13C chemical shifts of polyacetylene chains with charged conformational defects: A GIAO–DFT study

Chemical Physics Letters 503 (2011) 191–196

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13

C chemical shifts of polyacetylene chains with charged conformational defects: A GIAO–DFT study G. Colherinhas, T.L. Fonseca ⇑, M.A. Castro Instituto de Física, Universidade Federal de Goiás, CP 131, 74001-970, Goiânia, GO, Brazil

a r t i c l e

i n f o

Article history: Received 2 December 2010 In final form 5 January 2011 Available online 7 January 2011

a b s t r a c t The 13C chemical shifts of isolated polyacetylene chains bearing a singly or doubly charged defect have been studied using the GIAO approach through the B3LYP exchange–correlation functional with the pcS-2 basis set. Our results show that the distributions of chemical shift reflect the detailed structural distortions caused by the charged defects on the backbones of the polyenic chains. The results also show large variations of chemical shift between the corresponding charged chains with different charge states, which could be detected in nuclear magnetic resonance experiments. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Among conducting polymers, polyacetylene (PA) has received considerable attention due to its remarkable electronic properties. Upon doping, PA exhibits unusual transport properties (a huge enhancement of the electrical conductivity) [1–3] which have been explained in terms of the formation of charged defects. It is known that a charged defect is delocalized over several unit cells and the strong electron–phonon coupling produces bond length distortions of the regular chain. A study on the mobility of charged solitons in PA using the tight-binding model with electron–phonon interactions was reported by Su, Schrieffer, and Heeger (SSH) [4]. More recently, dynamical simulations of charged soliton transport in conjugated polymers using the SSH Hamiltonian with the inclusion of electron–electron interactions in combination with the extended Hubbard model have been reported [5]. In addition, other theoretical studies have dealt with the influence of charged defects on the nonlinear optical properties of polyacetylene [6–13]. In a previous investigation, de Melo and Silbey [6] have shown that the polarizabilities of PA chains are particularly affected by the presence of charged conformational defects. Nuclear chemical shifts and indirect spin–spin coupling constants are magnetic molecular properties that can be obtained from nuclear magnetic resonance (NMR) spectroscopy [14]. These magnetic properties are also sensitive to the influence of structural modifications [15–21]. For isolated PA chains, a previous study with the CNDO/2 model [17] has shown that the 13C chemical shift of the cis form is slightly higher, by 0.7 ppm, than that of the trans form. Experimentally, the 13C chemical shift (measured in solid) of the cis form is higher by 10 ppm than that of the trans form [18–20], indicating that the CNDO/2 model for isolated chains provides a ⇑ Corresponding author. Fax: +55 62 3512 1014. E-mail address: [email protected] (T.L. Fonseca). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.01.014

theoretical chemical shift difference in qualitative agreement with the experiment. For polymeric chains, a better concordance between experiment and theory for variations of chemical shift can be achieved using a density functional theory (DFT) scheme [21]. In fact, for a representative fragment of the isolated PA chain, we have obtained, through the B3LYP/6-311++G(2d,2p) model, a chemical shift difference between cis and trans isomerizations around 10 ppm [16], in very good agreement with the experiment. In the present study we investigate how the presence of a charged conformational defect affects the 13C chemical shifts [Dr(13C)] of isolated trans-PA chains using a standard DFT scheme. Closed-shell polyacetylene chains containing odd [even] numbers of carbon atoms are employed to model charged solitons [bipolarons]. There have been extensive theoretical studies to estimate such magnetic properties with high accuracy [22–32]. Highly correlated schemes provide accurate descriptions for the magnetic shielding constants [22,23] but their applicability is still nowadays restricted to small compounds. For large molecules, DFT schemes offer a good compromise between computational cost and reliability [33–36] and have been recently applied to calculate NMR chemical shifts of polymers [15,16,37,38]. Effects of nuclear motions [39,40], although not considered in this work, are expected to play an important role in the description of nuclear magnetic properties of polymers.

2. Computational details Following our previous work [16], the ground state geometry of each singly or doubly charged chain was fully optimized at the second-order Møller-Plesset perturbation theory (MP2) level (frozencore approach) using the correlation-consistent polarized valence double-zeta (cc-pVDZ) basis set. Also, the geometric parameters of all singly charged structures, and some doubly charged, were

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optimized at the Hartree–Fock (HF) level using the same basis set. A tight convergence threshold has been used in all geometry calcu lations. The charged soliton was modeled by the series C5 Hþ 7 ½C5 H7  þ  up to C39 H41 ½C39 H41  while the charged bipolaron was modeled by þþ  the series C4 Hþþ ½C4 H 6 6  up to C40 H42 ½C40 H42 . For these charged structures the chemical shifts were calculated employing the gauge-including atomic orbital (GIAO) approach [41,42] through the B3LYP exchange–correlation functional, as implemented in the GAUSSIAN 09 program [43]. The choice of this functional is based in recent benchmark calculations that reported magnetic properties in good agreement with experiment for a number of organic molecules [44–46]. It has been shown, within the DFT framework, that the 6311++G(2d,2p) basis set, or even smaller versions of this set, can provide a reliable description for shielding constants [45,46]. Here, we have used in all magnetic property calculations the polarization consistent (pcS-2) basis set [47] that is suitable for calculating nuclear magnetic shielding constants with density functional methods. This is a triple-zeta quality basis set with d- and f-type polarization functions augmented with one p-type function for an appropriate description of the inner valence region. A comparison with results obtained using the 6-311++G(2d,2p) basis set is also addressed. The values of Dr(13C) were calculated relative to the 13C isotropic shielding constant of the tetramethylsilane (TMS), which is a standard reference used in experimental measurements. The shielding constant of TMS, determined at the B3LYP/pcS-2 level, is given by 180.89 ppm. Both geometry optimization and property calculations were performed using the GAUSSIAN 09 [43] electronic structure package.

a

b

3. Results and discussion In order to assess the geometric distortion effects on the chemical shifts we have optimized the geometry of each charged structure. Figure 1 illustrates symmetric patterns, with respect to the central unit, for HF and MP2 bond lengths between successive carþþ bon atoms along the backbones of the C39 Hþ 41 and C40 H42 chains. Similar trends are observed for the negatively charged structures. One can see that the distortions caused by a charged bipolaron on the bond lengths tend to be more marked near the chain ends, due to the coulombic repulsion. For singly ionized chains, in opposition, the structural distortions are localized in the central part. In both cases, these changes can be highly modified by the effect of confinement of the chain ends. Following previous works [11,13], we have calculated the bond length alternation (BLA) of the charged structures as the average of the differences between consecutive CC bond lengths along the chain. It has been shown that the BLA is considerably affected by the presence of charged defects [48]. Our MP2 calculations show a rapid convergence of the BLA for both positively and negatively charged structures as the chain length is increased and that this geometric parameter is almost not affected by the ionization state. From MP2/cc-pVDZ optimized bond distances, we have calculated the converged BLA of doubly charged structures as 0.028 Å whereas for singly charged structures the converged BLA is of 0.038 Å. The BLA of the bipolaronic chain smaller than that of the solitonic chain is according to previous theoretical investigations [13,48]. For comparison the MP2/ccpVDZ model predicts a BLA of 0.061 Å for regular trans-PA chains [16]. The converged BLA values calculated at the HF/cc-PVDZ level for bipolaronic and solitonic chains are 0.077 and 0.093 Å, respectively. Thus, the corresponding HF BLA values are larger than the MP2 ones by amounts of 0.049 and 0.055 Å. Changes in the BLA, that in turn are responsible by modifications on the degree of pelectron delocalization, can have a marked effect on the chemical shift of the charged chains.

þþ Figure 1. HF and MP2 bond distances for C39 Hþ 41 (top) and C40 H42 (bottom) along the chain length. The results were obtained with the cc-pVDZ basis set.

Table 1 displays the B3LYP/pcS-2 13C chemical shifts of the largest singly and doubly charged chains as function of the site position along the chain length. The results were obtained using MP2 geometries. One can see that the Dr(13C) values can be significantly affected by the ionization state with large variations of Dr(13C) between corresponding carbon atoms of negative and positive structures. Figure 2 illustrates the chemical shift distribuþþ tions along the backbones of the C39 Hþ chains 41 and C40 H42 obtained using the HF and MP2 geometries. Again, similar patterns are found for the negatively charged chains. In all cases, there is a marked border effect but the results clearly show typical oscillatory patterns that reflect the conformational changes caused by the charged defects on the conjugated segments of the chains. This contrasts with the regular pattern presented by the Dr(13C) values of undoped PA chains [16]. For solitonic chains, the chemical shift distribution obtained with the HF geometry is characterized by an oscillation that exhibits a maximum at the center of the chain and decreases toward the chain ends. In contrast, the distribution with the MP2 geometry is more delocalized over the chain and the accommodation of the charged defect with the size of the oligomer still requires larger chains. This is consistent with smaller BLA values and larger delocalizations for geometries optimized at the MP2 level. For bipolaronic chains, the chemical shift distributions support the assertion that in the absence of end effects a doubly charged defect is unstable, resulting in two isolated charged solitons [48]. From these results, it is found that the chemical shifts can provide signatures of the structural properties of charged defects on the backbones of hydrocarbon chains that, in turn, may

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Table 1 B3LYP/pcS-2 results for the 13C chemical shifts [ppm] of the largest positively and negatively charged PA chains. The results were obtained with MP2/cc-pVDZ geometries. The carbon atoms are numbered sequentially from the chain end.

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20

C33 Hþ 35

C33 H 35

C35 Hþ 37

C35 H 37

C37 Hþ 39

C37 H 39

C39 Hþ 41

C39 H 41

C34 Hþþ 36

C34 H 36

C36 Hþþ 38

C36 H 38

C38 Hþþ 40

C38 H 40

C40 Hþþ 42

C40 H 42

143.52 153.06 162.50 147.12 163.30 147.03 164.18 146.59 164.85 146.55 165.17 146.54 165.28 146.57 165.28 146.58 165.27

114.91 156.01 136.82 152.30 134.38 153.22 134.26 153.27 133.91 153.37 133.72 153.31 133.60 153.20 133.56 153.11 133.54

142.60 153.11 161.64 147.18 162.39 147.08 163.31 146.61 164.05 146.57 164.45 146.55 164.62 146.58 164.66 146.60 164.65 146.61

115.80 155.93 137.59 152.14 135.20 153.07 135.04 153.14 134.67 153.29 134.43 153.26 134.28 153.15 134.20 153.05 134.18 153.00

141.77 153.15 160.87 147.24 161.55 147.13 162.50 146.64 163.30 146.58 163.77 146.56 164.02 146.58 164.10 146.61 164.09 146.63 164.08

116.62 155.85 138.29 151.99 135.95 152.91 135.77 153.02 135.36 153.21 135.09 153.21 134.89 153.12 134.79 153.01 134.74 152.93 134.73

141.01 153.20 160.16 147.30 160.78 147.18 161.75 146.67 162.59 146.59 163.13 146.56 163.45 146.58 163.58 146.61 163.60 146.64 163.59 146.65

117.37 155.78 138.93 151.84 136.64 152.76 136.44 152.89 136.01 153.12 135.70 153.16 135.46 153.11 135.32 152.99 135.25 152.89 135.23 152.84

162.30 153.02 178.43 147.49 177.81 148.14 175.74 148.70 173.57 149.95 170.95 151.65 167.87 153.96 164.27 156.93 160.48

96.86 156.97 122.96 153.91 121.05 153.59 123.28 152.12 125.46 150.47 128.20 148.38 131.38 145.74 135.01 142.51 138.82

160.60 152.95 176.64 147.35 176.28 147.92 174.73 148.29 173.09 149.28 170.93 150.65 168.29 152.52 165.09 154.98 161.55 158.06

98.65 156.97 124.20 153.93 122.14 153.76 124.05 152.46 125.87 151.05 128.21 149.32 130.96 147.15 134.15 144.41 137.64 141.16

158.91 152.83 175.66 147.07 175.53 147.49 174.12 147.78 172.53 148.67 170.58 149.86 168.33 151.44 165.62 153.50 162.49 156.11 159.20

100.02 156.84 125.25 153.73 123.11 153.78 124.78 152.72 126.34 151.56 128.34 150.11 130.69 148.29 133.47 145.97 136.61 143.13 139.92

157.24 152.92 174.38 147.18 174.41 147.55 173.34 147.73 172.08 148.47 170.46 149.42 168.56 150.69 166.23 152.37 163.42 154.56 160.32 157.27

101.45 156.79 126.29 153.67 124.07 153.85 125.51 152.93 126.83 151.93 128.54 150.70 130.56 149.19 132.98 147.24 135.78 144.80 138.84 141.93

a

b

a

b

þþ Figure 2. B3LYP/pcS-2 13C chemical shifts for C39 Hþ 41 (top) and C40 H42 (bottom) along the chain length. The results were obtained with the HF and MP2 geometries.

Figure 3. B3LYP/pcS-2 Mulliken atomic charges for the carbon atoms of C39 Hþ 41 (top) and C40 Hþþ 42 (bottom) along the chain length. The results were obtained with the HF and MP2 geometries.

be observed in NMR experiments [15]. For comparison, we have performed extra calculations using the 6-311++G(2d,2p) basis set

which give similar trends to Dr(13C) with respect to the increase of the chain length, but with values augmented around 8 ppm. Connections between variations of the charge distribution over the carbon atoms and the chemical shifts are observed for both

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Table 2 B3LYP/pcS-2 results for the chemical shifts [ppm] of the central carbon atoms of positively and negatively charged solitonic chains. The columns labeled |DD| give separately the  þ  first differences between two successive C4nþ1 Hþ 4nþ3 [C4nþ1 H4nþ3 ] or C4nþ3 H4nþ5 [C4nþ3 H4nþ5 ] chains. HF geometry

Dr(13C) C5 Hþ 7 C7 Hþ 9 C9 Hþ 11 C11 Hþ 13 C13 Hþ 15 C15 Hþ 17 C17 Hþ 19 C19 Hþ 21 C21 Hþ 23 C23 Hþ 25 C25 Hþ 27 C27 Hþ 29 C29 Hþ 31 C31 Hþ 33 C33 Hþ 35 C35 Hþ 37 C37 Hþ 39 C39 Hþ 41

219.05 144.93 195.09 142.87 183.40 141.56 177.91 141.11 174.50 140.81 172.32 140.64 170.83 140.53 169.76 140.47 168.98 140.45

|DD|

23.96 2.06 11.69 1.31 5.49 0.45 3.41 0.30 2.18 0.17 1.49 0.11 1.07 0.06 0.78 0.02

MP2 geometry

HF geometry

Dr(13C)

Dr(13C)

218.4 148.49 194.20 147.50 181.88 146.53 175.73 146.45 171.65 146.44 168.86 146.50 166.82 146.56 165.27 146.61 164.08 146.65

|DD|

24.20 0.99 12.32 0.97 6.15 0.08 4.08 0.01 2.79 0.06 2.04 0.06 1.55 0.05 1.19 0.04

charged structures. B3LYP/pcS-2 charge distributions obtained from Mulliken population analysis for the largest positively charged solitonic and bipolaronic chains using HF and MP2 geometries are displayed in Figure 3. As already observed for the distribution of chemical shift, a damped charge density wave (CDW), with excess charge localized in the central part of the solitonic chain, is observed only with the HF geometry. The CDW, with the MP2 geometry, is more delocalized and spread out more regularly over the chain as a result of a smaller BLA. These trends compare well with the results obtained previously by Monev et al. [49]. Con sidering the C39 Hþ 41 and C39 H41 chains, for example, the B3LYP/pcS2 atomic charge values for the central carbon atom, obtained with the HF geometry, are qC = 0.038e and 0.033e, respectively. The corresponding results with the MP2 geometry are qC = 0.030e and 0.012e. Comparing these figures (and similar results obtained for other chains) one can observe that the larger electron densities on the central carbons for the positively charged solitonic chains correlate with carbon atoms more shielded (see Table 1). Similar conclusions have been drawn for bipolaronic chains, but in this case, the central carbon atoms more shielded are those of negatively charged structures. It is interesting to analyze the behavior of the chemical shift of the carbon atom located at the central part of the chain as a function of the chain length. For solitonic chains, the structural distortion caused by presence of the defect divides the chain into two segments with double bonds at the two ends. This produces a conflicting bond length at the center that has a marked influence on  the chemical shift, distinguishing the C4nþ1 Hþ 4nþ3 [C4nþ1 H4nþ3 ] and þ  C4nþ3 H4nþ5 [C4nþ3 H4nþ5 ] series. Table 2 displays B3LYP/pcS-2 results for the chemical shifts of the central carbons of singly charged chains obtained with HF and MP2 geometries with increasing chain length. The results reveal the existence of two series with different asymptotic values for positively (or negatively) charged chains. Both series exhibit a rapid convergence pattern as indicated by the first differences between the values of Dr(13C) of two successive chains of the same series. Figure 4 shows that the chemical shift presents a monotonic decrease with the elongation of the chain for the C4nþ1 Hþ 4nþ3 series and a monotonic increase for the C4nþ1 H 4nþ3 series. Notice that, specially for the negative chains, the Dr(13C) values converge more quickly for the HF geometries as a consequence of smaller delocalization effects. On the basis

C5 H 7 C7 H 9 C9 H 11 C11 H 13 C13 H 15 C15 H 17 C17 H 19 C19 H 21 C21 H 23 C23 H 25 C25 H 27 C27 H 29 C29 H 31 C31 H 33 C33 H 35 C35 H 37 C37 H 39 C39 H 41

94.14 154.08 101.66 154.43 111.09 154.17 115.63 154.21 118.60 154.22 120.52 154.23 121.86 154.24 122.82 154.23 123.53 154.22

MP2 geometry

Dr(13C)

|DD|

7.52 0.35 9.43 0.26 4.54 0.04 2.97 0.01 1.92 0.01 1.34 0.01 0.96 0.01 0.71 0.01

98.82 156.57 107.16 156.11 117.83 154.97 123.41 154.37 127.29 153.87 129.99 153.50 132.01 153.22 133.54 153.00 134.73 152.84

|DD|

8.34 0.46 10.67 1.14 5.58 0.60 3.88 0.50 2.70 0.37 2.02 0.28 1.53 0.22 1.19 0.16

a

b

Figure 4. B3LYP/pcS-2 13C chemical shifts for the central carbon atoms of positively (top) and negatively (bottom) charged solitonic chains as function of the size of the chain. The results were obtained with the HF and MP2 geometries.

on the findings of Table 2, one can obtain an estimation of the influence of the ionization state on the chemical shift of the central carbon atom. The B3LYP/pcS-2 model predicts the chemical shift

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Table 3 B3LYP/pcS-2 results for the chemical shifts [ppm] of the central carbon atoms of positively and negatively charged bipolaronic chains. The results were obtained with MP2  þþ  geometries. The columns labeled |DD| give separately the first differences between two successive C4n Hþþ 4nþ2 [C4n H4nþ2 ] or C4nþ2 H4nþ4 [C4nþ2 H4nþ4 ] chains.

Dr(13C) C4 Hþþ 6 C6 Hþþ 8 C8 Hþþ 10 C10 Hþþ 12 C12 Hþþ 14 C14 Hþþ 16 C16 Hþþ 18 C18 Hþþ 20 C20 Hþþ 22 C22 Hþþ 24 C24 Hþþ 26 C26 Hþþ 28 C28 Hþþ 30 C30 Hþþ 32 C32 Hþþ 34 C34 Hþþ 36 C36 Hþþ 38 C38 Hþþ 40 C40 Hþþ 42

194.91 213.58 181.50 187.68 172.02 175.96 167.36 170.15 164.28 166.40 162.04 163.85 160.50 161.98 159.12 160.48 158.06 159.20 157.27

Dr(13C)

|DD|

13.41 25.90 9.48 11.72 4.66 5.81 3.08 3.75 2.24 2.55 1.54 1.87 1.38 1.50 1.06 1.28 0.79

 difference of 29.35 ppm [45] between the C37 Hþ 39 and C37 H39 chains with the MP2 [HF] geometry. For the C4nþ3 Hþ and [C H 4nþ3 4nþ5 4nþ5 ] 13 series, the Dr( C) values present a pattern that is almost not affected by delocalization effects. The chemical shift difference be tween the C39 Hþ 41 and C39 H41 chains attains 6.19 [13.77] ppm using the MP2 [HF] geometry. It should be stressed that the Dr(13C) values for the central carbon of smaller bipolaronic structures can also help distinguish the  þþ  C4n Hþþ 4nþ2 [C4n H4nþ2 ] and C4nþ2 H4nþ4 [C4nþ2 H4nþ4 ] series but, differently of the solitonic case, the first differences between the values of Dr(13C) for the central carbon of two successive chains of the same series indicate a common asymptotic value for both series of positively (or negatively) charged chains (see Table 3). Thus, for the largest bipolaronic chains the chemical shift difference between the central carbons of positive and negative structures is of 15.34 ppm, using the MP2 geometry. Therefore, the variations of Dr(13C) for both solitonic and bipolaronic chains provide a clear distinguishing of the charge state of charged defects that in turn may be observed in NMR experiments.

4. Conclusion The 13C chemical shifts of isolated polyacetylene chains with a charged solitonic or bipolaronic defect have been determined theoretically with the GIAO-B3LYP method using the pcS-2 basis set. The magnetic properties were calculated on the HF/cc-pVDZ and MP2/cc-pVDZ equilibrium geometries. It turns out that electron correlation effects are crucial for charactering the geometrical changes on the conjugated segment of charged chains. Our results also show that the chain end effects lead to a clear distinction be þ  tween the C4nþ1 Hþ 4nþ3 [C4nþ1 H4nþ3 ] and C4nþ3 H4nþ5 [C4nþ3 H4nþ5 ] series. For the bipolaronic chains these end effects are smaller and diminish with increasing chain length, reflecting the formation of isolated solitons. Converged results still demand for extended doped polyacetylene chains. For the solitonic chains, the B3LYP/ pcS-2 model predicts the chemical shift difference of 29 ppm be tween the central carbon atoms of the C37 Hþ 39 and C37 H39 chains (which stands out as the largest chain of the C4nþ1 Hþ 4nþ3 and þ  C4nþ1 H 4nþ3 series) and of 6 ppm between the C39 H41 and C39 H41 chains. For the bipolaronic chains, the corresponding chemical shift  difference is of 15 ppm between the C40 Hþþ 42 and C40 H42 chains.

C4 H 6 C6 H 8 C8 H 10 C10 H 12 C12 H 14 C14 H 16 C16 H 18 C18 H 20 C20 H 22 C22 H 24 C24 H 26 C26 H 28 C28 H 30 C30 H 32 C32 H 34 C34 H 36 C36 H 38 C38 H 40 C40 H 42

142.93 103.65 120.62 114.14 129.25 124.28 132.86 129.70 135.55 133.23 137.58 135.65 139.06 137.46 140.23 138.82 141.16 139.92 141.93

|DD|

22.31 10.49 8.63 10.14 3.61 5.42 2.69 3.53 2.03 2.42 1.48 1.81 1.17 1.36 0.93 1.10 0.77

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