Changes in the Electronic Structures of a Single Sheet of Sashlike

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Changes in the Electronic Structures of a Single Sheet of Sashlike Polydiacetylene Atomic Sash upon Structural Transformations Masanori Suhara,† Hiroyuki Ozaki,*,† Osamu Endo,† Toshimasa Ishida,‡ Hideki Katagiri,§ Toru Egawa,|| and Michio Katouda^ †

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Department of Organic and Polymer Materials Chemistry, Faculty of Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan ‡ Fukui Institute for Fundamental Chemistry, Kyoto University, Sakyou-ku, Kyoto 606-8103, Japan § Research Institute for Computational Sciences, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan College of Liberal Arts and Sciences, Kitasato University, Sagamihara, Kanagawa 252-0373, Japan ^ Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan ABSTRACT: Atomic sash (AS) is a single sheet of a sashlike macromolecule comprising a column of alkyl chains bridged by a polydiacetylene (PD) chain [H. Ozaki et al. J. Am. Chem. Soc. 1995, 117, 5596
5597]. The AS is produced by the intramonolayer polymerization of 17,19-hexatriacontadiyne molecules laid flat on a graphite (0001) surface under ultrahigh vacuum. In an AS conformer initially formed at low temperature (AS-I), the PD chain and the R carbon atoms of the alkyl chains are raised higher than other carbons of methylenes in contact with the substrate; with rising temperature, the AS-I is transformed to another conformer AS-II, in which all the carbon atoms are placed in a common plane [O. Endo et al. J. Am. Chem. Soc. 2004, 126, 9894
9895]. A simplified model is constructed in this study to obtain an optimized geometric structure of the AS-I, and its electronic structures are compared with those of the AS-II. The first-principles calculations for the model under periodic boundary conditions reveal that their energies are almost the same. The optimization also tells us the existence of the third stable conformer AS-III that has been suggested on the basis of STM images. In addition, it is found that the HOMO
LUMO energy gap of the AS-I is larger than that of the AS-II, and the orbital shapes dependent on the conformation successfully explain the result. This means that the AS-I f AS-II transformation of the ideal infinite polymer is not related to the chromatic transition of bulk PDs.

’ INTRODUCTION When diacetylene R
CtC
CtC
R0 molecules are arranged in a bulk crystal, a Langmuir
Blodgett (LB) film, or a selfassembled monolayer (SAM) etc. and irradiated with UV light, 1,4-polymerization takes place topochemically to yield a polydiacetylene (PD) (dCR
CtC
CR0 d)n.1
4 The π-conjugated systems have attracted attention on account of the electrical and optical properties.5,6 Though a correlation between the isomerization and color of PDs had been a controversial issue, the color transition is correlated to a change in the conjugation length7 or/ and that in the conformation of the substituents R and R0 containing methylene sequences.8,9 For such fundamental studies, the selection of simple substituents is crucial to elucidate the PD electronic and geometric structures interrelated closely. Most theoretical studies10 are limited to unsubstituted PDs (R = R0 = H), which are difficult to obtain in a laboratory owing to the extreme reactivity of the monomer, although there are a few first-principles theoretical studies on PDs with realistic substituents.11,12 An alternative to the hydrogen is a n-alkyl group: one might assume that polyalkadiyne retains simplicity to directly link the real system with the theoretical consideration. r 2011 American Chemical Society

To our knowledge, however, poly(2,4-hexadiyne) (R = R0 = CH3) is probably the only substituted PD for which the first-principles calculations have been reported.10,11 From the experimental point of view, on the contrary, the aggregates of diacetylene molecules having alkyl groups are usually prepared by wet techniques. This means that R0 inevitably contains a polar group at the end and complicates the intermolecular interactions and the molecular behavior upon polymerization. In addition, if the PD chains of an ordinary LB film3 or a SAM4 are buried in the close assembly of “standing” alkyl chains, they are hardly probed by extraordinarily surface-sensitive techniques such as Penning ionization electron spectroscopy (PIES)13,14 and scanning probe microscopy.15,16 For the direct observation of the local electronic and geometric structures, lying PD chains exposed outside the film are required, and atomic sash (AS) on a graphite (0001) surface17
22 is appropriate for this purpose.

Received: October 13, 2010 Revised: March 19, 2011 Published: April 26, 2011 9518

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The Journal of Physical Chemistry C The AS is produced by the UV polymerization of 17,19-hexatriacontadiyne (HTDY) molecules in an extrathin (4 Å) vapordeposited monolayer on graphite (see Figure 1). It is a single sheet of a sashlike macromolecule comprising a column of alkyl chains laid with the zigzag plane parallel to the substrate (flat-on orientation) and bridged by a PD chain. Lying PD chains can also be derived from a monolayer of 10,12-nanocosadiynoic acid (NCDA),23 5-(10,12-tricosadiynyloxy)isophthalic acid (TDIPA),24 or 2,5-bis(10,12-henicosadiynyloxy)terephthalic acid (HDTPA)24 prepared by an LB-like technique. However, the AS is much more favorable for us than either the “wet” monolayers or other PD aggregates to study the genuine nature of PDs for the following reasons. First, since R and R0 in the AS are the same slim alkyl chains n-C16H33 without bulky groups as well as polar groups forming hydrogen bonds between the neighbors, they can be arranged with the “natural” conformation. Second, the n-C16H33 group does not have the π electronic system but the pseudo-π (pπ) one,14 which does not smear the PD electronic structures around the Fermi level.18 Third, since the AS is prepared in an ultrahigh vacuum (UHV), there is a much lower risk of contamination for the AS. Forth, lowtemperature experiments, which led us to the discovery of AS phase transition,21 are not possible for the wet PD monolayers or the bulk PDs: the surface would be completely covered with water and other molecules in the air when cooled below room temperature. Due to

Figure 1. (a) Columnar structure of HTDY molecules laid flat in a monolayer with all-trans conformation and (b) atomic sash (AS) produced by the polymerization of HTDY molecules in (a). Note that this is one of AS conformers named AS-II later (see Figure 2).

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these advantages, the AS can be regarded as the most appropriate system to survey the relationship between the electronic and the geometric structures of PDs both experimentally and theoretically. Experimentally, we have studied the AS on graphite (0001),17
22 MoS2(0001),25 and Au(111),26,27 using PIES,17
19 ultraviolet photoelectron spectroscopy (UPS),19 scanning tunneling microscopy (STM),20
22,25,26 infrared reflection absorption spectroscopy (IRAS),26 and near-edge X-ray absorption fine structure spectroscopy (NEXAFS).27 It is found from these investigations that the AS is not such a simple system as first expected:17,18 each column of an HTDY monolayer is not directly converted into an AS with all-trans conformation and flat-on orientation, where all the carbon atoms in both PD and alkyl chains are placed in a common plane parallel to the substrate surface (Figure 1(b)). According to our UHV-STM study,21 the AS methylene units further than the β positions are all maintained in trans conformation and contact the substrate with the flat-on orientation throughout the reaction, while the β and R methylenes (CβH2 and CRH2) are twisted upon AS formation and expected to afford a gauche and a trans conformation for the β
γ and the R
β sequence, respectively. This results in the AS-I structure with the raised CRH2 and PD chain (see Figure 2(a)). The AS-I bears structural similarity to the above-mentioned “wet” PDs obtained from the monolayer of NCDA, TDIPA, or HDTRA.23,24 It is also revealed that the AS-I is gradually transformed to the firstexpected all-trans and flat-on structure (AS-II) (Figures 1(b) and 2(b)) with further UV irradiation or upon raising substrate temperature. Since a qualitative estimation tells us that the AS
substrate interactions should be the strongest for the AS-II having no gauche conformation but the largest number of hydrogen atoms in contact with the substrate, we felt it somewhat odd that the AS-I less similar to the monomer column in the structure and disadvantageous in energy, due to the presence of the gauche conformation and a smaller area of the molecular surface contacting the substrate, is formed at first. In addition, it was once suggested or presumed that the structural transformation of the AS has some relation to the chromatic transition of PDs in the bulk and LB films because of the resemblance between the AS-I and “blue form” and that between the AS-II and “red form”.21,22

Figure 2. Conformers of the AS: (a) AS-I, (b) AS-II, (c) AS-III, and (d) V-shaped structure. 9519

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Figure 3. (a) Total energy E(φ) of the AS with n = 1
6 dependent on φ upon the structural transformation AS-II f AS-I; E for the AS-II (E(180)) is taken as the origin. (b) and (c) Newman projections of the AS with n g 4/n = 3 for φ = 80 (AS-I) and 180 (AS-II).

As a first step to evaluate these assumptions, it is required to estimate the stability of each AS conformer quantitatively. Since information concerning the bond lengths and angles of the real AS is not provided by experiments, we try to obtain the structures by geometry optimization, which can be performed for the AS-II as easily as for gas phase small molecules. However, this is not the case for the AS-I. The full geometry optimization starting at an initial structure that is qualitatively constructed for the AS-I does not result in a refined one compatible with the STM image: the calculation unsuccessfully terminates at a V-shaped structure (Figure 2(d)) with the valley floor (apex) of the PD chain and the valley walls (sides) composed of the alkyl chains. It means that the AS-I structure is not the natural conformer (or one of local stable conformers) in the “gas phase”, and the geometry optimization must be carried out considering the effect of AS
substrate interactions to mimic the real AS-I structure on a graphite surface. However, the geometry optimization of a system comprising an AS-I and graphite is too heavy and unrealistic to perform. Though the optimized structure of the system may be obtained by molecular mechanics, it is doubtful whether the result is accurate enough to rigorously compare the stabilities and electronic structures of the AS-I and AS-II. In this study, we construct a simplified model system to enable the first-principles geometry optimization of the AS-I without adding graphite. Using the hybrid density functional theory,28 we calculate not only the stability but the electronic structures of the AS-I, AS-II, and other conformers. Although a geometry optimization based on the local density approximation29 was reported for a NCDA-derived PD chain, the electronic structure was not obtained, and the result was utilized to examine a trimer structure alone.30

’ METHODOLOGY AND CALCULATIONS In the real system, the AS-I is formed initially and then transformed into the AS-II, as the STM observation revealed.21 Since the optimized geometry of the AS-II is obtainable without constraints, however, we plan to search the AS-I structure with a local minimum in total energy more easily by transforming the geometry of the AS-II structure gradually to the AS-I structure. For this approach, it is preferable to simplify the structural transformation by expressing the energy change with respect to one variable which reflects the characteristics of the two structures. First of all, to take the effect of the AS
substrate interactions stabilizing an AS-I-like structure on graphite into account,

we forcibly retain the zigzag plane of the alkyl chains by freezing the C
C
C
C dihedral angles of the methylene sequences further than C2βH2 and C3βH2 (Ciβ (i = 2 or 3) denotes the β carbon of the alkyl chain attached to the PD carbon Ci; see Figure 2) to be 180 during each geometry optimization. Next, we set dihedral angles φ t φ(C3
C2
C2R
C2β) (= φ(C2
C3
C3R
C3β))31 to be equal to φ0 (C2R
C2β
C2γ
C2δ) (= φ0 (C3R
C3β
C3γ
C3δ)), upon transformation from the AS-II to AS-I (II f I), so that the PD backbone is maintained parallel to the zigzag of the alkyl chains further than Ciβ. It should be noted that conformation for the R- and the β-methylene sequence (CiRHiR2
CiβHiβ2; HiR denotes hydrogen attached to CiR) is also trans in this case. These constraints place both the PD backbone and alkyl chains parallel to the virtual graphite surface without adding the substrate itself to the model system. Besides the simplification of the structural transformation, we also reduce the number of carbons n in the alkyl chains of the ASI and AS-II to 1
6 from its real number 16, to diminish the amount of calculation and emphasize a difference between the two conformers. It will be shown that the electronic structure of the system is essentially retained for n g 4, which is based on a fact that the alkyl chains further than Ciβ are all in trans conformation for the model structures of the AS-I and AS-II. Calculations were all performed under periodic boundary conditions using Gaussian 03.32 Geometry optimization was carried out at the BLYP33
35/6-31G36 level for n g 4 with decreasing φ = φ0 from 180 to 60 by 10. Optimized structures for n = 1
3 were also searched to survey the origins of (in)stability of certain local structures. For n = 3, one of Hiγ (Hiγ1) was used in place of Ciδ to define the dihedral angle (CiR
Ciβ
Ciγ
Hiγ1) as φ0 . Since φ0 cannot be defined for n = 2, however, only φ was varied with the trans CiRHiR2
CiβHiβ2. Furthermore, since not only φ0 but also φ cannot be defined for n = 1, one of HiR (HiR1) was substituted for Ciβ to define dihedral angle (C3
C2
C2R
H2R1) or (C2
C3
C3R
H3R1) as φ. The total energies E and the density of states (DOS) of the resultant structures were obtained at the B3LYP37/6-31G level.

’ RESULTS AND DISCUSSION Figure 3(a) shows the φ-dependence of the total energy E; E(φ) for the AS-II (E(180)) is taken as the origin. There are three important findings. First, the curves for n = 4
6 exhibit features entirely different from the curves for n = 1 and 2. Second, 9520

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Figure 4. Unit cell of the AS with n = 1 for φ = 120 (a) and 180 (b), together with the corresponding Newman projections ((c) and (d)) and HOMO wave functions ((e) and (f)).

E(80) and E(180) are almost equal for n = 4
6. Third, the curve for n = 3 is similar to the curves for n = 4
6 in tendency, although E(80) is lower than E(180). Furthermore, longer chains (n = 8
10; not shown) gave almost the same E as shorter ones (n = 4
6) for φ = 80 and 180 (A-II). From these facts, it is natural to consider that the φ
ΔE relation for n = 16, which is the case for the real AS, bears a marked resemblance to those for n = 4
6, and the φ value for the real AS-I is close to 80. Newman Projections for the AS-I and AS-II are depicted in Figures 3(b) and 3(c). Prior to this work, we expected that the AS-I is less stable than the AS-II owing to the complexity of the former structure. In what follows, we will explain why both conformers exhibit almost the same energy. Let us investigate the different n-dependences of ΔE first to reveal the reason why the AS-I with the complicated conformation has such a considerable stability from the standpoint of the electronic structures as well as the geometric ones. It is natural that the energy curve for n = 1 changes in a 120 cycle since the side chains R are methyl groups having 3-fold symmetry. It seems unreasonable, however, that E(120) is more stable than E(180) = E(60) because eclipsed conformations are found at φ = 120 and 180 (60) for C3 = C2
C2R
H2R2 and C1
C2
C2R
H2R1, respectively (see Figures 4(a)
4(d)): the distance between C3 and H2R2 at φ = 120 is shorter than that between C1 and H2R1 at φ = 180, which destabilizes E(120) more than E(180). An electronic effect (i.e., orbital mixing) can explain the situation. A valence Walsh diagram for n = 1 (Figure 5) implies that the total energy difference mostly originates from a change in the highest occupied molecular orbital (HOMO), which becomes the most stable at 120 and the least stable at 180 and 60; it should be noted that the φ-dependences of two MOs at the top of the inner valence region (∼
18 eV) cancel out each other to exert little influence on the total energy. The drawings of the HOMO for 120 and 180 (60) are depicted in Figures 4(e) and 4(f). Both comprise the same kinds of atomic orbitals (AOs) and have nodes intersecting the C2
C2R and C3
C3R bonds: the linear combination of H2R1 (or H2R2) and H2R3 1s AOs together with C2R 2pz AO (with smaller contribution cannot be seen in Figures 4(e) and

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Figure 5. Walsh diagram for the valence MOs of the AS with n = 1. The MOs are crystal orbitals (COs) (Hofmann, R. Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures; VCH Publishers: NY, 1988) for k = 0, at which the gap between the highest occupied CO energy and the lowest unoccupied CO energy is the smallest.

4(f)) or that of H3R1 (or H3R2) 1s, H3R3 1s, and C3R 2pz AOs, which will be called “CRHR2 orbital” below, antibondingly interacts with the 2pz AO of the nearest-neighbor carbon C2 or C3 for both 120 and 180 (the xy plane is taken parallel to the PD backbone). The situation is different for second-neighbor interactions (SNI): the CRHR2 orbital bondingly interacts with C1 or C4 2pz AO at 120 and antibondingly interacts with C3 or C2 2pz AO at 180, which accounts for the unexpected stability of E(120). We can also make an alternative explanation. The nearest PD carbon bearing the 2pz AO in phase with the C2RH2R2 (C3RH3R2) orbital is C1 and C4 (C4 and C1) at 120 and 180, respectively. Since the C2R 3 3 3 C1 (C3R 3 3 3 C4) distance is shorter than the C2R 3 3 3 C4 (C3R 3 3 3 C1) distance, the HOMO energy must be more stabilized at 120. Katagiri et al. studied the potential energy function of side group rotation in the PD with R = R0 = CH3 and reported a φ
E dependence similar to the n = 1 case in Figure 3.12 Unlike n = 1 for which the φ-dependences of MO energies are almost negligible except for the HOMO, the highest inner valence MOs, and the lowest unoccupied MO (LUMO), those for n g 2 are not necessarily small because of more complicated interactions between the PD and the alkyl MOs (see below); resultant MOs exhibit minimum and maximum energies at different φ. This means that it is difficult, for example, to clearly explain in Figure 3(a) why the local minima of energies appear at such halfway angles 110 (n = 2) and 80 (n g 3) rather than 180 (all-trans conformation) on the basis of the φ-dependences of individual MOs. However, consideration based on steric repulsions sometimes explains the reason more easily as follows. Let us turn our attention to the curves for n g 4. When φ is decreased from 180 (AS-II) to φ = 80 (AS-I), the eclipsed conformation for C1
C2
C2R
C2β or C4
C3
C3R
C3β (only the former will be referred to in the following discussion unless necessary) is altered into a somewhat “twisted” one, and hence, the local structure becomes more stable. At the same 9521

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Figure 6. (a) Newman projection of the AS-III (n = 6, φ = 100). (b) Total energy (ΔE = E(φ)
E(180)) of the AS with n = 2, 4, and 6 dependent on φ upon the structural transformation AS-II f AS-III.

time, the anti (trans) conformation for C2R
C2β
C2γ
C2δ is changed to the nearly gauche one, which makes the local structure less stable. This trade-off relation makes the energies of the AS-I (E(80)) and AS-II (E(180)) almost the same, probably by chance. Since the AS with n = 2 lacks C2γ and C2δ, however, the former effect, i.e., stabilization due to leaving the eclipsed conformation for C1
C2
C2R
C2β with decreasing φ, determines the φ
ΔE relation. Namely, the curve for n = 2 can be regarded as the contribution of the C1
C2
C2R
C2β conformation to the curves for n g 4. Therefore, it is reasonable that the optimized local structure with φ = 110 for n = 2 is different from the AS-I structure for n g 4. Despite the fact that the maximum and minimum values of ΔE appear at the same angles for n g 3, the conformer corresponding to the AS-I is more stable than the AS-II for n = 3. This is attributed to the different definition of φ0 for n g 4 (C2R
C2β
C2γ
C2δ) and n = 3 (C2R
C2β
C2γ
H2γ1) (Figures 3(b) and 3(c)). Since moderate destabilization due to increased C2R 3 3 3 H2γ1 repulsion with decreasing φ0 can be overcome by stabilization due to the reduced C1 3 3 3 C2β repulsion, the total energy for n = 3 becomes the smallest at 80. Naturally, n must be larger than 3 to provide the model structure with the conformational characteristic of the AS: there is no C2δ for the shorter R. From the above discussion, we notice a possibility that another local structure of which conformations for C3
C2
C2R
C2β and C2R
C2β
C2γ
C2δ are twisted and anti, respectively (see Figure 6(a)), must be more stable than both AS-I and AS-II. We named it AS-III (see Figure 2(c)) and searched it by the same method as used for the AS-I structure except for keeping φ0 = 180 upon the transformation from the AS-II to AS-III (IIfIII): the conformation of the alkyl chains is fixed all trans, and only φ is changed from 180 to 60. Figure 6(b) shows energy curves for n = 2, 4, and 6. Note that the curve for n = 2 is the same as that in Figure 3 since φ0 cannot be defined and only φ is altered for trans ethyl groups during IIfI and IIfIII. All the curves in Figure 6(b) properly exhibit a similar tendency. Therefore, the structure exhibiting the minimum energy at φ = 110 (n = 2 and 4) or 100 (n = 6) in Figure 6(b) can be identified as the AS-III. Though the AS-III conformer is more stable than the AS-I and the AS-II conformer, the products by the photopolymerization of an HTDY monolayer exhibit the flat-on orientation of the PD and the alkyl chains, as mentioned above. A reason why the

AS-III is not the major species even at room temperature is attributable to the fact that the total energy of the system including the AS
substrate interactions is higher for the AS-III than for the AS-II. Neither the PD nor the alkyl chains on its one side alone can be laid flat because the PD backbone plane is not parallel to the zigzags of the alkyl chains in the AS-III. These results reveal that n = 4 is enough to simulate the transformation of the real AS. In case the AS is applied to nanowiring materials in the future, however, it is preferable to examine the effect of decreased n on the π electronic structure. As for the AS-I, the PD chain and methylenes except for C2RH2R2 are spatially separated because the PD and C2RH2R2 are raised away from the substrate, with which other methylenes are touched. Therefore, the change in the electronic structure of the alkyl chains caused by the truncation would not affect the π electronic structure fundamentally. It is expected, on the contrary, that the intermixing of the PD and the alkyl electronic structures is the strongest for the AS-II. The intermixing dependent on n will be estimated as follows. Figure 7 shows the DOS of the AS-II for n = 2, 6, and 16. The three curves have similar characteristics due to π MOs or bands located in the vicinity of the Fermi level, PD σ MOs or bands, and alkyl MOs. There are two types of π bands mainly distributed at the PD chain:17
19 π(^) bands are composed of the 2pz AOs of the PD carbons whereas π(//) bands are made up of the C2px and C2py AOs. Only those derived from the 2π(//), 2π(^) (HOMO), 3π(^) (LUMO), and 3π(//) MOs of the monomer (HTDY) are located in a energy region without alkyl MOs (pure π region). The alkyl MOs are classified into pseudo-π (pπ), σ2p, and σ2s MOs consisting of the C2pz and H1s AOs, the C2px, C2py, and H1s AOs, and the C2s and H1s AOs, respectively, for all trans methylene sequences.14 Of these alkyl MOs, the pπ MOs alone have the same symmetry as the π(^) bands derived from the π(^) MOs, and hence, they can be mixed as long as the energy difference is small enough and the relevant wave functions overlap sufficiently for the interaction. Actually, the 1π(^) and the 4π(^) band (or some of the constituent orbitals with a definite k vector) existing in the pπ region considerably intermix with the pπ MOs. One might expect that the 2π(^) band more or less interacts with the pπ MOs as well because the region of the pπ MOs is broadened with increasing n: the destabilized energy of the highest pπ MOs would make the π(^)
pπ interactions larger 9522

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Figure 8. Gap between the HOMO and the LUMO energy (Eg) of the AS with n = 2 and 4, dependent on φ.

Figure 7. Density of states (DOS) diagram of the AS-II with n = 2, 6, and 16. A magnified diagram for the DOS around the pure π region is shown on the right.

to push the top of the 2π(^) band (or HOMO energy) up. Similarly, the stabilized energy of the lowest unoccupied pπ (pπ*) MOs would make the pπ*
π(^)* interactions larger to pull the bottom of the 3π(^) band (or LUMO energy) down. Therefore, the π(^)
pπ and the pπ*
π(^)* mixing could result in a decrease in the HOMO
LUMO gap. However, it seems from Figure 7 that the increase in n produces little change in the energy gap: it does not affect the intermixing between the HOMO (LUMO) and the pπ (pπ*) MOs, which can be attributed to a decrease in the overlap integral of the π (π*) band (2π(^) (3π(^)) orbital at the Γ point) and the pπ (pπ*) ΜΟ as follows. With increasing size of the hydrocarbon molecule, electron density at a certain carbon atom generally becomes smaller on account of the normalization of the wave function. In addition, the highest pπ MOs of long n-alkanes have the largest electron distribution around the center methylene units but a small one at the methyl ends,14 and the situation is similar for conjugated alkadiynes having alkyl groups of the same length. Thus, orbital mixing enhanced by decreased difference between the 2π(^) and the highest pπ (and the 3π(^) and the lowest pπ*) energy is compensated by the decreased efficiency of π(^)
pπ (and pπ*
π(^)*) overlap; the HOMO and the LUMO energy are maintained roughly constant irrespective of n after all. We therefore consider that the π electronic structure of the AS-II as well as that of the AS-I can be evaluated with small n, e.g., n = 4 (see below). Figure 8 shows the φ-dependence of the HOMO
LUMO energy gap Eg for n = 2 and 4; it is noteworthy that there exist minute differences between the two curves. Since we found that n = 5 and 6 give almost the same curves as n = 4, the electronic structure of the AS-II is not altered by the elongated R longer than the propyl group. In other words, neither the relative position of the PD and the alkyl chain nor the intermixing of the π and the pπ electronic system is altered for R with n g 4, which reminds us of the “trade-off” relation holding in this case. We can examine with this figure the relation between the isomerism of the AS and the “colors” of PDs. The energy gap

of the AS-I is seen to be larger than that of the AS-II by 0.36 eV. It is not in line with an expectation that the AS-I and AS-II correspond to the blue and the red form with a smaller and a larger energy gap in the bulk PDs or LB films, respectively, which indicates that the AS-I and AS-II with ideal infinite PD chains do not directly correspond to the blue and red phase of the bulk PDs, respectively. The different energy gaps for the AS-I and AS-II can be explained with the φ-dependent shapes of their HOMO and LUMO, as in the discussion on the difference between E(120) and E(180) for n = 1. The wave functions of the HOMO and LUMO are compared in Figure 9 for n = 6 at φ = 180 (AS-II), 120, and 80 (AS-I); H2R1 (H3R1) for n = 1 (Figure 4) is replaced by C2β (C3β). The phases of interactions between the CRHR2 or CRHRCβ orbitals (the linear combination of AOs at the CRHRCβ unit) and neighboring carbon 2pz AOs are listed in Table 1. Though all the nearest-neighbor interactions in Table 1 are antibonding, the SNI depends on φ. Since the SNI in the HOMO is antibonding, bonding, and weakly antibonding at φ = 180, 120, and 80, respectively, the HOMO energy ordering is EHOMO (120) < EHOMO (80) < EHOMO (180), while since the SNI in the LUMO is bonding, antibonding, and weakly bonding at φ = 180, 120, and 80, the LUMO energy ordering is ELUMO (180) < ELUMO (80) < ELUMO (120). Therefore, the energy gap ordering becomes Eg(180) < Eg(80) < Eg(120), which is fully consistent with Figure 8. Now we briefly mention the reason why the AS-I is formed ahead of the AS-II; a more detailed picture will be presented elsewhere. Since angle θ0 between the alkyl and the PD chain in the AS-II (110 ( 2;20 Figure 1(b)) is much larger than angle θ between the alkyl chain and the column axis in an HTDY monolayer (92 ( 2;20,38 Figure 1(a)) and the direction of firstformed PDs coincides with that of the HTDY columns from which the PDs are produced,21,22 it would be necessary for the alkyl chains to be rotated about 20 around the center of the diacetylene unit upon polymerization if each HTDY column were directly transformed to the AS-II.17 On the other hand, since θ0 for the AS-I (∼94)21 is almost the same as θ, the polymerization to the AS-I requires relatively small motion of the HTDY molecules (i.e., the conformational change around CiRHiR2 and CiβHiβ2 followed by the slight translation of the alkyl chains due to the “shrinkage” of the column or sash width). 9523

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Figure 9. Wave functions for the HOMO and LUMO of the AS with n = 6 at φ = 180 (AS-II), 120, and 80 (AS-I). Newman projections for each φ are also shown in the middle.

Table 1. Phase of Interactions between the CrHr2 or CrHrCβ Orbitals and the Neighboring Carbon 2pz AOs for n = 6 linear combination at CR φ HOMO HOMO HOMO LUMO LUMO LUMO

180 120 80 180 120 80

bonding (B)/antibonding (A) interactions

(CRHR2 or CRHRCβ orbitals) H2R2 1s, H2R3 1s, C2R 2pz C2β 2s, 2pz, 2px, 2py, H2R3 C2β 2s, 2pz, 2px, 2py, H2R2 H2R2 1s, H2R3 1s, C2R 2pz C2β 2s, 2pz, 2px, 2py, H2R3 C2β 2s, 2pz, 2px, 2py, H2R2

nearest-neighbor

C3 2pz (A)

2

C1 2pz (B)

2

C3 2pz (weakly A)

2

C3 2pz (B)

2

C1 2pz (A)

2

C3 2pz (weakly B)

C 2pz (A) 2

1s, C

2

1s, C

R R

2pz 2pz

C 2pz (A) C 2pz (A) C 2pz (A)

2

1s, C

2

1s, C

Furthermore, since the direction of alkyl chains was found to be parallel to the graphite lattice vector in an HTDY monolayer,20 as widely observed for the alkanes and their derivatives adsorbed on graphite (0001) surfaces,39
42 the above observations mean that the parallel relation can be maintained during the conversion to the AS-I but cannot to the AS-II. Consequently, because of the smaller energy barrier or the activation energy for the polymerization, the monomer column is first altered to the AS-I, and it can be transformed to the more stable AS-II when supplied with enough energy by further irradiation or/and elevating the substrate temperature.

’ CONCLUSION Using the first-principles calculations under periodic boundary conditions, we obtained the optimized structures of the AS-I, a peculiar conformer of the sashlike PD atomic sash with a raised PD chain, which is formed at the early stage of photopolymerization taking place in an HTDY monolayer on graphite (0001). Since the real system comprising an infinite PD backbone and n-C16H33 side chains together with a graphite substrate is too complicated, we adopted a model structure in line with our STM observation to simplify the calculation: (1) dihedral angles for C3
C2
C2R
C2β, C2
C3
C3R
C3β, C2R
C2β
C2γ
C2δ, and C3R
C3β
C3γ
C3δ are equalized to φ; (2) the AS-I structure was searched by gradually altering φ in the “all-trans” AS-II although the AS-I is transformed into the AS-II with

R R

2pz 2pz

second-neighbor (SNI)

2

C 2pz (A) C 2pz (A)

progression of polymerization or upon warming the monolayer in reality; (3) the zigzag of the alkyl chains further than CβH2 is kept parallel to the PD backbone (and to the ideal, invisible substrate as well) during the transformation, which substitutes for the effect of the AS
substrate van der Wasls interactions; (4) the number of the methylene units in the alkyl chains is typically decreased to 6 and/or 4; the latter is the smallest value providing the same φ-dependence of energy E as larger n-alkyl groups. The AS-I structure thus obtained has a φ value of 80 and enabled us to calculate the electronic structures of the AS-I for comparison with those for the AS-II. It was revealed that the stabilities of the AS-I and AS-II are almost the same contrary to our expectation that the AS-II is more stable, which is ascribable to a trade-off relationship between destabilization for the C1
C2
C2R
C2β sequence and stabilization for the C2R
C2β
C2γ
C2δ sequence with increasing φ. Given a structural similarity between the HTDY column and the AS-II (i.e., the coplanarity of all the carbon atoms), an experimental fact that the AS-I is produced ahead of the AS-II upon polymerization brings a feeling of strangeness. It is, however, probably because a conversion from an HTDY column to an AS-II requires much molecular motion, destroying the parallel relation between the alkyl chains and the graphite lattice, whereas a conversion to an AS-I does not alter the direction of alkyl chains and preserves the relation. The analysis of the structural transformation also disclosed the existence of another conformer AS-III that is stable without substrate. The result is compatible with STM observations that 9524

dx.doi.org/10.1021/jp109822j |J. Phys. Chem. C 2011, 115, 9518–9525

The Journal of Physical Chemistry C the AS-III is produced on a MoS2(0001) surface exerting much weaker interactions on alkyl chains than a graphite (0001) surface.25 Furthermore, it was also found that the HOMO
LUMO energy gap for the AS-I is larger than that for the AS-II, and the φ-dependent shapes of the MOs successfully explain the result. This finding means that the AS-I f AS-II transformation is remotely correlated to the chromatic transition of bulk PDs provided that at least the conjugation length is unchanged upon transformation. The AS conformers will be valuable for experimental investigation on the genuine nature of the long π-conjugated system. We are now undertaking the selective observation of the π electronic structures peculiar to each AS by electron spectroscopy.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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