Fully Doped Oligomers of Emeraldine Salt: Polaronic versus

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Fully Doped Oligomers of Emeraldine Salt: Polaronic versus Bipolaronic Configuration Jasmina N. Petrova, Julia R. Romanova, Galia K. Madjarova, Anela N. Ivanova, and Alia V. Tadjer* Faculty of Chemistry, University of Sofia, 1 James Bourchier Avenue, 1164 Sofia, Bulgaria

bS Supporting Information ABSTRACT: Calculations for model oligomers of the emeraldine salt with UBLYP/6-31G*/PCM are performed. The models differ in number of monomers, in the position of the counterions (Cl), and in multiplicity. The molecular features affected most prominently by the protonation, namely, structure, energetics, and electron and spin density partitioning are analyzed. The results show unequivocally that the studied molecular characteristics are essentially size independent. The octamer profiles of all parameters are repeated in the dodecamer and the hexadecamer. The bipolaronic forms are energetically more favorable than the polaronic ones within the chosen protocol. The electronic structure in the intermediate multiplicities differs from the bipolaronic and polaronic periodicity. The geometrical changes and electron density redistribution upon increase of multiplicity illustrate the pathway of intramolecular bipolaronpolaron conversion. The orbital analysis rationalizes the observed behavior of the oligomers.

’ INTRODUCTION Polyaniline (PANI) attracts unalleviated interest due to its synthetic accessibility,1 stability, and sizable conductivity in doped state,2 alongside with a variety of potential applications in the fabrication of light-emitting diodes,3 electrooptical devices,4 anticorrosion coatings,5,6 etc. A generalized chemical formula of PANI is given in Figure 1:7 Among its stable forms, leucoemeraldine base (LEB, y = 1), emeraldine base (EB, y = 0.5), and pernigraniline base (PNB, y = 0), the conducting emeraldine salt (ES), obtained usually upon p-doping of EB, receives prime attention.8,9 The doping consists of protonation of the imine nitrogens in acidic medium resulting in a highly conducting state preserving the number of π-electrons in the polymer. There exists experimental evidence10,11 that two types of defects differing in their magnetic behavior are formed in this process: paramagnetic (polarons, which are polycation radicals) and magnetically inactive (bipolaronspolycations). Both types invoke substantial changes in the geometry and electron density distribution along the EB chain. Stafstr€om et al.12 suggest a model (Figure 2) describing the chemical structure of the two defects in compliance with the experimental data. The PANI polaron bears one positive charge and one unpaired electron and is fully described by a dimeric elementary unit, whereas the spinless bipolaron carries two positive charges in its tetrameric repeating motif. The introduction of these defects causes the emergence of localized electronic states in the EB band gap, close to its boundaries, forming a half-filled bonding band in the polaronic form and a vacant one in the bipolaronic structure. Each of these states has an antibonding partner in the band gap. r 2011 American Chemical Society

An extension of the applicability of conducting PANI requires detailed investigation of the mechanism of charge transport. Indepth understanding of the latter is closely related to the study of polarons and bipolarons, deemed to be the charge carriers in this polymer. Widely discussed from experimental and theoretical perspective but still open remain a number of issues, such as: the structural changes of the doped polymer chain, the relative stability of polaron and bipolaron defects, the nature of interand intrachain interactions, the origin of the optical properties, and the clarification of the conductivity mechanism. The experimental studies are summarized in a comprehensive review.13 Some authors consider the presence of bipolaronic lattices in ES,14,15 while others demonstrate the existence of polarons.16,17 The theoretical results are not unanimous either. The early computational studies address the above issues using semiempirical methods.12,1821 Some of them claim that bipolarons are the more favorable defects,22,23 others predict them as less stable.24 Oliveira and dos Santos25 suppose coexistence of the two defects in short chains and predominance of polarons in longer oligomers and in the polymer. Lately, various DFT functionals2630 have been expansively utilized for the theoretical treatment of PANI, since they afford results in good agreement with the available experimental data. It has been demonstrated that DFT provides correct description at the molecular level of biradical31 and polyradical32,33 structures.

Received: December 15, 2010 Revised: February 28, 2011 Published: March 21, 2011 3765

dx.doi.org/10.1021/jp111914n | J. Phys. Chem. B 2011, 115, 3765–3776

The Journal of Physical Chemistry B

Figure 1. General formula depicting the chemical structure of PANI.

Figure 2. Chemical structure of emeraldine base before protonation (A) and bipolarons (B), polarons (C), and separated polarons (D) after protonation (adapted from ref 12).

The geometry and spectral properties of polaronic and bipolaronic ES structures in periodic boundary conditions are estimated with a set of DFT functionals (LSDA, PBE, and PBEh)34 and the changes accompanying the processes presented in Figure 2 are discussed. Lower energy is found for the bipolaron form, promoting the conclusion that this state is responsible for the metallic behavior of ES. Yang and co-workers35 analyze with PBE/6-31G* in vacuum the electronic structure of oligoanilines doped with inorganic (HCl) and organic (HCSA) acids. On the basis of the bond lengths and Mulliken charge distribution, the authors speculate that the HCSA doping facilitates the charge transfer along the chain in the polaronic form compared to the bipolaronic, which in their opinion justifies the difference in the conductivity of HCland HCSA-doped polyaniline. However, the introduction of polar medium36 contests these conclusions. A recent paper37 investigates the size effect on PANI properties. Various combinations of DFT functionals and basis sets are tested on short models and BH&H/6-31G* is selected as the most appropriate. The method is applied further to longer PANI oligomers of EB, LB, PNB, and ES (cation as doublet and dication as singlet and triplet). Although the authors conclude that the UBH&H/6-31G* results for ES2þ(S) are nonrepresentative at any chain length, they employ the same protocol to contend that the bipolaron defect is more stable in shorter species, while chain elongation switches the balance in favor of the polaron configuration. However, the models used are artificially symmetrized as amino- or imino-capped ones. The numerous existing publications still leave unresolved the question which the more stable defect in conducting polyaniline is. The theoretical treatment of the magnetic behavior of ES is

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fragmentary, too. Moreover, the calculations are usually done in vacuum. Aiming to determine and characterize more thoroughly the defects formed in highly doped ES, this study examines models of fully protonated oligomers with two possible configurations of the counterions corresponding to bipolaron and polaron defects. The initial structures are based on the models suggested by Stafstr€om et al. (Figure 2). The magnetically active states are addressed in a systematic way. The experimental data do not always offer indisputable evidence for a completely polaronic state of PANI, thus allowing the hypothesis that polarons are limited to certain fragments of the chain. In order to investigate such structures, in addition to fully polaronic and bipolaronic forms, all possible intermediate multiplicities are considered. Octamer, dodecamer, and hexadecamer chains are computed for assessment of the size effect on the molecular properties. Foregoing estimates38 pointed out the importance of the medium for correct description of PANI properties. Therefore, all simulations are carried out in implicit aqueous solution. In a preceding paper, it was shown that the bipolaron defects involve three rings and the four nitrogens bound to them.39 The robustness of this pattern upon variation of the counterion configuration and spin state is tested. The computations are analyzed with respect to structural deformation, charge and spin distribution, energetics, and frontier molecular orbitals.

’ MODELS AND METHOD The models used for the description of bipolaron and polaron defects are borrowed from the seminal paper of Stafstr€om et al.12 The patterns suggested therein are employed for construction of octamers, dodecamers, and hexadecamers to the end of investigating the size dependence of structural characteristics and electron density distribution. The emeraldine salt is modeled as a fully protonated chain; i.e., all imine nitrogens are protonated. Schematic representation of the repeating unit of the studied oligomers and the notations used in the analysis below are given in Figure 3. The utilized doping agent is the inorganic HCl. The systems are neutral: the accumulated positive charge due to protonation is balanced by chloride counterions positioned at 3.5 Å from the protonating hydrogen in the initial geometries. Two configurations of the counterions are considered (Figure 4), denoted in the text as configuration I and configuration II. Earlier studies40 have anticipated the coexistence of isolated emeraldine chains in different multiplicities. Therefore, all possible spin states of the molecules are accounted for. The structure in the highest spin state is regarded as fully polaronic (Figure 5A), and the singlet one is termed bipolaronic (Figure 5C). The intermediate multiplicities (Figure 5B) vary in number depending on the chain length. The nomenclature used for the separate molecules has the generic form XM-Y(Z), where XM = OM (octamer), DM (dodecamer), and HM (hexadecamer); Y = I or II (denotes the configuration type), Z = S (singlet), T (triplet), Q (quintet), H (heptet), N (nonet). Previous investigations have demonstrated the importance of solvent introduction for realistic description of the emeraldine salt.38 The presence of aqueous medium is simulated by means of the implicit solvent model PCM.41 All computations are performed with Gaussian 0942 and follow identical protocol: 3766

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Figure 3. Model structure of the repeating unit in the studied oligomers and notations of the molecular fragments and torsion angles discussed in the text.

Figure 4. Chemical structure of emeraldine salt in configuration I (top) and configuration II (bottom).

Figure 5. Molecular graph of the studied forms of emeraldine salt and schematic electron configurations of the spin states. The modeled oligomers are octamers (x = 1), dodecamers (x = 1.5), and hexadecamers (x = 2).

unconstrained geometry optimization with UBLYP/6-31G* (the method proven most appropriate for emeraldine salt structural description39). Characterization of the systems includes spatial structure, energetics, charge and spin distribution, and frontier orbitals analysis. The electron density distribution discussion is based on NBO charges43 and Mulliken spin densities. The results for the octamers are compared to the emeraldine base.

’ SPATIAL STRUCTURE The bond length alternation (BLA) and the torsion angles are analyzed as general descriptors of the spatial structure and as measures of the structural inhomogeneity in the oligomer chains occurring upon protonic acid doping. Bond Length Alternation. The bonds in the rings along the oligomer chain (Figure 3) are divided in two subgroups: along the oligomer axis (further on named “shorter”) and in the transversal direction (denoted as “longer”), and are averaged separately. BLA of the rings is calculated as the difference between the averaged longer and shorter CC bonds. BLA for the N-containing

Figure 6. Bond length alternation of selected octamers: emeraldine base (OM-Base), OM-I(Q), and OM-II(S).

fragments is determined as the modulus of the difference between the lengths of two adjacent NC bonds. Standard deviations of BLA for both fragment types do not exceed 0.025 Å. Figure 6 presents BLA data for the octamer of the emeraldine base (OM-Base), the fully protonated polaronic form 3767



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Figure 7. Bond length alternation in the polaronic OM-I(Q), DM-I(H), and HM-I(N).

(OM-I(Q)) featuring four polarons, and the bipolaron form (OM-II(S)) with two bipolarons. The results visualize the structural changes invoked by polaron formation. The presence of four polarons affects the entire chain. Overall, aromaticity is enhanced in the base quinonoid rings and deteriorates in the remaining cycles; substantial change occurs in the nitrogen fragments bound to the ex-quinonoid rings. The loss of quinonoidicity in the protonated Ring 3 and Ring 7 is formidable in the polaronic (OM-I(Q)), in keeping with the model suggested by other authors.12 The two forms (OM-I(Q) and OM-II(S)) are easily distinguishable in these regions. BLA in these two fragments of OM-I(Q) decreases with respect to the undoped base by 0.058 and 0.061 Å, respectively, whereas for OM-II(S) the corresponding reduction is 0.033 and 0.031 Å. The ratio of the BLA change of the forms OM-I(Q):OM-II(S) is approximately 1:2. Upon doping, the former quinonoid rings in configuration I acquire even more pronounced aromatic character than the remaining ones. Correspondingly, the dearomatization of the latter is also better expressed in OM-I(Q). BLA of the nitrogens adjacent to rings 3 and 7 decreases too, again more markedly in OM-I(Q), at the expense of minor increase at the rest of the nitrogen fragments. The protonation-induced structural changes of the octamer base are less discernible in the central portion of the chain, which could be an implication that the drastic changes discussed above may be an end effect. Inspection of longer chains should support or reject such doubt. Therefore, analogous comparison is made for the dodecamer and the hexadecamer. Figure 7 allows juxtaposition of the BLA variation in OM-I(Q), DM-I(H), and HM-I(N), with four, six, and eight polarons, respectively. Upon chain extension, a repetition of the octamer profile is observed in the polaronic forms. Enhanced BLA of the nitrogen fragments at the chain termini is registered. These end effects monotonously vanish toward the interior part of the oligomers but act at longer range than in the bipolaronic forms.39 Equalization of the BLA values at the nitrogen fragments in the inner part takes place in longer species. Only in the core of the hexadecamer chain do the end effects vanish completely. The phenyl rings belong to two groups: the odd-numbered with lower BLA values and the even-numbered with higher ones. Both kinds fit in neither the quinonoid nor the aromatic geometry; they have rather an intermediate character.

Figure 8. Bond length alternation of dodecamer structures in configuration I (top) and II (bottom) in all possible multiplicities.

Apparently, the fully polaronic form is a serious structural perturbation with respect to the emeraldine base resulting in the emergence of a qualitatively new structure, dissimilar to the bipolaronic one.39 The BLA values of the two kinds of rings in polaronic chains of different size are very close, the difference between them negligibly decreasing with length. In other words, the polaronic structure is essentially size insensitive, each polaron being represented by two adjacent rings and two nitrogens bonded to them. This is the repeating unit presented in Figure 7, which corresponds to the classical structural formula12 but differs from the repeating structural fragment of the bipolaronic forms.39 3768


The Journal of Physical Chemistry B The BLA values of the terminal fragments of the octamer coincide with the respective magnitude of BLA for the residues at the end of the dodecamer and the hexadecamer. The large and identical BLA of the termini is an indication that these portions of the molecules do not interact appreciably with the remaining part of the chain. This means that the polarons do not delocalize efficiently on the two terminal segments. Figure 8 contains the BLA results for configurations I and II of the dodecamer in all possible multiplicities. In all dodecamers of configuration I, irrespective of their multiplicity, a tendency toward equalization of the ring types, i. e., enhancement of delocalization, is observed. The loss of quinonoidicity grows in the order DM-I(S), DM-I(T), DMI(Q), DM-I(H) in the rings closer to the chain termini (Ring 3, Ring 11) and in a nonmonotonous manner in the middle one (Ring 7). The loss of aromaticity is less expressed but has the same behavior: uniformity in BLA change with increase of multiplicity deteriorates toward the chain center. Finally, in the heptet the ex-quinonoid rings become more aromatic than most of the former aromatic ones and the repeating motif in the BLA profile of the rings transforms completely from 4-fold to 2-fold. For each multiplicity, the CN bonds have lower BLA values than the rings, their alternation being most expressed in the highest spin state DM-I(H). The trends pointed out for the dodecamer BLA can be identified in the remaining oligomers too. The singlets, the triplets, and the highest spin states of the two configurations are structurally similar; e.g., OM-I(Q) and OM-II(Q) resemble DM-I(H) and DM-II(H) as well as HM-I(N) and HM-II(N). Chain extension for a given counterion configuration and multiplicity invokes neither qualitative nor significant quantitative changes in BLA (Figures S1 and S2 in the Supporting Information). All the trendlines in chain deformation of configuration I oligomers with increase of multiplicity correspond to a great extent to those found for the configuration II species. The counterion position influences more the singlets and the lower spin states but the higher and particularly the highest multiplicities are less sensitive to this factor. The singlets in configuration II exhibit stronger alternation at the inner nitrogens and in the outer quinonoid rings, the latter peculiarity retained in the triplets as well. At higher multiplicities, however, the BLA values of the former quinonoid rings of the two configurations converge. OM(Q)-I and OM(Q)-II are essentially identical in terms of BLA, while DM(H)-II and HM(N)-II feature slightly higher BLA at the nitrogens and enhanced alternation along the chain, both trends insignificantly growing with length (Figures S1 and S2 in the Supporting Information). In order to quantify the structural changes upon increase of the number of unpaired electrons, we may average separately the BLA differences for the rings and the nitrogens. Comparing the singlets and the triplets of the octamer, the average BLA differences for ring and N-fragments are 0.001 and 0.002 Å for configuration I and 0.001 and 0.011 Å for configuration II. The values for the S-Q BLA differences are 0.005 and 0.007 Å for configuration I and 0.004 and 0.003 Å for configuration II, respectively. In the intermediate multiplicities, the milder alternation at the nitrogens is a result of the equalization of the bonds in the rings. Torsion Angles. Other important structural parameters responsible for electron delocalization are the dihedrals Θ between pairs of adjacent rings (Figure 3).

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Table 1. Values of the Torsion Angles (deg) between Pairs of Neighboring Rings along the Chain of Unprotonated and Fully Protonated Octamersa Θ1

Θ2

Θ3

Θ4

Θ5

Θ6

Θ7

OM-Base

45.0

49.0

48.4

45.4

45.8

48.5

48.3

OM-I(Q)

44.9

44.2

44.4

44.2

44.3

44.7

44.6

OM-II(S)

44.5

40.3

39.5

42.9

42.2

39.9

39.2

As denoted in Figure 3, each dihedral angle Θi is obtained by summing its two constituents Θi0 and Θi00 (Table S1 in the Supporting Information). a

Table 2. Values of the Torsion Angles (deg) between Pairs of Neighboring Rings along the Chain in the Respective Multiplicity of the Fully Protonated Dodecamer in Configuration I and IIa DM-I(S) DM-I(T) DM-I(Q) DM-I(H)

DM-II(S) DM-II(T) DM-II(Q) DM-II(H)

Θ1

Θ2

Θ3

Θ4

Θ5

Θ6

Θ7

Θ8

Θ9

45.0 45.1 45.2 44.9

39.4 40.7 43.3 44.2

40.1 40.9 42.9 44.3

41.4 40.6 41.5 44.0

41.3 40.7 41.7 44.2

40.0 41.7 41.2 44.1

40.4 41.6 41.6 44.3

41.3 40.4 41.6 44.2

41.3 40.7 41.9 44.3

Θ1

Θ2

Θ3

Θ4

Θ5

Θ6

Θ7

Θ8

Θ9

44.9 45.6 45.3 45.0

39.9 40.3 43.1 44.2

39.7 41.1 42.9 44.6

42.5 41.0 42.1 44.1

42.1 41.7 41.8 44.2

40.2 41.3 41.6 44.3

39.8 41.4 41.8 44.5

42.4 41.8 41.7 44.2

42.2 41.1 41.8 44.2

Θ10 Θ11 39.8 40.9 42.7 44.7

39.7 40.4 43.1 44.7

Θ10 Θ11 39.7 40.7 42.7 44.9

39.2 39.8 43.1 45.0

a As denoted in Figure 3, each dihedral angle Θi is obtained by summing its two constituents Θi0 and Θi00 (Table S3 in the Supporting Information).

Table 1 contains the values of Θi for the base OM-Base, the polaronic OM-I(Q) and the bipolaronic OM-II(S) forms of the octamer. The largest torsion angles in the octamer base OM-Base are at the quinonoid rings (Θ2, Θ3 and Θ6, Θ7). Doping reduces them, resulting in diminished deplanarization of the molecule and eased electron transport along the chain. This decrease, particularly in the defect regions, is more pronounced in the bipolaronic OM-II(S) than in the polaronic OM-I(Q) and can be attributed to the accumulation of sizable positive charge in and around the quinonoid rings of the former (see below) invoking the planarization of these fragments. Instead, the positive charge in OMI(Q) is distributed more uniformly in accordance with the equalized angles Θ. It should be noted that there exists another stable geometry of the octamers which is very close in energy to the above-discussed and differs only in the values of Θ (Table S2 in the Supporting Information). However, this has no impact on the remaining properties of interest in this study (Figures S3S6 in the Supporting Information). The torsion angles of the fully protonated dodecamers in all possible spin states are collected in Table 2 for configurations I and II. The alternation of dihedral angle sign along the chain is evidence of regular linear geometry of the oligomers, each subsequent ring bent in a different direction with respect to the plane of the nitrogen atoms. The absolute values are very close in magnitude and remain almost constant down the chain, except Θ1 which is somewhat larger. The latter explains why Ring 3769



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Table 3. Difference in Ring Group Charges of the Polaronic Form in Configuration I and the Bipolaronic Form in Configuration II octamer

dodecamer

hexadecamer

Ring 1

0.062

0.069

Ring 2

0.026

0.027

0.071 0.027

Ring 3

0.086

0.077

0.075

Ring 4

0.031

0.029

0.029

Ring 5 Ring 6

0.032 0.034

0.036 0.023

0.038 0.021

Ring 7

0.103

0.067

0.060

Ring 8

0.030

0.022

0.021

Ring 9

0.030

0.034

Ring 10

0.029

0.020

Ring 11

0.104

0.066

Ring 12

0.028

0.019

Ring 13 Ring 14

0.029 0.028

Ring 15

0.105

Ring 16

0.026

1 is less involved in the charge and spin redistribution (see below). The two configurations are analogous both qualitatively and quantitatively. The extension of chain length induces no substantial changes (Table S4 in the Supporting Information). Therefore, any difference in the behavior of the two configurations should be related to bond lengths dissimilarity rather than to torsion angle variation. With rise of multiplicity, dihedral angles grow, except Θ1, which is the largest and essentially invariant in the two configurations. The polaronic OM-I(Q), DM-I(H), and HM-I(N) feature average ring-to-ring torsion of 45.5°, 44.4°, and 42.8°, respectively. This implies moderate π-electron delocalization but provides better charge separation (see below). However, in a number of experimental studies,11,44,45 the emeraldine salt conductivity is deemed to result from the presence of polaron defects in a less twisted chain. A possible source of difference between the presented torsion angle values and the models suggested for interpretation of the experimental findings could be the singlemolecule approach employed here, i.e., the fact that the interaction between the oligomers is not taken into account. The latter most probably would lead to chain stretching, i.e., to restricted torsional freedom, thus facilitating the transport of charge carriers and enhancing conductivity. Nevertheless, the derived relationships are valuable for comparative purposes.

’ ELECTRON DENSITY DISTRIBUTION Charge Distribution. The electron density distribution in the rings of the polaronic and bipolaronic forms of oligomers with different chain lengths is represented in Figure 9. The charge distribution is described by means of NBO group charges obtained by summation of the atomic charges of all atoms in a fragment. The fragment notations are as in Figure 3. Difference between the ring group charges in the polaronic and bipolaronic forms is observed even in Ring 1. In all models, the first ring is the least electron-deficient but this loss of positive charge is more marked in the bipolaronic forms.

Figure 9. NBO group charges of the rings in the various polaronic and bipolaronic oligomers.

Figure 10. NBO group charges of the rings in dodecamers with configuration I (top) and II (bottom) in different multiplicities.

The major dissimilarities between the polaronic (OM-I(Q), DM-I(H), HM-I(N)) and bipolaronic (OM-II(S), DM-II(S), HM-II(S)) models are in the regions of the quinonoid rings, which is an expected consequence of the geometrical disparity. The changes occurring in these fragments upon introduction of the two defect types are completely inverse in the two forms. The differences in ring charge values are shown in Table 3. In the bipolaronic structures the positive charge is concentrated mainly in the quinonoid rings, while in the polaronic ones the latter rings bear higher electron density. The ring group charges of the quinonoid rings are weakly sensitive to chain length extension. A certain regularity in the charge variations in the two forms of a given oligomer can be outlined. In the polaronic forms the repeating units comprise two rings—one with a higher and one with a lower positive charge; i.e., the more and the less electrondeficient rings alternate in correspondence with the structural 3770


The Journal of Physical Chemistry B periodic unit (Figure 7). In the bipolaronic structures the repeating section spans four rings—two with growing positive charge reaching its maximum in the quinonoid ring followed by a fourth of intermediate value. Three rings in this motif have equidistantly lower charge versus the respective rings in the polaronic pattern, so an interconversion between the two forms would mean a redistribution of the quinonoid ring charge to the remaining three rings in the 4-fold bipolaronic repeating unit. Chain extension has no qualitative effect on charge distribution in both forms. A slight enhancement of charge delocalization with length could be registered in the polaronic species (Figure 9, configuration I). The patterns of the charge distribution schemes in the two forms of the fully protonated emeraldine salt are distinguishable already at the octamer level. Figure 10 allows a comparison of the NBO ring charge distribution in all the multiplicities of the fully protonated dodecamer. The discussed regularity in the charge variation of the polaronic forms is identical for both configurations (OM-I(Q), DMI(H), HM-I(N) and OM-II(Q), DM-II(H), HM-II(N)). With decrease of multiplicity the regularity changes its pattern. The singlets of configuration I resemble those of configuration II. However, the charge distribution of DM-I(S) changes less versus that of DM-I(H) than the respective transformation in configuration II. Hence, the proximity of counterions induces a more pronounced charge disproportion within the repeating unit. The charge waves of the triplets of configuration I (OM-I(T), DM-I(T), HM-I(T)) combine segments from those of the adjacent multiplicities. The charge distribution in the triplets of configuration II (OM-II(T), DM-II(T), HM-II(T)) is dissimilar from the other multiplicities at any chain length: their charge wave is completely flat except in the terminal fragments, where it resembles the singlets’ profile. The charge localization in the end ring grows slightly with chain length (Figures S7 and S8 in the Supporting Information). Overall, the triplets of configuration II seem exceptionally appropriate for electron transport. The triplets of configuration I also have chain portions with uniform ring charges but they are always divided by a ring of extremal charge in the middle of the chain. Depending on the oligomer size, the latter extremum is a maximum in the octamer and the hexadecamer and a minimum in the dodecamer. Another size-dependent peculiarity is the growing charge of the penultimate ring. The ring charge distribution of the higher intermediate multiplicities is a combination with different contributions of those of the lower and the higher spin states. For example, DM-I (Q) is closer to HM-I(H) rather than to HM-I(Q), although the former has two unpaired electrons in excess. In DM-I(Q) and HM-I(H) the first rings have charges as in the highest spin state, the next ones as in the triplets, followed by an intermediate and a singlet profile and ending again as the fully polaronic state. The two configurations differ most distinctly in the intermediate multiplicities. A common feature, however, is that in the inner portion of the chains occurs an effective charge redistribution and gradual equalization of the charges of the former aromatic and quinonoid rings. With increase of multiplicity, the charge distribution in the two configurations converges and they become indistinguishable. The variation of the charge wave upon the rise of multiplicity illustrates the pathway of the internal redox process of bipolaronpolaron conversion. For instance, in the case of the dodecamer the relatively small energy difference between the singlet and the triplet of configuration II (see below) allows a transition

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Figure 11. NBO group charges of the nitrogen atoms in the dodecamers with configuration I (top) and II (bottom) in different multiplicities.

involving the removal of the 4-fold charge wave which is replaced by a flat one resembling the quintet of configuration I which fluently transforms into the polaronic heptet DM-I(H). A previous investigation39 clearly shows the robustness of the charge distribution in configuration II against chain extension. This is confirmed in this study and it could be generalized that the shortest oligomer modeled here, the octamer, provides satisfactory description of the fully protonated structures. Figure 11 gives a summary of the computed NBO group charges of the nitrogen fragments in the dodecamers. The nitrogen group charges in a given multiplicity of chains of different length in each configuration coincide both qualitatively and quantitatively (Figures S9 and S10 in the Supporting Information). In DM-I(H) the nitrogen fragments have almost identical charges—the charge distribution is more uniform than in DM-II(H). The N-charges vary insignificantly with multiplicity but no clear tendency could be outlined in any of the two configurations. Overall, the dodecamer may be divided in three sectors of equal length: with increase of multiplicity from the lowest to the highest intermediate spin state the charges change monotonously in the terminal two and alternate in the central one. The charge distribution in the highest multiplicity shifts with a jump for the central eight nitrogens to acquire the most equalized partitioning. In summary, the charges of all nitrogen fragments (except the last) are slightly negative and vary within a very narrow range of values, least in the polaronic (OM-I(Q), DM-I(H), HM-I(N)) forms. These charges are influenced by the multiplicity and configuration type but are size independent. 3771



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Figure 12. Spin densities of the nitrogen atoms and group spins of the rings in the hexadecamers with configuration I (top) and II (bottom) in different multiplicities.

Spin Density Distribution. Figure 12 represents the spin distribution in the longest oligomer considered: the hexadecamer. The group spin density for each ring is the summed atomic spin density of the constituting carbon atoms. The spin densities at the hydrogen atoms do not exceed 0.005 in absolute value and are disregarded. The highest concentration of spin density at any chain length, configuration, and multiplicity is observed close to the oligomer ends. Except for the highest multiplicity, the largest values belong to the first and the last two nitrogens (N1, N2, N15, N16, Figure 12) and their common rings (Figure S11 in the Supporting Information). Similar spin localization pattern has been observed in EPR measurements of the cation radicals of phenyl-capped substituted PANI oligomers.46 Ring 1 features perfect spin polarization in all models, whereas the remaining fragments exhibit spin delocalization. The low multiplicities of the two configurations are qualitatively similar but the highest spin states diverge. The triplets (OM-I(T), DM-I(T), HM-I(T); OM-II(T), DM-II(T), HM-II(T)) are stabilized by additional spin polarization spanning three rings and the nitrogens bound to them close to both ends of the dodecamer and hexadecamer chains. For the octamers, the spin polarized rings are two— one on each chain end (Figure S12 in the Supporting Information). In all cases these spin-polarized sectors are adjacent to the fragments bearing maximum spin (Figure 12) and their presence contributes to the triplets’ stability (see below). The spin distribution in HM-II(T) matches the profile of HM-I(T) but the rings in the inner part of the chain are richer in group spin at the expense of those at the end (Rings 2 and 16). Spin polarization is observed also in the quintets HM-I(Q) and HM-II(Q) but it is limited solely to Ring 15. In the central part of the chains, the spin density is distributed more uniformly than in the chain ends. The predominant part of

the values is positive, revealing that the spin propagates via spin delocalization. With chain extension the portion of the delocalized section grows. Preserving the general profile, chain elongation results in natural decrease of the ring spin values at a given multiplicity (Figures S12 and S13 in the Supporting Information). Formally, the triplet state could be regarded as a model of a chain with two polarons. The accumulation of substantial spin density at the oligomer ends demonstrates the tendency for spatial separation of the two polarons. On the other hand, the presence of a spin-delocalized region at the chain core indicates that the two polarons are not completely isolated. In the intermediate multiplicities, the introduction of certain regularity expressed in alternation of high-density and spindeficient regions can be outlined. Some uniformity can be established even in the quintets of the hexadecamers. In the heptets the spin density resembles more a regular spinlattice. As with the charge distribution, the heptets of the hexadecamers are similar to the quintets of the dodecamers in spin distribution pattern (Figure 12, and Figure S13 in the Supporting Information). The resemblances of the lower multiplicities spin density profiles are an alternative illustration of the possibility for conversion of the bipolaronic configuration II into the polaronic configuration I initiated by partial spin polarization. The increase of multiplicity results in augmented spin density in the chains. In the highest spin states (OM-I(Q), DM-I(H), HM-I(N); OM-II(Q), DM-II(H), HM-II(N)) the equal number of unpaired electrons per monomer leads to a distinct regularity of the spin density distribution: rings with higher and lower ringspin alternate, i.e., in the fully polaronic forms periodic spinlattices emerge. The character of these polaronic structures 3772



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is clearly expressed even at the octamer level in OM-I(Q) and OM-II(Q) (Figure S12 in the Supporting Information). The analogy between oligomer chains of different length is both quantitative and qualitative. Chain extension has no impact on the interaction pattern of the polarons and they remain strongly coupled (Figure S14 in the Supporting Information). Comparison of the polaronic spinlattices of configurations I and II makes obvious the qualitative difference between the repeating motifs. The latter comprises two rings and two nitrogens in configuration I and spans four rings and four nitrogens in configuration II (Figure 12). This coincides with the formal structural repeating units of the polaronic and bipolaronic forms suggested by Stafstr€om et al.12 Our results show that depending on the arrangement of counterions different polaronic lattices can be achieved. This is supported by the fact that the atomic spin densities at the nitrogens are systematically influenced by the positions of the chloride ions: the spin density at nitrogen atoms closest to chloride ions is higher than at those nonscreened by anion; i.e., the negative particles invoke spin localization at the nitrogen sites closest to them (Figure S11 in the Supporting Information) and therefore two different spinlattices emerge. In contrast to the classical concept, a key factor for the distribution of unpaired electrons along the chain seems to be the location of the negative instead of the positive charges. The fact that in the polaronic forms of configuration I (OMI(Q), DM-I(H), HM-I(N)) the number of repeating motifs coincides with the number of polarons, while in the polaronic oligomers of configuration II (OM-II(Q), DM-II(H), HMII(N)) the number of motifs is half the number of unpaired electrons is a sign that the latter species have undergone Peierls deformation.

’ ENERGY Tables 4 and 5 summarize the computed energy data for the studied systems. Table 4 shows the total potential energy differences between the two configurations in a given spin state. The relative energies are obtained by subtracting the total Table 4. Relative Energy ΔE (kcal/mol) of the Two Configurations of Oligomers with Different Chain Length and Type of Defects, Calculated with UBLYP/6-31G*/PCM ΔEXIII = EXII EXI ; X = S, T, Q, H, N X

S

T

Q

H

N

octamers

2.958

0.665

0.104

dodecamers

3.792

1.516

0.648

0.127

hexadecamers

4.569

2.265

1.130

0.636

0.136

potential energy of the molecules in configuration I from the value for configuration II for each multiplicity (see the formula above Table 4). Table 5 presents the total potential energy splittings between the singlets and the higher multiplicities of each configuration. ΔESX results from subtraction of the total energy of each molecule with higher multiplicity from the total energy of the singlet structure within a given counterion configuration (the formula is provided above Table 5). The values in Table 4 demonstrate that the species in configuration II, irrespective of the chain length, are always more stable than the corresponding ones in configuration I. The energy difference systematically increases with chain extension and decreases with growth of multiplicity. For the octamer, the two configurations in the highest spin state are energetically indistinguishable, whereas for the longer chains the highest multiplicity of configuration II is slightly lower in energy within the chosen computational protocol and the single-molecule model. The energy splittings between singlets and higher spin states (Table 5) are evidence that the former are more stable regardless of chain length and configuration. With increase of the number of unpaired electrons, this destabilization grows in a nonlinear manner: the singlettriplet splitting is noticeably smaller than the tripletquintet one. The relative stability of the triplets is due to the already discussed partial spin polarization, which is milder and limited in the quintets and fully absent in the heptets and nonets of the hexadecamer. The energy difference between the singlet and a particular higher multiplet decreases with chain extension—the higher spin states are stabilized with increase of the number of monomers. The triplet state, especially in configuration I, requires relatively low excitation energy. Overall, the energy splittings of configuration I are smaller than those of configuration II. The energy gap between the bipolaronic and fully polaronic forms is quite large for both configurations. This implies that the achievement of a fully polaronic state in a single oligomer is impossible and indicates that the formation of the latter is feasible only in the presence of neighboring chains. Thus, the present results for isolated molecules should be regarded as an upper bound of the energy splittings in the real polymer.

’ FRONTIER MOLECULAR ORBITALS In addition to all the changes listed above, the protonation of PANI leads to the formation of a band of defect states located in the energy gap, regarded as potential electron-accepting molecular orbitals (AMOs). Each pair of protons causes the emergence of a bonding and an antibonding AMO (Figure 13, and Figure S15 in the Supporting Information). Figure 13 shows the canonic bonding frontier MOs in the defect states of the three oligomers

Table 5. Energy Gap ΔESX (kcal/mol) between Oligomers with Different Multiplicities Calculated with UBLYP/6-31G*/PCM ΔESX = ES EX; X = T, Q, H, N configuration I ΔEST

ΔESQ

ΔESH

octamer

3.799

15.690

dodecamer

2.534

11.338

24.812

hexadecamer

1.891

8.775

19.757

configuration II ΔESN

33.984 3773

ΔEST

ΔESQ

ΔESH

6.092

18.544

4.811

14.482

28.477

4.195

12.214

23.690

ΔESN

38.417



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Figure 13. Bonding canonical frontier orbitals of octamer (left), dodecamer (center), and hexadecamer (right), calculated with UBLYP/6-31G*. The plots are limited to an isodensity surface of 0.02.

under study, since only ground states of the models are discussed herein. As frontier bonding MOs are considered all the bonding AMOs corresponding to a fully protonated oligomer and an equal number of HOMOs necessary to achieve the highest possible spin state. For instance, the fully protonated octamer has two bonding AMOs; in order to reach the highest spin state, we need four singly occupied MOs and therefore HOMO and HOMO-1 are included in the set of frontier MOs. For the dodecamer, HOMO, HOMO-1, and HOMO-2, etc. are included in addition to the three AMOs, etc. The frontier molecular orbitals of the two configurations are essentially identical independent of multiplicity. Therefore, Figure 13 is representative for both configurations in any spin state. Chain extension does not change the character and type of the frontier molecular orbitals. The structural changes described above could be explained with account of the fragmentation of the frontier MOs. It is visible that the frontier MOs are characterized with AO overlap solely along the longer bonds in the chains. Thus, the population of AMOs upon increase of multiplicity would change the bond order of these bonds, which will be reflected in a variation of the BLA values. The contributions from regions with higher values of the atomic orbital coefficients result in shortening of the longer bonds and equalization of bond lengths in these regions, while the nodes of the MOs are responsible for the regions with enhanced bond alternation. Most prominent is the change in the ex-quinonoid rings with increase of multiplicity. For instance, in the dodecamer this leads to depopulation of HOMO-x with poorer overlap along the longer bonds in Rings 3 and 11 and population of AMOs with ever more pronounced one, thus gradually decreasing the BLA value. In Ring 7 the situation is the same for the triplet and the heptet and inverse for the quintet, and hence the BLA values alternate. Evidence that predominantly the longer bonds contract with rise of multiplicity is the overall gradual shrinking of the oligomer chain length (by ∼0.1 Å per exquinonoid ring). The evident fragmentation of the frontier MOs substantiates also the changes in the charge distribution in the different spin states. The large AO coefficients indicate higher electron density at a given atom, i.e., lower values of the positive charge. Let us follow the changes of the dodecamer in configuration I with increase of multiplicity. In the singlet DM-I(S), HOMO is doubly occupied, while in the triplet DM-I(T) the changes in the charge distribution are in correspondence with the contributions

from the singly occupied HOMO and AMO_1; for the quintet DM-I(Q) from the orbital coefficients of HOMO-1, HOMO, AMO_1, and AMO_2; and for the heptet DM-I(H) from HOMO-2, HOMO-1, HOMO, AMO_1, AMO_2, and AMO_3. The first ring has small AO coefficients, decreasing with increase of MO energy. Therefore, this ring has low positive charge, growing with the rise of multiplicity. The large and similar coefficients of the AOs in Ring 2 of DM-I(S), DM-I(T), DMI(Q) keep the summed charge constant in these states. In the heptet DM-I(H), AMO_3 is populated where Ring 2 is void of electron density and the positive charge grows. The fragmentation of HOMO in regions of large and small atomic contributions fully corresponds to the decrease and increase of the summed positive charges along the chain of DM-I(S). The fragmentation of AMO_1 is essentially complementary to that of HOMO and the same partially holds for each subsequent AMO with respect to the preceding one. Thus, the mild charge variation in DM-I(T) is due to the superposition of the contributions from HOMO and AMO_1. The involvement of AMO_2 in DM-I(Q) results in charge accumulation/deficit in every second odd-numbered ring with respect to the triplet. Finally, the involvement of AMO_3 which is almost completely delocalized leads to the strictly regular alternating profile of the ring charges in DM-I(H). The variation of the nitrogen charges with the number of unpaired electrons can be explained in a similar way. In brief, the analysis of the frontier MOs justifies and provides comprehensible interpretation of the oscillations of charge in certain molecular fragments and its relative steadiness in other upon variation of multiplicity.

’ CONCLUSIONS Emeraldine salt oligomers with several chain lengths—fully protonated octamer, dodecamer, and hexadecamer—are simulated. The polaronic and bipolaronic form of the oligomers are characterized and compared. Two configurations differing in the position of the chloride counterions are considered. Each structure in a certain configuration is modeled in all possible spin states, the diversity of the latter related to the high level of protonation and chain length. The obtained results show weak size dependence—the molecular characteristics most sensitive to defects introduction, such as geometry and electron density distribution, preserve both qualitative and quantitative steadiness. The same holds for the spin density distribution in the magnetically active species. 3774


The Journal of Physical Chemistry B Conclusions based on the analysis of one oligomer are valid for the whole series. The modeled polaronic and bipolaronic forms differ distinctly in the region of the ex-quinonoid rings of the base. The structural parameters outline two dissimilar motifs: dimeric for the polaronic form and tetrameric for the bipolaronic one. With increase of multiplicity, the structural changes become less responsive to the counterion position. In the highest spin state, the chain geometry of the two configurations is identical. Apart from the bond lengths, the protonation specifically affects the dihedral angles. The latter change most prominently in the quinonoid rings region too, decreasing in value and promoting the better delocalization and, hence, facilitating the electron transport. This decrease is more marked in the bipolaronic forms and is probably due to the withholding of higher positive charge in the exquinonoid fragments. Typically, the highest spin states feature complete equalization of the dihedrals along the chain. Overall, the torsion angle changes in the two configurations are analogous and quantitatively close, so any structural difference defining dissimilar behavior should stem from the bond lengths nonidentity rather than from the degree of nonplanarity. The NBO charge distribution is also patterned. The periodic unit in the polaronic and bipolaronic forms repeats the structural motif. The triplets of the two configurations are more delocalized than the other spin states: among all modeled oligomers the triplet HM-I(T) seems to be the most favorable species for electron transport. The variation of charge distribution with rise of multiplicity illustrates the route of the internal redox process converting the bipolaronic form into the conducting polaronic one. Unlike the structural and charge convergence of the two configurations upon increase of multiplicity, the spin density distribution changes from qualitatively identical spin waves in the triplets to formation of two different spinlattices in the highest multiplets of the two configurations. Particularly, the negative ions are responsible for the localization of spin density at the nitrogens they screen, resulting in dissimilar spinlattices in the two fully polaronic forms. The spin propagates along the chain due to spin delocalization, while mild spin polarization is observed in all triplets, gradually vanishing in the quintets of the dodecamer and hexadecamer. The energy differences between the corresponding high-spin structures of the two configurations are smaller than those between the lower multiplicities. In the framework of the chosen computational scheme, the singlets are more stable than any of the higher spin states, configuration II being preferred in all cases. The analysis of the bonding frontier AMOs allows rationalization of the changes occurring upon increase of multiplicity and explains the nonmonotonous behavior of structural descriptors and charge density distribution in some oligomer fragments.

’ ASSOCIATED CONTENT

bS

Supporting Information. Constituents of the torsion angles in the base and the polaron and bipolaron forms of octamers (Table S1) and summed angles in a second set of low-energy octamers (Table S2); constituents of the torsion angles in the two configurations of dodecamers (Table S3) and summed values in octamers and hexadecamers (Table S4) of the emeraldine salt. Bond length alternation of octamers (Figures S1, S3) and hexadecamers (Figure S2) in configuration I and II in all possible multiplicities. Group charges of the rings (Figure S4)

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and the nitrogen atoms (Figure S5), and spin densities (Figure S6) in the second set of octamer structures in different multiplicities of configuration I and II. Group charges of the rings in octamers (Figure S7) and hexadecamers (Figure S8), of the nitrogen atoms in octamers (Figure S9) and hexadecamers (Figure S10), Mulliken atomic spin densities in the hexadecamers (Figure S11) and dodecamers (Figure S14), and spin densities in octamers (Figure S12) and dodecamers (Figure S13) in configurations I and II. Antibonding canonical frontier orbitals of the octamer, dodecamer, and hexadecamer emeraldine salt (Figure S15). This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]fia.bg. Phone: þþ359-2-8161374. Fax: þþ359-2-9625438.

’ ACKNOWLEDGMENT The research is funded by Project BYX-202/2006 of the National Science Fund of Bulgaria and Project 24/2010 of the University of Sofia Research Fund. Partial support from Projects DCVP-02-2/2009, DO-02-136/2008, and DO-02-52/2008 of NSF-BG is appreciated. ’ REFERENCES (1) Diaz, A. F.; Logan, J. A. J. Electroanal. Chem. 1980, 111, 111. (2) Wang, Z.; Scherr, E.; MacDiarmid, A.; Epstein, A. Phys Rev B 1992, 45, 4190. (3) Gustafsson, G.; Cao, Y.; Treacy, G. M.; Klavetter, F.; Colaneri, N.; Heeger, A. J. Nature 1992, 357, 477. (4) MacDiarmid, A. G. Synth. Met. 1997, 84, 27. (5) MacDiarmid, A. G. Synth. Met. 2000, 125, 11. (6) Tatsuma, T.; Ogawa, T.; Sato, R.; Oyama, N. J. Electroanal. Chem. 2001, 501, 180. (7) MacDiarmid, A. G.; Epstein, A. J. Faraday Discuss. Chem. Soc. 1989, 88, 317. (8) Salaneck, W. R.; Lunstr€om, I.; Haung, W. S.; MacDiarmid, A. G. Synth. Met. 1986, 13, 291. (9) Yang, C. Y.; Cao, Y.; Smith, P.; Heeger, A. J. Synth. Met. 1993, 53, 293. (10) Kahol, P. K.; Raghunathan, A.; McCormick, B. J. Synth. Met. 2004, 140, 261. (11) Prigodin, V.; Samukhin, A.; Epstein, A. Synth. Met. 2004, 141, 155. (12) Stafstr€om, S.; Bredas, J. L.; Epstein, A. J.; Woo, H. S.; Tanner, D. B.; Huang, W. S.; MacDiarmid, A. G. Phys. Rev. Lett. 1987, 59, 1464. (13) Gospodinova, N.; Terlemezyan, L. Prog. Polym. Sci. 1998, 23, 1443. (14) Lippe, J.; Holze, R. Synth. Met. 1991, 43, 2927. (15) Tang, J.; Allendoerfer, R. D.; Osteryoung, R. A. J. Phys. Chem. 1992, 96, 3531. (16) Krinichnyi, V.; Chemerisov, S.; Lebedev, Y. Phys. Rev. B 1997, 55, 16233. (17) Kon’kin, A.; Shtyrlin, V.; Garipov, R.; Aganov, A.; Zakharov, A.; Krinichnyi, V.; Adams, P.; Monkman, A. Phys. Rev. B 2002, 66, 075203. (18) Ginder, J. M.; Epstein, A. J. Phys. Rev. B 1990, 41, 10674. (19) Libert, J.; Cornil, J.; dos Santos, D. A.; Bredas, J. L. Phys. Rev. B 1997, 56, 8638. iric-Marjanovic, G.; Trchova, M.; Stejskal, J. Collect. Czech. (20) (a) C iric-Marjanovic, G.; Trchova, M.; Chem. Commun. 2006, 71, 1407. (b) C iric-Marjanovic, Stejskal, J. Int. J. Quantum Chem. 2008, 108, 318. (c) C 3775



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Fully Doped Oligomers of Emeraldine Salt: Polaronic versus

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