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

FIGURE 14 Structures of the rac and meso rotomers that lead to isotactic and atactic polymer blocks in the polymerization of polypropylene. An example of an isotactic-atactic block copolymer is shown. The composition of the block copolymer is determined by the equilibrium constant for the interconversion between rac and meso forms of the catalyst. (Redrawn from Ref. 88.)

7. SUMMARY

Molecular mechanics has been used to model a variety of different catalytic processes. Almost all the major catalytic transformations in organometallic catalysis have been studied using some form of molecular modeling, and most with molecular mechanics. Workers have successfully built models that offer new insights into how a catalyst interacts with the substrate. In particular, molecular modeling has found a home within the chemical industry. Molecular modeling is used in both fundamental and applied research because it is more efficient to guide experiments using ligands designed via computational methods than by trial and error

in the laboratory. When we develop a molecular mechanics model of a reaction, we have to carefully examine the mechanism for that reaction in order to build the model. In the process of building the molecular mechanics model, we develop an ability to visualize reaction centers, which leads to new insights into catalytic reactivity. In this manner, we begin to allow our imaginations to guide the design of novel catalysts. These new designs can be tested using computational models far faster, and more efficiently, than by carrying out experiments in the laboratory.

ACKNOWLEDGMENTS

We thank Professor Theodore L. Brown, University of Illinois, for many helpful suggestions during manuscript preparation. We thank Ms. Rebecca Simon, University of Illinois, Thomas M. Thorpe, Procter and Gamble, David S. Brown, Shell Chemical Company, and Joseph T. Golab, BP Amoco Chemicals, for help with the section on industrial applications.

REFERENCES

1.TR Cundari. J Chem Soc Dalton Trans 2771–2776, 1998.

2.IV Pletnev, VL Mel’nikov. Russ J Coordination Chem 23:188–196, 1997.

3.NL Allinger. J Am Chem Soc 99:8127–8134, 1977.

4.AK Rappe´, CJ Casewit, KS Colwell, WA Goddard, WM Skiff. J Am Chem Soc 114:10024, 1992.

5.BP Hay. Coord Chem Rev 126:177–236, 1993.

6.J Hunger, G Huttner. J Comput Chem 20:445–471, 1999.

7.TR Cundari, WF Fu. Inorg Chim Acta, in press, 1999.

8.JD Atwood. Inorganic and Organometallic Reaction Mechanisms. New York: Wiley, 1997.

9.RB Jordan. Reaction Mechanisms of Inorganic and Organometallic Systems. 2nd ed. New York: Oxford University Press, 1998.

10.ML Tobe, J Burgess. Inorganic Reaction Mechanisms. Essex, UK: Longman, 1999.

11.P Comba, TW Hambley. Molecular Modeling of Inorganic Compounds. Wenheim, Germany: VCH, 1995.

12.AR Leach. Molecular Modelling Principles and Applications. Essex, UK: Longman, 1996.

13.AK Rappe´, CJ Casewit. Molecular Mechanics Across Chemistry. Sausalito, CA: University Science Books, 1997.

14.JA Osborne, FH Jardine, JF Young, G Wilkinson. J Chem Soc A:1711, 1966.

15.FH Jardine, JA Osborne, G Wilkinson. J Chem Soc A:1574, 1967.

16.S Montelatici, A vanderEnt, JA Osborne, G Wilkinson. J Chem Soc A:1054, 1968.

17.ACS Chan, JJ Pluth, J Halpern. J Am Chem Soc 102:5952, 1980.

18.CR Landis, J Halpern. J Am Chem Soc 109:1746–1754, 1987.

19.JM Brown, PA Chalconer. J Chem Soc Chem Commun, 344, 1980.

20.JM Brown. Chem Soc Revs 22:25–47, 1993.

21.ML Caffery, TL Brown. Inorg Chem 30:3907–3914, 1991.

22.KJ Lee, TL Brown. Inorg Chem 31:289–294, 1992.

23.DP White, TL Brown. Inorg Chem 34:2718–2724, 1995.

24.VS Allured, CM Kelly, CR Landis. J Am Chem Soc 113:9493, 1991.

25.TN Doman, CR Landis, B Bosnich. J Am Chem Soc 114:7264–7272, 1992.

26.TK Hollis, JK Burdett, B Bosnich. Organometallics 12:3385–3386, 1993.

27.TN Doman, TK Hollis, B Bosnich. J Am Chem Soc 117:1352–1368, 1995.

28.CR Landis, DM Root, T Cleveland. In: DB Boyd, KB Lipkowitz, eds. Reviews in Computational Chemistry. New York: VCH, 1995, pp 73–148.

29.JM Brown, PL Evans. Tetrahedron 44:4905–4916, 1988.

30.PL Bogdan, JJ Irwin, B Bosnich. Organometallics 8:1450–1453, 1989.

31.EK Davies, NW Murrall. J Comput Chem 13:149–156, 1988.

32.JS Giovannetti, CM Kelly, CR Landis. J Am Chem Soc 115:5889, 1993.

33.R Brooks, RE Bruccoleri, BD Olafson, DJ States, S Swaminathan, M Karplus. J Comput Chem 4:187, 1983.

34.AK Rappe`, WA Goddard. J Chem Phys 95:3358, 1991.

35.DG Allen, SB Wild, DL Wood. Organometallics 5:1009, 1986.

36.PK Weiner, PA Kollman. J Comput Chem 2:287, 1981.

37.WC Still, F Mohamadi, NGJ Richards, WC Guida, M Lipton, R Liskamp, G Chang, T Hendrickson, FD Gunst, W Hasel. ‘‘Macromodel V3.0.’’ Department of Chemistry, Columbia University, New York.

38.O Schwalm, J Weber, B Minder, A Baiker. Int J Quant Chem 52:191–197, 1994.

39.‘‘CAChe WorkSystem V3.7.’’ CAChe Scientific Inc., Beaverton, OR, 1995.

40.F Agbossou, J-F Carpentier, A Mortreux, G Surpateanu, AJ Welch. New J Chem 20:1047–1060, 1996.

41.‘‘Cerius2.’’ Molecular Simulations, Inc., San Diego, CA, 1999.

42.M Die´guez, A Ruiz, C Claver, MM Pereira, AMdAR Gonsalves. J Chem Soc Dalton Trans:3517–3522, 1998.

43.JP Collman, LS Hegedus, JR Norton, RG Finke. Principles and Applications of Organotransition Metal Chemistry. 2nd ed. Mill Valley, CA: University Science Books, 1987.

44.TW Swaddle. Inorganic Chemistry: An Industrial Environmental Perspective. San Diego, CA: Academic Press, 1997.

45.YV Kissin, RI Mink, T Nolin, AJ Brandolini. Top Catal 7:69–88, 1999.

46.EJ Arlman, P Cossee. J Catal 3:99, 1964.

47.KJ Ivin, JJ Rooney, CD Stewart, MLH Green, R Mahtab. J Chem Soc Chem Com- mun:604–606, 1978.

48.HW Turner, RR Schrock. J Am Chem Soc 104:2331–2333, 1982.

49.J Soto, ML Steigerwald, RH Grubbs. J Am Chem Soc 106:4479–4480, 1982.

50.L Clawson, J Soto, SL Buchwald, ML Steigerwald, RH Grubbs. J Am Chem Soc 107:3377–3378, 1985.

51.H Kraulendat, H-H Britzinger. Ang Chem Int Ed Engl 29:1412, 1990.

52.WE Piers, JE Bercaw. J Am Chem Soc 112:9406–9407, 1990.

53.SL Mayo, BD Olafson, WA Goddard. J Phys Chem 94:8897, 1990.

54.LA Castonguay, AK Rappe´. J Am Chem Soc 114:5832–5842, 1992.

55.H Kawamura-Kuribayashi, N Koga, K Morokuma. J Am Chem Soc 114:8687– 8694, 1992.

56.G Guerra, L Cavallo, V Venditto, M Vacatello, P Corradini. Makromol Chem Macromol Symp 69:237–246, 1993.

57.G Guerra, L Cavallo, G Moscardi, M Vacatello, P Corradini. J Am Chem Soc 116: 2988–2995, 1994.

58.G Guerra, P Corradini, L Cavallo, M Vacatello. Macromol Symp 89:307–319, 1995.

59.G Guerra, P Longo, L Cavallo, P Corradini, L Resconi. J Am Chem Soc 119:4394– 4403, 1997.

60.G Guerra, L Cavallo, P Corradini, R Fusco. Macromolecules 30:677–684, 1997.

61.L Cavallo, G Guerra, P Corradini. Gaz Chim Ital 126:463–467, 1996.

62.L Cavallo, G Guerra. Macromolecules 29:2729–2737, 1996.

63.P Corradini, V Busico, L Cavallo, G Guerra, M Vacatello, V Venditto. J Mol Catal 74:433–442, 1992.

64.M Toto, L Cavallo, P Corradini, G Moscardi, L Resconi, G Guerra. Macromolecules 31:3431–3438, 1998.

65.DY Yoon, PR Sundararajan, PJ Flory. Macromolecules 8:776, 1975.

66.UW Suter, PJ Flory. Macromolecules 8:765, 1975.

67.PR Sundararajan, PJ Flory. J Am Chem Soc 96:5025, 1974.

68.A Schafer, E Karl, L Zsolnai, G Huttner, HH Brintzinger. J Organomet Chem 328: 87, 1987.

69.T Ooi, RA Scott, K Vandekooi, HA Scheraga. J Phys Chem 46:4410, 1967.

70.RD Hancock. Prog Inorg Chem 37:187, 1989.

71.D Cozak, M Melnik. Coord Chem Rev 74:53, 1986.

72.P Ammendola, G Guerra, V Villani. Makromol Chem 185:2599, 1984.

73.LS Hegedus. Transition Metals in the Synthesis of Complex Organic Molecules. 2nd ed. Sausalito, CA: University Science Books, 1999.

74.H Klein, H Fuess. In: J Weitkamp, HG Karge, H Pfeifer, W Holderich, eds. Studies in Surface Science and Catalysis. Amsterdam: Elsevier Science, 1994, pp 2067–2074.

75.H Klein, C Kirschhock, H Fuess. J Phys Chem 98:12345–12360, 1994.

76.BF Mentzen, M Sacerdote-Peronnet. Mater Res Bull 29:1341–1348, 1994.

77.JA Horsley, JD Fellmann, EG Derouane, CM Freeman. Catalysis 147:231–240, 1994.

78.TA Hagler, S Lifson, P Dauber. J Am Chem Soc 101:5122, 1979.

79.E Jaramillo, SM Auerbach. J Phys Chem B 103:9589–9594, 1999.

80.R Millini, S Rossini. In: H Chon, S-K Ihm, YS Uh. ed. Studies in Surface Science and Catalysis. Amsterdam: Elsevier Science, 1997, pp 1389–1396.

81.K Teraishi. J Mol Catal A Chem 132: 73–85, 1998.

82.BM Bhawal, R Vetrivel, TI Reddy, ARAS Deshmukh, S Rajappa. J Phys Org Chem 7:377–384, 1994.

83.H Klein, H Fuess, S Ernst, J Weitkamp. Microporous Materials 3:291–304, 1994.

84.ER Freitas, CR Gum. Chemical Engineering Progress. 1979, pp 73–76.

85.MA Pietsch, AK Rappe´. J Am Chem Soc 118:10908, 1996.

86.AK Rappe´, MA Pietsch, DC Wiser, JR Hart, LM Bormann-Rochotte, WM Skiff. Mol Engin 7:385–400, 1997.

87.DS Brown, NO Gonzales, WM Skiff, JH Worstell. Applying molecular simulation to homogeneous catalysis. American Institute of Chemical Engineers, 1998 Annual Meeting, Miami Beach, FL, 1998.

88.JT Golab. Industrial chemistry modeling: in the new millennium. 216th American Chemical Society National Meeting, Boston, MA, 1998.

89.E Hauptman, RM Waymouth, JW Ziller. J Am Chem Soc 117:11586, 1995.

90.BP Amoco Chemicals. New Business Development Business Group. Private document.

91.P-O Norrby, B Akermark, F Haeffner, S Hansson, M Blomberg. J Am Chem Soc 115:4859, 1993.

92.PG Anderson, A Harden, D Tanner, P-O Norrby. Chem Eur J 1:12, 1995.

93.E Pena-Cabrera, P-O Norrby, M Sjogren, A Vitagliano, VD Felice, J Oslob, S Ishii, D O’Neill, B Akermark, P Helquist. J Am Chem Soc 118:4299–4313, 1996.

94.PS Pregosin, H Ruegger, R Salzmann, A Albinati, F Lianza, RW Kunz. Organometallics 13:83–90, 1994.

95.JD Oslob, B Akermark, P Helquist, P-O Norrby. Organometallics 16:3015–3021, 1997.

96.NL Allinger, X Zhou, J Bergsma. Theochem 118:69–83, 1994.

97.P-O Norrby, HC Kolb, KB Sharpless. J Am Chem Soc 116:8470–8478, 1994.

98.EJ Larson, VL Pecoraro. J Am Chem Soc 113:3810, 1991.

99.P-O Norrby, C Linde, B Akermark. J Am Chem Soc 117:11035–11036, 1995.

100.TR Cundari, L Saunders, LL Sisterhen. J Phys Chem A 102:997–1004, 1998.

101.KR Adam, M Antolovich, LG Brigden, LF Lindoy. J Am Chem Soc 113:3346– 3351, 1991.

102.MM Gugelchuk, KN Houk. J Am Chem Soc 116:330–339, 1994.

103.TR Cundari, LL Sisterhen, C Stylianopoulos. Inorg Chem 36:4029–4034, 1997.

104.JW Lauher. J Am Chem Soc 108:1521–1531, 1986.

105.L Bencze, R Szilagyi. J Organomet Chem 465:211–219, 1994.

106.VJ Burton, RJ Deeth, CM Kemp, PJ Gilbert. J Am Chem Soc 117:8407, 1995.

107.RJ Deeth, VJ Paget. J Chem Soc Dalton Trans, 537–546, 1997.

108.G Alberti, A Grassi, GM Lombardo, GC Pappalardo, R Vivani. Inorg Chem 38: 4249–4255, 1999.

109.RW Harrison. J Comp Chem 14:1112–1122, 1993.

110.AL Swain, M Miller, J Green, DH Rich, J Schneider, SBH Kent, A Wlodawer. Proc Natl Acad Sci USA 87:8805–8809, 1990.

111.IT Weber, RW Harrison. Protein Engineering 9:679–690, 1996.

112.FC Bernstein, TF Koetzle, GJB Williams, EF Meyer, MD Brice, JR Rodgers, O Kennard, M Shimanouchi, M Tasumi. J Mol Biol 112:535–542, 1977.

113.CE Sansom, J Wu, IT Webber. Protein Engineering 5:659–667, 1992.

114.W Goertz, W Keim, D Vogt, U Englert, MDK Boele, LAvd Veen, PCJ Kamer, PWNMv Leeuwen. J Chem Soc Dalton Trans:2981–2988, 1998.

115.P Faye, E Payen, D Bougeard. J Chem Soc Faraday Trans 92:2437–2443, 1996.

116.P Faye, E Payen, D Bougeard. In: GE Froment, B Delmon, P Grange, eds. Hydrotreatment and Hydrocracking of Oil Fractions. Amsterdam: Elsevier Science, 1997, pp 281–292.

117.D Gleich, R Schmid, WA Herrmann. Organometallics 17:2141–2143, 1998.

118.LA Castonguay, AK Rappe´, CJ Casewit. J Am Chem Soc 113:7177–7183, 1991.

119.JP Bowen, NL Allinger. J Org Chem 52:2937, 1987.

120.CP Casey, LM Petrovich. J Am Chem Soc 117:6007–6014, 1995.

121.CP Casey, GT Whiteker. Isr J Chem 30:299–304, 1990.

122.M Kranenberg, YEMvd Burgt, PCJ Kramer, PWNMv Leeuwen. Organometallics 14:3081–3089, 1995.

123.F Torrens. J Mol Cat A: Chem 119:393–403, 1997.

124.L Fan, D Harrison, TK Woo, T Ziegler. Organometallics 14:2018–2026, 1995.

125.Z Lin, TJ Marks. J Am Chem Soc 112:5515–5525, 1990.

126.MP Doyle, WR Winchester, JAA Hoorn, V Lynch, SH Simonsen, R Ghosh. J Am Chem Soc 115:9968–9978, 1993.

127.MP Doyle, LJ Westrum, WNE Wolthuis, MM See, WP Boone, V Bagheri, MM Pearson. J Am Chem Soc 115:958–964, 1993.

128.AA Varnek, AS Glebov, OM Petrakhin, RP Ozerov. Koord Khim 15:740, 1989.

129.HR Allcock, DC Ngo, M Parvez, RR Whittle, WJ Birdsall. J Am Chem Soc 113: 2628, 1991.

130.AA Varnek, A Maia, D Landini, A Gamba, G Morosi, G Podda. J Phys Org Chem 6:113–121, 1993.

131.RH Boyd, SM Breitling, M Mansfield. Am Inst Chem Eng 19:1016, 1973.

132.RD Hancock, SM Dobson, A Evers, PW Wade, MP Ngwenya, JCA Boeyens, KP Wainright. J Am Chem Soc 110:277, 1988.

133.RD Hancock, MP Ngwenya, PW Wade, JCA Boeyens, SM Dobson. Inorg Chim Acta 164:73–84, 1989.

134.E Brunet, AM Poveda, D Rabasco, E Oreja, LM Font, MS Batra, JC RodriguezUbis. Tetrahedron: Asymmetry 5:935–948, 1994.

135.F Verpoort, AR Bossuyt, L Verdonck, B Coussens. J of Mol Catal A Chem 115: 207–218, 1997.

136.L Bencze, RK Szilagyi. In: Y Imamoglu, ed. Metathesis Polymerization of Olefins and Polymerization of Alkynes. Dordrecht, The Netherlands: Kluwer Academic, 1998, pp 411–443.

137.B Altava, MI Burguete, JM Fraile, JI Garcia, SV Luis, JA Mayoral, AJ Royo, MJ Vicent. Tetrahedron: Asymmetry 8:2561–2570, 1997.

138.J Castro, A Moyano, MA Pericas, A Riera. Tetrahedron 51:6541–6556, 1995.

139.PD Beer, EL Tite, MGB Drew, A Ibbotson. J Chem Soc Dalton Trans 2543–2550, 1990.

140.Y-D Wu, KN Houk, JS Valentine, W Nam. Inorg Chem 31:718–720, 1992.

141.W Kaminsky, O Rabe, A-M Schauwienold, GU Schupfner, J Hanss, J Kopf. J Organomet Chem 497:181–193, 1995.

142.N Balcioglu, I Uraz (Unalan), C Bozkurt, F Serin. Polyhedron 16:327–334, 1997.

143.L Cavallo, G Guerra, G Moscardi, P Corradini. Polym Mater Sci Eng 73:465–466, 1995.

144.L Bencze, R Szilagyi. J Mol Cat 76:145–156, 1992.

145.M Clarke, RD Cramer, N Vanopden-Bosch. J Comput Chem 10:982, 1989.

146.RD Hancock, AE Martell, D Chen, RJ Motekaitis, D McManus. Can J Chem 75: 591–600, 1997.

147.AF Wells. Structural Inorganic Chemistry. Clarence, UK: Oxford, 1986, pp. 289.

148.JCA Boeyens, FA Cotton, S Han. Inorg Chem 24:1750, 1985.

149.NL Allinger, MI Quinn, K Chen, B Thompson, MR Frierson. J Mol Struct 194:1, 1989.

150.B Didillon, C Houtman, T Shay, JP Candy, JM Basset. J Am Chem Soc 115:9380– 9388, 1993.

151.F Humblot, D Didillon, F Lepeltier, JP Candy, J Corker, O Clause, F Bayard, JM Basset. J Am Chem Soc 120:137–146, 1998.

152.MGB Drew, PCH Mitchaell, S Kasztelan. J Chem Soc Faraday Trans 86:697, 1990.

153.TM Brunier, MGB Drew, PCH Mitchell. J Chem Soc Faraday Trans 88:3225– 3232, 1992.

154.S Ramdas, JM Thomas, AK Cheetham, PW Betteridge, EK Davies. Angew Chem Int Ed Engl 23:671–679, 1984.

155.PA Wright, JM Thomas, AK Cheetham, AK Nowak. Nature 318:611–614, 1985.

156.P Demontis, S Yashonath, ML Klein. J Phys Chem 93:5016–5019, 1989.

157.RL June, AT Bell, DN Theodorou. J Phys Chem 94:8232–8240, 1990.

158.S Yashonath. J Phys Chem 95:5877–5881, 1991.

159.G Schrimpf, M Schlenkrich, J Brickmann, P Bopp. J Phys Chem 96:7404–7410, 1992.

160.F Bosselet, M Sacerdote, J Bouix, BF Mentzen. Mat Res Bull 25:443–450, 1990.

161.M Sacerdote, F Bosselet, BF Mentzen. Mat Res Bull 25:593–599, 1990.

162.DE Williams. Acta Cryst A36:715–723, 1980.

163.DE Williams, DJ Houpt. Acta Cryst B42:286–295, 1986.

164.AL Kieselev, AA Lopatkin, AA Shulga. Zeolites 5:261, 1985.

165.MA Pietsch, AK Rappe´. J Am Chem Soc 118:10908–10909, 1996.

166.JR Hart, AK Rappe´. J Am Chem Soc 115:6159–6164, 1993.

167.DC Wiser, AK Rappe´. Polym Mater Sci Eng 74:423–424, 1996.

168.TR Cundari, J Deng, W Fu, TR Klinckman, A Yoshikawa. J Chem Inf Comput Sci 38:941–948, 1998.

169.AK Cheetham, JD Gale, AK Nowak, BK Peterson, SD Pickett, JM Thomas. Faraday Discuss Chem Soc 87:79–90, 1989.

Because it is electron deficient in most of its molecular environments, electronic structure calculations on compounds that contain titanium are generally more complicated than are analogous calculations on species that contain only lighter main group elements. One reason for this is that its electron deficiency results in the formation of unusual structural arrangements that are difficult to describe using simple computational methods. Likewise, since it is frequently impossible to draw one simple Lewis structure for Ti-containing compounds, the usual methods that are based on single configuration wavefunctions are often inappropriate.

This chapter reviews a range of recent calculations on several different problems involving titanium chemistry, performed primarily by this group. We begin, in Section 2, by considering the theoretical and computational methods that have been used. This is followed, in Section 3, by a discussion of unusual structures and associated potential energy surfaces that occur in titanium chemistry due in large part to the electron-deficient nature of this element. In Section 4, the potential use of divalent Ti as a catalyst is discussed. A summary and discussion of future topics is presented in Section 5.

2. THEORETICAL METHODS

Since titanium is a moderately heavy element, it can be beneficial to make use of effective core potentials (ECPs), in which the inner-shell electrons are replaced with a model potential (4). The advantage of this approach is that the computational effort is significantly reduced, since only the valence electrons are explicitly considered. Considerable effort has been expended in the development of efficient methods for obtaining analytic first and second energy derivatives, gradients, and hessians, in order to make geometry optimizations and frequency calculations more feasible. The primary disadvantage is that the most common ECPs, those developed by Hay and Wadt (5), Stevens and coworkers (6), and Christiansen et al. (7), use relatively small basis sets, since their initial developments occurred before the use of systematically large basis sets became commonplace. So one can expect at most semiquantitative accuracy using ECPs. It should be emphasized, however, that ECPs should be thought of as alternative basis sets, so that all of the common methods for recovering electron correlation can be used with them.

Fortunately, Ti is still small enough (22 electrons) that one can frequently perform all-electron calculations, at least to obtain the final energetics. Although far more effort has been expended in developing extended basis sets for main group elements, there are valence triple zeta (TZV) basis sets available for the first-row transition metals, and these are frequently used in this laboratory, augmented by polarization functions (8). This means one uses p functions on hydrogens, d functions on main group elements, and f functions on transition metals.

Because Ti has four valence electrons (s2d2), one expects that the chemistry

of this element may bear some resemblance to that of the Group IVA elements carbon and silicon (s2p2). On the other hand, a simple picture for the ground electronic valence state of C or Si would have all valence orbitals singly occupied, with none empty, whereas an analogous picture for Ti would leave two empty d orbitals. In this sense, titanium is more similar to the electron-deficient elements boron and aluminum. From this perspective, one might expect titanium compounds to have unusual structures, both molecular and electronic. An important consequence of this observation is that it will often be impossible to write a single, simple Lewis structure for compounds that contain Ti. This generally means that it is difficult to find a single electronic configuration that adequately describes what the electrons are doing in such species. Then a single configuration wavefunction, such as that employed by the Hartree–Fock molecular orbital method or by density functional theory, is unlikely to be appropriate, even as a starting point for subsequent correlated calculations. In such cases a multiconfigurational (MC) wavefunction must be considered. The most common approach is the complete active space (CAS) self-consistent field (SCF) or fully optimized reaction space (FORS) method. Both of these approaches are specific examples of the more general MCSCF method (9).

The key in carrying out MCSCF calculations is the determination of a reasonable ‘‘active space,’’ that set of orbitals and electrons that are directly involved in the chemistry to be described. The active space in turn defines the set of electronic configurations that determine the MCSCF wavefunction. The choice of active spaces is described in a recent review (9). While the MCSCF wavefunction provides a qualitatively correct description of a system, it does not account for the bulk of the electron correlation, usually referred to as ‘‘dynamic’’ correlation.

For systems that are adequately described by single-configuration wavefunctions, dynamic correlation is most commonly accounted for by second-order perturbation theory, referred to as many-body perturbation theory (MBPT2 (10)) or Moeller–Plesset perturbation theory (MP2 (11)). While higher orders of perturbation theory are frequently used, the reliability of these higher-order methods and the convergence of the perturbation expansion has been increasingly called into question (12,13). The more reliable endpoint for accurate energies is coupled cluster (CC) theory. These are most commonly implemented at the singleand double-excitation level, with triple excitations included perturbatively, CCSD(T) (14). When MCSCF wavefunctions are used as the reference, the most commonly used methods for recovering the electron correlation are multireference configuration interaction (MRCI) (15) and multireference perturbation theory (MRPT) (16). The former is usually implemented at the singleand double-excitation level, MR(SD)CI, but it is so computationally demanding that this level of theory is still limited to small active spaces. Second-order MRPT is more efficient, as indeed is its single-reference analog.

Geometry optimizations are generally carried out at the SCF, MCSCF, or