Effects Induced by Axial Ligands Binding to Tetrapyrrole-Based

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Effects Induced by Axial Ligands Binding to Tetrapyrrole-Based Aromatic Metallomacrocycles Yang Yang* Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106, United States

bS Supporting Information ABSTRACT: The axial positions of planar metallomacrocycles are unoccupied. The positively charged metal is thus a potential binding site for electron-donating groups. The binding strength is affected by the central metal, the ligand, and the macrocycle. One ligand leads to the out-of-plane displacement of the central metal, whereas two ligands from two sides structurally neutralize each other. The axial ligand donates charge to the central metal and the macrocycle when the lone pair orients along the interaction axis. The frontier orbital levels are elevated because of the charge donated to the macrocycle. Even though the singlet
triplet gap and the absorption maximum do not change significantly upon binding, the redox chemistry is considerably affected by the shifts of orbital levels. The macrocyclic M
N bonds are weakened by the binding, but their natures remain almost unchanged. Calcium phthalocyanine is a special case, as the central calcium is too large to fit the cavity. Accordingly, multiple ligands facilely bind to the calcium from one side. The aluminum phthalocyanine halogen is another special case, as it has a halogen ligand coordinating to the aluminum through a nondative bond. This leads to some effects different from those caused by dative binding. When there is no considerable steric demand, the lone pair points along the interaction axis to facilitate the donation. When in a stacked dimer, the electron-rich group is part of a large molecule, and the orientation of the lone pair is approximately perpendicular to the interaction axis. This induces the charge loss of the central metal. Because metallomacrocycles are widespread in the biological, medical, and material sciences, the results from this study are expected to bring useful insights to these fields.

1. INTRODUCTION According to the valence shell electron pair repulsion (VSEPR) model, a tetracoordinate molecule usually adopts a tetrahedral orientation to minimize interligand electron repulsions. A good illustration of this is offered by ubiquitous tetrahedral carbon systems. On the other hand, a planar tetracoordinate conformation is stable when two nonbonding lone pairs occupy the axial positions. In this case, the central element, such as xenon in XeF4, needs to have enough valence electrons to participate in four bonds and two lone pairs. To stabilize a planar tetracoordinate molecule, another route is to break the traditional VSEPR model, which assumes that the ligands are free. In the past 40 years, there has been substantial interest in designing planar tetracoordinate carbon systems with the aid of electronic or mechanical constraints.1,2 This seems quite simple and straightforward, and a tetracoordinate planar macrocycle would be a promising template. Because of the small size of a carbon atom, only a small number of planar tetracoordinate carbon systems have been identified experimentally.3,4 However, a large number of such systems whose central atoms are larger than carbon have been well-established.5 Phthalocyanines and porphyrins are among the best-known tetrapyrrolebased aromatic macrocycles, and each of these divalent macrocycles provides four coordination sites for a central atom. They are known to be able to coordinate to more than 70 central atoms. Because of the strong chelating effect, planar complexes containing such macrocycles usually exhibit high chemical and thermal stability.5 r 2011 American Chemical Society

With regard to XeF4, the two lone pairs at the axial positions hinder the approach of nucleophilic groups. In contrast, in a planar metallomacrocyle, a positively charged central metal is exposed along the axial direction. Consequently, the two axial positions are left susceptible to nucleophilic binding. Thus, a metallomacrocycle in solution or in the solid state can be considerably affected by other molecules. For example, the solvent-dependent behaviors of a number of metallophthalocyanines and metalloporphyrins have been investigated.6
9 Even though these behaviors are unlikely to be exclusively caused by the axial binding of solvent molecules, the binding could still play an important role. In addition, as indicated by a number of theoretical studies and gas-phase electron diffraction investigations, the geometries of some metallophthalocyanines have D4h symmetry. However, in many crystal structures, their central metals are above the phthalocyanine planes.10
13 This is attributable to the cocrystallization of the solvent molecule at the axial position. The axial binding of metallophthalocyanines is widespread and plays an important role. For example, many biological macromolecules contain metallomacrocycles whose central metals are important binding sites that are essential for biological functions.14
17 In addition, the axial ligand can serve as a bridge to construct assembled systems. Such systems can be used as models to investigate photoinduced energy and electron transfers.18
21 It is thus important to know whether and how Received: May 15, 2011 Revised: July 12, 2011 Published: July 14, 2011 9043

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Figure 1. Structure of the bare metallophthalocyanine.

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throughout this work. The shapes of Kohn
Sham (KS) orbitals are similar to those of canonical Hartree
Fock orbitals.24 KS orbitals, however, are preferred because, for example, all KS orbitals are subject to the same external potential.24 Because the topological analysis of the electron density is involved in this study, basis sets including the effective core potential (ECP) are not supported. The use of the 6-311+G(d) basis set to describe central transition metals in metallomacrocycles has been shown to be reliable.25
27 Therefore, the 6-311+G(d) basis set was used for Zn and Cu, and the 6-31G(d) basis set was used for the rest of the main group elements. All optimized stationary points were confirmed to be energy minima on the corresponding potential energy surfaces through vibrational frequency analyses (no imaginary frequency). The restricted B3LYP approach was used for singlet states, and the unrestricted B3LYP approach was used for open-shell systems. Charges from electrostatic potentials using a grid-based method (CHELPG charges) were produced according to the CHELPG scheme.28 These were all performed using the Gaussian 09 package.29 Natural bond orbital (NBO) analyses were carried out with NBO 3.0 implemented in Gaussian 09.30 The search for bond critical points (BCPs) and the topological analysis of BCPs were done in AIM2000.31

3. RESULTS AND DISCUSSION

Figure 2. Structures of bare magnesium macrocycles.

molecular properties of a metallomacrocycle will be affected by axial binding and whether the modeling of such a system is sufficient with a single metallomacrocycle. Therefore, a study in this area could provide useful information for understanding many experimental observations, such as metal binding in biomolecules, solvent-dependent properties of metallomacrocycles, crystal packing, and systems assembled through axial bindings. Magnesium phthalocyanine (MgPc, 1) has D4h symmetry and serves as a basic model. Magnesium-containing chlorophylls are also essential pigments in photosynthesis. In this work, various magnesium macrocycles (2
5) and metallophthalocyanines (6
11) were chosen to investigate effects of the central metal and the macrocycle (Figures 1 and 2). Molecules 1
11 are described as bare macrocycles because they do not have axial ligands. A compound bound by a ligand is denoted by adding a lowercase letter to the number used to label the corresponding parent bare macrocycle (see Table 1). Although a macrocycle could also be viewed as a ligand, the term “ligand” used in this context refers exclusively to the axial ligand, so that the macrocycle and the axial ligand can be distinguished easily.

2. COMPUTATIONS The B3LYP hybrid density functional has proved to yield satisfactory results for tetrapyrrole macrocycles22,23 and was used

3.1. Structures. Various ligands were studied, namely, pyridine, imidazole, ortho-picoline, meta-picoline, para-picoline, para-aminopyridine, and para-trifluoromethylpyridine. For bare metallomacrocycles 1
8, the central metals are within the macrocyclic planes. However, in each case, after binding to one ligand, the central metal locates outside the plane (Figure S1 in the Supporting Information). As a result, the M
Nm (macrocyclic nitrogen) bonds elongate, but they are still shorter than the axial M
Na (axial nitrogen in the ligand) bonds, except for the Be
Nm bonds (Table 1). The elongation of M
Nm bonds upon axial binding is expected, as it has been confirmed in different but similar metallomacrocycles.25,26 The changes of the M
Nm bond lengths are appreciable, but the ct
Nm (where ct is the centroid defined by four pyrrolic nitrogens) distances undergo many fewer changes upon axial binding. If a metallomacrocycle is viewed as the combination of a macrocycle and the tetracoordinate M
Nm bonds, then the macrocycle is relatively rigid, whereas the tetracoordinate bonds are relatively flexible. The position of the substituent on the picoline ligand could significantly alter the orientation of the ligand with respect to the metal, as well as the ligand
metal interaction. For example, the para- and meta-picolines in 1c and 1d, respectively, slightly enhance the binding because the M
Na bonds are shorter and the M
ct distances are longer than the corresponding values in 1a. In contrast, the ortho-picoline in 1b significantly tilts from having the M
Na axis perpendicular to the ring because of steric hindrance (Figure S2 in the Supporting Information). The greater M
Na bond length and the smaller M
ct distance in 1b suggest that this steric hindrance also weakens the axial binding. Two identical ligands at two sides in 1g structurally balance each other and lead to an in-plane position for the central metal. Moreover, two different ligands at two sides in 1f minimize the each other's effects. The central metal in 1f resides slightly out of the plane and points toward the imidazole side, that is, the side of the stronger ligand. The metal
ligand binding strength in metalloporphyrins is related to properties such as the ligand basicity constant (pKb) 9044

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Table 1. Selected Structural Parametersa (Å) and Binding Energies (kcal/mol) MMcb

ligand

MgPc

M
Nm

M
Na

M
ctc

ct
Nm

Ebindd

ONe

1

2.008

0.000

2.008

MgPc

pyf

1a

2.054

2.216

0.451

2.004

18.58

2

MgPc

o-picg

1b

2.067

2.258

0.518

2.001

17.30

2

MgPc

m-pic

1c

2.055

2.212

0.459

2.003

19.08

2

MgPc

p-pic

1d

2.055

2.209

0.460

2.003

19.33

2

MgPc

Imh

1e

2.058

2.185

0.474

2.003

21.34

2

MgPc

py + Imi

1f

2.029

2.478j

0.041

2.029

24.37

2

MgPc MgPc

py + Im py  2l

1f 1g

2.027

2.345k 2.433

0.000

2.027

22.48

2 2

MgPc

p-Apym

1h

2.060

2.191

0.482

2.002

21.27

2

MgPc

p-TFMpyn

1i

2.049

2.232

0.425

2.005

16.80

2

2.064

0.000

2.064

2a

2.097

0.335

2.070

3

1.986

0.000

1.986

py

3a

2.041

2.213

0.499

1.979

py

4 4a

2.089 2.120

2.234

0.000 0.317

2.089 2.096

5

2.015

0.000

2.015

5a

2.058

0.437

2.011

6

1.875

0.000

1.875

6a

1.928

0.315

1.902

7

2.000

0.000

2.000

py

7a

2.042

2.213

0.407

2.001

py

8 8a

1.967 1.976

2.632

0.000 0.115

1.967 1.973

9

2.329

1.095

2.055

MgP MgP

py

MgTAP MgTAP MgTBP MgTBP MgNc MgNc

py

BePc BePc

py

ZnPc ZnPc CuPc CuPc CaPc

2.243

2.217 1.867

2

2 2

15.26

2 2

18.65

2

16.91

2 2 2

18.66

2 2

13.87

2 2

12.64

2

4.48

2 2 2

CaPc

py

9a

2.356

2.571

1.164

2.048

25.11

2

CaPc

py  2o

9b

2.398

2.645

1.271

2.033

41.30

2

CaPc

py  3

9c

2.443

2.729

50.41

10

1.989

AlPcCl

1.370

2.022

0.465

1.934

2 3

AlPcCl

py

10a

1.974

2.439

0.211

1.963

4.56

3

AlPcCl AlPcF

Im

10b 11

1.976 1.994

2.263

0.163 0.479

1.969 1.935

7.40

3 3

AlPcF

py

11a

1.980

2.516

0.261

1.963

4.63

3

a

Average values given when small variances exist for bond lengths. b MMc, metallomacrocycle. c ct, centroid defined by four pyrrolic nitrogens. d Zeropoint energy correction included. e ON, oxidation number. f py, pyridine. g pic, picoline. h Im, imidazole. i Two different ligands binding from two sides. j Pyridine side. k Imidazole side. l Two identical ligands binding from two sides. m para-Aminopyridine. n para-Trifluoromethylpyridine. o Two identical ligands binding from one side.

and Gutmann donor number.32 The pKb value of imidazole is a factor of 1.75 smaller than that of pyridine.33 Consequently, compared to those in 1a, the M
Nm bond lengths and M
ct distance in 1e are slightly larger, and the M
Na bond length is slightly smaller. The ligand pKb values are in the order imidazole < para-picoline ≈ ortho-picoline < meta-picoline < pyridine.32 It should be noted that the methyl group in the ortho-picoline ligand significantly weakens the binding strength in 1b because of steric hindrance. If no significant steric hindrance exists, the pKb value serves as an indicator of the binding strength, in that a stronger ligand corresponds to a smaller pKb value. A metallomacrocyle bound by a stronger ligand has greater M
Nm bond lengths, M
ct distances, and binding energies and a smaller M
Na bond length. Calcium phthalocyanine, 9, is different from 1
8 because the calcium atom is too large to fit the phthalocyanine cavity comfortably. As a result, the central calcium atom is significantly

out-of-plane in the bare metallomacrocycle (Figure S3 in the Supporting Information). An axial ligand in 9a makes the central calcium move farther from the centroid. A calcium porphyrin was isolated in a solvated form in which three pyridine molecules bind to the central calcium from the same side.34 This indicates an interesting and different binding pattern for the calcium macrocycle. The attempt to obtain a bisligated calcium phthalocyanine in which two ligands bind from different sides failed. Previous studies also support the conclusion that two ligands cannot bind to calcium from two sides.25 It is possible that the cone-shaped conformation sterically hinders the approach of a second ligand from the other side. This is different from the previous case in which two ligands binding from two sides neutralize each other. Instead, multiple ligands can bind from the same side easily. Effects from multiple axial ligands aggregate and lead to greater Ca
Nm, Ca
Na, and M
ct lengths. There is, however, a shared feature for these two binding patterns: The 9045

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Table 2. NBO Charge Distributions MMc

ligand

Mc

L

NMc

NL

1

1.392


1.392

MgPc

py

1a

1.327


1.437

0.109


0.674


0.534

MgPc

Im

1e

1.321


1.441

0.120


0.669


0.582

MgPc

py + Imb

1f

1.300


1.481

0.081


0.660


0.484

MgPc

py + Imc

1f

MgPc

py  2

1g

1.312


1.482


0.666


0.491

2

1.406


1.406

2a 3

1.359 1.378


1.453
1.378

0.094 0.111

MgPc

MgP MgP MgTAP

py

MgTAP

py

MgTBP MgTBP

py

MgNc MgNc

py

BePc BePc ZnPc

py

ZnPc

py

CuPc CuPc

py

CaPc


0.704


0.542

0.100

3a

1.316


1.427

4

1.422


1.422

4a

1.374


1.469

5

1.397


1.397

0.085


0.672

0.095

1.331


1.440

1.199


1.199

6a 7

1.097 1.165


1.248
1.165

0.151 0.146

1.095


1.242

0.875


0.875

8a

0.875


0.950

9

1.677


1.677


0.524


0.696


0.531


0.623


0.533


0.698

5a

7a


0.649
0.724
0.649

6

8

Xa

0.109


0.667


0.535


0.685
0.644
0.661


0.534


0.637


0.499


0.590 0.075


0.583


0.465


0.716

CaPc

py

9a

1.588


1.660

0.073


0.687


0.565

CaPc

py  2

9b

1.535


1.663

0.064


0.666


0.543

CaPc AlPcCl

py  3d

9c 10

1.493 1.801


1.665
1.228

0.057


0.645
0.736


0.525

AlPcCl

py

10a

1.818


1.324

0.101


0.728


0.504


0.595

AlPcCl

Im

10b

1.809


1.334

0.124


0.718


0.574


0.599

11

1.955


1.265

11a

1.959


1.336

AlPc(ONO)2

1.877


1.376

AlPcONO

1.941


1.229

AlPcF AlPcF

a

M

py


0.574


0.732 0.082


0.716


0.690
0.500


0.706
0.750


0.740


0.712

X, axial ligands bound through nondative bondings. b Pyridine side. c Imidazole side. d Average values listed when small variances exist.

Ca
Na bond length always increases along with the increase of the ligand number, as does the Mg
Na bond length. The central aluminums in 10 and 11 are trivalent rather than divalent. 10 has an axial chloride ligand, and 11 has an axial fluoride ligand. Unlike previous ligands such as pyridine, the chloride and fluoride ligands bind to the central aluminums through nondative bonds. Similarly, their central metals are moderately out of the planes, but their out-of-plane displacements (illustrated by the M
ct distances) are appreciably smaller than those in calcium phthalocyanines (Figure S4 in the Supporting Information). In some sense, the structural features of 10 and 11 are quite similar to those of monoligated 1
8: One ligand leads to out-of-plane displacement, and two ligands neutralize each other. Structurally, the fluoride ligand is stronger than the chloride ligand, and a halogen ligand is stronger than a dative ligand because the central atom always points toward the halogen side when there are a halogen ligand and a dative ligand. Therefore, the ligand-induced structural effects are in the order F > Cl > Im > py. Consistent with this order, the displacements follow the order 11 > 10 > 11a > 10a > 10b. For the latter three compounds, the M
ct distance is related to the difference in strength between the halogen ligand and the dative ligand. In general, the structural effect of a halogen

ligand is no different from that of a dative one, though to a different extent. The binding strength is affected not only by the ligand but also by the metal and the macrocycle. The M
ct distances in metallophthalocyanines follow the order 1a > 7a > 6a > 8a. The M
ct distances in magnesium macrocycles follow the order 3a > 1a > 5a > 2a > 4a. A part of this order can be explained by the macrocyclic size. A larger macrocycle is more rigid and thus undergoes a smaller out-of-plane displacement when a ligand binds to its central metal. This rationalizes the relations 3a > 1a > 5a and 2a > 4a. The cavity size, reflected by the ct
Nm distance, follows the order 4a > 2a > 5a > 1a > 3a. The macrocycle with a larger cavity corresponds to a smaller out-of-plane displacement. Generally, meso tetraaza substitution leads to the reduction of the cavity and thus a larger out-of-plane displacement.35 For example, the cavity in 3a is smaller than that in 2a, and that in 1a is likewise smaller than that in 4a. Moreover, it seems that peripheral tetrabenzo annulation lead to a larger cavity. For example, the cavity in 4a is larger than that in 2a because the aromatic system in 4a has four more benzo rings at the peripheral positions than that in 2a (Figure 2). 3.2. Charge Distributions. The charge distribution (Table 2) offers an explanation for the structural and energetics features. It 9046

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The Journal of Physical Chemistry A is a property directly related to the electropositivity of the central metal and the electronegativity of the macrocycle. As expected, all central metals are positively charged, and all macrocycles are negatively charged. Both macrocyclic and axial nitrogens coordinating to the central metals are negatively charged. Despite the negatively charged axial nitrogen, an axial ligand as a whole is positively charged. This suggests that an axial ligand as a whole serves as an electron donor. For bare metallophthalocyanines, the order of positive charges in the central metals is Ca > Mg > Be > Zn > Cu, consistent with their electropositivity order. After the axial binding, the electron donation from the ligand makes the central metal less positively charged and the macrocycle more negatively charged. Thus, in most but not all cases, the axial ligand serves as an electron donor, whereas the metal and the macrocycle serve as electron acceptors. The positive charge of the central metal determines its ability to accept the electron donation from the axial ligand. For metallophthalocyanines, the order of the percentages accepted by the central metals is consistent with the order of their positive charges. For the least positively charged Cu in 8a, almost all donations flow to the macrocycle, and the charge at the central Cu remains almost unchanged. For the most positively charged Ca in 9a
9c, however, all donations flow to the central atom, and the macrocycle becomes another donor. Despite the electron donation from ligand to macrocycle, the macrocyclic nitrogen becomes less negative. The imidazole ligand is a stronger donor than the pyridine ligand, leading to a less positive magnesium, a more negative phthalocyanine ring, and a more positive ligand in 1e compared to those in 1a. Likewise, a similar trend can be found from 1g to 1f. Because the electron donation is accompanied by axial binding, it is not surprising that the structure and binding are associated with a positive charge of the central metal. The binding process can be viewed as the interaction between a Lewis base (ligand) and a Lewis acid (metal cation). A cation with a higher positive charge has a stronger capacity to accept electrons. Accordingly, the first ligand transfers charges to the central metal and makes it less positively charged, hence weakening the potential second binding. Aluminum phthalocyanines form a distinguishable class because of their halogen ligands. As mentioned previously, the structural effects of a halogen ligand and a dative ligand are not different. Nonetheless, their electronic effects appear to be opposite. Even though the halogen atom and the nitrogen in a dative ligand are both electronegative, the halogen ligand is an electron acceptor, and the dative ligand as a whole is an electron donor. This is probably because the lone pairs in the halogen are not involved in the metal
ligand interaction, whereas the lone pair in the dative ligand contributes to this interaction. In contrast to the dative ligand, a stronger halogen ligand accepts more charge and makes the metal more positively charged. Even though aluminum is only slightly more electropositive than zinc, the central aluminums are significantly more positively charged than any other central metals. The bisligated [AlPc(ONO)2]
,36 carrying a negative charge, is worth mentioning because of its symmetric ligands. As expected, the central Al is within the plane because of the two balanced ligands. The structural effects of two such nitrite ligands are no different from those of two dative ligands or two halogen ligands. The nitrite ligand in the monoligated neutral AlPc(ONO) can be viewed as a halogen ligand coordinating to the central metal through a nondative bonding. For [AlPc(ONO)2]
, the two nitrite ligands can be viewed as a resonance between a dative ligand and a halogen ligand. Therefore, the charge at

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the central aluminum in [AlPc(ONO)2]
is less negative than that in AlPc(ONO). Moreover, each nitrite ligand in [AlPc(ONO)2]
can be viewed as an intermediate between a dative ligand and a halogen ligand. The charge at the central aluminum in [AlPc(ONO)2]
is more positive than that in any other central metal, suggesting that the electronic effect of a halogen ligand is appreciably stronger than that of that of a dative ligand. To confirm the electron-transfer trend indicated by NBO charges, CHELPG charges were also calculated and are given in Table S2 in the Supporting Information. The general trend indicated by the NBO charges is consistent with that indicated by the CHELPG charges. For example, they both suggest an electron transfer from the ligand to the metallomacrocycle. The charge at a trivalent central aluminum is more positive than that at a divalent metal. The charge at the macrocyclic nitrogen becomes less negative after ligand binding. 3.3. Axial Binding Energies. The axial binding energy provides a direct means of evaluating the binding strength. The binding energy of 1e is greater than that of 1a, consistent with their structural features. The binding energies in 1c and 1d are greater than that of 1a, whereas that in 1b is smaller than that of 1a. This is also consistent with their structural features. The greater binding energies in 1c and 1d can be attributed to the electron donation from the methyl groups to the pyridine rings, whereas the smaller binding energy in 1b is mainly caused by the steric hindrance. To further check the substituent effect on the ligand, the binding energies of 1h and 1i are also included in Table 1. The ligand of 1h has a strong electron-donating group (amino group) at the para position, whereas the ligand of 1i has a strong electron-withdrawing group (trifluoromethyl group). Consistent with their electronic effects, the binding energy of 1h is greater than that in 1a, whereas that of 1i is smaller. The structural features (M
Nm bond lengths, M
Na lengths, and M
ct distances) of 1a, 1d, 1h, and 1i support their order of binding energies. The binding energy of a bisligated macrocycle is greater than that of a corresponding monoligated one, but the former is less than twice the latter. The positive charge of the central metal has a significant effect on the binding energy. For single-pyridine-bound phthalocyanines, the order of binding energies is consistent with the order of positive charges, which is Ca > Mg > Be > Zn > Cu. Moreover, the binding energy of 1g is slightly larger than that of 1a, whereas the binding energy of 9b is only slightly smaller than twice that of 9a. This is also attributable to the greater positive charge of Ca. The binding energies of aluminum phthalocyanines are significantly smaller than the others in Table 1. This is not surprising because each aluminum phthalocyanine already has a halogen ligand and the bind energy of an aluminum phthalocyanine is expected to be comparable to the bind energy difference between, for example, 1g and 1a. As discussed in the previous section, the binding strength can be related to the pKb value and Gutmann donor number.32 To provide preliminary insight into the relation between basicity (pKb value) and binding energy, the case was simplified to that of a basic ligand binding to a proton, rather than to a metal cation in a metallomacrocycle: B + H+ T (BH)+. For simplification, we also assume that the binding energy can be approximately denoted by the negative Gibbs free energy Ebind ≈
ΔG ¼ RT ln Keq ¼
RT ln Ka ¼ 2:3RTðpKa Þ ¼ 2:3RTð14
pKb Þ 9047

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Figure 3. Frontier orbital distributions of magnesium phthalocyanines at isovalues of 0.03: (a) HOMO of 1, (b) LUMO of 1, (c) HOMO of 1a, (d) LUMO of 1a, (e) HOMO of 1g, (f) LUMO of 1g.

which is 5.7(14
pKb) in kJ/mol or 1.4(14
pKb) in kcal/mol. The binding energy of pyridine is around 9.5 kcal/mol, and that of imidazole is around 11.9 kcal/mol. Even though the model is simplified, it can be inferred from the equation that a lower pKb value leads to a higher binding energy when no significant steric effect exists. This conclusion can be supported by the order of binding energies of 1a, 1c, 1d, and 1e. The binding energies in Table 1 are expected to deviate from the value in the above hypothetical model for two reasons. First, a metal cation is different from a proton. In addition, a central metal in a metallomacrocycle cannot be fully modeled as an isolated metal cation. The actual charge at the central metal is smaller than the charge at the metal cation. It is reasonable that the binding energies of 1a and 9a are substantially larger than 9.5 kcal/mol because the charges at the central metals in 1 and 9 are more positive than 1+. It is also understandable that the binding energies of 6a and 7a are close to 9.5 kcal/mol because their central metals have charges close to 1+. Moreover, it is not surprising that the binding energy of 8a is appreciably smaller than 9.5 kcal/mol in view of the small positive charge at the central copper atom. 3.4. Orbital Levels. The distribution of the highest occupied molecular orbital (HOMO) does not change considerably from 1 to monoligated 1a and bisligated 1g, whereas the distribution of the lowest unoccupied molecular orbital (LUMO) of 1 is significantly different from that of 1a (Figure 3). The energetic levels of the HOMO
1, HOMO, LUMO, and LUMO + 1 are

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given in Table 3. The orbital levels of 1, 6, and 7 are close to each other, as are those of 1a, 6a, and 7a. Generally, the dative binding elevates those orbitals, and the extent of elevation is greater for a stronger ligand. It can be seen from Figure 3 that the HOMOs and LUMOs are located almost exclusively in the aromatic macrocycles. Because a dative ligand donates charges to the macrocycle, it seems that a higher charge density contributes to higher orbital levels. The HOMO and LUMO are elevated to similar extents, and the HOMO
LUMO gap is not considerably affected by the axial binding. Comparison of the orbital levels between 1 and 4 and between 3 and 2 suggests that meso tetraaza substituents lead to lower-lying HOMOs and LUMOs. Comparison of the orbital levels between 2 and 4 and among 3, 1, and 5 suggests that tetrabenzo annulations lead to higher-lying HOMOs and smaller HOMO
LUMO gaps. The orbital levels of an aluminum phthalocyanine are lower than the corresponding ones in another metallophthalocyanine. This is as expected because the electronic effect of a halogen ligand is opposite to that of a dative ligand. A dative ligand donates charges and elevates orbital levels. In contrast, a halogen ligand accepts charge and, hence, lowers the orbital level. The charge acceptance effect of a halogen ligand is stronger than the donation effect of a dative ligand. However, the extent of orbital lowering of a halogen ligand is similar to the extent of elevation of a dative ligand. This might be because the halogen ligand mainly accepts charge from the central metal rather than the macrocycle. 3.5. Q Bands and Singlet
Triplet Gaps. Aromatic macrocycles are extensively utilized as photosensitizers in a noninvasive treatment called photodynamic therapy (PDT).37
40 In PDT, a photosensitizer first absorbs energy and is excited to the first singlet state (S1). An S1 f T1 intersystem crossing follows, and the triplet state (T1) transfers its energy to the triplet oxygen to generate singlet oxygen, which will eventually kill targeted cells. Some criteria must be met for a photosensitizer to generate satisfactory results. First, the photosensitizer should have a strong absorption band in the therapeutic window (600
900 nm) and preferably should be red-shifted because a higher wavelength stimulates a deeper penetration. Moreover, the energy gap between T1 and the ground singlet state (S0) must be greater than or equal to 22.5 kcal/mol.41,42 The application of a photosensitizer is usually conducted in a solvent. Moreover, in human bodies, biological molecules, including targeted tumors, might have electron-donating groups that are potential binding ligands for metallomacrocycles. Therefore, it is necessary to consider the effects of axial bindings on molecular properties associated with photodynamic therapy. Previous examinations have suggested that the B3LYP hybrid density functional is reasonable for use in studying the electronic transitions of phthalocyanines, although some other functionals might provide better agreement between experimental and calculated results.43 Therefore, we chose the B3LYP functional for the time-dependent density functional theory (TDDFT) investigations in this work because it was already used throughout the rest of this study. It is expected that this functional is, at least, sufficient to offer the trend of the Q band upon axial bindings. The solvent model was not included because previous studies suggest that the effects from solvent models are relatively small for systems such as those investigated here.41 Vertical excitation energies of 1, 1a, 1e, and 1g were calculated with the TDDFT at the TD-B3LYP/6-311+G(d,p) level. As can be seen from Table 3, the LUMO and LUMO
1 are almost degenerate for both nonligated and ligated phthalocyanines. The Qx band is 9048

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Table 3. Energy Levels of Selected Orbitals (au) MMc

ligand

HOMO
1

HOMO

LUMO

LUMO + 1

1


0.245


0.181


0.102


0.102

MgPc

py

1a


0.235


0.171


0.091


0.091

MgPc

Im

1e


0.231


0.168


0.088


0.087

MgPc

py + Im

1f


0.221


0.166


0.085


0.085

MgPc

py  2

1g


0.224


0.169


0.088


0.088

2


0.191


0.189


0.079


0.079

py

2a


0.180


0.175


0.069


0.068

py

3 3a


0.252
0.234


0.211
0.196


0.114
0.098


0.114
0.098

4


0.193


0.170


0.078


0.078

py

4a


0.182


0.162


0.069


0.069

5


0.219


0.166


0.098


0.098

5a


0.213


0.158


0.089


0.089

6


0.246


0.179


0.100


0.100

py

6a


0.235


0.170


0.090


0.089

py

7 7a


0.247
0.235


0.182
0.172


0.102
0.091


0.102
0.091

MgPc

MgP MgPpy MgTAP MgTAP MgTBP MgTBP MgNc MgNc

py

BePc BePc ZnPc ZnPc

9


0.234


0.172


0.091


0.091

CaPc

py

9a


0.224


0.162


0.084


0.081

CaPc

py  2

9b


0.217


0.157


0.076


0.074

CaPc

py  3

9c


0.210


0.152


0.070


0.070

10


0.254


0.188


0.110


0.110

CaPc

AlPcCl AlPcCl

py

10a


0.234


0.182


0.103


0.103

AlPcCl AlPcF

Im

10b 11


0.228
0.253


0.179
0.186


0.100
0.108


0.099
0.108

AlPcF

py

11a


0.243


0.180


0.101


0.101

Table 4. Absorption Energies, Wavelengths, Oscillator Strengths, Main Configurations, and Singlet
Triplet Gaps of Magnesium Phthalocyanines absorption transition ES
T E (eV) λ (nm)

f

main configuration

(kcal/mol)

2.0222

613

0.426 HOMO f LUMO (94.7%)

2.0222

613

0.426 HOMO f LUMO + 1 (94.7%)

1a 2.0141

616

0.372 HOMO f LUMO (93.1%)

24.0

2.0362 1e 2.0358

609 609

0.415 HOMO f LUMO + 1 (94.1%) 0.404 HOMO f LUMO + 1 (94.0%)

23.9

2.0385

608

0.418 HOMO f LUMO (94.1%)

1g 2.0277

611

0.375 HOMO f LUMO (92.2%)

2.0277

611

0.375 HOMO f LUMO + 1 (92.2%)

1

23.5

24.5

mainly contributed by the HOMO f LUMO transition, and the Qy band is mainly contributed by the HOMO f LUMO + 1 transition. As a result, the first two transitions forming the Q band exhibit little splitting (Table 4). Those two absorptions, denoted as Qx and Qy bands here, have almost the same oscillator strength. The experimental value for the Q band of 1 in vapor is 666 nm.44 The discrepancy between this value and the calculated result is within 0.2 eV, further justifying the validity of the functional employed. Apparently, axial binding causes no significant changes in the descriptors of the Q band, including the transition energy, the oscillator strength, and the main configuration.

The calculated singlet
triplet gaps are also included in Table 4. Magnesium phthalocyanine has a sufficient energy gap to excite the ground-state oxygen. Upon axial binding, only insignificant increases in the singlet
triplet gaps were found. Therefore, concerning the two properties important for PDT, the absorption maximum and the singlet
triplet gap, the effects of axial binding are relatively small. Accordingly, it is reasonable to omit the effects of axial binding when modeling these photophysical features of photosensitizers. 3.6. Redox Chemistry. The aromatic macrocycle can undergo facile oxidations and reductions because of its significant aromatic conjugation.45,46 These features are associated with many applications such as semiconductor devices and photocatalysis.47
50 These macrocycles also play key roles in transferring electrons in some biological processes. An understanding of oxidized and reduced macrocycles is thus essential to the understanding of related mechanisms in which tetrapyrrole-based macrocyclic radicals are important intermediates. It is not surprising that the absorption maximum is little affected by the axial binding. Even though the frontier orbitals are elevated by axial binding, the extents of elevation are similar for relevant orbitals. On the other hand, oxidation and reduction are related to the absolute levels of the HOMO and LUMO, respectively.25
27 Consequently, they are expected to be changed significantly by axial binding. To interpret structural changes upon oxidation or reduction, the monocation and the monoanion of MgPc were optimized. The netural MgPc has D4h symmetry. The removal of one electron from the HOMO, forming the cation, results in a 2A1u state. The D4h symmetry 9049

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was retained for the cation. The addition of one electron to one of the 2-fold-degenerate LUMOs, forming an anion, leads to the Jahn
Teller splitting of the Eg orbitals. The Eg orbitals split into B2g and B1g orbitals, and the lower B2g orbital is half-occupied. This leads to a 2B2g electronic state, and the symmetry is downgraded to D2h. Two adjacent subunits in the anion become inequivalent because of the splitting, but the differences are within 0.04 Å. Also, the structures of the neutral MgPc, the cation, and the anion are similar to each other. If the average values in the anion are used for comparison, the differences of the corresponding bond lengths among the neutral MgPc, the cation, and the anion are all smaller than 0.01 Å (Table S1 in the Supporting Information). For all three, the ring planarity is retained. Therefore, the geometric relaxation after vertical oxidation or reduction is expected to be relatively small. The electron affinity (EA) and ionization potential (IP) are defined so that both are positive. Both adiabatic and vertical processes were

investigated here EAðverticalÞ ¼ Eðoptimized MPcÞ
Eð½MPc
at the optimized geometry of neutral MPcÞ EAðadiabaticÞ ¼ Eðoptimized MPcÞ
Eðoptimized ½MPc
Þ IPðverticalÞ ¼ Eð½MPcþ at the optimized geometry of neutral MPcÞ
Eðoptimized MPcÞ

IPðadiabaticÞ ¼ Eðoptimized ½MPcþ Þ
Eðoptimized MPcÞ A higher EA value is associated with an easier reduction, whereas a lower IP value is associated with an easier oxidation. The EAs and IPs are listed in Table 5. The vertical IP of 1 is almost identical to the adiabatic value. This is not surprising because the symmetry group does not change after the oxidation. The vertical EA of 1 is slightly smaller than the adiabatic value, and the small difference is probably caused by the symmetry distortion of the Jahn
Teller splitting. The vertical EA is supposed to be smaller than the adiabatic one because the relaxation after the vertical transition leads to a more stable anion. For 1a, the difference between the adiabatic and vertical values is almost the same as that for 1. The strength and the number of ligands seem to have relatively small effects on the vertical values. Both the EA and IP values become smaller after axial binding. This corresponds to an easier oxidation but a less encouraged reduction and is consistent with the elevation of the HOMO and LUMO discussed in section 3.4.

Table 5. Electron Affinities and Ionization Potentials (kcal/ mol) EA a

a

IP b

vert

adia

vert

adia

1

38

42

138

138

1a

32

37

131

131

1e

30

130

1g

30

130

vert, vertical transitions. b adia, adiabatic transitions.

Table 6. Donor
Acceptor Interaction Energies Calculated from the Second-Order Perturbation Theory Analysis (kcal/mol)a Mc T M MMc

ligand

MgPc

LTM

Mc f M

Mc r M

bbb (%)

LfM

LrM

bb (%)

10

1

409

19

5

MgPc

py

1a

424

17

4

84

9

MgPc

Im

1e

421

17

4

90

8

8

MgPc

py + Imc

1f

465

23

5

64

7

10

MgPc

py + Imd

1f

80

7

8

MgPc

py  2

1g

464

22

5

68

7

10

MgP

2

371

15

4

MgP MgTAP

py

2a 3

389 433

15 22

4 5

79

8

10

MgTAP

py

3a

440

17

4

83

10

11

4

350

14

4

4a

369

14

4

80

7

8

5

403

18

4

5a

420

16

4

84

9

10

6

612

26

4

25 73

4 10

172

11

6

112

27

19

46

14

24

40

2

4

MgTBP MgTBP

py

MgNc MgNc

py

BePc BePc ZnPc

py

6a 7

644 643

ZnPc

py

7a

620

57

8

8

704

149

17

8a

695

74

10

9

197

8

4

9a

234

8

3

CuPc CuPc

py

CaPc CaPc

py

a

Sum of orbital interactions over 0.05 kcal/mol. b bb (%), percentage of the back-bonding energy in the total interaction energy. c Pyridine side. d Imidazole size. 9050

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The Journal of Physical Chemistry A It can also be rationalized by the charge distribution discussed in section 3.2. The charge donation to the macrocycle increases the electron density and, hence, increases its tendency to lose charges. 3.7. Donor
Acceptor Interaction Energies. For an idealized Lewis structure, a localized Lewis natural bond orbital (NBO) is fully occupied. The interaction between a donor and an acceptor leads to the delocalization of electrons from a fully occupied Lewis NBO to an empty non-Lewis NBO. Therefore, the occupancy of a Lewis NBO is usually slightly smaller than 2 and that of a non-Lewis NBO can be slightly larger than 0. The deviation from the zeroth-order idealized Lewis structure can be analyzed by second-order perturbation theory. The interaction energy between a donor and an acceptor estimated from this NBO analysis is correlated with the interaction strength between the central metal and the ligand or macrocycle51 Eð2Þ ¼ ΔEij ¼ qi

F 2 ði, jÞ εj
εi

where qi is the occupancy of the ith donor orbital, εi and εj are diagonal elements, and F(i,j) is the off-diagonal NBO Fock matrix element. The calculated interaction energies are given in Table 6. It is first necessary to examine the Lewis structures to establish which parts are the donors and which parts are the acceptors. For all cases, the most stabilized zeroth-order Lewis structure for a bare MMc is given as its ionic form, M2+ + Mc2
. No two-center M
N NBO bond orbital is present. This suggests that the ionic interaction contributes significantly to macrocyclic M
N bonding. Likewise, for an axially bound MMcL unit (L = ligand), the most stabilized Lewis structure is given as the ionic form of the bare metallomacrocycle plus the neutral ligand, denoted as M2+ + Mc2
+ L. This suggests that the nature of axial M
N bonding is probably no different from that of macrocyclic M
N bonding. The donation from the macrocycle or the ligand to the central metal is significant for each case. This suggests a significant deviation from the idealized Lewis structure. In other words, the charge at a central metal would be less positive than 2+. The donation from an axial ligand further increases the electron population in the central metal. The donation effect from the axial ligand has been discussed previously, and the donation effect from the macrocycle is probably contributed by the two dative M
N bonds (Figure 4). It should be noted that the four macrocyclic M
N bondings are actually equivalent, and each structure in Figure 4 is solely a Lewis structure rather than an actual structure. The final structure is contributed by the resonance of the two Lewis structures in which the four macrocyclic M
N bondings are viewed as distinguishable. A dative bonding in Figure 4 is no different from an axial dative metal
ligand bonding. A nondative bonding in Figure 4 is no different from an axial nondative aluminum
halogen bonding. It is thus expected that the four macrocyclic M
N bondings as a whole form an electron acceptor because, as discussed in section 3.2, the electronic effect of a nondative bonding is stronger than that of a dative bonding. In addition, it is possible that the axial M
N bonding also participates in this resonance, which could eventually decrease the differences between the axial and macrocyclic bondings.52 Such resonances seem to be common in hypercoordinate systems and probably contribute to the stabilization of hypercoordination.52 This also raises an important feature of the effect of the macrocyclic ring in which the donation from the two dative M
N bondings leads to the deviation from

ARTICLE

Figure 4. Resonance between two Lewis structures contributing equally to the final structure. Note that the four colored M
N bondings are equivalent in the final actual structure.

the ionic form. In other words, the shared interaction (covalent bond) contributing to the final structure probably arises from this donation. The axial binding is hence supposed to further increase the components of shared interactions in the macrocyclic bondings if the resonance exists. The donation strengths from phthalocyanine rings to different metals are in the order Cu > Zn > Be > Mg > Ca. This explains the order of positive charges at those metals, Ca > Mg > Be > Zn > Cu. Likewise, the donation strengths from different macrocycles to magnesium are in the order TAP > Pc > Nc > P > TBP. This also rationalizes the order of negative charges at those macrocycles. Moreover, the donation strengths from pyridine ligands to different metals are in the order Be > Zn > Mg > Cu > Ca. This is consistent with the order of positive charges at the pyridine ligands in those ligated macrocycles. In addition, these interaction energies provide another quantitative route to evaluate the donation strength. For example, the donation from the imidazole to the magnesium (90 kcal/mol) in 1e is slightly stronger than that from the pyridine (84 kcal/mol) in 1a. As expected, the back-donation from a central metal to a ligand or a macrocycle is much weaker. The back-donation from a central metal to an axial ligand is higher than that from a metal to a macrocycle (illustrated by the percentage of the back-donation energy in the total interaction energy). For a main-group MMc, the back-donation accounts for no more than 12% of the total interaction. The back-donation from a central zinc is significantly stronger, probably contributed by its d orbitals. The backdonation from the central copper, whose d orbitals are not full, is strongest. This is consistent with a previous work indicating that back-donation energies are generally larger for those metals whose d orbitals are not full.25 3.8. M
N Bondings. In the atoms-in-molecules (AIM) theory, descriptors at the bond critical point (BCP) contain information about the properties of the corresponding bond. The electron density at the BCP, FBCP, is an indication of the bond strength. The Laplacian at the BCP, r2F, is composed of three curvatures, λ1, λ2, and λ3. The first two are negative and perpendicular to the bond path. The third is positive and tangential to the bond path. A positive Laplacian is associated with electron depletion, and a negative Laplacian is associated with electron concentration. The local energy density, E(r), is the sum of the kinetic energy density, G(r), and the potential energy density, V(r). If all quantities are in atomic units, E(r) is related to the Laplacian by 1 EðrÞ ¼ ∇2 FðrÞ
GðrÞ ¼ GðrÞ þ V ðrÞ 4

ð1Þ

Generally, a shared bonding is related to a negative Laplacian, a negative E(r), and a large F(r). A closed-shell bonding is related 9051

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Table 7. AIM Descriptors at the M
N Bond Critical Points (au)a F

λ1

λ2

λ3

r2F

G(r)

V(r)

E(r)

dMb

dNc

ratiod

1

Mg
N

0.049


0.076


0.070

0.508

0.362

0.079


0.067

0.012

1.623

2.172

0.43

1a

Mg
Nme

0.044


0.064


0.061

0.436

0.311

0.067


0.056

0.011

1.653

2.228

0.43

1a

Mg
Naf

0.031


0.041


0.039

0.259

0.179

0.039


0.033

0.006

1.755

2.433

0.42

1e

Mg
Nm

0.043


0.063


0.061

0.430

0.306

0.066


0.055

0.011

1.656

2.233

0.43

1e

Mg
Na

0.032


0.044


0.042

0.281

0.195

0.042


0.035

0.007

1.740

2.389

0.42

1f

Mg
Nm

0.047


0.071


0.068

0.477

0.338

0.073


0.061

0.012

1.637

2.196

0.43

1f

Mg
Nag

0.017


0.016


0.015

0.113

0.083

0.018


0.016

0.002

1.924

2.758

0.41

1f 1g

Mg
Nah Mg
Nm

0.022 0.047


0.024
0.071


0.023
0.068

0.167 0.478

0.119 0.339

0.026 0.073


0.022
0.062

0.004 0.012

1.844 1.636

2.587 2.195

0.42 0.43

1g

Mg
Na

0.018


0.019


0.018

0.130

0.093

0.021


0.018

0.003

1.895

2.703

0.41

6

Be
N

0.050


0.084


0.068

0.374

0.222

0.061


0.067


0.005

1.173

2.371

0.33

6a

Be
Nm

0.043


0.064


0.055

0.310

0.191

0.052


0.056


0.004

1.200

2.444

0.33

6a

Be
Na

0.048


0.079


0.077

0.404

0.249

0.064


0.066


0.002

1.161

2.368

0.33

7

Zn
N

0.087


0.118


0.112

0.599

0.369

0.109


0.125


0.017

1.811

1.968

0.48

7a

Zn
Nm

0.078


0.101


0.096

0.523

0.325

0.095


0.109


0.014

1.845

2.015

0.48

7a 8

Zn
Na Cu
N

0.054 0.094


0.062
0.123


0.059
0.120

0.310 0.656

0.189 0.413

0.057 0.119


0.066
0.135


0.009
0.016

1.988 1.779

2.194 1.937

0.48 0.48

8a

Cu
Nm

0.091


0.118


0.116

0.640

0.406

0.116


0.131


0.015

1.786

1.949

0.48

8a

Cu
Na

0.024


0.021


0.020

0.113

0.072

0.020


0.022


0.002

2.423

2.550

0.49

9

Ca
N

0.044


0.055


0.048

0.327

0.225

0.052


0.049

0.004

2.157

2.246

0.49

9a

Ca
Nm

0.041


0.050


0.045

0.304

0.208

0.048


0.044

0.004

2.181

2.272

0.49

9a

Ca
Na

0.027


0.029


0.027

0.171

0.116

0.026


0.023

0.003

2.355

2.503

0.48

9b

Ca
Nm

0.037


0.044


0.040

0.269

0.185

0.042


0.038

0.004

2.217

2.316

0.49

9b 9c

Ca
Na Ca
Nm

0.023 0.033


0.024
0.039


0.023
0.036

0.139 0.237

0.093 0.162

0.021 0.037


0.019
0.033

0.002 0.004

2.415 2.254

2.583 2.364

0.48 0.49

9c

Ca
Na

0.019


0.019


0.018

0.111

0.074

0.017


0.015

0.002

2.479

2.679

0.48

a

Average values listed when small variances exist. b dM, distance between the metal and the BCP. c dN, distance between the nitrogen and the BCP. d ratio, ratio of dM to the bond length. e Macrocyclic M
N bonding. f Axial M
N bonding. g Pyridine side. h Imidazole side.

to a positive Laplacian, a positive E(r), and a small F(r). A positive Laplacian, a negative E(r), and a moderate F(r) are often regarded as the sign of an intermediate bonding.53 The descriptors at M
N BCPs are reported in Table 7. All Laplacian values in this table are positive, consistent with the relatively small FBCP values. This suggests that the contributions from closed-shell interactions (ionic bonds) to the M
N bondings, both macrocyclic and axial, are significant. The FBCP values in the bare metallophthalocyanines are in the order Cu > Zn > Be > Mg > Ca. This is consistent with the order of donation strengths. The E(r) values are negative for Be
N, Zn
N, and Cu
N bondings and positive for Mg
N and Ca
N bondings. Thus, Be
N, Zn
N, and Cu
N bondings bear some contributions from shared interactions (covalent bonds). Because the E(r) values for Mg
N and Ca
N bonds are only slightly positive, these bonds probably also have a small amounts of covalency. The order of the covalency is consistent with the order of donation strengths, supporting the conclusion that the covalency is contributed mainly, if not exclusively, by the donor
acceptor donation. Upon the first axial binding, macrocyclic M
N bondings become weaker. This is illustrated by their smaller FBCP values. Despite the weakening, the macrocyclic M
N bondings are still stronger than the corresponding axial ones, except for Be
N. The macrocyclic M
N bondings in bisligated 1g are stronger than those in monoligated 1a. In most cases, the absolute value of a descriptor in a macrocyclic M
N bonding is moderately larger

than the corresponding value in the axial case. Nonetheless, their signs do not vary in all cases. This is not inconsistent with the previous statement that the resonance among the hypercoordinate bondings minimizes their differences. The BCP is located in the middle of two nuclei for homoatomic bonding. There have also been some discussions about using the location of the BCP as an index for the polarity of a bonding.54,55 At least for bondings formed by the same atomic pair or analogous atomic pairs, a relation between this ratio and the polarity might still exist. The ratio of dM (the distance between the BCP and the central metal) to the bond length, which is expected to be 0.5 for homoatomic covalent bonding, was examined, and the results are included in Table 7. The ratio of a macrocyclic M
N bonding is similar to that of the corresponding axial bonding. This is not surprising in view of the resonance between them. The ratios in beryllium phthalocyanines are significantly smaller than those for the metals, and the ratios in copper, zinc, and calcium phthalocyanines are close to 0.5. It is thus unlikely that this ratio is directly related to the bond polarity because previous sections indicated the lower polarity of beryllium phthalocyanines. Instead, this ratio seems to be correlated with the atomic radius of the central metal. The general order of the radii of the central metals is Ca > Cu ≈ Zn > Mg > Be, which is consistent with the order of the ratios. According to the AIM theory, the zero-flux surface in the gradient vector field passing through the BCP is the shared border of two atoms. This seems to support a relation between the ratio and the 9052

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The Journal of Physical Chemistry A

Figure 5. Structure of the magnesium phthalocyanine dimer. The dotted lines denote the intermolecular Mg
N interactions.

atomic radii defined by the AIM theory. However, apparently, the ratio is not determined solely by the empirically common atomic radii because nitrogen must be larger than all of the central metals to make those ratios below 0.5. The AIM radius should be distinguishable from the commonly known atomic radius because this theory defines an atom in a molecule based on topological analyses of the electron density. An AIM atom is not necessarily spherical, and an AIM atomic radius should be specified with a bonding direction. Regarding a metal
nitrogen bonding contributed by dative donation from the nitrogen lone pair, the electron density of the nitrogen spreads toward the metal side, thus increasing the AIM radius of the nitrogen along the metal
nitrogen direction. 3.9. Orientation of the Lone Pair. In Figure 4, all four pyrrolic nitrogens have lone pairs, but only the two with lone pairs pointing along the metal
nitrogen axis contribute to the donation. This implies that the interaction is affected by the orientation of the lone pair. For a small ligand, the donating lone pair points perpendicular to the macrocycle ring to facilitate a considerable donating interaction. In a previous section, it was shown that a methyl substituent on the axial ligand can alter the orientation of the ligand and, hence, reduce the donation. The steric demand of a ligand is particularly important if the electronrich group is part of a large molecule such as a biological macromolecule. In the crystal structure of MgPc, it was found that the central Mg is not in the plane because of its interaction with a meso nitrogen from another MgPc molecule.56,57 In this case, the meso nitrogen lone pair points parallel to the macrocycle, whereas the Mg
N interaction is along the stacking axis. The optimized structure of the dimer is given in Figure 5. The charge at the central Mg is 1.409, which is more positive than that in an isolated MgPc. The charge at the meso nitrogen interacting with the central Mg is
0.591, which is more negative than that in an isolated MgPc. The charges at the other three meso nitrogens range from
0.480 to
0.487, close to the one in an isolated MgPc,
0.489. This indicates a small charge transfer from the Mg to the meso N. (Note that the charge obtained by the meso N is not exculsively from the Mg.) In view of the fact that the lone pair perpendicular to the macrocycle ring donates charges to the central Mg, it seems that two effects exist concerning the Mg
N interaction. For one side, the lone pair transfers charge to the metal acceptor. For the other side, the electronegative nitrogen attracts charge from the Mg because of the electronegativity difference. When the lone pair points along the interaction axis, the former behavior is encouraged, whereas when the lone pair points perpendicular to the interaction axis, the latter dominates. Because the charge distribution is related to many properties, the orientation of the lone pair significantly affects how properties of the system are changed by bonding.

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4. CONCLUSIONS The molecular properties of a tetrapyrrole-based aromatic macrocycle can be significantly affected by axial binding. In this work, we studied whether and how the properties of a macrocycle are affected. The results reported herein are expected to provide helpful information to fields such as metal bindings in biomolecules and axially constructed materials. The central metal no longer resides within the plane after the binding of one ligand. When two ligands bind to the central metal from two sides, they structurally neutralize each other. The binding strength is also affected by the central metal and the macrocycle. An axial ligand donates charges to the central metal and the macrocycle when the lone pair orients along the interaction axis. A second binding thus becomes less favorable because the first one makes the binding target less positively charged. Frontier orbital levels are elevated because of doping charges to the macrocycle. This does not significantly change the singlet
triplet gap and absorption maximum, but it does affect the redox chemistry of the metallomacrocycle. NBO analyses suggest that the ionic form (M2+Mc2
) of a metallomacrocycle is the most stable Lewis structure. Second-order perturbation theory indicates a significant deviation from the zeroth-order Lewis structure and significant donor
acceptor interactions between a macrocycle (or a ligand) and a central metal. The macrocyclic M
N bondings are weakened upon axial binding. A central calcium is too large to fit the cavity of a phthalocyanine. Accordingly, multiple ligands could bind to the calcium from one side. The aluminum phthalocyanine halogen is another special case because it has a halogen ligand bound to the aluminum through a nondative bond. The halogen ligand has some different effects on molecular properties. For example, it attracts rather than donates charges from the central metal. Consequently, the relevant orbital levels are lowered. The major part of this study focused on the case in which the lone pair points along the interaction axis to facilitate the donation. However, when the electron-rich group is a part of a large molecule, the lone pair might point perpendicular to the interaction axis because of the steric demand. This can lead to quite different effects compared to the former case. ’ ASSOCIATED CONTENT

bS

Supporting Information. Content as mentioned in the text (Figures S1
S4, Tables S1 and S2). This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The author thanks Dr. Malcolm E. Kenney for valuable suggestions and the Case High Performance Computing Cluster for the allocation of computing time. ’ REFERENCES (1) Firme, C. L.; Antunes, O. A. C.; Esteves, P. M.; Correa, R. J. J. Phys. Chem. A 2009, 113, 3171–3176. (2) Merino, G.; Mendez-Rojas, M. A.; Vela, A.; Heine, T. J. Comput. Chem. 2007, 28, 362–372. (3) Cotton, F. A.; Millar, M. J. Am. Chem. Soc. 1977, 99, 7886–7891. 9053

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