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76.N Kaltsoyannis, BE Bursten. J Organomet Chem 528:19–33, 1997.

77.(a) H Koch, P Jørgensen, T Helgaker. J Chem Phys 104:9528–9530, 1996. (b) K Pierloot, BJ Persson, BO Roos. J Phys Chem 99:3465–3472, 1995. (c) C Park, JJ Almlo¨f. Chem Phys 95:1829–1833, 1991. (d) HP Lu¨thi, PEM Siegbahn, J Almlo¨f, K Faegri Jr, A Heiberg. Chem Phys Lett 111, 1–6, 1984. (e) TE Taylor, MB Hall. Chem Phys Lett 114:338–342, 1985.

78.For discussion of the effects of Madelung potentials of the crystal field on the bond lengths of molecules in crystals, see, for example: J Li, S Irle, WHE Schwarz. Inorg Chem 36:100–109, 1996.

79.(a) See, for example: JE Huheey, EA Keiter, RL Keiter. Inorganic Chemistry: Principles of Structure and Reactivity. 4th ed. New York: Harper Collins, 1993, Chap 14. (b) For a recent theoretical analysis of actinide contraction and its comparison with the lanthanide contraction, see: M Seth, M Dolg, P Fulde, P Schwerdtfeger. J Am Chem Soc 117:6597–6598, 1995, and references therein.

80.F Takusagawa, TF Koetzle. Acta Crystallogr B35:1074–1081, 1979. An electrondiffraction study determines even a greater bending (3.7°): A Haaland, J Lusztyk, DP Novak, J Brunvoll, KB Starowieyski. J Chem Soc Chem Commun 54–55, 1974.

81.M Elian, MML Chen, MP Mingos, R Hoffmann. Inorg Chem 15:1148–1155, 1976.

82.IA Ronova, DA Bochvar, AL Chistyakov, Yu T Struchkov, NV Alekseev. J Organomet Chem 18:337–344, 1969.

83.We have examined the effects of spin-orbit coupling on the geometry structures and vibrational frequencies of U(C7H7)2 and found them to be negligible ( 1%) for the f1 actinide system. J Li, BE Bursten. To be submitted.

84.Experimental results: (a) L Brewer. J Opt Soc Am 61:1666–1682, 1971. (b) MSS Brooks, B Johansson, HL Skriver. In: AJ Freeman, GH Lander, eds. Handbook on the Physics and Chemistry of the Actinides. Vol 1. Amsterdam: North-Holland, 1984, Chap 3. (c) MS Fred. In: JJ Katz, GT Seaborg, LR Morss, eds. The Chemistry of the Actinides Elements. Vol 2. 2nd ed. New York: Chapman and Hall, 1986, Chap 15. (d) WT Carnall, HM Crosswhite. In: JJ Katz, GT Seaborg, LR Morss, eds. The Chemistry of the Actinides Elements. Vol 2. 2nd ed. New York: Chapman and Hall, 1986, Chap 16.

85.For theoretical results, see, for example: (a) P Pyykko¨, LJ Laakkonen, K Tatsumi. Inorg Chem 28:1801–1805, 1989. (b) KW Bagnall. The Actinide Elements. Amsterdam: Elsevier, 1972, Chap 1.

86.The multiplet effects are estimated to lower the Th and U atomic energies by 4.3 and 19.2 kcal/mol following the procedure described in Ref. 87.

87.Without spin-orbit coupling, atomic ground state multiplet energies can be calculated in DFT from D∞h determinants; see: EJ Baerends, V Branchadell, M Sodupe. Chem Phys Lett 265:481–489, 1997.

88.NT Kuznetsov, KV Kir’yanov, VA Mitin, VG Sevast’yanov, VA Bogdanov. Radiokhimiya 28:709–7121, 1986.

89.For a discussion of spin-orbit coupling of f electrons, see, for example: A Abragam, B Bleaney. Electron Paramagnetic Resonance of Transition Ions. Oxford: Clarendon Press, 1970.

90.Extensive compilations of all the singleand double-point groups can be found in:

(a) JA Salthouse, MJ Ware. Point Group Character Tables and Related Data. Lon-

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don: Cambridge University Press, 1972. (b) SL Altmann, P Herzig. Point-Group Theory Tables. Oxford: Clarendon Press, 1994.

91.K Zhao. Electronic Structure of Heavy-Element Molecules: Pa@C28, Pa(C8H8)2, and the Jahn–Teller Effect in VCl4. PhD dissertation, The Ohio State University, Columbus, Ohio, 1996.

92.JC Slater. Adv Quantum Chem 6:1–92, 1972.

93.See, for example: BE Douglas, CA Hollingsworth. Symmetry in Bonding and Spectra: An Introduction. Orlando, Fl: Academic Press, 1985.

94.JP Solar, HPG Burghard, RH Banks, A Streitwieser Jr, D Brown. Inorg Chem 19: 2186–2188, 1980.

95.NM Edelstein, J Goffart. In: JJ Katz, GT Seaborg, LR Morss, eds. The Chemistry of the Actinides Elements. Vol 2. 2nd ed. New York: Chapman and Hall, 1986, Chap 18.

96.KD Warren. Inorg Chem 14:3095–3103, 1975.

97.KO Hodgson, F Mares, DF Starks, A Streitwieser Jr. J Am Chem Soc 95:8650– 8658, 1973.

98.For a comprehensive review of vibrational spectra of transition metal π-complexes of CnHn (n 3–8) rings, see: HP Fritz. In: FGA Stone, R West, eds. Advances in Organometallic Chemistry. Vol 1. New York: Academic Press, 1964, pp 239– 316.

99.For a summary, see: DG Karraker, JA Stone, ER Jones Jr, N Edelstein. J Am Chem Soc 92:4841–4845, 1970.

100.J Goffart, J Fuger, B Gilbert, B Kanellakopulos, G Duyckaerts. Inorg Nucl Chem Lett 8:403–412, 1972.

101.J Goffart, J Fuger, D Brown, G Duyckaerts. Inorg Nucl Chem Lett 10:413–419, 1974.

102.L Hocks, J Goffart, G Duyckaerts, P Teyssie. Spectrochim Acta 30A:907–914, 1974.

103.FA Cotton. Chemical Applications of Group Theory. 3rd ed. New York: Wiley, 1990.

104.G Herzberg. IR and Raman Spectra. New York: Van Nostrand, 1945, p 154.

105.F Mares, K Hodgson, A Streitwieser Jr. J Organomet Chem 24:C68–C70, 1970.

106.(a) C Adamo, V Barone. J Chem Phys 110:6158–6170, 1999. (b) AD Becke. J Chem Phys 107:8554–8555 1997. (c) PJ Stephens, F Devlin, CF Chabalowski, MJ Frisch. J Phys Chem 98:11623–11627, 1994. (d) AD Becke. J Chem Phys 98: 5648–5652, 1993.

107.(a) AD Becke. J Comp Chem 20:63–69, 1999. (b) JP Perdew, S Kurth, A Zupan, P Blaha. Phys Rev Lett 82:2554–2547, 1999. (c) AD Becke. J Chem Phys 109: 2092–2098, 1998. (d) T Van Voorhis, GE Scuseria. J Chem Phys 109:400–410, 1998.

108.(a) EKU Gross, JF Dobson, M. Petersilka. Top Curr Chem 181:81–172, 1996. (b) R Singh, BM Deb. Phys Rep 311:47–94, 1999.

109.Assessments of the performances of various new exchange-correlation functionals have been carried out recently. See, for example: (a) AJ Cohen, NC Handy. Chem Phys Lett 316:160–166, 2000. (b) S Kurth, JP Perdew, P Blaha. Int J Quantum Chem 75:889–909, 1999. (c) AD Rabuck, GE Scuseria. Chem Phys Lett 309:450– 456, 1999.

15

Pi Bonding in Group 13–Group 15 Analogs of Ethene

Ashalla McGee, Freida S. Dale,

Soon S. Yoon, and Tracy P. Hamilton

The University of Alabama at Birmingham, Birmingham, Alabama

1. INTRODUCTION

The study of pi bonding in main group chemistry has been primarily concerned with organic molecules or analogs within Group 14, such as disilene. The latter was quite challenging, and much experimental and theoretical work went into its study and preparation (1). The difficulty of making pi bonds in the heavier elements is due to their weakness and reactivity (which necessitates steric protection). However, Power’s group has made a great deal of progress in synthesizing molecules that are isoelectronic to derivatives of famous organics, such as ethene and benzene, using heavy main group elements from families other than Group 14 (2). We will concentrate only on those that have two groups bonded to each atom, just as in ethene.

The pi bond strength in the case of ethene (and most other olefins) is 64 kcal/mol and is determined by several methods. We will discuss some of the most common and evaluate their prospects for being meaningful in Group 13– Group 15 pi bonds. The conceptually simplest is to twist the molecule so that the 2p orbitals no longer overlap. This has the advantage that the number obtained

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is able to be determined by kinetics; i.e., the pi bond strength is the activation barrier for rotation. For ethene, rotation produces an unpaired electron at each carbon (a diradical). This is poorly described by a single electronic configuration, and an electronic correlation method based on a single Slater determinant will have problems (3). Fortunately, in the study here, the pair of electrons that make the pi bond remains on the Group 15 atom. This enables the use of low-level theories for accurate rotation barriers.

Another procedure involves the hydrogenation of ethene. Assuming that the C–C sigma bond does not significantly change, then the energy of the reaction is the energy of the two newly formed C–H bonds minus the H–H bond energy and the C–C pi bond energy. Hydrogenation energies are typically 28 kcal/mol (ethene’s is 32.8 kcal/mol) (4), the C–H bond is 98 kcal/mol and the H–H bond energy is 103 kcal/mol (5). This gives 60 kcal/mol for the pi bond energy. The agreement between this and the foregoing is good. For the compounds we will consider, there is a serious problem, because hydrogenation produces a compound that has a significantly different sigma bond—an adduct!

A third option, closely related to the second, involves computing pi bond energies from a reaction and standard or assumed bond energies. Two ethenes could in principle dimerize to form cyclobutane so that the energy of the formation reaction is the two newly formed C–C bonds plus the strain energy minus the two C–C pi bond energies. Using the strain energy of 26.3 kcal/mol (5), the C–C sigma bond energy of 81 kcal/mol and the dimerization energy of 18.3 kcal/mol (from heats of formation of ethene and cyclobutane) (6), the computed pi bond energy is 59 kcal/mol. In this case, the prospect for obtaining a check on the pi bond energy is good, for dimerization will create what are definitely sigma bonds, but the strain energy of the resulting rings still needs to be known. This is apparent when one examines the variety of rings and cages, some with quite acute bond angles, as in the chemistry of Al-N compounds (7).

This chapter will present a comprehensive study of the ethene analogs produced by taking an element from the set M B, Al, Ga and one from Group 15 E N, P, As. Most of this work was performed by undergraduates in this lab over the years. It was ideally suited for an undergraduate research project because of the simplicity of the bonding concepts and of the absence of many complicated theoretical issues. Many of the systems here have been studied by other groups in the meantime, with results scattered throughout the literature. However, this chapter will include new material, such as an examination of the performance of relativistic effective core potentials.

Some of the early explanations of the weakness of pi bonding in the heavier elements rationalized it as being due to the weaker overlap between p orbitals. Now it is better understood to result from energetic effects. For the heavier elements there is an energetic preference to form lone pairs. Lappert first explained

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FIGURE 1 Dative bonding model proposed by Lappert. (From Ref. 8.)

the structure of a distannene as being due to the double dative interaction, as shown in Figure 1 (8).

Another way of rationalizing the bending associated with lack of pi bonding is by a second-order Jahn–Teller effect that mixes the pi and a σ* orbital (9). A third explanation, by Trinquier and Malrieu, is an extension of Lappert’s work. It predicts whether the Lappert model or the classic σ, π formation will take place based on the singlet–triplet splitting in the fragments created by dissociating the bond (10). As a consequence, electropositive substituents, which stabilize the triplet relative to the singlet, increase the pi bond strength. A very good review is given by Grev (11). No theoretical studies to date have attempted to see how these concepts work for the Group 13–Group 15 molecules here. It is reasonable to assume that the orbital mixing will work, since it explains pyramidalization, which is to be expected for P and As (and is seen in these compounds). The fragment electronic states are going to be doublets and quartets upon homolytic

FIGURE 2 Simple model for the pi bonding and dimerization in R2MCER2 molecules.

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bond dissociation into fragments, so how these apply is unclear. One thing we will briefly look at later is the effect of an electropositive substituent on the pi bond energy.

A good model of the bonding in the R2MCER2 compounds is given in Figure 2. This model, in which the weak pi bond is most like a dative donation of the lone pair on the Group 15 atom to the empty orbital on the Group 13 atom, is one reason why the pi bond is expected to be even weaker than between two Group 14 elements from the same rows. Elimination reactions that produce pi bonds rarely give end products with pi bonds, because the bonding allows easy dimerization (also shown in Fig. 2).

2. THEORETICAL METHODS

Geometries were initially optimized at the Hartree–Fock (HF) level of theory with the 3-21G basis set. Even though high levels of theory are not required to study these systems, the 3-21G basis set lacks d polarization functions. Because of that, the lone pairs of the Group 15 element are inadequately described. It is well known that a basis set that is saturated with s and p functions will predict that ammonia is planar. Subsequent geometry optimizations were carried out at the HF/6-31G** and MP2/6-31G** levels of theory.

For the heavier elements, relativistic effects due to the core may become important. To account for this in the simplest way, the electrons in the core can be replaced by a potential that produces the same valence electron distribution as an all-electron relativistic computation. This also reduces the computer time needed as well, since the number of functions is reduced. Another hazard of doing all-electron calculations with small basis sets on lower-row elements is that the bond lengths have large error. The relativistic effective core potential (RECP) that we employed was CEP-121G** (12). For this RECP, the geometry was optimized at the MP2 level of theory, and a single-point energy was computed at the CCSD(T) level of theory (13).

HF and MP2 optimized structures with the 6-31G** basis set were characterized by computing the harmonic vibrational frequencies. Given the popularity and success of the hybrid density functional method B3LYP, attempts were made to compare it with the MP2 results using the CEP-121G** basis. Since the capability for doing frequencies with RECP basis sets is not yet programmed into Gaussian, the frequencies were unable to be computed. Given the consistency of the structures for every level of theory and the clear understanding of whether the structures should be minima or transitions state or have two imaginary frequencies, the results will be reported as having the same hessian signature as the other levels of theory. Calculations were performed using various versions of the Gaussian program, the latest being Gaussian 98 (14).

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3. RESULTS AND DISCUSSION

3.1. Monoamides

The results break into two classes: the molecules with nitrogen as the Group 15 element, and those with heavier Group 15 elements. We will discuss the more interesting nitrogen-containing compounds first. Energies for the monoamides are given in Table 1, and the optimized geometrical parameters are given in Table 2.

The minimum structures are all planar (see Fig. 3). This alone indicates significant pi bonding, because there must be significant conjugation of the ‘‘lone pair’’ of electrons. This was previously computed by other groups for H2BNH2 and H2AlNH2 (15–18). In fact, we predicted that H2GaNH2 would be planar and have a nonnegligible pi bond energy based on the similarity of the behavior of the Ga–P and Ga–As structures to the corresponding Al– P and Al–As structures (vide infra).

First, the rotational barriers for the monoamides are close to those obtained previously by other groups. McKee (15) and Allen and Fink (16) computed the B–N pi bond to be 32 and 38 kcal/mol, respectively. Fink et al. (17) computed the pi bond strength to be 11.2 kcal/mol for Al–N and 12.8 for Ga–N. Davy and Jaffrey obtained 10.7 kcal/mol for Al–N earlier (18). These values are quite close, although it should be noted that Fink et al. used the energy difference between the planar and perpendicular forms, which exaggerates the difference between Al–N and Ga–N. This also explains why the previously published value of 38 kcal/mol for B–N is higher than the value from the rotational barrier.

A preliminary computation of the rotation barriers for silyl-substituted H2AlNH2 was performed in our laboratory, to see if the effects of electropositive (relative to H) groups would have the effect of strengthening the pi bond. These were computed at the B3LYP/6-31G* level of theory (19). The absolute energies are 881.039016 for H2AlN(SiH3)2 and 881.013040 for (SiH3)2AlNH2. This shows that the silyl group stabilizes the compound more when attached to nitrogen. However, the barrier to rotation for H2AlN(SiH3)2 (at 5.9 kcal/mol) is actually lower than in H2AlNH2. This is not the case when silyl groups replace hydrogen in silicon compounds; in that case pi bonds are strengthened. When silyl substitution is on the aluminum, the rotation barrier is unaffected (11.6 kcal/mol with no vibration correction).

Finally, we note that Muller also performed calculations on Me2AlNH2, finding a rotation barrier slightly less than in H2AlNH2 (at 9.7 kcal/mol) (20).

The transition state for rotation about the Group 13–N bond shows that the pi bond energy is significant, but not nearly as large as for ethene (except in the case of H2BNH2, which has a pi bond energy of 30 kcal/mol, ethene has a 65 kcal/mol pi energy). The transition-state structures are all of the same type

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TABLE 1 Absolute Energies (atomic units) and Relative Energies (kcal/ mol) for Ethene Analogs Having N as Group 15 Elementsa

	B–N	Al–N	Ga–N
SCF/6-31G**
Planar	81.499210	298.705968	1978.014931
	(0.0)	(0.0)	(0.0)
Perpendicular	81.446139	298.688487	1977.994129
	(30.5)	(9.7)	(11.7)
Transition state	81.452544		1977.995435
	(27.3)		(11.3)
MP2/6-31G**
Planar	81.765481	298.949746	1978.274816
	(0.0)	(0.0)	(0.0)
Perpendicular	81.704846	298.929494	1978.249167
	(35.3)	(11.4)	(14.7)
Transition state	81.713399	298.929643	1978.252197
	(30.6)	(11.6)	(13.3)
MP2/CEP-121G**
Planar	15.010717	14.213364	269.809824
	(0.0)	(0.0)	(0.0)
Perpendicular	14.951296	14.193298	269.785224
	(34.6)	(11.3)	(14.0)
Transition state	14.959744	14.193902	269.789012
	(29.9)	(11.2)	(12.2)
CCSD(T)b
Planar	15.044599	14.246036	269.803575
	(0.0)	(0.0)	(0.0)
Perpendicular	14.984415	14.225250	269.778913
	(35.1)	(11.7)	(14.1)
Transition state	14.993436	14.225985	269.782843
	(30.0)	(11.6)	(12.1)

aThe relative energies are in parentheses and have zero-point vibrational energy included.

bWith the CEP-121G** basis set, at a MP2/CEP-121G** optimized geometry.

(Fig. 3) and are essentially the linkage of a borane, alane, or gallane group with a pyramidal amide. The C2v twist structure has two imaginary frequencies and is hence is of less importance. The difference in energy between the C2v twist and the transition state for H2BNH2 is close to the inversion barrier of 5 kcal/ mol in ammonia. The inversion of nitrogen for the Ga analog is quite small, and it is almost nonexistent for Al. As a matter of fact, at the HF/6-31G** level of theory the twist structure goes to the perpendicular one, and zero-point energy

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TABLE 2 Geometrical Parameters for Group 13–N Ethene Analogs, (bond

˚

distances in, A bond angles in degrees)

Planar	B–N	Al–N	Ga–N
SCF/6-31G**	1.388	1.770	1.821
MP2/6-31G**	1.393	1.780	1.825
MP2/CEP-121G**	1.401	1.783	1.812
	HBH	HAlH	HGaH
HF/6-31G**	121.1	123.1	124.1
MP2/6-31G**	122.0	124.1	126.1
MP2/CEP-121G**	122.5	124.6	126.4
	HNH	HNH	HNH
HF/6-31G**	113.9	110.3	111.2
MP2/6-31G**	114.0	110.4	111.4
MP2/CEP-121G**	114.1	110.3	111.7
	B–H	Al–H	Ga–H
HF/6-31G**	1.193	1.581	1.573
MP2/6-31G**	1.189	1.576	1.564
MP2/CEP-121G**	1.193	1.577	1.537
	N–H	N–H	N–H
HF/6-31G**	0.994	0.997	0.996
MP2/6-31G**	1.005	1.008	1.007
MP2/CEP-121G**	1.009	1.012	1.011
Perpendicular	B–N	Al–N	Ga–N
SCF/6-31G**	1.455	1.792	1.853
MP2/6-31G**	1.458	1.801	1.857
MP2/CEP-121G**	1.467	1.805	1.848
	HBH	HAlH	HGaH
HF/6-31G**	116.6	117.5	119.6
MP2/6-31G**	116.5	117.2	119.7
MP2/CEP-121G**	117.2	118.1	120.9
	HNH	HNH	HNH
HF/6-31G**	114.1	109.4	110.8
MP2/6-31G**	114.0	109.4	110.9
MP2/CEP-121G**	113.9	109.3	111.3
	B–H	Al–H	Ga–H
HF/6-31G**	1.201	1.585	1.580
MP2/6-31G**	1.199	1.582	1.574
MP2/CEP-121G**	1.203	1.583	1.548
	N–H	N–H	N–H
HF/6-31G**	0.993	0.997	0.996
MP2/6-31G**	1.002	1.007	1.006
MP2/CEP-121G**	1.007	1.011	1.009