Structural and electronic effects of the interaction of metal cations with benzene

Journal of Molecular Structure (Theochem) 589–590 (2002) 337–347 www.elsevier.com/locate/theochem

Structural and electronic effects of the interaction of metal cations with benzene Jose´ Molina Molina1, Jose´ A. Dobado*, Santiago Melchor Grupo de Modelizacio´n y Disen˜o Molecular, Departamento de Quı´mica Orga´nica, Campus Fuentenueva, Universidad de Granada, 18071 Granada, Spain Received 4 December 2001; revised 24 January 2002; accepted 24 April 2002

Abstract Theoretical investigation of different benzene –transition metal cation (Vþ (1); Crþ þ (2); Mnþ (3); Feþ þ (4); Coþ (5); Niþ þ (6); Cuþ (7)) complexes has been performed at the B3LYP/6-311 þ Gp level. All the complexes show large interaction energy (250 to 2 230 kcal/mol). Complexes 3, 4 and 7 showed no benzene ring deformation. However, complexes 1, 2, 5 and 6 revealed a boat-like benzene disposition. The electronic properties of the complexes were analyzed by means of the atoms-inmolecules theory and electron localization function topological analysis. From the above analysis, 1 and 5 showed large benzene ring bond differentiation, and medium to low interaction energy, and consequently presented good properties as catalysts in dehydropolycondensation processes of polyaromatic hydrocarbons. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Benzene; Transition metals; Atoms-in-molecules; Electron localization function; Polymerization

1. Introduction In recent years, much attention has been focused on carbon nanotubes (CNs), due to their unusual electronic and mechanical properties [1,2], which make them suitable for a new generation of electronic components [3,4]. Very recently [5], measurements have been made of the current – voltage characteristic of CNs, and, more precisely, current – voltage plots with clearly rectifying character were obtained for a pair of joined nanotubes [6,7]. These brilliant results show the need for finding new synthesis methods that * Corresponding author. Tel./fax: þ 34-958-243186. E-mail address: [email protected] (J.A. Dobado). 1 Professor Jose´ Molina Molina passed away on the 13th June 2000.

would enable the construction of specific CN junctions, a goal that can be reached with the low-energy synthesis methods. Previous works on hemifullerenes [8 –10] show the possibility of insertion of pentagons in selected positions of a graphitic plane, and this can make it possible to develop intelligent synthetic pathways to two or more CN junctions. As a first step, a detailed study of the interaction of the usual catalysts in CN synthesis and the graphitic components is needed. Usually, the synthesis methods of CNs are classified in two groups depending on the temperature at which the nanotubes are synthesized. The highenergy methods are the most common [1,11], due to their relative simplicity and the high production rate. The high temperature can be reached by an arc discharge or a high-power laser, and the resulting

0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 1 8 7 - 2

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temperature is usually 1000 – 3000 K. In low-energy methods [12,13], the source of heat is not as powerful, and the production rate is also lower. Despite the efficiency of high-energy methods, there is no possibility of controlling the growth of the nanotubes, and the CNs generated are uniform. On the other hand, the slow growth due to the low-energy methods causes numerous tube defects [14]. Therefore, an intermediate solution, where defects could be introduced at the points needed, but that can also grow uniform tubes, would be the best option. In both highand low-energy methods the catalyst plays a very important role [15], as they boost the production rate of graphitic material, but their choice is critical in the low-energy methods. The catalysts used in the synthesis are usually complexes containing first-row transition metals, including metallic salts [16] and metal powder, leading to metal ions after dissolution or arc discharge, respectively, in each method. The interaction of metal ions with organic psystems [17] has relevance not only in the synthesis of polyaromatic hydrocarbons, but also in other catalytic processes [18 –20], organization of biological systems [21], or adsorption of organic molecules to metal surfaces [22]. Therefore, investigation of these types of interactions has been widespread both experimentally and theoretically. In geometric terms, metal cations are clearly attracted by the high electronic density produced by the p-delocalization [23,24], and usually the most favorable coordination site is over the center of the aromatic ring [25]. Nevertheless, the electronic properties of these complexes reportedly have a complex topology, with a broad variation in the geometrical distribution of the bond critical points (BCPs), due to the different nature of the interaction [26], encouraging us to delve deeply into their electronic properties. In this context, this paper focuses attention on the interaction of transition metal cations with benzene, the smallest one of the essential building blocks of the dehydropolycondensation [12,13], where the polymerization leads to graphitic nanostructures [16]. We have performed a systematic study over a family of seven first-row metal cations, with atomic numbers ranging from 23 to 29. As the first step, the cations were chosen to have closed-shell electronic configuration, resulting in the following cations: Vþ, Cr2þ, Mnþ, Fe2þ, Coþ, Ni2þ and Cuþ. For uniformity

reasons, the cations were chosen to be mono or divalent, because higher oxidation states could lead to very despair results. This study was designed to discover structural or electronic changes in the benzene molecule due to the interaction with the metal, in order to predict the chemical reactivity of the resulting graphitic elements, and also select good candidates for catalysts in dehydropolycondensation. The selected molecules have been chosen as reference systems to investigate the conditions a good catalyst has to fulfill, such as the easy binding and unbinding to the molecule, the ability of creation differentiated positions on the ring, and the bond weakening of the original structure. These actions can be observed, respectively, in the low interaction energy, ring deformation or bond differentiation (that shows partial destruction of the p-bond) and in the lowering of electronic density values for the C –C bonds.

2. Computational methods Ab initio density functional theory (DFT) calculations for six benzene – cation complexes were performed with the GAUSSIAN 98 software package [27]. The basis set used was 6-311 þ Gp, and the functional was the Becke’s three parameter hybrid one [28] with the correlation functional of Lee, Yang and Parr [29], (B3LYP). Previously [30], the B3LYP/ 6-31Gp method was shown to be accurate enough to describe electronic and magnetic properties of graphitic systems, but the metal cations in the complexes induced us to also include diffuse functions. All the structures were fully optimized without symmetry restrictions, resulting complexes 1, 2, 5 and 6 with C2v and 3, 4, 7 with C6v symmetry. Moreover, they were tested by frequency analysis at the same B3LYP/6-311 þ Gp level, yielding all real minima (with non-imaginary frequencies). The electronic density was analyzed in terms of the atoms-in-molecules (AIM) analysis [31], using of the AIMPAC [32] software package. The electron localization function (ELF) [33] was also analyzed with the ToPMoD [34] package. The 72 rðrÞ and rðrÞ contour-map representations were produced using the MORPHY 98 program [35], and the three-dimensional ELF isosurface representation with SciAn [36] scientific visualization package.

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The topology of the electronic-charge density, rðrÞ; introduced by Bader [31], accurately describes the chemical concepts of atom, bond, and structure. The principal topological properties are summarized in terms of their critical points (CP) [31,37], characterized by the eigenvalues of the Hessian matrix, called curvatures (l1, l2 and l3). The nuclear positions behave topologically as local maxima in rðrÞ: A BCP is found between each pair of nuclei, which are considered to be linked by a chemical bond, with two negative curvatures, (l1 and l2) and one positive (l3) (denoted as (3, 2 1) CP). The ellipticity, 1, of a bond is defined by means of the two negative curvatures in a BCP as 1 ¼ l1 =l2 2 1; where ll2 l , ll1 l: The ratio l1/l3 measures also the charge concentration. Finally, the ring CPs are characterized by a single negative curvature. Each (3,1) CP generates a pair of gradient paths [31] which begin at a CP and end at neighboring (3, 2 3) attractors. This gradient path defines a line through the charge distribution linking the neighboring nuclei. Along this line, rðrÞ is a maximum with respect to any neighboring line. Such a line is referred to as an atomic interaction line [31,37], and its presence of an atomic interaction line in such equilibrium geometry satisfies both the necessary and sufficient conditions that the atoms be bonded together. The Laplacian of the electronic charge density, 72 rðrÞ; describes two extreme situations. If 72 rðrÞ , 0; rðrÞ is locally concentrated, but if 72 rðrÞ . 0 the electronic density is locally depleted. Thus, a value of 72 rðrÞ , 0 at a BCP is unambiguously related to a covalent bond, indicating that a sharing of charge has taken place. While in a closed-shell interaction, a value of 72 rðrÞ . 0 is expected, as found in noble gas repulsive states, ionic bonds, hydrogen bonds, and van der Waals molecules. Bader has also defined a local electronic energy density, Ed ðrÞ; as a functional of the first-order density matrix Ed ðrÞ ¼ GðrÞ þ VðrÞ; where GðrÞ and VðrÞ correspond to a local kinetic and potential energy density, respectively [31]. The sign of the Ed ðrÞ determines whether accumulation of charge at a given point r is stabilizing ðEd ðrÞ , 0Þ or destabilizing ðEd ðrÞ . 0Þ: Thus, a value of Ed ðrÞ , 0 at a BCP presents a significant covalent contribution and, therefore, a lowering of the potential energy

339

associated with the concentration of charge between the nuclei. The ELF function [33,38 – 40], first introduced by Becke and Edgecombe [33], can be viewed as a local measure of the Pauli repulsion between electrons due to the exclusion principle, enabling us to define regions of space that are associated with different electron pairs. The ELF function is expressed by ELF ¼ 1þ

1


D Dh

2

ð1Þ

where D¼

Dh ¼

N 1X 1 l7rl2 l7wj l2 2 ; 2 j¼1 8 r

3 ð3p2 Þ2=3 r5=3 ; 10

r¼

N X

lwj l2

j¼1

which gives ELF values between 0 and 1, where the higher values correspond to regions where two antiparallel spin electrons are paired, and the lower values to regions between electron pairs. Given the scalar character of the ELF function, the analysis of their gradient fields yields their attractors (local maxima) and their corresponding basins. There are two type of basins: the core basins labeled by C(atom symbol) and the valence basins V(list of atoms). The valence basins are characterized by their synaptic order (the number of core basins with which they share a common boundary). Accordingly, they can be classified as mono-, di- and polysynaptic, corresponding to the lone pair, bicentric and polycentric bonding region, respectively. The quantitative population on the different basins is calculated by integrating a given density of property over the volume of the basins. The following definitions areÐused through  Vi Þ ¼ V rðrÞdr and the text: basin population Nð i Ð Ð 2 s ðVi Þ ¼ Vi Vi pðr; r0 Þdr dr0 þ its variance  Vi Þ 2 N 2 ðVi Þ in which pðr; r 0 Þ is the two Nð  Vi Þ·Nð  Vj Þ 2 electron density, covariance Bij ¼ Nð PðVi ; Vj Þ in which PðVi ; Vj Þ is the pair P population, and the fluctuation contribution Bij = i–j Bij :

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Fig. 1. Schematic representation of the benzene· · ·M (Vþ, Cr2þ, Mnþ, Fe2þ, Coþ, Ni2þ, Cuþ) complexes (1–7), as well as the definition of the geometrical parameters used in the text.

3. Results and discussion Theoretical studies (B3LYP/6-311 þ Gp) have been conducted on several transition metal ion – benzene complexes (1 – 7) shown in Fig. 1, where the different geometrical parameters have also been defined. The theoretical results are depicted in Tables 1 –5. Table 1 shows the interaction energy of the different complexes, Table 2 shows the geometrical parameters defined in Fig. 1, together with the squared quadratic mean deviation (sqmd) of the benzene C –C bond lengths in the complexes. Table 3 shows the electronic properties of the different critical bond points in rðrÞ; and Table 4 the numerical properties of the different ELF basins. For Tables 2 –4, the data for Table 1 Total energies of the metal–benzene complex, Ecomplex, and the interaction energy, DEb, for complexes 1–7 at the B3LYP/6311 þ Gp theoretical level Complex

Ecomplex (hartree)

DEb (kcal/mol)a

1 (Vþ) 2 (Cr2þ) 3 (Mnþ) 4 (Fe2þ) 5 (Coþ) 6 (Ni2þ) 7 (Cuþ)

21175.9845491 21275.9841764 21382.9728032 21495.2246522 21614.7487598 21739.8219486 21872.5575550

276.7 2167.3 2176.8 2199.0 279.2 2230.4 250.2

a

DEb ¼ Ecomplex 2 ðEmetal þ Ebenzene Þ; the calculated value of Ebenzene is 2232.3007049 hartree.

benzene itself were included for comparison. Table 5 shows the values of some (3, 2 1) CPs for the ELF, that are related to the separability of the ring and the metal. All the complexes are stable and true minima in the potential energy surface, with large interaction energy (DEb) ranging from 2 50 to 2 230 kcal/mol. The divalent ions showed larger DEb; however, the manganese ion also had very large interaction energy, even larger than in the chromium divalent complex. On the other hand, the monovalent copper complex showed the smallest DEb. The complex with smallest DE (7) also had the  despite that largest interaction distance ðr ¼ 1:845 AÞ there was no correlation between DEb and r (7 shows larger r values than the other monovalent complexes 3 and 5, and the shorter r corresponded to the monovalent complex 3 that showed also large DEb). The ring deformation was analyzed by u value, the bond distances and alternation values; the interaction energy, DEb, did not correlate with the overall benzene ring deformation, although the most and least stable complexes yielded high and low deformed geometries (u ¼ 9:18 and 0.08 for 6 and 7, respectively). For the other complexes, there was no correlation between geometries and DEb. This can be illustrated regarding complexes 3 and 5. Complex 3 had large DEb and very short r value, but the benzene ring was undeformed and totally flat (u ¼ 0; and both Ca – Ca and Ca – Cb bond lengths are

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341

Table 2 Geometrical data (distance from the metal to the benzene plane) for complexes 1–7 and benzene, bond distances, squared quadratic mean deviation of the C– C bond lengths, sqmd, and bending angle u Compounds

˚) ra (A

˚) Ca –Ca (A

˚) Ca –Cb (A

˚) Ca –Ha (A

˚) Cb –Hb (A

˚) sqmd (A

ub (deg)

1 (Vþ) 2 (Cr2þ) 3 (Mnþ) 4 (Fe2þ) 5 (Coþ) 6 (Ni2þ) 7 (Cuþ) C6H6

1.746 1.785 1.531 1.587 1.603 1.724 1.845

1.386 1.428 1.417 1.417 1.432 1.459 1.414 1.395

1.435 1.410 1.417 1.417 1.409 1.404 1.414 1.395

1.085 1.087 1.084 1.087 1.085 1.088 1.086 1.086

1.084 1.087 1.084 1.087 1.083 1.086 1.086 1.086

0.043 0.008 0.000 0.000 0.011 0.026 0.000 0.000

214.8 7.6 0.0 0.0 6.4 9.1 0.0 0.0

a b

Distance from the metal to the benzene plane. See Fig. 1 for definition.

˚ ). On the other hand, 5 had small DEb, 1.417 A (2 79 kcal/mol), relatively short r value, and large  benzene ring deformation (u ¼ 6:48; sqmd ¼ 0:011 A and Ca –Ca and Ca –Cb lengths equal to 1.432 and ˚ , respectively). In addition, structure 1 showed 1.409 A ˚ ) the largest the shortest Ca – Ca bond length, (1.386 A difference between Ca –Ca and Ca –Cb bond lengths  and the greater ring deformation (sqmd ¼ 0:043 A) (u ¼ 214:8) and has opposite sign. In general, structures 3, 4, and 7 yielded undeformed benzene

Fig. 2. rðrÞ and 72 rðrÞ contour plots in the symmetry plane containing the metal and the Cb atoms, for complexes 1, 5 and 7, obtained with the MORPHY 98 program [35], at the B3LYP/6311 þ Gp theoretical level.

ring complexes, and structures 1, 2, 5 and 6 yielded boat-like deformation of the ring. Complexes 1 and 5 with small DEb yielded large ring deformation, these characteristics making them good candidates as catalysts in dehydropolycondensation to yield CNs. Considering the geometrical behavior of the complexes studied, we made an electronic characterization, studying the rðrÞ and ELF topologies. Table 3 shows the numerical values of the rðrÞ BCPs for compounds 1 – 7, and benzene for comparison. Also, Fig. 2 shows the contour plot of rðrÞ and 72 rðrÞ for complexes 1 and 7. The representations for the other complexes are available in Section 5. Fig. 2 shows the different behavior of the undistorted complex 7 and the deformed complex 1. In 7, all the ring atoms lie in the same plane; there are bond paths between copper and all the carbon atoms, and there is no ring CP in the middle of the benzene ring. The overall interaction between the copper atom and the carbon atoms is of the closed-shell type, yielding positive 72 rðrÞ in the interaction region. For 5, the interaction is of the same nature ð72 rðrÞ . 0Þ: However, the ring deformation is visible in the representation. There is no bond path between Co and Cb atoms, yielding only four BCPs between the metal and the Ca atoms. In complex 1 the Cb atoms are oriented towards the Vanadium cation, presenting two bond paths between the metal and the Cb atoms. For all the complexes, no ring CP exists in the middle of the benzene ring, showing a sink to the metal atom in rðrÞ; and the metal is only bonded to the closest carbon positions through a bond path. The different behavior between distorted and undistorted complexes was also numerically evident.

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Table 3 Charge distribution values at the (3, 2 1) BCPs for the complexes 1–7 and benzene; electron density, rðrÞ; its Laplacian, 72 rðrÞ; ellipticity, 1, curvatures, ll1 =l3 l; and electronic energy density Ed(r ) Complex

Bond

rðrÞ (e/a3o)

72 rðrÞ (e/a5o)

1

ll1 =l3 l

Ed(r ) (hartree/a3o)

1 (Vþ)

Ca – Ca Ca – Cb Ca – Ha Cb –Hb Cb –Vþ

0.311 0.282 0.281 0.280 0.074

20.854 20.707 20.967 20.951 0.198

0.225 0.196 0.012 0.028 1.447

2.020 1.688 1.318 1.325 0.271

20.321 20.265 20.271 20.269 20.018

2 (Cr2þ)

Ca – Ca Ca – Cb Ca – Ha Cb –Hb Ca – Cr2þ

0.289 0.301 0.283 0.283 0.061

20.752 20.819 20.997 21.003 0.176

0.163 0.156 0.011 0.005 1.452

1.742 1.856 1.294 1.291 0.210

20.277 20.300 20.273 20.274 20.010

3 (Mnþ)

C–C C–H C–Mnþ

0.293 0.280 0.081

20.759 20.962 0.275

0.206 0.017 1.645

1.796 1.320 0.148

20.286 20.270 20.018

4 (Fe2þ)

C–C C–H C–Fe2þ

0.297 0.283 0.077

20.800 21.001 0.211

0.142 0.006 3.533

1.801 1.289 0.225

20.292 20.273 20.016

5 (Coþ)

Ca – Ca Ca – Cb Ca – Ha Cb –Hb Ca – Coþ

0.286 0.301 0.282 0.282 0.075

20.725 20.807 20.972 20.978 0.225

0.181 0.183 0.013 0.015 1.693

1.704 1.857 1.316 1.317 0.206

20.271 20.298 20.272 20.272 20.017

6 (Ni2þ)

Ca – Ca Ca – Cb Ca – Ha Cb –Hb Ca – Ni2þ

0.276 0.306 0.284 0.283 0.066

20.701 20.850 21.010 21.005 0.138

0.083 0.150 0.004 0.011 7.474

1.560 1.907 1.286 1.291 0.325

20.251 20.309 20.275 20.274 20.016

7 (Cuþ)

C–C C–H C–Cuþ

0.297 0.281 0.047

20.793 20.968 0.138

0.177 0.014 9.604

1.820 1.314 0.230

20.291 20.270 20.010

C6H6

C–C C–H

0.308 0.278

20.851 20.939

0.195 0.019

1.959 1.355

20.312 20.268

For 7, the rðrÞ BCPs for all the C –C bonds were equal and not markedly different from that of benzene (0.297 e/a3o for Ca – Ca and Ca – Cb, compared to 0.308 e/a3o for benzene). In addition, the ellipticity, 1, of these bonds also resembled benzene, but some destabilization in the Ca –Ca bonds was found, by the complex formation (EðrÞ value for Ca – Ca in benzene from 2 0.312 to 2 0.291 hartree/a3o in 7). Similar behavior was also observed for 3 and 4. Complex 5, with distortion, presented two different carbon – carbon BCPs. The Ca – Cb bonds have rðrÞ values very similar to benzene (0.301 e/a3o) and Ca – Ca bonds

with smaller values. The electron charge concentration 72 rðrÞ also changed accordingly. Also, for the last bond Ca – Ca, the destabilization was also higher than in the former bonds (Ca – Cb). All the above data agree with the bond differentiation in the benzene ring by complex formation with Co. Complexes 2 and 6 presented very similar behavior also, although the largest differentiation was for complex 6 (the one with highest DEb). The electronic data for 1 are somewhat different: the density, Laplacian, ellipticity and the electronic energy density of the C a – Ca BCP (rðrÞ ¼ 0:311 e=ao 3 ; 72 rðrÞ ¼ 20:854 e=ao 5 ; 1 ¼

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Table 4 ELF numerical analysis for the complexes 1–6 and benzene; type of basin, Vi, ELF value, hðrÞ; basin population, N i ; standard deviation, s2 ðVi Þ; relative fluctuation, lðVi Þ; and the principal contributions to the relative fluctuation from other neighboring basins

Vi

hðrÞ

N i ;

s2 ðVi Þ

lðVi Þ

Main contributions of the other basins to the relative fluctuation (%)

1

C(V) V(Ca –Ca) V(Ca –Cb) V(Ca –Ha) V(Cb – Hb) V(Cb – V)

1.000 0.940 0.941 1.000 1.000 0.785

21.62 2.96 2.42 2.15 2.15 0.54

1.120 1.186 1.102 0.812 0.818 0.665

0.058 0.476 0.502 0.307 0.311 0.826

V(Ca –Ca): 12.0; V(Ca –Cb): 7.3; V(Cb –V): 9.6 C(V): 10.7; V(Ca –Cb): 17.1; V(Ca –Ha): 16.9 C(V): 7.5; V(Ca –Ca): 19.7; V(Ca –Cb): 14.9; V(Ca –Ha): 15.6; V(Ca –Hb): 14.9 C(V): 4.9; V(Ca –Ca): 36.1; V(Ca –Cb): 29.0 C(V): 8.4; V(Ca –Cb): 27.0 C(V): 27.0; V(Ca –Cb): 20.0

2

C(Cr) V(Ca –Ca) V(Ca –Cb) V(Ca –Ha) V(Cb – Hb)

1.000 0.945 0.947 1.000 1.000

22.38 2.65 2.69 2.16 2.14

1.023 1.146 1.144 0.811 0.806

0.047 0.495 0.487 0.304 0.302

V(Ca –Ca): 13.3; V(Ca –Cb): 12.4 C(Cr):10.6; V(Ca – Cb): 18.4; V(Ca –Ha): 15.8 C(Cr): 9.9; V(Ca –Ca): 18.5; V(Ca –Cb): 18.5; V(Ca –Ha): 16.3; V(Ca –Hb): 16.0 C(Cr): 6.0; V(Ca –Ca): 31.6; V(Ca –Cb): 32.5 C(Cr): 4.2; V(Ca –Cb): 32.3

3

C(Mn) V(C–C) V(C–H) V(C–Mn)

1.000 0.943 1.000 0.695

23.23 2.62 2.17 0.21

1.299 1.136 0.820 0.443

0.073 0.493 0.310 0.929

V(C–C): 8.6 C(Mn): 11.2; V(C– C): 16.4; V(C–H): 15.7 C(Mn): 7.8; V(C– C): 30.1 C(Mn): 32.3; V(C– C): 19.2

4

C(Fe) V(C–C) V(C–H)

1.000 0.949 1.000

24.30 2.68 2.15

1.227 1.151 0.811

0.062 0.493 0.304

V(C–C): 12.7 C(Fe): 14.4; V(C– C): 17.6; V(C–H): 15.6 C(Fe): 7.8; V(C– C): 31.5

5

C(Co) V(Ca –Ca) V(Ca –Cb) V(Ca –Ha) V(Cb – Hb)

1.000 0.943 0.944 1.000 1.000

25.58 2.89 2.71 2.17 2.20

1.146 1.208 1.152 0.819 0.828

0.051 0.504 0.489 0.309 0.312

V(Ca –Ca): 18.4; V(Ca –Cb): 10.2 C(Co): 16.4; V(Ca –Cb): 17.1; V(Ca –Ha): 15.3 C(Co): 10.0; V(Ca –Ca): 18.8; V(Ca –Cb): 18.6; V(Ca –Ha): 16.1; V(Ca –Hb): 16.5 C(Co): 6.7; V(Ca –Ca): 33.2; V(Ca –Cb): 31.8 C(Co): 5.8; V(Ca –Cb): 32.0

6

C(Ni) V(Ca –Ca) V(Ca –Cb) V(Ca –Ha) V(Cb – Hb)

1.000 0.953 0.948 1.000 1.000

26.49 2.50 2.71 2.15 2.18

1.080 1.125 1.147 0.807 0.815

0.044 0.504 0.484 0.302 0.305

V(Ca –Ca): 17.1; V(Ca –Cb): 11.0 C(Ni): 15.6; V(Ca –Cb): 17.4; V(Ca –Ha): 15.1 C(Ni): 9.7; V(Ca –Ca): 16.7; V(Ca –Cb): 19.6; V(Ca –Ha): 16.5; V(Ca –Hb): 16.4 C(Ni): 7.0; V(Ca –Ca): 29.2; V(Ca –Cb): 33.4 C(Ni): 3.0; V(Ca –Cb): 32.6

7

C(Cu) V(Ca –Ca) V(Ca –Cb) V(Ca –Ha) V(Cb – Hb)

1.000 0.944 0.944 1.000 1.000

27.87 2.74 2.73 2.16 2.16

0.813 1.155 1.153 0.815 0.816

0.024 0.486 0.486 0.307 0.307

V(Ca –Ca): 13.6; V(Ca –Cb): 13.7 C(Cu): 6.7; V(Ca –Cb): 19.0; V(Ca – Ha): 16.5 C(Cu): 6.8; V(Ca –Ca): 19.0; V(Ca –Cb): 19.0; V(Ca –Ha): 16.4; V(Ca –Hb): 16.5 C(Cu): 2.6; V(Ca –Ca): 33.1; V(Ca –Cb): 32.9 C(Cu): 2.6; V(Ca –Cb): 33.0

C6H6

V(C–C) V(C–H)

0.943 1.000

2.75 2.14

1.138 0.809

0.472 0.306

V(C–C): 20.6; V(C–H): 17.2 V(C–C): 34.1; V(C–H): 4.0

0:225 and Ed ðrÞ ¼ 20:321 hartree e=ao 3 ) are the greatest values for all the carbon bonds considered in this work. These data is compatible with the length ˚ ), and a certain of this bond, the shortest one (1.386 A double bond character. The ELF analysis gave a complementary and useful approach to the study of the metal ion –benzene complexes. Table 4 shows the basin numerical properties for the different complexes, including the

ELF values, the population, standard deviation and relative fluctuation, as well as the main contributions of the other basins. For complexes 2, 4 and 6, containing a divalent metal cation, a net gain of electronic charge was observed in the metal (0.38, 0.30 and 0.49e2 for 2, 4 and 6, respectively). In general, the electron population for the V(C –C) basins for these complexes were smaller to that on benzene, indicating a charge transfer from the

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Table 5 ELF values of carbon valence basin–metal basin (3, 2 1) CPs for Ca and Cb positions. Complexes 2 and 6 did not presented such points at the Cb positions Complex

1 (Vþ) 2 (Cr2þ) 3 (Mnþ) 4 (Fe2þ) 5 (Coþ) 6 (Ni2þ) 7 (Cuþ)

ELF (3, 2 1) Critical point (Ca)

Critical point (Cb)

0.403 0.361 0.284 0.243 0.221 0.188 0.117

0.584 – 0.284 0.243 0.182 – 0.117

benzene to the metal. Ring deformation in complexes 2 and 6 yielded two different kinds of V(C – C) basins (V(Ca – Ca) and V(Ca –Cb)) with different populations each, showing larger values for 6 (2.65 and 2.50e2 for V(Ca – Ca) and 2.69 and 2.71 for V(Ca – Cb), for 2 and 6, respectively). For 4 the variation was small and all the valence basins yielded similar data, in accord with its undistorted geometry. The difference between the V(C – C) basins proved higher for complex 6, in accordance with its larger ring deformation, electronic gain and interaction energy. Similar behavior was found considering the main contributions of the different basins to a given basin (Table 4). Complex 4, with large interaction energy, gave a medium contribution from the metal core basin in the V(C – C) basins, with the same for the contributions of the V(C – C) basins to the metal core basin. Complex 2 yielded different contribution of V(Ca – Ca) and V(Ca – Cb) basins to the metal core basin, with one larger and another smaller than in 4. Complex 6 had the largest difference between the contribution of V(Ca – Ca) and V(Ca –Cb) basins to the C(Ni) basin (17.1% of V(Ca – Ca) and 11.0% of V(Ca – Cb)). In addition, the contributions of the C(Ni) basin to the corresponding V(C –C) basins also differ sharply, compatible with the complex with largest interaction energy and ring deformation. Structures 1, 3, 5 and 7 are monovalent metal –ion complexes. In these complexes, a net loss of charge from benzene occurred (0.38, 0.77, 0.42 and 0.13e2 for 1, 3, 5 and 7, respectively; see Table 4). Complex 7 showed a very small interaction energy and little geometrical deformation, compatible also with the V(C – C) basin population and very similar to that of

benzene (ca. 2.74e2). In addition, the contribution of the C(Cu) basin to the V(C – C) basins was very small (ca. 6.7%). Complex 3 presented very large interaction energy, and no geometrical deformation. The large interaction energy is in agreement with the small values of V(C – C) basin population (2.62e2), but does not agree with the electronic gain in the benzene ring from the metal cation. The contribution of the V(C – C) basins to the metal core basin was very small, as was also the contribution of the C(Mn) basin to the V(C –C) basins. The large interaction energy was explained by the existence of six V(C –Mn) basins, with small population each (0.21e2), but that yielded 1.26e2 overall. These basins collected the net electronic loss from the ion. The interaction was symmetrically shaped, accounting for the absence of ring deformation, but explaining the very large interaction energy. As a general feature of the metal cation – benzene interaction, there are no bond basins between the carbon and the metal, excluding the vanadium complex 1 and the small basins in the manganese complex 3. This, associated with the charge transfer observed, can be interpreted as an ionic interaction. In the special case of 1, the interaction produces repulsion between the vanadium and the Cb positions, and there is no bond path between them, therefore the basin cannot be interpreted as a bonding one. The vanadium is only bonded ionically to the Ca positions, and the extra basins have a certain lone-pair character. Table 5 shows the (3, 2 1) CPs of the ELF, located between the cation and the carbon positions, that connects the V(C –C) basins and the metal basin. It is remarkable to observe that those values decrease monotonically with the atomic number of the cation. This indicates that the metal and benzene systems become more independent as the atomic number increases. Complex 1 and 5 yielded geometrical and electronic data that agreed with vanadium and cobalt ions as good dehydropolycondensation catalysts. This possibility was also confirmed by the ELF data. The V(C – C) basins had markedly different electron populations (2.96e2 for V(Ca – Ca) and 2.42e2 for V(Ca –Cb) in 1, and 2.89e2 for V(Ca – Ca) and 2.71e2 for V(Ca – Cb) in 5). The contribution of the metal core basins to the V(C –C) basins also differed sharply (10.7% in V(Ca –Ca) and 7.5% in V(Ca – Cb) for 1, and

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Fig. 3. 3D representation for the different complexes (1–7) of the ELF isosurfaces at a value of 0.63e2. The basins created by the cation– benzene interaction are represented in clear gray tone. The letters indicate the nature of the basin. Basins denoted with ‘a’ are the basins generated from the aromatic bond electrons, with high occupancy, while those denoted with ‘b’ are regions with electronic pairing, but with much lower density.

16.4% in V(Ca – Ca) and 10.0% in V(Ca –Cb) for 5). The contribution of V(Ca –Ca) and V(Ca – Cb) to the metal core basins were also different, being the V(Ca – Ca) contribution in 5 the largest (18.3%). All this data agree with an extremely large bond discrimination in the aromatic ring, with medium to small interaction energy, suggesting vanadium and cobalt ions as good candidates to act as a catalysts. The different behavior of the complexes is clear in the three-dimensional basin representations shown in Fig. 3. In these representations the ring deformation is not clearly visible, but the form of the electronic-pair distribution near the metal ion is differentiated. The ion of the complexes with benzene ring deformation presented stronger asymmetry, while the other ions had cylindrical symmetry, inducing the symmetry of the benzene ring to be preserved. This is possibly due to the number of electrons present at the ion. Ions form complexes 1,

2, 5 and 6 have an odd number of electron pairs in the d-shell (4n þ 2 electrons), while complexes 3, 4 and 7 have an even number of electron pairs (4n electrons). The clearest behavior is that of the complex 7, where all data corresponded to a very weak interaction. In addition, the ELF distribution was almost spherical for the cation. Nevertheless, the interaction in complexes 3 and 4 was much stronger, as can be seen in the anisotropy of the ELF distribution. Complexes 5 and 6 presented a similar behavior due to their equal number of electrons in the molecule, but this time the difference between the interaction energies of complexes 5 and 6 was extreme, and the electronic properties of the C – C bonds were clearly differentiated. For 1, the bonds between vanadium and the Cb atoms are clearly presented by two basins with large volume (label ‘a’) and population (0.54e2). The presence of this two bonds caused the Ca – Ca bonds to

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be shorter and to have a relative double bond character. The manganese complex shows six metal –carbon basins (marked with label ‘a’ in Fig. 3), which were small but relatively populated, and a basin (label ‘b’) with extremely low population (0.07e2) but with relatively large volume. As in 3, complex 1 shows a basin with large volume, but with small population (0.06e2). These basins have no physical meaning and can be due to the DFT methodology.

4. Conclusions A first-principles DFT study was made on the benzene first-row transition-metal complexes 1 –7, in order to establish their relative stability, geometric characteristics, bond strength and electronic properties. All the complexes showed large interaction energy. However, there was no easy correlation between DEb and the geometrical and electronic characteristics of the complexes. The interaction has been characterized by their electronic properties by means of rðrÞ and ELF topological analysis. All the data agreed with complex 6, the one with the strongest DEb and large geometrical and electronic ring differentiation. However, complexes 1 and 5 showed also very large geometrical and electronic differentiation but low DEb values, being suitable as catalysts in dehydropolycondensation processes.

5. Supporting information Figures containing rðrÞ and 72 rðrÞ contour plots in the symmetry plane formed by the metal and the Cb atoms, for complexes 2, 3, 4 and 6 (pdf file) are available as supporting information.

Acknowledgments Financial support by INTAS Open Call 97-30810 is gratefully acknowledged. Computing time has been provided by the Universidad de Granada (Spain). We would like to thank Professors V.I. Kodolov and N.V. Khokhriakov for the fruitful discussions that made

possible this work. We are grateful to Professors R.F.W. Bader and B. Silvi for supplying us a copy of the AIMPAC and ToPMoD software packages. We also thank David Nesbitt for reviewing the language of the English manuscript.

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