']AXK = E'&~D,'XKO (5) where Ro'= AR',Ho'= H'A,DO'= AD'A. Let us discuss physical elements of Ro'Ho'. The I-th block of the matrix Ro'Ho' corresponding can be written in system K1 as
C (&/axll)OxOil,
C (dei/f.W)OxOil,
C (dei/W)OxOil
C (Wdxl')OyOil,
C (deil$Q)0y0il,
IL
C (%/dyl')OzOil, ,
C (dei/W)OzOil
*
(Ro’Ho,)l
=
sense of matrix to the I-th atom
z
IL
C (aei/an,l)0z0il,
z
i
i
1
(%/~z?)oyoi’
/I
The derivative (aei/&& in this matrix is a partial derivative of the i-th atoms charge in displacement Aal’ of the I-th atom with respect to Kl. aoi1 is equal to projection of Ro, onto the a! axis of Kl-th system. The following relation gives physical meaning of sums in (Ro'HO')l AP,G = [eel -I- c
1
(dei/8cu?)ocuoi’]AaI’
(6)
where Ap,l1 is the change of cr-th component of ~1in the system k’l under displacement of the I-th atom over A&. Then the sum in Eq. (5) is the partial derivative of pal1 accounting for only the changes in electron cloud of the molecule during the above displacement. Let us consider this sum for some molecules. To begin with we take the planar molecule, ethylene for example. All its atoms lie in the symmetry plane of the molecule.
IR INTENSITIES
I:IG. 2. Ethylene tems of atoms.
molecule.
FOR Cr, MO, W CARBONYLS
XYZ is the common
s: axes are perpendicular
coordinate
system;
n_Viai, the “own”
55
coordinate
sys-
to the plane of figure.
Let us make one of the axes of systems K1, for example z, perpendicular to this plane (Fig. 2). When some atom shifts along the z axis then on the basis of molecular symmetry one may ascertain that the change of any atomic charge is an even function with respect (&i/&l’)o at an equilibrium point would to the s coordinate. Then the derivatives vanish and consequently, the diagonal elements of matrix Do’ corresponding to the displacements Az,l are equal to ~1. We define such charges as the effective atomic charges of the molecule. For the hesacarbonyls when atom 1 shifts along yl (see Fig. 1) the contributions of atoms l-3, T-10 into the sum xi (aei/y 1l) ,, are equal to zero as in the previous case. But for atoms S-6 and 11-12 this is not the case. Thus the computed diagonal elements of Do’ corresponding to the bending vibrations are not exactly the effective charges. One may assume, however, that a comparison of these values within the series Cr(CO)G, MOM, W(CO)6 may rather accurately correspond to the changes of effective charges in going from one to the other molecules investigated. In terms of this approsimation the obtained atomic charges in hexacarbonyls are given in the main text. Tn order to determine the elements of matrix Do’ one should use the computation scheme described in (34). However, such computation could be made as well in following the steps: (1) computation by the Mayants-Averbukh method; (2) transition to ?vforcillo’s derivatives by means of transformation reported in (35). ACKNOWLEDGMENTS The authors are grateful to Dr. B. S. Averbukh for stimulating discussions, Dr. E. R. Razumova for assistance in computer work, Dr. N. S. Kolobova for providing chromium, molybdenum and tungsten hexacarbonyls, Dr. B. S. Bystrov for providing his computer programs of the vibrational problem, and Dr. S. L. Zimont for assistance in computer programming. RE(:EIVED:
August
25, 1972 REFERENCES
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Plrys. 23, 2422
56 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 13. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
SAMVELYAN,
ALEKSANYAN,
AND LOKSHIN
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