Electronic Charge Density Analysis of Li-Doped Polyacetylene

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Electronic Charge Density Analysis of Li-Doped Polyacetylene: Molecular vs. Periodic Descriptions and Nature of Li-to-Chain Bonding Minhhuy Hô, Alejandra M Navarrete-Lopez, Claudio Marcelo Zicovich-Wilson, and Alejandro Ramirez-Solis J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp3106343 • Publication Date (Web): 21 Dec 2012 Downloaded from http://pubs.acs.org on December 22, 2012

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The Journal of Physical Chemistry

Electronic Charge Density Analysis of Li-doped Polyacetylene: Molecular vs. Periodic Descriptions and nature of Li-to-chain Bonding Minhhuy Hôa , Alejandra M. Navarrete-Lópezb , Claudio M. Zicovich-Wilsonb and Alejandro Ramírez Solísb∗ a Centro de Investigaciones Químicas Universidad Autónoma del Estado de Morelos b

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos December 19, 2012 Abstract A detailed analysis of the electronic structure and charge distribution around the trigonal site of Li-doped polyacetylene is reported using finite chain and periodic descriptions of the polymer. Atoms-in-molecules (AIM) analysis is done to characterize the nature of the bond between Li and the polymer backbone through the location of the bond critical points and computation of the total charge on the atomic basins around the doping site. We find that the Li atom donates practically one electron to the π-system, in accordance with the classical Su-Schriffer-Heeger model. However, despite that the Li atom is equidistant from the three closest C atoms in the geometric soliton, a single Li-C bond critical point is found. The AIM quantitative analysis of the electronic density reveals that the Li+ ion is immersed into the polymer π-cloud in a way that resembles a metallic bonding interaction. *Corresponding author: [email protected] Keywords: Trans-polyacetylene; Lithium; AIM; Periodic system; Bond Critical Points

1

Introduction

In the last decade a large number of quantum-theoretical studies have addressed the molecular and electronic structure of alkali-doped trans-polyacetylene (PA). This arises 1 ACS Paragon Plus Environment


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mainly from the great interest in understanding the mechanisms at work when a conjugated polymer, such as PA, is doped with an electron donor or acceptor, since an enormous increase in conductivity can be achieved. [1–5] When alkali atoms interact with PA chains localized charged defects appear and this induces the creation of chain deformations called topological/geometrical solitons, [6] which are formed in conjunction with electronic charge transfer to the PA chain. The geometrical soliton corresponds to the region of the PA chain over which there is a reversal of the bond length alternation (BLA) pattern; it may extend over several double bonds neighboring the alkali atom docking site on both sides of the chain. Some works have addressed the molecular structure of alkali-doped PA finite chains from the molecular point of view [7, 8] either using ab initio or Density Functional Theory (DFT) based methods. Only very recently this has been done for the infinite polymer using periodic HF and density functional theory (DFT) calculations where both, uniform and non-uniform doping, have been considered for the specific case of Li at various doping concentrations for symmetric C2m H2m Li2 unit cells (m = 7−14) with P ¯1 rod symmetry chains. [9] In that work two of us addressed the dependence of the changes of geometry, atomic charges along the chain, soliton formation and dopant binding energies, band structures and densities of states as functions of dopant concentration. However, that study allowed us to acknowledge the fact that the Li-bonding and the charge transfer to the chain are actually driven by quite complex electronic mechanisms; that preliminary bonding analysis made us realize that a much more accurate and detailed study was needed to fully understand such issues. Those studies have addressed, in passing, the bonding mechanism of the alkali atoms with the PA chain [7, 8] but no clear conclusion concerning the nature of that bonding was there given. In particular, in [9] we examined the Mulliken charge distributions as a first naïve measure of the ionicity/covalency of the bonding of Li to the PA chain. It is well known that the magnitude of the Mulliken charges should be taken in general with caution, [10] although, for positively charged solitons (no dopant counterions), it has been found [11] that most other methods, such as Natural Population Analysis (NPA), [12] usually yield similar values. On the other hand, and quite surprisingly, the Mulliken and NPA charges on the metal atom in M-CH3 and M-CCH interactions (M ≡ alkaline metal) turn out to be very different. [13] In a more recent contribution [14] the charge magnitude transfered from Li and Na to PA at the B3LYP level with various basis sets and several charge analysis schemes has been addressed. The Mulliken analysis results on periodic (Li, Na)-doped chains were supplemented by charges on finite clusters obtained from NPA as well as the 2 ACS Paragon Plus Environment

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Merz-Kollman [15] and CHelpG [16]electrostatic potential methods. The key feature found in Refs. [9] and [14] is that much less than one electron (only around 1/3)seems to be transferred to the PA chain per Li atom, particularly when Mulliken charges are considered, thus leading to a much less ionic picture than usually thought. Whereas the doping site itself is almost neutral (slightly positive), roughly half the negative Mulliken charge is localized on the two nearest-neighbor CH units. The next-nearest neighbors are almost neutral and the remaining negative charge is spread out over subsequent neighbors in a characteristic oscillatory pattern (see figure 3 of Ref. [9]). The previous picture dramatically changes as concerns the cationic charge when criteria other than Mulliken are considered to estimate the electronic population. For instance, we found [14] that charges of about +0.5 and +0.9 |e| are obtained on Li with NPA and CHelpG, respectively. We recall that the Su-Schrieffer-Heeger (SSH) model, which is usually reckoned to explain the soliton creation, considers full charge transfer from the dopant to the PA chain. [6] Therefore, it turns out that different analyses of the electronic structure provide contradictory pictures of the Li-PA bonding, ranging from practically pure ionic to a kind partially covalent character of the interaction. In this work we shall concentrate on a precise bonding characterization for the highest Li concentration (y=1/7) of Li-PA we have previously studied at the periodic B3LYP level. We shall also assess the relative quality of a cluster description for this interaction by using a small finite PA chain, studied at the same computational level. Therefore, we intend to underpin the Li-C bonding effects brought in the borders with the cluster model by comparing it with the infinite periodic description. On the other hand, our previous periodic B3LYP-DFT results for y = 1/7, 1/9, 1/11 and 1/13 were shown to be quite similar to those obtained in previous work on a single dopant in C33 H33 Li [8]; in all cases the charge oscillations and BLA changes are found only on the five CH groups in the central region of the soliton. For this reason the present topologic study of the electronic density for the highest concentration is representative of a broad range of Li/C dopings. As found by most previous studies, we recall that our periodic B3LYP calculation also showed that Li is linked to three carbon atoms on each side of the PA chain, so a question that remained to be answered is: to what extent these bonds are real in the topological sense of the electronic density?, and if they are, what kind of interaction they represent? Another goal we pursue here is to quantitatively determine the nature of the Li bonding to the PA chain by providing accurate quantities derived from topological features of the electronic density that have been previously used to classify chemical bonds. The methodology and the computational details are summarized in 3 ACS Paragon Plus Environment


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Section II, while the results are presented in Section III. Finally, our conclusions are discussed, along with some perspectives in Section IV.

2

Computational methods

In order to describe the Li to PA bonding in Li-doped PA chains we used the y = Li/C = 1/7 dopant concentration; we considered both, the molecular case and the infinite periodic structures built from a C2m H2m Li2 unit cell (m = 7) with rod P 21 /m symmetry whose structure was already optimized and reported in [9] at the periodic B3LYP level. The center of inversion is consistent with a previous work [18] showing that successive Li atoms lie on opposite sides of the PA plane. In addition, we recall here that each Li atom is simultaneously coordinated to three carbon atoms (all three Li-C distances around 2.06 A) and that the C-C bonds on either side of the central doping site are of intermediate length in comparison to the bonds successively further removed, which alternate between long (formally single) and short (formally double), as seen in Figs. 1 and 2 of Ref. [9]. When m = 7, for example, the number of formal double bonds between doping sites may alternate between one and three instead of being two in each instance. If m is even only non-uniform doping structures are allowed. We concentrate here only on uniform doping. As in Ref. [9], periodic calculations were performed with the CRYSTAL09 code [19, 20] at the B3LYP level using the standard 6-31G** basis sets. The parameters controlling numerical accuracy in the integral evaluation are the default provided by the code [9]. The Brillouin zone shrinking factor has been set to 8 so as to build the Monkhorst net. In the B3LYP calculations standard CRYSTAL (75, 974) pruned grid (keyword XLGRID, see code manual [20]) were employed for numerical integrations involving the density. For the molecular calculations, a C14 H16 Li2 cluster was built from the optimized periodic structure (with H-saturated ends) and then optimized at the B3LYP level with the same 6-31G** basis, as was done for the periodic calculations.

Topological Analysis of the Electronic Density To study the nature of the Li bond to the polymer, we analyze the atomic charge distribution along the chain with the Mulliken scheme and the AIM method proposed by Bader [21], based on the topological properties of the charge density. For the

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molecular C14 H16 Li2 fragment (Fig. 1), a slighty modified version of the AIM [21] method was used. The topological properties of the electron density in the periodic system were calculated using two versions of the same program, Topond98 [22] and Topond09big. [23] The former is connected to an old version of the Crystal code [24] that employs auxiliary basis functions for the electronic density, while the latter uses the information generated with the Crystal09 version of the code. [20] The reason for using two versions of Topond is that the newer one does not evaluate all desired topological properties at the bond critical points (BCP). We verified that all comparable topological properties at the BCPs and their locations do not vary between both versions. In fact, the two versions yield the same locations for all bond critical points. The default options for the integration method [25] were used for H and Li atoms; for C atoms a double-integration scheme was considered. [26] The results were verified to be consistent with the total number of electrons. The AIM atomic integrations were double checked with the option SCULPT in the AIMALL suite of programs. [27]

Figure 1: C14 H14 Li2 finite model considered. Apart from the ending H atoms the atomic labeling is equivalent to that considered for the periodic model.

3

Results and discussion

In order to define the nomenclature, we present in Fig. 1 the atom numbering we shall use in the discussion of the results. Let us first discuss the charge distribution along the chain for the periodic case As usually done, the charges reported are given for each CH unit and are shown in Table 1. The Bader charges show a strong interaction between 5 ACS Paragon Plus Environment


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Li and the carbon chain where the three CH units closest to Li are the most negative; however, as previously found with the Mulliken scheme, [9] the central CH unit is less negative (-0.14) than its neighbors (-0.28). Model Finite C14 -0.04619 H28 -0.02731 -0.07350 C10 0.00360 H24 -0.02786 -0.02426 C6 -0.24895 H20 -0.04741 -0.29636 C1 -0.11135 H15 -0.01236 -0.12371 C3 -0.22184 H17 -0.05006 -0.27190 C7 -0.01511 H21 -0.02952 -0.04463 C11 -0.00827 H25 -0.03574 -0.04401 Li29 0.89781

Periodic -0.01422 -0.03693 -0.05115 -0.02006 -0.03057 -0.05063 -0.23148 0.04992 -0.28140 -0.12395 -0.01329 -0.13724 -0.23148 -0.04992 -0.28140 -0.02006 -0.03057 -0.05063 -0.01422 -0.03693 -0.05115 0.89976

Table 1: Bader Atomic Charges for the B3LYP calculation of finite (C14 H16 Li2 molecule) and periodic models (a single unit cell was considered as described in [9]). The number below C and H atomic charges in each row is the corresponding CH unit charge. The table also shows that the finite description yields Bader charges that are very similar to those obtained with the periodic model; as could be expected, only slight differences are found for the CH units close to both ends of the cluster (see Fig. 2). The main difference stands on the fact that in the infinite model a perfectly symmetric distribution is featured due to space symmetry. We stress here that the overall Bader charge of Li is ca. 0.89 |e| using both, the cluster and the infinite periodic models. This is in accordance with the NPA results already reported in Ref. [14] where the B3LYP NPA charge of Li was found to be 0.93 |e| for the C11 H13 Li doped molecule; although 6 ACS Paragon Plus Environment

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the Li/C doping level was slightly less (y = 1/11) for that case, the NPA charge is actually quite close to the Li Bader charge in the C14 H16 Li2 molecule we study here. The PA chain has a typical distribution of a conjugated system of covalent C-C bonds where the electrons are delocalized evenly all along the carbon backbone.

0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 1

2

3

4

5

6

7

Figure 2: AIM atomic charges condensed to CH units. Values correspond to the 7 closest units around the soliton. Unit 4 is the central one. Figure 3 shows the electronic density distribution around the doping site for the periodic chain at ρ = 0.005 |e|·Bohr−3 . It is quite remarkable that the overall electronic density distribution resembles a pipe and that the Li+ ions seem to be submerged or “stuck into the tube”, as shown in Fig. 3. Note the very small volume spanned by the Li+ ions (essentially described by the the 1s2 atomic configuration) as compared to the π + σ density along the carbon backbone. We shall later address the lack of a clear density maximum along the Li-C (central) line. The topological properties at the B3LYP level for the periodic and finite models are summarized in Tables 2 and 3. First of all, we found a single bond path between the Li(29) and C(1) atoms using both the finite and the periodic models. The Laplacian is about 0.18 at the BCP with both models. At this point we recall that Bianchi et al. [28] have made a quantitative classification of chemical bonds using the values of several topological and energetic properties calculated at the bond critical points. In particular, they use the values of 7 ACS Paragon Plus Environment


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Figure 3: B3LYP electronic density distribution of the periodic model at ρ = 0.005 |e| · Bohr−3 . Atom dBCP(Å) ρ(e·Å−3 ) ∇2 ρ(e·Å−5 ) λ1 (e·Å−5 ) λ2 (e·Å−5 ) λ3 (e·Å−5 ) C1 0.717 0.300 -0.760 -0.613 -0.481 0.334 C6 0.694 C1 1.303 0.030 0.177 -0.042 -0.011 0.230 Li29 0.747 C1 0.686 0.278 -0.963 -0.728 -0.711 0.476 H15 0.409 C1 0.544 0.300 -0.779 -0.613 -0.497 0.331 C3 0.544

ǫ 0.274 2.718 0.023 0.233

Table 2: Topological properties of the density for the finite model at the B3LYP/631G** level. The ellipticity is given by ǫ = ( λλ12 − 1).

the kinetic (G(r)) and the potential (V (r)) energy densities as important parameters. These authors have characterized closed-shell interactions as having low ρ and positive Laplacian of the electronic density at the BCP. Metallic and ionic bonds fall into this category. However, metallic bonds are characterized by relatively low ρ, G and |V |values, a positive Laplacian value and negative sum of G(r) + V (r). Ionic bonds differ from metallic ones in that the sum of G(r) + V (r) is positive. In our Li-doped polyacetylene case, the sum of G(r) + V (r) is very close to zero using both the cluster 8 ACS Paragon Plus Environment

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and the periodic models (0.0066 and 0.0069, respectively). This analysis leads to a very important result: the Li-C(1)interaction can be considered as somewhere between an ionic and a metallic-like bond. Atom dBCP(Å) ρ(e·Å−3 ) ∇2 ρ(e·Å−5 ) λ1 (e·Å−5 ) λ2 (e·Å−5 ) λ3 (e·Å−5 ) ǫ H15 0.412 0.277 -0.957 -0.717 -0.706 0.467 0.016 C1 0.682 C3 0.691 0.299 -0.762 -0.605 -0.469 0.311 0.292 C1 0.720 Li29 0.748 0.029 0.183 -0.041 -0.005 0.229 6.730 C1 1.299 Table 3: Topological properties of the density for the polymer at the B3LYP/6-31G** level. The ellipticity is given by ǫ = ( λλ21 − 1). When the long range effects are included using the periodic model, the largest topological difference with the finite model is the ellipticity of the Li-C(1) bond, which increases from 2.72 to 6.73 when going from the molecular to the periodic description. An examination of the eigenvectors of the Hessian of ∇2 ρ at the critical point for both models shows that this quantity around Li is strongly deformed in the direction parallel to the carbon backbone. This can be observed in the profile of the Laplacian of the density surrounding the Li ion in Fig. 4, where contours are found extending along the carbon chain and perpendicular to the Li-C axis. This deformation clearly shows that the Li-PA interaction is not a simple Li-C bond like that found in LiCH3 , [13] and that the presence of the π backbone significantly alters this simple two-center behavior. The ellipticity in the frame of the AIM theory has been mainly considered as a descriptor of the π character of a bond, [29] the existence of H-bonds of assisted resonance, [30] or to distinguish particular functional groups in a complex structure. [31] More recently, the applications of this index have been diversified towards the description of unusual bonds, for instance in charge transfer interactions, steric contacts and organometallic complexes. [32] A large ellipticity value at the critical point is in every case considered as an index of bond instability. [33] In the present case, an extremely large value for the periodic model is to be correlated with the well known mobility of the soliton (and the doping cation) along the carbon backbone under a parallel electric field. The lower value featured by the finite model does indicate that this phenomenon, crucial to explain the enhanced conductivity of doped polymers, is somehow lacking. It is interesting to note that, when this index is computed in a finite model whose geometry is constrained 9 ACS Paragon Plus Environment


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Figure 4: Contour map of ∇2 ρ along a plane that roughly contains the regions around the C (above) and Li (below) atoms of the soliton.

to be the same as that of the polymer unit cell (except for the ending H atoms), it becomes 10.33, even higher than the periodic value. This suggests that the soliton character is enhanced by the geometric constrains imposed by the whole structure in very large chains.


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4

Conclusions

We have performed a detailed topological analysis of the electronic density of Li-doped polyacetylene using both, finite and periodic models. Their geometries have been optimized at the B3LYP/6-31G** level in both cases, revealing that Li is coordinated to three carbon atoms that lie at the same distance from the metal. However, the Bader analysis revealed only one bond critical point connecting Li with the solitonic central carbon atom. In spite of the small differences found along the C backbone, the Bader analyses of both the finite model and the polymer agree in what concerns the nature of the Li-to-chain bonding. At variance with previous studies that considered Mulliken charges, [9] the present results closely concur with the SSH [6] model, as the Li-doping involves a metal oxidation that supplies nearly one electron per Li atom into the π-system. This process gives rise to the corresponding charge and topologic solitons around the doping site. What is interesting from the chemical point of view is the nature of the interaction between the resulting cation and the solitonic defect. As could be expected, the Li+ ion is strongly attached to the carbon chain owing to electrostatic forces arising from the net negative charge of the backbone. Nonetheless, it turns out from the present analysis that it is additionally stabilized through a partial “merging” of the cation into the π cloud. This particular arrangement of the Li+ ion somehow resembles that of cations in metallic bonds, as in both cases positively charged species appear stabilized by the short-to-medium range interaction with delocalized electrons. The fact that the cation is not completely surrounded by the electron cloud, as it does occur in a true metal, gives rise to a critical point similar to those appearing in ionic bonds. However, the fact that the negative charge in the soliton is not as localized as it should be in the anionic moiety of the ionic bond, together with the partial merging of the cation inside the π electronic cloud, support the idea of a partial metallic character of the Li+ /C backbone interaction. A closer examination of the topological properties of the Li-C bond shows that it is highly flattened in the direction parallel to the carbon chain. The bond is a result of the ovelap mainly between the s-orbitals of the respective atoms; the 2p-orbitals of C do not seem to play an important role as judged by the small magnitude of their AO coefficients in the density one-matrix. Connected to this, the AIM studies reveals that the Li+ -soliton bond in the periodic model features an unusually large ellipicity associated to a very low eigenvalue of the Laplacian Hessian at the critical point whose eigenvector lies along the C-backbone. 11 ACS Paragon Plus Environment


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This is lacking in the optimized finite model and is to be attributed to the ability of the cation+soliton to move along the chain as a characteristic property of these materials. Finally, we notice that the partially metallic nature of the Li-C bond is expected to be particularly important for Li+ as compared to other alkali cations, as their much larger ionic radii prevents them from being engulfed by the π electronic cloud.

Acknowledgments ARS thanks support from CONACYT basic science project No. 130931. AMNL acknowledges a CONACYT posdoctoral fellowship. The autors are grateful to Prof. C. Gatti for the prompt technical assistance and for providing the new version of the TOPOND program.

References [1] (a) Shirakawa, H.; Louis, E.J.; MacDiarmid, A.G.; Chiang, C.K.; Heeger, A.J., J. Chem. Soc. Chem. Commun., 1977, 578. (b) Chiang, C.K.; Fincher Jr., C.R.; Park, Y. W.; Heeger, A.J.; Shirakawa, H.; Gau, S.C.; MacDiarmid, A.G., Phys. Rev. Lett., 1977, 39, 1098. (c)Chiang, C.K.;Gau, S.C.; Fincher Jr., C.R.; Park, Y.W.; MacDiarmid, A.G.; Heeger, A.J., Appl. Phys. Lett., 1978, 33, 18. [2] Tsukamoto, J.; Takahashi, A.; Kawasaki, K. Jap. J. Appl. Phys., 1990, 29, 125. [3] Cao, Y.; Smith, P.; Heeger, A.J., Polymer, 1991, 32, 1210. [4] Schimmel, T.; Reiss, W.; Gmeiner, J.; Schworer, M.;Naarmann, H.; Theophilou, N., Solid Stat. Commun., 1988, 65, 1311. [5] Skotheim, T.A., Handbook of Conducting Polymers, Vols. I and II ; Dekker: New York, 1986. [6] Su, W.P.; Schrieffer, J.R., Heeger, A.J., Phys. Rev. Lett., 1979, 42, 1698; Phys. Rev. B, 1980, 22, 2099. [7] Champagne, B.; Spassova, M.; Jadin, J.B.; Kirtman, B., J.Chem. Phys., 2002, 116, 3935. [8] Champagne, B.; Spassova, M., Phys. Chem. Chem. Phys., 2004, 6, 3167. 12 ACS Paragon Plus Environment

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[9] Ramírez-Solís, A.; Zicovich-Wilson, C.; Kirtman, B., J. Chem. Phys., 2006, 124, 244703. [10] Streitwieser, A.; Bachrach, S. M.; Dorigo, A.; Schleyer, P. v. R.Lithium Chemistry: A Theoretical and Experimental Overview ; Wiley-Interscience: New York, 1995. [11] Monev, V.; Spassova, M.; Champagne, B., Int. J. Quantum Chem., 2005, 104, 354. [12] Reed, A. E.; Weinstock, R. B.; Weinhold, F., J. Chem. Phys., 1985, 83, 735. [13] Scalmani, G.; Bredas, J.L.; Barone, V.J., Chem. Phys., 2000, 112, 1178. [14] Ramírez-Solís, A.; Kirtman, B.; Bernal, R.; Zicovich-Wilson, C., J. Phys. Chem. C, 2008, 112, 9493. [15] Besler, B. H.; Merz, K.; Kollman, P. A. J. Comput. Chem., 1990, 11, 431. [16] Breneman, C. M.; Wiberg, K. B. J. Comput. Chem., 1990, 11, 361. [17] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J., J. A.; Stratmann, R. E.; Burant, J. C. et al., Gaussian 98 A.11.3; Gaussian, Inc.: Pittsburg, PA 2002. [18] Spassova, M.; Champagne, B.; Kirtman, B., Chem. Phys. Lett., 2005, 412, 217. [19] Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V. R.; ZicovichWilson, C. M., Z. Kristallogr., 2005, 220, 571. [20] Dovesi, R.; Saunders, V.R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C.M.; Pascale, F.; Civalleri, B.;Doll, K.; Harrison, N.M.; Bush, I.J.; D’Arco, P.; Llunell, M., CRYSTAL09 User’s Manual ; Università di Torino. Torino, Italia, 2009. http://www.crystal.unito.it [21] Obtained from R.F.W. Bader, Dept. of Chemistry, McMaster University, Ontario, Canada. [22] Gatti, C., TOPOND98 User’s Manual ; CNR-CSRSRC: Milano, Italy, 1999. [23] Gatti, C., J. Chem. Phys., 1994, 101, 10686. TOPOND09 (private communication).



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[24] Saunders, V.R.; Dovesi, R.; Roetti, C.; Causà, M.; Harrison, N.M.; Orlando, R.;Zicovich-Wilson, C.M., CRYSTAL98 User’s Manual, Università di Torino. Torino, Italia, 1998. [25] Keith, T.A., Ph.D. Thesis, McMaster University, Ontario, Canada, 1993. [26] Biegler-König, F.W.; Bader, R.F.W.; Tang, T.H., J. Comp. Chem., 1982, 13, 317. [27] AIMAll (Version 11.05.16), Keith, T.A., 2011 (aim.tkgristmill.com). [28] Bianchi, R., Gervasio, G.; Marabello, D., Inorg. Chem., 2000, 39, 2360. [29] Ziessel, R.; Stroh, C.; Heise, H., Köhler, F.H.; Turek, P.; Claiser, N.; Souhassou, M.; Lecomte, C., J. Am. Chem. Soc., 2004, 126, 12604. [30] Singh, R.N.; Kumar, A.; Tiwari, R.K.; Rawat, P.; Verma, D.; Baboo, V., J. Mol. Str., 2012, 1016, 97. [31] Burton, J.; Meurice, N.; Leherte, L.; Vercauteren, D.P., J. Chem. Informat. Model., 2008, 48, 1974. [32] López, C.S.; de Lera, A.R., Curr. Org. Chem., 2011, 15, 3576. [33] Popelier, P., Atoms in Molecules. An Introduction; Prentice Hall. Essex, England, 2000. TOC Graphical


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Figure 5: Graphical TOC


Electronic Charge Density Analysis of Li-Doped Polyacetylene

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