Energy Spectra and Electric and Magnetic Properties of One

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Energy Spectra and Electric and Magnetic Properties of One-Dimensional Stacks of Conjugated π-Electron Systems with Defect Surface States. II. π-Systems with Schottky and Chemisorption Surface States F. Dietz,*,† A. Staykov,‡ K. Mu¨llen,§ and N. Tyutyulkov| Wilhelm-Ostwald-Institut fu¨r Physikalische und Theoretische Chemie, UniVersita¨t Leipzig, D-04103 Leipzig, Johannisallee 29, Germany, Institute for Materials Chemistry and Engineering, Kyushu UniVersity, 744 Motooka, Nishi-ku, Fukuoka, 819-0395 Japan, Max-Plank-Institut fu¨r Polymerforschung, D-55128 Mainz, Ackermannweg 10, Germany, and Chair of Physical Chemistry, UniVersity of Sofia, 1 J. Bourchier BouleVard, BG-1126, Sofia, Bulgaria ReceiVed: March 21, 2010; ReVised Manuscript ReceiVed: June 28, 2010

The energy spectra and magnetic properties of one-dimensional stacks consisting of polycyclic aromatic hydrocarbons with Schottky, chemisorption, and Tamm-chemisorption-type surface defects are investigated theoretically by means of the many-electron band theory. The effective spin-exchange interaction between the electrons within the half-filled bands is calculated, and the results are compared for different ordering of the radicals in the stacks. The type of defects are systematically investigated, and the obtained results show that the supermolecular stack arrangement is of primary importance for the stability of the ferromagnetic coupling of electrons within the half-filled band. Systems with ferromagnetically coupled electrons are determined, which is promising for the possible experimental preparation of pure organic materials with magnetic properties characterized with high critical temperature. 1. Introduction The investigations in this paper are a continuation of our efforts to systematically study the electronic and magnetic properties of one-dimensional (1D) stacks of polycyclic aromatic hydrocarbons (PAHs) with different types of defects. In ref 1 we investigated stacks of PAHs with Tamm-type surface defects, and we showed the conditions, which stabilize the high-spin state, characterized with ferromagnetically (FM)-coupled electrons, over the low-spin state, characterized with antiferromagnetically (AFM) coupled electrons. However, the Tamm-type of surface states are a particular case of structural defects in the lattice of PAHs and nanographenes, and here we extend our study to PAHs containing Schottky, chemisorption, and Tamm-chemisorption-type of surface states.2-8 In this way, we will be able to make a general conclusion on the possibility to obtain experimentally pure organic polymers with macroscopic FM properties consisting of 1D stacks of PAHs. The magnetism as macroscopic phenomenon is a cooperative effect caused by the interaction of a large number of electrons with unpaired spins.9-13 If the number of interacting spins is reduced, macroscopic magnetism would not be observed. A huge number of compounds with magnetic properties containing metals or metal complexes are known and used everywhere in science and industry.9 However, only a few pure organic compounds possessing magnetic properties are known, and their critical temperatures are not higher than several Kelvins.9-12 The compounds suitable for the synthesis of organic materials with magnetic properties are stable radicals that build structures with transitional symmetry with unpaired electrons in their elementary units (EUs).1,14-18 1D stacks of PAHs are promising * Corresponding author. E-mail: [email protected]. † Universita¨t Leipzig. ‡ Kyushu University. § Max-Plank-Institut fu¨r Polymerforschung. | University of Sofia.

candidates for such materials.19,20 Not so long ago the synthesis of large PAHs seemed out of reach, and they were used only as theoretical models. In a recent paper, a new synthetic concept for the synthesis of huge PAHs and their derivatives was introduced.19 It was shown that PAHs and especially hexabenzocoronene show a large tendency to build 1D stacks.19 There are two kinds of 1D stacks of PAHs: stacks formed by PAHs without defects and stacks built by PAHs with defects characterized by singlet or high-spin ground state.1,21 In a recent work, the energy spectra of 1D stacks of PAHs without defects were investigated theoretically.21 The main characteristic of their energy spectra is the energy gap, which is different from zero. Different kinds of defect states in the PAH lattice, namely Tamm, Schottky, and chemisorptions, can cause significant changes in their energy spectra, and therefore that of the stacks, and can lead to an arising of molecule orbitals situated within the energy gap of the hydrocarbons and a half-filled band (HFB) within the energy gap of the stacks.1 Defects in nanographenes can be introduced by irradiation with different particles, i.e., neutrons, protons, R-particles, etc.22,23 Thus, a carbon atom from the periphery or the inner part of the PAH can be knocked out of the layer, and the result would be a Schottky or Tamm point defect state, respectively. Such processes are often observed on the graphite bars in the nuclear power plants used to slow down the chain reactions. However, in this manner is not possible to control the position of the defects, and the result would be a disordered system. Defects in PAHs can also be introduced by the “bottom-up” approach, where the PAHs are functionalized with heteroatoms during the synthetic route.19,20 In this way it is possible to design and create PAHs with defects on specific position.20 The arrangement of these PAHs in 1D stacks would result in well-ordered systems. In the past decades, carbon nanostructures have expanded their applications in the fields of nanoelectronics and nanoscience.13,24,25 Carbon nanotubes have found applications in electron-transport and ion-transporting devices; additionally, in

10.1021/jp1025398  2010 American Chemical Society Published on Web 07/23/2010

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Figure 2. Investigated monoradicals with Schottky point lattice vacancies, which constitute the 1D stacks.

Figure 1. Investigated monoradicals with Schottky point impurity defects, which constitute the 1D stacks.

strain resistant nanomaterials, nanographenes are often used as electrodes in the scanning tunneling microscopy (STM) technique, and PAHs are used in the fabrication of devices with interesting properties such diodes and field effect transistors.26 The remarkable ability of PAHs to form 1D stacks, which represent well-ordered nanostructures, is a bridge between the single molecule properties and the macroscopic properties of the system.19,20 Thus, a stack of PAHs with nonzero highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) gaps would show interesting semiconductive properties,21 and a stack of open-shell PAHs would eventually show a material with macroscopic FM properties.1 2. Objects of Investigations 2.1. Systems with Schottky Defects. The study in this work is concentrated on PAHs with defect states. Our previous work1 investigated the energy spectra and magnetic properties of 1D stacks of PAHs with Tamm defect states. Here we continue the systematic study on 1D stacks of PAHs with Schottky defects. There are two types of Schottky point defects in PAHs:2-5 (i) interstitial impurity defects, which could be created when one or more carbon atoms are substituted by heteroatoms; (ii) lattice vacancies: when one or more carbon atoms are deleted within a hydrocarbon. Systems with Schottky Point Impurity Defects. The investigated monoradicals with Schottky point impurity defects, which constitute the 1D stacks, are shown in Figure 1. The considered PAHs are derived by replacing of a carbon atom with a heteroatom, from pyrene, coronene, and hexabenzocoronene. They are denoted respectively as a-1, a-2, and a-3. Dimers of the closed-shell analogous of cation radicals b-1 (C30H15 N+) and b-2 (C36H15 N+), shown in Figure 1, are investigated in the paper of Tran et al.6 Systems with Schottky Point Lattice Vacancies. The investigated monoradicals with Schottky point lattice vacancies, which constitute the 1D stacks, are shown in Figure 2. The removing of one carbon atom will result in unsaturated dangling molecular orbitals on the three neighboring carbon atoms. The atoms on which the dangling orbitals are localized are highly reactive, which will certainly lead to changes in the geometry. We have performed geometry optimization of hexabenzocoronene containing Schottky point lattice vacancy with DFT/ B3LYP theory and 6-31G(d) basis set, implemented in the PCGAMESS/Firefly program.27 The optimized structure is

Figure 3. Optimized structure of hexabenzocoronene with one lattice vacancy. (A) Starting structure; (B) optimized structure.

Figure 4. Investigated monoradicals with delocalized states.

radical with a five-membered ring, as it is shown in Figure 3. This result corresponds to the results in refs 28-30, in which the properties of isolated PAHs with Schottky vacancies were studied. 2.2. Systems with Chemisorption States. Chemisorption states are the result31,32 of bonding of an atom or an atomic group to a periphery carbon atom of the PAH. We consider two types of systems with chemisorption states: systems with delocalized states, and systems with localized states. Systems with Delocalized Chemisorption States. The investigated monoradicals with delocalized defect states, which constitute the 1D stacks, are shown in Figure 4. In the case of radical d-2, coronene is substituted by the stable 2-azaphenalenyl radical (Az), synthesized by Rubin et al.33 The pure organic systems with metallic ground state synthesized by Huddon et al.34,35 are stacks whose EUs are composed of monomers containing the Az subunit. Thus, the combination of the easily building stacks coronene and the Az radical, known with its magnetic ground state, is a promising molecular design for organic magnetic material. Systems with Localized Chemisorption States. The existence of localized chemisorption states can be derived from the extended Coulson-Rushbrooke-Longuet-Higgins (CRLH) theorem.36-40 The theorem determines the basic structural principle of the systems with localized chemisorption states.36,37 Let us consider a π-system consisting of a radical subunit R · , for which the CRLH theorem or the extended CRLH theorem (ECRLH) is valid, i.e., R · has one nonbonding molecular orbital (NBMO), linked with one arbitrary closed-shell molecule M:

R · -M If the π-center r of R · , which is connected with M, belongs to the set of the nonstarred atoms (the MO coefficient Cr ) 0),

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Dietz et al. of two neighboring monoradicals in different pure molecular radical crystals (MRCs) vary in the range between 3.1 Å in the stacks of Wurster′s radicals49 up to 3.71 Å in the galvinoxyl stacks.50 The results of the magnetic characteristics are qualitatively identical when obtained with different values of the interplanar distance R as it is shown in Table 3. Throughout all other tables in this paper, we have adopted the value of R ) 3.35 Å, which is observed for the graphite.51

Figure 5. Localization of the NBMO within the Az radical of coronene substituted with a Az radical. C denotes the NBMO coefficients.

3. Methods of Investigation Here, the methods are described briefly, while a more detailed explanation is given in ref 1 (see also ref 15). 3.1. Energy Spectra. The MOs of the 1D system have the form of Bloch running waves

|k〉 ) N-1/2

∑ ∑ Cr(k) exp(-ikµ)|r, µ〉 r

Figure 6. Model of polymethines substituted by Weitz radicals as EUs of 1D stacks Scheibe aggregates).

then all NBMO coefficients in the fragment M are equal to zero, i.e., the NBMO coefficients are nonzero only for the starred π-centers in R · , and the NBMO is strictly localized within the radical subunit R · . In the case of a homonuclear alternant radical R · , this result was obtained by Dewar.41 An example with coronene (M) substituted with the Az radical is shown in Figure 5. The system shown in Figure 5 should not be confused with molecule d-2 in Figure 4. For the latter, the bonding between the coronene and Az radical is achieved through two bonds where one of the bonding radical π-centers belongs to the starred atoms subset, while the second belongs to the nonstarred atoms subset. Thus, a delocalization of the NBMO on the coronene subunit should be observed. 2.3. Systems with Tamm and Chemisorption States. PAHs are not the only hydrocarbons known to build 1D supermolecular ordered structures. Scheibe aggregates42,43 are formed by polymethine dyes, which consist of a polymethine chain with an odd number of methine groups linked with atoms of elements of the groups III, V, or VI of the Periodic Table. These heteroatoms attached to the ends of the methine chain (i.e., its periphery) can be considered Tamm defect states.31,32 The three main groups of polymethines are the strepto-cyanines (PC), strepto-oxonoles (PO), and the strepto-merocyanines (PM), shown in Figure 6.44 An additional chemisorption defect is introduced by substituting a H-atom with a Weitz type radical.44,45 The 1D system build by such radicals can be considered as Scheibe aggregates with defect states. These aggregates are the first π-systems with intermolecular conjugation whose physical andspectroscopicpropertieshavebeeninvestigatedsystematically.42-44,46,47 2.4. Models of the 1D Stacks. The stacks of the disk-like π-systems are considered to be 1D crystals for which the Born-Karman cyclic conditions are fulfilled. The arrangement of the stacks is of slipped face-to-face type. We have considered only structures in which the monomers are slipped, but not structures in which the monomers are rotated around the columnar axis. Such rotated structures have been observed often in discotic mesophases. In ref 48, a theorem was formulated, which shows that the π-π interaction in a full face-to-face arrangement of the 1D system is nonbonding, i.e., the structure of such systems tends toward a system with reduced symmetry and depression of the π-electron energy. The theorem is valid for an arbitrary 1D system consisting of homonuclear molecules or radicals.48 The intermolecular distances between the planes

(1)

µ

where k ∈ [-π, π] is the wave vector, µ denotes the number of the EU, and |r,µ〉 is the rth atomic orbital (AO) within the µth EU. In the Hu¨ckel-Hubbard version of the Bloch method, the MO energies e(k) are eigenvalues of the energy matrix:

E(k) ) E0 + V exp(ik) + V+ exp(-ik)

(2)

where E0 is the energy matrix for the EU, V is the interaction matrix between neighboring EUs (µth and µ + 1th), and V+ is the transposed matrix. 3.2. Spin-Exchange Interaction in the HFB. The spinexchange interaction between the electrons within the HFB is characterized by the effective exchange integral, Jeff, which can be expressed as a sum of three contributions:1,15

Jeff ) J - Jkin + Jind

(3)

J is the direct (Coulomb, Hund) exchange integral between the Wannier states. Jkin is the kinetic exchange parameter representing the AFM contribution to the spin exchange:

Jkin ) -∆ε2 /2U

(4)

where ∆ε is the HFB width, and U is the renormalized Hubbard parameter.52 The term Jind expresses the indirect exchange (superexchange) via delocalized π-electrons in the filled energy bands. 3.3. Parametrization. The calculations have been carried out using a standard set of parameters.1 The dependence of the resonance integrals between neighboring carbon atoms within the EU on the bond lengths R has been calculated with Mulliken’s formula:53

β(R, Θ) ) β0S(R, Θ)/S0 cos Θ

(5)

where S are the overlap integrals between 2p-2p AOs calculated with ZC ) 3.25, ZN ) 3.90 (Slater-type AOs were used). The intermolecular resonance integrals between two 2p-orbitals that belong to neighboring radicals have also been calculated with Mulliken’s relation, eq 5, taking into account the angular dependence of the 2p-2p AOs overlap integrals (Scheme 1).

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SCHEME 1

TABLE 2: Calculated Values of the Components of the Effective Exchange Integral between the Electrons in the HFB of 1D Stacks Consisting of the Radical b-2 (C36H15N)+ at Different Values of the Slip Parameters ∆y and ∆x (in Å), Considering First-Neighbor Interactions between the π-Centers Onlya

TABLE 1: Calculated Values of the Components of the Effective Exchange Integral between the Electrons in the HFB of 1D Stacks Formed by the Radical a-3 with Different Values of the Slip Parameters ∆x and ∆y (in Å)a ∆x 0 3.636 3.636 3.636b 3.636c 3.636d 0e 3.636 3.636f

0 -2.1 -0.7 -0.7 -0.7 -0.7 -2.8 0 0

∆y

J

Jkin

Jind

-6 17 44 50 42 76

155 7 1 1 1 2

-6 -3 -14 -16 -17 19

-167 7 29 33 24 55

137 126

0 21

3 9

140 114

All entries are in meV. D ) 10 in eq 6 (dielectric constant of graphite29). c Ohno approximation (see ref 55). d a-4 (X ) B-). e The HFB crosses the neighboring band. f Considering the first and second neighboring π-centers. a

∆x

∆


J

Jkin

Jind

Jeff

0.0 -1.4 -2.8 -4.2 -5.6 -7.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.7 -0.7 -1.4

0.0 0.0 0.0 0.0 0.0 0.0 1.212 2.424 3.636 4.848 6.060 7.272 1.212 3.636 4.848

855 0 0 356 0 0 0 278 0 161 0 0 0 0 0

0 24 9 0 9 1 9 0 5 0 3 0 9 7 14

44 0 0 7 0 0 0 4 0 1 0 0 0 0 0

-4 8 4 -5 2 1 5 -12 4 -4 2 -1 4 3 7

-48 32 13 -12 11 2 14 -16 9 -5 5 -1 13 10 21

a

∆ε is the HFB width. All entries are in meV.

b

The exchange parameter in eq 3 was calculated by means of the Mataga-Nishimoto potential for the two-center Coulomb atomic integrals:54

γrs(M) ) e2 /(a + DRrs)

(6)

where D is the screening constant. When no specific value is given, the results are obtained with D ) 1. The results obtained by means of the Ohno potential55 do not differ substantially from the results calculated using the Mataga-Nishimoto approximation. Standard values γC ) 10.84 eV, γN ) 12.28 eV, and γO ) 14.52 eV of the one-center Coulomb integrals were used.1 4. Numerical Results and Discussion The numerical results obtained for the components of the effective exchange integral for 1D systems, which belong to one and the same group, lead to similar qualitative conclusions. Therefore, the results for only one example from each group are discussed here. 4.1. Systems with Schottky Point Impurity Defects. In Tables 1-3 are collected the results of the calculated values for the components of the effective exchange integral for 1D systems with interstitial impurity Schottky defects, shown in SCHEME 2

∆y

TABLE 3: Calculated Values of the Components of the Effective Exchange Integral between the Electrons in the HFB of 1D Stacks Consisting of Radical b-1 (C30H15N)+ with a Value of the Slip Parameter ∆y ) -1.4 Å and Different Values of the Interplanar Distance R (in Å) and the Screening Constant D (eq 6)a R

D

J

Jind

Jeff

3.35 3.35 3.35 3.10 3.50 3.65

1 5 10b 1 1 1

21 18 17 55 13 8

8 8 8 18 5 3

29 26 25 73 18 11

a Only first-neighbor interactions are considered. All entries are in meV. In all cases, Jkin ∼ 0. b Dielectric constant of graphite.

Figure 1. Here, and below, the results are given for Wannier states localized at neighboring sites. All monoradicals are assumed to have ideal geometry, i.e., all bond lengths are 1.40 Å, and the valence bond angles in the six-member rings are 120°. In Table 1 are collected the results of 1D stacks consisting of radicals a-3, shown in Figure 1. The structure parameters of the stacks are shown in Scheme 2. The full face-to-face stacking is characterized with a large HFB width, ∆ε ) 4|βσ-σ |, where βσ-σ is the resonance integral between adjacent π-centers.48 The large value of the HFB width determines the dominant contribution of the AFM term Jkin. Slipping along the directions defined in Scheme 2 leads to stabilization of the geometry of the stack and stabilization of the FM coupling of the electrons in the HFB. Positive values of Jeff are obtained for all values of the slipping

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TABLE 4: Calculated Values of the Magnetic Characteristics (in meV) of 1D Stacks Consisting of c-1 Radicals at Different Values of the Slip Parameter ∆y (in Å)a

a

∆y

J

Jkin

Jind

Jeff

0.0 1.4 2.8 4.2 5.6

0 10 3 7 8

91 0 0 0 0

-2 2 1 -1 3

-93 12 4 6 11

Only first neighbor interactions are considered.

TABLE 5: Calculated Values of the Magnetic Characteristics (in meV) of 1D Stacks Consisting of c-3 Radicals with Different Values of the Slip Parameter ∆x and ∆y (in Å)a ∆y

∆x

J

Jkin

Jind

Jeff

-1.4 -2.8 -4.2 -4.2b 0 -1.4

0 0 0 0 1.212 1.212

44.3 30 59 57 26 43

1 2 0 0 4 6

-0.6 -1 -12 -20 -11 9

43.3 27 47 37 11 28

a Only first neighbor interactions are considered. second neighboring π-centers.

b

First and

TABLE 6: Calculated Values of the Components of the Effective Exchange Integral and the HFB Width, ∆ε, of 1D Stacks Consisting of Radicals c-1 at Different Values of the Slip Parameter ∆ya ∆y 0 -1.4 -1.4b -2.8

∆
1152 0 0 0

c

J

Jind

Jkin

Jeff

0 46 49 12

-60 0 -18 0

91 14 0 5

-151 32 31 7

a Only first neighbor interactions are considered. All entries are in meV. b D ) 10 in eq 6. c ∆ε ) 4|β|.

SCHEME 3

parameters. The results indicate that 1D stacks build by a-1, a-2, and a-3 are suitable candidates for magnetic organic

TABLE 7: Calculated Values for the Components of the Effective Exchange Integral and the HFB Width, ∆E, of 1D Stacks Constituting from Coronene Substituted with the Az Radical for Different Values of the Slip Parameters ∆y and ∆xa ∆y

∆x

J

Jkin

Jind

Jeff

1.4 2.8 5.6 0

0 0 0 1.212

36 20 21 48

0 0 0 0

12 8 9 21

48 28 30 69

a Taking into account first-neighbor interactions only. All entries are in meV. R ) 3.35 A.

materials. In Table 2 are summarized the results for b-2 where again the full face-to-face ordering of the stacks leads to AFM coupling of the electrons in the HFB, as it was explained above. However, in the case of b-2, different orderings of the stack lead to different conclusions for the coupling of the electrons in the HFB. The magnetic properties of 1D stacks build by b-2 are dependent on the geometry of the stack. Table 3 shows that the results for Jeff obtained with different values of the interplanar distance R are qualitatively identical. 4.2. Systems with Schottky Point Lattice Vacancies. Coulson56,57 was the first who has emphasized the significance of the lattice vacancies for the properties of 2D graphite layers. In Tables 4, 5 and 6 are collected the calculated values of the components of the effective exchange integral between the electrons in the HFB of 1D stacks consisting of radicals c-1 and c-3, shown in Figure 2. The results have been obtained with optimized geometry of the radicals. The optimized geometry shows that two of the three unsaturated highly reactive dangling orbials, on the three neighboring carbon atoms, build a bond, which results in a five-membered ring. These systems are nonalternant, and their properties cannot be predicted easily. The analysis of the optimized geometry shows that the spin density is strongly localized on the carbon atom with the unsaturated dangling orbital. The structure parameters of the stacks are shown in Scheme 3. The results in Table 5 and Table 6 show FM coupling of the electrons in the HFB for all 1D systems except the full face-to-face. As it was discussed above, the full face-to-face ordering of the stacks is geometrically unfavorable. Lattice vacancies can be obtained by irradiation of PAH’s crystals with different particles. Our calculations, summarized in Table 5 and Table 6, show that FM properties should be observed. In a recent experimental study, magnetic ordering was obtained for graphite and crystals of coronene irradiated with protons.22,23 The possible cause for this ordering is the Schottky point lattice vacancies induced as a result of the collisions between the protons and the carbon atoms.

Figure 7. Calculated values of Jeff of 1D stacks consisting of hexabenzocoronene substituted by a Weitz-type radical at different values of the slipping parameter ∆r. Geometry optimization of the monomer shows a torsion angle Θ ) 38°.

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SCHEME 4

4.3. Systems with Chemisorption States. In Table 7 and Figure 7 are summarized the results for the 1D systems consisting of radicals d-2 and d-3, shown in Figure 4. Those are PAHs for which the NBMO is delocalized throughout the molecule. The results show AFM coupling of the electrons in the HFB for the full face-to-face ordering in the 1D stacks and FM coupling for different values of the structural parameters shown in Scheme 4. The results suggest that PAHs with delocalized chemisorption states are suitable candidates for building units of 1D systems with magnetic properties. The results shown in Figure 7 suggest that highest values of Jeff are calculated for geometries for which the Weitz radical subunit is localized under the hexabenzocoronene subunit. B3LYP calculations show that higher spin density is localized on the Weitz part, while significantly lower spin density is localized on the hexabenzocoronene part. Thus, the highest values of Jeff

Figure 8. 1D stack consisting of coronene substituted with an Az radical.

TABLE 8: Comparison of the Calculated Values of the Magnetic Characteristics of Polymethines PC, PO, and PM Substituted with a Weitz-type Radicala EU

J

Jind

Jkin

Jeff

PC PO PM

49 48 41

11 11 12

5 6 6

33 31 23

The slip parameter is ∆r ) 2.424 Å. The interaction between only first neighboring π-centers is taken into account. Θ ) 60o (B3LYP result). a

TABLE 9: Calculated Values of the Magnetic Characteristics of Streptoheptacyanine Substituted with a Weitz-type Radical by Different Values of the Sip Parameter ∆ra ∆r

J

Jind

Jkin

Jeff

1.212b 2.424b 2.424c 4.848b 7.272b

28 49 28 14 3

9 -11 -11 -3 0

5 5 6 4 0

32 33 11 7 3

a Θ ) 37o (B3LYP result). b The interaction between only first neighboring π-centers is taken into account. c The interaction between first and second π-centers is taken into account.

Figure 9. Band structure of stacks composed of streptoheptacyanine substituted with a Weitz-type radical. ∆x ) ∆y ) 0 (full face-to-face arrangement).

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are calculated for 1D stack geometries with alternating highspin-density-low-spin-density subunits. 4.4. Systems with Localized Chemisorption States. In Figure 8 is shown an example of a 1D stack consisting of coronene substituted with an Az radical. Because the NBMOs are strictly localized within the Az fragments, only a weak indirect exchange through the delocalized π-electrons appears within the 1D stacks. For structural parameters ∆x ) 1.212 Å and ∆y ) 0.7 Å, we have obtained the value Jind ) 3 meV. 4.5. Systems with Substituted Polymethines: Scheibe Aggregates. In Tables 8 and 9 are collected the calculated values of the magnetic characteristics of 1D systems formed by substituted polymethines, which are shown in Figure 6. The results show FM coupling of the electrons in the HFB. Highest values of Jeff are calculated for geometries for which the Weitz radicals interact directly. In Figure 9 is shown the band structure of a stack composed of streptoheptacyanine substituted with a Weitz-type radical. 5. Conclusions and Outlook The theoretical results in this paper illustrate the possibility for the existence of 1D staple polymers consisting of PAHs with Schottky, chemisorption, or with Tamm-chemisorption-type of surface defects, respectively, with magnetic ordering. As in the case of the 1D polymers with Tamm defects,1 the main factor determining the energy spectra and the magnetic properties of the investigated 1D polymers is the arrangement of the radicals within the 1D stacks. The numerical results should be considered as quantitative illustration of qualitatively correct results. The structural variety of theoretically probable 1D stacks consisting of PAHs with surface defects is impressive. Some structures are characterized by high positive values of the effective exchange integral, Jeff. This gives rise to the hope that some of the experimentally accessible systems can be purely organic polymers with magnetic ordering with relatively high values of the critical temperature Tc. Acknowledgment. We (F.D. and N.T.) want to thank our friends in Sadovo for useful and valuable discussions. A.S. acknowledges DAAD (Deutscher Akademischer Austausch Dienst) for scholarship for Ph.D. study in Germany. Supporting Information Available: Atomic Cartesian coordinates for the optimized geometries of all investigated structures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Tyutyulkov, N.; Drebov, N.; Mu¨llen, K.; Staykov, A.; Dietz, F. J. Phys. Chem. C 2008, 112, 6232. (2) Schottky, W.; C. Wagner, C. Phys. Chem. B 1930, 11, 163. (3) Dietz, F.; Tyutyulkov, N.; Madjarova, G.; Mu¨llen, K. J. Phys. Chem. B 2000, 104, 1746. (4) Madelung, O. Festko¨rper Theorie III: Lokalisierte Zusta¨nde; Springer: Berlin, 1973. (5) Harrison, W. A. Surface and Defects. In Electronic Structure and Properties of Solids; W. H. Freemann & Co: San Fransisco, CA, 1980; Chapter 10. (6) Tran, F.; Alameddine, B.; Jenny, T. A.; Wesolowsky, T. A. J. Phys. Chem. 2004, 108, 9155. (7) Tamm, I. E. Z. Phys. 1932, 76, 849. (8) Tamm, I. E. Phys. Z. Sowjet. 1932, 1, 733. (9) Magnetism: Molecules to Materials I: Models and Experiments; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2002. (10) Magnetism: Molecules to Materials II: Molecule-Based Materials; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2002.

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