Adsorption of free-base phthalocyanine on Stone-Wales defect-containing carbon nanotubes: A DFT study

Diamond & Related Materials 97 (2019) 107443

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Adsorption of free-base phthalocyanine on Stone-Wales defect-containing carbon nanotubes: A DFT study

T

Vladimir A. Basiuk , Eduardo Chávez-Colorado ⁎

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., Ciudad de México 04510, Mexico

ARTICLE INFO

ABSTRACT

Keywords: Carbon nanotubes Single-walled Stone-Wales defects Free-base phthalocyanine Density functional theory

The present study addresses the influence of topological defects incorporated into sidewalls of single-walled carbon nanotubes (SWNTs) on the strength of noncovalent bonding and the state of adsorbed complex organic molecules. The interaction of free-base phthalocyanine (H2Pc) with Stone-Wales (SW) defect-containing armchair and zigzag nanotube models (ANT and ZNT, respectively) was studied at the PBE-D/DNP and M06-2X/631G(d,p) theoretical levels. The results obtained were analyzed by comparing them with those for DFT calculations on similar defect-free nanotube systems, with a particular emphasis on the data accounting for basis set superposition error (BSSE). As a whole, free-base H2Pc adsorbs on SW defect-containing SWNT models stronger than on the parent defect-free nanotubes. In PBE-D calculations, the increase in binding strength varies between 2.01 and 6.31 kcal/mol (0.087 and 0.274 eV), depending on SWNT chirality and defect orientation. In BSSEcorrected M06-2X calculations, this effect is less evident. C(H2Pc)…C(SWNT) are usually the shortest separations, followed by N(H2Pc)…C(SWNT) and H(H2Pc)…C(SWNT). Frontier orbital-related characteristics obtained exhibit insignificant differences as compared to similar systems based on defect-free ANT and ZNT models. For most systems, for both computational techniques HOMO-LUMO gap energies change by less than 0.06 eV. The pattern of HOMO-LUMO orbital distribution was found to be broadly variable.

1. Introduction While carbon nanotubes (CNTs) can be viewed as cylindrical graphene sheets, this turns to be a mere idealization, since all the known experimental synthetic procedures produce both multi-walled and single-walled CNTs (MWNTs and SWNTs, respectively) containing a large number of structural imperfections including Stone-Wales (SW) defects (often referred to as Stone–Thrower–Wales defects) [1,2], isolated pentagons, heptagons, and vacancies (see, for example, [3–6]). Naturally, their presence must be accounted when physical, chemical and biological properties of CNTs are analyzed and explored. Of all the types of defects, SW defects received special attention, since the CeC bond rotation by 90° in the plane of hexagonal network is the only mechanism of defect generation which does not alter the nature of sp2 backbone. Nevertheless, while the influence of SW defects on physical properties such as mechanical characteristics of CNTs and their polymeric composites is the most commonly addressed subject (see, for example, [7–11]), the relevant information on SW defect chemistry is relatively scarce and sometimes controversial, despite of its particular importance for both covalent and noncovalent functionalization of CNTs. Several theoretical studies showed that SW defective ⁎

versus ideal SWNT sidewalls have an enhanced H2 [12–15] and ozone [16] adsorption capacity, whereas incorporation of this type of defects does not notably change the nanotube affinity toward molecular oxygen [17] and dimethyl methylphosphonate nerve agent [18]. In terms of covalent bond formation, SW defects exhibit higher chemical reactivity as compared to that of perfect nanotube sidewalls when interacting with the single H and F atoms [19], methylene CH2 [20], NH3 molecule [21] and NH2 radical [22], NO2+ ion [23], and carboxyl groups COOH [24,25]. On the other hand, an evident opposite effect was observed by Lu et al. [26] for the addition of O, CH2 and O3 species, whereas in the case of 1,3-dipolar cycloadditions [27–29] the comparative reactivity of SW defects was found to strongly depend on their orientation with respect to nanotube axis. Thus, the above summary clearly shows that the (all theoretical) studies on the influence of SW defects on chemical properties of CNTs are limited to the consideration of relatively simple radical and molecular species. At the same time, there is a broad variety of nanotubebased systems of importance from both fundamental and practical points of view, a good example of which are CNTs covalently and noncovalently functionalized with phthalocyanines (Pcs). This class of hybrid materials exhibits very interesting properties and offers a

Corresponding author. E-mail address: [email protected] (V.A. Basiuk).

https://doi.org/10.1016/j.diamond.2019.107443 Received 4 March 2019; Received in revised form 31 May 2019; Accepted 4 June 2019 Available online 05 June 2019 0925-9635/ © 2019 Elsevier B.V. All rights reserved.

Diamond & Related Materials 97 (2019) 107443

V.A. Basiuk and E. Chávez-Colorado

number of potential applications related to photovoltaic and photoelectronic devices [30–36], electrochemical sensors [37–42], catalysts for the reactions of oxygen [43–49] and CO2 reduction [50], molecular spin-valves [51–53], nonlinear optical materials [54,55], high-resistance nanocomposites [56], field-emission devices [57], Li/SOCl2 batteries [49,58,59], among others. Performance of all the above functional materials and devices rely upon the state of Pc molecules on CNT sidewalls, especially in the case of noncovalent attachment of phthalocyanines, and therefore any specific relevant data are of crucial importance. Unfortunately, the known instrumental techniques are capable of providing very limited (to null) experimental information on such important characteristics as the geometry of adsorbed macrocyclic molecules, their electronic properties and bonding strength. Given the circumstances, the use of theoretical tools, first of all density functional theory (DFT), seems to be a logical solution. However, unfortunately, the related studies turn to be surprisingly scarce: they include two reports performed on periodic [60,61] and three (our own) reports performed on cluster SWNT models [62–64]. All of them employed ideal nanotube structures, which neglect the presence of sidewall imperfections in general, and of SW defects in particular, which well might be preferred sites for Pc adsorption and influence geometry and electronic state of macrocyclic molecules. Furthermore, our recent and partially failed attempt of sublimation deposition of free-base phthalocyanine (H2Pc) onto SWNTs and MWNTs [65] demonstrated that structural defects (presumably those containing pentagonal rings) can act as catalytic centers for undesirable H2Pc decomposition at temperatures above 400 °C. A general goal of the present theoretical study was to contribute to understanding the influence of topological defects incorporated into nanotube sidewalls on the strength of noncovalent bonding and the state of adsorbed complex organic molecules, by considering free-base phthalocyanine interacting with SW defect-containing armchair and zigzag SWNT models as a particular example of the systems of practical importance. The data obtained here were analyzed by comparing them with the results of our previous DFT calculations on similar defect-free nanotube systems [62].

noncovalent complexes were calculated according to the following equation:

EH2Pc + SWNT = EH2Pc + SWNT

(EH2Pc + ESWNT)

where Ei is the corresponding absolute energy. 3. Results and discussion To understand how the presence of SW defects can influence the noncovalent interactions of H2Pc with carbon nanotube sidewalls, a valid comparison with the results of previous DFT calculations on H2Pc adsorbed on defect-free SWNT models [62]. In order to fulfill this requirement, first of all, we followed the same computational methodology. Furthermore, SW defect-containing SWNT models used in the present study were directly derived from the armchair and zigzag nanotube cluster models employed previously [62]. The use of such models allows for all-electron treatment by means of spherical (DNP in the present case) and Pople-type (6-31G(d,p) equivalent to DNP) basis sets, along with PBE-D and M06-2X hybrid functional, respectively. The closed-cap SWNT models were derived from spherical fullerenes C60 and C80(Ih) to form armchair (5,5) and zigzag (10,0) SWNTs, which are composed of 120 and 140 carbon atoms, and referred to as ANT and ZNT, respectively. The length of both nanotube models is barely sufficient to accommodate H2Pc macrocycle, with an overwhelming part of the latter contacting the nanotube part with cylindrical curvature. We realize that longer SWNT models would be desirable. Nevertheless, even with the present length we faced convergence problems in some calculations, so that the use of longer cluster models turns to be very problematic. Detailed consideration shows that for each of the SWNT models, there are two different possibilities to incorporate a SW defect, depending on orientation of the latter with respect to the nanotube axis. In one of them, the (7,7) junction is tilted with respect to SWNT axis: correspondingly, the defects are referred to as SW_T, and nanotube models, as ANT_SW_T and ZNT_SW_T (Fig. 1). Alternatively, ANT_SW_P and ZNT_SW_P models contain SW defects with the (7,7) junction which is parallel (in ANT) and perpendicular (in ZNT) with respect to nanotube axis (SW_P notation in both cases). In order to obtain more precise results, for both calculation techniques employed, we attempted to account for basis set superposition error (BSSE) by using counterpoise (CP) technique (numerical data and graphs marked hereafter with superscripted ‘CP’). This is especially

2. Methods For a valid comparison with the results of our previous DFT calculations on H2Pc adsorbed on defect-free SWNT models [62], we followed the same computational methodology. Two sets of calculations were performed. In the first one, the DMol3 numerical-based DFT module of the Materials Studio 6.0 suite from Accelrys Inc. [66–69] was used. Perdew-Burke-Ernzerhof correlation functional PBE [70] in combination with a long-range dispersion correction by Grimme [71] (commonly referred to as PBE-D) was employed. All computations were carried out in conjunction with the double numerical basis set DNP, having a polarization d-function added on all non‑hydrogen atoms, plus a polarization p-function added on all H atoms. Full geometry optimization and calculation of electronic parameter was performed with the quality and convergence criteria set to finer values than the default ‘fine’ criteria in DMol3: this was done for a more valid comparison with the data set obtained by using Gaussian 09 package (see below). Namely, energy was set to 10−6 Ha; maximum force, to 4.5 × 10−4 Ha/ Å; maximum displacement, to 1.8 × 10−3 Å. The global orbital cutoff was set to 4.4 Å. In all cases, we used the ‘all-electron’ core treatment along with Fermi orbital occupation (no thermal smearing). The geometries optimized at PBE-D/DNP theoretical level served as the input structure for further calculations by using Gaussian 09 suite [72]. In the present work, however, we employed only M06-2X hybrid meta exchange-correlation functional [73], whereas M05-2X [74] was discarded due to systematic convergence problems. M06-2X functional was used in conjunction with the 6-31G(d,p) basis set, which is equivalent to DNP of DMol3. The formation energies ΔEH2Pc+SWNT (or ΔE for simplicity) for the

Fig. 1. Geometries optimized at M06-2X/6-31G(d,p) level of theory for the armchair (ANT) and zigzag (ZNT) nanotube models, incorporating SW defects in a parallel (in ANT) or perpendicular (in ZNT) and tilted orientation (SW-P and SW-T, respectively) of the (7,7) junction with respect to nanotube axis. Two pentagonal and two heptagonal rings forming SW defect are highlighted in yellow. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 2

3

c

b

a

(−30.4); (−25.5); (−30.4); (−25.5);

(−36.7); (−31.3); (−36.7); (−31.3);

(−24.8); (−15.5); (−24.8); (−15.5);

(−26.3); (−16.6); (−26.3); (−16.6);

−31.75 −30.63 −33.79 −31.81

−37.92 −35.33 −30.63 −33.31

−23.69 −14.44 −26.40 −16.73

−27.06 −17.74 −25.66 −16.70

ΔE (kcal/mol; eV)

−1.173 −0.769 −1.113 −0.724

−1.027 −0.626 −1.145 −0.725

−1.644 −1.532 −1.328 −1.444

−1.377 −1.328 −1.465 −1.379

(−1.140) (−0.720) (−1.140) (−0.720)

(−1.075) (−0.672) (−1.075) (−0.672)

(−1.591) (−1.357) (−1.591) (−1.357)

(−1.318) (−1.106) (−1.318) (−1.106)

−3.679 −4.745 −4.708 −4.567 −4.567 −4.493 −4.493 −5.503 −5.402 −5.253 −5.247 −5.211 −5.211 −2.276 −3.323 −3.167 −3.204 −3.203 −3.022 −3.022 −4.230 −4.234 −3.903 −3.902 −4.075 −3.991

−5.752 −5.717 −6.036 −5.549 −5.558 −5.813 −5.798 −6.415 −6.022 −5.928 −5.924 −5.884 −5.911

ELUMO (eV)

−5.069 −5.060 −5.291 −4.861 −4.861 −5.084 −5.084 −5.607 −5.531 −5.335 −5.328 −5.280 −5.280

EHOMO (eV)

One of the (N)H atoms. BSSE correction at PBE-D/DNP level of theory was done by means of single point calculations. For all ZNT-derived systems, the ground state is triplet.

PBE-D H2Pc ANT_SW-P ANT_SW-T H2Pc+ANT_SW-P H2Pc+ANT_SW-PCPb H2Pc+ANT_SW-T H2Pc+ANT_SW-TCP ZNT_SW-Pc ZNT_SW-T H2Pc+ZNT_SW-P H2Pc+ZNT_SW-PCP H2Pc+ZNT_SW-T H2Pc+ZNT_SW-TCP M06-2X H2Pc ANT_SW-P ANT_SW-T H2Pc+ANT_SW-P H2Pc+ANT_SW-PCP H2Pc+ANT_SW-T H2Pc+ANT_SW-TCP ZNT_SW-P ZNT_SW-T H2Pc+ZNT_SW-P H2Pc+ZNT_SW-PCP H2Pc+ZNT_SW-T H2Pc+ZNT_SW-TCP

System

3.476 2.394 2.868 2.345 2.356 2.791 2.776 2.186 1.788 2.025 2.022 1.809 1.920

1.390 0.315 0.583 0.294 0.294 0.591 0.591 0.104 0.129 0.082 0.081 0.069 0.069

(1.97) (1.97) (1.97) (1.97)

(2.77) (2.76) (2.77) (2.76)

(0.07) (0.07) (0.07) (0.07)

(0.63) (0.63) (0.63) (0.63)

HOMO-LUMO gap (eV)

3.022 2.945 3.277 3.321

3.093 3.171 3.162 3.174

3.058 3.058 3.344 3.344

3.169 3.169 3.201 3.201

dH(H2Pc)…C(SWNT) (Å)a

3.099 3.151 3.080 3.177

3.083 3.139 3.127 3.157

3.103 3.103 3.072 3.072

3.076 3.076 3.141 3.141

dN(H2Pc)…C(SWNT) (Å)

3.082 3.124 3.006 3.009

2.994 3.037 3.020 3.033

3.051 3.051 2.978 2.978

2.983 2.983 3.126 3.126

dC(H2Pc)…C(SWNT) (Å)

Table 1 Formation energies ΔE (in kcal/mol and eV) without and with counterpoise BSSE correction, HOMO, LUMO and HOMO-LUMO gap energies (in eV; including those for isolated H2Pc and SWNT models), the shortest dH(H2Pc)…C(SWNT), dN(H2Pc)…C(SWNT) and dC(H2Pc)…C(SWNT) distances (in Å) for noncovalent H2Pc+SWNT complexes, calculated by using PBE-D and M06-2X functionals. For comparison, ΔE and HOMO-LUMO gap values obtained previously for the defect-free structures [62] are presented in parenthesis.

V.A. Basiuk and E. Chávez-Colorado

Diamond & Related Materials 97 (2019) 107443

Diamond & Related Materials 97 (2019) 107443

V.A. Basiuk and E. Chávez-Colorado

important for Pople-type basis sets like 6-31G(d,p) in the case of M062X calculations (which included geometry optimization). In the case of PBE-D, even though the exact DFT spherical atomic orbitals in DNP basis set are known to minimize BSSE [66], we performed CP correction with PBE + D as well. However, since CP-corrected geometry optimization is not supported in DMol3 module, the BSSE correction was done by means of single point calculations. As a result, the PBE-D geometries remained the same, frontier orbital energies varied insignificantly, and only total (and correspondingly binding) energies notably changed. In Table 1, respective numerical data are presented for both uncorrected and CP-corrected calculations, though we will make an emphasis on CPcorrected values. As one can see from Table 1, in CP-corrected PBE-D calculations, H2Pc adsorbs stronger onto all SW defect-containing SWNT models as compared to the parent defect-free nanotube sidewalls. The increase in binding strength for H2Pc+ANT_SW-PCP, H2Pc+ANT_SW-TCP, H2Pc +ZNT_SW-PCP and H2Pc+ZNT_SW-TCP is by 5.13, 6.31, 4.03 and 2.01 kcal/mol (0.222, 0.274, 0.175 and 0.087 eV), respectively. In other words, the interaction strength depends on SWNT chirality and orientation of SW defect. It is stronger for both ANT models than for ZNT nanotubes. For ANT models, the binding is stronger (by 1.18 kcal/mol, or 0.051 eV) with tilted SW defect than with SW-P, and vice versa in the case of ZNT nanotubes (a difference of 2.02 kcal/mol, or 0.088 eV). The results of M06-2X calculations are somewhat different in terms of both formation energies (whose absolute values are roughly 15–18 kcal/mol, or 0.65–0.78 eV, lower than that obtained in PBE-D calculations) and their similarity for ideal and SW defect containing SWNTs. The interaction strength increases in the case of H2Pc +ANT_SW-TCP, H2Pc+ZNT_SW-PCP and H2Pc+ZNT_SW-TCP, but only by 1.23, 1.14 and 0.10 kcal/mol (0.053, 0.049 and 0.004 eV), respectively. For the remaining H2Pc+ANT_SW-PCP, an opposite effect is observed, where the binding decreases by 1.06 kcal/mol (0.046 eV). The molecule of H2Pc is essentially planar, and even though it suffers bending distortion to increase the surface of contact with nanotube sidewall [60–65], the only atoms which tend to go out of the molecular plain and approach SWNT surface closer than others are the central atoms: two H atoms in the present case. The strength of their interaction with C atoms of nanotube, however, makes an insignificant contribution into the interaction of such an extended polyaza annulene system as phthalocyanine with another polycyclic aromatic system, which is nanotube sidewall. As a result, one can expect that the closest contacts between H2Pc and SWNT model will not be H(H2Pc) …C(SWNT), but instead N(H2Pc)…C(SWNT) and C(H2Pc)…C(SWNT) contacts: first, merely statistically (there are 32 carbon and 8 nitrogen atoms, versus only two central H atoms), and second, due to a higher strength of the latter interactions. Indeed, in PBE-D calculations C(H2Pc)…C(SWNT) separations (Table 1 and Fig. 2) turn to be the shortest ones, from 2.978 (H2Pc+ZNT_SW-T) to 3.126 Å (H2Pc +ANT_SW-T) for all the complexes, whereas H(H2Pc)…C(SWNT) separations are found between 3.058 (H2Pc+ZNT_SW-P) and 3.344 Å (H2Pc+ZNT_SW-T); N(H2Pc)…C(SWNT) distances occupy an intermediate position slightly varying between 3.072 (H2Pc+ZNT_SW-T) and 3.141 Å (H2Pc+ANT_SW-T). In CP-corrected M06-2X calculations, the same trend is observed for three complexes of four, namely, for H2Pc+ANT_SW-PCP, H2Pc+ANT_SW-TCP and H2Pc+ZNT_SW-TCP. The exception is H2Pc+ZNT_SW-PCP, for which the closest H(H2Pc) …C(SWNT), C(H2Pc)…C(SWNT) and N(H2Pc)…C(SWNT) contacts are 2.945, 3.124 and 3.151 Å, respectively. The above contacts exhibit no general geometric pattern, being distributed rather randomly (Fig. 2). In most cases, they are formed between H2Pc molecule and carbon atoms belonging to SW defect. The two exceptions are H2Pc+ZNT_SWP (PBE-D calculations) and H2Pc+ANT_SW-PCP geometries (M06-2X), where N(H2Pc)…C(SWNT) and N(H2Pc)…C(SWNT) plus C(H2Pc) …C(SWNT) closest approaches, respectively, are formed with external (with respect to SW defect) C atoms of nanotube. In two cases of H2Pc +ANT_SW-P (PBE-D) and H2Pc+ANT_SW-PCP (M06-2X), N(H2Pc)

Fig. 2. Fragments of optimized geometries for the noncovalent complexes of H2Pc with Stone-Wales defect-containing ANT and ZNT models, showing the shortest dH(H2Pc)…C(SWNT), dN(H2Pc)…C(SWNT) and dC(H2Pc)…C(SWNT) distances (red lines; values are specified in Table 1). For clarity, SWNT carbon atoms, except for those belonging to SW defects and their immediate neighbors, are removed. Atom colors: carbon, gray, except for yellow C atoms belonging to SW defects; nitrogen, blue, hydrogen, white. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

…C(SWNT) and C(H2Pc)…C(SWNT) closest contacts are formed with the same C atom of nanotube. Compared to our previous calculations on similar systems based on defect-free ANT and ZNT models [62], frontier orbital-related characteristics obtained in this work exhibit insignificant differences. In quantitative terms, for most systems and for both computational 4

Diamond & Related Materials 97 (2019) 107443

V.A. Basiuk and E. Chávez-Colorado

techniques HOMO-LUMO gap energies change by less than 0.06 eV (almost do not change for H2Pc+ZNT_SW-T in PBE-D calculations). The exception is H2Pc+ANT_SW-P complex, for which the gap value decreases considerably: in particular, by 0.336 (PBE-D calculations) and 0.404 eV (CP-corrected M06-2X). As a general rule, the gap energies for the complexes tend to match the values for corresponding isolated SWNT models, rather than those for isolated H2Pc molecule (1.390 eV calculated with PBE-D and 3.476 eV, with M06-2X). Another related aspect is HOMO and LUMO orbital distribution. The most common pattern for noncovalent complexes of porphyrins, phthalocyanines and related macrocycles with carbon nanoclusters (fullerenes first of all) is when HOMO is mainly located on the macrocyclic molecule, whereas LUMO is found entirely (or almost entirely) on carbon component (see [62] and references therein). However, according to our observations [62–64], in the particular case of fulleroid nanotube models like ANT and ZNT, HOMO-LUMO plots very seldom comply with the above general rule. In the calculations on defect-free SWNT models [62], M06-2X without and with BSSE correction gave HOMO almost uniformly distributed between H2Pc and ANT, whereas both orbitals were located on the nanotube unit, according to PBE-D.

The HOMO and LUMO plots obtained with the latter functional for H2Pc+ZNT complex were somewhat unusual, where both orbitals were localized on nanotube, with some traces of LUMO extended on H2Pc molecule. And only M06-2X calculations on H2Pc+ZNT system produced the typical orbital distribution, that is, when HOMO is found on macrocyclic molecule and LUMO, on carbon nanocluster. In the present work, the ‘normal’ HOMO and LUMO plots were found for H2Pc +ZNT_SW-PCP and H2Pc+ZNT_SW-TCP as calculated with M06-2X (Fig. 3). These systems are followed by H2Pc+ANT_SW-TCP (M06-2X) and H2Pc+ZNT_SW-T (PBE-D), where LOMO is found completely on nanotube model, but HOMO notably extends from phthalocyanine to SWNT. Both orbital are localized completely on nanotube in the cases of H2Pc+ANT_SW-P, H2Pc+ANT_SW-T (both calculated with PBE-D) and H2Pc+ANT_SW-PCP (M06-2X). And finally, in H2Pc+ZNT_SW-P (PBED) both HOMO and LOMO are found mainly on nanotube, with some minor lobes appearing on phthalocyanine molecule. It is quite obvious that any numerical results of quantum-chemical calculations are model-sensitive. We realize that the size of fulleroid ANT and ZNT nanotube models employed in the present study are barely sufficient to accommodate such a large macrocycle as

Fig. 3. HOMO and LUMO plots (isosurfaces at 0.03 a.u.) for the noncovalent complexes of H2Pc with Stone-Wales defect-containing ANT and ZNT models. 5

Diamond & Related Materials 97 (2019) 107443

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results presented in Table 2, the BSSE-corrected energies of formation for the corresponding H2Pc+ANTL, H2Pc+ANTL_SW-P and H2Pc +ANTL_SW-T are −31.55, −28.35 and −32.28 eV (−1.368, −1.229 and −1.400 eV), compared to the values of −25.5 [62], −30.63 and −31.81 kcal/mol (−1.106, −1.328 and −1.379 eV) for H2Pc+ANTCP, H2Pc+ANT_SW-PCP and H2Pc+ANT_SW-TCP, respectively (Table 1). In other words, increasing ANT model length caused an increase in H2Pc adsorption strength in the case of ideal nanotube sidewall and the one having SW defect with tilted orientation, by 6.05 and 0.47 kcal/mol (or 0.262 and 0.021 eV), respectively, whereas in the case of SW-P orientation, an opposite effect can be observed, where the bonding strength decreased by 2.28 kcal/mol (0.099 eV). When comparing the BSSE-corrected energies of complex formation within the ANTL series (Table 2), introducing SW-T defect increases the interaction strength by 0.73 kcal/mol (0.032 eV), whereas for the case of SW-P defect it decreases by 3.20 kcal/mol (0.139 eV). Therefore, the answer to the question of whether there are tangible differences in the strength of H2Pc binding to longer ideal and SW defect-containing SWNT models is definitely yes. As regards HOMO-LUMO gap energies (Table 2), they follow the same trend as that observed above for short ANT models, where the gap energies for the complexes match the values for corresponding isolated SWNT models, rather than those for isolated H2Pc molecule (1.390 eV). Namely, the gap values of 0.288, 0.093 and 0.302 eV calculated for H2Pc+ANTL, H2Pc+ANTL_SW-P and H2Pc+ANTL_SW-T, respectively, are rather close to the corresponding values of 0.302, 0.108 and 0.308 eV obtained for isolated ANTL, ANTL_SW-P and ANTL_SW-T models. All of these energies are considerably lower than the corresponding values specified in Table 1 for ANT-related systems: this effect must be attributed to a more metallic character of longer armchair SWNT models. And, finally, the close contacts between H2Pc molecule and nanotube sidewall again exhibit no general geometric pattern, being distributed rather randomly. Like in both H2Pc+ANT_SW-P and H2Pc+ANT_SW-T complexes (Table 1), for H2Pc+ANTL_SW-P the shortest separation is C(H2Pc)…C(SWNT), followed by N(H2Pc) …C(SWNT) and H(H2Pc)…C(SWNT) (3.052, 3.107 and 3.370 Å, respectively). For H2Pc+ANTL_SW-T this order changes, and the shortest separation becomes H(H2Pc)…C(SWNT), followed by C(H2Pc) …C(SWNT) and N(H2Pc)…C(SWNT), though the differences in distances are very insignificant (3.105, 3.125 and 3.131 Å, respectively).

Fig. 4. Geometries optimized at PBE-D/DNP level of theory for the longer armchair nanotube model without (ANTL) and with SW defects in a parallel (ANTL_SW-P) and tilted (ANTL_SW-T) orientation of the (7,7) junction with respect to nanotube axis. Two pentagonal and two heptagonal rings forming SW defect are highlighted in yellow. For size comparison, H2Pc molecule is shown in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

phthalocyanine. Nevertheless, as we already commented above on, even with their present length we faced convergence problems in some calculations (especially persistent in the case of ZNT-based systems), so that systematic use of longer cluster models turned to be very problematic. Still, we attempted to verify whether there are tangible differences in the strength of H2Pc binding to longer ideal and SW defectcontaining SWNT models. It was possible to accomplish at the PBE-D/ DNP theoretical level for the series of armchair-type nanotubes shown in Fig. 4, which have the same armchair (5,5) chirality with C60-derived closed ends as ANT, ANT_SW-P and ANT_SW-T do (Fig. 1), but are composed of 180 instead of 120 carbon atoms. The H2Pc molecule highlighted in red (Fig. 4) shows that the macrocycle can be completely accommodated on the nanotube part with cylindrical curvature, without any contact with the C60 hemispheres. As one can see from the

4. Conclusions As a whole, free-base H2Pc adsorbs on Stone-Wales defect-containing SWNT models stronger than on the parent defect-free nanotube sidewalls. In CP-corrected PBE-D calculations, the increase in binding strength varies between 2.01 and 6.31 kcal/mol (0.087 and 0.274 eV), depending on SWNT chirality and SW defect orientation. In BSSE-

Table 2 Formation energies ΔE (in kcal/mol and eV) without and with counterpoise BSSE correction, HOMO, LUMO and HOMO-LUMO gap energies (in eV; including those for isolated H2Pc and SWNT models), the shortest dH(H2Pc)…C(SWNT), dN(H2Pc)…C(SWNT) and dC(H2Pc)…C(SWNT) distances (in Å) for noncovalent complexes of H2Pc with longer closed-cap ANT models (ANTL), calculated at the PBE-D/DNP level of theory. System H2Pc ANTL ANTL_SW-P ANTL_SW-T H2Pc+ANTL H2Pc+ANTLCPb H2Pc+ANTL_SW-P H2Pc+ANTL_SW-PCP H2Pc+ANTL_SW-T H2Pc+ANTL_SW-TCP a b

ΔE (kcal/mol; eV)

EHOMO (eV)

ELUMO (eV)

HOMO-LUMO gap (eV)

dH(H2Pc)…C(SWNT) (Å)a

dN(H2Pc)…C(SWNT) (Å)

dC(H2Pc)…C(SWNT) (Å)

−37.06; −31.55; −33.87; −28.35; −37.85; −32.28;

−5.069 −5.001 −4.884 −5.021 −4.876 −4.876 −4.757 −4.757 −4.893 −4.893

−3.679 −4.699 −4.776 −4.713 −4.588 −4.588 −4.664 −4.664 −4.591 −4.591

1.390 0.302 0.108 0.308 0.288 0.288 0.093 0.093 0.302 0.302

3.185 3.185 3.370 3.370 3.105 3.105

3.076 3.076 3.107 3.107 3.131 3.131

3.128 3.128 3.052 3.052 3.125 3.125

−1.607 −1.368 −1.469 −1.229 −1.641 −1.400

One of the (N)H atoms. BSSE correction is possible by means of single point calculations only. 6

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corrected M06-2X calculations, this effect is less evident: in three cases the interaction strength insignificantly increases, by 0.10–1.23 kcal/ mol (0.004–0.053 eV), whereas for one system an opposite effect is observed, with binding energy decreasing by 1.06 kcal/mol (0.046 eV). As regards inter-unit distances, C(H2Pc)…C(SWNT) are usually the shortest separations, followed by N(H2Pc)…C(SWNT) and H(H2Pc) …C(SWNT). The above close contacts exhibit no general geometric pattern, being distributed rather randomly. For most complexes (with two exceptions), they are formed between H2Pc molecule and carbon atoms belonging to SW defect. Frontier orbital-related characteristics obtained in the present work exhibit insignificant differences as compared to our previous calculations on similar systems based on defect-free ANT and ZNT models [62]. For most systems, for both computational techniques HOMOLUMO gap energies change by less than 0.06 eV. As a rule, the gap energies for the complexes tend to match the values for corresponding isolated SWNT models, rather than those for isolated H2Pc molecule. The pattern of HOMO-LUMO orbital distribution is broadly variable. Only M06-2X calculations on H2Pc+ZNT system produced the ‘usual’ orbital distribution, when HOMO is found on macrocyclic molecule and LUMO, on carbon nanocluster.

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