Do Nonbonded H--H Interactions in Phenanthrene Stabilize It Relative

Article pubs.acs.org/JPCA

Do Nonbonded H‑‑H Interactions in Phenanthrene Stabilize It Relative to Anthracene? A Possible Resolution to this Question and Its Implications for Ligands such as 2,2′-Bipyridyl Robert D. Hancock*,§ and Igor V. Nikolayenko*,† §

Department of Chemistry and Biochemistry, University of North Carolina Wilmington, Wilmington, North Carolina, 28403, and School of Chemistry and Physics (Pietermaritzburg), University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa

†

S Supporting Information *

ABSTRACT: The problem of whether interactions between the hydrogen atoms at the 1,10-positions in the “cleft” of the “bent” phenanthrene stabilize the latter molecule thermodynamically relative to “linear” anthracene, or whether the higher stability of phenanthrene is due to a more energetically favorable π-system, is considered. DFT calculations at the X3LYP/cc-pVTZ(-f)++ level of the ground state energies (E) of anthracene, phenanthrene, and the set of five benzoquinolines are reported. In the gas phase, “bent” phenanthrene was computed to be thermodynamically more stable than “linear” anthracene by −28.5 kJ mol−1. This fact was attributed predominantly to the phenomenon of higher aromatic stabilization of the π-system of phenanthrene relative to anthracene, and not to the stabilizing influence of the nonbonding H--H interactions in its cleft. In fact, these interactions in phenanthrene were shown to be destabilizing. Similar calculations for five benzoquinolines (bzq) indicate that ΔE values vary as: 6,7-bzq (linear) ≤ 2,3-bzq (linear) < 5,6-bzq (bent) ≤ 3,4-bzq (bent) < 7,8-bzq (bent, no H--H nonbonding interactions in cleft), supporting the idea that it is a more stable π-system that favors 7,8-bzq over 2,3-bzq and 6,7-bzq, and that the H--H interactions in the clefts of 3,4-bzq and 5,6-bzq are destabilizing. Intramolecular hydrogen bonding in the cleft of 7,8-bzq plays a secondary role in its stabilization relative 6,7-bzq. The question of whether H--H nonbonded interactions between H atoms at the 3 and 3′ positions of 2,2′-bipyridyl (bpy) coordinated to metal ions are stabilizing or destabilizing is then considered. The energy of bpy is scanned as a function of N−C−C−N torsion angle (χ) in the gas-phase, and it is found that the trans form is 32.8 kJ mol−1 more stable than the cis conformer. A relaxed coordinate scan of energy of bpy in aqueous solution as a function of χ is modeled using the PBF approach, and it is found that the trans conformer is still more stable than the cis, but now only by 5.34 kJ mol−1. The effect that the latter energy has on the thermodynamic stability of complexes of metal ions with bpy in aqueous solution is discussed. advanced the controversial view that it is in fact “bond paths” between the two closely approaching H atoms in the cleft of phenanthrene that stabilize it relative to anthracene. These two H atoms in phenanthrene are separated by 2.057 ± 0.070 Å in the five structures reported in the Cambridge Structural Database (CSD)3 that contain a phenanthrene molecule without a metal atom coordinated to any of its aromatic rings, Scheme 1. The H--H separation of 2.057 Å in the cleft of phenanthrene is considerably shorter than the sum of the van der Waals radii4 of 2.40 Å for two nonbonded H atoms. Such a close approach of two nonbonded H atoms has traditionally been regarded as a destabilizing interaction. The QTAIM (quantum theory of atoms in molecules) approach of Bader,2 and the suggestion that short H--H interactions stabilize phenanthrene relative to anthracene,

I

t has been known for some time1 that phenanthrene is thermodynamically more stable than anthracene, Scheme 1, as indicated by the enthalpy of formation in the gas-phase, ΔfH⊖. This has traditionally been attributed to a more stable π-system for “bent” phenanthrene than for “linear” anthracene. Bader2 has Scheme 1. Anthracene and Phenanthrene and the Close Approach of the Two H Atoms in the Cleft of Phenanthrene,3 Showing the Gas Phase ΔfH⊖ Values.1

Received: January 2, 2012 Revised: July 20, 2012 Published: July 23, 2012 © 2012 American Chemical Society

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dx.doi.org/10.1021/jp300035w | J. Phys. Chem. A 2012, 116, 8572−8583

The Journal of Physical Chemistry A

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has been criticized,5−14 with a subsequent paper by Bader defending these ideas.15 The QTAIM bond-path approach has been extended to an analysis of biphenyl.16 If H--H interactions in biphenyl are as strong as suggested16 by the QTAIM approach, then the minimum energy structure of biphenyl should be planar. DFT calculations17 indicate that the lowest energy form of biphenyl has a dihedral angle (φ) of 35.5° between the two planes defined by the phenyl rings. Some 20 structures reported in the CSD3 that contain biphenyl, excluding those with a metal coordinated to biphenyl, suggest values of φ ranging from 0 to 48.1°, with an average φ = (22 ± 13)°. Clearly, a problem with solid state structures is that crystal packing forces, particularly those causing π-stacking, can affect the structure of biphenyl. Another potential problem with solid state structures where φ is fairly small is that a seemingly planar structure may be determined crystallographically, where two disordered mirror image biphenyl molecules with nonplanar D2 symmetry are superimposed. The determined structure is then an apparently planar average of the two disordered structures, with the disorder masked by thermal parameters. Possibly the most reliable structure for solid biphenyl, a neutron diffraction study at low temperature,18 indicates a value of φ = 10.0°. However, at the present time the DFT result17 of φ = 35.5° is probably to be preferred because of the likely influence of crystal packing in altering φ. A traditional way of analyzing the role of nonbonded repulsive forces in molecules has been that of molecular mechanics (MM).19−21 MM essentially quantifies, in terms of simple mathematical expressions, forces that are believed to control molecular structure. Thus, calculations by the present authors using the MM2 force field of Allinger22 indicate a nonplanar structure for biphenyl with φ = 13.3°, while the OPLS force field21 predicts φ = 27.2°, fairly close to the result of DFT calculations.17 MM calculations using MM2 suggest that the total strain energy (ΣU) for anthracene is 16.0 kJ mol−1 lower than for phenanthrene, while OPLS indicates a difference in ΣU of 26.2 kJ mol−1. The MM approach is based on traditional views of nonbonded H--H interactions, which regard close proximity of nonbonded H atoms as a source of destabilization of molecules. MM calculations suggest that in the absence of some other stabilizing factor, for example, such as a lower energy π-system, phenanthrene would be less stable than anthracene by some 21 kJ mol−1, averaging the values from the MM2 and OPLS calculations. The interest of the present authors in the problem of stabilization of phenanthrene or biphenyl by attractive H--H nonbonded interactions relates to an interest in polypyridyl ligands such as bpy, tpy, or qpy23−25 (see Figure 1 for the structures of molecules discussed in this paper). The fact that bpy forms less stable complexes than phen, as indicated by the formation constants in aqueous solution,26 has traditionally been interpreted27 in terms of the destabilizing H--H nonbonded interactions that occur in bpy complexes on coordination to a metal ion, as indicated in Scheme 2. Thus, bpy complexes of numerous metal ions are a fairly constant27 1.3 log units less stable than the corresponding phen complexes, which one could reasonably interpret in terms of the energy required to rotate the bpy from the trans to the cis conformation essential for the complex formation. In 20 structures reported in the CSD3 that contain a free bpy molecule, the bpy is always trans, with the nitrogens on opposite sides of the molecule. Of these 20 structures, 14 contain a very close to planar bpy (φ ≤ 2°). Where larger φ values are observed,

Figure 1. Molecules discussed in this paper (bzq = benzoquinoline).

Scheme 2. Close Approach of the 3,3′ H-Atoms on the 2,2′Bipyridyl Ligand (bpy) on Forming a Complex with a Metal Ion (M)

these can all be understood as arising from hydrogen-bonding (H-bonding) interactions between the N atoms of bpy and other groups in the lattice. A single structure28 that may be mistaken in the search of the CSD database as having a free cis bpy, actually has the bpy coordinated to an iodine atom that is part of an organic molecule, with very long I−N bonds not identified as bonds by the CSD software. The fact that all free bpy molecules have a planar trans structure, when not involved in distorting Hbonding interactions, indicates that in bpy, unlike the case for biphenyl, the N atoms remove the H--H steric interactions that hinder the planarity of biphenyl, and result in the expected conjugated planar trans structure for bpy. In fact, such a structure is probably further stabilized somewhat by intramolecular Hbonding of hydrogen atoms to N-donors in the cleft. It might thus be possible to have molecules that resemble anthracene and phenanthrene in their π-systems, but where the nonbonded H--H interactions can be removed by the placement of a nitrogen atom. The five benzoquinolines (bzq) present such a set of molecules. Acridine and 6,7-bzq in Scheme 3 resemble linear anthracene, and so should be the least stable isomers of bzq because of a less favorable π-system. The remaining three bzq molecules in Scheme 3 resemble phenanthrene. If H--H nonbonded interactions in the cleft of 5,6-bzq and 3,4-bzq stabilize these molecules, as they are thought2 to do for phenanthrene in terms of bond-path concepts, then these two molecules should be more stable than 7,8-bzq, where such 8573



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Table 1. Ground State Energies, E, and Relative Energies, ΔE, of Anthracene (anth), Phenanthrene (phenan), and the Five Benzoquinolines (bzq) in the Gas Phase Calculated Here at the DFT (X3LYP/cc-pVTZ(-f) ++) Level Using the Jaguar Program31

Scheme 3. Five Benzoquinoline Bases, with the Two Linear Bases above That Resemble Anthracene and the Three Bent Bases below That Resemble Phenanthrenea

molecule a

anth phenan 6,7-bzq 2,3-bzq 5,6-bzq 3,4-bzq 7,8-bzq

shape

E/hartree

ΔEd/kJ mol−1

linear bent linear linear (bent + H--H)b (bent + H--H)b (bent, no H--H)c

−539.430 694 −539.441 551 −555.474 024 −555.477 003 −555.482 827 −555.483 978 −555.485 291

0 −28.50 0 −7.82 −23.11 −26.13 −29.58

a

See Figure 1 for key to abbreviations for molecules. 6,7-bzq and 2,3bzq resemble anthracene (anth) in being linear. b5,6-bzq and 3,4-bzq resemble phenanthrene (phenan) in being “bent and in having H--H nonbonded interactions in the cleft. c7,8-bzq resembles phenanthrene in being bent but does not have H--H nonbonded interactions in the clef. dΔE is the energy of isomerization of phenanthrene (bent) to anthracene (linear), or for the benzoquinolines the energy stabilization relative to 6,7-bzq, the least stable isomer of the set of five bases.

analogues. In our view, these data lend support to the idea that bond paths between the H atoms in the cleft of phenanthrene are not responsible for its stabilization relative to anthracene, Scheme 4. However, in principle, an alternative view that relative

a

Two of the bent phenanthrene-like benzoquinolines (below left) have H--H interactions that may potentially stabilize2 or destabilize13,14 the molecules. The final benzoquinoline (below, right) resembles phenanthrene but does not have such H--H nonbonded interactions in its cleft. The ΔfH⊖ values in the gas-phase for each benzoquinoline, where known, are from refs 29 and 30.

Scheme 4. Energy of Structural Change, ΔE (Isomerization from Linear to Bent), Calculated Here from the Gas-Phase QM Ground State Energies of Molecules, Ea

interactions are absent. Conversely, if these H--H nonbonded interactions in 5,6-bzq and 3,4-bzq are destabilizing,13,14 then 7,8-bzq should be the more stable. The available thermodynamic data for benzoquinolines29,30 suggest that the linear benzoquinoline acridine has a less favorable heat of formation than do bent benzoquinolines, and indicate that 7,8-benzoquinoline has the most favorable ΔfH⊖ in the gas-phase, as required by the above idea on the destabilizing role of H--H interactions in the benzoquinolines, Scheme 3 above. However, the ΔfH⊖ values for the benzoquinolines29,30 have associated uncertainties that are large in comparison with the differences in ΔfH⊖. It was therefore decided in this work to use high-level DFT calculations of the relative ground state energies (ΔE) of the anthracene, phenanthrene, and the five benzoquinolines from Scheme 3 to bolster the results suggested by the gas-phase ΔfH⊖ values. Also reported here is a DFT analysis of bpy, and of some of its complexes with metal ions. In particular, the aim is to elucidate the role of H--H steric interactions, as illustrated in Scheme 2, in the destabilization of complexes of metal ions with bpy relative to those of phen, where such H--H interactions are absent.

a

On the left is the transition from anthracene to phenanthrene; on the right is the transition from 6,7-bzq to 7,8-bzq.

stabilization of phenanthrene is conferred by the H--H interaction in the cleft, and that of 7,8-bzq is conferred by intramolecular H-bonding, might be advanced. In order to ascertain whether the lower ground state energy of phenanthrene in comparison to anthracene arises from the stabilizing influence of H--H interactions or some other feature of molecular geometry, we have conducted the analysis of orbital shapes, energies, and populations for these two molecules (as well as 6,7bzq and 7,8-bzq). Both molecular orbitals (MOs) and natural bond orbitals (NBOs) were considered. Anthracene versus Phenanthrene. A feature of these molecular systems that readily comes to mind is their aromaticity. Prior to ascribing stabilizing influence to any of the other factors, the question of aromatic stabilization needs to be addressed. Conventionally, the higher aromatic stabilization of phenanthrene in comparison to anthracene is attributed to its higher number of principal canonical resonance forms, 5 versus 4.32 It is also well-known33 that empirical resonance energies of anthracene and phenanthrene, 351 kJ mol−1 and 381 kJ mol−1, respectively, are not much more than that of two benzene rings, 2 × 151 kJ mol−1; that is, the third ring contributes relatively little

■

RESULTS AND DISCUSSION The Source of Stabilization of “Bent” versus “Linear” Aromatic Molecules. The ground state energy of phenanthrene, computed at the DFT (X3LYP/cc-pVTZ(-f)++) level, Table 1, turned out to be 28.50 kJ mol−1 lower than that of anthracene. A very similar difference of 29.58 kJ mol−1 was computed for the analogous benzoquinoline pair, 6,7-bzq and 7,8-bzq. Hence, computational results support experimental findings of the standard enthalpies of formation in the gas phase, and reinforce the established opinion that bent aromatic (or heteroaromatic) molecules are more stable than their linear 8574



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Scheme 5. Shapes and Energies of the Bonding Molecular Orbitals (MOs) with π-Character for Anthracene and Phenanthrene

orbitals, of which natural bond orbitals (NBOs)34 have become a popular choice. Results relevant to the π-system part of the NBO analysis,35 carried out by means of the Jaguar software,31 are presented in Table 2. Canonical molecular structures derived from this analysis and the numbering schemes for the two molecules in question are shown in Scheme 6. As can be seen from this scheme, the π-system of anthracene is characterized by six π-type bonding orbitals and two lone pair orbitals, one bonding another antibonding, centered on carbon atoms C2 and C1, respectively (they effectively represent the seventh double bond). The population of each π-orbital is significantly reduced from the expected two electrons, see Table 2, due to the strong donor− acceptor delocalization into predominantly π*-type orbitals. Specifically, there are 10 cases of π → π*, 4 cases of π → LP/LP*, and two cases of LP → π* delocalization. In contrast, the πsystem of phenanthrene is characterized by seven genuine π-type bonding orbitals, which are symmetrically delocalized into seven

additional resonance stabilization, a characteristic reflected in the reactivities of these hydrocarbons. We have attempted to estimate the extent of aromatic stabilization of phenanthrene versus anthracene through the inspection of orbitals with distinct π- or pz-character (where z is the direction perpendicular to the molecular plane). First of all, as is evident from Scheme 5, there is close similarity in the symmetry of these orbitals but for MO 44. Both systems are characterized by substantial delocalization of the electron density within the confines of the carbon framework. Second, as expected, the phenanthrene π-system appeared to be 16.40 kJ mol−1 more stable than that of anthracene (totaling the energies of these orbitals on assumption of their double occupancy). However, this leaves 12.10 kJ mol−1 of the computed energy difference unaccounted for. In reality, the figure reported above is a rough estimate in view of its derivation, while the shapes of MOs do not easily lend themselves to meaningful chemical interpretation. An alternative approach is to consider localized 8575



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Table 2. Natural Bond Orbital (NBO)34 Summary for the States with Distinct π- or pz-Character of Anthracene and Phenanthrene, Generated Using the Jaguar Program31

Scheme 6. Canonical Molecular Structures According to the NBO Analysis35 and the Numbering Schemes for Anthracene and Phenanthrenea

molecular unit 1 (C14H10) NBO 7 12 17 20 25 30 47 48 573 578 583 586 591 596

2 8 13 18 22 26 31 567 573 578 583 587 591 596

occupancy

energy

1.778 60 1.775 34 1.622 53 1.618 44 1.775 36 1.768 62 1.010 05 0.969 92 0.224 74 0.220 94 0.373 57 0.366 70 0.220 97 0.218 92

−0.264 28 −0.263 04 −0.251 65 −0.246 74 −0.263 05 −0.260 98 −0.104 31 −0.097 82 0.040 73 0.041 21 0.036 34 0.032 53 0.041 10 0.036 88

total Lewis valence non-Lewis Rydberg non-Lewis

90.677 87 3.057 44 0.264 69

(96.4658%) (3.2526%) (0.2816%)

total unit 1 charge unit 1

94.000 00 0.000 00

(100.0000%)

1.570 27 1.710 42 1.718 43 1.791 75 1.568 25 1.718 08 1.710 26 0.438 41 0.275 78 0.276 09 0.194 06 0.436 15 0.276 31 0.276 00

−0.244 57 −0.256 31 −0.258 49 −0.263 66 −0.243 54 −0.258 48 −0.256 38 0.035 70 0.032 62 0.037 29 0.041 61 0.037 07 0.037 21 0.032 63


91.125 32 2.635 97 0.238 71

(96.9418%) (2.8042%) (0.2539%)


94.000 00 0.000 00

(100.0000%)

BD(2) BD(2) BD(2) BD(2) BD(2) BD(2) LP(1) LP*(1) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2)

BD(2) BD(2) BD(2) BD(2) BD(2) BD(2) BD(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2)

Anthracene C3−C4 C5−C6 C 7−C14 C 8−C15 C 16−C17 C 18−C19 C2 C1 C3−C4 C5−C6 C7−C14 C8−C15 C16−C17 C18−C19

Phenanthrene C1−C2 C3−C4 C5−C6 C7−C12 C14−C15 C16−C17 C18−C19 C1−C2 C3−C4 C 5−C6 C7−C12 C14−C15 C16−C 17 C18−C19

a

The red circle designates LP(1), a bonding lone pair orbital, while the blue circle designates LP*(1), an anti-bonding lone pair orbital; each of them is populated by approximately one electron.

In addition, the difference in molecular geometries affects the energies of single bond (σ-type) orbitals, in particular, those of the carbon atom framework, as well as delocalization into orbitals of symmetry other than π*. From Table 2, it is evident that the overall number of electrons delocalized into antibonding π*-type orbitals is noticeably higher for phenanthrene than for anthracene (2.1728 against 1.6258). Therefore, one may conclude that overall energy lowering of the orbitals that constitute the π-system, as well as higher donor−acceptor delocalization of π-electrons into antibonding π*-orbitals of bent phenanthrene in comparison to linear anthracene, are responsible for what might be called the “aromatic stabilization”. Can any part of the total computed stabilization of 28.50 kJ mol−1 be attributed to the H--H interactions in the cleft of phenanthrene? From our calculations there is no evidence for it. First, the inspection of all occupied and some 20 unoccupied MOs, as well as all 598 NBOs failed to return an orbital centered on both H8 and H23 atoms in the cleft. Second, the computed electron density for phenanthrene, Scheme 7, shows no local Scheme 7. Various Molecular Surfaces for Phenanthrene

π*-type antibonding orbitals, affording in total 18 cases of delocalization. Adding up the π-system NBO energies scaled by their occupancies afforded huge aromatic stabilization of −295.4 kJ mol−1 for phenanthrene. Of course, this figure does not tell the whole story, as only a few out of the total of nearly 600 orbitals were considered. Even some quite high energy orbitals are occupied; they are only sparsely populated, but including them reduces the level of stabilization to the final figure of −28.50 kJ mol−1, which is reasonably close to the experimentally found difference of −23.4 kJ mol−1 between the gas phase enthalpies of formation of anthracene and phenanthrene.

maximum between these two hydrogen atoms. Third, the computed electrostatic potential for phenanthrene, Scheme 7, shows no domain of energy stabilization for a positive test charge in the cleft, as would have been expected if a bonding H--H interaction took place. In addition, we made an attempt to evaluate the magnitude of possible destabilizing H--H interaction in the cleft of phenanthrene. The idea was to compute the ground state energy of five phenanthrene monoanions deprotonated at various sites. One of them has H--H interaction eliminated, while four other 8576



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Table 3. Ground State Gas Phase Energies, E, Relative Energiesa, ΔE, and the Distance between the Atoms in the Cleft of the Five Phenanthrene Anions Deprotonated at Different Sites, Calculated Here at the DFT (X3LYP/cc-pVTZ(-f)++) Level Using the Jaguar Program31

a

monoanion

deprotonation site

E/hartree

ΔE/kJ mol−1

RC−C/Å

RH−H/Å

phenan_a phenan _b phenan _c phenan _d phenan _e

C19 C18 C17 C16 C12

−538.807 040 −538.802 273 −538.802 908 −538.804 939 −538.806 651

0 12.51 10.85 5.52 1.02

2.892 3.008 3.010 2.976 2.984

n/a 1.965 2.037 1.994 2.003

With respect to monoanion (a), deprotonated at atom C19, Scheme 3, i.e., the one without a possibility of a nonbonding H--H interaction.

Scheme 8. Shapes and Energies of the Bonding Molecular Orbitals (MOs) with π-Character for 6,7-bzq and 7,8-bzq

still have it present. The results of these calculations are presented in Table 3. They clearly indicate that H--H interaction in the cleft of phenanthrene is unfavorable, as all anions with it present have higher ground state energies than the one without it.

Unfortunately, quantifying this destabilizing effect proved to be problematic, as the placement of the electron lone pair on different carbon atoms of the phenanthrene ring structure has significant impact on the relative aromatic stabilization of the 8577



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relative destabilization of asymmetric MOs 43 and 46 of 7,8-bzq in comparison to the symmetric ones of 6,7-bzq. To understand the nature of bonding in these heteroaromatic molecules better, once again we reviewed the localized natural bond orbitals (NBOs). Results relevant to the π-system part of the NBO analysis,35 carried out by means of Jaguar software,31 are presented in Table 4. Canonical molecular structures derived

anions. The best we may conclude from our calculations is that the steric repulsion of two hydrogen atoms in the cleft of phenanthrene is probably not as extensive as 21 kJ mol−1 suggested by molecular mechanics, but rather of the magnitude between 1 and 13 kJ mol−1. Benzoquinolines. The results of the DFT calculations on anthracene and phenanthrene presented above have highlighted the importance of aromatic stabilization. From this point of view, the nitrogen atoms in 6,7-bzq and 7,8-bzq may be affecting the stabilization produced by the π-system, and other effects arising from their presence in benzoquinolines should also be borne in mind. As discussed above, largely from a consideration of interaction between the two H atoms in the cleft of phenanthrene, contributions from Pauli forces should destabilize phenanthrene relative to anthracene by up to 13 kJ mol−1. This result suggests that of the five benzoquinolines in Scheme 3, the most stable should be 7,8-bzq, where such potentially unfavorable Pauli forces are absent. From a consideration that the π-system of the bent benzoquinolines should stabilize these relative to the linear benzoquinolines, by analogy with the bent phenanthrene and linear anthracene, one would expect the order of stability of the benzoquinolines, as evidenced by ΔfH⊖ values, to be: 6,7-bzq ≤ 2,3-bzq (acridine) < 5,6-bzq ≤ 3,4-bzq < 7,8bzq. The ground state energies in the gas phase of five benzoquinolines, computed at the DFT (X3LYP/cc-pVTZ (-f)++) level, are shown in Table 1. As can be seen from these results, “bent” 7,8-bzq turned out to be 29.58 kJ mol−1 more stable than “linear” 6,7-bzq, a result very similar to the one found for the phenanthrene−anthracene pair. The order of relative stability of benzoquinolines (ΔE values) actually obtained by us in the DFT calculations is exactly as suggested above. Consequently, these DFT calculations support the traditional view that phenanthrene has a more favorable ΔfH⊖ than anthracene29,30 not because of favorable interactions between the closely approaching H atoms in its cleft2 but because of the more stable π-system of this bent isomer. One should consider, of course, what role might be played by attractions between the H atom in the cleft of 7,8-bzq and the adjacent N atom. This would be a form of hydrogen bond (H-bond).36 However, because of the weakness of H-bonds involving C−H hydrogen atoms (typically less than 9 kJ mol1),36 it seems unlikely that this contribution would rise to the point of stabilizing 7,8-bzq relative to 6,7-bzq by as much as 29.6 kJ mol−1. In addition, one has to take into account the poor directionality of the C−H bond relative to the N atom. Ideally, the H-bonding C−H group and the N atom should be in a linear arrangement,36 whereas in 7,8bzq this angle is 97.5°.37 6,7-bzq versus 7,8-bzq. In order to estimate the extent of heteroaromatic stabilization of 7,8-bzq versus 6,7-bzq, we performed an inspection of orbitals with distinct π- or pzcharacter (where z is the direction perpendicular to the molecular plane). Yet again, as evident from Scheme 8, there is close similarity in the shapes and symmetry of orbitals of these two molecules, though the 7,8-bzq orbital analogous to MO 39 of 6,7-bzq now has the number 38. Both systems are still characterized by substantial delocalization of the electron density within the confines of the heteroaromatic fused rings. Somewhat surprisingly, the 7,8-bzq π-system appeared to be 39.04 kJ mol−1 less stable than that of 6,7-bzq (totaling the energies of these orbitals on assumption of their double occupancy). The bulk of this difference arises from

Table 4. Natural Bond Orbital (NBO)34 Summary for the States with Distinct π- or pz-Character of 6,7-bzq and 7,8-bzq, Generated Using the Jaguar Program31 molecular unit 1 (C14H10) NBO

occupancy

energy

1.617 50 1.773 64 1.774 65 1.603 94 1.759 88 1.817 25 1.016 08 1.911 95 0.963 46 0.001 05 0.372 58 0.219 02 0.220 03 0.356 97 0.206 28 0.256 97

−0.255 93 −0.267 28 −0.267 58 −0.255 24 −0.277 26 −0.313 90 −0.116 43 −0.352 69 −0.103 99 1.663 01 0.023 54 0.036 83 0.037 51 0.032 56 0.027 45 0.015 65


90.670 67 3.088 50 0.240 83

(96.4582%) (3.2856%) (0.2562%)


94.000 00 0.000 00

(100.0000%)

1.544 32 1.765 86 1.703 95 1.792 27 1.569 36 1.709 51 1.699 32 1.910 12 0.001 70 0.418 66 0.327 60 0.265 64 0.194 86 0.438 51 0.272 51 0.263 03

−0.253 67 −0.308 60 −0.271 55 −0.269 10 −0.246 07 −0.257 26 −0.253 92 −0.348 79 5.153 81 0.026 77 0.009 55 0.024 15 0.036 06 0.034 44 0.032 10 0.040 94


91.087 70 2.673 83 0.238 47

(96.9018%) (2.8445%) (0.2537%)


94.000 00 0.000 00

(100.0000%)

6,7-bzq 4 8 13 18 25 30 46 47 48 302 563 567 572 577 584 589

2 8 12 17 21 25 30 47 534 559 565 569 574 578 582 587

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BD(2) BD(2) BD(2) BD(2) BD(2) BD(2) LP(1) LP(1) LP*(1) RY*(1) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2)

BD(2) BD(2) BD(2) BD(2) BD(2) BD(2) BD(2) LP(1) RY*(1) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2) BD*(2)

C1−C8 C3−C4 C5−C6 C 7−C14 C16−C17 C18−N19 C15 N19 C2 H11 C1−C8 C3−C4 C5−C6 C7−C14 C16−C17 C18−N19

7,8-bzq C1−C2 N3−C4 C5−C6 C7−C11 C13−C14 C15−C16 C17− C18 N3 H22 C1−C2 N3−C4 C5−C6 C7−C11 C13−C14 C 15−C16 C17−C18



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delocalization (2.1808 electrons against 1.6319 electrons) are behind this time the “heteroaromatic stabilization”. On the other hand, considering that similarly computed π-system stabilization for phenanthrene was at −295.4 kJ mol−1 more than 120 kJ mol−1 stronger, it is likely an additional source plays a role in the molecular stabilization of 7,8-bzq. A plausible candidate for such a role would be intramolecular H-bonding. One indication of more pronounced intramolecular H-bonding for 7,8-bzq in comparison to 6,7-bzq comes from the occupancy of the RY*(1) orbital on the relevant H atoms (H22 and H11, respectively): 0.00170 versus 0.00105. Unfortunately, there is no simple way to partition the contribution of the latter effect. We have tried to estimate the energy of this intramolecular H-bond by calculating the ground state energies of five 7,8-bzq anions deprotonated at various sites, Table 5. Although removal of the H atom from the cleft resulted in significant destabilization of ion (a) in comparison to other anions, a rather large energy difference was observed between anions (b)−(e), all with the H atom in the cleft; relative stabilization of these ions in comparison to ion (a) varied from −19.37 kJ mol−1 to −46.65 kJ mol−1. Clearly, only part of this stabilization is attributable to the formation of Hbond. The balance arises from the differences in molecular geometry, see Table 5, and variable stabilization of the heteroaromatic system when lone pair bearing orbital is placed on different carbon atoms. If one reverts to an empirical estimate36 of about −9 kJ mol−1 for such a bond, one may conclude that the lesser heteroaromatic stabilization of 7,8-bzq versus 6,7-bzq than for the phenanthrene−anthracene pair is complemented by an intramolecular H-bonding interaction, so that the combined effect is similar to the case of anthracene−phenanthrene. Two molecular surfaces for 7,8-bzq are shown in Scheme 10.

from this analysis and the numbering schemes are shown in Scheme 9. As can be seen from this scheme, the 6,7-bzq π-system Scheme 9. Canonical Molecular Structures According to the NBO Analysis35 and the Numbering Schemes for 6,7-bzq and 7,8-bzqa

a

Red circle on C15 represents LP(1), a lone pair bonding orbital, while blue circle on C2 represents LP*(1), a lone pair antibonding orbital; each of them is populated by approximately one electron. Bonding lone pair orbitals on nitrogen atoms, denoted by ellipses, are populated by about 1.91 electrons each.

is characterized by six π-type bonding orbitals and three lone pair orbitals, two bonding and one antibonding, centered on atoms C15, N19, and C2, respectively. The population of each π-orbital is significantly reduced from the expected two-electron occupancy, see Table 4, due to the strong donor−acceptor delocalization into predominantly π*- or LP-type orbitals. In addition, there is noticeable delocalization of the electron from the LP orbital based on atom C15 into three π*-type orbitals located on atomic pairs C1−C8, C7−C14, and C16−C17. There is also minor delocalization of the electron from the LP orbital based on atom N19 into σ*-orbitals located on atomic pairs C14−C15 and C17−C18. In comparison, the π-system of 7,8bzq is made up of seven π-type bonding orbitals and one LP(1) orbital based on atom N3. Similarly, each π-orbital is involved in donor − acceptor electron delocalization into predominantly π*type orbitals. In addition, the electrons from the LP orbital based on N3 atom are delocalized to about the same degree as similar electrons of 6,7-bzq into two σ*-type orbitals located on atomic pairs C1−C2 and C4−C5. Adding up the energies of the NBO orbitals listed in Table 4 (excluding antibonding Rydberg type RY* orbitals on H11 atom for 6,7-bzq and H22 atom for 7,8-bzq; they are included in the table for the discussion of the intramolecular H-bonding), scaled by their occupancies, this time produced aromatic stabilization of −173.1 kJ mol−1 for 7,8-bzq. Though this figure is merely an estimate, it indicates that sizable part of the overall −29.58 kJ mol−1 stabilization for 7,8-bzq is of an aromatic origin. Yet again, both the lower energy of the bonding π-type orbitals for 7,8-bzq in comparison to 6,7-bzq and the greater extent of π → π*

Scheme 10. Two Molecular Surfaces for 7,8-bzq

The Favored Conformation of 2,2′-Bipyridyl (bpy). There have already been extensive theoretical studies of the conformation of bpy in the gas-phase,38−41 which demonstrated that the global minimum is the planar trans form (φ = 180°). All these studies found the cis-form to be at an energy maximum for bpy, and a local minimum at φ of 30° to 40°. We have carried out a relaxed coordinate scan of the bpy energy profile at the

Table 5. Ground State Gas Phase Energies, E, Relative Energiesa, ΔE, and the Distance between the Atoms in the Cleft of the Five 7,8-bzq Anions Deprotonated at Different Sites, Calculated Here at the DFT (X3LYP/cc-pVTZ(-f)++) Level Using the Jaguar Program.31

a

monoanion

deprotonation site

E/hartree

ΔE/kJ mol−1

RN−C/Å

RN−H/Å

7,8-bzq_a 7,8-bzq_b 7,8-bzq_c 7,8-bzq_d 7,8-bzq_e

C18 C17 C16 C15 C11

−554.836 723 −554.844 102 −554.847 664 −554.850 598 −554.854 490

0 −19.37 −28.73 −36.43 −46.65

2.872 2.899 2.889 2.852 2.845

n/a 2.519 2.562 2.522 2.488

With respect to monoanion a, deprotonated at atom C18, Scheme 9, i.e., the one without a possibility to form intramolecular H-bond. 8579



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now must have the cis conformation, one finds that these are frequently nonzero. Thus, for seven bpy complexes of La(III), excluding a further four La(III)/bpy complexes43−46 where the bpy ligands appear to be flattened (χ ≤ 2°) by π-stacking, the average value of χ is (9.2 ± 4.5)°. Three solid state structures are reported for Ba(II) with bpy.3 One structure47 is again eliminated because of the π-stacking of bpy, but the remaining two have χ values averaging (25.1 ± 6.2)°. For metal ions such as Cu(II) (>1100 structures) and Ni(II) (nearly 300 structures), the geometry of numerous complexes containing bpy has been reported.3 With no attempt to remove structures where the bpy is π-stacked, the average values of χ are (4.5 ± 4.3)° for Cu(II), and (4.3 ± 3.8)° for Ni(II). For Pd(II) (230 structures), χ averages (4.0 ± 3.7)°. The impression these χ values give is that χ is large for ionically (weakly) bound metal ions, such as La(III) and, particularly, Ba(II), and becomes smaller for more covalently (strongly) bound metal ions, such as Ni(II), Cu(II), and Pd(II). From this point of view, the more covalently bound metal ions would constrain the ligand more strongly to be planar. A further contribution to the conformation of coordinated bpy comes from the size of a metal ion. As a metal ion becomes smaller, it distorts the bpy ligand and makes the N−C−C angles involving the C−C bond between the two pyridyl groups smaller, and so pulls the H atoms in the 3,3′-positions of the pyridyls further apart, lessening the H--H interaction, and facilitating planarity of the bpy ligand. This is illustrated in Scheme 11 for the Ba(II) complex of bpy,

DFT(X3LYP/6-311G**++) level (Figure 2) as a function of the N−C−C−N torsion angle (χ), which is in essential agreement

Figure 2. Relative energy (ΔE) of the 2,2′-bipyridyl (bpy) molecule calculated in a relaxed coordinate scan at DFT(X3LYP/6-311G**++) level as a function of the N−C−C-N torsion angle (χ) in the gas phase and in simulated aqueous solution (by means of the PBF method31). In the gas phase the cis form of bpy is 32.8 kJ mol−1 higher in energy than the trans form, while in solution the difference is reduced to 5.34 kJ mol−1. Each curve represents the difference in energy relative to the most stable conformation of bpy.

Scheme 11. Geometries of bpy in Complexes with Planar bpy (χ ≤ 2°) of (a) Ba(II)47 and (b) B(III),3 Showing the Effect of Metal Ion Size on the Separation between the Non-Bonded H Atoms at the 3 and 3′ Positions of bpy (Gray Spheres)a

with these previous calculations (since the aromatic rings of bpy are nearly planar, χ and φ angles are effectively equivalent). Our interest was in the conformation of bpy in aqueous solution, where solvation might alter the energy profile for it. The Jaguar module31 of Schrodinger 2011 software suite42 uses Poisson− Boltzmann formalism (PBF) to simulate aqueous medium; the latter is modeled as a layer of charges at the molecular surface computed in the SCF manner. One can see from Figure 2 that the energy profile for bpy in the simulated aqueous medium has been considerably flattened, but that the trans form is still more stable than the cis form of bpy by 5.34 kJ mol−1. Interestingly, the trans form with χ = 180° is not predicted to be the global energy minimum in aqueous solution. There is rather a shallow minimum at χ = 158°. It may be that the presence of a dielectric medium reduces attractive electrostatic forces between the H atoms in the cleft of trans bpy, and the adjacent N atoms, leaving only destabilizing Pauli forces that favor a slightly twisted conformation. The energy difference between the global minimum for bpy at χ = 158°, and the cis form with χ = 0°, is 6.65 kJ mol−1. This translates into a destabilizing contribution of 1.16 units toward log K1 as part of the conformational change into the cis form, required for the binding of metal ions. The latter can be compared to a more or less constant difference27 of 1.3 units in log K1 for bpy and phen complexes. This supports the generally held opinion27 that phen forms more stable complexes than bpy (by some 1.3 log units) because it is locked into the cis arrangement of N donor atoms required for the coordination of metal ions. On the other hand, bpy must expend the 6.65 kJ mol−1 required to rotate it from the minimum energy conformer with χ = 158°, indicated here to be the most stable in aqueous solution, to the cis conformer required to form a complex. The Geometry of bpy−Metal Complexes. The conclusion that the H--H nonbonded interactions in the cis form of bpy are repulsive has an interesting consequence for the complexes of bpy (and also tpy and qpy) with metal ions. If one analyzes χ values in the CSD3 for coordinated bpy, which

a

The geometry of the boron/bpy complex is the average of 20 structures of B complexes of bpy, all planar, reported in the CSD.3 Drawing made with the Mercury program available as part of the CSD.3

with Ba(II) being the largest metal ion coordinated to a planar bpy, and for the B(III) complexes of bpy, with boron ion being the smallest Lewis acid forming a chelate ring with bpy. In the bpy complex with Ba(II) the bpy is planar (χ < 2°)47 due to the πstacking in the solid state. One sees that the H--H nonbonded distances for the Ba(II) complex of bpy are very short at 1.98 Å, while those for the B(III) complexes are long at 2.55 Å. In all 20 reported structures3 for B(III)/bpy complexes, the bpy is close to planar, with χ averaging (1.9 ± 1.4)°. Because of the potential sensitivity of χ values to crystal packing effects, the gas phase structures of [B(bpy)(H2O)2]3+, [Ba(bpy)(H2O)7]2+, and [La(bpy)(H2O)7]3+, Figure 3, were computed at the DFT(X3LYP/6-311G**++, LACV3P**++,48 and CSDZ**+ +49) level of theory, respectively. Complex structures in simulated aqueous medium were computed using the PBF 8580



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in particular, with Maestro53 (Version 9.2.112) interface, MMshare (Version 2.0.111) shell, and Jaguar31 (Version 7.8.111) QM module, on the WIN32-x86 and WIN64-x86 platforms. In addition, Mercury54 2.4.6 (Build RC5) and ORTEP52 (Version 1.08) were used for molecular visualization and presentation. The structures were computed within the framework of density functional theory (DFT) with the X3LYP hybrid functional and correlation consistent basis set cc-pVTZ (-f)++ for the molecules with light atoms only. Energy profiles for the intramolecular rotation in 2,2′-bipyridyl were computed with the split-valence basis set 6-311G**++, while the [Ba(bpy)(H2O)7]2+ and [La(bpy)(H2O)7]3+ complexes were treated with the LACV3P**++48 and CSDZ**++49 basis sets, respectively. In all cases we have used basis sets augmented with the polarization and diffuse functions (cc-pVTZ basis set is intrinsically polarized). Solvated molecular systems were treated with a self-consistent reaction field method, using a standard Poisson−Boltzmann solver.50,51 Solvent parameters for water were set to: 80.37 for “the dielectric constant”,55 and 1.40 for “the probe radius”. More particulars are given in the Supporting Information.

Figure 3. Structure of [La(bpy)(H2O)7]3+ generated at the DFT(X3LYP/CSDZ**++) level in aqueous solution by means of the PBF method.31 The calculations predict the NCCN torsion angle (χ) of the nonplanar bpy ligand to be 11.94° in the La(III) complex and 20.8° in the [Ba(bpy)(H2O)7]2+, in comparison with crystallographic values of χ averaging 9.2° and 25.1°, respectively. The drawing was made with ORTEP.52

method.50,51 The generated gas phase structures indicate χ = 8.2° for the La(III) complex, compared to an average of χ = 9.2° for structures3 where π-stacking is absent, and χ = 20.7° for the Ba(II)-bpy complex, compared to an average of χ = 25.1° for structures3 where π-stacking is absent. Some observed and calculated bond lengths and angles for the Ba(II) and B(III) complexes with bpy are given in Table 6. The large values of χ for

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CONCLUSIONS In the gas phase, “bent” phenanthrene was computed to be thermodynamically more stable than “linear” anthracene by −28.5 kJ mol−1, in accord with the difference of experimental ΔfH⊖ values (−23.4 kJ mol−1). This fact was attributed predominantly to the phenomenon of higher aromatic stabilization of the π-system of phenanthrene relative to anthracene, and not to the stabilizing influence of the nonbonding H--H interactions in its cleft, as has been suggested.2 In fact, these interactions in phenanthrene were shown to be destabilizing to the extent between 1 and 13 kJ mol−1. The computed order of relative ground state energies, −ΔE, for benzoquinolines in the gas-phase, 6,7-bzq ≤ 2,3-bzq < 5,6-bzq ≤ 3,4-bzq < 7,8-bzq, also supports the idea that the H--H nonbonded interactions in the clefts of 3,4-bzq and 5,6-bzq are destabilizing, since 7,8-bzq, which lacks such H--H interactions, is the most stable isomer. These −ΔE values bolster the available29,30 ΔfH⊖ data, which indicate, albeit with large uncertainties, the same order of stability in the gas-phase for the benzoquinolines. Intramolecular hydrogen bonding in the cleft of 7,8-bzq probably plays a role in its stabilization relative to 6,7-bzq, but is unlikely to exceed an empirical estimate of −9 kJ mol−1. Nearly identical stabilization of 7,8-bzq versus 6,7-bzq (−29.6 kJ mol−1) to that of the phenanthrene−anthracene pair (−28.5 kJ mol−1) is attributed to a smaller extent of heteroaromatic stabilization in comparison with the aromatic one, which is complemented by weak intramolecular N···H−C hydrogen bonding in the cleft of 7,8-bzq. A scan of ΔE versus N−C−C−N torsion angle for bpy in the gas-phase supports previous theoretical studies,38−41 in that it shows that the trans-conformer is some 32.8 kJ mol−1 more stable than the cis-conformer. The same scan carried out in an aqueous medium simulated by means of the PBF method31 still favors the trans form of the free bpy ligand over the cis conformer, although now only by 5.34 kJ mol−1. The latter result supports the interpretation that complexes of bpy with metal ions, where the bpy must have the cis conformation, are destabilized by unfavorable H--H nonbonded interactions between the H atoms at the 3 and 3′ positions of bpy. There is a shallow local minimum in ΔE at a χ angle of 40° for bpy in the gas-phase, and of 37° in solution, that represents some relief of H--H

Table 6. Experimental (XRD)3 and Calculated Geometric Parameters for bpy Complexes of Barium and Boron Ions Where Computed Structures in the Gas Phase and Simulated Aqueous Medium Were Obtained by DFT Using the Jaguar Program31 [Ba(bpy)(H2O)7]2+ computed: DFT(X3LYP/LACV3P**++) geometric parameter

XRD

RH−H/Å RM−N/Å ∠MNC/deg ∠NCC/deg ∠NCCN/deg

1.98 2.87 125.1 116.8 25.1

gas phase

simulated aqueous medium (PBF)

2.10 unable to complete calculations at the same level of theory 3.00/2.95a 121.8/123.9a 117.8/117.7a 20.8 [B(bpy)(H2O)2]3+ computed: DFT(X3LYP/6-311G**++)

geometric parameter

XRD

gas phase

simulated aqueous medium (PBF)

RH−H/Å RM‑N/Å ∠MNC/deg ∠NCC/deg ∠NCCN/deg

2.55 1.62 112.8 109.6 1.9

2.54 1.52b 109.7b 109.1b 1.1

2.50 1.54b 110.8b 109.3b 1.2

a

The complex is asymmetric, hence two sets of parameters. bIn both cases the complex is nearly symmetrical; at the reported level of precision two sets of geometric parameters are indistinguishable.

the Ba(II) and La(III) complexes with bpy, calculated here by DFT, reinforce the idea that large χ values for the bpy complexes of large, weakly bound metal ions are not due to crystal packing effects, but rather reflect the Pauli repulsive forces between the H atoms at the 3 and 3′ positions of bpy. Computational Methods. Molecular modeling was performed with the aid of the Schrodinger-2011 suite of software,42 8581



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(2) Bader, R. F. W. In Atoms in Molecules: A Quantum Theory: Clarendon Press: Oxford, U.K., 1990. (3) Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, U.K. (4) Bondi, A. J. Phys. Chem. 1964, 68, 441. (5) Martín Pendás, A.; Costales, A.; Luaña, V. Phys. ReV. B 1997, 55, 4275. (6) Abramov, Y. A. J. Phys. Chem. A 1997, 101, 5725. (7) Tsirelson, V.; Abramov, Y. A.; Zavodnik, V.; Stash, A.; Belokoneva, E.; Stahn, J.; Pietsch, U.; Feil, D. Struct. Chem. 1998, 9, 249. (8) Tsirelson, V. G.; Avilov, A. S.; Lepeshov, G. G.; Kulygin, A. K.; Pietsch, U.; Spence, J. C. H. J. Phys.Chem. B 2001, 105, 5068. (9) Cioslowski, J.; Edgington, L.; Stefanov, B. B. J. Am. Chem. Soc. 1995, 117, 10381. (10) Farrugia, L. J.; Evans, C.; Tegel, M. J. Phys. Chem. A 2006, 110, 7952. (11) Cioslowski, J.; Mixon, S. T. J. Am. Chem. Soc. 1992, 114, 4382. (12) Cioslowski, J.; Mixon, S. T. Can. J. Chem. 1992, 70, 443. (13) Poater, J.; Visser, R.; Sola, M.; Bickelhaupt, F. M. J. Org. Chem. 2007, 72, 1134. (14) Cerpa, E.; Krapp, A.; Flores-Moreno, R.; Donald, K. J.; Merino, G. Chem.Eur. J. 2009, 15, 1985. (15) Bader, R. F. W. J. Phys. Chem. A 2009, 113, 10391. (16) Matta, F.; Hernandez-Trujillo, J.; Tang., T.-H.; Bader., R. F. W. Chem.Eur. J. 2003, 9, 1940. (17) Poater, J.; Sola, M.; Bickelhaupt, F. M. Chem.Eur. J. 2006, 12, 2889. (18) Cailleau, H.; Baudour, J. L.; Zeyen, C. M. E. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1979, 35, 426. (19) Allinger, N. L. J. Comput.-Aid. Mol. Design 2011, 25, 295. (20) Maciejczyk, M.; Spasic, A.; Liwo, A.; Scheraga, H. A. J. Comput. Chem. 2010, 31, 1644. (21) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. (22) Allinger, N. L. J. Am. Chem. Soc. 1977, 98, 8127. (23) Hamilton, J. M.; Whitehead, J. R.; Williams, N. J.; Thummel, R. P.; Hancock., R. D. Inorg. Chem. 2011, 50, 3785. (24) Cockrell, G. M.; Zhang, G.; VanDerveer, D. G.; Thummel, R. P.; Hancock, R. D. J. Am. Chem. Soc. 2008, 130, 1420. (25) Hamilton, J. M.; Anhorn, M. J.; Oscarson, K. A.; Reibenspies, J. H.; Hancock, R. D. Inorg. Chem. 2011, 50, 2764. (26) Martell, A. E.; Smith, R. M. Critical Stability Constant Database 46; National Institute of Science and Technology (NIST): Gaithersburg, MD, 2003. (27) Hancock, R. D.; Martell, A. E. Chem. Rev. 1989, 89, 1875. (28) Frohn, H.-J.; Hirschberg, M. E.; Westphal, U.; Florke, U.; Boese, R.; Blaser, D. Z. Anorg. Allg. Chem. 2009, 635, 2249. (29) CRC Handbook of Chemistry and Physics, 88th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2008; pp 5−41. (30) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: New York, 1986; p 161. (31) Jaguar, version 7.8, Schrödinger, LLC: New York, 2011. (32) March, J. Advanced Organic Chemistry, 3rd ed.; WileyInterscience: New York, 1985; p 40. (33) Streitwieser Jr., A.; Heathcock, C. H. Introduction to Organic Chemistry, 2nd ed.; Macmillan: New York, 1981; p 1049. (34) Weinhold, F.; Landis, C. R. Chem. Educ: Res. Pract. Eur. 2001, 2, 91. (35) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohman, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001; http://www.chem.wisc.edu/∼nbo5. (36) Steiner, T. Angew. Chem., Int. Ed. 2002, 41, 48. (37) Shaanan, B.; Shmueli, U. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1980, 36, 2076. (38) Alkorta, I.; Elguoro, J.; Roussel, C. Comp. Theor. Chem. 2011, 966, 334. (39) Howard, S. T. J. Am. Chem. Soc. 1996, 118, 10269.

nonbonded repulsions, and lone pair to lone pair repulsions involving the N atoms, as the bpy rotates somewhat away from a planar cis conformation. The idea of unfavorable H--H nonbonded interactions of the H atoms at the 3 and 3′ positions of bpy is further supported by the nonplanarity of bpy when coordinated to large ionically bound metal ions, such as La(III) or Ba(II), where χ is large with average values of 9.2° and 25.1°, respectively. It has been previously pointed out17 that the concept of energetically unfavorable nonbonded H--H interactions at short H--H separations has been very productive in explaining organic stereochemistry, and so the idea2 that such interactions are energetically favorable would, if correct, overturn much chemical thinking built up over many decades. The usefulness of the idea that H--H nonbonded interactions at short HH separations close to 2.0 Å are energetically unfavorable is seen in the extension of this logic by the present authors56 to understanding the thermodynamic stability of complexes of metal ions with analogues of tpy where such interactions are absent, as seen in Scheme 12. Although, other contributions to the difference in Scheme 12. Ligand Design Principle Involving the Absence of Sterically Hindering Non-Bonded H--H Interactions in the TPTZ Complex Compared to the tpy Complex, Which Leads to Greater Thermodynamic Complex Stability of the TPTZ Complex with Ca(II)56

complex stability, such as intramolecular H-bonding and different extent of aromatic stabilization in TPTZ, might play a role, the impact of unfavorable nonbonded H--H interactions is undoubtedly present, and possibly is the decisive one.

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ASSOCIATED CONTENT

S Supporting Information *

Computational methods. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.D.H.); [email protected]. za (I.V.N.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.D.H. thanks the Department of Energy (Grant # DE-FG0707ID14896) for generous support for this work. I.V.N. is thankful to the University of KwaZulu-Natal for the support of his visit to UNCW.

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REFERENCES

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Do Nonbonded H--H Interactions in Phenanthrene Stabilize It Relative

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