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Semi-empirical molecular orbital calculations on ruthenium(III) and rhodium(III) octahedral complexes
.CHEhllCAL
PHYSlCS LETTERS
1 April 1976
SEMI-EMPIRICA-L MOLECULAR ORBITAL CALCULATIONS ON RUTHENIUM(IR) AND RHODIUM(II1) OCTAHEDRAL COMPLEXES P.K. hfEHROTRA and P.T. MANOHARAN Srr~ctu& Cltetniscry Group, Departmennt of C?zemisrry, Indian Institvte of Technology. Madras 600036, Iti& Received
29 November
2975
Semi-empikl Wolfsberg-Helmholz molecular orbital (WHMO) calculations were performed on some octahedral compIcxes of second-row transition ions employing the approximations of ii) Basch and Gray and (ii) Cotton and Harris, for calctiting the valence orbital ionization potentials (VOIP’s)of the metal. A critiwl analysis indicates that the latter approximation gives better results in general. A charge dependence of the overlap was found to be necessary when the self-consisten: charges were not very close to inte@ numbers. An attemp; has also been made to interpret the optical spectra of these complexes. The rhodium complexes exhibit crystal-field bands while there is considerable overlapping of crystal-field and charge-transfer bands in the r&henium complexes.
1. Introduction
Though it is possible to do theoretically bettersounding calculations on first-row transition metal compiexes, e.g., ab initio, CNDO, INDO type calculations, it is more difficult and cumbersome to carry them out on second- and t&d-row metal complexes. One’has then to be content with simpler approximations Iike the WHMO method. Although this method has been a subject of criticism [l-3] , it has been extensively employed [4-8j to interpret the electronic spectra of transition metal complexes with reasonable success. The valence orbital ionization potentials (VOWS) or valence state ionization energies (VSIE’s) med to calculate one-electron integrals ffii hive been tabulated for the first transition series by Basch and others 191, using Moore’s atomic spectral tables [lo] . The extension of this procedure to second and third transition series becomes difficult due to insufficient atomic spectral data; Even when the VOIP’s of a few neutral atoms are obtained by unjustified approximations (like neglect of spin-orbit coupling), the charge dependence of the VOIP’s is left as a matter of trial. The charge dependence of the VOIP hr been a matter of great discussion. Cotton [l l] ; Fenske 1123 and Rds [13] have suggested a moderate dependence of the VOIP on charge (1 eV to 2 eV) and the reasons for
194
this have been well discussed by them. In caIcuIating the energy levels of PtCl$-, Basch and Gray [ 143 have subtracted 10 000 cm-1 (= 1 eV) from Ni” VOIP’s to get Pt” VOIP’s and assumed the same charge dependence as for nickel, while Cotton and Harris [35] have calculated the VOIP’s from atomic spectral terms of the metal but ahowed a l-2 eV Iinear dependence on charge. Both methods have yielded similar ordering and quite similar splittings. A better insight into the above schemes can be obtained by studying some complexes of the second and third transition series (where the VOIP’s for various metal configurations are not experimentally available) of different covalency. We lrave chosen the halide, amino and aquo complexes of Ru(II1) and Rh(II1) in order to investigate the relative merits of the two schemes for the VOIP’s and to interpret their optical spectra. The electronic spectra of Ru(III) and Rb(IIl) octahedral complexes have been reported and interpreted using qualitative molecdar orbital theory [16,17] The two d-d bands of Rh(III) complexes appearing in the visible region are assigned unambiguously as crystal field transitions from ‘Ais -+ ITI, and IT,, (terms arising from t&e: configuration). The assignments of the electronic bands from Ru(II1) complexes are more uncertain, due tp’tbe appearance of
Volume
39, nmynber 1
CHEMICAL iHY%CS LETTERS
charge transfer trtisitiom_from a l&and n-level to metal dx-orbitals in the visible region as broad bands. The spectrum of R&l%- is, however, rich in bands. The semi-empirical WHMO calculations reported here confirm the tentative assignments given earlier’[17] in .additian to making spectral assignments of Ru(III) complexes more understandable.
2- Methods Ballhausen and Gray [IS] type WHMO calculations were performed with a k-factor of 2.00. We have employed for our calculations the 4d-functions of Richardson et al. 119 ] according to the charge obtained on the metal and the Ss, Sp functions of Basch and Gray [20] given for a +l charge. For those cases where the self-consistent-charge on the metal turns out not to be close to an integral number, the overlaps of metal d-orbitals with ligand o and n-orbitals were calculated, using an A$- t Bq i C dependence of overlap on charge. The terms A, B and C were obtained by a least square fitting of the overlap of the ligand orbitals with the metal d-orbit& in different oxidation states. The bond lengths for rhodium complexes were taken from Sutton’s table [21] and were calculated for the corresponding ruthenium complexes making covalent radii corrections. o- and n-bonding were considered for the chloro complexes while only u-bonding was considered in the case of the amino and aqua complexes. figand s and p valence basis sets were used and no hybridisation was considered on the ligvld orbitals as a prior restriction. In order to overcome the difficulties experienced in calculating the VOIP’s from insufficient atomic spectral terms, two different approaches were made. In case I, the VOIl?‘s (hereafter referred to as Gray-type VOIP’s) for Ru and Rh neutral atoms were obtained by subtracting 10 000 cm-1 from those of Fee and Coo. The charge dependence of the VOIP’s was followed in a manner similar to that of Basch and Gray for the values of Fe0 and Coo. In case II (hereafter referred to as Cotton-type VOIP’s) 10 000 cm-1 was added to the VOIP’s of Fe0 and Coo to obtain the VOIP’s of Rue and Rho and a 1 eV/ unit charge dependence was used to get the VOIP’s for different charges and configurations. Since overlap is one of the factors deciding the amount of splitting we have also varied the overlap values as a function of
L.Aprii 1976
charge whenever the tilf-consistent close to integral numbers.
charges were not
3. ResuIts and discussions Table 1 lists the fmal charges on the metal, and the es-t% splitting values for RhC!I~-, Rh&O)t’ and Rh(NH&+. The calculated (tz_-e& splitting values for all the three complexes are farger uld the output charges on the metals are smaller in case I than-in case II. These differences increase with the ionicity of the complexes. This can be cleari seen from the results of Rh(NH3)g and Rh(H20)6*$ where the Gray-type VOIP gives much higher splittings (more than twice Rh(H20)F). One of the strongest criticisms of WHMO calculations is that it yields a very high covalency in metal complexes; this seemingly can be rectified using Cotton-type VOIP’s. A charge of 1.7 in Rh(H20)$ may be considered too large in the traditional WHMO calculations, but certainly not unexpected of highly ionic aquo-complexes. Ammonia has a relatively higher position in the spectrachemical series after HZO. The Gray-type VOIP’s predict the trend NH, > H,O > Cl-, but the Cotton-type VOIP’s interchange the positions of Cl- and H,O. Also, the t2g-eg separations obtained from the MO calculations cannot be compared with the IO& value of the crystal field [22] . Particularly irt view of the fact that 7rbonding is considered only for the chlorocomplex, the difference in the crystal-field trend in the second case is not surprising. It is, therefore, better justified to interpret the optical spectra by writing the transition energies in terms of A, and electron repulsion integrals J and K, taking the virtual orbitals of ground state calculations as excited orbitals. The transition enTable 1 Splitting v&es and resultant
seif-consistent
charges of
rhodium complexes FWg-
eg-tzg sepantion inkK
i;i 2$
charge on rhodium (A) (B)
. 0.398 0.462
WNH,)3,+
Rh(H20):+
48.0 37.0
46.5 17.8
0.429 0.638
0.628 1.I54
(A) Gray-type; (B) Cottw-type. 135
Volume 39, number 1
CHEMICAL PHYSICS-LEmERS
ergks for the.twG d-d bands in the singie determinantal approximation are given by the following expressions: -
6, - t?, - J(d,:! +,
es’
to: -J(d,z, >
d,,,) + =W,2
dsYJ,)*X(d,z,
_y >dx,J
dXY)= E(‘AI,
-+ lT2,).
The J and K integrals, though they are expressed here .in terms of d-orbitals, actually represent the corresponding molecular orbitals witli the dominant contributions from the said d-orbitak. From the observed first transition energy (1 A,, + 1T,,) and the calculated splitting values A, we find from i. Gray-type caiculation that the values for-J + 2K are -1.14 eV, -1.9 eV and -2.6 eV respectively for the halo, amino and aquo complexes. These values are quite large because electron repulsion corrections in LIMO calculations are generally very small {6,7,14,15] (3000 to 4000 cm-L). Also for the same transition, the Cotton-type calculstion gives the electron repulsion energies as -0.4, -0.53, +0.95 eV respectively for the three complexes in reasonable agreement with expected values. When the &If-consistent output charge on the metal for a particular complex is low, the differences between the splitting values A, obtained in the two calculations are small, but with an increase in self-consistent output metal charge, differences between the splitting values of the two calculations aIso increase. This is seen in the results of table 1. This suggests that both types of calculation would yield reasonable results for fairly covalent complexes, particularly when we have to account for both a- and -R-bonding. The two earlier calculations on PtCli- by Basch and Gray 1141 and Cotton and Harris [lS] yield more or less similar results in Agreement with this suggestion. It is worth poistitig out here that the k-factors used in these two c&&&ions are different, It is, therefore, inferred that very similar rksults can -be obtained for fairly covalent complexes by Using these two different methods and by minor adjustments of k-fac’tors. However, in com.plexes where only u-bond&g is dominant, Cotton.type calculations yield more reasonable results. This conclusion is in conformity with the resuits obtained by Cotton et al. [ll]‘ and Ros [12].
1 Apd 19j6
An interesting part of the discussion centres around ‘he optical spectra of Ru(IU) complexes. Since the op-tical spectrum of the RuCl~- complex is rich in bands, most of the discussion is based on the R&I%- cornplex. The optical spectrum of RuC@ was first published by Wgensen 1171 and Hartmann 1161 later published a better resolved one. There are four bands: the first one appearing at 20 000 cm-l with a very low-intensity (log E = 1.5) is certainly a d-d transition because of its low intensity, and is assigned to the one-electron transition (t& + t&e:). Since WHMO calculations give only the average energy of a canfiguration it is assumed that in both Gray and Cotton type calculations this transition is from 2T2,0 to one of the terms from the configuration t&e:. No attempt has been made to calculate the actual energy of this term since the electron repulsion parameters even if available are not reliable for a Ru atom for various charges. The other three bands of relatively higher intensity appear at 27 000,29 000 and 33 000 cm-l. These are charge-transfer transitions from ligand n-orbitals to the metal tzg orbital. The charge-transfer transitions either from a u-orbital to metal d-orbitals or from ligand n-orbit& to metal eg orbitals are of very high energy. There are three ligand Ir-combinations, which have tha energy ordering 2t,, <3tlu < I&, as shown in table 2. The three transitions observed can be assigned as charge-transfer transitions from these three levels to the metal t29 level. The excited states involving 2tIu and 3tlU levels belong to the same symmetry viz. 2T1U and hence configuration interaction is expected. The calculated energy differences between the metal t.+ orbital and the 1tzu, 3tlu and 2tlU levels are 28 0’00 cm-l, 32 000 cm-l and 34 000 cm-* by the Cotton-type method. Because of configuration interaction, one of the T,, terms will be pushed down while another term will be pushed up. The transitions at 27 000 cm-l and the other at 33 000 cm-l can be assigned as transitions from the two tlu levels with electron repulsion adjustment. The third transition at 29 000 cm-l is assigned as being from ltZu to 2tsg. The calculated energy differences between the two Ievels is 28 000 cm-l, quite close to the measured 29 000 cm-l. The same assignment can be given to results of the Gray-type method but the fit is better for the Cotton-type method without explicitly taking electron rep&ion parameters into account. Further, the k-factor C& al-
Volume 39, number 1
.CHEMICAL PHYSICS LE’l-PERS
_
Table 2 Orbital energies (in kK1 of a few relevant molecular orbit& Ru&
1 April 1976
ec- tag separation, and self-consistent charge of ruthenium complexes
Ru(NH&+
Ru(HlO);+
(A)
(B)
(A)
(B)
(A)
(B)
3%
- 54.1
2tzg
- 86.7 -108.3
- 53.6 - 80.6 -108.7
- 42.7 - 86.7 -106.6
- 49.2 - 88.7 -108.2
- 79.8 -125.1 -
-68.2 -86.2
-111.8 -113.8
-112.4 -114.3
-109.6 -129.9
-110.1 -127.8
-
1t2lJ
3t1,
2tzu
es-‘2s separation charge on Ru
32.6 0.439
27.0
44.0
0.610
0.450
39.5 0.858
45.3 0.672
_
18.0
1.857
(A) Gray-type; (B) Cotton-type.
ways be varied to adjust the actual differences. Qualitative interpretation given earlier for these assignments is further confirmed by these calculations. The complex Ru(NH3)F gives just one broad band appearing at 36 OaO cm-t - The intensity of this band again being high suggests its charge-transfer nature. Because of its broadness one may even suspect it as the combination of both a charge-transfer transition and a d-d transition. The Cotton-type VOIP gives 39 000 cm-l as the tzg-eg splitting. Since only o-bonding is considered, the n-orbitals of NH3 are non-bonding. Charge-transfer transitions from ligand o-orbitals to metal d-orbitals are certainly ruled out because of their higher energy. Hence the charge transfer transitions are from non-bon&g ligand n-orbit& to metal t2s orbitals. Further because the ligand-ligand overlap in the hexamine complex is smaller than that in the hexachloro complex, these non-bonding ligand n-orbitals will be more or less degenerate in the case of the earlier complex. Hence, a broad band will be made up of various charge transfer tran‘sitions of ligand n-orbitals to the metal tzs orbital. Looking at the broad band of Ru(NH~)~C~~ as published by Hartmann 1161, there appears a shoulder at 30 000 cm-r of reIatively low intensity. Cotton-type VOWS giive the tzg-eg splitting around 39 000 cm-l. So we believe that the shoulder at 30 000 cm-l must be due to a crystal-field transition from the ground state t& configuration to the lowest energy term of the excited state configuration t&e:; the transitions due to the rest of the terms must have been masked by the
intense charge transfer transition. A Basch-type calculation will also lead to a similar as+gnment. There is some uncertainty in the published optical spectrum [16] of Ru(H,O)z* as to the nature of the species in solution and h&ce no attempt has been made to interpret the optical spectra of Ru(H20)F. The charge on the metal obtained from the Cottontype calculation of ~Ru(H20)~ is +1-S, much larger than the charge of i-O.63 obtained from a Gray-type calculation. This further confirms that Gray-type VOIP’s give rise to too much covalency.
Acknowledgement One of us (PKM) thanks the Council of Scientific and Industrial Research, India, for a research fellowship.
References [l] F.A. Cotton, Rev. Pure Appl. Chem. 16 (1966) 175. [2) J.P. Dahl and C.J. Ballhausen, Advan. Quantum Chem. 4 (1967) 170. [ 3) D.k Brown, W.J. Chambers and N.J. Fitzpatrick, Inorg. Chim. Acta RCV. 7 (1972). [4) hf. Wolfsberg and L Helmholz, J. Chem. Phys. 20 (1952) 837. IS] C-J. BaBhausen and H.B. Gr%y, Inorg. Chem. 1 (1962) 111. (61 A. Viste and H-B. Gray, Inorg. Chem. 3 (1964) 1113.
197
‘-Vdu~tifi39, numkr 1 .: . ;.-, ,.
._-,
6HEMICALPHYSlCS
LEflEtiS. .
‘[i’] P.T.
&fatioha& and H.B; Gray, J. Am:Cheti. Sot. 87 : ._(1965) 3340. ,[S] M. Zernei, M:Couterman ~nd’Ii. Kqbay#i, Theoret. ‘. Chim.Acta 6 (1965) 363. ’ 19j H; Basch,‘A. Viste and H.B. Gr;iy, Theoret. &him. Acta 3 (1965) 458; T. Anno and V. Sakai, Theoret. Chim. Acta 18 (1970) 208. [ipi C.E Moore, Atomic Energy Ltivels.~US Nat&al Bureau .of Standards Circular 467 (US Govt; Printing Office, Washitigton, 1949, 1952). [Ill F.A. Cotton 2nd T.E. Haas, Inorg. Chem. 3 (1964) 1004. .[?2] R.F. Fenske, 5-G. Caulton, D.D,Radtke and CC. Sweeney, Inorg. Chem. 5 (i966) 964. -[f3] P. Ros and G.C.&.Schuit,Theoret. Chim. kcta 4 (1966) 1.
. .
114) ff.Basch :nd H.B. Gray, &IO=. &em. 6 (1967; 3651 [IS] F.A. Cotton and C.B. Harris, Idor& Chem. 6 (1967) 369. [16J H. Ha~t~~nn and C. Bushbeck, 2. Physik. Chem. NF ll(19.57) 120. 11.71 C.Ki JQrgensen, Acta Chem. Stand. 10 (1956).518. fl!] C-J. Ballhausen and H.B. Gray, iMolecular oibita! theory (Benjamin. New York, 1965). 1191 3.W. Richa&on, MJ. Blackti and J.E. Raaodhak, J. Chem. phys 58.(1973) 3010. 1201 H. Basch and H.B. Gray, Theoret. Chim. Acfa 4 (1966)
367.
121.1Tables of Inte&omic
Distance and Configurations in Molecules and Ions, Special Publication No. 11 (The Chemical Society, London. 1956). [ 22) J.P. Dti and C.J. B~lllwsen, Advan. Quantum Chem. 4(1967)170.
ERRATA. W. van Megen and I. Snook, A hard sphere model for order-disorder
transitions
in colloidal
dispersions,
Chem. Phys. Letters 35 (1975) 399. Line 4 of table 1 should read, 5
x 10-l 1.08
7
35-5010
and line 4 of table 2 should 5 X IO-’
1.30(f)
2.28 (f)
(1.15)
(1.72)
43?;
4.30 (f) (3.01)
triplet,
Eq. (41 should read -
Q2~OH+R%+$2~OH+R’H.
39%
read,
M.R. Topp, Activation-controlled by bcnzophenone (1975) 144.
1 April 1976.
-
8.86 (0 (6.20)
19.8(s)
(11.62)
hydrogen abstraction Chem. Phys. Letters 32
PHYSlCS LETTERS
1 April 1976
SEMI-EMPIRICA-L MOLECULAR ORBITAL CALCULATIONS ON RUTHENIUM(IR) AND RHODIUM(II1) OCTAHEDRAL COMPLEXES P.K. hfEHROTRA and P.T. MANOHARAN Srr~ctu& Cltetniscry Group, Departmennt of C?zemisrry, Indian Institvte of Technology. Madras 600036, Iti& Received
29 November
2975
Semi-empikl Wolfsberg-Helmholz molecular orbital (WHMO) calculations were performed on some octahedral compIcxes of second-row transition ions employing the approximations of ii) Basch and Gray and (ii) Cotton and Harris, for calctiting the valence orbital ionization potentials (VOIP’s)of the metal. A critiwl analysis indicates that the latter approximation gives better results in general. A charge dependence of the overlap was found to be necessary when the self-consisten: charges were not very close to inte@ numbers. An attemp; has also been made to interpret the optical spectra of these complexes. The rhodium complexes exhibit crystal-field bands while there is considerable overlapping of crystal-field and charge-transfer bands in the r&henium complexes.
1. Introduction
Though it is possible to do theoretically bettersounding calculations on first-row transition metal compiexes, e.g., ab initio, CNDO, INDO type calculations, it is more difficult and cumbersome to carry them out on second- and t&d-row metal complexes. One’has then to be content with simpler approximations Iike the WHMO method. Although this method has been a subject of criticism [l-3] , it has been extensively employed [4-8j to interpret the electronic spectra of transition metal complexes with reasonable success. The valence orbital ionization potentials (VOWS) or valence state ionization energies (VSIE’s) med to calculate one-electron integrals ffii hive been tabulated for the first transition series by Basch and others 191, using Moore’s atomic spectral tables [lo] . The extension of this procedure to second and third transition series becomes difficult due to insufficient atomic spectral data; Even when the VOIP’s of a few neutral atoms are obtained by unjustified approximations (like neglect of spin-orbit coupling), the charge dependence of the VOIP’s is left as a matter of trial. The charge dependence of the VOIP hr been a matter of great discussion. Cotton [l l] ; Fenske 1123 and Rds [13] have suggested a moderate dependence of the VOIP on charge (1 eV to 2 eV) and the reasons for
194
this have been well discussed by them. In caIcuIating the energy levels of PtCl$-, Basch and Gray [ 143 have subtracted 10 000 cm-1 (= 1 eV) from Ni” VOIP’s to get Pt” VOIP’s and assumed the same charge dependence as for nickel, while Cotton and Harris [35] have calculated the VOIP’s from atomic spectral terms of the metal but ahowed a l-2 eV Iinear dependence on charge. Both methods have yielded similar ordering and quite similar splittings. A better insight into the above schemes can be obtained by studying some complexes of the second and third transition series (where the VOIP’s for various metal configurations are not experimentally available) of different covalency. We lrave chosen the halide, amino and aquo complexes of Ru(II1) and Rh(II1) in order to investigate the relative merits of the two schemes for the VOIP’s and to interpret their optical spectra. The electronic spectra of Ru(III) and Rb(IIl) octahedral complexes have been reported and interpreted using qualitative molecdar orbital theory [16,17] The two d-d bands of Rh(III) complexes appearing in the visible region are assigned unambiguously as crystal field transitions from ‘Ais -+ ITI, and IT,, (terms arising from t&e: configuration). The assignments of the electronic bands from Ru(II1) complexes are more uncertain, due tp’tbe appearance of
Volume
39, nmynber 1
CHEMICAL iHY%CS LETTERS
charge transfer trtisitiom_from a l&and n-level to metal dx-orbitals in the visible region as broad bands. The spectrum of R&l%- is, however, rich in bands. The semi-empirical WHMO calculations reported here confirm the tentative assignments given earlier’[17] in .additian to making spectral assignments of Ru(III) complexes more understandable.
2- Methods Ballhausen and Gray [IS] type WHMO calculations were performed with a k-factor of 2.00. We have employed for our calculations the 4d-functions of Richardson et al. 119 ] according to the charge obtained on the metal and the Ss, Sp functions of Basch and Gray [20] given for a +l charge. For those cases where the self-consistent-charge on the metal turns out not to be close to an integral number, the overlaps of metal d-orbitals with ligand o and n-orbitals were calculated, using an A$- t Bq i C dependence of overlap on charge. The terms A, B and C were obtained by a least square fitting of the overlap of the ligand orbitals with the metal d-orbit& in different oxidation states. The bond lengths for rhodium complexes were taken from Sutton’s table [21] and were calculated for the corresponding ruthenium complexes making covalent radii corrections. o- and n-bonding were considered for the chloro complexes while only u-bonding was considered in the case of the amino and aqua complexes. figand s and p valence basis sets were used and no hybridisation was considered on the ligvld orbitals as a prior restriction. In order to overcome the difficulties experienced in calculating the VOIP’s from insufficient atomic spectral terms, two different approaches were made. In case I, the VOIl?‘s (hereafter referred to as Gray-type VOIP’s) for Ru and Rh neutral atoms were obtained by subtracting 10 000 cm-1 from those of Fee and Coo. The charge dependence of the VOIP’s was followed in a manner similar to that of Basch and Gray for the values of Fe0 and Coo. In case II (hereafter referred to as Cotton-type VOIP’s) 10 000 cm-1 was added to the VOIP’s of Fe0 and Coo to obtain the VOIP’s of Rue and Rho and a 1 eV/ unit charge dependence was used to get the VOIP’s for different charges and configurations. Since overlap is one of the factors deciding the amount of splitting we have also varied the overlap values as a function of
L.Aprii 1976
charge whenever the tilf-consistent close to integral numbers.
charges were not
3. ResuIts and discussions Table 1 lists the fmal charges on the metal, and the es-t% splitting values for RhC!I~-, Rh&O)t’ and Rh(NH&+. The calculated (tz_-e& splitting values for all the three complexes are farger uld the output charges on the metals are smaller in case I than-in case II. These differences increase with the ionicity of the complexes. This can be cleari seen from the results of Rh(NH3)g and Rh(H20)6*$ where the Gray-type VOIP gives much higher splittings (more than twice Rh(H20)F). One of the strongest criticisms of WHMO calculations is that it yields a very high covalency in metal complexes; this seemingly can be rectified using Cotton-type VOIP’s. A charge of 1.7 in Rh(H20)$ may be considered too large in the traditional WHMO calculations, but certainly not unexpected of highly ionic aquo-complexes. Ammonia has a relatively higher position in the spectrachemical series after HZO. The Gray-type VOIP’s predict the trend NH, > H,O > Cl-, but the Cotton-type VOIP’s interchange the positions of Cl- and H,O. Also, the t2g-eg separations obtained from the MO calculations cannot be compared with the IO& value of the crystal field [22] . Particularly irt view of the fact that 7rbonding is considered only for the chlorocomplex, the difference in the crystal-field trend in the second case is not surprising. It is, therefore, better justified to interpret the optical spectra by writing the transition energies in terms of A, and electron repulsion integrals J and K, taking the virtual orbitals of ground state calculations as excited orbitals. The transition enTable 1 Splitting v&es and resultant
seif-consistent
charges of
rhodium complexes FWg-
eg-tzg sepantion inkK
i;i 2$
charge on rhodium (A) (B)
. 0.398 0.462
WNH,)3,+
Rh(H20):+
48.0 37.0
46.5 17.8
0.429 0.638
0.628 1.I54
(A) Gray-type; (B) Cottw-type. 135
Volume 39, number 1
CHEMICAL PHYSICS-LEmERS
ergks for the.twG d-d bands in the singie determinantal approximation are given by the following expressions: -
6, - t?, - J(d,:! +,
es’
to: -J(d,z, >
d,,,) + =W,2
dsYJ,)*X(d,z,
_y >dx,J
dXY)= E(‘AI,
-+ lT2,).
The J and K integrals, though they are expressed here .in terms of d-orbitals, actually represent the corresponding molecular orbitals witli the dominant contributions from the said d-orbitak. From the observed first transition energy (1 A,, + 1T,,) and the calculated splitting values A, we find from i. Gray-type caiculation that the values for-J + 2K are -1.14 eV, -1.9 eV and -2.6 eV respectively for the halo, amino and aquo complexes. These values are quite large because electron repulsion corrections in LIMO calculations are generally very small {6,7,14,15] (3000 to 4000 cm-L). Also for the same transition, the Cotton-type calculstion gives the electron repulsion energies as -0.4, -0.53, +0.95 eV respectively for the three complexes in reasonable agreement with expected values. When the &If-consistent output charge on the metal for a particular complex is low, the differences between the splitting values A, obtained in the two calculations are small, but with an increase in self-consistent output metal charge, differences between the splitting values of the two calculations aIso increase. This is seen in the results of table 1. This suggests that both types of calculation would yield reasonable results for fairly covalent complexes, particularly when we have to account for both a- and -R-bonding. The two earlier calculations on PtCli- by Basch and Gray 1141 and Cotton and Harris [lS] yield more or less similar results in Agreement with this suggestion. It is worth poistitig out here that the k-factors used in these two c&&&ions are different, It is, therefore, inferred that very similar rksults can -be obtained for fairly covalent complexes by Using these two different methods and by minor adjustments of k-fac’tors. However, in com.plexes where only u-bond&g is dominant, Cotton.type calculations yield more reasonable results. This conclusion is in conformity with the resuits obtained by Cotton et al. [ll]‘ and Ros [12].
1 Apd 19j6
An interesting part of the discussion centres around ‘he optical spectra of Ru(IU) complexes. Since the op-tical spectrum of the RuCl~- complex is rich in bands, most of the discussion is based on the R&I%- cornplex. The optical spectrum of RuC@ was first published by Wgensen 1171 and Hartmann 1161 later published a better resolved one. There are four bands: the first one appearing at 20 000 cm-l with a very low-intensity (log E = 1.5) is certainly a d-d transition because of its low intensity, and is assigned to the one-electron transition (t& + t&e:). Since WHMO calculations give only the average energy of a canfiguration it is assumed that in both Gray and Cotton type calculations this transition is from 2T2,0 to one of the terms from the configuration t&e:. No attempt has been made to calculate the actual energy of this term since the electron repulsion parameters even if available are not reliable for a Ru atom for various charges. The other three bands of relatively higher intensity appear at 27 000,29 000 and 33 000 cm-l. These are charge-transfer transitions from ligand n-orbitals to the metal tzg orbital. The charge-transfer transitions either from a u-orbital to metal d-orbitals or from ligand n-orbit& to metal eg orbitals are of very high energy. There are three ligand Ir-combinations, which have tha energy ordering 2t,, <3tlu < I&, as shown in table 2. The three transitions observed can be assigned as charge-transfer transitions from these three levels to the metal t29 level. The excited states involving 2tIu and 3tlU levels belong to the same symmetry viz. 2T1U and hence configuration interaction is expected. The calculated energy differences between the metal t.+ orbital and the 1tzu, 3tlu and 2tlU levels are 28 0’00 cm-l, 32 000 cm-l and 34 000 cm-* by the Cotton-type method. Because of configuration interaction, one of the T,, terms will be pushed down while another term will be pushed up. The transitions at 27 000 cm-l and the other at 33 000 cm-l can be assigned as transitions from the two tlu levels with electron repulsion adjustment. The third transition at 29 000 cm-l is assigned as being from ltZu to 2tsg. The calculated energy differences between the two Ievels is 28 000 cm-l, quite close to the measured 29 000 cm-l. The same assignment can be given to results of the Gray-type method but the fit is better for the Cotton-type method without explicitly taking electron rep&ion parameters into account. Further, the k-factor C& al-
Volume 39, number 1
.CHEMICAL PHYSICS LE’l-PERS
_
Table 2 Orbital energies (in kK1 of a few relevant molecular orbit& Ru&
1 April 1976
ec- tag separation, and self-consistent charge of ruthenium complexes
Ru(NH&+
Ru(HlO);+
(A)
(B)
(A)
(B)
(A)
(B)
3%
- 54.1
2tzg
- 86.7 -108.3
- 53.6 - 80.6 -108.7
- 42.7 - 86.7 -106.6
- 49.2 - 88.7 -108.2
- 79.8 -125.1 -
-68.2 -86.2
-111.8 -113.8
-112.4 -114.3
-109.6 -129.9
-110.1 -127.8
-
1t2lJ
3t1,
2tzu
es-‘2s separation charge on Ru
32.6 0.439
27.0
44.0
0.610
0.450
39.5 0.858
45.3 0.672
_
18.0
1.857
(A) Gray-type; (B) Cotton-type.
ways be varied to adjust the actual differences. Qualitative interpretation given earlier for these assignments is further confirmed by these calculations. The complex Ru(NH3)F gives just one broad band appearing at 36 OaO cm-t - The intensity of this band again being high suggests its charge-transfer nature. Because of its broadness one may even suspect it as the combination of both a charge-transfer transition and a d-d transition. The Cotton-type VOIP gives 39 000 cm-l as the tzg-eg splitting. Since only o-bonding is considered, the n-orbitals of NH3 are non-bonding. Charge-transfer transitions from ligand o-orbitals to metal d-orbitals are certainly ruled out because of their higher energy. Hence the charge transfer transitions are from non-bon&g ligand n-orbit& to metal t2s orbitals. Further because the ligand-ligand overlap in the hexamine complex is smaller than that in the hexachloro complex, these non-bonding ligand n-orbitals will be more or less degenerate in the case of the earlier complex. Hence, a broad band will be made up of various charge transfer tran‘sitions of ligand n-orbitals to the metal tzs orbital. Looking at the broad band of Ru(NH~)~C~~ as published by Hartmann 1161, there appears a shoulder at 30 000 cm-r of reIatively low intensity. Cotton-type VOWS giive the tzg-eg splitting around 39 000 cm-l. So we believe that the shoulder at 30 000 cm-l must be due to a crystal-field transition from the ground state t& configuration to the lowest energy term of the excited state configuration t&e:; the transitions due to the rest of the terms must have been masked by the
intense charge transfer transition. A Basch-type calculation will also lead to a similar as+gnment. There is some uncertainty in the published optical spectrum [16] of Ru(H,O)z* as to the nature of the species in solution and h&ce no attempt has been made to interpret the optical spectra of Ru(H20)F. The charge on the metal obtained from the Cottontype calculation of ~Ru(H20)~ is +1-S, much larger than the charge of i-O.63 obtained from a Gray-type calculation. This further confirms that Gray-type VOIP’s give rise to too much covalency.
Acknowledgement One of us (PKM) thanks the Council of Scientific and Industrial Research, India, for a research fellowship.
References [l] F.A. Cotton, Rev. Pure Appl. Chem. 16 (1966) 175. [2) J.P. Dahl and C.J. Ballhausen, Advan. Quantum Chem. 4 (1967) 170. [ 3) D.k Brown, W.J. Chambers and N.J. Fitzpatrick, Inorg. Chim. Acta RCV. 7 (1972). [4) hf. Wolfsberg and L Helmholz, J. Chem. Phys. 20 (1952) 837. IS] C-J. BaBhausen and H.B. Gr%y, Inorg. Chem. 1 (1962) 111. (61 A. Viste and H-B. Gray, Inorg. Chem. 3 (1964) 1113.
197
‘-Vdu~tifi39, numkr 1 .: . ;.-, ,.
._-,
6HEMICALPHYSlCS
LEflEtiS. .
‘[i’] P.T.
&fatioha& and H.B; Gray, J. Am:Cheti. Sot. 87 : ._(1965) 3340. ,[S] M. Zernei, M:Couterman ~nd’Ii. Kqbay#i, Theoret. ‘. Chim.Acta 6 (1965) 363. ’ 19j H; Basch,‘A. Viste and H.B. Gr;iy, Theoret. &him. Acta 3 (1965) 458; T. Anno and V. Sakai, Theoret. Chim. Acta 18 (1970) 208. [ipi C.E Moore, Atomic Energy Ltivels.~US Nat&al Bureau .of Standards Circular 467 (US Govt; Printing Office, Washitigton, 1949, 1952). [Ill F.A. Cotton 2nd T.E. Haas, Inorg. Chem. 3 (1964) 1004. .[?2] R.F. Fenske, 5-G. Caulton, D.D,Radtke and CC. Sweeney, Inorg. Chem. 5 (i966) 964. -[f3] P. Ros and G.C.&.Schuit,Theoret. Chim. kcta 4 (1966) 1.
. .
114) ff.Basch :nd H.B. Gray, &IO=. &em. 6 (1967; 3651 [IS] F.A. Cotton and C.B. Harris, Idor& Chem. 6 (1967) 369. [16J H. Ha~t~~nn and C. Bushbeck, 2. Physik. Chem. NF ll(19.57) 120. 11.71 C.Ki JQrgensen, Acta Chem. Stand. 10 (1956).518. fl!] C-J. Ballhausen and H.B. Gray, iMolecular oibita! theory (Benjamin. New York, 1965). 1191 3.W. Richa&on, MJ. Blackti and J.E. Raaodhak, J. Chem. phys 58.(1973) 3010. 1201 H. Basch and H.B. Gray, Theoret. Chim. Acfa 4 (1966)
367.
121.1Tables of Inte&omic
Distance and Configurations in Molecules and Ions, Special Publication No. 11 (The Chemical Society, London. 1956). [ 22) J.P. Dti and C.J. B~lllwsen, Advan. Quantum Chem. 4(1967)170.
ERRATA. W. van Megen and I. Snook, A hard sphere model for order-disorder
transitions
in colloidal
dispersions,
Chem. Phys. Letters 35 (1975) 399. Line 4 of table 1 should read, 5
x 10-l 1.08
7
35-5010
and line 4 of table 2 should 5 X IO-’
1.30(f)
2.28 (f)
(1.15)
(1.72)
43?;
4.30 (f) (3.01)
triplet,
Eq. (41 should read -
Q2~OH+R%+$2~OH+R’H.
39%
read,
M.R. Topp, Activation-controlled by bcnzophenone (1975) 144.
1 April 1976.
-
8.86 (0 (6.20)
19.8(s)
(11.62)
hydrogen abstraction Chem. Phys. Letters 32