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

FIGURE 7 Flowchart for planning a computational study of a spin-forbidden reaction.

for the ab initio investigation. Great care should be taken at this stage to ensure that the chosen model and computational method will give a reasonably accurate description of the relative energetics of different spin states. After locating the minima and transition states that are present in the initial reaction scheme, one can compute single-point energies on other PESs at these optimized geometries. In some cases, this may lead to sufficiently useful qualitative understanding of the spin-forbidden behavior, and no further work is then needed.

However, in other cases, the initial calculations may lead to a reevaluation of the whole reaction scheme, and possibly to the consideration of supplementary spin states. Less drastically, it may lead to a change in which atoms of the real system are included in the model or to the use of a different computational method should the initial one prove too inaccurate or too computationally demanding.

As a final step, if quantitative information is required about the crossing behavior, the structure of MECPs relevant to the mechanism should be optimized. When analytical gradients are unavailable at the level of theory required to pro-

vide a reliable description of the relative energies of the different PESs, the hybrid method can be used to optimize the MECP.

Overall, one can certainly expect that the coming years will see a growing number of contributions addressing the role of spin in transition metal chemistry. It is hoped that the present overview will provide useful insights into the challenges implicit in ab initio computational studies of spin-forbidden processes, and will to some degree assist in attaining a higher degree of predictive power in such work.

REFERENCES

1.JL Detrich, OM Reinaud, AL Rheingold, KH Theopold. J Am Chem Soc 117: 11745–11748, 1995.

2.TA Seder, AJ Ouderkirk, E Weitz. J Chem Phys 85:1977–1987, 1986.

3.A Szabo, NS Ostlund. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Mineola, NY: Dover, 1996, p 43.

4.For a description of other terms entering into the electronic Hamiltonian, see any textbook on quantum mechanics, e.g., C Cohen-Tannoudji, B Diu, F Laloe¨. Quantum Mechanics. New York: Wiley, 1977, Chap XII.

5.BA Hess, CM Marian, SD Peyerimhoff. In: DR Yarkony, ed. Modern Electronic Structure Theory. Singapore: World Scientific, 1995, pp 152–278 and work cited therein.

6.S Koseki, MW Schmidt, MS Gordon. J Phys Chem 96:10768–10772, 1992.

7.DS Sholl, JC Tully. J Chem Phys 109:7702–7710, 1998.

8.DR Yarkony. Acc Chem Res 31:511–518, 1998.

9.See, e.g., M Bixon, J Jortner. In: Adv Chem Phys 106:35–202, 1999.

10.For a typical application, see JC Tully, RK Preston. J Chem Phys 55:562–572, 1971.

11.N Sutin. Acc Chem Res 15:275–282, 1982.

12.K Ohta, K Morokuma. J Phys Chem 91:401–406, 1987.

13.ML Hung, ML McKee, DM Stanbury. Inorg Chem 33:5108–5112, 1994.

14.O Kitao, H Ushiyama, N Miura. J Chem Phys 110:2936–2946, 1999.

15.S Shaik, A Shurki. Angew Chem Int Ed 38:586–625, 1999.

16.F Jensen. J Am Chem Soc 114:1596–1603, 1992.

17.E Ko¨nig, G Ritter, SK Kulshreshtha. Chem Rev 85:219–234, 1985.

18.P Gu¨tlich, HA Goodwin, DN Hendrickson. Angew Chem Int Ed Engl 33:425–427, 1994.

19.JK Beattie. Adv Inorg Chem 32:1–53, 1988.

20.C-L Xie, DN Hendrickson. J Am Chem Soc 109:6981–6988, 1987.

21.CC Wu, J Jung, PK Gantzel, P Gu¨tlich, DN Hendrickson. Inorg Chem 36:5339– 5347, 1997, and work cited therein.

22.KM Barkigia, NY Nelson, MW Renner, KM Smith, J Fajer. J Phys Chem B 103: 8643–8646, 1999.

23.E Buhks, G Navon, M Bixon, J Jortner. J Am Chem Soc 102:2918–2923, 1980.

24.BS Brunschwig, N Sutin. Coord Chem Rev 187:233–254, 1999.

25.AH Janowicz, HE Bryndza, RG Bergman. J Am Chem Soc 103:1516–1518, 1981.

26.R Poli, KM Smith. Eur J Inorg Chem 877–880, 1999.

27.R Poli. Acc Chem Res 20:494–501, 1997.

28.AA Cole, JC Fettinger, DW Keogh, R Poli. Inorg Chim Acta 240:355–366, 1995.

29.KM Smith, R Poli, JN Harvey. New J Chem 24:77–80, 2000.

30.E Buhks, J Jortner. J Chem Phys 83:4456–4462, 1985.

31.BS Gerstman, N Sungar. J Chem Phys 96:387–398, 1992.

32.AP Shreve, S Franzen, MC Simpson, RB Dyer. J Phys Chem B 103:7969–7975, 1999, and work cited therein.

33.BA Arndtsen, RG Bergman, TA Mobley, TH Peterson. Acc Chem Res 28:154–162, 1995.

34.PEM Siegbahn. J Am Chem Soc 118:1487–1496, 1996.

35.H Yang, KT Kotz, MC Asplund, MJ Wilkens, CB Harris. Acc Chem Res 32:551–

560, 1999.

˚

36. C Linde, B Akermark, PO Norrby, M Svensson. J Am Chem Soc 121:5083–5084, 1999.

37. M Torrent, L Deng, T Ziegler. Inorg Chem 37:1307–1314, 1998. 38. C Limberg, R Ko¨ppe. Inorg Chem 38:2106–2116, 1999.

39. PEM Siegbahn, RH Crabtree. J Am Chem Soc 121:117–127, 1999.

40. S Shaik, M Filatov, D Schro¨der, H Schwar. Chem Eur J 4:193–199, 1998. 41. N Leadbeater. Coord Chem Rev 188:35–70, 1999.

42. E Weitz. J Phys Chem 98:11256–11264, 1994.

43. PG House, E Weitz. Chem Phys Lett 266:239–245, 1997.

44. PG House, E Weitz. J Phys Chem A 101:2988–2995, 1997.

45. MC Heitz, K Finger, C Daniel. Coord Chem Rev 159:171–193, 1997. 46. K Eller, H Schwarz. Chem Rev 91:1121–1177, 1991.

47. JC Weisshaar. Acc Chem Res 26:213–219, 1993.

48. Y Wen, A Yethiraj, JC Weisshaar. J Chem Phys 106:5509–5525, 1997.

49. PA Willis, HU Stauffler, RZ Hinrichs, HF Davis. J Chem Phys 108:2665–2668, 1998.

50. PB Armentrout. Acc Chem Res 28:430–436, 1995.

51. D Walter, PB Armentrout. J Am Chem Soc 120:3176–3187, 1998.

52. D Schro¨der, H Schwarz. Angew Chem, Int Ed Engl 34:1973–1995, 1995.

53. A Fiedler, D Schro¨der, S Shaik, H Schwarz. J Am Chem Soc 116:10734–10741, 1994.

54. N Harris, S Shaik, D Schro¨der, H Schwarz. Helv Chim Acta 82:1784–1797, 1999. 55. AK Rappe´, TH Upton. J Chem Phys 85:4400–4410, 1986.

56. MC Heitz, C Ribbing, C Daniel. J Chem Phys 106:1421–1428, 1997.

57. HB Schlegel. In: DR Yarkony, ed. Modern Electronic Structure Theory. Singapore: World Scientific, 1995, pp 459–500.

58. PY Ayala, HB Schlegel. J Chem Phys 107:375–384, 1997.

59. DG Musaev, K Morokuma. J Chem Phys 101:10697–10707, 1994.

60. MC Holthausen, A Fiedler, H Schwarz, W Koch. J Phys Chem 100:6236–6242, 1996.

61. FA Carey, RJ Sundberg. Advanced Organic Chemistry. 2nd ed. Part A: Structures and Mechanisms. New York: Plenum, 1984, p 219.

62. K Yoshizawa, Y Shiota, T Yamabe. J Chem Phys 111:538–545, 1999.

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

64.N Koga, K Morokuma. Chem Phys Lett 119:371–374, 1985.

65.A Farazdel, M Dupuis. J Comput Chem 12:276–282, 1991.

66.DR Yarkony. J Phys Chem 97:4407–4412, 1993.

67.MJ Bearpark, MA Robb, HB Schlegel. Chem Phys Lett 223:269–274, 1994.

68.KM Dunn, K Morokuma. J Phys Chem 100:123–129, 1996.

69.JM Anglada, JM Bofill. J Comput Chem 18:992–1003, 1997.

70.JN Harvey, M Aschi, H Schwarz, W Koch. Theor Chem Accts 99:95–99, 1998.

71.JN Harvey, M Aschi. Phys Chem Chem Phys 1:5555–5563, 1999.

72.WH Press, SA Teukolsky, WT Vetterling, BP Flannery. Numerical Recipes in Fortran 77. Cambridge, UK: Cambridge University Press, 1996.

73.JC Lorquet, B Leyh-Nihant. J Phys Chem 92:4778–4783, 1988.

74.Q Cui, K Morokuma, JM Bowman, SJ Klippenstein. J Chem Phys 110:9469–9482, 1999.

75.DK Malick, GA Petersson, JA Montgomery Jr. J Chem Phys 108:5704–5713, 1998.

76.JN Harvey. To be published.

77.DG Musaev, K Morokuma. J Phys Chem 100:11600–11609, 1996.

78.JL Tilson, JF Harrison. J Phys Chem 95:5097–5103, 1991.

79.S Ye. J Mol Struct (Theochem) 417:157–162, 1997.

80.A Irigoras, JE Fowler, JM Ugalde. J Am Chem Soc 121:574–580, 1999.

81.Gaussian 98, Revision A. 6. MJ Frisch, GW Trucks, HB Schlegel, GE Scuseria, MA Robb, JR Cheeseman, VG Zakrzewski, JA Montgomery Jr, RE Stratmann, JC Burant, S Dapprich, JM Millam, AD Daniels, KN Kudin, MC Strain, O Farkas, J Tomasi, V Barone, M Cossi, R Cammi, B Mennucci, C Pomelli, C Adamo, S Clifford, J Ochterski, GA Petersson, PY Ayala, Q Cui, K Morokuma, DK Malick, AD Rabuck, K Raghavachari, JB Foresman, J Cioslowski, JV Ortiz, BB Stefanov, G Liu, A Liashenko, P Piskorz, I Komaromi, R Gomperts, RL Martin, DJ Fox, T Keith, MA Al-Laham, CY Peng, A Nanayakkara, C Gonzalez, M Challacombe, PMW Gill, B Johnson, W Chen, MW Wong, JL Andres, C Gonzalez, M Head-Gordon, ES Replogle, JA Pople, Gaussian, Inc., Pittsburgh, PA, 1998.

82.A Scha¨fer, H Horn, R Ahlrichs. J Chem Phys 97:2571–2577, 1992.

83.JN Harvey. To be published.

84.W Wang, E Weitz. J Phys Chem A 101:2358–2363, 1997.

85.O Gonzalez-Blanco, V Branchadell. J Chem Phys 110:778–183, 1999.

86.DW Keogh, R Poli. J Am Chem Soc 119:2516–2523, 1997.

and extend old ones. Organometallic chemistry provides a particularly diverse and fruitful field for such endeavors. Procedures such as effective core potentials, now well established in chemistry, have found some of their most impressive applications here (4), and many of the recent advances in density functional theory have had particular impact in organometallic chemistry (5).

Complexes of the Group 9 metals containing the moiety ML2X (M Rh, Ir; L tertiary phosphine; X a formally anionic ligand) form a group of important and widely used catalysts. For example, Rh(PPh3)3Cl (Wilkinson’s catalyst) is perhaps the best-known catalyst for olefin hydrogenation (6). Related reactions catalyzed by Rh(PR3)2Cl-containing complexes, including the photoand transfer-dehydrogenation of alkanes, have been reported (7,8). More recently, H2Ir(PCP) [PCP η3-1,3-C6H3(PtBu2)2] was found to catalyze the thermochemical dehydrogenation of alkanes to give alkenes and dihydrogen (9). Efficient methods for alkane functionalizations, such as oxidation and dehydrogenation, have tremendous value from industrial and environmental perspectives. These catalyses undoubtedly involve formal oxidative addition reactions to threecoordinate, 14e M(I) complexes to give five-coordinate, 16e M(III) complexes. Whether the actual operation of a catalyst such as H2Ir(PCP) proceeds via an oxidative addition/reductive elimination mechanism, formally including both Ir(III) and Ir(V) complexes, or by a series of concerted displacements is a topic of current research (10,11).

In this chapter, we will focus on oxidative addition of one or two molecules of dihydrogen (H2) to coordinatively unsaturated M(PH3)2Cl, M Rh and Ir. We will examine the performance of first-principles computational methods based on the traditional molecular orbital approach and on density functional theory, with a focus on thermodynamic and kinetic parameters.

2. COMPUTATIONAL METHODS

It is well appreciated that thermodynamic and kinetic parameters are difficult to compute for organometallic molecular systems (see, e.g., Refs 12–14 and Chap. 4 by Frenking in the present volume). In particular, such quantities cannot be predicted within an independent-particle, single-determinant Hartree–Fock type of approach; electron correlation must be included in the computational methods applied to achieve reliable and accurate results. In this work, we examine the performance of three first-principles methods, generally acknowledged by the abbreviations BLYP, B3LYP, and MP2. The first two are methods based on density functional theory (DFT) (15); the latter is an ab initio, molecular orbital (MO)–based method (16).

If we write the expression for the total energy (17) as the sum of the oneelectron kinetic energy, ET, the electron–nuclear attraction and nuclear–nuclear

repulsion energies, EV, the electron–electron repulsion energy, E J, and the elec- tron–electron exchange and correlation energies, EXC EX EC,

we may further identify the principal computational methods used here as follows. The MP2 method is defined by setting EX equal to the full Hartree–Fock exchange and evaluating EC from second-order perturbation theory with the Hartree–Fock Hamiltonian as the reference, zeroth order Hamiltonian (18). Some of our calculations incorporated the electron correlation (EC) from Møller–Plesset perturbation theory applied fully through fourth-order (MP4(SDTQ)) (19) or through the coupled-cluster, single and double excitation method (with triple excitations treated noniteratively), CCSD(T) (20,21). The last method is generally considered state of the art at present. In the BLYP method, EX is obtained from Becke’s 1988 nonlocal exchange functional (22) and EC is produced by the nonlocal correlation functional of Lee et al. (23). Finally, in the method denoted B3LYP, the three-parameter exchange functional proposed by Becke in 1993 (24), which incorporates some exact Hartree–Fock exchange, replaces his 1988 exchange functional.

We make use of an effective core potential (ECP) on the metal atom and basis sets of valence double-zeta or better quality. The Hay–Wadt relativistic, small-core ECPs and corresponding basis sets (split valence double-zeta) were used for Rh and Ir (LANL2DZ model) (25). These ECPs release the penultimate electrons (4s, 4p for Rh; 5s, 5p for Ir) for explicit basis function coverage along with the valence electrons. We used Dunning/Huzinaga all-electron, full doublezeta plus polarization function basis sets for the third-row elements (P, Cl) (26). Hydrogen atoms in H2, which formally become hydrides in the product complexes, were described by the 311G(p) basis set (27); hydrogen atoms in phosphine groups carried a 21G basis set (28). In selected cases, we replaced the hydrogen atoms on the phosphines with methyl groups in which the C atoms were described by the Dunning/Huzinaga double-zeta plus polarization function basis set (D95d, 26), and H atoms were described by the STO-3G basis set (29).

Reactant, transition-state, and product geometries were fully optimized using gradient methods (30); symmetry constraints were imposed, when appropriate. The stationary points were further characterized by normal-mode analysis. The (unscaled) vibrational frequencies formed the basis for the calculation of vibrational zero-point energy corrections and, together with thermodynamic corrections for finite temperature, provided the data needed to convert from internal energies to reaction or activation enthalpies (∆H; T 298 K, P 1 atm) (31). The higher-level MP4/CCSD calculations always used MP2 optimized geometries, and energy–enthalpy conversions were made based on the data derived at

the MP2 level. All the electronic structure methods used here are implemented in the GAUSSIAN 98 series of computer programs (32).

3.MOLECULAR STRUCTURES AND SPIN STATES OF M(PH3)2Cl, M Rh and Ir

The two limiting Jahn–Teller structures available to singlet ML3 fragments with d8 metal electronic configuration may be characterized as T and Y, respectively, both of molecular C2v symmetry (33). When the composition of the fragment is ML2L′, additional intermediate distorted structures become possible. Early computational studies of Rh(PH3)2Cl using ab initio methods (34–38) considered only the T structure, with Cl at the base of the T (trans-1a, TCl) (39). In some cases a low-lying triplet state was identified as the ground state for trans-1a, although it was recognized that this result could be due to insufficient or unbalanced treatment of electron correlation (37,38). Margl et al. (40) found during a detailed DFT study of C–H bond activation by Rh(PH3)2Cl, that a second T- type structure with a phosphine at the base of the T (cis-1a, TPH3) was distinctly the ground state, 16.5 kcal/mol below TCl. These authors included relativistic energy corrections in their calculations and computed the energies of the triplet (as well as open-shell singlet) states to be well above the energies of the (closedshell) singlet states for 1a. However, the recent B3LYP study of Su and Chu (41) reported a triplet ground state for trans-1a and did not consider any cis structures.

All computational methods applied here agree that both trans-1a (TCl) and cis-1a (TPH3) structures exist as discrete minima in singlet states (Fig. 1), and that there are no additional minima (YCl, etc.) of low energy on the singlet potential energy surface for Rh(PH3)2Cl. The singlet cis–trans enthalpy difference is 10–12 kcal/mol from the DFT methods, smaller than that obtained from ab initio perturbation theory (14–16 kcal/mol); with the most accurate MO-based model used (CCSD(T)), the cis–trans enthalpy difference is 8.0 kcal/mol (Table 1). The trans-1a structures formally attain the electronic configuration dxy(2)dxz(2)dyz(2)

FIGURE 1 Optimized geometries of M(PH3)2Cl isomers, M Rh and Ir (singlet

˚

trans-1, singlet cis-1). Bond lengths in A, angles in degrees. BLYP: regular font; B3LYP: italics font; MP2: bold font.

dz2(2)dx2 y2(0) (Rh, P, and Cl form the xy plane), and the low-lying triplet state formally has one electron promoted from the dz2 orbital to dx2 y2. Triplet trans- 1a maintains C2v symmetry with the two DFT methods, and the energy is more than 10 kcal/mol above the singlet state. However, the MP2 method breaks the molecular symmetry for triplet trans-1a and collapses the structure toward a cis conformation. The cis-1a isomer formally has an electronic configuration identical to that of trans-1a. All three computational methods locate minima for triplet cis-1a, but the BLYP method is unique in predicting a slightly pyramidal structure; the two other methods predict planar structures for triplet cis-1a. The energies of the cis-1a triplet states are computed well above the cis-1a singlet states in the DFT methods (11–13 kcal/mol), but the difference is smaller from MP2/ MP4 calculations (8–9 kcal/mol) and even less, 5.6 kcal/mol, with CCSD(T).

All methods thus predict that singlet cis-1a (TPH3) represents the global minimum for Rh(PH3)2Cl (Table 1). The overall energetic ordering of the isomers based on the two DFT methods is cis-1a (singlet) trans-1a (singlet) cis-1a (triplet) trans-1a (triplet), confirming the results of Margl et al. (40). From the MO-based methods, the ordering is cis-1a (singlet) cis-1a (triplet) trans-