Disappearance of MCD A term in the fingerprint band of cation radicals of phthalocyanine metal complexes

4 May 2001

Chemical Physics Letters 339 (2001) 125±132

www.elsevier.nl/locate/cplett

Disappearance of MCD A term in the ®ngerprint band of cation radicals of phthalocyanine metal complexes Naoto Ishikawa *, Youkoh Kaizu Department of Chemistry, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152±8551, Japan Received 28 December 2000; in ®nal form 14 March 2001

Abstract The magnetic circular dichroism (MCD) spectrum and assignment of the characteristic `®ngerprint band' of the p-cation radical of phthalocyanine complexes are studied using a semiempirical MO method. Two types of excited con®gurations from occupied eg orbitals to the a1u singly occupied molecular orbital (SOMO) were present between Q band and B-band manifolds. The magnetic dipole moments of the two con®gurations were similar in magnitude but the signs were opposite. Because of the vicinity in energy, the two excited con®gurations couple to give an excited state, 2Eg , having an extremely reduced A term. The `®ngerprint band' is assigned to this state. Ó 2001 Elsevier Science B.V. All rights reserved.

1. Introduction Magnetic circular dichroism spectroscopy (MCD) has been a powerful tool to analyze the excited state electronic structure of phthalocyanine (Pc) and porphyrin related compounds. For a doubly degenerate excited state which is split under a magnetic ®eld by Zeeman e€ect [1±3], a characteristic derivative-shaped spectral pattern called an `A term' is observed. It is generally true that MCD A term is associated to the transition to a degenerate E type excited state in the Pc and porphyrin compounds. It is known that upon oxidation of Pc compounds an additional intense band emerges at ca. 500 nm between the Q band and B-band manifold. The band is characteristic for p radical of Pc

*

Corresponding author. Fax: +81-3-5734-2655. E-mail address: [email protected] (N. Ishikawa).

complexes, hence called `®ngerprint' band of such species. Stillman et al. [4,5] reported measurement and detailed analysis of absorption and MCD spectrum of ZnPc‡ and MgPc‡ [6]. The deconvolution analysis of the MCD of the ®ngerprint band was completely achieved using only B-term patterns. Because of the lack of A term, they concluded that the band was assigned to a nondegenerate transition from a low-lying MO into a1u singly occupied MO (SOMO) [6]. The assignment, however, has a diculty in explaining the large transition intensity of the band because there is no such transition that is nondegenerate yet symmetrically allowed in the energy region. On the other hand, Ishikawa et al. [7] reported an ab initio calculation of excited states of MgPc‡ showing that the second allowed 2 Eg state, which is characterized by the degenerate transition from occupied eg orbital to SOMO a1u , is present in the ®ngerprint-band region. However, there has been no theoretical explanation on the observed MCD

0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 3 1 9 - 0

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N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132

pattern which appears inconsistent with the degeneracy. This Letter studies the MCD A term of the p-radical MPc‡ (M: divalent metal ion such as Mg2‡ and Zn2‡ ) by MO calculation with semiempirical parameterization. The main focus is on why the `disappearance of A term' in the ®ngerprint band occurs. It will be shown that there are two eg -toSOMO transitions, each of which has an A term of opposite signs to the other, and the A term can vanish by coupling of the two excited con®gurations. We will show that the assignment of the ®ngerprint band to the excited state composed of the two eg -to-SOMO transitions does explain both the absorption and MCD data. 2. Theoretical calculations 2.0.1. p electron systems of the Pc p radical MO calculations of the MPc‡ p radical were carried out within the p approximation using a semiempirical method. Parameters and formulas to evaluate molecular integrals used for the calculation were the same as those previously used for Pc monomer [8], dimer [9,10] and trimer [11,12]. The ground state of the open shell MPc‡ was treated by the restricted open-shell Hartree±Fock (ROHF) method [13], which uses a single set of spatial functions for both alpha and beta spinorbitals. The numerical values for the parameters and de®nitions are described in the reference [12]. Two-electron interactions between two centers at a distance r were evaluated with the formula prescribed by Nishimoto and Mataga [14] …e2 =…a ‡ r†† which reasonably reproduced closed shell Q and B bands. For the one-center Coulomb interaction e2 =a, the values determined by Gouterman et al. [15,16] were used. 2.1. Excited states Doublet excited states of the open shell MPc‡ were calculated by a method equivalent to what is referred to as `XCIS' [17] (extended restricted openshell CIS). The ROHF ground state j Gi, from which excited con®gurations are constructed, is

j Gi ˆ j . . . ii . . . mj and the singly excited con®gurations included in the calculations are j Dm

ii ˆ j . . . im . . . mj;

j Da

mi ˆ j . . . ii . . . aj;

j Sa

ii ˆ fj . . . ai . . . mj

j Ta

ii

p j . . . ai . . . mjg= 2;

ˆ f2j . . . ai . . . mj

j . . . ai . . . mj p j . . . ai . . . mjg= 6;

where m; i and a denote the SOMO, a doubly occupied orbital and a virtual orbital, respectively. The calculations in the present Letter used 127 excited con®gurations involving seven lowest virtual orbitals, one SOMO and eight highest doubly occupied orbitals. 2.2. MCD A/D ratios MCD A term and square of transition dipole moment D of a doubly degenerate excited state of E representation are calculated by the following equations. o n 1n ^ x jUihUjM ^ y jGi AU ˆ hUj bL^z jUi Im hGjM 2 o ^ y jUihUjM ^ x jGi ; hGjM …1† ^ x jUihUjM ^ x jGi ‡ hGjM ^ y jUihUjM ^ y jGi; DU ˆ hGjM ^ y are electric dipole operators and ^ x and M where M ^ Lz is the z component of the orbital angular momentum operator. b denotes Bohr magneton. The z-axis was set along C4 -axis of the molecule. We use the following notations for the electric dipole moment and orbital angular momentum operators throughout the Letter: ^ ˆM ^y j ‡ M ^zk ^xi ‡ M M ˆ

N X i

^ ˆ m

^ x …i†i ‡ m ^ y …i†j ‡ m ^ z …i†kg ˆ fm

N X i

^xi ‡ m ^y j ‡ m ^ z k; e…xi ‡ yj ‡ zk† ˆ m

^ m…i†;

N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132

L^z ˆ

N X

l^z …i†;

iˆ1

^ y and m ^ z are one-electron electric di^x; m where m pole operators and l^z is the z component of oneelectron orbital angular momentum operator. N is the number of electrons in the system. The contributions from spin angular momenta are omitted in the Eq. (1) since this Letter discusses excited states having the same spin quantum number as the ground state. The excited state wave function U is in a complex form,
p jUi ˆ jUx i ‡ ijUy i = 2 or jUi ˆ jUx i


p ijUy i = 2;

where jUx i and jUy i are the two components of the degenerate excited state in real forms. Matrix elements in the AO basis for the angular momentum operator   o o ^ lz ˆ i h x y oy ox are calculated with the origin ®xed at the center of the complex.

127

5eg i and of transition energies of jD2a1u jD2a1u 4eg i are located between those of jD6eg 2a1u i and jS6eg 4a2u i. Because the two excited con®gurations are close in energy, substantial mixing of them by con®guration interaction is expected. Table 1 shows the orbital transition moments involved in the excitation jD2a1u 5eg i and jD2a1u 4eg i. The signs of the values depend on the phases of the orbitals. In the present Letter, we choose the orbital phases as shown in Fig. 1 so ^ y ja1u † and …egy jm ^ x ja1u † become positive: that …egx jm     ^ y ja1u ˆ egy jm ^ x ja1u > 0; egx jm     ^ x ja1u ˆ egy jm ^ y ja1u ˆ 0; egx jm where egx;y denotes the two highest occupied eg orbitals, namely, 4egx;y and 5egx;y orbitals, and a1u the singly occupied 2a1u orbital. The orbital angular momenta of 5eg and 4eg orbitals with the choice of phases are also listed in Table 1. It should be noted that …5egx jl^z j5egy † and …4egx jl^z j4egy † have the opposite signs. The ground state wave function is written as jGi ˆ j . . . egx egx egy egy . . . a1u j: The degenerate excited con®gurations Wx and Wy are de®ned as follows:

3. Results and discussion Fig. 1 shows calculated ROHF p-MO energies of the MPc‡ . The employed de®nition of the orbital energies in ROHF method is described in the reference [12]. The SOMO and LUMO are 2a1u and 6eg orbitals, respectively. The transition from the SOMO to LUMO, jD6eg 2a1u i, gives the lowest excited state, which corresponds to the Q band observed at 12 000 cm 1 [4±6]. The transition is shown as arrow 1 in Fig. 1. The highest doubly occupied MO is 4a2u . The jS6eg 2a2u i transition, shown as arrow 2 in Fig. 1, should contribute mainly to B band as in neutral MPc. Occupied 5eg and 4eg p-orbitals are located closely in energy. Since the 2a1u orbital is half-occupied, the promotion of an electron from the eg orbitals to the SOMO, shown as arrow 3 and 4 in the Fig. 1, is allowed. From the orbital energies, it is likely that

Wx ˆ jDa1u

egy i ˆ j . . . egx egx egy a1u . . . a1u j;

Wy ˆ jDa1u

egx i ˆ j . . . egx a1u egy egy . . . a1u j

^ y ja1u † and …egy jm ^ x ja1u † are set to be Since …egx jm positive, the transition dipole moments for the con®gurations are positive:   ^ x jGi ˆ egy jm ^ x ja1u > 0; hWx jM   ^ y jGi ˆ egx jm ^ y ja1u > 0: hWy jM The excited con®gurations appropriate under the external magnetic ®eld are p W ˆ …Wx  iWy †= 2: The electric dipole moment operators corresponding to the right- and left-circularly polarized light are

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N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132

Fig. 1. Energy levels of the highest occupied and lowest unoccupied ROHF p orbitals of MPc‡ . The diagrams on the right-hand side show shapes of selected orbitals. The circle radii are proportional to the magnitude of LCAO coecients.

^ ^  ˆ …i  ij†
M: M

^ jGi ˆ hW jM ^ ‡ jGi ˆ 0: hW‡ jM

The con®gurations W‡ and W are excited by right- and left-circularly polarized light, respectively, since:

The magnetic dipole moments of the con®gurations are

^ ‡ jGi ˆ hW jM ^ jGi hW‡ jM n o p ^ ^ ˆ i
hWx jMjGi ‡ j
hWy jMjGi = 2 n op ^ x ja1u † ‡ …egx jm ^ y ja1u † 2 6ˆ 0; ˆ …egy jm

hW j

bL^z jW i ˆ ib…egx jl^z jegy †:

Using the values in the Table 1, D E   …2a 5e † …2a 5e † W 1u g j bL^z jW 1u g ˆ ib 5egx jl^z j5egy ˆ 0:87bh;

N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132 Table 1 Calculated transition moments and orbital angular momenta for the highest two occupied 4eg and 5eg p-orbitals 1:05ea0 a 0:69ea0 )0:87ih 0:70ih 0:15ih

^ y j2a1u †, …5egy jm ^ x j2a1u † …5egx jm …4egx jm ^ y j2a1u †, …4egy jm ^ x j2a1u † …5egx jl^z j5egy † …4egx jl^z j4egy † …4egx jl^z j5egy †, …5egx jl^z j4egy † a

a0 is Bohr radius.

D …2a W 1u

4eg †

j

bL^z jW

…2a1u

4eg †

E

  ˆ ib 4egx jl^z j4egy

ˆ 0:70b h: At this point, it is clear that W‡ , to which the system is excited by the right-circularly polarized …2a 5e † light, goes to the lower energy in the jW 1u g i …2a1u 4eg † pair and higher in the jW i pair under the magnetic ®eld aligned to the z-axis. The ®rst factor of the A term expression, the right-hand side of Eq. (1), is the magnetic dipole moment of the con®guration. The second factor is reduced to: n o ^ x jW ihW jM ^ y jGi hGjM ^ y jW ihW jM ^ x jGi Im hGjM ^ x ja1u †…ex jm ^ y ja1u †: ˆ …ey jm …2a

5e †

The factor takes a positive value in jW‡ 1u g i …2a 4e † and jW‡ 1u g i and negative in jW…2a1u 5eg † i and …2a 5e † jW…2a1u 4eg † i. Therefore, A term of jW 1u g i is …2a1u 4eg † negative while that of jW i is positive: the signs of the A terms are opposite in the two con®gurations. As the vicinity of 5eg and 4eg orbitals in energy indicates, the two con®gurations are expected to be mixed to a large extent by con®guration interaction. The magnetic dipole moment of a twocon®guration state, …2a1u

U  ˆ c1 W

5eg †

…2a1u

‡ c2 W

4eg †

129

In a hypothetical condition that c1 ˆ c2 , which can occur if the two con®gurations have the same energy, the magnetic dipole moments of the U states are 0:063b. These values are less than 10th of that of the states before the CI coupling. Fig. 2 shows the variation of the angular momentum Lz ˆ hU‡ jL^z jU‡ i with c1 ˆ cos h and c2 ˆ sin h, where h is the variable. The ®gure shows that Lz takes an extreme value in the vicinity of h ˆ 0 and p=2, while it becomes zero near h ˆ p=4 and 3p=4, speci®cally when …c1 ; c2 † ˆ …0:73; 0:68† or …c1 ; c2 † ˆ …0:60; 0:80†. This behavior cannot be seen if the Lz values of the two W‡ con®gurations have the same sign. Table 2 summarizes the wave functions of the excited states obtained by the CI calculation with 127 con®gurations. Fig. 3 shows the calculated excitation energies and MCD A term values. The ®rst allowed excited state 1Eg is calculated at 10 000 cm 1 . This corresponds to the Q band of MgPc‡ and ZnPc‡ observed at about 12 000 cm 1 . The dominant character of this state is jD6eg 2a1u i con®guration, which is analogous to the main component of Q band of neutral MPc. The next allowed excited state is 2Eg , whose main components are two eg -to-SOMO excited con®gurations, namely, jD2a1u 5eg i and jD2a1u 4eg i. From the calculated energy, oscillator strength and A=D value, the state is assigned to the ®ngerprint band observed at 500 nm (20 000 cm 1 ). Calculated A=D value is smaller

…2†

is hU j

bL^z jU i

ˆ ibf…c1 †2 …5egx jl^z j5egy † ‡ c1 c2 …5egx jl^z j4egy † ‡ c1 c2 …4egx jl^z j5egy † ‡ …c2 †2 …4egx jl^z j4egy †g 2 ˆ ibf…c1 † …5egx jl^z j5egy † ‡ 2c1 c2 …5egx jl^z j4egy † 2 ‡ …c2 † …4egx jl^z j4egy †g:

Fig. 2. A plot of the orbital angular momentum of the U‡ state in Eq. (2) with c1 ˆ cos h and c2 ˆ sin h as a function of h (solid line). The broken line shows the plot for the state orthogonal to the U‡ state.

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N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132

Table 2 Calculated excitation energies, oscillator strengths f, MCD A=D ratios, and wave functions of doublet excited states of MPc‡

1Egxz 1A2u 1B1u 2Egxz 2A2u 1B2u 3Egxz 2B2u 2B1u 4Egxz 3A2u 5Egxz 3B1u a

m~=103 (cm 1 )

f

A=Da

Wave functions

10.11 18.47 20.44 20.47 21.95 22.78 24.12 25.99 26.46 27.92 29.52 29.76 30.13

0.33 ± ± 0.028 ± ± 0.12 ± ± 1.4 ± 0.091 ±

1.26 ± ± )0.035 ± ± 0.17 ± ± 0.24 ± )0.35 ±

0:97 j D6egx 0:97 j D2a1u 0:83 j D2a1u 0:69 j D2a1u 0:88 j D2a1u 0:66 j D2a1u 0:76 j D2a1u 0:75 j D4b2u 0:95 j D3b1u 0:59 j S6egy 0:54 j S6egx 0:66 j S6egy 0:45 j S6egx

2a1u i ‡ 0:15 j S6euy 4a2u i 0:20 j T6egx 2b1u i 0:27 j T6egx 5egx i 0:42 j D2a1u 3a2u i 0:23 j T6egx 3b2u i 0:64 j D4b2u 4egx i ‡ 0:41 j D2a1u 2a1u i ‡ 0:61 j D2a1u 2a1u i 0:16 j T5a2u 4a2u i 0:49 j T6egy 5egy i ‡ 0:54 j S6egy 2b1u i ‡ 0:46 j S6egy 4egy i 0:45 j S6egy

4a2u i 0:10 j D2a1u 5egy i 0:20 j T6egy 5egy i 0:27 j T6egy 4egx i 0:35 j T6egy 4egy i 0:23 j T6egy 2a1u i ‡


5egx i 0:29 j T6egx 3b2u i ‡


3b2u i ‡


4a2u i 0:34 j T6egy 5egx i ‡


3a2u i 0:32 j T6egy 4egx i ‡




5egx i ‡


5egx i ‡


5egx i ‡


4a2u i ‡


4egx i ‡


3b2u i ‡


3a2u i ‡


2b1u i ‡




The unit of the values in the column is Bohr magneton.

than that of the Q band by two orders of magnitude. The lack of MCD A-term pattern in the band is ascribed to the extremely reduced A term. The third allowed 3Eg state also has the two eg -to-SOMO excited con®gurations. Although the composition of the state is similar to 2Eg , the state has a positive MCD A term, whose magnitude is

Fig. 3. Energies, oscillator, strengths (top) and MCD A terms (bottom) of excited states of MPc‡ calculated by the SCF-MOCI method. The squares denote Eg states and the open circles other forbidden states.

not negligibly small. Stillman et al. reported another additional band showing MCD A term at 411 nm (24 300 cm 1 † in MgPc‡ . They assigned the band to the red-shifted B1 band composed of highest-a2u -to-LUMO-eg transition. Our calculation, however, indicates that the band can be assigned to the 3Eg state composed of the two eg -to-SOMO transitions. The fourth allowed state 4Eg has a large oscillator strength and should be assigned to the band observed at 319 nm (31 300 cm 1 ) in MgPc‡ . The main con®guration of the state is jS6eg 4a1u i, which gives predominantly a large transition moment to the state. The similar situation is also seen in the excited states in the B-band region of the neutral MPc case. To see the e€ect of the con®guration mixing to the A-term values, Fig. 4 shows plots of angular momentum jLz j ˆ jhUjL^z jUij and transition dipole ^ moment jMj ˆ jhUjMjGij of 2Eg and 3Eg states against a coecient which is multiplied to o€-diagonal terms of the CI matrix. In the limit where the coecient is zero, each state is just a single con®guration. The other limit with the coecient being 1.0 corresponds to the normal CI treatment, which is already shown in Table 1 and Fig. 3. At the single-con®guration limit, 2Eg state is jD2a1u 5eg i, and has a modest amount of jLz j. Increase of CI mixing leads to a rapid decrease of jLz j. The result indicates that the assignment based on single-con®guration states is not adequate to

N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132

131

explain the lack of A-term contribution in the ®ngerprint band. The mixing of the con®guration must be taken into account to explain the disappearance of the A term. Lastly, it is worth comparing the calculated excitation energies with those obtained under an approximation of di€erent level, since the hypothesis that two eg -to-a1u con®gurations are present between Q band and B-band manifold is crucial to our argument. Table 3 compares the results obtained by the present p approximation and those by ab initio XCIS method [7]. The largest components of the ®rst three states are exactly the same in the two cases, and the energies are reasonably matched. In the both levels of approximation, 2Eg and 3Eg states are located between Q band and B-band manifold. Although even ab initio XCIS calculation is said to have error of 1 eV in the transition energy, the comparison indicates that the presence of the two eg to-a1u con®gurations in the similar energy region is quite plausible. 4. Conclusion

Fig. 4. Variation of A term, angular momentum jLz j and transition dipole jMj with respect to the coecient multiplied to the o€-diagonal terms in the CI matrix. The squares and triangles denote 2Eg and 3Eg states, respectively. The inlet shows A-term values for 1Eg (circle) and 4Eg (cross).

The ®ngerprint band of MPc‡ is assigned to the 2Eg excited state, which is mainly described by excitations from doubly occupied eg orbital to SOMO a1u orbital. The disappearance of A term of the band is explained as follows: 1. Two types of allowed excited con®gurations, jD2a1u 5eg i and jD2a1u 4eg i, are located closely in energy.

Table 3 Comparison of the calculated excitation energies doublet excited states of MPc‡ by the semiempirical method and ab initio XCIS method with 6-31G basis XCIS/6-31Ga

This work

a

State

m~=103 cm

1Eg 2Eg 3Eg 4Eg

10.11 20.47 24.12 27.92

1

Largest component

State

Energy/cm

j D6egx j D2a1u j D2a1u j S6egy

1Eg 2Eg 3Eg 4Eg 8Eg

8.71 20.88 26.45 32.26 43.79

2a1u i 5egx i 4egx i 4a2u ib

1

Largest component j D6egx j D2a1u j D2a1u j S7egy j S6egy

2a1u i 5egx i 4egx i 2a1u i 5a2u ib

Ref. [7]. The fourth a2u -type p orbital …4a2u † in this work corresponds to the ®fth a2u -type orbital …5a2u † in the ab initio calculation, since there is one a2u -type occupied r orbital, which is not counted in the present calculation under the p approximation. b

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N. Ishikawa, Y. Kaizu / Chemical Physics Letters 339 (2001) 125±132

2. The orbital angular momenta of the two con®gurations are similar in magnitude, but the signs are taken in the opposite way: the Lz value of the right-circularly polarized-light-absorbing sublevel in jD2a1u 5eg i is negative while that of jD2a1u 4eg i is positive. 3. Con®guration interaction mixes the two con®gurations, leading to a substantial reduction of Lz value and hence A term in the excited 2Eg state.

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