**Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations**

Irena Kratochvilova *Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic* 

## **1. Introduction**

26 Will-be-set-by-IN-TECH

158 Quantum Chemistry – Molecules for Innovations

Stegner, A. R.; Boehme, C.; Huebl, H.; Stutzmann, M.; Lips, K. & Brandt, M. S. (2006). Electrical

Stokbro, K.; Taylor, J.; Brandbyge, M. & Guo, H. (2005). Ab-initio Non-Equilibrium Green's

Tada, T. & Watanabe, S. (2006). Submatrix Inversion Approach to the ab initio Green's function

Tada, T. (2008). Hyperfine switching triggered by resonant tunneling for the detection of a single nuclear spin qubit. *Physics Letters A*, 372, 6690-6693, 03759601 (ISSN). Taylor, J.; Guo, H. & Wang, J. (2001). Ab initio modeling of quantum transport properties of

Vandersypen, L. M. K.; Steffen, M.; Breyta, G.; Yannoni, C. S.; Sherwood, M. H. & Chuang,

Ventra, M. D. (2008). *Electrical Transport in Nanoscale Systems*, Cambridge University Press,

Vosko, S. H.; Wilk, L. & Nusair, M. (1980). Accurate Spin-dependent Electron Liquid

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nuclear magnetic resonance. *Nature*, 414, 883-887, 00280836 (ISSN).

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of Molecular Junctions. *Science*, 301, 1221-1223, 00368075 (ISSN).

Springer, 3540279946 (ISBN-10), Heidelberg.

484-489, 13480391 (ISSN).

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detection of coherent 31P spin quantum states. *Nature Physics*, 2, 835-838, 17452473

Function Formalism for Calculating Electron Transport in Molecular Devices. In: *Introducing Molecular Electronics*, Cuniberti, G.; Fagas, G. & Richter, K. (Ed.), 117-151,

method for electrical transport. *e-Journal of Surface Science and Nanotechnology*, 4,

molecular electronic devices. *Physical Review B*, 63, 245407(1)-245407(13), 01631829

I. L. (2001). Experimental realization of Shor's quantum factoring algorithm using

Correlation Energies for Local Spin-Density Calculations - A Critical Analysis.

Self-Assembled Monolayers. In: *Introducing Molecular Electronics*, Cuniberti, G.; Fagas, G. & Richter, K. (Ed.), 275-300, Springer, 3540279946 (ISBN-10), Heidelberg. Xu, B. & Tao, N. J. (2003). Measurement of Single-Molecule Resistance by Repeated Formation The main goal of this chapter is to show how and why quantum chemistry modeling can /should be applied on class of organic materials with relatively high carrier mobility – phthalocyanines (H2Pc, NiPc and NiPc(SO3Na)x) . It will be shown how Density Functional Theory (DFT) can be used to calculate/model main parameters that influence the group of material properties that are crucial from practical point of view.

With the ongoing miniaturization of microelectronics, functional elements in electronic circuits may soon consist of only a couple of electrons or molecules. We therefore address the question how the physical laws which hold for macroscopic solids become modified when one deals with very small structures. It turns out that down-scaling of electronic properties from the macro world to the atomic or molecular level does not work at all. For example, the famous Ohm's law does not hold anymore, because the resistance does not scale with the length of a ''quantum wire'' [1-15].

Once having realized this fundamental issue, one immediately conceives this as a chance to develop new concepts. Instead of continuously scaling down, as in industrial chip designs, one considers building up electronic circuits with tailored properties ''bottom up''. The first questions which have to be answered now are: ''Which atoms or molecules have to be combined in which way to achieve the desired properties?'' and: ''Which physical and chemical properties determine the electrical conductance of atomic-size or molecular-size circuits?''.

In most areas of science, there are free major steps that need to be taken for understanding to be gleaned: the first is synthesis and preparation, the second is measurements and characterization and third is theory and modelling [12-20]. The great advance in measurement and characterization was clearly the advent of scanning probe microscopy which permitted measurements both of structure and of transport at the level of one to a few molecules. The critical advances in theory and modelling came with adaption of the coherent tunnelling models originally developed by Landauer to the study of transport in molecular tunnel junctions [20-31].

Current research focuses, among others, on the design and implementation of nanometer scale electronic systems which exhibit new classical and quantum mechanical effects. The

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 161

dipolar species results in the mobility decrease due to the increase of the transfer integral dispersion. Polar group chemically attached to the molecular wire, can cause the orbital localization. The charge transport in 3D samples can be described by the theory of disordered polarons which postulates that the activation energy of the charge carrier mobility is composed of contribution both from the dynamic disorder, i.e. the polaronic barrier, and from the static disorder, i.e. the variation of the energy of transport states as a result of the environment. The main contribution to the polaron binding energy results from molecular deformation; electron-phonon term makes for 20 % only. Dipolar additives make the distribution of hopping states broadened and new localized states for charge carriers are

Experimentally measured conductivity is a macroscopic phenomenon and reflects on-stack mobility plus intra-stack hopping mobility. Intra-stack transport mainly contributes to the

From the charge carrier mobility point of view phtalocyanines seem to be promising materials - in devices with vacuum evaporated phthalocyanine thin films, the values reached from 10-5 to 10-4 cm2 V-1 s-1, when phthalocyanine was evaporated on hot substrates the value increased up to 10-2 cm2 V-1 s-1 [15-22]. Preliminary results obtained on sulphonated phthalocyanines, i.e., materials containing both electronic and electrolytic segments, seem to be very promising. The charge carrier mobility determined from the dependences of the source-drain current vs. the source-drain voltage of the OFET was surprisingly high. In the case of NiPc(SO3Na)4, the field-effect mobility was 0.02 cm2

Phthalocyanines can be organized in columns at a supramolecular level, giving rise to conducting properties. The cofacial stacking of metallophthalocyanines enables electron delocalization along the main axis of the column through π-π orbital overlapping. Metallophthalocyanines generally crystallize in an inclined stacked insulating arrangements called α or β-modifications that do not allow an appropriate overlap of π-orbitals and hence no formation of a conduction band. Only in few cases stacked arrangements are found, being the most representative the nonplanar cone-shaped phthalocyaninatolead (II) (PbPc)

In the last few years, phthalocyanines (Fig. 1) are being intensively studied as targets for optical switching and limiting devices, organic field effect transistors, sensors, light-emitting devices, low band gap molecular solar cells, optical information recording media, photosensitizers for photodynamic therapy, and nonlinear optical materials, among others.

Phthalocyanine is an intensely blue-green coloured macrocyclic compound. Phthalocyanines form coordination complexes with most elements of the periodic table. Phthalocyanines are structurally related to other macrocyclic pigments, especially the porphyrins. Four pyrrolelike subunits are linked to form a 16-membered ring. The pyrrole-like rings within H2Pc are closely related to isoindole. Both porphyrins and phthalocyanines function as planar tetradentate dianionic ligands that bind metals through four inwardly projecting nitrogen centers. Such complexes are formally derivatives of Pc2-, the conjugate base

Phthalocyanines will burst also in a very near future into the nanotechnology field.

whole resistivity – i.e. the main charge-transport obstruction is between stacks.

formed; it results in the reduction of charge mobility [17-19].

V-1 s-1 [12].

of H2Pc.

in its monoclinic modification.

motivation for creating such elements has been two-fold: first, to create nanoscale laboratories to explore physics in a new way, and second, to develop novel devices with significant applications. The architecture of molecular-scale electronic devices can be designed starting from molecular segments whose properties have been known from experiment and/or suitable theoretical models. The field of ''Molecular Electronics'' has been opened by the seminal proposition of A. Aviram and M. Ratner in 1974 to build a diode from a single molecule [1-2]. Since then, it took almost 20 years before the first molecular diode was experimentally realized. By now, molecular electronics is a broad field of research world-wide [3-21].

Some examples of molecular nanostructures that might be used as switching units, memories, logic elements and devices embodying a negative resistance have recently been demonstrated (e.g., [1-5]). A pioneering construction of a molecular switch was based on the electron tunneling principle [1]. An electron travels along a 'molecular wire' (e.g., a conjugated polymer chain) containing a finite series of periodic potential walls. The tunnel switch is 'on' if the transmission coefficient of the electron is close to unity, i.e., if the electron energy matches pseudostationary energy levels of the walls, and can be turned off by either changing a barrier height or the depth of a potential well, which can be controlled by the dipole moment of polymer side groups.

As we have already mentioned the charge transport in molecular electronic materials is a very complex process which can be affected by many physical and chemical parameters; the knowledge of its nature is crucial for the development and optimization of molecular-based devices. Each step forward in understanding and controlling the charge transport is extremely important for the practical applications of molecular systems in electronics [1-16].

One of the reasons for the difficulties in charge-transport phenomena/conditions description is the lack of a well-understood mechanism of charge transport in organic materials. The charge-carrier transport in molecular systems is a very complicated and comprehensive event affected by many parameters. In the early days, band theory was applied to predict the charge-carrier mobility in organic materials. However, it was repeatedly pointed out by several authors [18-21] that this approach is not suitable. Comparing organic and inorganic semiconductors, the materials from the latter class are usually less disordered and have molecular sites closer to one another. For disordered materials, the hopping mechanism seems to be more appropriate for the description of the charge-carrier behaviour. In this approach, the charge carrier is localised on the molecular site and jumps to the other site by overcoming some energy barrier. However, for materials possessing a preferred direction of charge-carrier transport like phtalocyanines we need a combination of different approaches for the description of the charge-carrier motion along the preferred paths and for hopping among them.

Molecular materials are generally not very good conductors. Main limitation follows from low charge carrier "on-chain" mobility which mostly using the microwave photoconductivity was found to be 10-5 m2 V-1 s-1 and 10-4 m2 V-1 s-1, for - and -conjugated molecular materials, respectively. The mobility is limited by polaron formation and by the dispersion of transfer integrals among the monomer units the wire. Electrical current through a single molecule is influenced by charge tunnelling – the Fowler-Nordheim model seems to be a good approximation for the description of charge transport. The presence of

motivation for creating such elements has been two-fold: first, to create nanoscale laboratories to explore physics in a new way, and second, to develop novel devices with significant applications. The architecture of molecular-scale electronic devices can be designed starting from molecular segments whose properties have been known from experiment and/or suitable theoretical models. The field of ''Molecular Electronics'' has been opened by the seminal proposition of A. Aviram and M. Ratner in 1974 to build a diode from a single molecule [1-2]. Since then, it took almost 20 years before the first molecular diode was experimentally realized. By now, molecular electronics is a broad field of research

Some examples of molecular nanostructures that might be used as switching units, memories, logic elements and devices embodying a negative resistance have recently been demonstrated (e.g., [1-5]). A pioneering construction of a molecular switch was based on the electron tunneling principle [1]. An electron travels along a 'molecular wire' (e.g., a conjugated polymer chain) containing a finite series of periodic potential walls. The tunnel switch is 'on' if the transmission coefficient of the electron is close to unity, i.e., if the electron energy matches pseudostationary energy levels of the walls, and can be turned off by either changing a barrier height or the depth of a potential well, which can be controlled by the

As we have already mentioned the charge transport in molecular electronic materials is a very complex process which can be affected by many physical and chemical parameters; the knowledge of its nature is crucial for the development and optimization of molecular-based devices. Each step forward in understanding and controlling the charge transport is extremely important for the practical applications of molecular systems in electronics [1-16]. One of the reasons for the difficulties in charge-transport phenomena/conditions description is the lack of a well-understood mechanism of charge transport in organic materials. The charge-carrier transport in molecular systems is a very complicated and comprehensive event affected by many parameters. In the early days, band theory was applied to predict the charge-carrier mobility in organic materials. However, it was repeatedly pointed out by several authors [18-21] that this approach is not suitable. Comparing organic and inorganic semiconductors, the materials from the latter class are usually less disordered and have molecular sites closer to one another. For disordered materials, the hopping mechanism seems to be more appropriate for the description of the charge-carrier behaviour. In this approach, the charge carrier is localised on the molecular site and jumps to the other site by overcoming some energy barrier. However, for materials possessing a preferred direction of charge-carrier transport like phtalocyanines we need a combination of different approaches for the description of the charge-carrier motion along

Molecular materials are generally not very good conductors. Main limitation follows from low charge carrier "on-chain" mobility which mostly using the microwave photoconductivity was found to be 10-5 m2 V-1 s-1 and 10-4 m2 V-1 s-1, for - and -conjugated molecular materials, respectively. The mobility is limited by polaron formation and by the dispersion of transfer integrals among the monomer units the wire. Electrical current through a single molecule is influenced by charge tunnelling – the Fowler-Nordheim model seems to be a good approximation for the description of charge transport. The presence of

world-wide [3-21].

dipole moment of polymer side groups.

the preferred paths and for hopping among them.

dipolar species results in the mobility decrease due to the increase of the transfer integral dispersion. Polar group chemically attached to the molecular wire, can cause the orbital localization. The charge transport in 3D samples can be described by the theory of disordered polarons which postulates that the activation energy of the charge carrier mobility is composed of contribution both from the dynamic disorder, i.e. the polaronic barrier, and from the static disorder, i.e. the variation of the energy of transport states as a result of the environment. The main contribution to the polaron binding energy results from molecular deformation; electron-phonon term makes for 20 % only. Dipolar additives make the distribution of hopping states broadened and new localized states for charge carriers are formed; it results in the reduction of charge mobility [17-19].

Experimentally measured conductivity is a macroscopic phenomenon and reflects on-stack mobility plus intra-stack hopping mobility. Intra-stack transport mainly contributes to the whole resistivity – i.e. the main charge-transport obstruction is between stacks.

From the charge carrier mobility point of view phtalocyanines seem to be promising materials - in devices with vacuum evaporated phthalocyanine thin films, the values reached from 10-5 to 10-4 cm2 V-1 s-1, when phthalocyanine was evaporated on hot substrates the value increased up to 10-2 cm2 V-1 s-1 [15-22]. Preliminary results obtained on sulphonated phthalocyanines, i.e., materials containing both electronic and electrolytic segments, seem to be very promising. The charge carrier mobility determined from the dependences of the source-drain current vs. the source-drain voltage of the OFET was surprisingly high. In the case of NiPc(SO3Na)4, the field-effect mobility was 0.02 cm2 V-1 s-1 [12].

Phthalocyanines can be organized in columns at a supramolecular level, giving rise to conducting properties. The cofacial stacking of metallophthalocyanines enables electron delocalization along the main axis of the column through π-π orbital overlapping. Metallophthalocyanines generally crystallize in an inclined stacked insulating arrangements called α or β-modifications that do not allow an appropriate overlap of π-orbitals and hence no formation of a conduction band. Only in few cases stacked arrangements are found, being the most representative the nonplanar cone-shaped phthalocyaninatolead (II) (PbPc) in its monoclinic modification.

In the last few years, phthalocyanines (Fig. 1) are being intensively studied as targets for optical switching and limiting devices, organic field effect transistors, sensors, light-emitting devices, low band gap molecular solar cells, optical information recording media, photosensitizers for photodynamic therapy, and nonlinear optical materials, among others. Phthalocyanines will burst also in a very near future into the nanotechnology field.

Phthalocyanine is an intensely blue-green coloured macrocyclic compound. Phthalocyanines form coordination complexes with most elements of the periodic table. Phthalocyanines are structurally related to other macrocyclic pigments, especially the porphyrins. Four pyrrolelike subunits are linked to form a 16-membered ring. The pyrrole-like rings within H2Pc are closely related to isoindole. Both porphyrins and phthalocyanines function as planar tetradentate dianionic ligands that bind metals through four inwardly projecting nitrogen centers. Such complexes are formally derivatives of Pc2-, the conjugate base of H2Pc.

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 163

interplane distance 3.46 Å (experiment 3.4 Å) and parameter b = 4.87 Å (experiment 4.72 ). The inclusion of diffusion functions (6-31+G\* basis) does not substantially change the structural parameters. As shown in Table 1, for -modification the functional MPW1B95 slightly better describes the distance parameter b than MPWB1K. For -modification, the performance of both functional is comparable. Standard B3LYP functional strongly overestimates the separation of molecular planes and fails to predict the real structure.

DFT Functional MPW1B95 MPWB1K Experiment

 (Å) (Å) (Å) **H2Pc dimer polymorph α**

a1 3.463 3.478 3.442 3.466 3.4 b2 3.744 3.768 3.721 3.752 3.81

**H2Pc dimer polymorph β**

a1 3.428 3.456 3.428 3.432 3.4 b2 4.849 4.871 4.840 4.841 4.72

**H2Pc tetramer polymorph α** a1 3.388 3.4 b2 3.715 3.81 **H2Pc tetramer polymorph β** a1 3.399 3.4 b2 4.833 4.72

Table 1. Calculated structural parameters (in Å) and stabilization energies (kcal/mol) of

Basis Set 6-31G\* 6-31+G\* 6-31G\* 6-31+G\*

neutral

cation

anion

neutral form

cation

anion

1 interplanar distance

E3 5.1 4.6

E3 3.6 3.0

a1 3.440 b2 3.665

a1 3.450 b2 3.804

a1 3.289 b2 5.255

a1 3.325 b2 4.678

2 the average distance of corresponding atoms 3 stabilization energy of neutral dimers in kcal/mol

phthalocyanine dimers and tetramers.

Fig. 1. Chemical structure of H2 phthalocyanine (H2Pc).

Many derivatives of the parent phthalocyanine are known, where either carbon atoms of the macrocycle are exchanged for nitrogen atoms or where the hydrogen atoms of the ring are substituted by functional groups like halogens, hydroxy, amino, alkyl, aryl, thiol, alkoxy, nitro, etc.

Due to phthalocyanine stack formation and the presence of ionic groups charge transport consists of an electronic feature through the stack, charge hopping among the stacks and ionic type of the transport.

In order to model the physical properties of H2Pc layer, quantum chemical calculations on H2Pc dimers and tetramers were performed at DFT level. The and types of polymorph of H2Pc dimer structures were optimized using several density functionals. The optimizations lead to geometry with almost parallel orientation of H2Pc planes. The optimised conformer structures are depicted in Fig. 2, the structural parameters calculated for different functional and basis sets are listed in Table 1.

Fig. 2. DFT calculated optimized structures of H2Pc dimers and tetramer. In the figure, a) modification of H2Pc dimer b) -modification of H2Pc dimer c) -modification of H2Pc tetramer, respectively.

Calculated geometry of H2Pc dimer reasonably well represents the local part of the experimental structure of phthalocyanine films [15-19]. The best performance was found for MPW1B95/6-31+G\* calculations, where calculated structures fit the phthalocyanine stacking in the crystal. For -modification, the calculated structural parameter b = 3.77 Å, derived as averaged distances of corresponding atoms at individual monomers well reproduces the experimental value of 3.81 Å . The calculated approximate interplane distance (3.48 Å) is close to experimental value of 3.4 Å [15] as well. For -modification, the calculations give the interplane distance 3.46 Å (experiment 3.4 Å) and parameter b = 4.87 Å (experiment 4.72 ). The inclusion of diffusion functions (6-31+G\* basis) does not substantially change the structural parameters. As shown in Table 1, for -modification the functional MPW1B95 slightly better describes the distance parameter b than MPWB1K. For -modification, the performance of both functional is comparable. Standard B3LYP functional strongly overestimates the separation of molecular planes and fails to predict the real structure.


1 interplanar distance

162 Quantum Chemistry – Molecules for Innovations

Many derivatives of the parent phthalocyanine are known, where either carbon atoms of the macrocycle are exchanged for nitrogen atoms or where the hydrogen atoms of the ring are substituted by functional groups like halogens, hydroxy, amino, alkyl, aryl, thiol, alkoxy,

Due to phthalocyanine stack formation and the presence of ionic groups charge transport consists of an electronic feature through the stack, charge hopping among the stacks and

In order to model the physical properties of H2Pc layer, quantum chemical calculations on H2Pc dimers and tetramers were performed at DFT level. The and types of polymorph of H2Pc dimer structures were optimized using several density functionals. The optimizations lead to geometry with almost parallel orientation of H2Pc planes. The optimised conformer structures are depicted in Fig. 2, the structural parameters calculated for different functional

Fig. 2. DFT calculated optimized structures of H2Pc dimers and tetramer. In the figure, a) modification of H2Pc dimer b) -modification of H2Pc dimer c) -modification of H2Pc

Calculated geometry of H2Pc dimer reasonably well represents the local part of the experimental structure of phthalocyanine films [15-19]. The best performance was found for MPW1B95/6-31+G\* calculations, where calculated structures fit the phthalocyanine stacking in the crystal. For -modification, the calculated structural parameter b = 3.77 Å, derived as averaged distances of corresponding atoms at individual monomers well reproduces the experimental value of 3.81 Å . The calculated approximate interplane distance (3.48 Å) is close to experimental value of 3.4 Å [15] as well. For -modification, the calculations give the

Fig. 1. Chemical structure of H2 phthalocyanine (H2Pc).

a) b) c)

nitro, etc.

ionic type of the transport.

tetramer, respectively.

and basis sets are listed in Table 1.

2 the average distance of corresponding atoms

3 stabilization energy of neutral dimers in kcal/mol

Table 1. Calculated structural parameters (in Å) and stabilization energies (kcal/mol) of phthalocyanine dimers and tetramers.

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 165

At room temperature, the charge carrier transport can be described by a hopping within the Marcus theory. Subsequently, the rate expression of a self-exchange process is provided by

where is the reduced Planck constant, *k* is the Boltzmann constant, *T* is the temperature an *λ*+ is the reorganisation energy and *t+* is the electronic coupling matrix element (the measure of charge transport probability – electron transfer integral) for the charge transfer. In order to estimate the electronic coupling between individual monomeric units, electron transfer integrals were calculated for α and β crystallographic modifications of the

For the configuration with doubly occupied HOMO on the first monomer and singly occupied HOMO of the second one, calculation gives electron transfer integral (for otimized geometry MPW1B95/6-31G\*) values for non-relaxed cation radical 11.7 meV and 5.7 meV (hole transfer) for the α and β modification, respectively. It is supposed that in the course of electron or hole hopping, the atoms can relax in order to reach the minimum of energy at the potential surface. Transfer integral for optimized cation radical α crystal form with relaxed atoms (UMPW1B95/6-31G\*) is 18.7 meV. The calculations indicate that electron mobility is smaller than hole mobility because optimized geometry of anionic form is characterized by larger interplane parameter b (see Tab. 1) - for anionic form b=3.804 Ǻ, for cationic form

> 2 ( )/2

, (2)

+ + λ2+, where the deformation energy of the system

*S*

1 *RP RP RR PP RP*

*HRP* is the interaction energy between reactant and product states, *SRP* is the overlap between the reactant and product states and HRR is electronic energy of the reaktant state andHPP is electronic energy of the product state. All these terms were obtained via the direct coupling of localised monomer orbitals. On the molecular level, three factors, the electronic coupling (transfer integral *t*+) between the individual parts of the molecule, the reorganisation energy λ+ during charge transport and the effective length of hole transfer *L*, are usually considered to be important for charge transport in organic materials. The reorganization energy *λ*<sup>+</sup>

was calculated as the difference between the vertical and cationic state: λ1+ = *E*+(*QN*) – *E*+(*Q*+) and λ2+ = *E*+(*Q*+) – *E*+(*QN*). Here, *E*+(*QN*) is the total electronic energy of the cationic state in the neutral geometry, *E*+(*Q*+) is the total energy of the cationic state in the cationic state geometry, *EN*(*Q*+) is the total energy of the neutral state in the cationic state geometry and *EN*(*QN*) is the total energy of the neutral state in the neutral geometry. λ1+ is frequently called

The diffusion coefficient *D* of charge carriers can be expressed using the Einstein-

*H SH H <sup>t</sup>*

2 1 <sup>2</sup> ( ) exp <sup>4</sup> <sup>4</sup> *et k t*

phthalocyanine dimer in HF approximation.

The transfer integral *t+* was calculated according to

consists of the sum of *λ*1+ and *λ*2+, λ+ = λ<sup>1</sup>

as deformation energy of the system.

Smoluchowski equation

*kT kT*

 

, (1)

the expression [19]

b=3.665 Ǻ.

Calculated stabilization energies listed in Table 1 are typical for – stacking interactions and indicate that the polymorph is more stable than the -modification; the calculated difference of stabilization energies is 1.5 kcal/mol for the functional MPW1B95. Table 1 shows that the withdrawal of electron from α polymorph leads to geometry with more closely lying interplanar arrangements of monomeric subunits characterized by the distances a = 3.44 Å and b = 3.67 Å. Optimized geometry of anionic form is characterized by similar interplane distance 3.45 Å and larger parameter b = 3.80 Å. Cationic form of polymorph is characterized by the distances a = 3.29 Å and b = 5.26 Å, anionic form of this polymorph by distances a = 3.33 Å and b = 3.68 Å. All following single point calculations were done at optimized geometries.

On the basis of the dimer calculations, the geometry optimization of H2Pc tetramer was done by MPW1B95/6-31G\* calculations on both polymorphs. The middle part of the optimized tetramer structure interprets well the H2Pc crystal structure (the calculated interplane distance is 3.39 Å [15]).

The optical spectroscopy was used for the characterization of the phthalocyanine layer. Figure 3 shows the experimental spectrum in the region of the phtalocyanine Q band. The comparison of characteristic features of this spectrum with the previously measured spectra [36] of different polymorphs of H2Pc layers indicates the presence of the polymorph.

TD DFT calculated transitions on this polymorph reasonably well reproduce the strong features of characteristic Q band and the effect of aggregation. The experimental transition energies measured at 1.77 and 1.93 eV are slightly overestimated by TD DFT calculations (obtained at 2.15 and 2.21 eV) with oscillator strengths 0.52 and 0.58, respectively. Transitions with low oscillator strength calculated at 1.65 and 1.71 eV describe the appearance of the week features in the long wave region. The TD DFT calculation on the polymorph describes correctly the shift of the intense transitions to the longer wavelengths.

Fig. 3. The experimental spectrum of H2Pc layer in the region of the Q band. Inset shows calculated transitions for H2Pc dimer.

At room temperature, the charge carrier transport can be described by a hopping within the Marcus theory. Subsequently, the rate expression of a self-exchange process is provided by the expression [19]

$$k\_{\rm et} = \frac{2\pi}{\hbar} \frac{1}{\sqrt{4\pi\mathcal{E}^+kT}} (t^+)^2 \exp\left(-\frac{\mathcal{X}^+}{4kT}\right),\tag{1}$$

where is the reduced Planck constant, *k* is the Boltzmann constant, *T* is the temperature an *λ*+ is the reorganisation energy and *t+* is the electronic coupling matrix element (the measure of charge transport probability – electron transfer integral) for the charge transfer. In order to estimate the electronic coupling between individual monomeric units, electron transfer integrals were calculated for α and β crystallographic modifications of the phthalocyanine dimer in HF approximation.

For the configuration with doubly occupied HOMO on the first monomer and singly occupied HOMO of the second one, calculation gives electron transfer integral (for otimized geometry MPW1B95/6-31G\*) values for non-relaxed cation radical 11.7 meV and 5.7 meV (hole transfer) for the α and β modification, respectively. It is supposed that in the course of electron or hole hopping, the atoms can relax in order to reach the minimum of energy at the potential surface. Transfer integral for optimized cation radical α crystal form with relaxed atoms (UMPW1B95/6-31G\*) is 18.7 meV. The calculations indicate that electron mobility is smaller than hole mobility because optimized geometry of anionic form is characterized by larger interplane parameter b (see Tab. 1) - for anionic form b=3.804 Ǻ, for cationic form b=3.665 Ǻ.

The transfer integral *t+* was calculated according to

164 Quantum Chemistry – Molecules for Innovations

Calculated stabilization energies listed in Table 1 are typical for – stacking interactions and indicate that the polymorph is more stable than the -modification; the calculated difference of stabilization energies is 1.5 kcal/mol for the functional MPW1B95. Table 1 shows that the withdrawal of electron from α polymorph leads to geometry with more closely lying interplanar arrangements of monomeric subunits characterized by the distances a = 3.44 Å and b = 3.67 Å. Optimized geometry of anionic form is characterized by similar interplane distance 3.45 Å and larger parameter b = 3.80 Å. Cationic form of polymorph is characterized by the distances a = 3.29 Å and b = 5.26 Å, anionic form of this polymorph by distances a = 3.33 Å and b = 3.68 Å. All following single point calculations

On the basis of the dimer calculations, the geometry optimization of H2Pc tetramer was done by MPW1B95/6-31G\* calculations on both polymorphs. The middle part of the optimized tetramer structure interprets well the H2Pc crystal structure (the calculated

The optical spectroscopy was used for the characterization of the phthalocyanine layer. Figure 3 shows the experimental spectrum in the region of the phtalocyanine Q band. The comparison of characteristic features of this spectrum with the previously measured spectra [36] of different polymorphs of H2Pc layers indicates the presence of the polymorph.

TD DFT calculated transitions on this polymorph reasonably well reproduce the strong features of characteristic Q band and the effect of aggregation. The experimental transition energies measured at 1.77 and 1.93 eV are slightly overestimated by TD DFT calculations (obtained at 2.15 and 2.21 eV) with oscillator strengths 0.52 and 0.58, respectively. Transitions with low oscillator strength calculated at 1.65 and 1.71 eV describe the appearance of the week features in the long wave region. The TD DFT calculation on the polymorph describes correctly the shift of the intense transitions to the longer wavelengths.

Fig. 3. The experimental spectrum of H2Pc layer in the region of the Q band. Inset shows

were done at optimized geometries.

interplane distance is 3.39 Å [15]).

calculated transitions for H2Pc dimer.

$$t^{+} = \frac{H\_{RP} - S\_{RP}(H\_{RR} + H\_{PP})/2}{1 - S\_{RP}^2} \,\text{,}\tag{2}$$

*HRP* is the interaction energy between reactant and product states, *SRP* is the overlap between the reactant and product states and HRR is electronic energy of the reaktant state andHPP is electronic energy of the product state. All these terms were obtained via the direct coupling of localised monomer orbitals. On the molecular level, three factors, the electronic coupling (transfer integral *t*+) between the individual parts of the molecule, the reorganisation energy λ+ during charge transport and the effective length of hole transfer *L*, are usually considered to be important for charge transport in organic materials. The reorganization energy *λ*<sup>+</sup> consists of the sum of *λ*1+ and *λ*2+, λ+ = λ<sup>1</sup> + + λ2+, where the deformation energy of the system was calculated as the difference between the vertical and cationic state: λ1+ = *E*+(*QN*) – *E*+(*Q*+) and λ<sup>2</sup> + = *E*+(*Q*+) – *E*+(*QN*). Here, *E*+(*QN*) is the total electronic energy of the cationic state in the neutral geometry, *E*+(*Q*+) is the total energy of the cationic state in the cationic state geometry, *EN*(*Q*+) is the total energy of the neutral state in the cationic state geometry and *EN*(*QN*) is the total energy of the neutral state in the neutral geometry. λ1+ is frequently called as deformation energy of the system.

The diffusion coefficient *D* of charge carriers can be expressed using the Einstein-Smoluchowski equation

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 167

Fig. 5. The schematic representation of the HOMO (top) and HOMO-1 (bottom) of the dimer

Fig. 6. The density of the states (DOS) for [NiPc(SO3Na)2]2. The black line indicates the total density of the states of the whole system, the blue dashed line the contributing Ni orbitals and the red one the contribution from the SO3Na group. The vertical dashed line indicates

an approximate midpoint of the HOMO–LUMO levels.

[NiPc(SO3Na)2]2.

$$D = \frac{L^2 k\_{et}}{2} \,. \tag{3}$$

This makes it possible to evaluate the drift mobility of the charge carriers using the Einstein relation *μ* = *eD*/*kT*. It should also be noted that the calculated charge mobility mentioned here represents the zero electric field approximation value.

To explain the differences between the charge carrier mobility in sulphonated and nonsulphonated Ni phthalocyanines (NiPc), quantum chemical calculations were performed on the DFT (density functional theory) level for H2Pc, NiPc and NiPc(SO3Na)x (x = 1, 2) dimers and their cationic and anionic forms. Quantum chemical modeling was found to be very useful – we were able to see states of various molecular systems from new and comprehensive perspectives.

The optimized structure of the [Ni(Pc(SO3Na)2)]2 is depicted in Fig.4. The calculated geometry of the NiPc dimer and tetramer reasonably well represents the local part of the NiPc crystal structure [34]. The best performance for the NiPc dimer was found by the MPW1B95/6-31+G\* method. The calculated approximate interplane distance (3.383 Å) is close to the experimental value of 3.4 Å [15,19].

The calculated stabilization energies are typical for π–π stacking interactions. The calculated stabilization energies with the BSSE correction are 4.1, 5.4, 7.4 and 11.3 kcal/mol for the [H2Pc]2, [NiPc]2, [NiPc(SO3Na)]2 and [NiPc(SO3Na)2]2 dimers, respectively. The MPWB1K/6- 31G\* calculations yield similar results, whereas the calculated stabilization energies are slightly higher. The increasing stabilization energies in the series of dimers going from [H2Pc]2 to [NiPc(SO3Na)2]2 indicate the better stability and organization of the NiPc(SO3Na)2 layers in comparison with the others.

Fig. 4. The DFT-calculated optimized structure of the dimer [NiPc(SO3Na)2]2. The dashed line indicates the shortest distance between the O and Na atoms.

2 2

This makes it possible to evaluate the drift mobility of the charge carriers using the Einstein relation *μ* = *eD*/*kT*. It should also be noted that the calculated charge mobility mentioned

To explain the differences between the charge carrier mobility in sulphonated and nonsulphonated Ni phthalocyanines (NiPc), quantum chemical calculations were performed on the DFT (density functional theory) level for H2Pc, NiPc and NiPc(SO3Na)x (x = 1, 2) dimers and their cationic and anionic forms. Quantum chemical modeling was found to be very useful – we were able to see states of various molecular systems from new and

The optimized structure of the [Ni(Pc(SO3Na)2)]2 is depicted in Fig.4. The calculated geometry of the NiPc dimer and tetramer reasonably well represents the local part of the NiPc crystal structure [34]. The best performance for the NiPc dimer was found by the MPW1B95/6-31+G\* method. The calculated approximate interplane distance (3.383 Å) is

The calculated stabilization energies are typical for π–π stacking interactions. The calculated stabilization energies with the BSSE correction are 4.1, 5.4, 7.4 and 11.3 kcal/mol for the [H2Pc]2, [NiPc]2, [NiPc(SO3Na)]2 and [NiPc(SO3Na)2]2 dimers, respectively. The MPWB1K/6- 31G\* calculations yield similar results, whereas the calculated stabilization energies are slightly higher. The increasing stabilization energies in the series of dimers going from [H2Pc]2 to [NiPc(SO3Na)2]2 indicate the better stability and organization of the NiPc(SO3Na)2

Fig. 4. The DFT-calculated optimized structure of the dimer [NiPc(SO3Na)2]2. The dashed

line indicates the shortest distance between the O and Na atoms.

here represents the zero electric field approximation value.

comprehensive perspectives.

close to the experimental value of 3.4 Å [15,19].

layers in comparison with the others.

*<sup>D</sup> L ket* . (3)

Fig. 5. The schematic representation of the HOMO (top) and HOMO-1 (bottom) of the dimer [NiPc(SO3Na)2]2.

Fig. 6. The density of the states (DOS) for [NiPc(SO3Na)2]2. The black line indicates the total density of the states of the whole system, the blue dashed line the contributing Ni orbitals and the red one the contribution from the SO3Na group. The vertical dashed line indicates an approximate midpoint of the HOMO–LUMO levels.

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 169

Fig. 9. The energies of the frontier orbitals of the NiPc dimer, calculated with different

Figure 5 depicts two highest occupied molecular orbitals (HOMO, HOMO-1) of [NiPc(SO3Na)2]2, the character of which can influence the hole conductivity. The plot of the density of the states in Fig. 6 shows the distribution of one-electron molecular orbitals and indicates that the Ni and SO3Na orbitals do not substantially contribute to the frontier molecular orbitals of the dimer [NiPc(SO3Na)2]2. These orbitals are formed by Pc orbitals. Owing to the mutual interaction of the monomer orbitals, the frontier orbitals of the supersystem form groups of two closely lying molecular orbitals. The contribution of the 3d metal orbitals is negligible as in the case of the monomeric NiPc. The second pair of lower-lying occupied orbitals lies about 1.57 eV lower. Thus, it can be supposed that these orbitals do not strongly influence the charge carrier transport. The calculated HOMO– HOMO-1 separations are visualized in Figs. 7 and 8 while HOMO–LUMO gaps are listed in Tables 4 and 5. Figure 7 depicts the splitting of the frontier orbitals and their mutual position in the series of the systems studied; Fig. 8 compares orbital splitting in the series of the NiPc monomer, dimer and tetramer. The splitting of the frontier orbitals reflects the mutual interaction and thus the probability of charge transfer between individual monomeric subsystems. It should be mentioned that calculated HOMO-LUMO gap (Fig. 8) is diminishing in the series NiPc, [NiPc]2 and [NiPc]4 and approaching to the experimental value of 1.8 eV [13]. Fig. 9 shows how the variation of functional influences the energies of

The rate constant *kET* of the electron transfer between molecular orbitals was expressed – see (1). The electronic coupling between the individual monomeric units *VRP*, the electrontransfer integral, can be calculated by several procedures [8-13]. Koopman's approximation, where the electronic coupling is estimated as half of the corresponding orbital energies, was used for the matrix-element estimation [14-18]. This method has already been used in the

density functional for geometry optimized with corresponding functional.

frontier orbitals.

case of interacting metal-containing dimmers [22].

Fig. 7. The energies of the frontier orbitals of the studied phthalocyanine dimers.

Fig. 8. The energies of the frontier orbitals of the NiPc monomer, dimer and tetramer.

Fig. 7. The energies of the frontier orbitals of the studied phthalocyanine dimers.

Fig. 8. The energies of the frontier orbitals of the NiPc monomer, dimer and tetramer.

Fig. 9. The energies of the frontier orbitals of the NiPc dimer, calculated with different density functional for geometry optimized with corresponding functional.

Figure 5 depicts two highest occupied molecular orbitals (HOMO, HOMO-1) of [NiPc(SO3Na)2]2, the character of which can influence the hole conductivity. The plot of the density of the states in Fig. 6 shows the distribution of one-electron molecular orbitals and indicates that the Ni and SO3Na orbitals do not substantially contribute to the frontier molecular orbitals of the dimer [NiPc(SO3Na)2]2. These orbitals are formed by Pc orbitals. Owing to the mutual interaction of the monomer orbitals, the frontier orbitals of the supersystem form groups of two closely lying molecular orbitals. The contribution of the 3d metal orbitals is negligible as in the case of the monomeric NiPc. The second pair of lower-lying occupied orbitals lies about 1.57 eV lower. Thus, it can be supposed that these orbitals do not strongly influence the charge carrier transport. The calculated HOMO– HOMO-1 separations are visualized in Figs. 7 and 8 while HOMO–LUMO gaps are listed in Tables 4 and 5. Figure 7 depicts the splitting of the frontier orbitals and their mutual position in the series of the systems studied; Fig. 8 compares orbital splitting in the series of the NiPc monomer, dimer and tetramer. The splitting of the frontier orbitals reflects the mutual interaction and thus the probability of charge transfer between individual monomeric subsystems. It should be mentioned that calculated HOMO-LUMO gap (Fig. 8) is diminishing in the series NiPc, [NiPc]2 and [NiPc]4 and approaching to the experimental value of 1.8 eV [13]. Fig. 9 shows how the variation of functional influences the energies of frontier orbitals.

The rate constant *kET* of the electron transfer between molecular orbitals was expressed – see (1). The electronic coupling between the individual monomeric units *VRP*, the electrontransfer integral, can be calculated by several procedures [8-13]. Koopman's approximation, where the electronic coupling is estimated as half of the corresponding orbital energies, was used for the matrix-element estimation [14-18]. This method has already been used in the case of interacting metal-containing dimmers [22].

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 171

Fig. 10. The dependence of electron-transfer integrals on the Ni-Ni separation. [NiPc]2 - blue

Fig. 11. The density of the states (DOS) for the system [Ni2Pc2(SO3Na)3(SO3)]-. the black line indicates the total density of the states of the whole system, the blue dashed line the

contributing Ni orbitals and the red one the total contribution from the SO3Na and SO3 groups; the vertical dashed line indicates an approximate midpoint of the HOMO–LUMO levels.

In comparison with the unperturbed system, the set of HOMOs is no longer separated from the lower-lying occupied orbitals and contains contributions from the SO3- group. It can be supposed that after Na+ ion dissociation the whole layer contains mobile Na+ and fixed

ions surrounded by water molecules. In this case, the highest molecular

squares, [NiPc(SO3Na)2]2 – red triangles.

[NiPc(SO3Na)(SO3)]-

The values of the electron-transfer integrals for the closed-shell systems were estimated from the separation of HOMO and HOMO-1 for the optimized structures. The values of the electron-transfer integrals based on the MPW1B95/6-31G\* functional model are 47.5 meV, 54.3 meV, 63.1 meV and 88.6 meV for [H2Pc]2, [NiPc]2, [NiPc(SO3Na)]2 and [NiPc(SO3Na)2]2, respectively (see Table 2).


a an average of the calculated values for the two different Na ions locations

Table 2. The calculated stabilization energies – ∆E, (kcal/mol), electron-transfer integrals – ET coupling (meV) and magnitude of the gap between the HOMO a LUMO orbitals of the various types of phthalocyanine dimers.

From these values, it follows that the electronic contribution to the rate constant of the electron transfer (proportional to the power of the electronic coupling – *V2 RP*) for [NiPc(SO3Na)2]2 should be 2.7 times larger than for [NiPc]2 and 3.5 times larger than for [H2Pc]2, whereas the electronic contribution for [NiPc(SO3Na)]2 is only about 1.4 times larger than for [NiPc]2. The dependence of the electron-transfer integrals on the Ni-Ni separation for [NiPc]2 and [NiPc(SO3Na)2]2 dimers is depicted in Fig. 10. The electron-transfer integral value varies strongly with the intermolecular separation, nevertheless the ratio between *VRP*  calculated for SO3Na substituted and unsubstituted systems is close to this ratio obtained from equilibrium intermolecular separation.

Both water molecules surrounding or the application of an electric field can cause the dissociation of the ionic Na-SO3 bond. In order to explain the effect of the Na+ dissociation, calculations were performed on the model dimeric systems, where Na+ ions were stepwise removed from the NiPc(SO3Na)2 dimer . The stabilization energy of the system with one Na+ removed (13.2 kcal mol-1) is even larger than that of [NiPc(SO3Na)2]2. From Table 2, it can be seen that [Ni2Pc2(SO3Na)3(SO3)]- is the most stable and thus the best organized of all the structures investigated. The density of the states plot depicted in Fig. 11 shows how the withdrawal of one Na+ influences the electronic structure. Projected Densities of States reported in this chapter were broadened using discrete molecular orbital levels – the broadening parameter used in our PDOS calculations (the full width at half maximum) was 0.3 eV.

The values of the electron-transfer integrals for the closed-shell systems were estimated from the separation of HOMO and HOMO-1 for the optimized structures. The values of the electron-transfer integrals based on the MPW1B95/6-31G\* functional model are 47.5 meV, 54.3 meV, 63.1 meV and 88.6 meV for [H2Pc]2, [NiPc]2, [NiPc(SO3Na)]2 and [NiPc(SO3Na)2]2,

kcal mol-1 meV eV

 MPW1B95/6-31G\* Dimer ∆E ∆E(BSSE) ET coupling Gap

[H2Pc]2 14.8 4.1 47.5 2.46 [NiPc]2 19.4 5.4 54.3 2.53 [NiPc(SO3Na)]2 22.1 7.4 63.1 2.51 [NiPc(SO3Na)2]2 27.6 11.3 88.6 2.41

(NiPc(SO3Na) SO3 )]- 31.2a 13.2 a 2.34 a [NiPc(SO3Na)(SO3)]22- 6.3 a -13.1 a 2.41 a [NiPc(SO3)2]24- -79.4 -100.5 2.44

Table 2. The calculated stabilization energies – ∆E, (kcal/mol), electron-transfer integrals – ET coupling (meV) and magnitude of the gap between the HOMO a LUMO orbitals of the

From these values, it follows that the electronic contribution to the rate constant of the electron transfer (proportional to the power of the electronic coupling – *V2RP*) for [NiPc(SO3Na)2]2 should be 2.7 times larger than for [NiPc]2 and 3.5 times larger than for [H2Pc]2, whereas the electronic contribution for [NiPc(SO3Na)]2 is only about 1.4 times larger than for [NiPc]2. The dependence of the electron-transfer integrals on the Ni-Ni separation for [NiPc]2 and [NiPc(SO3Na)2]2 dimers is depicted in Fig. 10. The electron-transfer integral value varies strongly with the intermolecular separation, nevertheless the ratio between *VRP*  calculated for SO3Na substituted and unsubstituted systems is close to this ratio obtained

Both water molecules surrounding or the application of an electric field can cause the dissociation of the ionic Na-SO3 bond. In order to explain the effect of the Na+ dissociation, calculations were performed on the model dimeric systems, where Na+ ions were stepwise removed from the NiPc(SO3Na)2 dimer . The stabilization energy of the system with one Na+ removed (13.2 kcal mol-1) is even larger than that of [NiPc(SO3Na)2]2. From Table 2, it can be seen that [Ni2Pc2(SO3Na)3(SO3)]- is the most stable and thus the best organized of all the structures investigated. The density of the states plot depicted in Fig. 11 shows how the withdrawal of one Na+ influences the electronic structure. Projected Densities of States reported in this chapter were broadened using discrete molecular orbital levels – the broadening parameter used in our PDOS calculations (the full width at half maximum) was

a an average of the calculated values for the two different Na ions locations

various types of phthalocyanine dimers.

from equilibrium intermolecular separation.

respectively (see Table 2).

[(NiPc(SO3Na)2)

0.3 eV.

Fig. 10. The dependence of electron-transfer integrals on the Ni-Ni separation. [NiPc]2 - blue squares, [NiPc(SO3Na)2]2 – red triangles.

Fig. 11. The density of the states (DOS) for the system [Ni2Pc2(SO3Na)3(SO3)]-. the black line indicates the total density of the states of the whole system, the blue dashed line the contributing Ni orbitals and the red one the total contribution from the SO3Na and SO3 groups; the vertical dashed line indicates an approximate midpoint of the HOMO–LUMO levels.

In comparison with the unperturbed system, the set of HOMOs is no longer separated from the lower-lying occupied orbitals and contains contributions from the SO3 - group. It can be supposed that after Na+ ion dissociation the whole layer contains mobile Na+ and fixed [NiPc(SO3Na)(SO3)]- ions surrounded by water molecules. In this case, the highest molecular

Charge Carrier Mobility in Phthalocyanines: Experiment and Quantum Chemical Calculations 173

3. The system is strongly affected by an external electric field and water molecules in the vicinity, which can cause the dissociation of the ionic Na–SO3 bond. After the Na–SO3 bond's dissociation, the whole layer contains mobile Na+ and fixed [Ni2Pc2(SO3Na)3(SO3)] anions which allows the mobile holes to delocalize and increase the probability of hole transfer through the layer structure. We found that the highest molecular orbitals in [Ni2Pc2(SO3Na)3(SO3)]- contain new electronic contributions to the density of the states from

Other aspects which can increase charge carrier mobility in of the OFET structures based on sulphonated phthalocyanine derivatives should be mentioned: 1. Better resistivity to oxygen and thus the stability of the system in atmospheric air. 2. The interface SiO2/[NiPc(SO3Na)2]x is between two hydrophilic groups and thus adheres materials enabling the formation of a molecular layer on the SiO2 surface with proper and regular

The objective of this chapter was to present results of DFT studies of class of organic materials with relatively high carrier mobility – phthalocyanines. It was shown how DFT can be used to calculate/model some parameters that influence charge carrier mobility on essentially level [18]. The calculations indicate that electron mobility in H2Pc is smaller than hole mobility because optimized geometry of anionic form is characterized by larger interplane parameter.

HOMO orbital system enables the mobile holes to be more delocalized; thus the change charge transport (hopping) mechanism becomes more ballistic (less scattered and more effective). The withdrawal of one Na+ ion leads to a further stabilization of the structure and

 Larger stabilization energies of the systems with (SO3Na) groups - layers with (SO3Na) groups are organized more regularly – resulting in better π–π interaction and consequently better charge carrier mobility than in the case of nonsubstituted ones. The withdrawal of one Na+ ion leads to a further stabilization of the structure and thus

 The dissociations of more than one Na+ ion strongly destabilize the layer structure. The probability of charge transfer through sulphonated Ni-phthalocyanine dimers with totally removed Na+ ions is lower than in the case of standard sulphonated Ni


, the contribution from the SO3 anions to the whole

standard sulphonated Ni phthalocyanines dimers.

molecular orientation which increases the conductivity .

thus a higher probability of charge-carrier transport.

a higher probability of charge-carrier transport.

In the case of [NiPc(SO3Na)(SO3)]-

phthalocyanines dimers.

[1] M. A. Reed, *Proc. IEEE* , 1999 , 87, 652.

[2] D. Braga, G. Horowitz, *Adv. Mater.*, 2009, 21, 1.

[3] J. Health, M. Read, Molecular Electronics, Physics Today, 2003, 43

**2. References** 

the SO3

groups, it can be assumed that layers with (SO3Na) groups are organized more regularly – resulting in better – interaction and consequently better charge carrier mobility than in the case of nonsubstituted ones. The withdrawal of one Na+ ion leads to a further stabilization of the structure and thus a higher probability of charge-carrier transport. The dissociations of more than one Na+ ion strongly destabilize the layer structure. The probability of charge transfer through sulphonated Ni-phthalocyanine dimers with totally removed Na+ ions should, therefore, be lower than in the case of

orbitals, which contain contributions from the SO3 - group and are close to the lower-lying occupied orbitals, allow the whole system to contain electronic states that are more extended and therefore more conductive in character.

Due to the withdrawal of the remaining Na+ ions, the stabilization energies decrease. The least stable dimer in the series [NiPc(SO3Na)2]2, [NiPc(SO3Na)(SO3)]2 2- and [NiPc(SO3)2]2 4- is the last, completely dissociated dimer, i.e. [NiPc(SO3)2]2 4-. This fact can induce reduced layer organization and thus lower the conductivity of the systems with more than one Na+ ion removed.

How can the selected chemical modifications of Ni phthalocyanine affect on the molecular level the charge carrier mobility?

At zero-gate bias, the HOMO band is filled. As the gate voltage is swept more negative, the positions of the LUMO and HOMO bands rise in energy, allowing mobile holes to sustain a source-drain current via the HOMO band. Materials based on NiPc and [NiPc(SO3Na)x] are hole semiconductors, which means that the source of the charge carriers in the structure electrode-semiconductor – electrode is not the injecting metal electrode but the semiconductor. In the case of [NiPc(SO3Na)(SO3)]- , the contribution from the SO3 anions to the whole HOMO orbital system enables the mobile holes to be more delocalized; thus the change charge transport (hopping) mechanism becomes more ballistic (less scattered and more effective).

The stability of dimers (the calculated stabilization energy), which induces better layer organization and consequently better charge mobility37 grows in the series [H2Pc]2, [NiPc]2, [NiPc(SO3Na)]2, [NiPc(SO3Na)2]2 and [(NiPc(SO3Na)2)(NiPc(SO3Na)SO3)]- . The withdrawal of more than one Na cation leads to destabilization and consequently to a decrease in layer organization. The layer of [Ni2Pc2(SO3Na)3(SO3)]- should be the most regular (is supposed to be the most conductive) of all the structures examined.

In the case of NiPc(SO3Na)3.3 the charge carrier mobility (0.02 cm2 V-1 s-1) is lower than for NiPc(SO3Na)1.5 (1.08 cm2 V-1 s-1) - see Tab. 3.


Table 3. The mobilities for the various types of nickel phthalocyanines.

From calculating spatial models it was figured out that due to the sterical communication hindrance caused by third and fourth SO3Na groups the NiPc(SO3Na)3.3 dimers are less stable. This fact results in reduced organized layer structure with reduced charge mobility.

Using DFT calculations, several aspects that influence the charge-carrier mobility in the case of the materials were compared:


groups, it can be assumed that layers with (SO3Na) groups are organized more regularly – resulting in better – interaction and consequently better charge carrier mobility than in the case of nonsubstituted ones. The withdrawal of one Na+ ion leads to a further stabilization of the structure and thus a higher probability of charge-carrier transport. The dissociations of more than one Na+ ion strongly destabilize the layer structure. The probability of charge transfer through sulphonated Ni-phthalocyanine dimers with totally removed Na+ ions should, therefore, be lower than in the case of standard sulphonated Ni phthalocyanines dimers.

3. The system is strongly affected by an external electric field and water molecules in the vicinity, which can cause the dissociation of the ionic Na–SO3 bond. After the Na–SO3 bond's dissociation, the whole layer contains mobile Na+ and fixed [Ni2Pc2(SO3Na)3(SO3)] anions which allows the mobile holes to delocalize and increase the probability of hole transfer through the layer structure. We found that the highest molecular orbitals in [Ni2Pc2(SO3Na)3(SO3)]- contain new electronic contributions to the density of the states from the SO3 - group, which should lead to an increase in the hole mobility and thus conductivity.

Other aspects which can increase charge carrier mobility in of the OFET structures based on sulphonated phthalocyanine derivatives should be mentioned: 1. Better resistivity to oxygen and thus the stability of the system in atmospheric air. 2. The interface SiO2/[NiPc(SO3Na)2]x is between two hydrophilic groups and thus adheres materials enabling the formation of a molecular layer on the SiO2 surface with proper and regular molecular orientation which increases the conductivity .

The objective of this chapter was to present results of DFT studies of class of organic materials with relatively high carrier mobility – phthalocyanines. It was shown how DFT can be used to calculate/model some parameters that influence charge carrier mobility on essentially level [18]. The calculations indicate that electron mobility in H2Pc is smaller than hole mobility because optimized geometry of anionic form is characterized by larger interplane parameter.

In the case of [NiPc(SO3Na)(SO3)]-, the contribution from the SO3 anions to the whole HOMO orbital system enables the mobile holes to be more delocalized; thus the change charge transport (hopping) mechanism becomes more ballistic (less scattered and more effective). The withdrawal of one Na+ ion leads to a further stabilization of the structure and thus a higher probability of charge-carrier transport.


## **2. References**

172 Quantum Chemistry – Molecules for Innovations

occupied orbitals, allow the whole system to contain electronic states that are more extended

Due to the withdrawal of the remaining Na+ ions, the stabilization energies decrease. The least stable dimer in the series [NiPc(SO3Na)2]2, [NiPc(SO3Na)(SO3)]22- and [NiPc(SO3)2]24- is the last, completely dissociated dimer, i.e. [NiPc(SO3)2]24-. This fact can induce reduced layer organization and thus lower the conductivity of the systems with more than one Na+ ion

How can the selected chemical modifications of Ni phthalocyanine affect on the molecular

At zero-gate bias, the HOMO band is filled. As the gate voltage is swept more negative, the positions of the LUMO and HOMO bands rise in energy, allowing mobile holes to sustain a source-drain current via the HOMO band. Materials based on NiPc and [NiPc(SO3Na)x] are hole semiconductors, which means that the source of the charge carriers in the structure electrode-semiconductor – electrode is not the injecting metal electrode but the semiconductor.

orbital system enables the mobile holes to be more delocalized; thus the change charge transport (hopping) mechanism becomes more ballistic (less scattered and more effective).

The stability of dimers (the calculated stabilization energy), which induces better layer organization and consequently better charge mobility37 grows in the series [H2Pc]2, [NiPc]2,

of more than one Na cation leads to destabilization and consequently to a decrease in layer organization. The layer of [Ni2Pc2(SO3Na)3(SO3)]- should be the most regular (is supposed to

In the case of NiPc(SO3Na)3.3 the charge carrier mobility (0.02 cm2 V-1 s-1) is lower than for

Phthalocyanine Film preparation Mobility (cm2 V-1 s-1) NiPc evaporation 10-5 NiPc(SO3Na)3.3 spin-coating 0.02 iPc(SO3Na)1.5 spin-coating 1.08

From calculating spatial models it was figured out that due to the sterical communication hindrance caused by third and fourth SO3Na groups the NiPc(SO3Na)3.3 dimers are less stable. This fact results in reduced organized layer structure with reduced charge mobility. Using DFT calculations, several aspects that influence the charge-carrier mobility in the case

1. Charge transfer probability grows in the series [H2Pc]2, [NiPc]2, [NiPc(SO3Na)]2 and [NiPc(SO3Na)2]2 because of the increasing electronic coupling. The presence of (SO3Na) groups increases the probability of electron transfer between the composing units. 2. At the same time, the stabilization energies grow in the series [H2Pc]2, [NiPc]2 and [NiPc(SO3Na)2]2. Due to larger stabilization energies of the systems with (SO3Na)

[NiPc(SO3Na)]2, [NiPc(SO3Na)2]2 and [(NiPc(SO3Na)2)(NiPc(SO3Na)SO3)]-

Table 3. The mobilities for the various types of nickel phthalocyanines.

be the most conductive) of all the structures examined.

NiPc(SO3Na)1.5 (1.08 cm2 V-1 s-1) - see Tab. 3.

of the materials were compared:


, the contribution from the SO3 anions to the whole HOMO

. The withdrawal

orbitals, which contain contributions from the SO3

and therefore more conductive in character.

level the charge carrier mobility?

In the case of [NiPc(SO3Na)(SO3)]-

removed.


**8** 

*China* 

**Theoretical Study for High Energy** 

Kun Wang, Jian-Guo Zhang\*, Hui-Hui Zheng,

*State Key Laboratory of Explosion Science and Technology,* 

Hui-Sheng Huang and Tong-Lai Zhang

*Beijing Institute of Technology* 

**Density Compounds from Cyclophosphazene** 

The phosphazenes have distinguished ancestry. The reaction between phosphorus pentachloride and ammonia was described by Rose in 1834[1], and in an editorial comment, Liebig [13] reported work carried out in conjunction with Wöhler. The major reaction product was phospham and a small quantity of a stable crystalline compound containing nitrogen, phosphorus, and chlorine was obtained. Gerhardt and Laurent established that the empirical composition was NPCl2, and Gladstone and Holmes and Wichelhaus measured

Phosphorus nitrogen compounds are renowned for their ability to form a variety of ring and cage structures. The most prominent P–N ring systems are phosphazanes, featuring single P–N bond[3], and phosphazenes, having multiple P–N bonds[4-8]. The two kinds of systems tend to occur in different ring sizes. The polyphosphazene has been used in medical community widely because its excellent biocompatibility and biological activity. The chemists have synthesized the medical polyphosphazene in 1977 with the substituent of glycine-ethylester[9]. In addition, There are applications of polyphosphazene in membrane

Cyclophosphazene as a kind of phosphazene compounds attracts many researchers for a long time due to their unique properties. The energetic cyclophosphazene compounds without heavy metal elements are environmentally friendly and have very high energy density. Cyclophosphazene containing amino, nitro, nitramino and azido groups would be a kind of possible high-energy compound. It is a polymer where alternate regularly with the double and single bond between the nitrogen and the phosphorus [11]. The generally accepted "island model"[12]. supposes the σ-bonds in the phosphanzenes being formed by *sp*3 hybrid orbital of phosphorus. The orbital available for out-of-plane *π*-bonding is dyz orbital being combined into sets of three-center *π*-molecular orbital. These three-center orbital overlap only weakly with one another and the *π*-electrons are effectively localized in definite three-center-*π*-bonds. Unusual chemical bonding in P-N backbone causes many

the vapor density and deduced the molecular formula, N3P3Cl6[2].

**1. Introduction** 

separation, dye and catalysts [10].

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