Cundari Th.R. -- Computational Organometallic Chemistry-0824704789

22.W Koch, RH Hertwig. In: PvR Schleyer, NL Allinger, T Clark, PA Kollman, HF Schaefer III, PR Scheiner (eds.) Encyclopedia of Computational Chemistry. Vol. 1. Chichester, UK: Wiley, VCH, 1998, pp 689–700.

23.A Ricca, CW Bauschlicher. Theor Chim Acta 92:123–131, 1995.

24.Representative examples: (a) MN Glukhotsev, RD Bach, CJ Nagel. J Phys Chem A 101:316–323, 1997. (b) I Bytheway, GB Bacskay, NS Hush. J Phys Chem 100: 6023–6031, 1994. (c) EA McCullough Jr, E Apra`, J Nichols. J Phys Chem A 101: 2502–2508, 1997. (d) TV Russo, RL Martin, PJ Hay. J Chem Phys 102:8023– 8082, 1995. (e) A Rosa, AW Ehlers, EJ Baerends, JG Snijders, G te Velde. J Phys Chem 100:5690–5696, 1996. (f) MC Holthausen, C Heinemann, HH Cornehl, W Koch, H Schwarz. J Chem Phys 102:4931–4941, 1995. (g) B Delley, M Wrinn, HP Lu¨thi. J Chem Phys 100:5785–5791, 1994.

25.AD Becke. Phys Rev A 38:3098–3106, 1988.

26.JP Perdew. Phys Rev B 33:8822–8827, 1986.

27.C Lee, W Yang, RG Parr. Phys Rev B 37:785–792, 1988.

28.JP Perdew, Y Wang. Phys Rev B 45:13244–13254, 1992.

29.SH Vosko, L Wilk, M Nuisar. Can J Phys 58:1200–1206, 1980.

30.(a) AD Becke. J Chem Phys 98:1372–1377, 1993. (b) AD Becke. J Chem Phys 98:5648–5652, 1993.

31.PJ Stephens, FJ Devlin, CF Chabalowski, MJ Frisch. J Phys Chem 98:11623– 11627, 1994.

32.(a) V Jonas, W Thiel. Organometallics 17:353–360, 1998. (b) V Jonas, W Thiel. J Chem Phys 102:8474–8484, 1995. (c) V Jonas, W Thiel. J Chem Phys 105:3636– 3646, 1996. (d) V Jonas, W Thiel. J Phys Chem A 103:1381–1393, 1999.

33.FA Hamprecht, AJ Cohen, DJ Tozer, NC Handy. J Chem Phys 109:6264–6271, 1998.

34.AD Becke. J Chem Phys 109:2092–2098, 1998.

35.AD Becke. J Comput Chem 20:63–69, 1999.

36.(a) CR Landis, TK Firman, DM Root, T Cleveland. J Am Chem Soc 120:1842– 1854, 1998. (b) CR Landis, T Cleveland, TK Firman. J Am Chem Soc 120:2641– 2649, 1998. (c) TK Firman, CR Landis. J Am Chem Soc 120:12650–12656, 1998.

(d) CA Bayse, MB Hall. J Am Chem Soc 121:1348–1358, 1999.

37.(a) V Jonas, G Frenking, MT Reetz. J Comput Chem 13:919–934, 1992. (b) M Couty, MB Hall. J Comput Chem 17:1359–1370, 1996.

38.PJ Hay, WR Wadt. J Chem Phys 82:299–310, 1985.

39.WJ Stevens, M Krauss, H Basch, G Jasien. Can J Chem 70:612–630, 1992.

40.(a) M Dolg, U Wedig, H Stoll, H Preuss. J Chem Phys 86:866–872, 1987. (b) D Andrae, U Ha¨ussermann, M Dolg, H Stoll, H Preuss. Theor Chim Acta 77:123– 141, 1990.

41.(a) LF Pacios, PA Christiansen. J Chem Phys 82:2664–2671, 1985. (b) MM Hurley, LF Pacios, PA Christiansen, RB Ross, WC Ermler. J Chem Phys 84:6840–6853, 1986. (c) LA LaJohn, PA Christiansen, RB Ross, T Atashroo, WC Ermler. J Chem Phys 87:2812–2824, 1987. (d) RB Ross, JM Powers, T Atashroo, WC Ermler, LA LaJohn, PA Christiansen. J Chem Phys 93:6654–6670, 1990.

42.(a) L Seijo, Z Barandiara´n, S Huzinaga. J Chem Phys 91:7011–7017, 1989. (b) Z Barandiara´n, L Seijo, S Huzinaga. J Chem Phys 93:5843–5850, 1990.

43.(a) P Pyykko¨. Chem Rev 88:563–594, 1988. (b) J Almlo¨f, O Gropen. Rev Comput Chem 8:203–244, 1996. (c) P Schwerdtfeger, M Seth. In: PvR Schleyer, NL Allinger, T Clark, PA Kollman, HF Schaefer III, PR Scheiner (eds.). Encyclopedia of Computational Chemistry. Vol. 4. Chichester, UK: Wiley-VCH, 1998, pp 2480– 2499.

44.(a) LA Barnes, M Rosi, CW Bauschlicher. J Chem Phys 93:609–624, 1990. (b) I Antes, G Frenking. Organometallics 14:4263–4268, 1995.

45.K Balasubramanian. In: PvR Schleyer, NL Allinger, T Clark, PA Kollman, HF Schaefer III, PR Scheiner (eds.). Encyclopedia of Computational Chemistry. Vol. 4. Chichester, UK: Wiley-VCH, 1998, pp 2471–2480.

46.B Hess. In: PvR Schleyer, NL Allinger, T Clark, PA Kollman, HF Schaefer III, PR Scheiner (eds.). Encyclopedia of Computational Chemistry. Vol. 4. Chichester, UK: Wiley-VCH, 1998, pp 2499–2508.

47.C van Wu¨llen. J Comput Chem 20:51–62, 1999.

48.E van Lenthe, JG Snijders, EJ Baerends. J Chem Phys 105:6505–6516, 1996.

49.S Dapprich, U Pidun, AW Ehlers, G Frenking. Chem Phys Lett 242:521–526, 1995.

50.(a) J Li, G Schreckenbach, T Ziegler. J Phys Chem 98:4838–4841, 1994. (b) J Li, G Schreckenbach, T Ziegler. J Am Chem Soc 117:486–494, 1995.

51.RK Szilagyi, G Frenking. Organometallics 16:4807–4815, 1997.

52.V Jonas, G Frenking, MT Reetz. J Am Chem Soc 116:8741–8753, 1994.

53.AJ Lupinetti, V Jonas, W Thiel, SH Strauss, G Frenking. Chem Eur J 5:2573– 2583, 1999.

54.(a) E van Lenthe, A Ehlers, EJ Baerends. J Chem Phys 110:8943–8953, 1999. (b) A Rosa, EJ Baerends, SJA van Gisbergen, E van Lenthe, JA Groeneveld, JG Snijders. J Am Chem Soc 121:10356–10365, 1999.

55.(a) K Wichman. Diplom Thesis, University of Marburg, 1999. (b) K Wichmann, G Frenking. In press.

56.(a) AW Ehlers, S Dapprich, SF Vyboishchikov, G Frenking. Organometallics 15: 105–117, 1996. (b) AW Ehlers. PhD dissertation, University of Marburg, 1994.

57.C van Wu¨llen. J Comput Chem 18:1985–1992, 1997.

58.AW Ehlers, G Frenking, EJ Baerends. Organometallics 16:4896–4902, 1997.

59.C van Wu¨llen. J Chem Phys 103:3589–3599, 1995.

60.(a) T Ziegler, JG Snijders, EJ Baerends. J Chem Phys 74:1271–1284, 1981. (b) T Ziegler, V Tschinke, EJ Baerends, JG Snijders, W Ravenek. J Phys Chem 93:3050– 3055, 1989.

61.(a) C Chang, M Pelissier, Ph Durand. Phys Scr 34:394–407, 1986. (b) JL Heully, I Lindgren, E Lindroth, S Lundquist, AM Martensson-Pendrill. J Phys B 19:2799– 2808, 1986. (c) E van Lenthe, EJ Baerends, JG Snijders. J Chem Phys 99:4597– 4610, 1993.

62.RA Fischer, J Weiss. Angew Chem 111:3002–3022, 1999; Angew Chem Int Ed Engl 38:2830–2850, 1999.

63.C Boehme, J Uddin, G Frenking. Coord Chem Rev 197:249–276, 2000.

64.SF Vyboichshikov, G Frenking. Theor Chem Acc 102:300–310, 1999.

65.T Wagener, G Frenking. Inorg Chem 37:1805–1811, 1998.

66.WJ Hehre, L Radom, PvR Schleyer, JA Pople. Ab Initio Molecular Orbital Theory. New York: Wiley, 1986.

67.E Forsellini, U Casellato, R Graziani, L Magon. Acta Cryst B 38:3081–3083, 1982.

68.S Ritter, R Hu¨bener, U Abram. J Chem Soc Chem Commun: 2047–2048, 1995.

69.S Ritter, U Abram. Z Anorg Allg Chem 622:965–973, 1996.

70.CE Laplaza, WM Davis, CC Cummins. Angew Chem 107:2181–2183, 1995; Angew Chem Int Ed Engl 34:2042–2044, 1995.

71.NC Zanetti, RR Schrock, WM Davis. Angew Chem 107:2184–2186, 1995; Angew Chem Int Ed Engl 34:2044–2046, 1995.

72.M Torrent, M Sola`, G Frenking. Organometallics 18:2801–2812, 1999.

73.DC Gross, PC Ford. Inorg Chem 21:1704–1706, 1982.

74.LS Sunderlin, RR Squires. J Am Chem Soc 115:337–343, 1993.

75.(a) PO Norrby, HC Kolb, KB Sharpless. Organometallics 13:344–347, 1994. (b) PO Norrby, HC Kolb, KB Sharpless. J Am Chem Soc 116:8470–8478, 1994.

76.A Veldkamp, G Frenking. J Am Chem Soc 116:4937–4946, 1994.

77.U Pidun, C Boehme, G Frenking. Angew Chem 108:3008–3011, 1996; Angew Chem Int Ed Engl 35:2817–2820, 1996.

78.S Dapprich, G Ujaque, F Maseras, A Lledo´s, DG Musaev, K Morokuma. J Am Chem Soc 118:11660–11661, 1996.

79.M Torrent, L Deng, M Duran, M Sola, T Ziegler. Organometallics 16:13–19, 1997.

80.AJ Del Monte, J Haller, KN Houk, KB Sharpless, DA Singleton, T Strassner, AA Thomas. J Am Chem Soc. 119:9907–9908, 1997.

81.DV Deubel, G Frenking. J Am Chem Soc 121:2021–2031, 1999.

82.(a) A Beste, G Frenking. Z Allg Anorg Chem 626:381–391, 2000. (b) A Beste. Diplom thesis, University of Marburg, 1999.

83.SA Decker, M Klobukowski. J Am Chem Soc 120:9342–9355, 1998.

84.T Wagener. PhD dissertation, University of Marburg, 1998.

85.(a) H Nakatsuji. Chem Phys Lett 167:571–574, 1990. (b) H Nakatsuji, T Inoue, T Nakao. J Phys Chem 96:7953–7958, 1992. (c) M Sugimoto, M Kanayama, H Nakatsuji. J Phys Chem 96:4375–4381, 1992. (d) H Nakatsuji. In: JA Tossell (ed.). Nuclear Magnetic Shieldings and Molecular Structure. Dordrecht, The Netherlands: Kluwer Academic, 1993, pp 263–278.

86.(a) W Kutzelnigg. Isr J Chem 19:193–200, 1980. (b) M Schindler, W Kutzelnigg. J Chem Phys 76:1919–1933, 1982. (c) W Kutzelnigg, U Fleischer, M Schindler. NMR: Basic Princ Prog 23:165–262, 1990.

87.(a) F London. J Phys Radium 8:397–409, 1937. (b) RM Stevens, RM Pitzer, WN Lipscomb. J Chem Phys 38:550–560, 1963. (c) R Ditchfield. J Chem Phys 56: 5688–5691, 1972. (d) H Hameka. Mol Phys 1:203–215, 1958.

88.U Fleischer, C van Wu¨llen, W Kutzelnigg. In: PvR Schleyer, NL Allinger, T Clark, PA Kollman, HF Schaefer III, PR Scheiner (eds.). Encyclopedia of Computational Chemistry. Vol. 3. Chichester, UK: Wiley-VCH, 1998, pp 1827–1835.

89.VG Malkin, OL Malkina, ME Casida, DR Salahub. J Am Chem Soc 116:5898– 5908, 1994.

90.G Schreckenbach, T Ziegler. Theor Chem Acc 99:71–82, 1998.

91.M Bu¨hl, M Kaupp, OL Malkina, VG Malkin. J Comput Chem 20:91–105, 1999.

92.M Kaupp, VG Malkin, OL Malkina. In: PvR Schleyer, NL Allinger, T Clark, PA Kollman, HF Schaefer III, PR Scheiner (eds.). Encyclopedia of Computational Chemistry. Vol. 3. Chichester, UK: Wiley-VCH, 1998, pp 1857–1866.

93.(a) M Bu¨hl. Chem Phys Lett 267:251–257, 1997. (b) M Bu¨hl. Organometallics 16: 261–267, 1997. (c) M Bu¨hl, OL Malkina, VG Malkin. Helv Chim Acta 79:742– 754, 1996. (d) M Bu¨hl, FA Hamprecht. J Comput Chem 19:113–122, 1998. (e) M Bu¨hl. Angew Chem 110:153–155, 1998; Angew Chem Int Ed Engl 37:142–144, 1998.

94.(a) M Kaupp. Chem Ber 129:527–533, 1996. (b) M Kaupp. Chem Eur J 2:348– 358, 1996. (c) M Kaupp. Chem Ber 129:535–544, 1996. (d) M Kaupp. J Chem Soc Chem Commun 1141–1142, 1996. (e) M Kaupp. J Am Chem Soc 118:3018– 3024, 1996.

95.(a) N Godbout, R Havlin, R Salzmann, PG Debrunner, E Oldfield. J Phys Chem

A102:2342–2350, 1998. (b) MC McMahon, AC deDios, N Godbout, R Salzmann,

DDLaws, H Le, RH Havlin, E Oldfield. J Am Chem Soc 120:4784–4797, 1998.

(c) N Godbout, E Oldfield. J Am Chem Soc 109:8065–8069, 1997. (d) R Havlin,

MMcMahon, R Srinivasan, H Le, E Oldfield. J Phys Chem A 101:8908–8913, 1997.

96.(a) G Schreckenbach, T Ziegler. Int J Quantum Chem 61:899–907, 1997. (b) Y Ruiz-Morales, G Schreckenbach, T Ziegler. J Phys Chem 100:3359–3367, 1996.

(c) Y Ruiz-Morales, G Schreckenbach, T Ziegler. Organometallics 15:3920–3923, 1996. (d) AW Ehlers, Y Ruiz-Morales, EJ Barends, T Ziegler. Inorg Chem 36: 5031–5036, 1997.

97.AM Lee, NC Handy, SM Colwell. J Chem Phys 103:10095–10109, 1995.

98.(a) M Kaupp, OL Malkina, VG Malkin. J Chem Phys 106:9201–9212, 1997. (b)

MKaupp, VG Malkin, OL Malkina, DR Salahub. Chem Phys Lett 235:382–388, 1995. (c) M Kaupp, VG Malkin, OL Malkina, DR Salahub. Chem Eur J 2:24–30, 1996. (d) R Salzmann, M Kaupp, M McMahon, E Oldfield. J Am Chem Soc 120: 4771–4783, 1998. (e) GM Bernard, G Wu, RE Wasyleshen. J Phys Chem A 102: 3184–3192, 1998. (f) Y Ruiz-Morales, T Ziegler. J Phys Chem A 102:3970–3976, 1998.

99.(a) PWNM van Leeuwen, K Morokuma, JH van Lenthe (eds.). Theoretical Aspects of Homogeneous Catalysis. Dordrecht, The Netherlands: Kluwer Academic, 1995.

(b) DG Truhlar, K Morokuma (eds.). Transition State Modeling for Catalysis. ACS Symposium Series 721. Washington, DC: American Chemical Society, 1999. (c)

MSola´, M Torrent, G Frenking. Chem Rev 100:439–493, 2000.

100.AW Ehlers, G Frenking. J Am Chem Soc 116:1514–1520, 1994.

101.LA Barnes, B Liu, R Lindh. J Chem Phys 98:3978–3989, 1993.

102.J Li, G Schreckenbach, T Ziegler. J Phys Chem 98:4838–4841, 1994.

103.KE Lewis, DM Golden, GP Smith. J Am Chem Soc 106:3905–3912, 1984.

104.M Diedenhofen, G. Frenking. Unpublished results.

the additional intricacies connected to using these methods, i.e., the construction of the appropriate reference wavefunction to be used as a starting point for the treatment of dynamic correlation. There are not, and cannot be, any general rules for constructing such a wavefunction, nor can such rules be implemented in any computer code. The only constant factor is that the reference wavefunction should include all important nondynamic correlation effects. What precisely these effects incorporate is dependent on the specific electronic structure of the molecule to be treated. In other words, the construction of an appropriate reference wavefunction requires at least some a priori knowledge of the answer to be obtained from the calculation. It is therefore often based on trial and error or, in the case of a more experienced user in the field, on ‘‘chemical intuition.’’ By making use of the CASSCF (complete active-space self-consistent field) method for constructing the reference wavefunction, the problem can be reduced to selecting a set of active orbitals (10). However, since the number of configurations, and hence the computational effort, increases very rapidly with the size of the active space, a certain skill is still required to define the active space in such a way that all important nondynamic correlation effects are included while at the same time keeping the number of active orbitals to a minimum (with a maximum of 12– 14 orbitals, depending on the symmetry of the molecule).

In this chapter, we will try to formulate some general guidelines for treating nondynamic correlation in molecules containing transition metals. The way we will do this is by looking for connections between the appearance of such correlation effects and the specific molecular electronic structure arising from certain metal–ligand combinations, and from there trying to provide some trends. Before starting it should be emphasized, however, that the picture given in the rest of this chapter will by no means be complete. For one thing, we will confine the discussion to systems containing only one transition metal atom or ion, so, for example, the treatment of magnetic interactions between different centers will not be considered. Furthermore, most of the chapter will be devoted to ‘‘large’’ transition metal systems, i.e., molecules containing a transition metal surrounded by at least four ligands. A crucial distinction between the correlation effects appearing in these large systems and the smaller molecules built from only one or two ligands is connected to their ground state electronic structure: the first one or two ligands that bind to a transition metal atom will find the latter in a hybridized state composed of a mixture of the configurations dns2, dn 1s1 and dn 2, with a composition that may be strongly dependent on the metal–ligand distance. The description of such systems therefore requires an accurate treatment of differential correlation effects connected to states with such varying configurations. As more ligands surround the metal, the (n 1)s [and (n 1)p] orbitals are pushed upward in energy (see also Sec. 3) so that the important correlation effects in these larger systems are confined to the nd electrons and their interaction with the ligand environment. For obvious reasons, the correlation problem in smaller

transition systems was the first to be recognized and has already been discussed on several occasions (2,5,11–12). We will touch on the problem shortly in Section 2. The rest of the chapter will be devoted to the discussion of nondynamic correlation effects connected to the interaction between the metal nd shell and its environment.

Another introductory remark concerns the distinction between nondynamic and dynamic correlation effects. Starting from the restricted Hartree–Fock (RHF) solution, dynamic correlation is defined as the energy lowering due to correlating the motion of the electrons. On the other hand, nondynamic, or static, correlation is the energy lowering obtained when adding additional flexibility to the (RHF) wavefunction to describe near-degeneracy effects (two or more configurations having almost the same energy). In other words, by dealing with nondynamic correlation, an improved starting point for treating dynamic correlation can be constructed in cases where RHF fails. However, clearly the ‘‘failure’’ of RHF or also the definition of ‘‘near’’-degeneracy is to some extent dependent on the elaboration of the method used for treating dynamic correlation. For instance, ferrocene, a typical organometallic system, has been found in the past to be hard to treat using rather simple single-reference methods (13,14), e.g. MP2 (Møeller– Plesset second-order perturbation theory) or MCPF (modified coupled-pair functional). It was therefore concluded that nondynamic correlation effects are very important in this molecule. And indeed, accurate results for the bonding may be obtained by using instead second-order perturbation theory based on a CASSCF wavefunction (14), i.e., the so-called CASPT2 method (15). However, it was also shown (16) that a similar accuracy may be reached by using instead the singlereference CCSD(T) approach (coupled-cluster singles-and-doubles with a perturbative correction for triples). In this chapter we will consider nondynamic correlation effects in a broad sense; e.g., all near-degeneracy effects that are too strong to be handled efficiently by second-order perturbation theory, such as those appearing in ferrocene, will be considered as nondynamic correlation effects. This option is based on our experience with the CASSCF/CASPT2 method (1). Indeed, the success of this method is on the one hand critically dependent on whether or not all important correlation effects are included in the CASSCF reference wavefunction, but is on the other hand guaranteed in many large transition metal systems by the ability of the method to combine very extended CASSCF reference wavefunctions (containing up to 1 million or more determinants) with a large number of correlated electrons.

2. THE ATOMIC CASE: THE 3d DOUBLE-SHELL EFFECT

One of the most important correlation effects in transition metal systems is the so-called 3d double-shell effect. This correlation effect appears in particular in

first-row transition metal atoms or ions with a more-than-half-filled 3d shell, and is related to the presence of a large number of electrons in a compact 3d shell, giving rise to very large 3d radial correlation effects. But of course such an effect should be classified as dynamic rather than nondynamic, and one may therefore wonder whether its description really belongs in this chapter. It does, because this is one of the exceptional cases where an accurate description of dynamic correlation effects really benefits from a reoptimization of the orbitals involved, i.e., from a multireference treatment. The effect was first noted in a multiconfigurational Hartree–Fock calculation on the copper atom (17), where it was found that a large fraction of the electron correlation in the 3d104s state could be described by including the electronic configuration 3d93d′4s, with 3d′ a more diffuse shell than 3d. A more general description of the effect in first-row transition metals was given by Dunning et al. (18,19). The first quantitative calculations, showing that the inclusion of a second d shell in a multireference treatment is indeed a prerequisite to obtaining accurate results, were performed on the relative energies of the 3d84s2, 3d94s, and 3d10 states in the Ni atom, using either the MRCI (20) or CASPT2 (21) approach.

In this section we will illustrate the occurrence of the double-shell effect by a set of CASSCF/CASPT2 calculations on the ground and lowest excited states of the monopositive ions Ti , Co , and Rh . The motivation for this choice is twofold: (1) Since monopositive ions are characterized by low-lying states belonging to either the configurations dn 1 or dns1, calculations of their spectra allow for an investigation of the double-shell effect on the energy of d → d as well as d → s excitations. (2) The specific choice of transition metal makes it possible to compare the effect of an increasing number of 3d electrons (Ti versus Co ) as well as an increasing main quantum number (Co versus Rh ). The double-shell effect is investigated by comparing the results obtained from a CASSCF calculation with an active space including only the Ti, Co 3d, 4s orbitals or Rh 4d, 5s orbitals [denoted as CAS(6)] to a calculation where this active space is extended with a second d shell [denoted as CAS(11)]. Relativistic effects (which are quite important for the 4d → 5s transitions in Rh ) were accounted for by performing the calculations using the relativistic core–AIMP (ab initio model potential) of Barandiaran (22). These potentials were used in combination with the corresponding valence basis sets with contraction [3s3p4d] and further enhanced with one f-type function. Given the moderate size of these basis sets, it is certainly not our intention to present quantitative results for the considered excitation energies. It is known from the calculations on the Ni atom (20) that (apart from a multireference treatment) an accurate description of radial correlation effects in the 3d shell would require much larger basis sets, including angular momentum functions up to g and higher. The results of our calculations are presented in Table 1. Both Co and Rh are characterized by an 3F ground state, corresponding to a d8 configuration, and three d → d transitions (to 1D, 3P, 1G)

TABLE 1 Calculated CASSCF and CASPT2 Excitation Energies (eV) of the Lowest Excited States in Ti , Co , and Rh , Using an Active Space Consisting of Either Six Orbitals [3d, 4s or 4d, 5s, Denoted as CAS(6)] or 11 Orbitals [3d, 3d′, 4s or 4d, 4d′, 5s, Denoted as CAS(11)]

Source: Taken from Ref. 58 for Ti , Ref. 59 for Co , and Ref. 60 for Rh . The values were obtained as the weighted average of all J levels corresponding to each LS state.

as well as three d → s transitions (to 5F, 3F, 5P) have been included in the calculations. On the other hand, Ti has an 4F ground state corresponding to 3d24s1; here, we only consider the lowest s → d (to 4F) and d → d (to 2F) transition.

The importance of radial correlation effects within the d shell is already obvious from the CASSCF results obtained with the smallest active space [CAS(6)], where any description of such effects is lacking. Because the importance of these correlation effects strongly increases with the number of d electrons present, neglecting them leads to a preferential stabilization of states corresponding to the dns1 rather than the dn 1 configuration. Thus, at the CAS(6) level we find both the 3F, 5F (3d74s1) states at a considerably lower energy than the 3F (d8) ground state in Co , while the 5P state is also calculated more than 1.2 eV too low. The corresponding errors are considerably smaller, up to 0.6 eV, for Rh , indicating that correlation effects are much less important within the (less compact), 4d shell. In Ti the splitting between the 4F states corresponding to