Structural motifs, thermodynamic properties, bonding and aromaticity of sandwich complexes formed by alkaline earth metals with pentafulvene. A theoretical approach

Structural motifs, thermodynamic properties, bonding and aromaticity of sandwich complexes formed by alkaline earth metals with pentafulvene. A theoretical approach

Journal of Organometallic Chemistry 708-709 (2012) 10e17 Contents lists available at SciVerse ScienceDirect Journal of Organometallic Chemistry jour...

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Journal of Organometallic Chemistry 708-709 (2012) 10e17

Contents lists available at SciVerse ScienceDirect

Journal of Organometallic Chemistry journal homepage: www.elsevier.com/locate/jorganchem

Structural motifs, thermodynamic properties, bonding and aromaticity of sandwich complexes formed by alkaline earth metals with pentafulvene. A theoretical approach Wojciech P. Oziminski a, b, * a b

National Medicines Institute, Chełmska 30/34, 00 725 Warsaw, Poland Institute of Nuclear Chemistry and Technology, Dorodna 16, 03 195 Warsaw, Poland

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 January 2012 Received in revised form 2 February 2012 Accepted 8 February 2012

Structure of M(h5-C6H6)2 complexes, where M¼(Be, Ma, Ca, Sr, Ba), and C6H6 is the pentafulvene, was optimized at the B3LYP/6e311þþG(d,p)/ECP level of theory. Two types of complexes were found: (cis-) singlet ansa-metallocenes with the cis-arrangement of two pentafulvene rings and (trans-) triplet sandwich type pentafulvene complexes of trans-where two pentafulvene molecules are rotated in respect to each other by various degrees. All metals except beryllium are bonded in h5-mode of coordination. The charge transfer of 1.6e1.8 e from the metal atom to the pentafulvene ring estimated by Natural Population Analysis results in aromatization of the fulvene rings, which is documented by three aromaticity indices: electronic pEDA, geometric HOMA and magnetic NICS(1)ZZ. For sandwich complexes pEDA and NICS(1)ZZ are linearly correlated. Bonding situation in systems under study was analyzed by Energy Decomposition Analysis at the B3LYP/TZP/ZORA level. The electrostatic contribution is dominant, especially in the case of cis-complexes, however the covalent contribution is substantial, especially for beryllium complex. Exceptionally low dissociation energy of magnesium complex can be explained by the fact that the electrostatic and orbital contributions are not fully compensating the high Pauli repulsion term. Ó 2012 Elsevier B.V. All rights reserved.

Keywords: Pentafulvene Alkaline earth pEDA HOMA Aromaticity Bonding

1. Introduction Since the accidental discovery of ferrocene [1,2] there exist a growing interest in investigating sandwich type organometallic complexes called metallocenes, which have important applications particularly in synthetic [3] and industrial [4] chemistry. Metallocenes with many different metal atoms from main block elements were synthesized and structurally characterized by X-ray spectroscopy, including alkaline earth metals like Mg or Ca and p-block metals like Al, Ga, In, Sn and Pb [5]. Experimental work in this area was complemented by many theoretical studies, reviewed recently by Kwon and McKee [6]. The cyclopentadiene radical (Cp), which act as a ligand in metallocenes, withdraws an electron from a metal atom, thus acquiring the electronic sextet according to Huckel’s rule [7]. The energetic stabilization stemming from this process overcomes the energy needed to put the metal atom into its ionized state and thus,

* National Medicines Institute, Che1mska 30/34, 00 725 Warsaw, Poland. Tel.: þ48 22 841 21 21x166; fax: þ48 22 841 06 52. E-mail address: [email protected]. 0022-328X/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jorganchem.2012.02.012

such sandwich complexes are stable species. Because of the shift of the electron density from the metal atom to the Cp, bonding in metallocenes is commonly thought to be mainly ionic, but it was shown by Frenking and Lein that it is rather a mixture of ionic and covalent contributions and the relative proportion of both types of bonding varies along the groups of Periodic Table [8]. Geometric shapes and bonding in metallocenes formed by s-block elements were extensively investigated by means of theoretical methods [9,10]. However, the Cp is not the only unsaturated five-membered carbon ring which tends to withdraw the electron density from a metal atom. Another interesting ligand is the pentafulvene molecule [11]. This hydrocarbon has a five-membered ring with only two double bonds. Contrary to the cyclopentadiene, in the pentafulvene, all ring carbon atoms are sp2-hybridized because there exist a third exo-double bond (Fig. 1). This molecule readily withdraws the electron density from substituents [12] or from metal atoms as it was shown in the case of lithium atom [13]. The presence of C1]C6 exo-double bond additionally facilitates aromatization of the ring, being additional source of the electron density which can be transferred into the ring. After transferring the electron density from metal atom to the

W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17

H

H

6

1 5

2 4 3

Fig. 1. Atom numbering scheme in pentafulvene.

ring, the later acquires considerable negative charge, which is mainly transferred to 2pz orbitals of the ring carbon atoms, so similarly to the Cp complexes, the bonding forces are supposed to be both covalent and electrostatic. During this aromatization process the CC bond lengths of the ring tend to equalize, and there arises a diatropic ring current [13] which can be detected in simplified manner by calculating the NMR shielding in the centre of the ring. There is a rising interest in studying aromaticity and properties of fulvenes [14e19] and theoretical tools seem to be particularly suitable for them, because of unstable nature of these hydrocarbons [20]. Metal-pentafulvene complexes being similar but different than metal-Cp complexes, can find their applications in similar fields, like catalysis or drug design. The cis-arrangement of two fulvene rings leads to ansa-complexes which find their application as catalysts [21] or drugs [22]. The number of papers dealing with metal-pentafulvene complexes is increasing [23e25]. Regarding the alkaline earth metals, the reductive coupling of dimethyl-fulvene by magnesium was investigated [26]. More recently, the ansa-bridged magnesocenes [27] and metallocenes containing strontium and calcium [28,29] were also described. However there were no systematic study on structure and bonding in pentafulvene e alkaline earth metal complexes, and this prompted us to undertake the current study. The main purpose of this project is to investigate the geometric parameters, electronic properties and aromaticity of metalpentafulvene sandwich type complexes of the following formula M(h5-C6H6)2 (M ¼ Be, Mg, Ca, Sr, Ba). The main questions are: (1) what is the preferred geometry of such complexes (2) how much of the electron density is transferred from the metal atom into the pentafulvene rings (3) what is the degree of aromatization of both pentafulvene rings in these complexes (4) how large is the binding energy (5) what is the nature of bonding (ionic/covalent) in this class of molecules. 2. Methods Geometry optimization of metal-pentafulvene complexes was performed using the hybrid B3LYP [30,31] DFT functional with Pople style valence triple-z basis set 6e311þþG(d,p) [32e34] with polarization and diffuse functions on all atoms, to properly account for long-range metal-ring interactions. For the Sr and Ba atoms the Stuttgart-Dresden Effective Core Potentials (ECP) with accompanying basis set were employed. Particularly, in the case of strontium atom (6s6p5d)/[4s4p2d] basis set was employed while 28 core electrons were replaced by MWB28 ECP, and in the case of barium (6s6p5d1f)/[4s4p2d] basis set was employed while 46 core electrons were replaced by MWB46 ECP [35]. In all cases a frequency calculation was performed to prove that there are no imaginary frequencies, thus the structures obtained are true energetic minima. To ensure that all the possible minima on the Potential

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Energy Surface are identified, several starting point structures of each complex were employed for geometry optimization. Apart from obvious parallel (cis-) and antiparallel (trans-) isomers, other starting structures were generated by rotation of one pentafulvene molecule respectively to the other. Electron density distribution after the formation of metalpentafulvene complex was analysed using Natural Population Analysis (NPA) [36]. Further, we employed the pEDA [37] approach which we previously used successfully to analyze the pi-electron structure of heptafulvene [38], substituted pentafulvenes [12] and its complex with lithium [13]. This parameter can be conventionally used for analyzing the donation/withdrawal of electron density to/ from a ring. For the 5-membered ring of the pentafulvene it is defined in the following way:

pEDA ¼

5 X i¼1

pifulvene  5

(1)

where pi is the 2pz Natural Atomic Orbital (perpendicular to the plane of the molecule) of the i-th ring carbon atom. The five sp2hybridized carbon atoms of the ring contributes five electrons to the ring, so the pEDA index for this non-aromatic system is close to zero. If some electron density is added to ring pi-system, pEDA becomes positive, achieving the value of 1 for the fully aromatic sextet. In the case of aromatization of the pentafulvene by substituents, the maximum value of pEDA ¼ 0.31 was observed for NMe2 substituent [12], and in the case of aromatization by h5 coordinated lithium atom [13], pEDA was equal to 0.8 which is a value close to 1. This parameter we can use as an electronic aromaticity index, which can be applied to characterize the degree of aromatization of the pentafulvene ring. Because of multidimensional character of aromaticity [39] it is necessary to compare several indices of different nature. Thus, the second index we employ is a geometry-based index HOMA (Harmonic Oscillator Model of Aromaticity) [40,41]. It is defined as a normalized sum of squared deviations of bond lengths from the values for a system assumed as fully aromatic. For hydrocarbons the appropriate expression has the following form:

HOMA ¼ 1 

n  aX

n

Ropt  Ri

2

(2)

i

where “n” is the number of CC bonds taken into summation, a ¼ 257.7 is an empirical normalization constant chosen to give HOMA ¼ 0 for completely non-aromatic system and HOMA ¼ 1 for a system where all bonds are equal to Ropt ¼ 1.388 Å which is the optimal aromatic bond length and Ri are the experimental or computed bond lengths. As the third aromaticity index we use NICS(1)ZZ which is calculated as the shielding constant of a ghost atom located 1 Å above the geometric centre of the fulvene ring. NICS(1)ZZ which is equal to the Z-component of the induced magnetic field [42,43] is at present, the recommended [44] variant of the original NICS index [45]. Binding energy of the complexes was calculated according to two schemes. First scheme: according to supramolecular approach, it was calculated as the difference between the energy of the complex and the sum of the energies of the free metal atom and the two free, optimized, isolated pentafulvene molecules (Eq (3)). Total electronic energy of the complex was corrected for Basis Set Superposition Error (BSSE) according to Boys Counterpoise method [46] (assuming neutral fulvene molecules and neutral metal atom as references), and for ZPE (Zero-Point Vibrational Energy) correction. The energy of the free fulvene molecule was also corrected for ZPE.

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De ¼

W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17





Emetal atom þ 2*Efree pentafulvene  Ecomplex BSSE

(3)

A binding energy calculated in this manner is an estimation of the complex dissociation energy De. All calculations in this part of the study were performed using Gaussian 03 suite of programs [47]. Second scheme: the binding energy was calculated according to EDA (Energy Decomposition Analysis) scheme developed by ZieglereRauk [48] and further extended by Baerends and coworkers [49,50]. In this method the Interaction Energy: DEint, which measures interaction between metal and ligand fragments (in complex geometry), is calculated. The interaction energy of the complex can be further decomposed into electrostatic (DEelstat), Pauli repulsion (DEPauli) and orbital interactions (DEorb) terms:

DEint ¼ DEelstat þ DEPauli þ DEorb

(4)

Calculations of EDA were performed with the B3LYP functional and uncontracted Slater-type orbitals [51] as basis functions of triple zeta quality basis set (TZP) with one set of polarization functions for all atoms. Relativistic effects were accounted for via Zeroth Order Relativistic Approximation (ZORA) [52] correction. ADF program [50,53] was employed for EDA analysis. Two sets of calculations were performed: for decomposition to neutral fragments and to charged fragments. The former approach resembles more closely the actual dissociation/formation process for these complexes where the sandwich dissociates into a neutral alkaline earth atom and neutral fulvene molecule and is well suited for analyzing the binding energy of the complex. The later approach is better suited for analyzing the bonding situation and to comparing electrostatic and orbital (charge transfer) interactions because in the complex the estimated charge on metal ion is close to þ2, thus seeing such complex as an association of positively charged ion and negatively charged ligand is legitimated for bonding analysis (8). DEint differs from the De by the term DEprep which is the energetic cost of deforming neutral fulvene molecule from its free state equilibrium geometry to the geometry of the complex (Eq (5)).

De ¼ DEprep þ DEint

(5)

Because two different theoretical approaches were employed there is a need to compare them. Therefore we made additional Gaussian B3LYP/6e311þþG(d,p) calculations of the energy of separated ligands in complex geometry (Edeformed ligand) and made an estimation of DEint at this level of theory:





DEint ðSupraÞ ¼ Emetal atom þ Edeformed ligand  Ecomplex BSSE (6) This allowed us to make a direct comparison of interaction energies obtained by Gaussian and ADF approach and check their consistency.

all the complexes, we performed two optimizations: for singlet state and for tripled state. It follows that complexes with transgeometry in triplet state are more stable by more than 6 kcal/mol than singlet states. Thus, only the triplet states of trans-complexes will be analyzed. On the contrary, in cis-complexes a covalent bond forms between fulvene fragments and singlet state is much more stable (several dozens of kcal/mol) so triplet states of cis-complexes shall not be discussed here. 3.1. cis-M(h5-C6H6)2 complexes As was mentioned in the previous paragraph, if the two rings are positioned in cis-position, the two exo-CH2 groups are joined by a bond and as a result, one ligand molecule is formed (Fig. 2). The reason behind this behaviour is that when a metal atom is approaching to the fulvene moiety, it donates its charge, and the charge mainly locates at the ring and at the exo-CH2 carbon atom, thus forming a partial radical, which is very reactive. If two such radicals meet, they dimerize forming a new covalent connection. The resulting complex is actually a metallocene where two Cp rings are connected by an ansa-bond (Fig. 2). The smaller the ionic radius of an element, the smaller is the Mring distance (Table 1) and the larger the XeMeX0 angle. For barium this angle equals to 112.9 , quite close to 90 , so the metal atom is more outside the rings. For smaller atoms this angle is much larger, for magnesium about 140 , so the metal atom is more enclosed by the two rings. Two dihedral angles can be used to measure the degree of C1eC6eC60 eC10 linker steric strain: XeC1eC10 eX0 and C1eC6eC60 eC10. They are defined differently but the trend in their changes is similar e they are largest for barium and smallest for magnesium (Table 1). If C1eC6eC60 eC10 angle becomes too small, steric strain for C6 and C60 sp3 hybridized carbon atoms becomes too large and indeed in the case of beryllium this geometry is no longer possible. Instead a complex is formed, where the beryllium atom is coordinated to one ring in h5mode and to the other ring in h1-mode via a covalent BeeC bond (Fig. S1, Electronic Supplementary InformationeESI). The distance of Be atom to C1eC6 ring is very small (1.464 Å) and strong polarization of charge may be expected here. The distance to C50 carbon atom is equal to 1.75 Å. For this new bonding scheme of beryllium complex both XeC1eC10 eX0 and C1eC6eC60 eC10 dihedral angles have values between these for Mg and Ca, thus the steric strain is relieved. Bond lengths between carbon ring atoms are similar in these complexes because of aromatization of the ring. One interesting thing is that the C3eC4 bond (nominally single) is longest only in magnesium complex. In other complexes this bond is the shortest.

3. Geometries and dissociation energies Contrary to the simple Cp ligand, complexes with pentafulvene exhibit broader range of different structural configurations. The two fulvene molecules can be positioned in cis- or trans-positions and in several in-between (“twisted”) modes. The other difference between Cp and fulvene ligands is that in M(Cp)2 complexes charged metal and charged Cp fragments are undoubtedly in singlet states, but in the case of M(C6H6)2 complexes (where C6H6 is the pentafulvene), the charged fulvene rings can be singlet or triplet. We observe that the charge donated by metal atom is close to the formal charge of þ2, so the two fulvene molecules accepts approximately 2 e of electron density. However, these two electrons do not necessarily have to be of opposite spin. Therefore, for

Fig. 2. cis-M(h5-C6H6)2 (M ¼ Mg, Ca, Sr, Ba) complexes.

W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17

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Table 1 Selected geometric parameters [Å, deg], and complex dissociation energy [kcal/mol] of cis-M(h5-C6H6)2 complexes.

MeX C1eC2 C2eC3 C3eC4 C1eC6 XeMeX0 XeC1eC10 eX0 C1eC6eC60 eC10 De

Bea

Mg

Ca

Sr

Ba

1.464 1.423 1.424 1.422 1.507 142.368 26.782 44.751 111.86

2.012 1.423 1.423 1.428 1.511 139.898 15.800 36.765 69.44

2.339 1.420 1.421 1.417 1.513 126.177 22.563 47.884 114.69

2.522 1.421 1.421 1.416 1.513 119.594 25.621 52.385 108.63

2.717 1.420 1.421 1.413 1.512 112.886 28.901 56.516 119.99

a Beryllium complex is of different bonding scheme (Fig. S1) and cannot be compared directly. Only the geometry of the h5-mode bonded ring is presented here.

Magnesium complex is also the least stable with dissociation energy (De) only 69.44 kcal/mol. One of the reasons is the mentioned steric strain in the linker connecting two pentafulvene rings. In magnesium complex this destabilizing interaction is largest in the series Ba, Sr, Ca, Mg and in the complex of the next metal e beryllium, it is relieved because of different geometry. With the exception of magnesium, the De of all studied complexes are of similar magnitude and do not follow any obvious trend. The binding energy of the cis-complexes is high e over 100 kcal/mol. This is not surprising as the complex can be described as ansabridged metallocene with two Cp rings. The binding energy of these complexes seems to be a rather complicated function of metal-ring distance, metal and ring charge (both contributing to electrostatic interactions) and the angle between the two rings (which is related to some steric strain in the rings). It will be further decomposed into various contributions in following paragraphs. 3.2. trans-M(h5-C6H6)2 complexes We performed full geometry optimizations for various possible arrangements of two fulvene molecules. As a result, depending on the metal atom, various geometrical arrangements of the two fulvene rings were found as the minima of the energy. Because of the tendency of the 5-membered ring to withdraw electron density and acquire aromatic sextet the fulvene molecule is polarized in such a way that the ring possess a negative charge and the exo-carbon atom positive charge. Thus, in addition to the interaction with positively charged metal atom, the trans-complexes should be stabilized by favourable electrostatic interactions between oppositely charged fragments of the fulvene molecules. Despite of this effect, the most stable isomers are not fully trans but are between cis- and trans-arrangements (Fig. 3). A parameter which quantitatively characterizes this “twist” is C1eXeX0 eC10 dihedral angle (Table 2). Other important parameter is XeMeX0 angle which characterizes to which extent the two fulvene rings are not parallel. This parameter is equal to almost 180 for magnesium complex and is decreasing to 146 for barium complex. Thus, in most of the studied complexes the two rings are not planar. This is a well known phenomenon is Cp complexes (5, 8). The metal e fulvene centre distance is increasing monotonically as the ionic radius of a metal atom increases just as in the case of cis-complexes. Different pattern is however observed for ring carbon bond length. In transcomplexes the bonds distances are more altered, for example C1eC2 bond is distinctly longer than C2eC3 bond. Thus, the expected degree of aromatization (indicated by HOMA) in transcomplexes is expected to be smaller. Beryllium forms a different trans-complex where one ring is bound in h1-mode and another in

Fig. 3. trans-M(h5-C6H6)2 (M ¼ Mg, Ca, Sr, Ba) complexes.

h5-mode (Fig. S2, ESI). The two rings are almost antiparallel e they

are twisted by 150 relative to each other. In a way, similar situation takes place for magnesium complexes. In the most stable isomer the two rings are rotated by 124 . In complexes of CaeBa metals the rotation angle between rings varies from 64 for calcium, through 75.3 for strontium to 147.8 for barium (Table 2). There is no clear correlation between metal-ring distance and C1eXeX0 eC10 angle for the most stable complex. For Be, Mg and Ba this angle is high which means almost trans-arrangement which is expected from the electrostatic point of view (pentafulvene is polarized in such way that the antiparallel arrangement should be favourable). On the contrary, in the Ca and Sr complexes the angle C1eXeX0 eC10 is quite small (Table 2). Thus, it seems that the geometric arrangement of trans-complexes is the result of interplay of electrostatic and covalent interactions. 4. Aromaticity indices 4.1. cis-M(h5-C6H6)2 complexes The reason behind high stability of studied compounds is the increase of aromaticity of the fulvene ring upon charge transfer from the metal atom. Three different measures of aromaticity are applied to quantify this phenomenon: HOMA, pEDA and NICS(1)ZZ. The results are gathered in Table 3. For the beryllium case the results for both rings are given separately because of presence of two different modes of bonding in this case. For other metals the average value for the two rings is presented.

Table 2 Selected geometric parameters [Å, deg], and complex dissociation energy [kcal/mol] of trans-M(h5-C6H6)2 complexes.

MeX C1eC2 C2eC3 C3eC4 C1eC6 XeMeX0 C1eXeX0 eC10 De

Bea

Mg

Ca

Sr

Ba

1.493 1.441 1.416 1.424 1.418 153.548 150.305 66.38

2.029 1.446 1.415 1.427 1.411 179.823 124.295 26.40

2.367 1.444 1.407 1.425 1.408 164.298 64.230 72.45

2.565 1.445 1.405 1.427 1.407 158.331 75.283 67.53

2.767 1.444 1.403 1.426 1.405 145.904 147.834 78.21

a Beryllium complex is of different bonding scheme (Fig. S2) and cannot be compared directly. Only the geometry of the h5-mode bonded ring is presented here.

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W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17

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Table 3 Aromaticity indices of cis-M(h5-C6H6)2 complexes. HOMA

pEDA

NICS(1)ZZ

0.681 0.070 0.666 0.736 0.738 0.753

0.769 0.652 0.848 0.820 0.830 0.825

31.34 24.83 32.03 31.76 31.51 31.15

A good reference for theses systems is the aromaticity of Lifulvene complex (HOMA ¼ 0.563, pEDA ¼ 0.784, NICS(1)ZZ ¼ 24.19) (13). First let’s look at Mg, Ca, Sr, Ba series. All indices show that these ansa-metallocenes are more aromatic than Li-fulvene complex. Bond equalization is higher (HOMA) and the pi-electron system is closer to the aromatic sextet (pEDA). Also the magnetic index NICS(1)ZZ indicates more pronounced diatropic ring current. These indices confirm different nature of Li-fulvene and ansa-metallocene complexes. Extraordinarily small stability of magnesium complex is not significantly reflected in its aromaticity. Only HOMA value is markedly smaller for this complex and two other indices are similar to Ca, Sr, Ba. A reason for this behaviour can lie in pronouncedly longer C3eC4 bond length of magnesium complex (Table 1). In the beryllium complex the two rings behave differently. First ring is h5 coordinated and its aromaticity is high but a little smaller than in MgeBa complexes according to HOMA and pEDA. According to NICS(1)ZZ it is very similar. Second ring, coordinated in h1-mode, is less aromatic than first, especially according to HOMA. Despite quite large charge transferred from Be atom to this ring (pEDA), the bond equalization documented by HOMA is not high. This is because hybridization of C50 atom (partially covalently bound to beryllium) is almost sp3 and CeC bonds to neighbouring carbon atoms are almost of typical single bond lengths.

4.2. trans-M(h5-C6H6)2 complexes Aromaticity indices of trans-complexes show that the bonding mode here is different from cis-complexes. In the MgeBa series the aromaticity represented by HOMA is very similar to Li-fulvene complex with the exception of the least stable magnesium complex which has much lower value of HOMA. The reason is that in magnesium complex the C2eC3 bond length is longer than in CaeBa complexes (Table 2). The pEDA values span quite broad range (0.69e0.80) which is probably caused by the fact that the larger the distance from the metal ion to the centre of the ring, the smaller the polarization caused by the metal ion. This results in smaller amount of charge withdrawn from exo-CH2 moiety to the pentafulvene ring. The trend in NICS(1)ZZ changes in linearly correlated with pEDA which is shown in the Fig. 4. The beryllium complex is again an exception, its two differently coordinated rings have different aromaticity values. Aromaticity indices (especially HOMA) of the h5 bonded ring are close to the values for calcium, but values for h1 bonded ring are very different. Especially striking is the very low value of HOMA (Table 4) which indicates similar non-aromatic character of this ring as in the free pentafulvene. Like in cis-complexes this is caused by lengthening of the CeC bonds of carbon atom connected to beryllium. Despite significant charge transferred to this ring, bond lengths resemble these found in free fulvene. The pEDA and NICS(1)ZZ indices behave similarly as in cis-complexes and their values are located somewhere in-between h5 and free fulvene.

-12 -14 -16 NICS(1)ZZ

Be(h ) Be(h1) Mg Ca Sr Ba 5

-18 -20 -22 -24 -26 -28 -30 0.5

0.6

0.7

0.8

pEDA Fig. 4. Linear regression of NICS(1)ZZ vs pEDA for trans-M(h5-C6H6)2. Correlation coefficient ¼ 0.978; regression equation: y ¼ 49.968x þ 12.25.

5. Bonding analysis 5.1. cis-M(h5-C6H6)2 complexes Energy Decomposition Analysis (EDA) of the complex with the reference to neutral fragments is presented in Table 5. To verify that the results obtained by both model chemistries e Gaussian 03 B3LYP/6e311þþG(d,p)/ECP and ADF B3LYP/TZP/ZORA gave consistent results, the total interaction energies obtained by those two methods: DEint (Supra) and DEint are compared. It follows that the two values differ no more than 1 kcal/mol which is an acceptable agreement (Table 5). The general trend expected for DEint changes is that DEint will be less negative in the series: Be, Mg, Ca, Sr, Ba, because of larger distance between metal and the ring, and thus weaker electrostatic interaction. However, the actual trend is more complicated. The DEint is most negative for beryllium complex, which is partly caused by the different binding mode of this system e h1 and h5 e which is more covalent and stronger. This is compensated by high deformation penalty of the fulvene (DEprep) which causes the actual dissociation energy De (Table 1) of the beryllium complex being of much smaller magnitude than DEint. Calcium and strontium follow the trend of less negative DEint and in the case of barium this value is slightly more negative. However, the real exception is the magnesium complex for which DEint is much less negative than for any other complex. Comparison of various contributions to DEint for Mg and Ca reveal more details. The DEint of magnesium is almost 40 kcal/mol less negative than calcium, but the electrostatic interaction is similar, despite much smaller M-ring distance for magnesium complex (Table 1). Also the orbital interaction energy is only about

Table 4 Aromaticity indices of trans-M(h5-C6H6)2 complexes and free fulvene molecule.

Be(h5) Be(h1) Mg Ca Sr Ba Free fulvene

HOMA

pEDA

NICS(1)ZZ

0.5628 0.2906 0.5024 0.5690 0.5667 0.5717 0.297

0.7505 0.5431 0.7963 0.7255 0.7070 0.6903 0.060

26.37 14.34 26.07 24.15 23.18 22.89 0.94

W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17

2 kcal/mol more stabilizing for Mg. These two contributions do not balance much higher Pauli contribution for magnesium and thus the total binding energy of magnesium is so low. Decomposition into neutral fragments is suitable for analysing the total interaction energy and trends in dissociation energy, but not for actual bonding situation. It gives too low percentages of electrostatic contribution e from 37% for beryllium to only 42% for strontium and barium. The reason for this is that in the actual complex the metal ion and fulvene rings are highly polarized e the charge separation is almost 2 e (Table 5). Thus, when decomposition is done with reference to the neutral fragments, this large charge transfer is artificially counted as orbital interaction contribution. The situation is different if we assume M2þ and [(h5-C6H6)2]2 as fragments. The absolute values of total interaction energies are now very large (Table 5 e lower part) because they represent energies required to separate the two charged fragments, they are not well suited for analysing the dissociation energies but they are adequate for analysing the electrostatic and covalent contributions to bonding. This model is supported by the total NPA charge on metal atom estimated as close do 2 e. It follows that the electrostatic contribution is dominant for all the analysed metals and is markedly lowest for beryllium as expected e only 57%. Next metals have much more electrostatic character of bonding e over 70% and the percentage is raising from magnesium to barium. The last two cases e strontium and barium have very similar electrostatic contribution. It should be noted that although the electrostatic contribution is dominant, the orbital interactions contribution, which represents covalent type interactions cannot be neglected for such complexes (8).

15

electrostatic and more covalent. The electrostatic contribution approaches almost 50% for beryllium and starts to be much higher from magnesium (66.5%) to barium (75%). 5.3. Comparision of bonding in cis- and trans-M(h5-C6H6)2 complexes The direct comparison of DDEprep, DDEint and DDe between cisand trans-complexes is presented in Fig. 5. It follows that DDEprep is positive which means that penalty of deformation of the fulvene ring is higher for cis-complexes which is understandable as the two fulvene molecules have to be highly bent to assume the geometry of cis-complexes. The trend is the series is that the lowest difference is observed for beryllium and it is raising along the series. For both cis- and trans-complexes this deformation energy is highest for beryllium as this small ion polarizes and deforms the fulvene moiety in the highest degree. For larger ions, the M-ring distance is increasing and the penalty energy is lowered. However, this is easier in trans-complexes and these molecules are less constrained than cis-. Therefore the DDEprep energy is increasing in favour of trans-complexes. Next, let us analyze the DDEint energy. This is much more negative for cis-complexes as these systems are bonded in metallocene-like manner: two Cp rings are strongly interacting with metal atom inside. The interaction energy for both series individually changes in broad range: for cis-complexes between 175 kcal/mol and 121 kcal/mol and for transcomplexes between 104 kcal/mol and 43 kcal/mol. However their cis-trans difference changes only a little. Only for beryllium it is about 71 kcal/mol but for all other metals it is about 76 to 78 kcal/mol. Beryllium is a special case because of its bonding pattern. A factor which can influence the less negative DDEint for beryllium is the very favourable arrangement in trans-complex (interaction energy as high as 104 kcal/mol). Similar difference for other metals means that this is caused by the very different types of cis- and trans-interactions: ansa-metallocene in the first case and metal-fulvene in the second case. Preparation and interaction energy trends sum up in the dissociation energy trend DDe which shows very little changes. For beryllium DDe is equal to 45.5 kcal/ mol and for other metals it is 41e43 kcal/mol which differences less that 2 kcal/mol. For analysis of bonding situation another comparison is done e the differences of DDEorb, DDEPauli and DDEelstat for cis- and transcomplexes (Fig. 6). It follows that the electrostatic contribution favours cis-complexes and orbital contribution is favours for transsystems. It is important to keep in mind that cis-complexes are of singlet nature which causes its much more closed-shell ionic nature of interactions. On the contrary, trans-complexes are triplets which favours more covalent interactions. The range of changes is

5.2. trans-M(h5-C6H6)2 complexes First, let us look at the EDA to neutral fragments. The absolute values of total interaction energy for trans- complexes are much lower that for cis-complexes, as in the later the two fulvene molecules create a CeC covalent bond. However, the trend for different metals is very similar e the most negative value of DEint for beryllium and markedly the least negative for magnesium. The reason in similar to cis-complexes. The electrostatic and orbital interaction terms for magnesium complex are unexpectedly weak and large Pauli term causes the complex to be less stable than expected (Table 6). The total NPA charges of metal ions (Table 6) are very similar to cis-complexes which shows that this is rather a property of a metal and not depends on the geometry of the complex. The percentage of electrostatic contribution is similar to that found in cis-complexes but slightly lower. The decomposition into charged fragments reveal that bonding in trans-complexes is less

Table 5 Total interaction energy calculated by supramolecular approach and EDA approach, electrostatic, Pauli and orbital interaction components of the total interaction energy for cis-M(h5-C6H6)2 complex assuming neutral metal atom and neutral cis-(h5-C6H6)2 ligand as fragments. Total interaction energy calculated by EDA approach, electrostatic, Pauli and orbital interaction components of the total interaction energy and NPA charges on metal atom for cis-M(h5-C6H6)2 complexes assuming charged M2þ and [cis-(h5-C6H6)2]2 ligand as fragments. Be Neutral fragments DEint (Supra) DEint (EDA) DEelstat DEPauli DEorb Charged fragments DEint (EDA) DEelstat DEPauli DEorb q(M)

175.05 174.15 286.22 595.37 483.3 793.51 485.24 59.4 367.67 1.605

%

Mg

37.19

121.03 122.03 238.78 434.54 317.79

62.81

56.89 43.11

635.1 484.75 49.51 199.85 1.777

%

Ca

42.90

163.97 163.21 234.19 386.64 315.66

57.10

70.81 29.19

556.53 468.48 77.47 165.53 1.755

%

Sr

42.59

157.78 157.05 212.35 342.17 286.87

57.41

73.89 26.11

518.37 456.88 79.93 141.42 1.788

%

Ba

%

42.54

169.00 169.02 201.23 316.2 283.99

41.47

57.46

76.36 23.64

491.43 443.96 86.02 133.49 1.786

58.53

76.88 23.12

16

W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17

Table 6 Total interaction energy calculated by supramolecular approach and EDA approach, electrostatic, Pauli and orbital interaction components of the total interaction energy for trans-M(h5-C6H6)2 complex assuming neutral metal atom and neutral trans-(h5-C6H6)2 ligand as fragments. Total interaction energy calculated by EDA approach, electrostatic, Pauli and orbital interaction components of the total interaction energy and NPA charges on metal atom for trans-M(h5-C6H6)2 complexes assuming charged M2þ and [trans(h5-C6H6)2]2 ligand as fragments. Be Neutral fragments DEint (Supra) DEint (EDA) DEelstat DEPauli DEorb Charged fragments DEint (EDA) DEelstat DEPauli DEorb DEint (EDA)

104.05 103.64 283.53 615.35 435.45 794.53 455.81 61.8 400.52 1.617

%

Mg

39.44

42.82 44.61 226.56 420.16 238.21

60.56

53.23 46.77

635.93 453.66 45.99 228.26 1.811

%

Ca

48.75

86.77 86.15 223.95 369.67 231.86

51.25

560.44 443.78 67.33 183.98 1.758

66.53 33.47

40 ΔΔEprep

20 transEnergy [kcal/mol]

0 cis-

-20 -40 -60

−ΔDe

ΔΔEint

-80 -100 Be

Mg

Ca

Sr

Ba

Fig. 5. Differences in the bond dissociation energies DDe, the interaction energies DDEint and the preparation energies DDEprep between cis-M(h5-C6H6)2 and trans-M(h5C6H6)2 complexes. Negative values indicate that cis-M(h5-C6H6)2 is more stable than trans-M(h5-C6H6)2.

40

ΔΔEorb

30

Energy [kcal/mol]

20

-10

Sr

49.13

81.31 80.62 202.02 322.78 201.38

50.87

70.69 29.31

522.89 433.3 67.98 157.57 1.775

%

Ba

%

50.08

91.15 91.5 191.43 296.53 196.61

49.33

49.92

73.33 26.67

495.27 422.35 70.09 143 1.762

50.67

74.71 25.29

smaller for DDEelstat e from about 30 kcal/mol for beryllium to 22 kcal/mol for barium. Beryllium cis-complex is stabilization is highest because of small M-ring distance. For the next metal, magnesium, we observe even more negative value 31 kcal/mol. For calcium, strontium and barium, the electrostatic contribution difference is becoming less negative because when M-ring distance increase, the difference between cis- and trans-complexes is becoming smaller. The changes in DDEorb energy are more pronounced. For beryllium it is almost 33 kcal/mol more stabilizing the trans-complex but for barium the difference is as little as 9.5 kcal/mol. The reason is similar to electrostatic interaction trend e when the M-ring distance is smaller, the covalent interactions become stronger. The trend in Pauli repulsion energy changes is another interesting topic. It is negative for beryllium which means that it favours the cis-complex and for other metals it becomes increasingly positive, up to the value of 16 kcal/mol for barium. This is caused by the semi-closed nature of cis-complexes. The small beryllium cation can fit into this space without problems, but as the ionic radium of an atom increases, the Pauli repulsion term starts to become significant, and for barium it dominates over orbital interactions (Fig. 6). The sum of these three contributions DDEint is very close to zero which means that if we compare dissociation of these two types of complexes into charged fragments, their interaction energy is quite similar. This is because cis-fulvene ligand with double negative charge is highly destabilized when isolated in complex geometry.

6. Conclusions

10

0

%

ΔΔEint

transcis-

ΔΔEPauli

-20

-30

ΔΔEelstat -40

Be

Mg

Ca

Sr

Ba

metal atom Fig. 6. Differences in EDA terms DDEelstat, DDEPauli and DDEorb between cis-M(h5C6H6)2 and trans-M(h5-C6H6)2 complexes. Decomposition into charged fragments. Differences in total interaction energy DDEint are also shown. Negative values indicate that cis-M(h5-C6H6)2 is more stable than trans-M(h5-C6H6)2.

- Complexes of alkaline earth metals with pentafulvene tend to form the ansa-metallocene compounds. There exist however also the true sandwich complexes where two pentafulvene rings are rotated by various degrees to each other. - While Mg, Ca, Sr and Ba form h5 connections, Be coordination mode is different: one ring is connected via h5 and the second ring via h1-mode. - Aromaticity indices HOMA, pEDA and NICS(1)ZZ indicates strong aromatization of pentafulvene ring due to charge transfer from the metal atom. NICS(1)ZZ and pEDA are linearly correlated. - Natural Population Analysis shows that 1.6e1.8 e of charge is transferred to the ring. - Energy Decomposition Analysis of bonding shows that the electrostatic contribution is dominant, however the covalent contribution is also substantial, especially for Be, Mg, Ca. - Total binding energy for magnesium complexes is much lower than expected. This is because the electrostatic and orbital

W.P. Oziminski / Journal of Organometallic Chemistry 708-709 (2012) 10e17

interactions for this complex do not balance the Pauli repulsion energy. - Comparision of various contribution to bonding of cis- and trans-complexes shows that electrostatic contribution favours cis-complexes and orbital contribution favours transcomplexes. Acknowledgement Computational Grant from the Wroclaw Centre for Networking and Supercomputing (WCSS) is gratefully acknowledged. Appendix. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jorganchem.2012. 02.012. References [1] [2] [3] [4] [5] [6] [7] [8]

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