Kekulene: Structure, stability and nature of HH

Molecular Astrophysics 8 (2017) 19–26

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Research paper

Kekulene: Structure, stability and nature of H•••H interactions in large PAHs J. Poater a,b,∗, J. Paauwe c, S. Pan d, G. Merino d, C. Fonseca Guerra c,e, F.M. Bickelhaupt c,f,∗ a

Departament de Química Inorgànica i Orgànica & IQTCUB, Universitat de Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Catalonia, Spain ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain c Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling (ACMM), Vrije Universiteit Amsterdam, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands d Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados Unidad Mérida, Km. 6 Antigua carretera a Progreso, Apdo. Postal 73, Cordemex, 97310, Mérida, Yuc., México e Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands f Institute of Molecules and Materials (IMM), Radboud University, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands b

a r t i c l e

i n f o

Article history: Received 4 December 2016 Revised 25 May 2017 Accepted 25 May 2017 Available online 26 May 2017 Keywords: Kekulene Polycyclic aromatic hydrocarbons (PAHs) N–heterocycles DFT calculations H•••H interaction Energy decomposition analysis (EDA) H stripping

a b s t r a c t We have quantum chemically analyzed how the stability of small and larger polycyclic aromatic hydrocarbons (PAHs) is determined by characteristic patterns in their structure using density functional theory at the BLYP/TZ2P level. In particular, we focus on the effect of the nonbonded H•••H interactions that occur in the bay region of kinked (or armchair) PAHs, but not in straight (or zigzag) PAHs. Model systems comprise anthracene, phenanthrene, and kekulene as well as derivatives thereof. Our main goals are: (1) to explore how nonbonded H•••H interactions in armchair configurations of kinked PAHs affect the geometry and stability of PAHs and how their effect changes as the number of such interactions in a PAH increases; (2) to understand the extent of stabilization upon the substitution of a bay C–H fragment by either C• or N; and (3) to examine the origin of such stabilizing/destabilizing interactions. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Kekulene is a large polycyclic aromatic hydrocarbon (PAH) with formula C48 H24 , firstly synthesized by Diederich and Staab (1978). It is constituted by 12 annelated C6 cores that are arranged in the shape of a closed six-membered super-ring (see Fig. 1). Kekulene is expected to act like a “superbenzene” and, hence, a “superaromatic” system due to its planar cyclic conjugation and its D6 h structure. However, despite its 48 π -electrons neither bond length equalization nor any appreciable extra stabilization energy is perceived that would justify to consider it as a superaromatic molecule (Diederich and Staab, 1978; Krieger et al., 1979; Jiao and Schleyer 1996; Steiner et al., 2001). As any PAH, kekulene is also relevant in an either direct or indirect way in astrochemical and prebiotic biochemistry contexts. PAHs are the major repository of gaseous carbon in the galaxy (Ehrenfreund and Charnley, 20 0 0) and their presence in the in-

∗

Corresponding authors. E-mail addresses: [email protected] (J. Poater), [email protected] (F.M. Bickelhaupt). http://dx.doi.org/10.1016/j.molap.2017.05.003 2405-6758/© 2017 Elsevier B.V. All rights reserved.

terstellar medium has been proven through the observation of the so-called aromatic infrared bands in infrared emission spectra (Candian et al., 2014; Zhen et al., 2016; Tielens, 2008; Blasberger et al., 2017). Nevertheless, an unambiguous radio-frequency identification is difficult due to a small (or, in symmetrical PAHs, even nil) permanent dipole moment (Charnley et al., 2005). On the other hand, heteroaromatic PAHs involving CH/N substitution (NPAHs) are crucial in astrochemistry because, given their strong dipole moment, they can be spectroscopically detected via their rotational transitions. Furthermore, NPAHs were proposed to be involved in the astrochemical evolution of the interstellar medium (Parker et al., 2015; Koziol and Goldman, 2015). For instance, NPAHs have been detected in the atmosphere of Titan (Imanaka et al., 2004; Landera and Mebel, 2010; Ricca et al., 2001). In addition, the simplest nitrogen heterocycles, like pyridine or pyridine, may have been detected on Comet Halley (Ehrenfreund and Charnley, 20 0 0). Even though pyridine itself has not been confirmed to be detected, it is relevant in its role of the archetypal building block of biomolecules that have been observed, such as, nucleobases or NPAHs (Parker et al., 2015). A variety of such (hetero) aromatic compounds are confirmed to play a key role in terrestrial

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J. Poater et al. / Molecular Astrophysics 8 (2017) 19–26

˚ computed at the BLYP/TZ2P level. Fig. 1. Definition of C–H groups in anthracene, phenanthrene and kekulene together with bond distances (in A),

biochemistry and were almost certainly crucial ingredients in prebiotic chemistry of the Earth (Ehrenfreund et al., 2006). So, clearly the structural and bonding properties of PAHs are of importance for many areas of chemistry. Particularly, the nature of the interactions between adjacent hydrogen atoms in PAHs is an essential issue. PAHs may have, among others, zigzag edges, such as in the linear anthracene molecule, and armchair edges, such as in the bent or kinked phenanthrene molecule (see Fig. 1). The former has solo hydrogen atoms, that is, non-adjacent hydrogens or hydrogens pointing away from each other. On the other hand, kinked PAHs with armchair edges have pairs of hydrogens, in the so-called bay regions, that are oriented towards each other (A and B in phenanthrene, Fig. 1). Introducing a kink in a PAH stabilizes the system with respect to its linear isomer, despite the occurrence of sterically crowded bay hydrogens in the kinked PAH. This is illustrated by the archetypal linear and kinked PAHs, anthracene and phenanthrene, respectively. The higher stability of the kinked phenanthrene compared to the linear anthracene was previously examined by means of molecular orbital (MO) and quantitative bond energy decomposition analyses (EDA) (Poater et al., 2007a). The nonbonded H•••H interaction in the bay region of phenanthrene is not responsible of such stability because it is Pauli repulsive and hence destabilizing (Poater et al., 2007a). This outcome was supported by numerical experiments removing bay hydrogens of phenanthrene, which enhances the stability of kinked system relative to a corresponding linear form. Spectroscopic evidence for the repulsive nature of the H•••H interaction in phenanthrene was provided by Grimme and Erker (Grimme et al., 2009). These findings falsify earlier atoms-in-molecules (AIM) investigations, which claimed that the H•••H interactions are stabilizing and that they are responsible for the higher stability of phenanthrene relative to anthracene (Matta et al., 2003). Kekulene is an interesting case for exploring the nature of larger PAHs and how they are affected by nonbonded H•••H interactions. It contains six such H•••H interactions in its internal bay or cavity, in contrast to only one such H•••H interaction in phenan-

threne. Herein, we quantum chemically analyze how the stability of small and larger PAHs is determined by patterns in their structure using density functional theory at the BLYP/TZ2P level. In particular, we focus on the effect of the nonbonded H•••H interactions that occur in the bay region of kinked (or armchair) PAHs, but not in straight (or zigzag) PAHs. Our model systems comprise anthracene, phenanthrene, and kekulene and derivatives thereof. We aim at three main objectives: (1) to explore how nonbonded H•••H interactions in armchair configurations of kinked PAHs play on the geometry and stability as the number of such interactions in a PAH increases; (2) to understand the extent of stabilization upon the substitution of a bay C–H fragment by either C• or N; and (3) to examine the origin of such stabilizing/destabilizing interactions. To this end, we first formulate the hypothesis that if close H•••H contacts are destabilizing, then removing one of the involved H atoms would relieve it. Later on, the analysis is complemented by substituting the C–H groups from which H atoms were stripped by N atoms. What makes the resulting hetero PAHs interesting is that they are significantly more viable than their equivalent PAH radicals and biradicals. Thus, they also offer a way to probe the effect of switching off destabilizing H•••H interactions experimentally! Besides, hetero PAHs are also relevant for astrochemistry, as pointed out above. Finally, in order to clarify the nature of the bonding in the various situations, we extend our detailed bonding analyses to simple bimolecular model systems, [X•••Y], with all possible combinations of X, Y = nonaromatic CH4 , CH3 • and NH3 ; or aromatic C6 H6 , C6 H5 • and C5 H5 N, arranged in such a way that the mutual distance of the [C] –H, [C]• and [N] moieties correspond to those in our aromatic and heteroaromatic PAH models. 2. Methods 2.1. General procedure All computations were done with the ADF program (te Velde et al., 2001; http://www.scm.com) using the BLYP functional in


conjunction with a TZ2P basis set (Slater 1974; Becke, 1988; Lee et al., 1988; Johnson et al., 1993; Russo et al., 1994). The unrestricted formalism was used for open-shell species. The TZ2P is a large uncontracted set of Slater-type orbitals (STOs), containing diffuse functions, which is of triple-ζ quality and has been augmented with two sets of polarization functions: 2p and 3d on hydrogen and 3d and 4f on carbon. All stationary points were characterized through harmonic vibrational frequency analysis. Ab initio calculations were performed at the coupled cluster level with single, double, and perturbative triple excitations, using Dunning’s correlation consistent augmented triple-ζ (cc-pVTZ) basis set at optimized BLYP/TZ2P molecular geometries. These calculations were done with the Gaussian 09 program (Raghavachari et al., 1989; Kendall et al., 1992; Frisch et al., 2009). The agreement between our calculated and the ab initio data justifies the correct election of the BLYP/TZ2P level. 2.2. Bonding analyses In order to obtain a deeper insight into the origin of the stability trends, we analyzed the nature of the interaction between molecular fragments of selected model systems in the framework of Kohn-Sham molecular orbital (MO) theory using a quantitative energy decomposition analysis (EDA) (Bickelhaupt and Baerends, 20 0 0; Poater et al., 2006a; Bickelhaupt et al., 1992; Ziegler and Rauk, 1977). Here, the interaction energy (Eint ) is decomposed into electrostatic attraction, Pauli repulsive orbital interactions, and stabilizing orbital interactions:

Eint = Velstat + EPauli + Eoi

(1)

Velstat corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the fragments that adopt their positions in the overall molecule and it is usually attractive. EPauli comprises the destabilizing interactions between occupied orbitals and it is responsible for the steric repulsion. This repulsion is caused by the fact that, as a consequence of the Pauli principle, two electrons of same spin cannot occupy the same region in space. Finally, Eoi accounts for electron-pair bonding, charge transfer (i.e., donor–acceptor interactions between occupied orbitals on one moiety with unoccupied orbitals of the other, including HOMO–LUMO interactions), and polarization (empty– occupied orbital mixing on one fragment because of the presence of another fragment). Electron density distributions have been analyzed using Voronoi deformation density (VDD) atomic charges (Fonseca Guerra et al. 2004; Bickelhaupt et al., 1996). Quantumtheory of atoms-in-molecules (QTAIM) analysis has also been carried out with ADF (Rodríguez et al., 2009a,b; Rodríguez, 2013). 3. Results and discussion 3.1. Anthracene and phenanthrene Let us first consider anthracene and phenanthrene. In line with previous work, we find that the latter is 4.3 kcal/mol more stable than the former at the BLYP/TZ2P level (Poater et al., 2007a; Randic´ ´ 2003; Portella et al., 2005a,b; Cyranski et al., 20 0 0; Hemelsoet et al., 2005; Fukui, 1982). The higher stability of phenanthrene is the result of more favorable interactions in the π -electron system and not due to the stabilizing H•••H interaction in the bay region (Poater et al., 2007a). The latter is in fact destabilizing due to steric (Pauli) repulsion between the bay C–H bonds that point toward each other (Poater et al., 2007a). Based on this physical picture of repulsive bay C–H•••H–C interactions, one may speculate that structural motifs in PAHs involving this type of close H•••H contacts cause a destabilization which is relieved in the radical or biradical species in which the

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hydrogen atoms involved are removed. This is relevant because it would also imply that C–H bonds in bay regions are destabilized and may strip off their hydrogen atoms more easily in all kinds of PAHs. Here, we systematically explore this hypothesis and we start out with the already well-known anthracene and phenanthrene. Our results obtained at the BLYP/TZ2P level are collected in Table 1. In the case of anthracene, there is only a tiny difference in homolytic bond dissociation energies (BDE1s) between the different C–H bonds: all of them are between 115.1 and 115.2 kcal/mol (see Table 1). However, the situation is different for phenanthrene: stripping off a hydrogen atom from a C–H bond in the bay region, leading to Phe(A), costs a BDE1 of 113.4 kcal/mol, which is about 1.6 kcal/mol less than for any of the other H atoms. Our BDE1 values for Phe(A) and Phe(E) agree well with MP2 and QCISD(T) values computed earlier (Blanquart, 2015). This effect is reproduced again if we examine homolytic cleavage of a second C–H bond leading to the corresponding biradicals in their lowest-energy triplet state. Again, for anthracene, the energy required to remove a second H atom (BDE2) is quite similar for the various positions and almost the same as BDE1, between 115.2 and 116.0 kcal/mol. There is one exception, namely, Ant(C,D), in which case stripping the second H atom costs 122.8 kcal/mol. This high BDE2 value can be ascribed to the fact that the resulting product fragment, Ant(C,D), is destabilized by the relatively high exchange repulsion between the neighboring same-spin radical centers that are formed by removing two H atoms from vicinal positions in the terminal ring. This destabilization raises the energy of Ant(C,D) by about 7 kcal/mol as compared to other cases in which the radical centers are further away from each other. On the other hand, the biradicals in phenanthrene which involve one H atom of the bay region present quite similar BDE2 values (115.1–115.9 kcal/mol). The removal of two H atoms from the bay region, leading to Phe(A,B), does not yield the lowest energy structure by only 0.8 kcal/mol. This implies that the abstraction of one H atom from the bay region is enough to remove the repulsive interaction. The only exception is Phe(B,C) (BDE2 destabilized by 8.2 kcal/mol), which experiences a similar destabilization as for previous Ant(C,D) that stems from repulsion between parallel spins on contiguous radical C atoms in the outer ring (Poater et al., 2007b). The same effect is also observed for Phe(C,D) and Phe(D,E) (6.8 and 8.1 kcal/mol higher in BDE2, respectively). Note that BDE2 in the former is somewhat smaller because of the longer C–C bond between the radical C atoms than in the case of ˚ respectively). Thus, a larger distance the latter (1.410 vs. 1.383 A, between the parallel spins in the vicinal biradical results in a lower Pauli repulsion which is, in turn, responsible for lower BDE2 values. In those cases, where the second hydrogen atom is stripped directly next to the first one (i.e., two contiguous C–H bonds are broken), the triplet biradical of the remaining organic fragment is not the ground state. Instead, a closed-shell singlet configuration becomes the ground state, in which the electrons of the two adjacent carbon radicals pair up to form an additional carbon–carbon π bond (Poater et al., 2007b). This happens in our model systems in the cases Ant(C,D)CS , Phe(B,C)CS , Phe(C,D)CS , and Phe(D,E)CS , but also in the double-stripped kekulene species Kek(B,C)CS (see Table 1: subscript CS indicates the closed-shell species with the extra π bond). The extra π bond occurs in a geometrically strained context, yet it provides an additional stabilization of about 34– 39 kcal/mol as compared to their corresponding triplet biradical (see Table 1). The second C–H bond dissociation energy (BDE2) in those cases is accordingly lower in energy. Thus, although the triplet biradical is the appropriate state for a consistent comparison of all species that serves to determine the magnitude of the H•••H repulsion in the parent compound, it is the closed-shell

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J. Poater et al. / Molecular Astrophysics 8 (2017) 19–26 Table 1 Homolytic bond dissociation energies (in kcal/mol) for stripping one (BDE1, doublet monoradical) or two (BDE2, triplet biradical) H atoms from positions A-I in anthracene, phenanthrene or kekulene.a , b Anthracene

BDEb

Phenanthrene

BDEb

Kekulene

BDEb

Monoradical (BDE1) Ant(A) Ant(B) Ant(D)

115.1 (0.0) 115.2 (0.1) 115.2 (0.1)

Phe(A) Phe(C) Phe(D) Phe(E) Phe(F)

113.4 115.2 115.4 115.2 115.0

Kek(A) Kek(B) Kek(F)

115.3 (4.9) 114.9 (4.5) 110.4 (0.0)

Biradical (BDE2) Ant(A,B) Ant(A,C) Ant(B,D) Ant(C,D)

116.0 (0.8) 115.2 (0.0) 115.6 (0.4) 122.8 (7.6)

Phe(A,B) Phe(A,C) Phe(A,D) Phe(A,E) Phe(A,F) Phe(B,C) Phe(C,D) Phe(D,E) Phe(E,F)

115.9 (0.8) 115.6 (0.4) 115.4 (0.3) 115.3 (0.1) 115.1 (0.0) 123.3 (8.2) 121.9 (6.8) 123.2 (8.1) 115.6 (0.5)

Kek(A,B) Kek(A,C) Kek(A,D) Kek(B,C) Kek(F,G) Kek(F,H) Kek(F,I)

115.8 (6.4) 115.2 (5.9) 115.4 (6.0) 122.6 (13.3) 112.4 (3.1) 109.7 (0.4) 109.4 (0.0)

Extra π bond (BDE2)c Ant(C,D)CS

84.1

Phe(B,C)CS Phe(C,D)CS Phe(D,E)CS

84.6 87.5 85.5

Kek(B,C)CS

81.7

(0.0) (1.8) (2.0) (1.8) (1.6)

a

Computed at the BLYP/TZ2P level. See Fig. 1 for definitions of positions. Relative energies ࢞Erel of resulting mono- or biradical species in parentheses. Homolytic BDE2 in the case of stripping two H atoms from contiguous carbon atoms under formation of a closed-shell singlet fragment (subscript CS) involving an extra C–C π bond instead of a triplet biradical species. b c

singlet state that determines the lowest-energy pathway for stripping a second hydrogen atom from a vicinal carbon atom. 3.2. Kekulene Next, we move to the larger and more complex kekulene system. This PAH possesses six vicinal H•••H repulsive interactions in the bay region, instead of only one as in the above-discussed phenanthrene. One may, therefore, envisage an amplification of effects. Note that although the H•••H interactions among the six H atoms in the bay region of kekulene are repulsive in nature, this molecule does not undergo deformation from planarity and preserves planar (D6 h ) symmetry. Apparently, although H•••H repulsions cause destabilization, the strain created is compensated by an efficient bonding in the π -electron system, akin to the situation in phenanthrene. In other words, kekulene prefers to maintain planarity to keep its π -electron system intact, rather than undergoing deformation in order to avoid H•••H repulsions in the bay area. We have analyzed kekulene using the same procedure as for the smaller PAHs. What we find is that removing one H atom from kekulene’s bay region costs 4.5 kcal/mol less energy than from the outside zigzag edge: BDE1 = 110.4 kcal/mol for Kek(F) vs. 114.9 kcal/mol for Kek(B). This difference is about two times larger than the corresponding one discussed for phenanthrene because the removal of one H atom causes the simultaneous disappearance of two destabilizing vicinal H•••H interactions. Our analyses furthermore reveal that kekulene’s inner C–H bond-weakening effect stemming from H•••H repulsion is still present if a second H atom is abstracted from the inner region of kekulene. Thus, BDE2 values of inner C–H bonds are similar to the inner BDE1, and still weaker than a regular arylic C–H bond, such as an outer BDE1 of kekulene. The abstraction of a second inner H atom to yield Kek(F,I) or Kek(F,H) is energetically less costly with a BDE2 of 109.4–109.7 kcal/mol than for Kek(F,G) with a BDE2 value of 112.4 kcal/mol, respectively. The reason for this is that in the case of Kek(F,I) and Kek(F,H) more H•••H interactions are removed. In contrast, in the case of the H atoms at the outer zigzag edge, the position from which the second H atom is abstracted

does not matter, with variations in BDE2 of not more than only 0.5 kcal/mol among Kek(A,B), Kek(A,C) and Kek(A,D). The only exception occurs when two contiguous H atoms are stripped as in the case of Kek(B,C) for which we find a sizable stabilization associated with going from two neighboring same-spin radical centers to a closed-shell configuration with pairing up of two electrons to form an extra π bond: Kek(B,C)CS is 41 kcal/mol more stable than the triplet biradical Kek(B,C) (see Table 1). Thus, similar to the situation found for stripping contiguous hydrogen atoms from anthracene or phenanthrene, we find that the lowest energy pathway for stripping two contiguous H atoms leads to the closed-shell singlet species Kek(B,C)CS and not to the triplet Kek(B,C). Our computational results are evidence of H•••H steric (Pauli) repulsion between the inner H atoms of kekulene. They also show that kekulene’s inner C–H bonds are exceptionally weak. Such weakness of the bay H atoms should have implications in the photodissociation of these species, i.e., the weakest bonds dissociate first (Buch, 1989; Petrignani et al., 2016; Zhen et al., 2016). 3.3. N–heteroaromatic analogues of anthracene and phenanthrene The above numerical experiments are now complemented by substituting the C–H groups from which H atoms were stripped by N atoms, yielding N–heterocyclic PAHs or NPAHs (see Table 2). NPAHs are significantly more viable species than the abovediscussed PAH radicals and biradicals. Note that while the H stripping analyses were discussed in terms of relative C–H bond strength, this is evidently not possible for the corresponding N substituted heterocycles in which there is no H atom at those substituted positions. Instead, we will examine the relative stability, ࢞Erel , of the various N substituted isomers which are collected in Table 2. For anthracene, the singly (within 2.4 kcal/mol) and doubly (within 0.7 kcal/mol) N-substituted isomers are, with one exception, all relatively close in energy, similar to the situation for the corresponding anthracene mono- and biradicals resulting from single and double H-atom stripping, respectively (compare the data in Tables 2 and 1). The exception occurs again, as in the case


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Scheme 1. Model systems for analyzing intramolecular interactions in phenanthrene derivatives; see also text. Table 2 Relative energy ࢞Erel (in kcal/mol) to the most stable isomer of substituting one or two CH groups by N atoms of positions A-I in anthracene, phenanthrene, or kekulene.a Anthracene

࢞Erel

Phenanthrene

࢞Erel

Kekulene

࢞Erel

Monosubstituted Ant-N(A) Ant-N(B) Ant-N(D)

1.3 0.0 2.4

Phe-N(A) Phe-N(C) Phe-N(D) Phe-N(E) Phe-N(F)

0.0 2.6 1.4 2.2 1.0

Kek-N(A) Kek-N(B) Kek-N(F)

7.3 7.9 0.0

Disubstituted Ant-N(A,B) Ant-N(A,C) Ant-N(B,D) Ant-N(C,D)

0.0 0.4 0.7 21.2

Phe-N(A,B) Phe-N(A,C) Phe-N(A,D) Phe-N(A,E) Phe-N(A,F) Phe-N(B,C) Phe-N(C,D) Phe-N(D,E) Phe-N(E,F)

5.0 2.0 1.5 0.0 0.6 21.0 21.6 22.0 2.8

Kek-N(A,B) Kek-N(A,C) Kek-N(A,D) Kek-N(B,C) Kek-N(F,G) Kek-N(F,H) Kek-N(F,I)

18.0 17.9 16.5 38.1 8.2 1.7 0.0

a

Computed at the BLYP/TZ2P level. See Fig. 1 for definitions of positions.

of H stripping, when positions C and D are substituted: Ant-N(C,D) is 21.2 kcal/mol higher in energy than Ant-N(A,B). This exceptionally high destabilization originates from the occurrence of a highly unstable N–N bond in one of the outer rings of Ant-N(C,D). Previously, bonding analyses showed that the higher stability of such pyrimidine compared to pyridazine systems originates, among others, from more favorable σ -orbital interactions in the 1,3-isomer as well as from more closed-shell/closed-shell Pauli repulsion in the 1,2-isomer (El-Hamdi et al., 2011; Bickelhaupt et al., 1992; Krapp et al., 2006). For phenanthrene, mono-substituted Phe-N(A) is the most stable isomer. For example, substitution of C–H by N at position C yields a mono-substituted isomer, Phe-N(C), that is 2.6 kcal/mol higher in energy than Phe-N(A) (see Table 2). In general, all other mono-N-substituted phenanthrene-derived hetero-PAHs are higher in energy than Phe-N(A) by 1.0–2.6 kcal/mol. Note that the variation in the relative energies of N-substituted phenanthrene isomers (Table 2: 1.0–2.6 kcal/mol) is slightly larger (i.e., less constant) than the variation in stability in the case of the H-stripped

phenanthrene radicals (Table 1: 1.6–2.0 kcal/mol). This can be ascribed to the fact that N-substitution not only eliminates H•••H repulsion but also affects the π -electron system, a phenomenon that interferes with the former effect. For the doubly N-substituted phenanthrene systems, we find a few marked differences in the trends of relative energies as a function of the position at which the substitution occurs as compared to the doubly H-stripped phenantrene radicals. The most stable system is Phe-N(A,E), involving only one N in the bay region. All other isomers involving one N in the bay are very close in energy, i.e., Phe-N(A,C), Phe-N(A,D), and Phe-N(A,F)) to Phe-N(A,E). This can be traced to the fact that a C–H•••N interaction is more stable than either C–H•••H–C or C• •••• C (vide infra). The occurrence of a direct N–N bond in one of the doubly N-substituted phenanthrene rings, i.e., in the case of Phe-N(B,C), Phe-N(C,D) and Phe-N(D,E), significantly destabilizes the system by more than 20.0 kcal/mol relative to Phe-N(A,E) (see Table 2); this trend is very similar to the situation for the doubly N-substituted anthracene isomer Ant-N(C,D) (vide supra). Interestingly, the doubly N-substituted hetero-phenanthrene Phe-N(A,B) is not the most stable isomer. In fact, this isomer is destabilized by 5.0 kcal/mol with respect to Phe-N(A,E) (see Table 2). Our bonding analyses reveal that the latter is caused by the fact that N•••N interactions between the bay N atoms in Phe-N(A,B) are even more destabilizing than the corresponding H•••H interactions in Phe. These bonding analyses are based on two series of fictitious systems that model the various types of intramolecular bonds in terms of two molecular fragments, thus allowing for the computation of an interaction energy. The first series consists of the relatively small, nonaromatic 1a, 2a, and 3a, and derivatives thereof, whereas the second series models have the same intramolecular interactions using the aromatic 4a, 5a, and 6a, and derivatives thereof (see Scheme 1). Species 1a, 2a, and 3a consist of two methane, one methane and one ammonia, and two ammonia molecules, respectively. In this way, we focus on C and N atoms alone, avoiding the possible influence of the aromatic rings. All species are in their own equilibrium geometry, arranged in an eclipsed D3 h or C3 v conformation in such a way that they reproduce the close contacts of interest, that is, C–H•••H–C, C–H•••N

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J. Poater et al. / Molecular Astrophysics 8 (2017) 19–26 Table 3 Energy decomposition analysis (in kcal/mol) for various nonbonded interactions in nonaromatic model systems inspired by phenanthrene and derivatives thereof together with CCSD(T)/cc-pVTZ data.a System 1ab 1bc 1cc 2ad 3ae

H3 C–H•••H–CH3 H3 C–H•••• CH3 H3 C• •••• CH3 H3 C–H•••NH3 H3 N•••NH3

EPauli

Velstat

Eoi

࢞Espin-pol

Eint

Eint CCSD(T)

1.97 0.68 0.62 3.49 10.76

−0.40 −0.39 0.10 −2.10 1.57

−0.85 −1.76 −3.08 −1.25 −1.46

0.00 1.45 2.91 0.00 0.00

0.72 −0.01 0.56 0.13 10.87

0.26 −0.31 0.16 −1.20 9.59

a EDA computed at the BLYP/TZ2P level: CH4 and NH3 molecules fully optimized and positioned in eclipsed conformation. ࢞Espin-pol is the spin polarization of open-shell fragments. VDD atomic charges in fragments: H3 C–H, q(C) = − 0.08 a.u.; H3 C•, q(C) = − 0.03 a.u.; and H3 N, q(N) = − 0.24 a.u.. b ˚ as in bay H•••H of phenanthrene. Two CH4 molecules with H•••H distance (2.020 A) c Calculated at the same geometry as system 1a, but removing one H atom (system 1b) or two H atoms (system 1c). d ˚ as in Phe-N(A). CH4 and NH3 molecules with H•••N distance (2.503 A) e ˚ as N•••N in Phe-N(A,B) (system 3a). Two NH3 molecules with N•••N distance (2.785 A)

and N•••N with exactly the H•••H, H•••N and N•••N distances as in phenanthrene, phe-N(A), or phe-N(A,B), respectively (see Scheme 1). In addition, we examine the C–H•••• C and C• •••• C interactions in doublet 1b and triplet 1c that occur if we strip one or both close-contact H atoms in 1a. The results of the corresponding energy decomposition analyses (EDA) are collected in Table 3. System 1a indeed reveals a repulsive H•••H interaction of 0.7 kcal/mol, caused by a Pauli repulsion term of 2.0 kcal/mol between C–H bonding orbitals on either CH4 fragment (see Table 3). If one hydrogen atom is removed (system 1b), the C–H•••• C interaction becomes essentially zero (−0.01 kcal/mol) which is due to the decrease of Pauli repulsion to only 0.7 kcal/mol. If the second H atom is removed (system 1c), the Pauli repulsion further decreases to 0.6 kcal/mol. Yet, the C• •••• C interaction is repulsive by 0.6 kcal/mol because of an unfavorable electrostatic interaction between the negatively charged C atoms (−0.03 a.u.) of the long C• •••• C moiety and the relatively large spin-polarization in the case of two radical fragments. Next, system 2a reveals that, despite more Pauli repulsion, the C–H•••N interaction (࢞Eint = 0.1 kcal/mol) is more stable than the C–H•••H–C interaction (࢞Eint = 0.7 kcal/mol) because of more favorable electrostatic and orbital interactions (see Table 3). The N•••N interaction in 3a appears to be the most repulsive one (10.9 kcal/mol) among the various types of interaction studied here (see Table 3). The destabilizing nature mainly originates from a strong Pauli repulsion between the nitrogen lone pairs, together with destabilizing electrostatic interactions between the negatively charged N atoms (−0.24 a.u.). We note that our interaction energies ࢞Eint computed at BLYP/TZ2P agree well with those of our ab initio benchmark values ࢞Eint CCSD(T) computed at CCSD(T)/cc-pVTZ level (see Table 3). The CCSD(T) data are consistently a few tenths to ca. 1 kcal/mol more stabilizing but they show exactly the same trend. For example, ࢞Eint CCSD(T) is repulsive by 0.3 kcal/mol for the H•••H interaction, −1.2 kcal/mol stabilizing for C–H•••N and +9.6 kcal/mol repulsive for N•••N. The above bonding analyses for the simpler nonaromatic model systems 1–3 are confirmed by equivalent analyses of the more realistic, aromatic systems 4–6 consisting of benzene and pyridine fragments (see Scheme 1 and Table 4). The data in Table 4 show again that also for arylic C–H and N moieties, C–H•••H–C interactions are repulsive, C–H•••N interactions are more stable than the former, whereas N•••N interactions are significantly more repulsive in nature. The only relevant difference between the two sets is when going from 2a to 5a. Because of its staggered conformation, the latter presents a lower ࢞EPauli by 0.30 kcal/mol than that in the former with the eclipsed form. But, most importantly, 5a also presents a 0.50 kcal/mol more stabilizing ࢞Velstat due to the

more positive charge on the H pointing to the N than those in 2a (0.05 a.u.in 5a vs. 0.02 a.u. in 2a), in contrast to the N atoms that present similar charges (−0.19 a.u. in 5a vs. −0.24 a.u. in 2a). 3.4. N–heteroaromatic analogues of kekulene More drastic changes occur if we carry out C–H substitution by N in kekulene. Single N-substitution with N in the internal bay region (Kek-N(F)) is more stable by 7.3–7.9 kcal/mol than those in the outer part (Kek-N(A) and Kek-N(B)). The effect of double N-substitution is even more pronounced. Substitution of para-positioned C–H groups in the internal bay region of kekulene yields the most stable isomer, Kek-N(F,I), although the meta-substituted isomer Kek-N(F,H) is only 1.7 kcal/mol higher in energy. In line with our results for Phe-N(A,B), the orthosubstituted Kek-N(F,G) isomer is substantially higher in energy, namely, by 8.2 kcal/mol. As explained above, this can be attributed to strong Pauli repulsion between the nitrogen lone-pairs. Finally, all hetero-kekulene isomers resulting from double N substitution for outer C–H groups are higher in energy by 16.5–18.0 kcal/mol, and even larger in the case of two contiguous N atoms (Kek(B,C)). This is again indicative for the enormous H•••H repulsion in the inner bay region which is relieved only by reducing the number of such close H•••H contacts. 3.5. QTAIM analyses We have also carried out quantum-theory of atoms-inmolecules (QTAIM) analysis of the bonding in selected model systems (Bader, 1990). The resulting molecular graphs in Fig. 2 reveal a bond path along with a bond critical point in between two H atoms in the bay regions of both phenanthrene and kekulene. However, note that as soon as any of the two CH groups involved in the bay region of phenanthrene or kekulene is converted into a radical or substituted by an N atom, the corresponding bond critical point disappears (see Fig. 2c). According to QTAIM, this signals the presence of a stabilizing interaction in the original systems and the loss of the bonding interaction after H-stripping or N-substitution. This is in sharp contradiction with our computational exploration and bonding analyses above, which show that H•••H interactions destabilize the isomers in which they occur and those isomers in which such H•••H interactions are eliminated become relatively more stable. This is yet a further falsification of the interpretation in QTAIM that bond paths and bond critical points can be associated with a stabilizing contact (see also: Poater et al., 2006a,b; Cioslowski and Mixon, 1992a,b; Frenking, 2003; Frenking et al., 2006; Cerpa et al., 20 08,20 09).


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Table 4 Energy decomposition analysis (in kcal/mol) for various nonbonded interactions in aromatic model systems inspired by phenanthrene and derivatives thereof.a System 4ab 4bc 4cc 5ad 6ae

H5 C6 –H•••H–C6 H5 H5 C6 –H•••• C6 H5 H5 C6 • •••• C6 H5 H5 C6 –H•••NC5 H5 H5 C5 N•••NC5 H5

EPauli

Velstat

Eoi

࢞Espin-pol

Eint

1.75 0.72 0.62 3.19 10.39

−0.13 −0.58 0.20 −2.60 0.82

−0.95 −2.17 −4.08 −1.32 −1.65

0.00 1.89 3.78 0.00 0.00

0.67 −0.14 0.52 −0.73 9.56

a Computed at BLYP/TZ2P: C6 H6 and C5 H5 N molecules fully optimized and positioned in perpendicular conformation. ࢞Espin-pol is the spin polarization of open-shell fragments. VDD atomic charges in fragments: H5 C6 –H, q(C) = − 0.05 a.u.; H5 C6 •, q(C•) = − 0.05 a.u.; and H5 C5 N, q(N) = − 0.19 a.u. b ˚ as in bay H•••H of phenanthrene. Two C6 H6 molecules with H•••H distance (2.020 A) c Calculated at the same geometry as system 4a, but removing either one (system 4b) or two (system 4c) hydrogen atoms. d ˚ as in Phe-N(A). C6 H6 and C5 H5 N molecules with H•••N distance (2.503 A) e ˚ as N•••N in Phe-N(A,B) (system 6a). Two C5 H5 N molecules with N•••N distance (2.785 A)

Fig. 2. QTAIM molecular graphs with bond critical points (red), ring critical points (green) and bond paths of: a) anthracene, b) phenanthrene, c) Phe-N(A), d) kekulene, and e) Kek-N(F,H). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

4. Conclusions Nonbonded H•••H interactions in bay regions or internal cavities of small and large polycyclic aromatic hydrocarbons (PAHs) are destabilizing. These repulsive interactions weaken the C–H bonds involved in the C–H•••H–C moiety which may lead to more facile H-stripping processes. Interestingly, kinked PAHs, in which such sterically crowded bay H atoms occur, can still be more stable than linear or bay-less PAHs because of more efficient bonding in the π -electron system. The loss of a second H atom is energetically facile if that second C–H bond is adjacent to the first one. The reason is the formation of a closed-shell configuration of the doubly H-stripped PAH which corresponds to the formation of an additional carbon–carbon π bond. The H•••H repulsion is the result of Pauli repulsion between closed-shell C–H bonding orbitals of each of the two C–H bonds

that are oriented towards each other. Thus, our results once more falsify the QTAIM interpretation which signals stabilizing H•••H bonds whereas their effect is a destabilization. H•••H bond paths and bond critical points indeed exist but interpreting them as an indicator of stabilizing contacts is wrong. Rather, these features are symptoms of proximity between two atomic charge distributions. Such close contacts can be either destabilizing due to closed-shell (Pauli) repulsion, as in model systems of this study, or stabilizing, for example, due to dominant donor–acceptor orbital interactions. Finally, besides their astrochemical relevance, our results are also of importance for chemical bonding theory and chemistry in general. Our quantum chemical analyses have revealed the destabilizing nature of nonbonded H•••H interactions in PAHs through bonding analyses as well as by computationally demonstrating the stabilizing effect of eliminating them. This is done by stripping the involved H atoms. The resulting mono- and triplet biradical

26


species are, however, elusive and obtaining them as structurally well-defined and pure samples is a challenge. In an alternative approach, we have demonstrated the destabilizing nature, e.g., in the internal cavity of kekulene, also through substitution of C–H by N. Note that most of the resulting singly or doubly N-substituted hetero-PAHs are in principle viable species. If they exist, they could be handled in a laboratory setting more easily, opening the possibility of an experimental thermodynamic analysis and, thus, an experimental verification of the destabilizing nature of nonbonded H•••H interactions. This shifts the challenge now to organic and physical chemistry with the hetero-PAHs in question as targets for synthesis and thermochemical analysis. Acknowledgments We thank the Netherlands Organization for Scientific Research (NWO) for financial support through the Dutch Astrochemistry Network (DAN) and the Spanish MINECO (project CTQ201677558-R). The work in Mexico was funded by Conacyt (Grant CB-2015-252356). Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.molap.2017.05.003. References Bader, R.F.W., 1990. Atoms in Molecules: A Quantum Theory. Clarendon Press, Oxford. Becke, A.D., 1988. PhRvA 38, 3098. Bickelhaupt, F.M., Nibbering, N.M.M., van Wezenbeek, E.M., Baerends, E.J., 1992. JPhCh 96, 4864. Bickelhaupt, F.M., van Eikema Hommes, N.J.R., Fonseca Guerra, C., Baerends, E.J., 1996. Organometallics 15, 2923. Bickelhaupt, F.M., Baerends, E.J., 20 0 0. In: Lipkowitz, K.B., Boyd, D.B. (Eds.). Reviews in Computational Chemistry, vol. 15. Wiley-VCH, New York. Blanquart, G., 2015. IJQC 115, 796. Blasberger, A., Behar, E., Perets, H.B., Brosch, N., Tielens, A.G.G.M., 2017. ApJ 836, 173. Buch, V., 1989. ApJ 343, 208. Candian, A., Sarre, P.J., Tielens, A.G.G.M., 2014. ApJ 791, L10.

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