Aromaticity of heptafulvene charge transfer complexes with lithium and caesium atoms: A computational approach

Computational and Theoretical Chemistry 998 (2012) 46–50

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Aromaticity of heptafulvene charge transfer complexes with lithium and caesium atoms: A computational approach Wojciech P. Oziminski a,b,⇑, Tadeusz M. Krygowski c a

National Medicines Institute, Chełmska 30/34, 00 725 Warsaw, Poland Institute of Nuclear Chemistry and Technology, Dorodna 16, 03 195 Warsaw, Poland c Department of Chemistry, University of Warsaw, Pasteura 1, 02 093 Warsaw, Poland b

a r t i c l e

i n f o

Article history: Received 5 April 2012 Received in revised form 21 May 2012 Accepted 23 May 2012 Available online 2 June 2012 Keywords: Heptafulvene Complex Aromaticity HOMA pEDA NICS

a b s t r a c t Geometry optimization of heptafulvene complexes with Li and Cs atoms at B3LYP/6-311++G(d, p) level of theory using Gaussian 03 software allowed us to estimate the magnitude of charge transfer from metal atoms to the heptafulvene moiety (charges equal to +0.938 and +0.994 for Li and Cs, respectively) and energies of dissociation of the complex (36.65 and 20.44 kcal/mol, respectively). A substantial increase of aromatic character of the ring results from the charge transfer leading to aromaticity index HOMA equal 0.439 and 0.515, for Li and Cs complex respectively, comparing to HOMA = 0.165 for isolated heptafulvene. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Monocyclic non-alternant pi-electron hydrocarbons are either electron attracting, as e.g. fulvene or electron repelling as e.g. heptafulvene. In both cases in line with the Huckel rule [1] they tend to have 4N + 2 pi-electrons. As a result, fulvene derivatives with electron donating exocyclic substituents becomes more stable, and exhibit partly aromatic character [2–4]. In a similar way, derivatives of heptafulvene becomes more stable for exocyclically substituted species with electron attracting groups [5]. In line with the above it was shown that aromaticity of the rings increased with the power of electron donating character of substituents for fulvenes and electron accepting character of substituents for heptafulvenes [6]. It is important to note that in these particular two families of molecules, various aromaticity indices are nicely correlated one with another [7], what is not always the case [8,9]. Recently it was also found, that strongly electron donating substituents attached in exo-position of fulvene cause appearance of a ring current which is absent in unsubstituted species [10]. Substituent effect was also studied in triplet states of substituted fulvenes [11] and very recently the effect of substituent on electron affinities and ionization energies of tria-, penta- and heptafulvenes exhibiting some regularities dependent on nature of substituent [12]. ⇑ Corresponding author at: National Medicines Institute, Chełmska 30/34, 00 725 Warsaw, Poland. Tel.: +48 22 841 21 21x166; fax: +48 22 841 06 52. E-mail address: [email protected] (W.P. Oziminski). 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.05.030

It is known that fulvenes can coordinate metals upon reduction [13,14]. Modeling interaction between fulvene and atomic Li it was found that an equilibrium complex is formed [15] exhibiting clear aromatic character documented by aromaticity indices as NICS [16] or HOMA [17,18] and the ring current [19]. In the case of heptafulvene it was found by quantum chemical modeling that halogen atoms form complexes in which some charge from the ring is transferred onto halogen atoms [20]. As a result the ring becomes positively charged as number of pi-electrons becomes closer to 4N + 2, and hence the ring becomes more aromatic in character. This is documented by the use of aromaticity indices such as NICS [21], HOMA [17,18] and pEDA [22]. The complexes formed are equilibrium type only for heavier halogens as Iodine and Astatium, the other are transition states, but the binding energy of these complexes is quite large, in the range of 6 to 32 kcal/mol. The purpose of this paper is to study modeling of interaction between heptafulvene and atoms of Li and Cs. For the comparison also the free heptafulvene anion is calculated.

2. Methods Geometry optimizations of the molecules were performed at the Density Functional Theory level using Becke hybrid B3LYP functional [23,24] by using the Gaussian 03 suite of programs [25]. The standard Pople 6-311++G(d, p) basis set [26–28] of valence triple-f quality with polarization and diffuse functions on

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all atoms was used. Geometry optimizations were followed by a frequency check to ensure that the computed stationary points are true energy minima on the potential energy surface. Additional series of constrained geometry optimizations at the B3LYP/631G(d, p) level was performed using a special z-matrix, where for each step, the distance between the metal atom and the center of the ring was kept constant and all bond lengths of the heptafulvene were kept unconstrained. This process was repeated for 40 steps in the range of 1–4 Å with step length of 0.1 Å which resulted in a potential energy well describing the shape of the potential well of metal–heptafulvene interaction. The geometry based aromaticity index Harmonic Oscillator Model of Aromaticity (HOMA) [17,18] was calculated according to Eq. (1). HOMA 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

ðRopt  Ri Þ2

ð1Þ

DEint ¼ DEelstat þ DEPauli þ DEorb

ð4Þ

Calculations of EDA were performed with the B3LYP functional and uncontracted Slater-type orbitals [36] employed 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) [37] correction. The 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:

De ¼ DEprep þ DEint

ð5Þ

Graphical representations of molecules were done by employing the Chemcraft visualization software [38]. 3. Results and discussion

i

where a = 257.7 is an empirical normalization constant chosen to give HOMA = 0 for model non-aromatic system and HOMA = 1 for a system where all bonds are equal to Ropt = 1.388 Å, n is the number of CC bonds taken into summation, Ropt is the optimal aromatic bond length and Ri are the experimental or computed bond lengths. Magnetism based aromaticity index NICS (Nucleus Independent Chemical Shift) [16] and its modifications NICS(1) and NICS(1)ZZ [21] values are calculated as the negative values of the shielding constant of a ghost atom located at the geometric center of the fulvene ring. The NICS(1) values are calculated at point located 1 Å above the ring (on the other side than the metal atom) and the NICS(1)ZZ is the ZZ component of the shielding tensor where Z is the axis perpendicular to the molecular plane. NICS(1)ZZ is at present, the recommended [29] variant of the original NICS index and was used in this study. As a third criterium of aromaticity we employed the pEDA index [22] which can be used to estimate the pi-electron occupancy of the heptafulvene ring. This parameter calculated within the NBO methodology [30] and particularly the natural population analysis scheme [31], is obtained according to Eq. (2) by summing up the 2pz atomic orbital occupations of heptafulvene ring carbon atoms and subtracting the nominal number of pi-electrons in the ring (i.e. 7). Therefore pEDA indicates the pi-electron excess relative to nominal value of pi- electrons in heptafulvene:

pEDA ¼

be further decomposed into electrostatic (DEelstat), Pauli-repulsion (DEPauli) and orbital interactions (DEorb) terms according to the following equation:

7 X

piheptafulv ene  7

Approaching of lithium and caesium atoms to heptafulvene moiety leads to the formation of equilibrium complexes. The energy well for approaching the lithium atom to the heptafulvene molecule (of approximate depth of 28 kcal/mol at B3LYP/631G(d, p) level of theory) is illustrated in Fig. 1. In the equilibrium complex (Fig. 2A) the lithium atom is located 1.552 Å above the point projected from lithium atom into the heptafulvene ring, whereas caesium atom is located 2.994 Å above this point (Fig. 2B). If from these distances we subtract the ionic radii of Li+ and Cs+ for coordination number 6:0.76 Å and 1.67 Å, respectively [39], then we find that Li is approaching to the plane of the ring closer than Cs (0.79 Å vs 1.32 Å). Even if we take ionic radius for Li+ as for coordination number 4, then its proximity is still smaller (0.96 Å). The use of ionic radii for Li and Cs atoms in these complexes is justified because the charge of these atoms estimated by NPA is close to +1e (see Table 1). Stability of Li complex is also greater than Cs, the De values are 36.65 and 20.44 kcal/mol. The point of projection of Li atom into the heptafulvene ring is located 0.169 Å from the geometric center of the ring, towards C4 and C5 atoms (for numbering scheme of the heptafulvene molecule see Fig. 3). On the contrary, the point projected from Cs atom into the heptafulvene ring is located only 0.0506 Å from the geometric center of the ring, towards C1 atom, so the caesium atom lies almost exactly over the geometric center of the ring. These findings allow

ð2Þ 0.0

i¼1

De ¼ ðEmetal atom þ 2  Efree heptafulv ene Þ  Ecomplex BSSE

ð3Þ

The nature of bonding in studied complexes was analyzed by means of the EDA (Energy Decomposition Analysis) [33–35] by employing the ADF (Amsterdam Density Functional) program [34,35]. 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

1.5

2

2.5

3

3.5

4

-5.0 -10.0

E (rel)

where plfulv ene is the occupancy of the i-th 2pz natural atomic orbital perpendicular to the plane of the molecule. The NBO analysis was done by NBO 5.G program interfaced to Gaussian 03. Dissociation energies De of the complexes were calculated according to Eq. (3) using supramolecular approach and were corrected for ZPE (Zero-Point Vibrational Energy) correction and BSSE (Basis Set Superposition Error) correction, according to Boys Counterpoise method [32], assuming non-charged pentafulvene and neutral alkaline atoms as reference fragments:

1

-15.0 -20.0 -25.0 -30.0

d (Li-hepta)

Fig. 1. The approximate binding energy of the Li-heptafulvene complex (relative to energy of the complex at the 4 Å distance) calculated at the B3LYP/6-31G(d, p) level using constrained approach.

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Fig. 2. Selected geometrical parameters and NPA charges of lithium and caesium complexes of heptafulvene.

Table 1 Metal-ring distance, NPA charge, aromaticity indices HOMA (7B), HOMA (5B), NICS(1)ZZ, pEDA and complex dissociation energy De.

Free heptafulvene Li-complex Cs-complex Heptafulvene anion

d(M-ring) (Å)

q(M) (e)

HOMA (7B)

HOMA (5B)

NICS(1)ZZ (ppm)

pEDA (e)

De (kcal/mol)

– 1.552 2.994 –

– 0.938 0.994 –

0.165 0.439 0.515 0.597

0.441 0.874 0.916 0.940

19.243 17.389 18.584 28.519

0.10 0.79 0.74 0.68

– 36.65 20.44 –

Fig. 3. Atom labeling of heptafulvene molecule.

to assume that the Li is less ionically bound to the ring than Cs which is documented also by charges at Li and Cs equal to 0.938 and 0.994, respectively. Additionally, Li is closer coordinated towards C4 and C5, whereas Cs prefers position with possibility of coordination with all carbon atoms of the ring. As a result both HOMA values, for the whole ring, HOMA (7B) and for the part of the ring with 5 CC bonds excluding C1C2 and C1C7, HOMA (5B), are greater for the caesium see Table 1. As we see in Fig. 2, geometry characteristics show that five of seven CC bonds (C2C3, C3C4, C4C5, C5C6, C6C7) in the ring exhibit strongly equalized CC bonds in both cases, complexes with Li and

Cs. These bond lengths are very close to the optimal CC bond in HOMA [17,18] model, 1.388A. Hence for these parts of heptafulvene ring HOMA equals to 0.874 and 0.917 for Li and Cs complexes, respectively. For comparison in free heptafulvene this is only 0.441 Å. Two long CC bonds, C7C1 and C1C2 are almost equal for all three cases: 1.468 Å, 1.464 Å respectively and 1.465 Å for free heptafulvene. The situation presented above resembles to some extent the cases known for homoaromatic systems [40,41], in which an aromatic ring is associated with the two long CC-bonds, the remaining part being typically aromatic. Classic HOMA index (HOMA7B) calculated for all seven ring CC bonds reflects aromaticity increase in Li and Cs complexes. However, if the HOMA index is calculated only for five bonds where the bond equalization occurs (C2C3, C3C4, C4C5, C5C6, C6C7), the aromatization appears to be much larger – HOMA (5B) approaches 0.917 for caesium complex (Table 1). Interestingly, HOMA values for radical anion of heptafulvene are very alike, HOMA (7B) and HOMA (5B) are 0.597 and 0.940 respectively. Both HOMA indices have the highest value for free anion, lower value for caesium complex and the lowest for lithium. One explanation can be that the metal cation is a perturbation which affects the bond lengths and this perturbation is more pronounced in the case of lithium atom as it approach to the heptafulvene ring more closely. Looking at the data of Table 1 it follows that according to HOMA there is substantial increase of aromaticity and according to NICS there is only slight increase of aromaticity in Li-fulvene complex. In both complexes the pEDA value is close to one which should } ckel 4N + 2 rule suggest antiaromatic properaccording to the Hu

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Fig. 4. Selected geometrical parameters and NPA charges of heptafulvene and heptafulvene anion.

Table 2 Total interaction energy, Pauli repulsion, electrostatic and orbital interactions terms. In parentheses are given the percentages of contributions to total attractive interaction. Energy is given in (kcal/mol). Neutral fragments

DEint DEPauli DEelstat DEoribtal

Charged fragments

Li complex

Cs complex

Li complex

Energy (kcal/mol)

Energy (kcal/mol)

Energy (kcal/mol)

% contribution in binding energy

Cs complex Energy (kcal/mol)

% contribution in binding energy

46.43 222.47 106.24 162.66

32.72 92.59 48.69 76.61

163.85 16.43 122.78 57.51

– – 68.10% 31.90%

117.57 17.89 102.47 32.99

– – 75.65% 24.35%

ties. Going from the free anion, through Cs complex to Li complex we can observe a trend, namely the pEDA is lowest for the anion and highest for the lithium complex. This can be explained by the fact that the metal cation approaching to the heptafulvene ring causes some polarization of the charge and as a result, some of the pi-charge can be withdrawn from the exocyclic = CH2 group to the ring and hence the increase of the pEDA. The effect is larger in the case of lithium as its distance and charge concentration is much larger than caesium. This effect can be observed for total NPA charges – see Figs. 2A and B and 4B. This again suggest similarity of Li and Cs complexes to mentioned earlier homo-aromatic systems. The dissociation energy De of the complex obtained at the supermolecular approach (complex energy minus heptafulvene fragment minus lithium atom fragment) equals to 36.65 kcal/ mol for lithium complex. This may be compared with the energy for Cs complex equal to 20.44 kcal/mol. The complex with caesium is apparently much less strongly bound. One reason can be much larger metal-ring distance and hence, weaker interaction. This is caused by large atomic core which prevents the Cs atom to approach to a closer distance. To analyze more deeply bonding in these molecules, the Energy Decomposition Analysis (EDA) was performed at the B3LYP/TZP level of theory resulting in DEint = 46.43 kcal/mol for lithium

complex and 32.72 kcal/mol for caesium complex. Interaction energy DEint can be further decomposed into electrical, Pauli repulsion and orbital interactions terms as presented in Table 2. There are two possible decomposition schemes: (1) neutral fragments, e.g. metal atom and neutral heptafulvene molecule and (2) charged fragments, e.g. metal cation and heptafulvene anion (with an unpaired electron). The choice is difficult in this case because for both schemes there is one fragment open-shell. The first choice is better for describing the total binding energy of the complex because if such complex would actually dissociate it would do it into neutral fragments. But if one wants to describe the actual bonding scheme is such associate the charged system is probably better. According to neutral fragment scheme the total interaction energy the relative contributions of electrostatic and orbital terms for Li and Cs are very similar. More intuitive picture can be obtained from charged fragment decomposition where it follows that the interaction in the case of caesium is more electrostatic in nature than the Li-complex. The orbital (covalent) contribution to bonding between metal and ring is larger for lithium (31.9% vs 24.35%) which is an expected result, in line with former discussion on geometric characteristics. This finding agrees well with results of Bickelhaupt et al. [42] where it was found that in methyl alkalimetal oligomers, where metal can be Li, Na, K, Rb, the carbon–metal bond is most covalent for lithium. The authors show that enhanced covalency

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is related to empty, low-lying 2p atomic orbitals of the lithium atom, which heavily interact with occupied orbitals. Similar mechanism can be assumed also in lithium–heptafulvene complexes. 4. Conclusions Li and Cs atoms form stable complexes with heptafulvene in which they become cations with 0.94 and 0.994 positive charges, respectively. As a result seven member ring increases its aromatic character from HOMA value of 0.165 for the isolated heptafulvene up to 0.439 and 0.515 for Li and Cs complexes, respectively. The dissociation energies of the complexes are 36.65 and 20.44 kcal/mol, respectively. If only five CC bonds are taken into account (excluding C1C2 and C1C6) then HOMA values are 0.874 and 0.916 for Li and Cs complexes respectively. The Li complex exhibit more covalent form of binding with the ring than it does the Cs complex which is reflected in the Energy Decomposition Analysis of the bonding. Acknowledgements This paper is dedicated to the memory of our friend Professor Marvin Charton (1932–2012) in recognition of his outstanding contribution to physical organic chemistry. Computational Grant G36-9 from the Interdisciplinary Centre for Mathematical and Computational Modeling at Warsaw University (ICM UW) is gratefully acknowledged. Computational Grant from the Wroclaw Centre for Networking and Supercomputing (WCSS) is gratefully acknowledged. References [1] A. Streitwieser Jr., Molecular Orbital Theory for Organic Chemists, J. Wiley, New York, 1961. 256ff. [2] H.L. Ammon, The structure of 6-(N,N-dimethylamino)pentafulvene and 2formyl-6-(N,N-dimethylamino)pentafulvene. Bond length evidence for dipolar resonance forms, Acta Cryst. B30 (1974) 1731–1738. [3] T.M. Krygowski, A. Ciesielski, M.K. Cyranski, Aromatic character and energy of the five- and seven-membered rings in derivatives of penta- and heptafulvene substituted in exocyclic position, Chem. Pap. 49 (1995) 128–132. [4] M.L. Peterson, J.T. Strand, T.P. Markotan, C.A. Morales, D.V. Scaltrito, S.W. Staley, Structural effects of C6 substitution in 6-(4(dimethylamino)phenyl)fulvenes, J. Org. Chem. 64 (1999) 9067–9076. [5] C. Reichardt, K.Y. Yun, W. Massa, R.E. Schmidt, O. Exner, Syntheses with aliphatic dialdehydes, XLII. – (2,4,6-cycloheptatrien-1-ylidene)malonaldehyde (8,8-diformylheptafulvene) – synthesis, structure, and reactions, Liebigs Ann. (1985) 1997–2011. [6] B.T. Stepien, M.K. Cyranski, T.M. Krygowski, Aromaticity strongly affected by substituents in fulvene and heptafulvene as a new method of estimating the resonance effect, Chem. Phys. Lett. 350 (2001) 537–542. [7] B.T. Stepien, T.M. Krygowski, M.K. Cyran´ski, Extent of cyclic p-electron delocalization modification in exocyclically substituted fulvenes, J. Org. Chem. 67 (2002) 5987–5992. [8] M.K. Cyran´ski, T.M. Krygowski, A.R. Katritzky, P.V.R. Schleyer, To what extent can aromaticity be defined uniquely, J. Org. Chem. 67 (2002) 1333–1338. [9] M.K. Cyran´ski, P.V.R. Schleyer, T.M. Krygowski, H.J. Jiao, G. Hohlneicher, Facts and artifacts about aromatic stability estimation, Tetrahedron 59 (2003) 1657–1665. [10] W.P. Oziminski, T.M. Krygowski, P.W. Fowler, A. McKenzie, Aromaticity of substituted fulvene derivatives: substituent-dependent ring currents, Phys. Chem. Chem. Phys. 12 (2010) 10740–10745. [11] H. Ottosson, K. Kilsa, K. Chajara, M.C. Piqueras, R. Crespo, H. Kato, D. Muthas, Scope and limitations of baird’s theory on triplet state aromaticity: application to the tuning of singlet–triplet energy gaps in fulvenes, Chem. Eur. J. 13 (2007) 6998–7005. [12] C. Dahlstrand, K. Yamazaki, K. Kilsa, H. Ottosson, Substituent effects on the electron affinities and ionization energies of tria-, penta-, and heptafulvenes: a computational investigation, J. Org. Chem. 75 (2010) 8060–8068. [13] T. Kawase, N. Nisato, M. Oda, Reductive coupling of 6-dimethylaminofulvenes furnishing 6,60 -bifulvenyls, J. Chem. Soc. Chem. Commun. (1989) 1145–1146. [14] M. Tacke, S. Fox, L. Cuffe, J.P. Dunne, F. Hartl, T. Mahabiersieg, A study of the reduction of substituted fulvenes using spectro-electrochemistry and ab initio theory, J. Mol. Struct. 559 (2001) 331–339.

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