Journal of Molecular Structure: THEOCHEM 908 (2009) 55–60

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Journal of Molecular Structure: THEOCHEM

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The ‘‘steric acidity” of the zirconium methyl amide complexes: A theoretical study

Xin Zhao, Yuntao Zhang *

Institute of Applied Chemistry, China West Normal University, Nanchong, Sichuan 637002, PR China

a r t i c l e i n f o

Article history:Received 19 December 2008Received in revised form 13 April 2009Accepted 3 May 2009Available online 18 May 2009

Keywords:Steric acidityZirconium methyl amide complexesDeprotonationDFT

0166-1280/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.theochem.2009.05.007

* Corresponding author. Tel.: +86 0817 2314462.E-mail address: nczyt@yahoo.com.cn (Y. Zhang).

a b s t r a c t

Density functional theory calculations have been used to study the acidity of the N–H proton in the zir-conium methyl amide complexes. A process containing two steps has been proposed by us to understandthe acidity of the N–H proton in these amide complexes: the first step is their deprotonation; and the sec-ond one is the reactions of the resultant anions from the deprotonation step with the Li(THF)n cation toform the lithium zirconimidate complexes. The present calculations show that the acidity of the N–H pro-ton in the zirconium methyl amide complexes is determined by the deprotonation step since the reac-tions of the resultant anions from the deprotonation with the LiTHF cation are barrierless. Solvationdoes not influence the deprotonation step. Thus, the acidity of these zirconium methyl amide complexescan be compared directly. In the deprotonation step, all these N–H bond lengths in these zirconiummethyl amide complexes are 1.02 Å and the difference in the structures of these complex are these sub-stituents on the two CP ligands. The repulsion between these substituents on the two CP ligands can bedecreased by the loss of the N-bound proton. Thus, the steric strain, including the repulsion betweenthese substituents on the two CP ligands as well as the angle stain of the linking group (CH2–CH2) thatconnect the two CP ligands coordinating to the Zr center, should be responsible for the acidity strengthorder of the zirconium methyl amide complexes. The zirconium methyl amide complexes represent arare ‘‘steric acidity”. The proposed process can account well for the experimental observation. This workis very helpful for experimentalist to better understand the ‘‘steric acidity” of the zirconium methylamide complexes.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Early-transition-metal imide complexes have been the interestof synthetic chemist since they can mediate numerous nitrogen-transfer reactions [1]. Generally, these imide complexes can beprepared from the metal amide species via a hypothetical stepwiseprocess, which may involve a potential intermediate of an imidatecomplex [2–4]. However, the structural characterization of theseimidate complexes are difficult since they are very active [5–8].

Recently, Bergman and co-workers reported [9] that they hadacquired the crystal structures of these lithium zirconimidate com-plexes and investigated their basicity by analyzing the acidity ofthe N–H proton in the zirconium methyl amide complexes. Theexperimental results show that from 1 to 3 (Scheme 1), the zirco-nium methyl amide complexes with more methyl groups on theancillary cyclopentadienyl (CP) ligands have stronger acidity. Thus,Bergman et al. suggested that these lithium zirconimidate com-plexes represented a rare ‘‘steric acidity” [10,11]. Furthermore,Bergman et al. have presumed that it is difficult to compare theacidity between the zirconium methyl amide complexes 1–4 since

ll rights reserved.

the non-ansa zirconimidate complex 1a–3a are solvated by oneTHF molecule, while the rac-(ebthi) zirconimidate complex 4a issolvated by two THF molecules (Scheme 1). Considering the repul-sion between the N-bound tBu, the Zr-bound CH3, the C-bound Phand the Li-bound THF groups, it is very difficult to convert 1–4 into1a–4a in one step. Therefore, we propose a process containing twosteps to understand the acidity of these amide complexes: the firststep is the deprotonation of 1–4; and the second one is the reac-tions of the resultant anions from the deprotonation step withthe Li(THF)n cation to form 1a–4a (Scheme 2, just using the forma-tion of 1a from 1 to illustrate this process). Observably, the acidityof the zirconium methyl amide complexes 1–4 should be deter-mined by the rate-limiting step of the process to convert 1–4 into1a–4a.

Numerous reports [12–15] have shown that the theoretical cal-culation is a power tool to understand the mechanistic details ofthe experimental observations. For example, Mota et al. haveinvestigated the acidity of zeolite (Brønsted acid) through the the-oretical calculations and proposed a new viewpoint to account forthe catalytic property of zeolite [16]. All of these zirconium methylamide complexes 1–4 that are studied in this work are Brønstedacids. Their acidities have been investigated through density func-tional theory calculations. The present calculations show that the

Table 1Selected bond lengths (Å) from X-ray and PBE-optimized structures of 1a and 3a.

Bond lengths 1a 3a

X-ray (exp.) PBE X-ray (exp.) PBE

Zr–C 2.36 2.39 2.37 2.39Zr–N 1.91 1.94 1.91 1.94Zr–Li 2.79 2.78 2.81 2.76N–Li 2.00 1.98 2.00 1.98Li–O 1.89 1.95 1.85 1.95

+ Ph3CH+[Ph3C][Li(THF)4]1-4 1a-4aKeq

[D8]THF

R'

R

Me

N

tBu

Zr LiTHF

1: R=R'=Me;2: R=H, R'=Me;3: R=R'=H;

R'

R

Me

NH

tBu

Zr

1a: R=R'=Me;2a: R=H, R'=Me;3a: R=R'=H;

Me

N

tBu

Zr Li(THF)2

Me

NH

tBu

Zr

4 4a

Scheme 1. The reactions that identify the acidities of methyl amide complexes 1–4.

Me

NH

tBu

Zr

1

[Ph3C]

Me

N

tBu

Zr + Ph3CH[LiTHF]

RMe

N

tBu

Zr LiTHF

1a1anion

Scheme 2. The reaction path to produce 1a from 1 proposed by us.

56 X. Zhao, Y. Zhang / Journal of Molecular Structure: THEOCHEM 908 (2009) 55–60

acidity of these zirconium methyl amide complexes 1–4 is deter-mined by the deprotonation step since the reactions of the resul-tant anions with the LiTHF cation are barrierless. In thedeprotonation step, all these N–H bond lengths in these zirconiummethyl amide complexes are 1.02 Å and the difference in the struc-tures of these complex are the quantities of these CH3 groups onthe two CP ligands. Thus, the steric strain, including the repulsionbetween the two CP ligands as well as the angle stain of linkinggroup (CH2–CH2) that result from the coordination of the two CPligands to the Zr center, should be responsible for the aciditystrength order (4 > 1 > 2 > 3). Furthermore, the Zr–N bond strengthand solvent effect also have influence on the acidity of the zirco-nium methyl amide complexes. The proposed process can accountwell for the experimental acidity strength order and is very helpfulfor experimentalist to better understand the ”steric acidity” of thezirconium methyl amide complexes.

2. Computational details

All calculations are performed with the PBE [17] method imple-mented in Gaussian 03 program [18]. For the Zr atom, relativisticeffective core potential [19] (ECP) is employed and the basis setis a modified LANL2DZ double-n basis set plus an f-type polariza-tion function, [20] in which the two 5p functions of the standardLANL2DZ have been replaced by the optimized 5p functions fromCouty and Hall [21]. The 6-31++G(d, p) basis set is employed forthese C atoms of the two CP ligands that coordinate to the Zr atom,the Zr-bound N and C atoms, the N-bound H atom as well as the Liand O atoms. The rest of atoms are treated with 6-31G(d, p) basisset. Vibrational frequencies are obtained for all stationary pointsto check whether the optimized geometry corresponds to a mini-mum and to obtain Gibbs free energies at the temperature of298.15 K.

To consider the bulk solvent effects on the free energies of allspecies, we have employed the CPCM [22,23] method with tetrahy-drofuran as the solvent to calculate the Gibbs free energy of solva-tion for these species using their gas-phase optimized geometries.In CPCM, the calculated energies and properties depend on the cav-ity size. We have used the UAKS cavity in our calculations, as sug-gested by previous work [24]. The free energy for each species insolution is taken as the sum of the gas-phase free energy and thefree energy of solvation.

3. Result and discussion

The crystal structures of the lithium zirconimidate complexes1a and 3a have been acquired by Bergman et al. In the experimentsthat identify the acid strength of the N–H proton in 1–4, the Zr–C,Zr–N, Zr–Li, N–Li and Li–O bonds are main involved. According toTable 1, the Zr–C, Zr–N, Zr–Li, N–Li and Li–O bonds in the opti-mized 1a and 3a at the PBE level are in good agreement with thesefrom the corresponding X-ray structures, in which the smallest andthe largest deviations from the corresponding X-ray values arefound in the Zr–Li bond of 1a (0.01 Å) and the Li–O bond of 3a(0.1 Å), respectively. Thus the used theoretical method is appropri-ate for studying the acidity of these zirconium methyl amide com-plexes. The optimized geometries of all stationary points and therelated data are shown in Figs. 1–5 and Table 2, respectively.

Just as mentioned above, the process converting 1–4 into 1a–4acontains two steps: the first step is the deprotonation of 1–4; andthe second one is the reactions of the resultant anions from thedeprotonation step with the Li(THF)n cation to form 1a–4a. In thefollowing, we will discuss the two steps separately.

3.1. The deprotonation of the zirconium methyl amide complexes

Density functional theory calculations have been widely used tostudy the acidity of Brønsted acids via calculating the deprotona-tion energies [15,16,25]. Thus, we investigate the deprotonationstep by calculating the deprotonation energies of the N–H protonin the zirconium methyl amide complexes.

After considering the solvent effect (Table 2), one can see that 4has the smallest deprotonation energy (324.0 kcal/mol), followedby 1 (326.6 kcal/mol), 2 (326.7 kcal/mol) and 3 (328.1 kcal/mol).

According to Fig. 1, one can see that all the N–H bond lengths in1–4 are 1.02 Å. Furthermore, the lengths of the Zr–C, Zr–N bonds in1–4 and that of the Zr–C and Zr–N bonds in 1anion–4anion arenearly identical. However, in 1, the two CP ligands that coordinatewith the Zr center both have five CH3 groups. For 2, there are fiveCH3 groups on the CP ligand below the Zr–N–C plane and four CH3

groups on the CP ligand above the Zr–N–C plane. In 3, just four CH3

groups are on both two CP ligands. Except for the substituentes(CH2CH3CH3CH2) on the two CP ligands of 4, there still is a CH2–CH2 group to link the two CP ligands together (Fig. 1).

When the CP ligands coordinate with the Zr center, the morethe CH3 groups on the CP ligands are, the larger the repulsion be-tween the two CP ligands is. From 1 to 3, the distances betweenthe Zr center and the CP ligand below the Zr center are 2.64 Å,2.63 Å and 2.59 Å (Fig. 1), respectively, indicating the compromiseof the repulsion between the CP ligands and the coordination of theCP ligand with the Zr center. Thus, the zirconium methyl amidecomplexes with more CH3 groups on the CP ligands are less stablethan these complexes with less CH3 groups on the CP ligands sincethe former should endure the larger repulsion than the latter. Afterthe deprotonation, the repulsion between the two CP ligands de-crease and the interaction between Zr and N increase, indicatingby the 1.88 Å of the Zr–N bond length and 2.89 Å, 2.88 Å, 2.81 Åof the distances between the Zr center and the CP ligand below

Fig. 1. The optimized geometries of stationary points in the deprotonation step of the zirconium methyl amide complexes 1–4. Hydrogen atoms (except the N-bound H) areomitted for clarity.

Fig. 2. The optimized geometries of 1a–4a in the reactions of the resultant anions with the Li(THF)n cation. Hydrogen atoms are omitted for clarity.

Rel

ativ

e en

ergy

(K

cal/m

ol)

R(N-Li)/angstrom

Me

Me

Me

N

tBu

Zr + Li O

Me

Me

Me

N

tBu

Zr LiTHF

1.902.002.102.202.302.402.502.602.702.802.903.00

-125

-120

-115

-110

01anion LiTHF cation

1a

-130

Fig. 3. The relaxed potential energy scan for the formation of the N–Li bond in thereaction of 1anion with LiTHF cation to form 1a.

X. Zhao, Y. Zhang / Journal of Molecular Structure: THEOCHEM 908 (2009) 55–60 57

the Zr center in 1anion–3anion (Fig. 1). Deprotonation can lowerthe repulsion between the two CP ligands. Thus, 1 is of the smallestdeprotonation energy, followed by 2 and 3 (3 > 2 > 1). For 4, whenthe two CP ligands coordinate with the Zr center, the repulsion be-

tween the two CP ligands with the substituentes (CH2CH2CH2CH2)and the angle strain of the linking group (CH2–CH2) that resultfrom the coordination of the CP ligands with the Zr center all make4 unstable, which may result in the lowest deprotonation energy of4 in 1–4 (324.0 kcal/mol).

According to these mentioned above, one can see that 4 hasthe lowest deprotonation energy (324.0 kcal/mol), followed by1 (326.6 kcal/mol), 2 (326.7 kcal/mol) and 3 (328.1 kcal/mol).All the N–H bond lengths in 1–4 are 1.02 Å and the lengths ofthe Zr–C, Zr–N bonds in 1–4 and that of the Zr–C and Zr–Nbonds in 1anion–4anion are nearly identical. Deprotonationcan lower the repulsion between the two CP ligands. Thus, thesteric strain, including the repulsion between these two CP li-gands as well as the angle stain of linking group (CH2–CH2 in4) that result from the coordination of the two CP ligands tothe Zr center, should be responsible for the order of the depro-tonation energies (4<1<2<3).

3.2. The reaction of the resultant anions with the Li(THF)n cation

In this step, the resultant anions 1anion–4anion should reactwith the Li(THF)n cation to form these lithium zirconimidate com-plexes 1a–4a (Fig. 2). Bergman and co-workers have acquired the

Fig. 4. The optimized geometries of stationary points in the deprotonation step of the zirconium methyl amide complexes 5–9. Hydrogen atoms (except the N-bound H) areomitted for clarity.

Fig. 5. The optimized geometries of 10–13. Hydrogen atoms are omitted for clarity.

Table 2The calculated deprotonation energies of 1–4.

The deprotonation of 1–4 DG (kcal/mol) DGsol (kcal/mol)

1?1anion + H+ 349.6 326.62?2anion + H+ 350.2 326.73?3anion + H+ 352.4 328.14?4anion + H+ 349.7 324.0

58 X. Zhao, Y. Zhang / Journal of Molecular Structure: THEOCHEM 908 (2009) 55–60

crystal structures of 1a and 3a [9]. Furthermore, these optimizedbond lengths are in good agreement with these from the corre-sponding X-ray structures (Table 1), indicating that the bondlengths from the optimized 2a and 4a is also reliable. In 1a–3a,the lengths of the Zr–C, Zr–N and N–Li bonds are nearly identical;

but the distances between the Zr center and the CP ligand belowthe Zr center are 2.81 Å, 2.76 Å and 2.70 Å (Fig. 2), respectively,representing the coordination of the CP ligands with the Zr centerincreases when the repulsion between the CH3 groups on the CP li-gands decreases. Complex 4a is solvated by two THF molecules.The distances between Zr and N as well as Zr and O are obviouslylonger than the corresponding values of 1a–3a (Fig. 2), being due tothe repulsion between the two THF molecules and the Zr-boundCH3 group, the N-bound tBu group.

We have investigated the reactions of these anions 1anion–4anion with the Li(THF)n cation through a detailed relaxed poten-tial energy scan by fixing the N–Li distance at various values in therange of 2.20–3.00 Å (Fig. 3, for simplicity, just the potential energyprofile of the reaction of 1ainon with LiTHF cation to form 1a is

X. Zhao, Y. Zhang / Journal of Molecular Structure: THEOCHEM 908 (2009) 55–60 59

shown). The starting point of the potential energy scan is the 1an-ion and LiTHF cation. Then, we decrease the N–Li distance gradu-ally from 3.00 to 2.20 Å and optimize all the other degrees offreedom. As seen from Fig. 3, the energy decreases monotonouslywith an exothermicity of 126.1 kcal/mol (from 1anion + LiTHF cat-ion to 1a). The present results show that the reaction of the anion1anion with the LiTHF cation is a barrierless process. It is true forthe reactions of 2anion–4anion with the LiTHF cation to form 2a–4a.

According to the results mentioned above, the acidity of the N–H proton in these zirconium methyl amide complexes 1–4 is deter-mined by the deprotonation step since the reactions of 1anion–4anion with the LiTHF cation to form 1a–4a are barrierless. Inthe deprotonation step, the present results show that 4 has thelowest deprotonation energy (324.0 kcal/mol), followed by 1(326.6 kcal/mol), 2 (326.7 kcal/mol) and 3 (328.1 kcal/mol). Thelower the deprotonation energy is, the stronger the acidity is[15–16,25]. Thus, 4 is the most acidic, then followed by 1, 2 and3 (4 > 1 > 2 > 3). All the N–H bond lengths in 1–4 are 1.02 Å. Fur-thermore, the lengths of the Zr–C, Zr–N bonds in 1–4 and that ofthe Zr–C and Zr–N bonds in 1anion–4anion are nearly identical.Deprotonation can lower the repulsion between the CH3 groups.Therefore, the repulsion between the CH3 groups on the two CP li-gands and the angle strain of the linking group (CH2–CH2) that re-sult from the coordination of the CP ligands with the Zr centershould be responsible for the acidity strength order. The zirconiummethyl amide complexes 1–4 represent a rare ‘‘steric acidity”.

4. Comparison with the experimental results

Bergman and co-workers have investigated [9] the acidity of theN–H proton in the zirconium methyl amide complexes by the reac-tions of 4 with 3a as well as 1a–4a with Ph3CH. In the reaction of 4with 3a, the resultant 3 and 4a show that 4 is more acidic than 3.From the reactions of 1a–4a with Ph3CH, Bergman et al. have ac-quired the pKa values for the zirconium methyl amide complexes1–4, which indicate 4 is the most acidic, followed by 1, 2 and 3(4 > 1 > 2 > 3). Our calculations are very good consistent with theexperimental acidity strength order. All of these N–H bond lengthsin 1–4 are 1.02 Å, the difference in the structures of 1–4 are thequantities of these CH3 groups on the two CP ligands and deproto-nation can lower the repulsion between the two CP ligands. Thus,the steric strain, including the repulsion between the two CP li-gands in 1–4 and the angle stain of linking group (CH2–CH2) in 4when the two CP ligands coordinate to the Zr center, should beresponsible for the acidity strength order. Our results support thesuggestion of ‘‘steric acidity” proposed by Bergman et al. But, Berg-man et al. thought that the acidity between the species 1–3 and 4can not be compared directly since the non-ansa zirconimidatecomplex 1a–3a are solvated by one THF molecule and the rac-(ebthi) zirconimidate complex 4a is solvated by two THF molecules(Scheme 1). According to our results, the acidity of these zirconiummethyl amide complexes 1–4 is determined by the deprotonationstep since the reactions of the anion 1anion–4anion with theLiTHF cation are barrierless. Thus, we think that the acidity of 1–4 can be compared directly because the steric strain is the domi-nant role in the deprotonation step.

For deeper understand the acidity of the zirconium methylamide complexes, we have recalculated the deprotonation energyof the N–H proton in some zirconium methyl amide complexes:(1) removing the five CH3 groups gradually from the CP ligand be-low the Zr–N–C plane while keep the quantity of the CH3 groups onthe CP ligand above the Zr–N–C plane in the zirconium methylamide complexes 1 unchangeable (Fig. 4); (2) fixing the Zr–CP dis-tance after deprotonation of the zirconium methyl amide com-

plexes 1–4. In the following, we will discuss the two situationsseparately (Fig. 5).

When the CH3 groups of the CP group below the Zr–N–C planeare removed one by one, our calculation show that 9 is the mostacidic, followed by 8, 6, 7 and 5 since their deprotonation energyare 322.9 kcal/mol, 323.3 kcal/mol, 323.6 kcal/mol, 325.4 kcal/moland 327.3 kcal/mol, respectively. According to Fig. 4, the distancebetween the Zr atom and the CP ligand above the Zr–N–C planein 5–9 does not shorten obviously after the CH3 group on the CP li-gand below the Zr–N–C plane is removed one by one, implying thesteric strain not only come from the repulsion between the CH3

groups on the two CP ligands, but also from the repulsion betweenthe CH3 groups on the CP ligand and the Zr-bound CH3 group. Fur-thermore, the Zr–N distance shortens slowly and gradually from 5to 9, which will influence the coordination of CP ligand with the Zratom. In addition, from 5anion to 9anion, the free energy of solva-tion increases with the decrease of the CH3 group on the CP ligandbelow the Zr–N–C plane. The free energy of solvation of 5anion is�11.86 kcal/mol, then �13.42 kcal/mol for 6anion, �14.69 kcal/mol for 7anion, �16.15 kcal/mol for 8anion, �17.25 kcal/mol for9anion. Thus, the present calculation here show that the acidityof the zirconium methyl amide complexes is influenced by manyfactors, such as the steric strain, the interaction between the Zratom and N atom, solvent effect et al. The zirconium methyl amidecomplexes just represent the ‘‘steric acidity” when the steric strainbecome predominant, such as 1–4. But for 5–9, with the decreaseof the quantities of CH3 group on the CP ligand, steric strain isnot the predominant role in determining the acidity. Thus, theiracidity does not change monotonously with the decrease of theCH3 group on the CP ligand below the Zr–N–C plane.

When the Zr–CP distance is fixed after the deprotonation, thecalculated deprotonation energy (electronic energy plus the freeenergy of solvation) is 338.2 kcal.mol (10), 338.3 kcal/mol (13),340.9 kcal/mol (12) and 341.7 kcal/mol (11). According to Fig. 5,it is clearly to see that when the Zr–CP distance is fixed, the Zr–N distance in the restrict optimization is longer than that in the fulloptimization (see Fig. 1). This may be due to the repulsion betweenthe fixed CP ligand and the N-bond CH3 group. The long Zr–Ndistance will result in that the interaction between the negativecharge center (the Zr-bound N atom) and the solvent molecule ismore easily to occur. For example, the free energy of solvation of1anion is �11.06 kcal/mol and that of 10 is �12.86 kcal/mol;2anion (�11.82 kcal/mol) and 11(�13.22 kcal/mol); 3anion(�12.97 kcal/mol) and 12(�14.63 kcal/mol); 4anion (�19.21 kcal/mol) and 13(�19.73 kcal/mol). Thus, when the Zr–CP distance isfixed after the deprotonation, the solvent effect shall play a verysignificant role in the acidity of the zirconium methyl amide com-plexes as well. The combination of the steric strain and the solventeffect result in that the acidity of 10–13 does not alter monoto-nously with the change of steric strain.

5. Summary

In this article, we have presented a detailed density functionaltheory to investigate the acidity of the N–H proton in these zirco-nium methyl amide complexes 1–4. We have proposed a processcontaining two steps to understand the acidity of the N–H protonin these zirconium methyl amide complexes: the first step is thetheir deprotonation; and the second one is the reactions of theresultant anions from the deprotonation step with the Li(THF)n cat-ion to form the lithium zirconimidate complexes. Our results showthat the acidity of these zirconium methyl amide complexes 1–4 isdetermined by the deprotonation step since the reactions of 1a-nion–4anion with the LiTHF cation are barrierless. 4 is the mostacidic, followed by 1, 2 and 3 (4 > 1 > 2 > 3). All the N–H bond

60 X. Zhao, Y. Zhang / Journal of Molecular Structure: THEOCHEM 908 (2009) 55–60

lengths in 1–4 are 1.02 Å. Furthermore, the lengths of the Zr–C, Zr–N bonds in 1–4 and that of the Zr–C and Zr–N bonds in 1anion–4anion are nearly identical. Thus, the steric strain, including therepulsion between these substituentes on the two CP ligands in1–4 and the angle stain of linking group (CH2–CH2) in 4 whenthe two CP ligands coordinate to the Zr center, should be responsi-ble for the acidity strength order. The further study show that theacidity of the zirconium methyl amide complexes is influenced bymany factors, such as the steric strain, the interaction between theZr atom and N atom, solvent effect et al and only express as ‘‘stericacidity” when the steric strain become predominant, such as thezirconium methyl amide complexes 1–4.

The proposed process can account well for the experimentalacidity strength order and is very helpful for experimentalist tobetter understand the acidity of the zirconium methyl amidecomplexes.

Appendix A. Supplementary material

Supplementary data (electronic energies and Gibbs free ener-gies of all related species, as well as Cartesian coordinates of all sta-tionary points) associated with this article can be found, in theonline version, at doi:10.1016/j.theochem.2009.05.007.

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