.4ug. 5 , 1964
300 1
ACETYLACETONATE A N I O N
very little affected b y the severe thermal pretreatments of the catalyst which were employed. Since there is little a priori reason to expect this, the results are of particular interest. The importance of applying a method such as t h a t described in this paper to study
[CONTRIBUTIOS FROM THE
DEPARTMEST OF
the factors influencing the catalytic activities of supported metals cannot be overemphasized. Acknowledgment.-The authors gratefully acknowledge the contributions of Messrs. R. C , Parker and E . M . Kelley in the performance of the experiments.
CHEMISTRY, USIVERSITY OF ARIZONA, T U C S O N , ARIZONA]
The Acetylacetonate Anion. Molecular Orbital Calculations in the Huckel and Self-consistent Field Approximations’ BY LESLIES. FORSTER RECEIVED FEBRUARY 7, 1963 Huckel and self-consistent field calculations of the acetylacetonate ion rr-electron structure have been made. In contrast t o the marked sensitivity of the Huckel results t o the parameter choice, the s.c.f.results are relatively independent of these quantities. T h e effects of metal ion charge and penetration integrals largely cancel out, and a simplified s.c.f.treatment is adequate for the calculation of transition energies and intensities.
Introduction In the interpretation of the spectra of metal comelectronic tranplexes, i t is often useful t o distinguish ” sitions largely localized within the ligands from those involving charge transfer between the metal ion and ligands. The spectra of metal complexes in which the acetylacetonate ion is the ligand have been studied in detail,2 and attempts to distinguish ligand-localized from charge-transfer transitions have been made. 3 - 6 Such an analysis generally proceeds by first examining the spectrum of the free ligand and then considering the perturbing effect of the metal ion on the ligand states. The electronic structure of the acetylacetonate anion has been calculated by two semiempirical procedures-the H ~ c k e l ~and , ~ self-consistent field (s.c.f.)methods.6 The success of the Hiickel method in the interpretation of the spectra of alternant hydrocarbons coupled with the computational simplicity of this scheme has led to its extensive applications to a-electron systems. The widespread availability of digital computers has now minimized the computational advantages of the Huckel method. I n this paper, the electronic structures of the acetylacetonate ion as determined by the Huckel method and a computationally simple version of the s.c.f. method are compared in order to determine the relative rnerits of each technique. The determination of the electronic structures of metal acetylacetonates with two and three ligands should be based on a knowledge of the single ligand structure. In this study, the first step in the treatment of the more general problem, the acetylacetonate ion (as in alkali metal complexes), is considered. Hiickel Cal~ulations.~-In the Huckel method, the normalized molecular orbitals are of the LCAO form
4i
=
Ccipxp
(1)
P (1) Supported by t h e United States Atomic Energy Commissiog. (‘2) R. H. Holm and F. 4.C o t t o n , J . A m . Chem. SOL.,80, 5658 (1958). (3) D W Barnum, J . Inovg. S u c i . Chem., $1, 221 (1961). (4) J . P. Fackler, J r . , F A C o t t o n , and D. W , Barnum, lnorg C h e m . , I , 97, 102 (1963). ( 5 ) T. S. Piper and R. I. Carlin, J . Chrm P h y s . , 36, 3330 (1962). (6) K . DeArmond and L S. Forster, Sprcluochim. A d a , 19, 1393 (1963). ( 7 ) For a comprehensive survey of this method see A Streitwieser, J r , “Molecular Orbital Theory for Organic Chemists,” John Wiley and Sons, I n c , S e a I’ork, S Y . , 1961.
where the summation index p extends over all the atoms in the a-electron framework or “core.” Neglecting overlap, the coefficients, tip, and orbital energies, ~ i are , determined by diagonalizing the H matrix, with elements defined as
The Coulomb integrals, Hpp= up, and the resonance integrals, Hpq= pPq(these are assumed to be zero unless p and q refer to neighboring atoms), are assigned semiempirically, and the H matrix may be diagonalized with a digital computer using a program in which the ciP and ~i are evaluated. In the simple Huckel method, electron repulsion is not incorporated explicity, but is included to some extent by the choice of a p and Ppq parameters. This procedure has been fairly successful in treating the spectra of alternant hydrocarbons, but serious ambiguities arise when heteroatoms are included in the aelectron system.E9 The ap parameters must then be adjusted for the differential electronegativity of the atoms and the pPqaltered for the varying bond lengths. The uncertainties inherent in this approach can be seen by reference to Table I where the results of the three Huckel calculations are summarized. The numbering system is shown in Fig. 1. In calculation I a ,
Figure 1
parameters rather similar to those suggested by Streitwieser’ were employed. The effect of the metal ion in increasing the electronegativity of the oxygen atoms was intentionally overestimated in calculation I b , while in calculation IC another “reasonable” choice of parameters was employed.lO The six a-electrons fill the and in all three cases three lowest orbitals. +1-+3, 44. the lowest energy transition is assigned as 43 The assignment of the next higher transition is doubtful, however. Not only are the transition energies
-
(8) M .J . S . Dewar, Rev. M o d . P h y s . , 36, 586 (1963). (9) G. Del Re and R. G . P a r r , i b i d , 36, 604 (1963). (10) D. W . Barnum, J . Inovg. Nucl. Chem , P I , 163 (1961), and p r i v a t e communication
3002
LESLIES. FORSTER TABLE I HUCKEL RESULTS’ Ia
Ib
IC
Parameters, e.v. -2.74 +0.27 0 -2.46 - 2 74
011
a2 cy3
1912
1923
---
-5.48 0 0 -2.74 -2.74
-1.67 -0.16 0 -4.08 -2.74
Transition energies, e.v. &i
6:i
3 44 6.26 j.78
64
45 6 2 64 Charge densities
3.87 7.02 ?
i
r-
ia
4.01 5.95 8 29
1 ,098 1.812 1.406 0,704 0.620 0 887 P,ia 1 196 1 136 1.414 * Calculation Ia parameters are similar to those recommended by Streitwieser?; calculation Ib parameters are overcorrected for metal ion charge; calculation IC parameters are those employed by Barnum.’O I n all three cases 6c-c = -2.74 e.v., and ( ~ 3= 0 was chosen as the reference energy. 1’11
P??
-
Fpp = a p
P,,
=
2
tities: cyp = JXpHcoreXpdr and Ppq = J X p H C o r e X c l d T , in addition to the Coulomb repulsion integrals, yprl, and the valence state ionization potentials, IVp. I t has been asserted from a detailed study of aniline that the s.c.f. results are “not so sensitive to the parameter choice as are the results of the Huckel It must now be determined if this is also true i n the case of the acetylacetonate ion in which an additional complication due to the metal ion charge is present. Parameter Evaluation.-The two-center repulsion integrals, ypq, are dependent upon the geometry. The geometry of the chelate ring in ferric acetylacetonate’d was chosen for the acetylacetonate ion. The interatomic distances are listed in Table 11. A number of prescriptions have been devised for evaluating y p q , ” but the results are not sensitive to the procedure used. In calculation I I a , the formulas of Roothaan l 5 were employed, but the effective atomic numbers were adjusted semiempirically from the expressionL6
=r,
-
dependent upon the parameter choice, but the relative 46 and 62 44 is sensitive to the paorder of 4:i rameters employed. This uncertainty coupled with the inability of the Hiickel method to distinguish singlet and triplet states suggests the application of a more suitable procedure. I t now remains to be determined if the “simplified” s.c.f. procedure is superior for this purpose. S.c.f. Calculations. “-Electron repulsion can be included by using a self-consistent field method. The general s.c.f. method, in the LCAO approximation, which has been utilized in purely theoretical calculations of the electronic structure of small molecules, is too cumbersome for application to large molecules. X semiempirical modification has been developed which provides a straightforward computational framework.I2 I t is this method which is here designated “the s.c.f. method” and to which all subsequent reference is made. In the s.c.f. method the orbital energies are determined by diagonalizing the F matrix. In contrast t o the H matrix in the Huckel method, the elements of the F matrix depend upon the ciP coefficients. Consequently, an iterative procedure must be employed. An initia1 set of molecular orbitals of the form given in eq. 1 is assumed. These are generally obtained by a Huckel calculation, but need not be so determined. The elements of the F matrix are
+
l/*PppYpp
+c
Vol. Xlj
5.321 TABLE I1 PARAMETER CHOICEFOR S.C.F. CALCULATIONS ._____ ypq e v ---Interatomic distance, 8,
01-Cs 01-c3
01-Ca 01-05
c2-c3
c2-c., &I-01
M-C, M-CB
1 2 2 2 1 2 1 2 3
280 310 981 840 390 553 950 972 235
-
IIa
Ilb
8 5 4 4 7
521 644 ,536 823 723 5 095
8 5 4 4
47 91 82 95 7 53 5 33
e
----ypp,
IIC
8 5 5 5 7 5
-
\.
Wp, e v
IIa
(C)
11 42
10 84
11 08
(0)
17 21
14 52
14 52
+
+
47 91 12 98 52 56
IIb, ~ I C
In I I b , the formulas of h n o , et (11 , I 7 were used for all but 7 1 6 . The effect of changing the geometry is largely evidenced in the value of this quantity. In calculation Ilc, the Anno formulas were used with a geometry in which the ligand bond angles were set a t l%Oo. -1very large value of was also chosen in this calculation. In the expression
PqqYpq
q # P
cipciri(sum over all occupied orbitals) 1
The F matrix is then computed and diagonalized. The resultant cip are then used to calculate a new F matrix. This procedure can be programmed and the iteration repeated until the desired degree of “self-consistency” is obtained. In place of the two a p and Ppq parameters that appear in the Hiickel theory, in the s.c.f. method four semiempirical parameters are employed. These are the quan( 1 1 ) FOI-a critical review of semiempirical methods a n d a collection of pertinent reprints, see R . G. P a r r , “ T h e Q u a n t u m Theory of Molecular Electronic S t r u c t u r e , ” 11‘ A Benjamin, I n c , S e w Y o r k , N . Y . , 1963. 12) J A Pople, T v a i i s F n r n d a y Soc , 49, 1875 (1953), reprinted in ref 11.
the index q refers to atoms in the n-framework while the index r includes all atoms in the molecule. In calculations IIa,b,c, the penetration integrals ( r / p p ) and the metal ion charge were neglected. The effects of this neglect are considered below. The nearest neighbor approxiyation is used for PPq; for a C-C distance of 1.39 A . , ~ C - C = -2.4% e.v.I6 The P c - 0 was computed from Kon’s formula‘* (13) I Fischer-Hjalmers, A i k i a F y s i k , 21, 123 ( 1 9 6 2 ) , reprinted i n ref 11. (14) R . B. Roof, A c t a Ci’ysl , 9 , 781 (1956). (1.5) C. C . J R o o t h a a n . J . Chum. Phys., 19, 1445 (19.51) (16) R . I.. Miller, P G 1-ykos, and H N Schmeising, J A m Chrin S o c , 84, 4623 (1962). (17) T Anno. I . M a t u b a r a , a n d A Sodo, Bull. Chrm. SOC.J a p a n , 3 0 , 168 (1957) (18) H K o n , $bid , $8, 275 i l 9 5 5 ) , reprinted in ref. 11.
Aug. 5 , 1964
ACETYLACETONATE A N I O N
as -2.00 e.v. Changing this to -2.20 e.v. increased the transition energies by about 0.1 e.v. The values of the parameters used are listed in Table I1 and the results are summarized in Table 111.
-
10.0
LO
.
8.0
-
20
-
LO
SI
--
T +AS1 s2
So, e.v. &, e.v. So)
-f
b4,e.v.
IIa
IIb
I IC
4.533 2.700 0.368
4.362 2.440 0.416
4.144 2.302 0.322
P11
p22
P33
6.909 6.626 1 663 0.641 1.391
6.743 6.467 1.663 0.671 1.332
Discussion
I eo
Exptl
4 25 3 (?) 0.19
6.636 6.354 1.628 0.702 1.340
>6.4
-
TABLE 11'
aa
o s TRASSITION EXERGIES =
0" SI + Sa
Sa = 4 . 2 5 e . v . OLV
T
Sa
ea
-
4.50 e . v .
a?
T
+
a
Sa
0 -2.5 1.70 -5 0 -1.7 2.15 -3 0 -0 2 2.30 -3.0 -1 0 1.70 -1.0 0.5 1.90 -1.0 1.2 2 50 0 1 2 200 0 1 8 255 2 0 2 4 2.10 2 0 3 0 265 4.0 3 6 205 4 0 4 2 2.60 5 0 4.1 1 95 5 0 4s 260 5s 225 7.0 5 2 180 7 0 All other parameters as in calculation I I a ; values in e.v. -5
(19)
R E. Whan
-
-1.0
-3.0
-
-40
-
-2.0
-7.0
-
-
?
0 -
-
I
SI
1.0
-60 -
+
aip
cr"
4.0
The lowest x-x* transition, S1 So,is observed a t 4.25 e.v. in the spectra of a large group metal acetylacetonates.' The energy of the next higher transition, Sz+ So,is not always known, but in most cases i t exceeds 6.4 e . v . In the copper acetylacetonate spectrum, the transition a t 6.2 e.v. has been assigned as Sz + The position of the lowest triplet state is uncertain, but in the phenyl-substituted acetylacetonate ions, benzoylacetonate, and dibenzoylmethide, the T + So transitions have been observed at 2 . 7 and 2.5 e.v., r e s p e ~ t i v e l y . ' ~The shoulder at 3.2 e.v. in the absorption spectrum of sodium acetylacetonate So,6 The lowest triplet state may be due t o T energy is then estimated to be about 3 e . v It can be seen in Table I11 t h a t , in general, the transition energies and oscillator strengths (f) obtained in all three s.c.f. calculations are in reasonable agreement with experiment, and that in particular the Sz + Sa and T + So energies obtained in I I a correspond to experiment as well as can be expected. However, in all three examples the SI-T split is -2 e.v. instead of the 1.25 e.v. observed. I n order to determine if this large S1-T separation results from a poor choice of up (due perhaps to the neglect of penetration integrals and or metal ion charge), a systematic variation of these parameters was made. The effect of the variation of cyp on the SI Soand T +So transition energies is indicated in Fig. 2 and 3. If we choose to set the S1 + Soexactly a t 4.25 e.\'., then the highest value of T + So obtainable is 2.1 e.v. If we choose 4.5 e.v. for S1 So,then the best value for T +- Sa is 2.7 e.\-. It can be seen in Table IV t h a t in EFFECT OF
-
40
0 . 3
so
/43 +. +6, e.v. 'i$2
-
LO
TABLE I11 S.C.F.RESULTS
3003
and G A . Crosby, J . .Uol. Specti.>,., 8, 315 (1Y62).
-3.0
10.0
-
9.0
-
8.0
-2.0
-I 0
0
1.0
2.0
3.0
4,O
5.0
6.0
-
5.0 4.0 7.0
6.0
5a"
3.0
-
2.0
-
I.0-
0-
-2.0-
-1.0
-3.0
-
4.0 -
-5.0
-6.0
'
I
I
310
Fig. 3.-T7ariation
4.0
in T
5.0 SI -So Energy (ax).
-
Soenergy wrth
6.0 olP
,O
( a l = 0)
either event, a number of combinations of ap will yield nearly the same results. I t is noteworthy that although in some cases, for a given cyl and 0 3 , two values of LYZ correspond to the same S1 So energy, only one of these will give a reasonable value of T +- So. The computed SI-T splitting can be reduced, but only by sacrificing agreement with the observed SI So and T Soenergies. The inclusion of configuration interaction does not alter the results significantly. Even though the $2 --t $4 and $3 --t $5 singlet states are nearly degenerate, the matrix element connecting the two states is very small (ca. 0.1 e.v.). Neglect of Penetration Integrals and Metal Ion Charge.-From the foregoing i t is seen that calculation I I a , in which a2 - cy1 = 3.43 e.v. and 013 - cy1 = 2.58 e.v., very nearly represents the optimum obtainable with this s.c.f. formalism. These cyp were computed with all penetration integrals neglected and by assuming the metal ion was without influence. It has been found that the protonation of pyridine could best be described by a point charge model, i.e., by reducing each cyp by the electrostatic potential due to a bare
-
-
-
300-1
LESLIES.FORSTER
proton.?" In view of the observed insensitivity of the acetylacetonate a-a* transition energies to the metal ion charge? i t may be assumed that the oxygen lone pairs shield the positive charge to some extent. The effective charge to be used in the sodium acetylacetonate case is probably somewhat less then +1 and this quantity is not changed much in the divalent and trivalent metal chelates involving acetylacetone. A similar conclusion has been reached for the effect of metal ion charge on pyridine ligands.21 The reductions of cyp for atoms 1 , 2, and 3 . due to a $1 charge are G.73. &S4, and 1.45e.\'., respectively-. Although accurate values of the penetration integrals have not been evaluated. the effect of including such integrals can be estimated. T h e oxygen atoms are bonded to one other atom, while each carbon in the a-framework is bonded to three other atoms. If each penetration integral is equal to about 1 e.\'.. then the 2 e.v. lowering a t C-2 and C-3 by the penetration integrals is partially offset by the electrostatic effect a t 01, i.c, the two effects tend to cancel. I t is then not surprising that the results obtained by neglecting these two opposing effects are fairly good, Charge Distribution.-Both the Huckel and s.c.f. methods predict a markedly inhomogeneous a-electron density on the carbon atoms. In accord with the high reactivity of the %positions toward electrophilic reagents. the charge density is higher on C-3.*? The deactivation of the ring when the methyl groups are replaced by trifluoro groups might then be explained by the lowering of CYZ. -4 reduction of a2 by 2 e.v. would reduce the charge on C.3 to near unity, but the S I -+So transition energy would bc decreased by 1 e.v. Such a shift is not observed either in the free enols or the metal complexes containing trifluoro- or hexafluoroacetylacetonate ligands. In the variable electronegativity modification of the s.c.f.method (v.e.s.c.f.), the aP and ypqare functions of the charge densities Ppp.saUtilization of this procedure generally leads to a diminution of the charge inhornogeneities without affecting the transition energies appreciably. I t is, however, unlikely that the application of the v.e.s.c.f. method to the acetylacetonate ion will lead to improved results. The effect of cyp variation has already been considered (Fig. 2 and 3). Although a more uniform charge distribution can be obtained by adjusting a,,. the resultant T + SOtransition energy will be w r y small (or negative!). T h e changes in the off-diagonal ypi, are negligible arid the diagonal ( 2 0 ) S \l,Ltaqa ancl S . 11;it;iga. Bzdl C h ~ , n .Soc. . J a p a > i ,32, R l l (10,jCJ) ( 2 1 ) S Ilatiiga a n d S . RIntaga, Z p h y s i k . C l i ~ ~ n (i F r a n k f u r t ) , 3 3 , 3 7 1 1O i i ? 1 1 2 2 %J) 'E Collm;in, Advances in Chemistry Series. X o 37, American Chemical S o c i c t y , \Vasl~ington9 . ; . I ) . C , l V B : j , p. 28. (2:3) R. I ) . 133own a n d 11 I , . Heifernan, ? v a n s . F a r a d a y S O L . ,6 4 , 757 (lKX3).
,
Vol. 80:
ypp are included in cyp. Therefore, in cases of very heteropolar a-systems the s.c.f. procedure may suffer from the same defect as the Hiickel method, v i z . , the failure to obtain good results for both transition energies arid ground-state properties. Open-Shell S.c.f. Calculations for T + So.-In the calculations described above, the excitation energies were computed by promoting an electron from a doubly occupied orbital to an empty (virtual) orbital. For singlet-singlet transitions this is the only procedure within the s.c.f. fornialism. In the case of T +- So, an alternative exists-the open-shell procedure in which the energies of the ground state (So)and excited state (T) are separately computed.?4 The T + Sc, energy corresponding to calculation I Ia determined in this way is 2.31 e.v. The agreement with experiment is poorer and the usual (closed-shell) technique appears to be preferable,
Conclusions The results indicate that the simplified version of the s.c.f. method is adequate for the determination of the transition energies and intensities. but that the calculated charge distribution may not be quantitatively reliable. The prescriptions commonly used for the determination of the s.c.f. parameters are suitable, largely due to the relative insensitivity of the s.c.i. results to the parameter choice. The s . c . ~and . Hiickel methods are in agreement in the assignment of SI + Soas q!,j -t d4,but differ in the Sp Su assignment. This transition is assigned as r$:# -+ ~ $ 5 or 42 + $13 by the Huckel method depending 011 the parameters used, while the d4 being slightly lower in s.c.f. results point to ~2 energy than +,j ---t $I~. This conclusion is of importance in the calculations of the electronic structure of metal complexes with two and three acetylacetonate ligands. In this connection it must be kept in mind t h a t while the transition energies are not very dependent 011 the parameter choice, the s.c.f. orbital energies do vary greatly with cyp. Consequently, if ligand orbitals are to be combined with metal orbitals in LCXO-\IO calculations, considerable uncertainty in ligand orbital energies must be expected. A description of the s.c.f. program Esed in this work and a FORTRAN listing of the program are available from the author. Acknowledgments.-The matrix diagonalization routine was obtained through the kindness of Dr. H . E. Simmons of the Central Research Department, Experiment Station, E. I. du Pont de Neniours Co. This work woulcl not have been possible without the programming assistance of Professor Robert Baker of the University of Arizona Sumerical Analysis Laboratory.
-
-
(24) 0.W , Adams and P G. I.ykos, J C k r i n P h y s , 3 4 , 1.144 (19633
