Excited States of the Lutetium Phthalocyanine Trimer: Semiempirical

The most intense band in the Q-band region is assigned to an excited state mainly of exciton coupling character. ... Xiaoping Yang and Richard A. Jone...
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J. Phys. Chem. 1996, 100, 8722-8730

Excited States of the Lutetium Phthalocyanine Trimer: Semiempirical Molecular Orbital and Localized Orbital Study Naoto Ishikawa and Youkoh Kaizu* Department of Chemistry, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152, Japan ReceiVed: May 15, 1995; In Final Form: August 28, 1995X

The electronic structure of the lutetium triple-decker phthalocyanine (Pc) trimer is studied by semiempirical quantum chemical calculation. The study employs a localized orbital (LO) basis set which is obtained by a transformation of the trimer’s canonical MOs, such that the orbital populations on a certain ligand are maximum. Characteristic energy differences between LOs on the central Pc ring and those on outer Pc rings are discussed with regard to environmental changes around each Pc ring. Assignment of the electronic absorption bands of the trimer is discussed using the configuration interaction (CI) method with the LO basis, which provides characterization of the excited state in terms of inter- and intraligand excitation. The most intense band in the Q-band region is assigned to an excited state mainly of exciton coupling character. The second intense band can be assigned to a charge resonance state, which obtains spectral intensity from the exciton component. The near-IR bands and the band at higher energy of the most intense Q band are also characterized by combinations of excitations from highest occupied LOs to lowest unoccupied LOs. A comparison between MO basis CI calculation and that of the LO basis is carried out. The effects of the molecular structure distortions (twisting of Pc rings around the C4 axis and elongation of interplanar distance) on the excited states are discussed.

Introduction Phthalocyanine, a π-conjugated macrocycle, is known to form several kinds of face-to-face dimer structures: [MIII(Pc)2], [MIV(Pc)2], [(PcSi)2O], etc. (Pc, phthalocyanine; MIII, lanthanide, scandium, and yttrium; MIV, tin and zirconium).1-7 These stacking structures of phthalocyanines have been subjected to extensive investigations as minimum models of dimensional structures such as molecular semiconductors or the photosynthetic reaction center. In particular, the lanthanide phthalocyanine dimers have been intensively studied from the standpoint of electrochemistry because of their electrochromic property8-11 and intrinsic semiconductivity.12-16 Similar structures are seen in porphyrins and have also been studied as analogs of the photosynthetic reaction center.17-19 While many studies on the Pc dimer systems have been carried out, those on larger finite stacking systems, such as trimer or tetramer, are few to date.20-24 These systems can be regarded as the first expansion from the minimum unit toward a dimensional structure. The first report of lanthanide phthalocyanine trimer was made by Kirin et al. for [Nd2(Pc)3].20 The triple-decker structure (Figure 1), however, was first proposed by M’Sadak et al.21 It was shown in the report by Kasuga et al. that the trimer exhibits two distinct absorption bands similar to those of the dimer [Lu(Pc)2]- in the Q-band region.22 Recently, we synthesized a highly soluble triple-decker phthalocyanine trimer [(Pc)Lu(CRPc)Lu(Pc)] (CRPc ) crown-ethersubstituted phthalocyanine).23 The introduction of crown ether to the periphery is known to give phthalocyanine compounds far greater solubility without causing significant change in the lowest absorption band profile.27-30 The spectral measurement of [(Pc)Lu(CRPc)Lu(Pc)] at higher concentration revealed that the trimer exhibits near-IR bands at 7.4 × 103, 10.5 × 103, and 12.0 × 103 cm-1.23 These bands were qualitatively explained using a localized orbital model. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, May 1, 1996.

S0022-3654(95)01346-3 CCC: $12.00

Figure 1. Schematic diagram of the molecular structure of the lutetium phthalocyanine dimer and trimer.

Electronic structure of these stacking systems composed of discrete chemical parts can be described by two factors: the local electronic structure and the collective electronic structure. For the dimer case, to study electronic structure from this viewpoint, we employed the localized molecular orbital (LO) basis which is obtained by a unitary transformation of the canonical molecular orbital (MO) basis such that orbital populations on a certain ligand become maximum. Using the LO basis, the lowest excited states are described as linear combinations of intra- and interligand (π-π*) transitions, i.e. exciton coupling and charge resonance configurations.25,26 It was shown using a semiempirical parametrization that the two main absorption bands in the Q-band region (16 × 103 and 14 × 103 cm-1 for [Lu(Pc)2]-) correspond to an excited state characterized by an exciton coupling configuration and that of a charge resonance configuration, respectively.25 In this paper, we study the electronic structure of the trimer using the same approach. The organization of the paper is as follows. (1) First we present the orbital localization method for the cases involving more than two ligands. (2) This method is then applied to the Pc trimer. The differences in orbital energy shifts among the individual Pc rings are discussed. (3) Next the excited states of the trimer are studied by CI calculation © 1996 American Chemical Society

Excited States of Lutetium Phthalocyanine Trimer

J. Phys. Chem., Vol. 100, No. 21, 1996 8723

with the LO basis. The assignment of the absorption bands in the Q-band and near-IR region is discussed. (4) A CI calculation with MO basis is shown in order to provide an assignment from the MO point of view. Although the two methods give seemingly different state wave functions, they are essentially mathematically equivalent. (5) Effects of structural distortions on the spectral feature of the trimer are discussed. In what follows, abbreviations HOLO and LULO refer to “highest occupied localized molecular orbital” and “lowest unoccupied localized molecular orbital”, respectively.

The Fock matrix elements in the occupied-virtual block are equal to zero because no mixing occurs between the two spaces. The above process is repeated with replacing A and A h by B and B h (B h ) C ∪ D ‚‚‚ ∪ Z), then by C and C h (C h ) D ∪ E ‚‚‚ ∪ Z), etc., and finally by Y and Y h ) Z. The resultant LO basis gives the Fock matrix expressed as

Computational Method Localization of the MO onto Chemical Components. Localization of the canonical SCF-MO of trimer or larger systems onto respective component parts can be carried out by successive performances of the procedure for the dimer.25 Suppose the system is composed of segments A, B, C, ..., Z. First the MOs of the whole system are localized onto either A or the counterpart A h , which consists of all the other segments, B, C, ..., and Z. The MOs can be given by (5)

A∪A h ψp ) ∑cµp φµ

(1)

µ

A∪A h cµp

indicates where the label A ∪ A h on the LCAO coefficient the orbital is delocalized over A and A h . In this paper, we use 2pz orbitals on carbon and nitrogen atoms as the basis set {φµ}. The overlap integral over the segment A is defined by A∪A h A∪A cνq h (φµ|φν) (P)pq ) Ppq ) ∑ ∑cµp

(2)

µ∈Aν∈A

Diagonalization of the occupied-occupied block of P gives occupied LO sets localized on either A or A h . The diagonal elements of P, which were extremized, correspond to orbital population on A in the LO basis. The MO coefficient matrix is divided into two LO coefficient matrices as A∪A h A A h f (coccupied |coccupied ) coccupied

(3)

h A A h A∪A h, N Here, the size of cA∪A occupied, coccupied, and coccupied are N × O A A h × O , and N × O , respectively (N, the number of the basis functions; OA∪Ah , the number of occupied MOs; OA, the number of occupied LOs on A; OAh ) OA∪Ah - OA). The orbital whose diagonal element of P exceeds 0.5 falls to the LO set on A. To obtain a unique solution, two blocks of the Fock matrix spanned by the occupied LOs of A and A h , are then individually diagonalized. The localization of the virtual space is similarly accomplished by the diagonalization of the virtual-virtual block of P, followed by the diagonalization of two blocks of the Fock matrix spanned by virtual LOs of A and A h . The resultant Fock matrix in the LO basis is

The diagonal Fock elements can be interpreted as energies of the LOs and nonzero off-diagonal elements as interactions between LOs on different segments. The ground state energy given by a Slater determinant wave function is invariant under the orbital localization, which is a series of unitary transformations carried out separately for occupied and virtual spaces. For excited states, we used the configuration interaction method within singly excited configurations on the LO basis. The interaction between the ground state and a singly excited determinant

〈|‚‚‚aaj‚‚‚||H ˆ ||‚‚‚raj‚‚‚|〉 ) (a|fˆ|r)

(6)

remains zero after the orbital localization. Here, a and r denote occupied and virtual LOs, respectively. The diagonal matrix elements of the singly excited determinants on the LO basis have the same expression as those of the canonical MO basis. The off-diagonal terms can include nonzero off-diagonal Fock matrix elements that appear in eq 5 when the two determinants differ by only one LO:

〈|‚‚‚raj‚‚‚||H ˆ ||‚‚‚saj‚‚‚|〉 ) (r|fˆ|s) + (ra|as) - (rs|aa) (7) 〈|‚‚‚raj‚‚‚||H ˆ ||‚‚‚rbh‚‚‚|〉 ) -(b|fˆ|a) + (ra|br) - (rr|ba)

(8)

where b and r represent occupied and virtual LOs, respectively. When the two determinants differ by two LOs, the expression is again the same as that of the canonical MO basis. Using these expressions, matrix elements for singlet excited state functions

|1(r r a)〉 ) {|‚‚‚raj‚‚‚| - |‚‚‚rja‚‚‚|}/x2

(9)

are given by

〈1(r r a)|H ˆ |1(r r a)〉 ) 〈Ψground|H ˆ |Ψground〉 + (r|fˆ|r) (a|fˆ|a) - (aa|rr) + 2(ar|ra) (10) 〈1(r r a)|H ˆ |1(s r a)〉 ) (r|fˆ|s) + 2(ra|as) - (rs|aa) (11) 〈 (r r a)|H ˆ |1(r r b)〉 ) -(b|fˆ|a) + 2(ra|br) - (rr|ba) (12) 1

(4)

8724 J. Phys. Chem., Vol. 100, No. 21, 1996

Ishikawa and Kaizu

〈1(r r a)|H ˆ |1(s r b)〉 ) 2(ra|bs) - (rs|ba) (13) π-Electron Systems of the Trimer. The SCF π-electron system of the phthalocyanine trimer was calculated by a semiempirical method which takes into account all the nonnearest-neighbor interactions.25,33 Parameters and formulas to evaluate molecular integrals used for the calculation were the same as those used previously for the monomer and dimer.25,33 The practical performance of the semiempirical parameters for the calculation on the divalent metallophthalocyanine monomer was assessed in a preceding paper.33 Two-electron interactions between two centers within a macrocycle at a distance R were evaluated with the formula described by Nishimoto and Mataga31 (e2/(a + R)) which reasonably reproduced monomer Q and B bands.33 For the one-center interaction e2/a, we used the values determined by Gouterman et al.32 The interactions between two centers on different macrocycles were scaled as Re2/(a + R), in which R is a parameter. In this paper, R ) 0.8, which best reproduced the Q bands of [Lu(Pc)2]-,25 was employed. The molecular geometry of [Lu2(Pc)3] was assumed to be three phthalocyanine macrocycles being placed in parallel with a common C4 axis. The charges on the central metal ions were assumed to be neutralized by charge donation from the coordinated nitrogen atoms so that the total metal charge is equally distributed among three Pc rings. Results and Discussion Orbital Energy Shifts in the Dimer and Trimer. Figure 2 shows LO energy levels of [Lu2(Pc)3] calculated at a D4h geometry. The orientational angles between adjoining Pc rings along the C4 axis are assumed to be 45°, with an interplanar distance of 2.9 Å, which is the same value used in the study of [Lu(Pc)2]-.25 As mentioned earlier, the diagonal Fock matrix elements of LOs are taken to be the orbital energies. The three Pc rings are referred to as A, B, and C, where B is the middle ring. Each LO is denoted by a Mulliken symbol, which indicates the corresponding monomer MO, associated with A, B, or C on its shoulder, showing where the LO belongs to. The ordering of orbital energy levels of the monomer MOs33 was mostly conserved in the trimer LOs. This was also the case for the dimer calculation.25 The respective LOs of ring A are completely equivalent to the corresponding LOs of C in energy and shape. The LOs on B are generally destabilized compared to the corresponding LOs of A and C. The energy shifts can be attributed to the difference in the environments where the respective Pc rings are placed. To see the relation between the position of Pc ring and the orbital energy shift, the orbital energy levels of the monomer, dimer, and trimer are compared in Figure 3. [SnIV(Pc)2] and [LuIII2(Pc)3] are electrically neutral and can be regarded as stacking systems composed of neutral [MII(Pc)]. The LOs of [Lu(Pc)2]- are destabilized compared to the other three neutral complexes because of its negatively charged nature. The HOLO-LULO gaps of the dimers are both decreased by 0.24 eV from the corresponding value of the monomer. The energy gap narrowing in the trimer is 0.35 eV for ring A and C and 0.65 eV for B. The energy shifts in ring A and C have a tendency similar to that of [Sn(Pc)2]. This can be interpreted as follows. The rings A and C chiefly interact with one adjacent ring, as in the dimer, whereas the central ring B interacts with two Pc’s on both sides. The energy shift and the HOLO-LULO gap narrowing are therefore greater in the central Pc than in the outer Pc’s. This result is consistent with an experimentally obtained conclusion that the diagonal energies of the local excitation from HOLO to LULO within ring B should be smaller than those of rings A and C.23 Excited States of the Trimer. Figure 4 shows the electronic spectrum of [(Pc)Lu(CRPc)Lu(Pc)] in chloroform solution. In

Figure 2. Energy levels of the LOs of [Lu2(Pc)3] (R ) 0.8, D4h, interplanar distance ) 2.9 Å).

Figure 3. Energy levels of the highest occupied and lowest unoccupied orbitals of [M(Pc)] (M ) divalent metal ion), [SnIV(Pc)2], [LuIII2(Pc)3], and [LnIII(Pc)2]-. The numbers beside the arrows indicate the energy gap (in eV) between the LOs.

Q-band region, two major bands, similar to [Lu(Pc)2]-, are observed at 15.8 × 103 cm-1 (633 nm) and 14.0 × 103 cm-1 (716 nm). Both bands were shown to be doubly degenerate from MCD measurement.23 Two shoulder bands are observed at 17.2 × 103 cm-1 (580 nm) and 18.2 × 103 cm-1 (550 nm). The former can be assigned to a vibronic band of the intense 15.8 × 103 cm-1 band since it has common characteristics with the vibronic bands of the Q band of the monomer [MII(Pc)] (M ) divalent metal such as Zn, Mg, or Fe)34-36 and dimer [Lu(Pc)2]-:25 they are located ca. 1.4 × 103 cm-1 higher than the 0-0 band and exhibit a large MCD B-term contribution. The latter 18.2 × 103cm-1 band, which shows a large A-term contribution, does not have a counterpart in either the dimer or

Excited States of Lutetium Phthalocyanine Trimer

J. Phys. Chem., Vol. 100, No. 21, 1996 8725 does not. The ratio of squares of the transition dipole moment of |EC+-+〉 and |EC+++〉 can be estimated at (x2 - 1)2/(x2 + ˆ |j) ) (b|m ˆ |k) ) 1)2 ≈ 1/34 with an assumption that (a|m (c|m ˆ |l).23 In the actual CI calculations, the linear combinations of the same coefficients as eqs 18-20 are used as basis vectors (Table 1, footnote). The orbital energy differences and nonˆ |LEC〉 term cause admixing of |EC+-+〉 and negligible 〈LEA|H +++ 〉. |EC From singlet charge transfer configurations,

Figure 4. Absorption spectrum of [(Pc)Lu(CRPc)Lu(Pc)] in chloroform (top) and calculated excitation energies and oscillator strengths of [Lu2(Pc)3] (bottom, R ) 0.8, D4h, interplanar distance ) 2.9 Å).

monomer. In the lower energy region, two bands at 10.5 × 103 cm-1 (950 nm) and 12 × 103 cm-1 (830 nm) are observed. In the near-IR region, a broad band with a maximum at 7.4 × 103 cm-1 (1360 nm) is observed. In the B-band region, a broad band is observed at 30.3 × 103 cm-1 (330 nm) with a shoulder band at 27 × 103 cm-1. In the localized orbital view, the ground state can be written as

|G〉 ) |aajbbhccj|

(14)

and locally excited singlet configurations as

|LEA〉 ) |{jajbbhccj| - |jhabbhccj|}/x2

(15)

|LEB〉 ) {|aajkbhccj| - |aajhkbccj|}/x 2

(16)

|LEC〉 ) {|aajbbhlcj| - |aajbbhhl c|}/x2

(17)

where a, b, and c are HOLOs on A, B, and C, and j, k, and l are LULOs on A, B and C. Provided the diagonal terms of the three excited configurations are equal and the interaction term ˆ |LEC〉 is negligible compared to 〈LEA|H ˆ |LEB〉 and 〈LEA|H ˆ |LEC〉, the following exciton-coupling-type linear com〈LEB|H binations diagonalize the energy matrix:

1 1 1 |EC+-+〉 ) |LEA〉 |LEB〉 + |LEC〉 2 2 x2 |EC+•-〉 )

1 1 |LEA〉 |LEC〉 x2 x2

1 1 1 |EC+++〉 ) |LEA〉 + |LEB〉 + |LEC〉 2 2 x2

(18)

(19)

(20)

ˆ |j), In the D4h Pc trimer case, where the transition moments (a|m (b|m ˆ |k), and (c|m ˆ |l) are oriented in the same direction, |EC+-+〉 and |EC+++〉 have nonzero transition intensity, while |EC+•-〉

|CTBrA〉 ) {|kajbbhccj| - |khabbhccj|}/x2

(21)

|CTBrC〉 ) {|aajbbhkcj| - |aajbbhhkc|}/x2

(22)

|CTCrA〉 ) {|ajbbhccj| - |lhabbhccj|}/x2

(23)

|CTArC〉 ) {|aajbbhjcj| - |aajbbhhj c|}/x2

(24)

|CTArB〉 ) {|aajjbhccj| - |aajhj bccj|}/x 2

(25)

|CTCrB〉 ) {|aajlbhccj| - |aajhl bccj|}/x 2

(26)

charge resonance configurations are written as

|CRAfBrC (〉 ) {|CTBrA〉 ( |CTBrC〉}/x2

(27)

|CRATC (〉 ) {|CTCrA〉 ( |CTArC〉}/x2

(28)

|CRArBfC (〉 ) {|CTArB〉 ( |CTCrB〉}/x2

(29)

In the case of the D4h Pc trimer, the plus and minus combinations correspond to allowed and forbidden states, respectively. The allowed states |CRAfBrC +〉, |CRATC +〉, and |CRArBfC +〉 belong to the same irreducible representation as |EC+++〉 and |EC+-+〉 and therefore can borrow transition intensity from the exciton coupling states. The bottom of Figure 4 presents calculated excitation energies and oscillator strengths of [Lu2(Pc)3] in D4h symmetry. The wave functions are summarized in Table 1. The CI calculation was carried out with 36 excited configurations that involve six HOLOs (two per Pc ring) and six LULOs (two per Pc ring). In the D4h symmetry, Eu states are dipole-transition allowed. The five excitation bands below 21 × 103 cm-1 are characterized by the excited configurations from HOLOs, 2aX1u, to LULOs, 6 eXg (X ) A, B, or C). The 4 Eu state, which has the largest oscillator strength below 21 × 103 cm-1, is predominantly ascribed to the |EC+++〉 configuration. From the calculated excitation energy and intensity, the absorption band at 15.8 × 103 cm-1 is assigned to this state. The calculation supports the previous assignment by a qualitative treatment.23 The state of the next largest oscillator strength is 3 Eu, which is mainly characterized by the |CRATC +〉 configuration. The CR character reaches 78% if another CR configuration, |CRAfBrC +〉, is taken into account. This state obtains most of its intensity from the |EC+++〉 configuration, which forms 8% of the state. The less intense band in the Q-band region at 14.0 × 103 cm-1 is attributable to this state. A notable similarity between the trimer and dimer is in the assignments of the two Q bands: the higher energy bands are attributable to an exciton coupling state in which all the transition moments in the Pc planes are in the same direction (Figure 5, right column), and the lower energy bands are attributable to a state whose main character is CR between two outer Pc’s (Figure 5, left column).

8726 J. Phys. Chem., Vol. 100, No. 21, 1996

Ishikawa and Kaizu

TABLE 1: Excitation Energies, Oscillator Strengths, Wave Functions of the Lowest Excited Singlet States of [Lu2(Pc)3] in D4h Symmetry Calculated with r ) 0.8 in the LO Basis νj/103 cm-1 1 Eux 1 Egx 2 Eux 2 Egx 3 Eux 3 Egx 4 Eux 4 Egx 5 Eux

wave functiona

f

1.7 3.4 9.6 11.9 15.0 16.0 16.9 18.6 20.4

+〉 - 0.582|EC+-+〉 - 0.234|CRAfBrC +〉 + ... 0.894|CRArBfC -〉 - 0.354|EC+•-〉 - 0.267|CRATC -〉 + ... 0.604|EC+-+〉 + 0.580|CRArBfC +〉 + 0.453|CRAfBrC +〉 + ... 0.739|EC+•-〉 + 0.500|CRAfBrC -〉 + 0.380|CRATC -〉 + ... 0.771|CRATC +〉 + 0.432|CRAfBrC +〉 + 0.285|EC+++〉 + ... 0.637|CRATC -〉 - 0.496|EC+•-〉 + 0.428|CRAfBrC -〉 + ... 0.836|EC+++〉 + 0.329|EC+++(6eg r 4a2u)〉 - 0.326|CRATC +〉 + ... 0.751|CRAfBrC -〉 - 0.612|CRATC -〉 - 0.210|EC+•-〉 + ... 0.732|CRAfBrC +〉 - 0.459|CRATC〉 - 0.395|EC+-+〉 + ...

0.743|CRArBfC

0.0004 forbidden 0.082 forbidden 0.488 forbidden 3.209 forbidden 0.059

a The configurations used as basis are defined as follows. |CRArBfC (〉 ) (1/x2){|6eA r 2aB 〉 ( |6eC r 2aB 〉}; |CRAfBrC (〉 ) (1/x2){|6 gy 1u gy 1u B egy r 2aA1u〉 ( |6eBgy r 2aC1u〉}; |CRATC (〉 ) (1/x2){|6eCgy r 2aA1u〉 ( |6eAgy r 2aC1u〉}; |EC+(+〉 ) (1/2)|6eAgy r 2aA1u〉 ( (1/x2)|6eBgy r B C C A A C C 2a1u〉 + (1/2)|6egy r 2a1u〉; |EC+•-〉 ) (1/x2)|6egy r 2a1u〉 - (1/x2)|6egy r 2a1u〉; |EC+++(6eg r 4a2u)〉 ) (1/2)|6eAgx r 4aA2u〉 + (1/x2)|6eBgx r 4aB2u〉 + (1/2)|6eCgx r 4aC2u〉.

TABLE 3: Off-Diagonal Fock Matrix Elements and Major Two-Electron Integrals Seen in Eqs 30, 31, and 32 Calculated for [Lu2(Pc)3] in D4h Symmetry with r ) 0.8a

Figure 5. Dominant electronic configurations in the excited states which correspond to the two main Q bands of the dimer (top two) and trimer (bottom two). The outlined arrows represent the transition dipole moments in the respective Pc planes. The solid arrows indicate an excitation from a HOLO to LULO which belong to different rings.

TABLE 2: Configuration Interaction Matrix Elements (eV) among Lowest Excited Configurations for [Lu2(Pc)3] in D4h Symmetry Calculated with r ) 0.8 in the LO Basis |EC+++〉 |CRAfBrC +〉 |CRATC +〉 |EC+-+〉 |CRArBfC +〉 |EC+++〉

|CRAfBrC +〉 |CRATC +〉 |EC+-+〉 |CRArBfC +〉

2.374

0.219 1.996

0.003 -0.243 1.919

0.182 -0.603 0.004 1.189

0.027 0.000 0.434 0.552 0.767

We shall now look into how the CR configurations interact with the EC configuration. Using eqs 11, 12, and 13, the interaction between |CRATC +〉 and |EC+++〉 is given by

a

aC1u,

integrals

calculated value (eV)

(a|fˆ|b), (b|fˆ|c) (a|fˆ|c) (j|fˆ|k), (k|ˆf|l) (j|fˆ|l) (kk|ba), (kk|bc) (ka|aj), (kc|cl) (ka|bk), (kc|bk) (kj|aa), (kl|cc)

-0.443 -0.023 -0.242 -0.027 0.015 -0.013 -0.008 -0.002

The LOs are expressed as in the text: a ) 2aA1u, b ) 2aB1u, c ) 2 j ) 6eAg , k ) 6eBg , l ) 6eCg .

The two matrix elements are expressed by

1 〈CRATC + |H ˆ |CRAfBrC +〉 ) {(l|fˆ|k) + 2(la|ak) 2 1 1 (lk|aa)} + {(j|fˆ|k) + 2(jc|ck) - (jk|cc)} + {2(la|ck) 2 2 1 (lk|ca)} + {2(ak|jc) - (ac|jk)} (31) 2 and

ˆ |EC+++〉 ) 〈CRAfBrC + |H

1 {(k|fˆ|j) + 2(ka|aj) 2x2

1 〈CRATC + |H ˆ |EC+++〉 ) {(j|fˆ|l) + 2(la|aj) - (lj|aa)} + 2 1 1 {(j|fˆ|l) + 2(jc|cl) - (jl|cc)} + {-(a|fˆ|c) + 2(la|cl) 2 2 1 (ll|ca)} + {-(a|fˆ|c) + 2(aj|jc) - (ac|jj)} + 2 1 1 {2(la|bk) - (lk|ba)} + {2(bk|jc) - (bc|jk)} (30) x2 x2

1 {(k|fˆ|l) + 2(kc|cl) - (kl|cc)} + x 2 2 1 1 {-(b|fˆ|a) + 2(ka|bk) - (kk|ba)} + {-(b|fˆ|c) + 2 2 1 {2(aj|kc) - (ac|kj)} + 2(kc|bk) - (kk|bc)} + 2x2 1 {2(ka|cl) - (kl|ca)} (32) x 2 2

The Fock matrix elements in the right-hand side of the equation are of distant pairs of LOs, namely, those belonging to A and C, and therefore are expected to be small. The two-electron integrals in the equation are also small since either side of each integral has a distant LO pair which has small overlap. In fact the actual values in the calculation (Table 2) for the interaction term is smaller than the diagonal energy difference by 2 orders of magnitude. This means that the significant contribution from the exciton configuration in the 3 Eu state is not a result from a direct interaction between the two configurations but a secondary coupling through other configurations. Table 2 shows ˆ |CRAfBrC +〉 and 〈CRAfBrC that, through 〈CRATC +|H +++ ATC +|H ˆ |EC 〉, |CR +〉 can indirectly couple with |EC+++〉.

respectively. Because of the Fock matrix elements of near pairs of LOs, the two coupling terms can become much larger than 〈CRATC +|H ˆ |EC+++〉. Consequently, the 3 Eu state gains transition moment from the EC configuration by containing the |CRAfBrC +〉 configuration, through which |CRATC +〉 can mix with |EC+++〉. The contributions to the coupling terms from the two-electron integrals were negligibly small except from those presented in Table 3: all of the four integrals contained three LOs on the same Pc site, respectively. The way the EC character mixes with the CR state in a dimer contrasts with that of the trimer. As mentioned above, in the lutetium Pc dimer, [Lu(Pc)2]-, the lower energy Q band is

(kj|aa)} +

Excited States of Lutetium Phthalocyanine Trimer

J. Phys. Chem., Vol. 100, No. 21, 1996 8727

attributable to a state which is dominated by a CR configuration,

1 1 |CTBrA〉 + |CTArB〉 x2 x2 1 1 ) {|kajbbh| - |khabbh|} + {|aajjbh| - |aajhj b|} 2 2

|CR +〉 )

(33)

The EC configuration which composes the main character of the state corresponding to the higher energy Q band is similarly written as

1 1 |LEA〉 + |LEB〉 x2 x2 1 1 ) {|jajbbh| - |jhabbh|} + {|aajkbh| - |aajhkb|} 2 2

|EC +〉 )

(34)

The interaction between the two configurations is

1 〈CR + |H ˆ |EC +〉 ) (j|fˆ|k) - (a|f|b) + (ja|ak) - (jk|aa) + 2 1 1 1 (ja|bj) - (jj|ba) + (kb|ak) - (kk|ab) + (kb|bj) - (kj|bb) 2 2 2 (35) The expression contains Fock matrix elements of near LO pairs, which can lead to a large and direct mixing between the two configurations. It is worth noting that the Fock matrix element of the two HOLOs also determines the excitation energy of the “valence resonance” band observed at 7 × 103 cm-1 in the radical species, [Lu(Pc)2]•, in which a hole is delocalized over the highest occupied π orbitals of the two Pc rings in the dimer. The excitation energy has been shown to be approximately |2(a|fˆ|b)|, where the one-electron Fock operator is the one defined in the closed shell system.26 Substituting the calculational value for the closed shell [Lu(Pc)2]- (0.464 eV, also notice the proximity to the value of (a|fˆ|b) for the trimer shown in Table 3) well reproduces the excitation energy of the near-IR band of the radical. In other word, in the closed shell species, the EC and CR configurations are coupled by a term which is potentially on the same order of magnitude as the excitation energy of the “valence resonance” band of the radical dimer. The same argument is valid for the trimer as well. The trimer radical, [(Pc)Lu(Pc)Lu(Pc)]•+, shows a near-IR band at 5 × 103 cm-1, which is theoretically expressed as |x2(a|fˆ|b)|.38 On the other hand, the coupling terms, eqs 30 and 31, for the closed shell trimer also contain large Fock matrix elements and the unoccupied LOs’ counterparts. It is therefore quite reasonable that the lutetium Pc dimer and trimer have a several thousand wavenumber for the interaction term, which leads to a large intensity in the CR band. Needless to say, the values of the coupling terms vary in different dimers. In other dimers such as the one which is formed from crown-ether-substituted Pc’s in the presence of potassium ion, the CR band is not clearly identified. Whether the CR band is manifested or not may be strongly governed by geometrical factors such as orientational angle and interplanar distance. For example, in our calculation for the dimer with a fixed interplanar distance at 2.9 Å, the ratio of oscillator strength of the CR band to that of the EC band is 1:26 for D4h structure (orientational angle 0°) and 1:4 for D4d (45°). Returning to the calculational result for the trimer, another CR-dominated state is 5 Eu. It also mainly comprises |CRATC +〉 and |CRAfBrC +〉 configurations, but the latter is the main character. The band observed at 18.2 × 103 cm-1 can be assigned to this state from its energy and intensity. Because the LULO 6eBg has higher energy than 6eAg and 6eCg , and the

HOLOs 2aA1u and 2aC1u lie lower than 2aB1u, the charge transfer configurations 6eBg r 2aA1u and 6eBg r 2aC1u have higher energies than any other 6eXg r 2aX1u excited configurations. Consequently, their linear combination, |CRAfBrC +〉, gives the largest contribution to the highest HOLO-LULO charge resonance state. Both the lowest two excited states, 1 Eu and 2 Eu, have comparable contributions from two configurations, |CRArBfC +〉 and |EC+-+〉. This is the result of the close proximity in energy of the two configurations. In the present calculational condition, since the |CRArBfC +〉 configuration is given a lower diagonal energy than the |EC+-+〉 configuration, the leading configuration in 1 Eu is |CRArBfC +〉 and that of 2 Eu is |EC+-+〉. However, it may be altered in a more accurate approximation. The leading characters of the two states are still open to question at present. From the calculated energies, the broad band at around 7 × 103 cm-1 is assigned to the 1 Eu state. The two bands at 12 × 103 and 10.5 × 103 cm-1 should be concluded to be a vibrational progression of an electronic transition to the 2 Eu state if the molecular symmetry is strictly D4h. Assignment of the Absorption Bands in the MO Basis. Besides a LO-based treatment which emphasizes the chemical discreteness among Pc rings, a CI calculation with a delocalized MO basis is of course possible. Although the interpretations of the calculational results may look different from each other, the two calculations are essentially mathematically equivalent. Table 4 shows the result of a CI calculation in the MO basis. Since CI expansions in both cases are truncated and there exists a difference between the spaces spanned by MO and LO basis configurations, small differences are seen in the calculated energies and oscillator strengths. However, the two results would be completely identical if all singly excited configurations were included. The MO energy levels are shown in Figure 6 accompanied by the LO levels. Three HOMOs of the trimer, 3a1u, 2a2g, and 4a1u in D4h, correspond to bonding, nonbonding (node at central Pc plane), and antibonding combinations of monomer HOMOs, 2a1u, respectively. This is also the case for the three LUMOs (11eg ≈ bonding, 6eu ≈ nonbonding, 12eg ≈ antibonding combinations of monomer 6eg). From the six MOs, five singly excited configurations (|11eg r 4a1u〉, |12eg r 4a1u〉, |6eu r 2a2g〉, |11eg r 3a1u〉, and |12eg r 3a1u〉) belong to Eu representation. In the MO picture, the dominant contribution of the lowest allowed excited state, 1 Eu, is HOMO-LUMO excitation (|11eg r 4a1u〉). The second allowed state, 2 Eu, is characterized by HOMO-third-LUMO excitation (|12eg r 4a1u〉). By contrast to the LO basis expressions, the two lowest excited states are described predominantly by a single configuration with the MO basis. The main contributions to the 3 Eu state (corresponds to the 14.0 × 103 cm-1 band) and 4 Eu (15.8 × 103 cm-1 band) are |6eu r 2a2g〉 (nonbonding r nonbonding) and |11eg r 3a1u〉 (bonding r bonding), respectively. These two configurations have approximately the same transition moments. An interaction between them results in a larger-intensity state at higher energy (4 Eu) and a smaller intensity state at lower energy (3 Eu). A similar situation was also seen in the two Q bands of the dimer ([Lu(Pc)2]-): the interaction between two excited configurations (HOMO to next-LUMO and next-HOMO to LUMO) which have similar transition moments leads to two excited states with different intensities.25 Effect of Symmetry Lowering by Ring Rotation. Shirk et al. reported that closed shell phthalocyanine dimers exhibit a near-IR band spreading over 8 × 103 to 12 × 103 cm-1.3 When the molecular symmetry is assumed to be D4h, in which the

8728 J. Phys. Chem., Vol. 100, No. 21, 1996

Ishikawa and Kaizu

TABLE 4: Excitation Energies, Oscillator Strengths, Wave Functions of the Lowest Excited Singlet States of [Lu2(Pc)3] in D4h Symmetry Calculated with r ) 0.8 in MO Basis 1 Eux 1 Egx 2 Eux 2 Egx 3 Eux 3 Egx 4 Eux 4 Egx 5 Eux

νj/103 cm-1

f

wave function

1.2 3.3 9.4 11.6 14.9 15.9 16.9 18.6 20.3

0.0003 forbidden 0.091 forbidden 0.344 forbidden 3.380 forbidden 0.055

0.992|11egy r 4a1u〉 + 0.102|6euy r 2a2g〉 - 0.055|12egy r 4a1u〉 + ... 0.995|6euy r 4a1u〉 + 0.062|11egy r 2a2g〉 - 0.054|6euy r 3a1u〉 + ... 0.874|12egy r 4a1u〉 - 0.350|11egy r 3a1u〉 - 0.312|6euy r 2a2g〉 + ... 0.943|11egy r 2a2g〉 + 0.291|6euy r 3a1u〉 - 0.089|11egx r 4a1g〉 + ... 0.834|6euy r 2a2g〉 - 0.471|11egy r 3a1u〉 + 0.214|12egy r 3a1u〉 + ... 0.894|6euy r 3a1u〉 + 0.338|12egy r 2a2g〉 - 0.262|11egy r 2a2g〉 + ... 0.776|11egy r 3a1u〉 + 0.413|12egy r 4a1u〉 + 0.319|6euy r 2a2g〉 + ... 0.933|12egy r 2a2g〉 - 0.310|6euy r 3a1u〉 + 0.162|11egy r 2a2g〉 + ... 0.970|12egy r 3a1u〉 - 0.218|6euy r 2a2g〉 + 0.061|12egx r 8a2u〉 + ...

Figure 6. Energy levels of the highest occupied and lowest occupied orbitals of [LuIII2(Pc)3] in LO and MO basis sets (R ) 0.8, D4h, interplanar distance ) 2.9 Å).

Figure 8. Absorption spectrum of [(Pc)Lu(CRPc)Lu(Pc)] in near-IR and Q-band regions in chloroform (top) and calculated excitation energies and oscillator strengths of the trimer with a symmetry distortion from D4h symmetry by rotation of two outer Pc rings in the same direction (a f b, c). The circles on abscissas indicate forbidden states.

Figure 7. Absorption spectrum of [Lu(Pc)2]- in near-IR and Q-band regions in dichloromethane (top) and calculated excitation energies and oscillator strengths of the dimer with varied orientational angles of Pc’s around the C4 axis: (a) 45°, D4d symmetry (b) 40°, D4, and (c) 35°, D4 (R ) 0.8). The circles on abscissas indicate forbidden states.

orientational angle is 45°, no allowed excited state is predicted below the two Q bands. However, there is a symmetryforbidden state in the region, which can have a transition intensity when the symmetry is lowered. Figure 7 shows the observed spectrum and theoretical calculations with varied orientational angles between the two Pc rings. The twisting of Pc rings around the C4 axis (Figure 7, a f b) gives a transition

intensity to the lowest excited state, as well as the fourth excited state. Those intensities become larger by further distortion (Figure 7, b f c). The emergence of the additional near-IR band thus indicates that the dimer structure is subjected to some kind of symmetry lowering such as vibrational distortion around an equilibrium D4h structure or rigid structural relaxation to a lower symmetry. If twisting of this kind also arises in the trimer, there are two cases to be considered. One is “conrotatory” distortion, in which the two outer Pc rings rotate in the same direction resulting in C4h symmetry. The other is “disrotatory” distortion, where the two rings rotate in opposite direction, leading to D4 symmetry. In the former case, as seen in Figure 8, the conrotatory distortion gives rise to no additional allowed excited state. The representations of the allowed states and forbidden states, i.e. Eu and Eg in D4h symmetry, remain unchanged in C4h symmetry, and the same selection rule holds. By contrast, the disrotatory distortion gives transition intensity to the forbidden states (Figure 9b,c). Both of the two representations fall into E representation of the D4 group. A notable result here is that the forbidden 2 Eg state becomes allowed and appears at around 12 × 103 cm-1. Two absorption bands observed in the corresponding region (12

Excited States of Lutetium Phthalocyanine Trimer

Figure 9. Absorption spectrum of [(Pc)Lu(CRPc)Lu(Pc)] (top) and calculated excitation energies and oscillator strengths of the trimer with a symmetry distortion from D4h symmetry by rotation of two outer Pc rings in opposite direction (a f b, c). The circles on abscissas indicate forbidden states.

× 103, 10.5 × 103 cm-1) can be assigned to different electronic states if the disrotatory distortion actually occurs in the trimer structure. Effect of Elongation of Interplanar Distance. To date, a clear absorption spectrum of the lanthanide phthalocyanine trimer has been reported only for the lutetium complex. The effect of substitution of lanthanide ions on the molecular structure is expected to be straightforward; the interplanar distance should be lengthened as the atomic number of the trivalent lanthanide ions becomes smaller because of the lanthanide contraction. It has been reported for the dimer series that the Q-band splitting decreases as the distance increases.37 To see the effect of the distance change on the spectrum of the trimers, calculations with varied interplanar distances were performed (Figure 10). As the distance becomes larger, 1 Eu, 2 Eu, and 3 Eu states shift to higher energy, while 5 Eu shifts in the opposite direction. The energy difference between the two most intense bands becomes smaller for larger distance. This indicates that the decrease of atomic number of the lanthanide ions as well reduces the trimer Q-band splitting. The calculation also indicates that the near-IR bands show blue shift with the change to smaller atomic number. Conclusion Electronic structure of the lutetium phthalocyanine trimer [Lu2(Pc)3] was studied using the LO basis as well as the MO basis. The LO basis was obtained from the semiempirical canonical MO so that the population on a Pc ring becomes a maximum. The localization was carried out by repetitive use of the localization method for the dimer. The ordering of orbital energy levels of the monomer is mostly conserved in each Pc ring of the trimer. The LOs on the central Pc ring generally have higher energy than those of

J. Phys. Chem., Vol. 100, No. 21, 1996 8729

Figure 10. Absorption spectrum of [(Pc)Lu(CRPc)Lu(Pc)] (top) and calculated excitation energies and oscillator strengths of [Lu2(Pc)3] with varied interplanar distances (R ) 0.8, D4h).

the two outer Pc rings. The HOLO-LULO gaps of every site are narrower than the corresponding monomer HOMO-LUMO gap. The narrowing is even larger on the central ring than on the outer rings. The energy shift pattern seen in the outer rings is similar to that of the dimer. The difference in energy shift is attributable to the environment felt by each Pc ring; the outer rings mainly interact with one central ring, while the central ring interacts with two. Excited states of the trimer were calculated by the configuration interaction method. With the LO basis, the excited states are described by inter- and intraligand electron excitations. In D4h symmetry, the HOLO-LULO transitions give five allowed excited states: two exciton coupling states, |EC+++〉 and |EC+-+〉, and three charge resonance states, |CRATC +〉, |CRAfBrC +〉 and |CRArBfC +〉. The most intense band in the Q-band region (15.8 × 103 cm-1) is assigned to the 4 Eu state (an exciton coupling state |EC+++〉), and the second intense band at 14.0 × 103 cm-1 to the 3 Eu state (a charge resonance state |CRATC +〉). A similarity to the dimer case is seen in the assignments; in both cases, the higher energy band is attributed to the transition whose transition moments in the Pc planes are all oriented in the same direction, and the lower energy band is attributed to the transition that results from charge resonance between two “outermost” Pc rings. In the MO treatment, the leading configurations of the 4Eu state (15.8 × 103 cm-1 band) and the 3Eu state (14.0 × 103 cm-1 band) are |11eg r 3a1u〉 (LUMO r third HOMO) and |6eu r 2a2g〉 (second LUMO r second HOMO), respectively. These two configurations have transition moments of similar magnitude. The interaction between the two causes a redistribution of the transition moment: the higher energy state 4Eu has a greater intensity than the lower energy state 3Eu. From the calculation of the dimer, it was shown that the symmetry lowering from D4d by twisting of Pc rings around

8730 J. Phys. Chem., Vol. 100, No. 21, 1996 the C4 axis causes the emergence of an allowed transition below the Q-band region. The broad band observed for [Lu(Pc)2]spreading over 8 × 103 to 12 × 103 cm-1 is attributable to this state. In the trimer, distortions from the D4h structure can exist as two combinations of ring rotations. One combination in which the two outer Pc rings rotate in the same direction does not lead to any additional allowed transition. Another combination, in which the two rings rotate in the opposite direction, gives transition intensity to the states which are forbidden at D4h. This leads to different assignments of the near-IR bands: the two bands at 12 × 103 and 10.5 × 103 cm-1 most likely belong to different electronic states if the disrotatory distortion is assumed, while they should be assigned to the same electronic state with different vibrational levels if the conrotatory or no distortion is assumed. Elongation of interplanar distance reduces the Q-band splitting. The near-IR bands are predicted to shift to higher energy as the distance increases. References and Notes (1) De Cian, A.; Moussavi, M.; Fischer, J.; Weiss, R. Inorg. Chem. 1985, 24, 3162. (2) Moussavi, M.; De Cian, A.; Fischer, J.; Weiss, R. Inorg. Chem. 1988, 27, 1287. (3) Shirk, J. S.; Lindle, J. R.; Bartoli, F. J.; Boyle, M. E. J. Phys. Chem. 1992, 96, 5847. (4) Bennett, W. E.; Broberg, D. E.; Baenziger, N. C. Inorg. Chem. 1973, 12, 930. (5) Silver, J.; Lukes, P. J.; Hey, P. K.; O’connor, J. M. Polyhedron 1989, 8, 1631. (6) Hush, N. S.; Woolsey, I. S. Mol. Phys. 1971, 21, 465. (7) Wheeler, B. L.; Nagasubramanian, G.; Bard, A. J.; Schechtman, L. A.; Dininny, D. R.; Kenny, M. E. J. Am. Chem. Soc. 1984, 106, 7404. (8) Corker, G. A.; Grant, B.; Clecak, N. J. J. Electrochem. Soc. 1979, 126, 1339. (9) Riou, M.-T.; Auregan, M.; Clarisse, C. J. Electroanal. Chem. 1985, 187, 349. (10) L’Her, M.; Cozien, Y.; Courtot-Coupez, J. C. R. Acad. Sci. Paris, Ser. II 1985, 11, 487. (11) Chang, A. T.; Marchon, J.-C. Inorg. Chim. Acta 1981, 53, L241. (12) Andre´, J.-J.; Holczer, K.; Petit, P.; Riou, M.-T.; Clarisse, C.; Even, R.; Fourmigue, M.; Simon, J. Chem. Phys. Lett. 1985, 115, 463.

Ishikawa and Kaizu (13) Turek, P.; Petit, P.; Andre´, J.-J.; Simon, J.; Even, R.; Boudjema, B.; Guillaud, G.; Maitrot, M. J. Am. Chem. Soc. 1987, 109, 5119. (14) Maitrot, M.; Guillaud, G.; Boudjema, B.; Andre´, J.-J.; Strzelecka, H.; Simon, J.; Even, R. Chem. Phys. Lett. 1987, 133, 59. (15) Petit, P.; Holczer, K.; Andre´, J.-J. J. Phys. 1987, 48, 1363. (16) Belarbi, Z.; Sirlin, C.; Simon J.; Andre´, J.-J. J. Phys. Chem. 1989, 93, 8105. (17) Buchler, J. W.; Elsasser, K.; Kihn-Botulinski, M.; Scharbert, B.; Tansil, S. ACS Symp. Ser. 1986, 321, 94. (18) Buchler, J. W.; Scarbert, B. J. Am. Chem. Soc. 1988, 110, 4272. (19) Buchler, J. W.; Huttermann J.; Loffler, J. Bull. Chem. Soc. Jpn. 1988, 61, 71. (20) Kirin, I. S.; Moskalev, P. N.; Ivannikova, N. V. Russ. J. Inorg. Chem. 1967, 12, 497. (21) M’Sadak, M.; Roncali, J.; Garnier, F. J. Chim. Phys. 1986, 83, 211. (22) Kasuga, K.; Ando, M.; Morimoto, H.; Isa, M. Chem. Lett. 1986 1095. (23) Ishikawa, N.; Kaizu, Y. Chem. Phys. Lett. 1994, 228, 625. (24) Ishikawa, N.; Kaizu, Y. Chem. Phys. Lett. 1993, 203, 472. (25) Ishikawa, N.; Ohno, O.; Kaizu, Y.; Kobayashi, H. J. Phys. Chem. 1992, 96, 8832. (26) Ishikawa, N.; Ohno O.; Kaizu, Y. J. Phys. Chem. 1993, 97, 1004. (27) Koray, A. R.; Ahsen V.; Bekaˆroglu, O ¨ . J. Chem. Soc., Chem. Commun. 1986 932. (28) Kobayashi, N.; Nishiyama, Y. J. Chem. Soc., Chem. Commun. 1986, 1462. (29) Hendriks, R.; Sielcken, O. E.; Drenth, W.; Nolte, R. J. M. J. Chem. Soc., Chem. Commun. 1986, 1464. (30) Kobayashi, N.; Lever, A. B. P. J. Am. Chem. Soc. 1987, 109, 7433. (31) Mataga, N.; Nishimoto, K. Z. Phys. Chem. (Munich) 1957, 13, 140. (32) Weiss, C.; Kobayashi, H.; Gouterman, M. J. Mol. Spectrosc. 1965, 16, 415. (33) Ohno, O.; Ishikawa, N.; Matsuzawa, H.; Kaizu, Y.; Kobayashi, H. J. Chem. Phys. 1989, 93, 1713. (34) Nyokong, T.; Gasyna, Z.; Stillman, M. J. Inorg. Chem. 1987, 26, 1087. (35) Ough, E.; Nyokong, T.; Creber, K. A. M.; Stillman, M. J. Inorg. Chem. 1988, 27, 2724. (36) Ough, E.; Stillman, M. J. Inorg. Chem. 1994, 33, 573. (37) Konami, H.; Hatano, M.; Tajiri, A. Chem. Phys. Lett. 1989, 160, 163. (38) Ishikawa, N.; Kaizu, Y. Chem. Phys. Lett. 1995, 236, 50.

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