Systematic ab initio study of the ligand field spectra of

Nov 1, 1993 - Carl Ribbing, Kristine Pierloot, and Arnout Ceulemans. Inorganic Chemistry 1998 37 (20), 5227-5232. Abstract | Full Text HTML | PDF | PD...
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J . Phys. Chem. 1993, 97, 12220-12228

12220

Systematic ab Initio Study of the Ligand Field Spectra of Hexacyanometalate Complexes K. Pierloot,' E. Van Praet, and L. G. Vanquickenborne Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B- 3001 Heverlee- Leuven, Belgium

B. 0. Roos Department of Theoretical Chemistry, Chemical Centre, P.O. Box 124, S-221 00 Lund, Sweden Received: July 12, 1993'

The ground and ligand field excited states of the first-row hexacyanometalate complexes V(CN)&, Cr(CN)&, Mn(CN)a3-qb, Fe(CN)a3-v4, and Co(CN)a3- have been studied using the complete active space (CAS) selfconsistent field (SCF) method and a second-order perturbation approach (CASPT2), which applies the CASSCF wave function as a reference, It is shown that the major features of the electronic structure of both the ground state and the excited states are properly described by a CASSCF wave function based on an active space of the 10 orbitals directly involved in the metal-cyanide bonding: the 2t2, and 6e, orbitals with mainly metal 3d character and their ligand counterparts 3t2,(CNrS) and Se,(CNa). Remaining correlation effects are dealt with in the second, CASPT2, step. Two sets of CASPT2 calculations were performed. In the first set, the metal 3d and C and N 2s, 2p valence electrons are correlated, while the second set also includes the metal 3s, 3p core electrons. The final CASPT2 excitation energies are in excellent agreement with the experimental excitation energies for the d3 and d6 systems. The theoretical results have also been used to judge between different experimental assignments for Mn(CN)b3- and Fe(CN),j3- and to predict the position of the ligand field transitions in Mn(CN)&.

1. Introduction

In spite of the fact that cyanide acting as amonodentate ligand always appears to have carbon as the donor atom, metal cyanide complexes are generally not considered to be organometallics. Their properties are indeed more akin to Werner complexes: they do not, in general, obey the 18-electron rule, and their central metal ion usually has a high (+2,+3) formal oxidation number.' Yet, CN- is closely related to the isoelectronicC O ligand, its next neighbor at the strong-field end of the spectrochemical seriesS2 They both form covalent bonds with the metal, acting both as a u-donor (CN- more than CO) and a *-acceptor (CO more than CN-). Due to their high values of lODq, the d d transitions in their electronic spectra often occur at wavelengths comparable to those of charge-transfer bands with much higher intensities. The exact observation and assignment of the ligand field transitions is therefore much more difficult for complex cyanides and carbonyls than for many other complexes. These transitions do however play a very important role in photosubstitutionreactions. Both cyanide and carbonyl compounds exhibit a very rich photochemi~try,~.~ and it is now widely believed that the ligand field states are thestates responsible for efficient photosubstitution, even when they are hidden by strong charge-transfer transitions. Cyanide forms hexacoordinated complexes with transition metals with a formal d 3 4 occupation.' The first-row hexacyanometalate(I1) and -(III) ions form a classic series, whose electronic spectra have been extensively studied in the past, both in solution and in the solid state. An assignment of both the d d and charge-transfer transitions was reported in 1968 by Alexander and Gray.5 Since then, somedoubts have been raised concerning their assignment of the ligand field bands for M I I ( C N ) ~ ~ - and Fe(CN)63-,8 but textbooks on inorganic spectroscopy9 usually still refer to the Alexander and Gray paper. Up to now, efforts to predict the spectra of large organometallics using ab initio techniques have been rather scarce.1° Selfconsistent field (SCF) and limited configuration interaction (CI) calculations on the cyanides, although valuable for a qualitative

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*Abstract published in Aduance ACS Abstracts. October 15, 1993.

0022-3654/93/2097-12220$04.00/0

understanding of the metal-ligand bonding, have proven to be inadequate when it comes to obtaining accurate excitation energies, leading to errors of 1 eV and more.ll.12 More accurate estimates of excitation energies, based on (externally contracted) CI calculations with a complete active space SCF (CASSCF) reference wave function, have been reported for a number of carbonyl systems like Fe(CO)5, HzFe(C0)4, HCo(C0)4, and HMn(CO)5.I3 Thesecalculations seem to yield theoretical results which are probably accurate to within 0.5 eV.Io CASSCF/MRCI calculations should in principle be able to yield very accurate theoretical excitation energies. However, due to the size of the systems under consideration, severe restrictions have to be imposed in order to keep the size of the CI expansion within a manageable limit. In the first place, one is faced with the problem of the size of the reference space. Very often a rather crude selection of reference configurations has to be made from which the single and double replacement states are constructed. This may seriously impair the accuracy due to a loss of balance in the correlation treatment of different states. A second restriction concerns the number of correlated electrons. Ideally, one would like to include at least all valence electrons in the CI treatment. Again however, this would lead to very lengthy CI expansions, and in practice one is forced to limit the number of correlated electrons to the metal 3d electrons and, if possible, a selected number of ligand valence electrons. The second-order perturbation (CASPT2) method14J5 used in the present study does not suffer from these restrictions. Like the CASSCF/MRCI method, it is based on a CASSCF wave function, incorporating the most important nondynamical correlation effects. The remaining correlationeffects are now treated using second-order perturbation theory, where the CASSCF wave function is used as the zero-order approximation. As opposed to MRCI, no selection of reference configurations has to be made: CASPT2 uses the full CASSCFspace as a reference. The method is also not limited by the number of correlated electrons. We will present in this study the results of calculations correlating up to 74 electrons. The CASSCF/CASPT2 approach has recently been applied with considerable success in studies of the excited states of the 0 1993 American Chemical Society

The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12221

Ligand Fields of Hexacyanometalate Complexes

TABLE I: Averaged Experimental M-C and C-N Bond LenPtbs Used in the Calculations crvstal

mean mean r(M-C) (A) (r(C-N) (A) ref 2.16 2.08 1.98 1.95 1.95 1.92 1.93 1.91 1.90

1.15 1.14 1.15 1.16 1.14 1.15 1.17 1.17 1.15

18 19 20 21 22 23 24 21 22

nickel atomI6 and a large number of organic molecule^.^^ In all cases an accuracy of approximately 0.3 eV or less is obtained. In the present study we will show that a similar accuracy can also be obtained for the d d transitions in large transition metal systems. We will present results for the hexacyano complexes of the ions V(II), Cr(III), Mn(II,III), Fe(II,III), and Co(II1).

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2. Details of the Calculations Hexacyano complexes of the first-row transition metals are found in a variety of crystal surroundings with different space groups, of which the potassium salts are the best known. In most cases, the site symmetry of the metal is not perfectly octahedral. Although M-C-N bonds are generally linear and C-M-C bonds rectangular, variations in the M-C bond lengths can be quite significant. Yet, the experimental assignments of the spectra are always based on a purely octahedral symmetry. Therefore we decided to do all calculations using average experimental bond distances, as shown in Table I. Furthermore, all calculations were performed on the isolated anions, neglecting environmental effects. Although it is fairly straightforward to incorporate the effect of the surrounding crystal by embedding the anion in a Madelung potential;25 such a procedure would lead in the present case to a substantial reduction of the symmetry, making the calculations much more demanding. Experimental studies of the absorption and diffuse reflectance ~pectra2~.*~ of hexacyanoferrate(I1) and -(III) in different crystals have shown that their spectra are indeed to some extent dependent on the counter ions. For both iron complexes, the spectrum was therefore calculated a t two distances, corresponding to the experimental distance in two different crystals. In this way we hope to catch a glimpse of the effect of the surrounding crystal on the transition energies. The basis sets used in this work are of the generally contracted A N 0 (atomic natural orbital) type. The starting primitive sets are 17s12p9d4f for the metal and 10s6p3d for C and N. The ANO’s were constructed by averaging over several atomic states positive and negative ions.Z8 They were contracted to the following final structure: 5s4p3dlf for the metal and 3s2pld for C and N, yielding a total of 207 contracted functions. The spectra of all considered molecules were calculated using the same computational method, consisting of two major steps. First, all states are individually optimized in a CASSCF calculation. The choice of the CASSCF active space will be considered in more detail in the next section. Here we only mention that it consists of 10 molecular orbitals: the metal 3d orbitals, contained in 2t2,(d,) and 6e,(d.), and the corresponding bonding 5e,(CNu) and antibonding 3tze(CNr*) orbitals. The number of electrons correlated in the CASSCF step varies from 7 in the d3 systems to 10 in the d6 systems. The number of configurations included ranges from 2300 to 7450. Remaining correlation effects are dealt with in a second, CASPT2 step,l4J5 where the CASSCF wave function constitutes the reference function. The CASPT2 methodcomputes the firstorder wave function and the second-order energy in the full space of configurations generated by the basis set. The zero-order Hamiltonian is constructed from a Fock-type one-electron

operator that reduces to the Mprller-Plesset HartreeFock operator for a closed-shell case. In all calculations the so-called “nondiagonal” approach has been used; that is, the full Fock matrix (including the nondiagonal elements) is used in the construction of the zero-order Hamiltonian. For each state, two CASPT2 calculations were performed, differing only by the number of correlated electrons. In a first calculation, denoted as CASPTZ(v), all valence electrons, originating from the metal 3d and the C and N 2s, 2p orbitals arecorrelated, while thesecond calculation, denoted as CASPT2(c-v), includes also the metal core 3s and 3p electrons. The size of the first-order interacting space is roughly 2 293 800 in the former case and 2 807 300 in the latter. A final set of CASPT2 results, CASPT2(a), was obtained by adding to the CASSCF energy that part of the correlation energy originating from the active-active terms in the first-order wave function. These results should serve as an indication as to how far an accurate description of the spectra can be obtained by including in the dynamical correlation treatment only a limited number of valence electrons, that is, the metal 3d and C N u electrons which are active in the CASSCF treatment. In the case of MII(CN)~~-, a second set of calculations was performed, with an extended CASSCF active space, including now alsothe lt2,(CNr) shell. With anactivespaceof 13 orbitals; the size of the CASSCF CI space is drastically raised to up to 322 203, and the CASPT2 calculations are getting much more demanding. Only the CASPTZ(v) calculation was performed in this case; the 3s,3p correlation correction was taken from the 10 orbital active space calculation. All calculations were done using Dzh symmetry, with additional symmetry restrictions in the CASSCF step to prevent mixing between molecular orbitals originating from a different Oh representation. For degenerate states however, deviations from octahedral symmetry can still occur, since no additional equivalence restrictions between different octahedral subrepresentations were imposed. Finally, we will also present the results of a set of test calculations on the spectra of the atomic ions V2+ and Cr3+. The calculations are intended to check the adequacy of the metal basis set to describe (3s,3p) correlation effects. A comparison is made between the transition energies obtained with the 5s4p3d 1f basis sets and with an extended 9s7p6dlf set, obtained by uncontracting functions in the core-valence region. The calculations have been performed with the MOLCAS-2 quantum chemistry s ~ f w a r e ?either ~ on an IBM RS6000/550 workstation or on an IBM 3090-600VF. It may be of interest to mention some timing data. The CPU time needed (both on IBM RS6000and on IBM 3090) for thecalculation oftheintegrals is 147 min. The CASSCF calculations are on the whole readily convergent (5-30 iterations, depending on the starting orbitals), taking less than 1 CPU min/iteration with 10 orbitals active, and about 5 min with 13 active orbitals. As for the CASPT2 calculations, CPU times between 30 and 80 min were noted for the calculations based on a 10 orbital active space, while the largest calculation with 13 active orbitals took 11.7 CPU h. 3. Metal-Cyanide Bonding and the Choice of the Active Space

Since carbon-bonded cyanide lies at the strong-field end of the spectrochemical series, it is the ligand most likely to produce low-spin complexes, and all six coordinate systems considered here have a ground state corresponding to a maximum occupation of the 2t&dr) shell. The bonding arises mainly from u-donation from the carbon lone pairs into the formally empty 3d, orbitals, counteracted to some extent by r-back-donation from the filled 3d, orbitals into the C N r * orbitals. The importance of both bonding types in the different molecules can most easily be exemplified by their metal 3d, and 3d, populations, presented in

Pierloot et al.

12222 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993

TABLE 11: Ground-State Metal 3d Orbital Populations. SCF and CASSCF Results SCF compound

CASSCF

difference

state

3d,

3d.

3d.

3d.

3d.

3d.

4A2g(d3) 4A28(d3) 'Tlg(d4) *T2,(ds) 2Tzg(ds) 'Al,(d6) 'Al,(d6) 'Al,(d6)

0.823 1.182 1.338 1.083 1.394 1.092 1.490 0.924

3.060 3.190 4.190 4.952 5.1 11 5.899 6.061 4.831

0.939 1.346 1.585 1.382 1.698 1.465 1.839 1.096

2.992 3.154 4.099 4.732 4.985 5.619 5.912 4.601

0.116 0.164 0.247 0.299 0.304 0.373 0.349 0.172

-0.068 -0,036 -0.091 -0.220 -0.126 -0.280 -0.149 -0.230

TABLE III: CASSCF Natural Orbital Occupation Numbers for the Ground State and a Selected Number of Excited States compound state 5e.(CNa) 6en(3d,) 2t2.(3d.) 3t2,(CNr*)

ar(Fe-C) = 1.95 A; r(C-N) = 1.14 A. br(Fe-C) = 1.91 A; r(C-N)

= 1.17 A.

Table 11. The table includes the Hartree-Fock values as a reference as well as the results of a CASSCF calculation with an active space consisting of the 10 orbitals describing the metalcyanide interaction: 6e, and 2t2,, with predominantly metal 3d character, and their ligand counterparts 5e,(CNu) and 3 t ~ (CNr*). Due to the extended nature of the basis sets used in this study, the absolute figures in Table I1 are of no relevance. In fact the Hartree-Fock values are somewhat misleading, in that they indicate CN- as a *-donor instead of a *-acceptor in the trivalent complexes: the 3d, population is in all cases larger than the formal 3d occupation number. A previous Hartree-Fock study by Sano et al.30 performed with a smaller basis sets, resulted in considerably lower populations for both 3d, and 3d,. Yet the general trends in Table I1 are the same as observed by Sano. Within a series of complexes with constant oxidation number, both u-donation and ?r-back-donation become more extensive with increasing formal 3d occupation number, though the effect is certainly smaller for r than for u. Apart from the 3d occupation number, the formal charge on the metal also plays a crucial role: as can be expected on purely electrostatic grounds, cyanide behaves a much better a-donor and a much poorer x-acceptor in the trivalent than in the divalent complexes. We have also added in Table I1 the results of a ground-state calculation on Cr(C0)6. The Cr 3d, and 3d, population in this molecule nicely illustrate the stronger a-accepting and weaker u-donating property of CO, as compared to CN- in the isoelectronic Fe(I1) and Co(II1) hexacyano complexes. Although the populations in Table I1 should be used with caution, they confirm a general observation made in a number of studies on various transition metal systems like CrF63-,25 MnOd-," and Fe(CO)3.3Z The introduction of correlation induces a shift of electron density from the ligands to the metal in the u oribtals and a concomitant opposite shift in the A orbitals, thus increasing both the covalency of the u-bonding and x-backbonding. The results in Table I1 also indicate that nondynamical correlation effects are becoming more important as the inherent covalency of the metal-ligand bonding increases: thecorrelationinduced electron density shifts are increasing drastically when going from Cr(1II) to Co(II1) and from V(I1) to Fe(I1). This observation can of course be traced back to the nature of the CASSCF wave function. Apart from the Hartree-Fock reference, the most important CASSCF contributions are of the typeCNu2- 3dU2,3drZ+CNx** and CNd3d,l- 3d,lCN**', leading to the observed flux of electron density. In Table 111 we have collected the occupation numbers of the active orbitals in the CASSCF wave function of the ground state and a selected number of excited states in the different molecules. The groundstate natural orbital occupation numbers again reflect the growing Hartree-Fock defect as the bonding gets more covalent. Apart from the generally increasing occupation number of the correlating orbitals 6e, and 3tzg with an increasing formal 3d occupation number, we notice for example that wcorrelation effects are significantly more important and u-correlation effects less

CO(CN)63Cr(C0)6

5T2; 'Ai, 'TI, 5T2e 'AI,

3.983 3.915 3.939 3.975 3.958

0.025 1.012 0.053 1.029 0.082 1.049 0.076 1.042 2.009 0.104 1.063 2.012 0.081 1.050 2.016 0.099 1.006 2.021 0.049

2.955 1.976 2.971 1.984 3.933 2.969 4.863 3.910 2.972 4.907 3.950 2.985 5.853 4.892 3.925 5.905 4.936 3.970 5.764

0.045 0.026 0.029 0.018 0.056 0.03 1 0.117 0.086 0.029 0.068 0.046 0.016 0.130 0.102 0.076 0.081 0.059 0.034 0.230

a r(Fe-C) = 1.95 A; r(C-N) = 1.14 A. r(Fe-C) = 1.91 A; r(C-N) = 1.17 A.

important for the divalent than for the trivalent complexes, in accordance with the observed trends in the bonding. Notice also that the 3tzg(CO**) population is significantly higher in Cr(CO)6 than the 3tzg(CNr*) population in any of the cyano complexes, while the 6e,(COu) occupation number is relatively low. This is consistent with the fact that CO is the stronger *-acceptor and the weaker a-donor. The trends in Table 111areindicative of thedifficulty oftreating organometallics, characterized by strongly covalent bonds, with single-reference based methods. Werner complexes are characterized by much more ionic metal-ligand bonds and should be much easier to handle in this respect. A typical example is CrF&. In a previous study3' we haveshown that a quantitativedescription of the spectrum of this ion can be obtained in CASSCF/MRCI calculations based on a small reference space, including only the Cr3d orbitals. The cyanides considered in the present study are situated on the borderline between both fields, with bonds becoming more covalent when moving from the left to the right in the periodic table. It is clear that if we want to treat all systems under consideration on an equal footing, a multireference treatment based on the presently considered CASSCF space is the only possible way to proceed. This is the more true since we are interested in electronic transitions between orbitals that are both directly involved in the metal-ligand bonding. Table 111gives additional information regarding the correlation contributions to the CASSCF wave function of the different excited states. In each case we have included one of the excited states corresponding to a single 2t2, 6e, excitation (the lowest state with the same spin multiplicity as the ground state). For the d5 and d6 systems, we have also added the lowest doubly excited state. The sequence of numbers for the different states exhibits the same general trend for all molecules. In all cases, the occupation number of the 3tzs(CNr*) correlating orbitals decreases with a decreasing number of 2tz8(3d,) electrons. At the same time, the increasing population of the antibonding 6e,(3d,) orbitals inhibits the 5e, 6e, excitations, thus resulting in an increased Se,(CNa) occupation number. As a consequence, nondynamical correlation effects tend to get less important as more electrons are moved from the bonding 2t2, shell into the antibonding 6e, shell. The sequence of numbers in Table 111 thus offers an explanation for the well-known fact that HartreeFock invariably tends to underestimate seriously the value of the ligand field strength in the consideredIlJ2 and otherj4 transition metal systems. It also illustrates again the need for a multireference treatment in order to obtain an accurate description of the ligand field transitions.

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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12223

Ligand Fields of Hexacyanometalate Complexes

TABLE I V Ground-State CASSCF and CASPT2 Energies (hartrees), with 10 Active Orbitls [Se,(CNa), 6e8(3d,), 2tz8(3d,), 3t~g(CNr*)I compound ground state CASSCF CASPTZ(v) W d CASPT~(C-V) WC-V" 4A~, 4A2, 'TI, 'Tz~ 'Tz~ 'AI, 'AI, 'A18

V(CNhC Cr(CN)63Mn(CN)s3Mn(CN)& Fe(CN)63Fe(CN)& e CO(CN)& Cr(C0)6

-1496.578 -1597.306 -1703.706 -1703.346 -1816.357 -1816.033 -1935.380 -1720.028

80 97 13 29 97 71 88 78

-1498.335 -1599.065 -1705.533 -1705.201 -1818.203 -1817.933 -1937.281 -1722.026

11 89 21 75 34 41 23 48

0.578 0.585 0.574 0.571 0.578 0.568 0.574 0.585

-1498.566 -1599.305 -1705.773 -1705.442 -1818.441 -1818.171 -1937.509

56 03 05 42 94 23 15

0.562 0.568 0.562 0.558 0.567 0.557 0.565

Weight of the CASSCF wave function in the first-order wave function. br(Fe-C) = 1.95 A; r(C-N) = 1.14 A. Cr(Fe-C) = 1.91 A;r(C-N) =

1.17 A.

TABLE V CASSCF and CASPT2 Excitation Energies (eV) for V(CN)& transition CASSCF CASPT2(a) CASPTZ(v) W"a 'E8

'TI, 'T2g 4T2g 4T~g(a) 4TI ,( b) a

1.50 1.59 2.25 3.15 4.13 6.44

1.41 1.49 2.05 2.97 3.80 6.07

1.23 1.31 1.74 3.04 3.75 6.06

0.576 0.575 0.573 0.574 0.572 0.570

1.12 1.22 1.64 3.04 3.64 6.07

wc-va

expt36

0.559 0.559 0.557 0.558 0.556 0.555

2.78 3.53 5.88

Weight of the CASSCF wave function in the first-order wave function.

TABLE VI: CASSCF and CASPTZ Excitation Energies (eV) for Cr(CN)6* transition CASSCF CASPT2(a) CASPT2(v) WY" 'E, 'TI, 'Tz~ 4T~, 4T~,(a) 4T~g(b) a

CASPT~(C-V)

2.15 2.24 3.24 3.71 4.75 7.67

2.08 2.18 3.03 3.51 4.45 7.31

1.94 2.01 2.76 3.62 4.43 7.32

0.583 0.582 0.580 0.584 0.582 0.581

CASPT2( C-V) 1.77 1.85 2.56 3.64 4.30 7.35

wc-va

0.567 0.567 0.565 0.569 0.567 0.567

expts.35 1.54 1.62 2.28 3.31 4.06 >6.20

Weight of the CASSCF wave function in the first-order wave function.

Finally one can wonder whether all important nondynamical correlation effects are indeed included in a CASSCF calculation with only 10 active orbitals, and if we should in fact not have included more valence orbitals. An obvious candidate is the 1t2,( C N r ) shell. In order to check its importance we have performed a test calculation on Cr(CN)63-, including now in the active space the lt2g shell instead of 3t2, (which is not very important in this case anyway). The resulting natural orbital occupation of 1t2, is 5.999 for the 4A2, ground state and 5.996 for the 4Tzgexcited state. For Mn(CN)b3-we will present the results of theexcitation energies, calculated with an active space including the lt2, shell. But also in this case its importance is only minor, with an occupation number ranging from 5.996 in the 3T1, ground state to 5.993 in the 3E, excited state. An additional argument for the adequacy of the CASSCF space used comes from the weightsof the CASSCF wave function in the final CASPTZ first-order wave function. In Table IV the ground-state energies calculated with the different methods and the corresponding weights are presented. This weight gives a measure of how large a fraction of the wave function is treated variationally in the CASSCF calculation and how much is treated by perturbation theory. The weights in Table IV are all rather low, which is obviously caused by the large number (up to 74) of electrons included in the CASPTZ treatment. But they are about the same in all cases, indicating that the CASSCF space used is large enough to give a balanced treatment of all considered molecules. We have again added Cr(C0)6 for comparison, and we notice that the weight is practically the same in this case too, indicating again the strong similarity of CO and CN-as transition metal ligands. It may be ofinterest to mention that an estimateof a reasonable weight, w , of the CASSCF reference in the final first-order wave function can be obtained from the simple formula: w = (1 + x)-N/2 where Nis the number of electrons included in the CASPT2 treatment and x is a small number (0.015-0.020) measuring the

weight of a single double excitation. Note that the weight goes to zero with an increasing number N of correlated electrons, consistent with the fact that CASPTZ is a size-consistent method. The weights of the excited states of the cyanides will be presented in the next section. We will then be able to show that the CASSCF space presented in this section is indeed capable of producing a balanced treatment of all ligand field states, resulting in very accurate CASPT2 excitation energies.

4. Results and Discussion 4.1. d3 Systems V(CN)6C and Cr(CN)6*. Of all the cyanide systems studied, the spectra of the d3 systems are undoubtedly characterized by the simplest structure. In this case, the ligand field exerted by CN- is not as strong as for the other metals, and most of the ligand field transitions are well separated from the charge-transfer bands. The ground state 4A2, corresponds to a 2tzr3configuration, and the d d transitions can be subdivided into two groups: the spin-forbidden intraconfigurational transitions within the 2t283 manifold 4A2r 2E,, 2T1,, and 2T2g, appearing as very weak bands at the low-energy tail of the visible region, and the slightly more intense spin-allowed interconfigurational transitions 4A2s 4T2g,4Tl,(a), and 4T18(b), corresponding to a single or double 2t2, versus 6e, excitation. The calculated CASSCF and CASPT2 excitation energies for both molecules are presented in Tables V and VI, together with the available experimental information. The spectrum of Cr(CN)63- is well-established, and experimental band positions have been reported both in solution and in host crystal l a t t i c e ~ . ~ J ~ V(CN)64 is less stable, and its solution spectrum has only been reported on one occasion.36 The tables also include the weight, w, of the CASSCF reference function in the total first-order wave function of the different states. The weights are practically equal

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Pierloot et al.

12224 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 for all states. This shows that the essential features of the electronic structure of the different ligand field states are indeed included in the CASSCF active space introduced in the previous section. A clear distinction can also be made in the way the two different groups of transitions are affected by correlation, and we will therefore discuss them separately. Spin-Allowed Interconfigurational Transitions. Of the three spin-allowed transitions, only the lowest transition to 4T2,can be assigned unequivocally as a single 2t2,- 6e, transition. In ligand field terms, its transition energy exactly corresponds to the value ofthe 1ODqparameter. Ofthe t ~ o ~ T ~ , s t a t e s , ~ T lcorrespond ,(a) to a single and 4Tl,(b) to a double 2t2, 6e, transition a t the HartreeFock level, but the introduction of correlation results in considerable mixing between them. The quartet-quartet transitions in Tables V and VI are systematically overestimated a t the CASSCF level. For the lODq transition, the error is about 0.4 eV for both molecules. This is opposed to the HartreeFock situation, where the corresponding transition for Cr(CN)63- is calculated about 0.45 eV too low.11 The CASSCF error for the 4A2r 4 T ~transitions , is even higher: up to 0.7 eV. Obviously, CASSCF tends to overemphasize the occupation of the antibonding 3t2, and 6e, orbitals (Table 111) and the differential effect on configurations with a different 6e, occupation number. Thus it leads to an artificial stabilization of the ground state. The situation is remedied completely by including only the active electrons in a dynamical correlation treatment: the excitation energies are lowered considerably in the CASPT2(a) calculation, and, except for the 4Tl,(a) state, correlating more electrons does not lead to any further improvement. The 4A2,-4T2g and 4A2g-4Tl,(b) excitation energies are even slightly raised at the CASPTZ(v) level, while being virtually unaffected by correlation of the metal core electrons. The remaining errors a t the CASPT2(c-v) level are slightly higher for Cr(CN)63- than for V(CN)6', with a maximum error of 0.33 eV for the 4A2g 4T2, transition. Spin-Forbidden Intraconfigurational Transitions. The quartet-doublet excitation energies are again overestimated by up to 1.0 eV at the CASSCF level. Since no 2t2, 6e, excitation is involved in this case, the origin of the CASSCF error must be of a different nature. By not accounting adequately for the differential Pauli correlation effects, the quartet d3 state is favored over the doublet states. In this case, a definite improvement of the results can only be obtained at the expense of correlating all cyanide valence electrons as well as the metal core electrons. The final CASPT2(c-v) excitation energies for Cr(CN)63- are very satisfactory, with all errors falling below 0.3 eV. At this stage it is necessary to check whether the rather limited metal basis set used in the present study is indeed capable of capturing the main core-valence correlation effects included in the CASPT2(c-v) calculations. The general A N 0 contraction scheme, although optimal for the description of valence correlation effects, only produces a minimal number of contracted functions in the core-valence region. Normally, in correlated calculations including the core electrons, one would enlarge the basis set by uncontracting the primitive Gaussians with the appropriate exponents. Since this procedure would lead here to a prohibitively large total number of basis functions, we decided to perform some test calculations on the lowest excited states of the atomic ions V(I1) and Cr(III), both with the 5s4p3dlf basis set and with an enlarged 9s7p6dlf set. The d3 ions V(I1) and Cr(II1) are the most suitable candidates for such a test. Indeed, only in the d3 case do the lowest ligand field states in the molecules correspond to the lowest atomic ion states. Due to the strength of the cyanide ligand field the molecular ground state is achieved by a single spin-flip in the d4 system MII(CN)~~and by a double spin-flip in the d5 and d6 systems, making the correspondence between the molecular and ionic states rather obscure.

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-

-

TABLE VII: CASSCF and CASPT2 Excitation Ener (eV) for the Atomic Ions V*+and Cr3+, with the 3d O r E l s Active transition CASSCF CASPTZ(v)'

w* CASPT2(c-v)

w-b

expP7J8

V2+,Basis 5s4p3dlf ,F+'P 4F+2G

1.81 1.82

1.63 1.66

4F+4P 4F+2G

1.82 1.84

1.63 1.65

4F-.4P 'F-.2G 4F+4P 4F+2G

0.990 0.986

1.35 1.40

0.949 0.945

1.40 1.46

1.33 1.37

0.943 0.939

1.40 1.46

2.17 2.19

Cr3+, Basis 5s4p3dlf 2.02 0.994 1.84 2.10 0.995 1.96

0.958 0.958

1.71 1.81

2.18 2.21

2.04 2.10

0.952 0.952

1.71 1.81

V*+,Basis 9s7p6dl f 0.990 0.986

Cr3+,Basis 9s7p6dlf 0.995 0.995

1.83 1.95

a CASPTZ(v) = CASPT2(a) for the atomic ions. Weight of the CASSCF wave function in the first-order wave function.

In the d3 case the lowest ionic states 4F, 4P, and 2G are split as follows by the octahedral field:

4F

-

4A2, + 4T2, + 4Tlg

4P

'G

-

-

*E,+ 'TI,

4T,,

+ 'T,, + 'A,,

Therefore, the various transitions in the spectra of the cyanides correspond to only two transitions in the free ion. The calculated excitation energies, and their experimental ~ a l u e s , ~ are ~ J *presented in Table VII. Only the 3d orbitals were included in the active space of these calculations, resulting in only one, ROHF, reference state in each case. Both the 4F-2G and the 4F-4P excitation energies are grossly overestimated at the CASSCF level and are gradually improved in the CASPTZ(v) and CASPT2(c-v) calculations. But the results are hardly affected by the modification of the basis set. The reference weight, in the CASPT(c-V) wave function is very slightly lower for the enlarged basis set, indicating that more correlation is included in the CASPT2(c-v) treatment, but both states are equally affected, so that their energy difference does not change. Overall, the 5s4p3dlf basis set seems to be well capable of describing core-valence correlation effects, both in the atomic ions and in the molecules. The agreement between the resulting CASPT2(c-v) and the experimental excitation energies in V(I1) and Cr(II1) is excellent, bearing in mind that the present CASPT2 approach is based on a single-reference R O H F wave function. 4.2. d4 MII(CN)~%.The Mn(CN),j3- ion is the only d4 hexacyano complex considered in this study. Cr(CN)& is unstable with respect to oxidation,' and its spectrum has not been reported. Thecalculated excitation energies for Mn(CN)6%with the 10 orbital active space and the experimental band positions are presented in Table VIII. Apart from the 3T1,ground state, the t284 configuration gives rise to the three singlet states ITzS, IE,, and IAl,, while5E,and3Egare thelowest states corresponding to t2,3egl. As one can see from the experimental results in Table VIII, the situation concerning the ligand field spectrum of Mn(CN)& is rather confused. In the early work by Alexander and Gray,s performed in aqueous 1.5 M KCN solution, a very weak band was observed a t 2.60 eV, which was assigned as the "1, 'AI, transition. Another parity-forbidden transition appearing at 4.1 1 eV, was tentatively, assigned as 3TI, 3Eg. The lowest spinforbidden 3Tlg ITz,, 'E, transitions at 1.30 eV could not be detected in aqueous solution. Instead, they were taken over from

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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12225

Ligand Fields of Hexacyanometalate Complexes

TABLE VIII: CASSCF and CASFTZ Excitation Energies (eV) for Mn(CNh* with 10 Active Orbitals ...

transition IT28

CASSCF

CASPT2(a)

CASPTZ(v)

W""

1.48 1.60 3.09 1.72 4.12

1.52 1.49 2.83 1.48 3.41

1.37 1.26 2.42 1.54 3.44

0.573 0.557 0.504 0.571 0.534

'E, 'AIS

'E, 0

CASPT~(C-V) 1.25 0.97 2.13 1.44 3.17

w&'

ref 5

ref 6

ref 7

0.560 0.544 0.493 0.558 0.522

1.30 1.30 2.60

1.55 1.67 3.00 1.49 3.34

0.99 1.08 2.29

4.11

2.57

Weight of the CASSCF wave function in the first-order wave function.

TABLE I X CASSCF and CASFTZ Excitation Energies (eV) for Mn(CN)6*, with 13 Active Orbitals transition IT28 IE*

'AI,

'E, 'E, 0

CASSCF

CASPTZ(v)

wy"

1.44 1.56 2.98 1.71 4.08

1.33 1.44 2.44 1.57 3.61

0.574 0.574 0.570 0.573 0.570

CASPTZ(c-v)

ref 5

1.21 1.15 2.15 1.47 3.34

1.30 1.30 2.60 4.41

expt ref 6 1.55 1.67 3.00 1.49 3.34

ref 7 0.99 1.08 2.29 2.57

Weight of the CASSCF wave function in the first-order wave function. Core-valence correlation correction taken from Table VIII.

earlier w0rk3~on a red crystal of K3[Mn(CN)6]. Later, however, it was suggested that M ~ I ( C N )undergoes ~~extensive hydrolysis in basic media. A fresh, acidic solution of the product revealed a new band at 3.34 eV and a weak shoulder a t 3.00 eV, assigned as 3T1, 'E, and 3T1, IAl,, respectively.6 The band at 2.60 eV is again observed, only more intense, and it is assigned as a Itl, 2t2, (L M) charge-transfer transition. This study also reports a series of weak maxima in the near-IR region, assigned as spin-forbidden transitions to *T2,, IE,, and 5Eg. The most recent spectral analysis7 was performed on single crystals of K3[Mn(CN)6]. The3T1,-. ITz,, lE,transitionsarenowobserved at a much longer wavelength. The main difference between this and the earlier work is that the band appearing around 2.60 eV is now assigned as the spin-allowed transition to 3Eg, with a new shoulder appearing at 2.29 eV as 3Tl, IAl,. The different assignment of the 3T1g 'E, transition in the different studies goes together with a thoroughly different assessment of the ligand field parameter 1ODq. The first estimate of lODq in MII(CN)~~was made by Ballhausen.2 From the expected trend in the Dq values of Cr(CN)b3- < M I I ( C N ) ~ ~ CASFT2(a) wya CASSCF transition CASPT2(v)

TI^

3.46 4.05 4.44 5.62 5.86

3.90 4.55 4.91 6.30 6.55

CASPT2(c-v)

wC-va

3.14 3.63 3.98 4.80 5.58

0.559 0.557 0.558 0.554 0.555

0.569 0.561 0.567 0.564 0.565

3.38 3.89 4.23 5.22 5.89

'TI, IT21 'Tg 0 Weight of the CASSCF wave function in the first-order wave function.

expt'C2 3.22 4.03 4.86

TABLE XI: CASSCF and CASPT2 Excittion Energies (eV) for Fe(CN)sC. (A) r(Fe-C) = 1.93 A; r(C-N) = 1.17 A. (B) r(Fe-C) 1.91 A; r(C-N) = 1.17 A CASSCF CASPT2(a) CASPTZ(v) CASPT~(C-V) expt transition A B A B A B wv" A B wwa ref 5 ref 21

TI^

3.31

3.57

2.93

3.12

2.91

3.10

0.564

2.61

2.85

0.552

2.94

3.33 0.551 0.563 3.14 3.52 3.71 3.42 3.60 4.21 4.02 3T2g 3.77 0.551 0.562 3.60 4.13 3.85 4.02 4.56 3.95 4.38 'TI, 0.549 4.33 4.49 5.23 4.77 4.92 0.560 5.07 5.13 5.90 lT2g 4.30 4.10 0.550 5.01 0.562 4.49 4.89 4.62 5.60 5.20 'T2g a Weight of the CASSCF wave function in the first-order wave function, for r(Fe-C) = 1.93 8, and r(C-N) = 1.17 A.

3.84 4.59

3.80-3.94 4.43417

TABLE XII: CASSCF and CASPT2 Excitation Energies (eV) for Fe(CN)6s. (A) r(Fe-C) = 1.95 A; r(C-N) = 1.14 A. (B) 1.92 A; r(C-N) = 1.15 A 4Fe-C) CASSCF CASPT2(a) CASPTZ(v) CASPT~(C-V) expt transition A B A B A B a"" A B wwa ref 5 ref8 'TI, 2.42 2.17 2.08 2.44 2.09 2.43 0.514 1.93 2.28 0.563 2.23 ___

2T~g 2A2, 2Ea

a

3.09 4.09 4.31 4.94 3.33

3.44 4.41 4.10 5.25 4.06

2.12 3.10 3.94 4.43 2.90

3.07 4.02 4.29 4.76 3.61

2.62 3.52 3.73 4.11 3.14

2.96 3.83 4.09 4.46 3.83

0.512 0.571 0.501 0.554 0.573

2.42 3.31 3.38 3.72 2.99

2.76 3.62 3.74 4.1 1 3.68

0.560 0.561 0.491 0.542 0.561

6AIg Weight of the CASSCF wave function in the first-order wave function, for r(Fe-C) = 1.95 A and r(C-N) = 1.14 A.

TABLE XIII: CASSCF and CASPT2 Excitation Energies (eV) for Mn(CN)& transition CASSCF CASPT2(a) CAsPTZ(v) %a 'TI, 2.13 2.45 2.39 0.511 'T2, 3.33 3.01 2.88 0.567 2A2g 4.19 3.85 3.60 0.556 2TIg 4.21 3.98 3.78 0.564 4.63

2Ea

4.23

3.91

4.08 3.63 3.79 6AIg 0 Weight of the CASSCF wave function in the first-order wave function.

-

Alexander and Gray at 3.86 and 4.55 eV, respectively. On the other hand, if it is a Laporte-forbidden Itl, 2tzgtransition, as assumed by Chawla,6 we would have expected the 'E, state associated with this transition to interfere in the CASPT2 calculation on the nearby 'E, ligand field state. A definite answer to this question can only be obtained by including the 1tl, orbitals in the CASSCF active space. 4.3. d5 and d6 Systems Mn(CN)&, Fe(CN)>, Fe(CN)6&, and Co(CN)6>. The ligand field absorption spectra of the d5 and d6 cyanides show an analogous structure, and we will consider them together in this section. In both cases only one state arises from the ground-state configuration 2t~gS.~: in the d6 systems the 2t2, shell is completely filled, giving rise to a 'AI, ground state, while the hole in the 2t2, level gives the d5 complexes a 2T28 ground state. Thus the spectrum mainly consists of interconfigurational 2t2, 6e, transitions. The high-spin state, corresponding to a double 2tze versus 6e, excitation, 5T2, for d6 and 6A1, for d5, is also expected to fall into the UV-visible region, but it has only been observed on one occasion in ferricyanide.8 We have included this state in the calculations on the four complexes. The calculated CASSCF/CASPT2 excitation energies and the available experimental results for the four molecules are shown in Tables X-XIII. The spectra of the d6 complexes CO(CN)~'(Table X) and Fe(CN)& (Table XI) are very simple and wellunderstood.s.40 The 2tZg56e,lconfiguration gives rise to only four terms: 3T18,'Tz,, lTl,, and ITzg,all situated well-below the first

-

0.552 0.563

CASPT~(C-V) 2.22 2.67 3.27 3.57 3.59 3.61

3.87 3.87 4.43

3.69 3.14 4.12 3.34

wc-vLI

expt5

0.558 0.554 0.543 0.551 0.542 0.550

3.39 3.39

-

M L charge-transfer state. The d5 spectra are definitely more complex. The dimension of the 2t2:6es1 configuration space is 60, resulting in 10 group theoretical states. Therefore, both complexes might be expected to have very rich d-d spectra, if it were not that the d-d bands are obscured by much more intense L M charge-transfer transitions, filling up the hole in the 2t2, shell. The spectrum of the ferricyanide ion has been intensively studied, and conflicting assignments of the lowest spin-allowed transitions have been reported (Table XII). The extreme sensitivity to oxidation of Mn(CN)& has obstructed a detailed analysis of its ligand field spectrum, so that only the lowest spinallowed transitions to 2Tlg,2A28have been assigned in this case (Table XIII). A first look at the calculated results in Tables X-XI11 shows that the CASSCF reference weights for the different excited states are again very stable. With one exception (the 2A2, state in Fe(CN)63-) the fluctuations in the weights are never larger than 0.02, thus indicating that the 10 orbital active space is large enough to include all essential electronic structure features even for the most covalent cyano complexes considered in this work. This does not mean of course that the CASSCF method by itself should give reliable results for the excitation energies. Indeed one can see that all CASSCF excitation energies are again much too high, with errors amounting up to 1.4 eV for the 'AI, IT2, transition in C O ( C N ) ~ ~It- . is worth noting for example that the error on the first spin-allowed 2tzg+ 6e, transition is much higher

-

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Ligand Fields of Hexacyanometalate Complexes for C O ( C N ) ~(0.88 ~ - eV; Table X) than for Cr(CN)63- (0.40 eV; Table VI). The corresponding HartreeFock errors are almost exactly opposite: -0.95 eV for Co(CN)63- 12 and -0.45 eV for Cr(CN)63-.11 This typically illustrates how CASSCF tends to overemphasize the occupation of the antibonding orbitals (Table 111) and the corresponding electron density shifts (Table II), leading to bonds that are too covalent and a corresponding ligand field that is too strong. As for the d3 complexes, this CASSCF behavior is already to a large extent corrected for by a perturbation treatment including only the active electrons. The CASFT2(a) excitation energies in Tables X-XI11 represent a considerable improvement over the CASSCF results for all transitions. The contribution of the remaining valence electrons to the differential correlation energy is much smaller. We also notice that this contribution is negative for all 2t2, 4.56e,1states, but positive for the high-spin 2t2, 3v46e,2 state. Apparently, dynamic correlation of the valence electrons still contributes to some extent in the description of the differential Pauli correlation between a high- and low-spin dn state. This is in fact the only feature of the molecular spectra still reminding us of the free ion situation. Correlation of the metal 39,3pelectrons strongly lowers the excitation energies in all cases, even for the doubly excited high-spin states. The reduction can be quite substantial: up to 0.4 eV for the ‘A1,-lT2, transition energy in Co(CN)63- and Fe(CN)&. It is clear that correlation of the metal core electrons cannot be neglected if one wants to obtain an accurate description of the ligand field spectra of the d5 and d6 hexacyano complexes. It may be somewhat surprising to see that the effect of 3s, 3p correlation is so important even for the heavier transition metal systems. It is known43that in the transition metal atoms the importance of 3s. 3p correlation for the energy separation between states with a different number of 3d electrons decreases with increasing atomic number. A detailed analysis of the role of 3 p 3 d correlation effects on the 3d-3d transitions in the metal ions will be presented in a separate study.44 We will show there that, even if the specific 3 p 3 d part of the correlation energy decreases with an increasing number of 3d electrons, the size of the combined core-core and core-valence contributions is on the average of the same order of magnitude for all first-row transition metal ions. The quality of the final CASPT2(c-v) results is remarkable. For Co(CN)& (TableX), thecalculated excitation energies agree with the experimental values to within 0.1 eV. The error is in each case slightly negative, implying that the splitting of the different 2t2,56eg1states is described even more accurately. The same remark holds for theiron systems Fe(CN)64and Fe(CN)6%. If we compare the two different sets of CASPT2(c-v) results in Tables XI and XII, we notice that the results obtained with the smallest Fe-C distance in both cases are generally in considerably better agreement with experiment. Yet, the relative energies of the different 2t284s6eB1states are hardly dependent on the bond distance. They agree to within 0.05 eV with the experimental splitting reported by Alexander and Gray5 for Fe(CN)& and to within 0.1 5 eV with the more recent experimental results* for Fe(CN)63-. We consider this as a very strong argument in favor of the latter assignment, which is based on absorption and magnetic circular dichroism spectra of F~(CN),S~-, in two host lattices (KCl and poly(methy1 methacrylate)). As for Mn(CN)& (Table XIII), the available experimental information is in fact too limited to help in evaluating our calculated results. Both the calculated 2T2g-2A2g and 2T28-2T1g transition energies are in good agreement (less than 0.2 eV) with the only reported band at 3.39 eV. We are confident however that the predicted splitting of the 2t2,56eg1states is very accurate in this case, too, as it is for the other three molecules. Finally we note the extreme dependence of the calculated excitation energies for Fe(CN)64- and Fe(CN)63- on the F e C

The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12221 bond distance. A shortening of this distance by 0.03 A results in a uniform upward shift with as much as 0.3 eV of all singly excited states in Fe(CN)6>. For Fe(CN)6” the shift is smaller, about 0.2 eV, in accordancewith the fact that the distancevariation is also smaller, 0.02 A for this molecule. The doubly excited high-spin state however is shifted about twice as much in both cases: 0.6 eV in Fe(CN)& and 0.4 eV in Fe(CN)&. In order to make sure that it is really the Fe-C bond distance that is important, and not the C-N distance (which was also varied by 0.01 A in Fe(CN)63-), we repeated the calculation of the 2T28 2T18transition with a Fe-C bond distance of 1.92 A and a C-N distance of 1.14 A; the result did not differ significantly from the result reported for r(Fe-C) = 1.92 A and r(C-N) = 1.15 A. The shifts are obviously connected to the strong u-donating powerofCN-in thedSandd6systems. Owing totheu-antibonding nature of the 6e8(3d,) orbitals, the equilibrium geometries of the excited states associated with a 2t2g4.56eglconfiguration can be expected to differ considerably from the ground-state geometry, as a consequence of enlargements of the metal-cyanide bonds in the excited states. A quantitative estimate of this effect has been obtained from the3T1,- IA1,emission wavelength in CO(CN)~>. The ‘AI, ’T1, transition in this molecule is characterized by a very large Stokes shift (1.36 eV4I). The excited state is most probably tetragonally Jahn-Teller with Co-C bonds that are approximately 0.1 A longer than in the ground state.45 An even larger geometrical distortion can be expected for a double 2tzg 6e, transition. As a consequence, the d- d absorption bands must necessarily be very broad, and the large shifts of thevertical transition energies with a varying Fe-C distance in the iron complexes nicely illustrate this fact. The shifts are not due to a variation of the ground-state energies; an optimization of the Fe-C bond distance (keeping the C-N distance fixed at 1.14 8, for Fe(CN)63- and 1.17 A for Fe(CN)&) yields a value that is intermediate between the two distances used in the calculation of the spectra: 1.942 1% for Fe(CN)63- and 1.927 8, for Fe(CN)& (at the CASPT2(c-v) level). Rather they reflect the large slope in the excited-state potential energy curves at the ground-state geometry. As can be expected, this slope is virtually equal for the different singly excited states, while it is about twice as large for the doubly excited high-spin state. One can now wonder whether there is any connection between the calculated variations of the excitation energies with the Fe-C bond distance and the experimentally observed variations between different crystals.26J7 Table XI (last column) shows the range of values observed for the spin-allowed transitions in different crystals of ferrocyanide. One can see that the variations (0.150.45 eV) are of the same order as the calculated differences, using the bond distances of two different crystals. For ferricyanide, analogous variations of the band positions have been reported, but no definite assignment of the bands was given. However, the experimentally observed variations can only be explained if one may assume that, apart from the ground-state equilibrium geometry, the relative position of the excited-state and ground-state potential energy curves is also altered by the different crystal environments. While this hypothesis does not seem unlikely, a more definite answer can only be obtained after recalculating the spectra using different embedding potentials.

-

-

-

5. Summary and Conclusions

The present contribution has demonstrated that it is possible to obtain very accurate ligand field excitation energies in the considered hexacyano complexes using second-order perturbation theory based on a CASSCF wave function. The presented results are accurate to within 0.35 eV in all cases where reliable experimental results are available. An even higher accuracy (less than 0.15 eV) is obtained for the relative energies of the different singly excited states in the d5 and d6 systems. The method has

Pierloot et al.

12228 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993

also been used to judge between different experimental assignments in problematic cases like Mn(CN)6)- and Fe(CN)&, and to predict the position of the d d transitions in the unstable Mn(CN)6’. The success of the present approach mainly depends on the choice of the CASSCF active space. A prerequisite for a loworder perturbation treatment to work well is that the dominant electronic configurations are already included in the reference wave function. We have shown that a CASSCF space of 10 orbitals, consistingof the bonding and antibonding combinations of the metal 3d and the cyanide Q and T* valence orbitals, is capable of describingthe main features of the electronic structure in the considered series, ranging from the rather ionic d3 to the much more covalent d6 hexacyano complexes. This active space is large enough to produce a balanced treatment of the ligand field states in all cases. However, the inclusion of dynamic correlation in the second CASPTZ step is essential for an accurate description of the spectra. It is shown that in most cases the number of correlated electrons cannot be limited to the valence electrons already included in the CASSCF treatment. Correlation of the remaining valence electrons, and, more important, the metal 3s, 3p electrons, is essential for the description of the spin-forbidden transitions in the d3 and d4 systems, and for all transitions in the d5 and d6 systems. In this respect, the present approach represents a valid alternative for the CASSCF/MRCI method, which is bound to meet serious limitations concerning the number of correlated electrons and the selection of the reference space. For the first time, it has been possible to obtain an accurate treatment of the spectra of a systematic series of large transition metal systems, with a rather limited computational effort.

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Acknowledgment. K.P. thanks the Belgian National Science Foundation (NFWO) and the Belgian Government (DPWB) for a research grant. References and Notes (1) Sharp, A. G. The Chemistry ojCyano Complexes of the Transition Metals: Academic Press: London. 1976. ( 2 j Ballhausen, C. J. Introduction to Ligand Field Theory; McGrawHill: New York, 1962. (3) Geoffroy, G. L.; Wrighton, M. S.Organometallic Photochemistry; Academic Press: New York, 1979. 14) Ferraudi. G. J. Elements of - Inoraanic - Photochemistry;Wiley: New York, i988. ( 5 ) Alexander, J. J.; Gray, H. B. J. Am. Chem. Sot. 1968, 90, 4260. (6) Chawla, I. D.; Frank, M.J. J. Inorg. Nucl. Chem. 1970, 32, 555. (7) Mukherjee, R. K.; Chowdhury, M. Chem. Phys. Lerr. 1975,34,178. ( 8 ) Gale, R.; McCaffery, A. J. J. Chem. Sot., Dalton Trans. 1973,1344.

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