Chemical Physics Letters 483 (2009) 143–146

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Chemical Physics Letters

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Theoretical investigations of the charge transfer characteristicsin dichlorotitanium phthalocyanine (TiCl2Pc) and tin phthalocyanine (SnPc)

Ahmad Irfan, Jingping Zhang *, Yingfei ChangFaculty of Chemistry, Northeast Normal University, Changchun 130024, China

a r t i c l e i n f o

Article history:Received 8 June 2009In final form 13 October 2009Available online 15 October 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.10.037

* Corresponding author. Fax: +86 431 85099521.E-mail address: zhangjingping66@yahoo.com.cn (J

a b s t r a c t

By employing a diabatic model and a first-principle direct method, we have investigated the carrier trans-port properties of dichlorotitanium phthalocyanine (TiCl2Pc) and tin phthalocyanine (SnPc). The intermo-lecular electronic couplings for a wide variety of nearest-neighbor charge transfer pathways have beenobtained by directly evaluating the dimer Fock matrix with unperturbed monomer’s molecular orbitsat the DFT/pw91pw91/6-31g* (Lanl2dz) level. The solvent reorganization energies have been calculatedin different polar and non-polar solvents. The computed reorganization energies, transfer integrals, andmobilities showed that TiCl2Pc and SnPc are hole transfer materials which is verified by experiment. Thereorganization energy is solvent independent. The hole mobility of SnPc may boost by minimizing thepolarization.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Organic materials are also emerging as promising candidates forthe fabrication of transistors, photodiodes, solar cells, and(bio)chemical sensors [1–4]. The efficiency of charge transportwithin the organic layer(s) plays a key role [5]. Since the first or-ganic field-effect transistor (OFET) [6] was reported in 1986, therehas been remarkable progress in the development of OFETs. More-over, quantum mechanical calculations [7,8] and structural analy-sis [9] have predicted that high mobility can be obtained whenconjugated molecules have strong interactions with neighboringmolecules to maximize the overlap of p molecular orbits. Hence,theoretically speaking, a p stacked structure is expected to providemore efficient orbital overlap and thereby facilitates carrier trans-port. The molecular structure, relative orientations and solid statepacking have a strong influence on the charge transport behavior[10–12].

Phthalocyanines have attracted attentions in OFETs for manyyears because of their remarkably chemical and thermal stabilities,as well as non-toxicity and good field-effect properties [13,14]. Theunique properties of phthalocyanine dyes and pigments makethem the colorant of choice for most blue and green colours.Phthalocyanines are also finding extensive use in modern high-tech areas [15].

The dichlorotitanium phthalocyanine (TiCl2Pc) and tin phthalo-cyanine (SnPc) (see Fig. 1) are typical phthalocyanine using inOFETs. In this work, our aim is to theoretically investigate theircharacteristics for OFET application by calculating the reorganiza-

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. Zhang).

tion energies, transfer integrals, and mobilities of TiCl2Pc and SnPc.On the basis of these results, we have explained the charge careerbehavior of TiCl2Pc and SnPc, which may give more useful hints onthe design of novel OFET materials.

2. Theoretical background and methodology

The charge transport in OFETs is also as a Brownian motion pro-cess, as described by a particle diffusion process [16,17], coupledwith the Marcus theory of the electron-transfer rate for a self-ex-change reaction process [18–20]

K ¼ V2=hðp=kkBTÞ1=2 expð�k=4kBTÞ: ð1Þ

There are two major parameters that determine the self-exchangeelectron-transfer (ET) rate: the intermolecular transfer integral (V)and the reorganization energy (k). Fig. 2 represents the potential en-ergy surfaces for electronic states 1 and 2 corresponding to the neu-tral state and the ground or excited cation/anion state of themolecule; the geometry relaxation energies upon vertical transitionfrom the neutral state to a charged state and vice versa (kð1Þrel and kð2Þrel )are given by Eqs. (2) and (3)

kð1Þrel ¼ Eð1ÞðMÞ � E0ðMÞ; ð2Þkð2Þrel ¼ Eð1ÞðM��Þ � E0ðM��Þ: ð3Þ

Here E0(M) and E0(M±�) are the ground-state energy of the neutralstate and the energy of the considered cation/anion state, respec-tively; E(1)(M) is the energy of the neutral molecule at the optimalcation/anion geometry, and E(1)(M±�) is the energy of the cation/an-ion state at the optimal geometry of the neutral molecule.

Fig. 1. The structure of tin phthalocyanine (left) and the dichlorotitanium phthalocyanine (right).

Fig. 2. Sketch for the potential energy surfaces for neutral state 1 and ionic state 2,showing the vertical transitions and relaxation energies kð1Þrel and kð2Þrel .

144 A. Irfan et al. / Chemical Physics Letters 483 (2009) 143–146

We have calculated the reorganization energies at the densityfunctional theory (DFT) level using the B3LYP functional and 6-31g* (lanl2dz) basis set [21]. The B3LYP/6-31g* (Lanl2dz) level alsowas used for the solvent reorganization energies of hole in acetoni-trile, dimethylsulfoxide, chloroform, toluene, acetone, and tetrahy-drofuran solvents, respectively, using PCM and CPCM models. Itshould be pointed out that, in this work, the polarization effectsfrom the surrounding molecules, as well as the charge reorienta-tion, have been neglected. This value is difficult to evaluate theo-retically and is one of the challenges for theoretical chemistry[22–24]. The next step is to calculate the electronic coupling term.Here, we have used the single-crystal structures of Ticl2Pc and SnPcto generate all the possible nearest-neighbor intermolecular hop-ping pathways. The electronic coupling can be obtained either byKoopmans’ theorem, which has been widely employed [25], or bydirectly evaluating the coupling element for the frontier orbitals[26,27]. In the former case, the charge transfer integral correspondsto half of the splitting of the HOMO or LUMO levels for holes orelectrons. Bredas and co-workers have extensively investigatedthe parameters governing the transport on many conjugated sys-tems by frontier orbital splitting [28]. Valeev et al. cautioned re-cently that when the dimer is not cofacially stacked, the site-energy correction due to the crystal environment should be takeninto account [29].

In this work, we have adopted a direct approach to investigatethe charge transport properties [26,27]. The electronic couplingfor hole/electron transfer in this scheme can be written as

Te=h ¼ /0;site1LUMO=HUMOjF

0j/0;site2LUMO=HUMO

D E

¼ /0;site1LUMO=HUMOjhcorej/0;site2

LUMO=HUMO

D EþXlðoccÞ

/0;site1LUMO=HUMO/0

l j/0;site2LUMO=HUMO/0

l

D E�

� /0;site1LUMO=HUMO/0;site2

LUMO=HUMO/0l /

0l

D E�; ð4Þ

where te/h is the charge transfer coupling integral for the electron/hole and /0;site1

LUMO=HOMO and /0;site2LUMO=HOMO represent the LUMOs/HOMOs

of the two adjacent molecules 1 and 2 when no intermolecularinteraction is presented. F0 is the Fock operator for the dimer fora fixed pathway, and the suffix zero indicates that the molecularorbitals appearing in the operator (the density matrix, for instance)are unperturbed. The summation over l includes all of the occupiedlevels for both sites and represents the Coulomb and exchangeinteractions between the transferred electron/hole and the wholesystem. It has been shown that the exchange term can contributeto the spin dependence of the charge recombination rates in excitonformation [30]. The non-interacting molecular orbitals of the twoindividual molecules are calculated separately by the standardself-consistent-field (SCF) procedure. These non-interacting orbitalsare used to construct the dimer Fock matrix as well as the two-elec-tron integrals in Eq. (4). More specifically, the non-interacting orbi-tals and associated density matrix are used in evaluating the Fockmatrix of the dimer structure. The density matrix of F0 is con-structed from non-interacting molecular orbitals. In practice, theFock matrix is evaluated as

F ¼ SCeC�1; ð5Þ

where S is the overlap matrix for the dimer taken from the crystalstructure, and the Kohn–Sham orbital C and eigenvalue e are ob-tained by diagonalizing the zeroth-order Fock matrix without anyself-consistent field iteration [26]. The intermolecular electroniccouplings have been obtained by directly evaluating the dimer Fockmatrix with unperturbed monomer’s molecular orbits at the DFT/pw91pw91/6-31g* (Lanl2dz) level [21]. Huang and Kertesz have re-ported that this functional gave the best description for intermolec-ular coupling term [31]. Yang et al. have mentioned that this directmethod for the coupling is equivalent to the site-energy correctedfrontier orbital splitting method [32] and this direct method offersremarkable simplicity in computation. INDO based calculationswhich use the ‘energy-splitting-in-dimer’ method [29] often overestimate electronic couplings and also ignore the orthogonalisation

Table 3The electronic couplings V of TiCl2Pc for the 10 pathways at the DFT/pw91pw91/(6-31g*, Lanl2dz) level.

Route Centre-to-centre distance(Å)

Vh

(eV)Ve

(eV)

A. Irfan et al. / Chemical Physics Letters 483 (2009) 143–146 145

of the basis set thus we used direct method which has been provedto give good and accurate results [16,26,32–34].

Based on the Einstein relation, the carrier mobility is obtainedfrom the following Eq. (6):

l ¼ eD=kBT; ð6Þ

where D is the diffusion constant. If we assume the charge motion isa homogeneous random walk, the diffusion constant can be evalu-ated as [8]:

D ¼ limt!1

12nhxðtÞ2i

t� 1

2n

Xi

d2i kipi ¼

12n

Pid

2i k2

iPiki

: ð7Þ

d is the intermolecular centre-to-centre distance and n = 3 is thespatial dimension. The hopping time between two adjacent mole-cules is the inverse of the rate constant 1/k. The probability for a

specific hopping route is pi ¼ kiPiki

. Namely, it is a 3-d averaged dif-

fusion process. It is clear that the mobility is linearly proportional tothe electron transfer rate. Within this mechanism, it has been as-sumed that the localized electron can only hop between adjacentmolecules, in sharp contrast to the band-like picture, where theelectron is delocalized in several molecules. All the quantum chem-istry calculations have been performed with the GAUSSIAN03 package[35].

3. Results and discussion

The calculated internal reorganization energies of the TiCl2Pc/SnPc for hole (k(h)) and electron (k(e)) are 0.074 eV/0.061 eV and0.648 eV/0.224 eV, respectively (see Table 1). In Table 2 solventreorganization energies (ksolvent) for hole of TiCl2Pc and SnPc havebeen reported. It can be found that the average ksolvent of SnPc is0.054 eV and ksolvent of TiCl2Pc is 0.050. We have found that differ-ent solvents (polar and non-polar) at both the models (PCM andCPCM) used in this study do not affect the reorganization energies,i.e., the reorganization energy is solvent independent.

On the basis of the crystal structures of TiCl2Pc/SnPc, we haveidentified 10/9 distinct nearest-neighbor hopping pathways,respectively. Using the method described above in Eq. (4), the cor-responding coupling integrals have been computed for both the

Table 1Calculated reorganization energies of TiCl2Pc and SnPc (in eV) for hole k(h) andelectron k(e) at the B3LYP/(6-31g*, Lanl2dz) level.

Complexes k(h) k(e)

TiCl2Pc 0.074 0.648SnPc 0.061 0.224

Table 2The solvent reorganization energies (ksolvent) of hole in eV of SnPc and TiCl2Pc at theB3LYP/6-31g* (Lanl2dz) level.

Model Solvent SnPc (ksolvent) TiCl2Pc (ksolvent)

PCM CH3CN 0.053 0.051DMSO 0.054 0.050CHCl3 0.054 0.052Toluene 0.053 0.048THF 0.053 0.050Acetone 0.055 0.049

CPCM CH3CN 0.053 0.051DMSO 0.054 0.050CHCl3 0.053 0.052Toluene 0.054 0.052THF 0.054 0.048Acetone 0.055 0.049

electron and hole, and these have been presented in Tables 3 (forTiCl2Pc) and 4 (for SnPc).

We have found that the hole reorganization energies of TiCl2Pcand SnPc are lower than that of electron ones, and the hole transferintegral values are higher than electron ones. In TiCl2Pc the stron-gest nearest-neighbor electronic coupling is as high as 0.042 eV,which is almost similar with CuPc—another typical organic semi-conductor, the largest coupling is �0.048 eV and the hole reorgani-zation energy of CuPc is predicted to be 0.17 eV. The TiOPc isanother potential candidate of OFET, theoretically calculated reor-ganization energy of this molecule is 0.079 eV [21]. The reorganiza-tion energy of TiCl2Pc is lower than that of CuPc and almost sameas TiOPc. As far as SnPc is concerned, the hole reorganization en-ergy of SnPc (0.061 eV) is smaller than those of CuPc and TiOPc.The strongest nearest-neighbor hole transfer integral of SnPc is0.1643 eV when centre-to-centre distance is 6.692 Å, while elec-tron transfer integral is�0.0483 eV. The calculated strongest trans-fer integral of SnPc is higher than those of TiOPc (0.143 eV) andCuPc (�0.048 eV). The reorganization energy and transfer integralsindicated that SnPc would possess higher mobility than TiOPc andCuPc.

Furthermore, we have calculated the mobilities of TiCl2Pc andSnPc. The computed hole and electron mobilities for TiCl2Pc (SnPc)are 1.977 cm2/V s (26.363 cm2/V s) and 1.642 � 10�5 cm2/V s(0.270 cm2/V s), respectively, indicating TiCl2Pc and SnPc to be holetransfer materials, which is in good agreement with experiment[36]. In general, by considering the solvent reorganization energieshole mobilities for TiCl2Pc and SnPc have been predicted0.944 cm2/V s and 11.390 cm2/V s. From Table 5 it can be foundthat hole mobility of SnPc is higher than that of TiCl2Pc which isvalidated by experiment [36].

Experimental hole mobility of SnPc is 0.4 cm2/V s [36]. Numer-ous reports have been published on transistors with an active layerof CuPc. The mobility is in the range 0.01–0.04 cm2/V s [37–39]. Li

1 7.345 0.042 �0.38 � 10�2

2 13.043 �2.94 � 10�4 9.19 � 10�5

3 8.170 4.21 � 10�2 0.25 � 10�2

4 11.149 �1.03 � 10�2 �3.59 � 10�4

5 8.744 3.70 � 10�3 6.93 � 10�4

6 10.783 1.41 � 10�6 �3.29 � 10�4

7 12.244 �3.92 � 10�4 1.53 � 10�4

8 12.835 �2.29 � 10�5 �3.00 � 10�5

9 13.313 7.25 � 10�4 �2.80 � 10�4

10 11.685 7.4 � 10�3 �4.73 � 10�5

Table 4The electronic couplings V of SnPc for the nine pathways at the DFT/pw91pw91/6-31g* level.

Route Centre-to-centre distance(Å)

Vh

(eV)Ve

(eV)

1 6.692 �0.1643 �4.83 � 10�2

2 7.218 �6.01 � 10�2 �3.60 � 10�3

3 8.671 �1.10 � 10�3 �1.20 � 10�3

4 12.236 6.07 � 10�4 �1.40 � 10�3

5 12.387 �7.71 � 10�7 3.03 � 10�6

6 12.630 3.70 � 10�3 �2.80 � 10�3

7 13.853 1.05 � 10�6 2.95 � 10�6

8 15.974 �2.20 � 10�3 �2.10 � 10�3

9 16.538 �1.43 � 10�4 �1.65 � 10�4

Table 5Computed hole and electron mobilities (cm2/V s) of TiCl2Pc and SnPc.

Complexes Hole mobility Expa Electron mobility

TiCl2Pc 1.977 0.15 1.642 � 10�5

SnPc 26.363 0.4 0.270

a Experimental data from Ref. [36].

146 A. Irfan et al. / Chemical Physics Letters 483 (2009) 143–146

et al. measured the hole mobility of TiOPc 3.31 cm2/V s [21]. As wementioned above that mobility of SnPc would be higher than TiOPcand CuPc but these experimental values indicated that hole mobil-ity of TiOPc is higher than SnPc. We agreed that reorganization en-ergy and transfer integrals are not the solely factors which affectthe mobility but these play important role.

To estimate the effect of polarization of the surrounding med-ium, we have calculated the mobilities of SnPc and TiCl2Pc by con-sidering external reorganization energy 0–0.2 eV [33]. Inspectionof Fig. 3 reveals clearly that by increasing the external reorganiza-tion energy, mobility decreases. By considering the external reor-ganization energy 0.2 eV, mobility of SnPc has been decreasedfrom 26.363 cm2/V s to 1.842 cm2/V s. By including the ksolvent,mobility finally reaches to 0.994 cm2/V s. In TiCl2Pc the hole mobil-ity has been computed to be 0.15 cm2/V s (which is equal to exper-imental hole mobility [36]) at 0.2 eV external reorganizationenergy. However, when ksolvent has been considered, 0.15 cm2/V shole mobility has been observed if external reorganization energyis 0.15 eV. Therefore, we can found that in SnPc there is morepolarization due to which experimentally its mobility is lower thancalculated. This nuclear polarization term of the localized chargesin molecular crystals may be much more pronounced in the crystalwith impurities or structural defects [40]. In the single crystal ofrubrene field-effect transistors, mobility has been found to begreater than 15 cm2/V s, Podzorov et al. explained that threshold-less operation in ruberene is due to high purity of the rubrene crys-tals, low concentration of defects and traps at the rubrene–parylene interface, and good hole injection ability of the contacts[41]. For the purified pentacene single crystal, the FET mobilityhas been measured to be 35 cm2/V s [42].

We believe that polarization of the surrounding medium cannotbe neglected and due to other molecules in the bulk material therewill be lattice relaxation. But by considering the above mentionedeffects, mobility can be improved in SnPc, e.g. by purifying thecrystal of SnPc polarization can be reduced and hole mobilitymight be enhanced.

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.320

2

4

6

8

10

12 SnPc (λext+i) SnPc (λext+i+solvent) TiCl2Pc (λext+i) TiCl2Pc (λext +i+solvent )

Mob

ility

(cm

2 / Vs)

)

λ (eV)

Fig. 3. Theoretical estimation of the room temperature carrier mobilities for SnPcand TiCl2Pc. Here kextþiþsolvent means the external, internal and solvent reorganiza-tion energies, respectively.

4. Conclusions

By employing the first-principles DFT techniques and the Mar-cus electron transfer theory, we have investigated the transportproperties for dichlorotitanium phthalocyanine (TiCl2Pc) and tinphthalocyanine (SnPc). The coupling terms are evaluated by a di-rect diabatic model, and the reorganization energies are calculatedthrough adiabatic potential energy surfaces. The reorganizationenergies, transfer integral values, and computed mobilities indi-cated that TiCl2Pc and SnPc are hole transfer materials which isverified by experiment. By changing the polarity of the solvents,no change has been observed for solvent reorganization energiesof hole for SnPc and TiCl2Pc. By increasing the external reorganiza-tion energy, mobility decreased. Experimentally observed lowmobility in SnPc is due to the polarization of the surrounding med-ium. The hole mobility of SnPc might be enhanced by minimizingthe structural defects or purifying.

Acknowledgements

Financial supports from the NSFC (50873020), NCET-06-0321,and NENU-STB07007 are gratefully acknowledged. A. Irfanacknowledges the financial support from China Scholar Council(CSC) and Ministry of Education (MoE), Pakistan.

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