Ab initio investigations on three isomers of polyacetylene under the interaction of the external electric field

Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20 www.elsevier.com/locate/theochem

Ab initio investigations on three isomers of polyacetylene under the interaction of the external electric field Yuanfeng Ye a, Milin Zhang a, Jianwei Zhao a

b,*

School of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, PR China b School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, PR China Received 24 May 2007; received in revised form 10 July 2007; accepted 10 July 2007 Available online 18 July 2007

Abstract Three isomers of polyacetylene (trans-transoid polyacetylene (Tt-PA), cis-transoid polyacetylene (Ct-PA), and trans-cisoid polyacetylene (Tc-PA)), as backbones of many conducting molecular wires, in contact with a pair of chemically inert electrodes have been investigated theoretically at the HF/6-31G* level by considering the interaction of an external electric field (EF). It is found that the external EF modifies both the geometry and electronic structure of the molecular wires. The application of EF may increase the molecular conjugation and the induced dipole moment, while decrease the HOMO–LUMO gap. It may also make the spatial distributions of the frontier molecular orbitals move from a fully delocalized form to a partially localized one depending on the EF strength. Moreover these changes of three isomers show the structural dependence obviously, the longer the conjugation chain is, the stronger the influence of EF.  2007 Elsevier B.V. All rights reserved. Keywords: Molecular wire; Polyacetylene; Ab initio; Electric field; Molecular electronics

1. Introduction The continuous miniaturization of conventional siliconbased electronics has led to a revival of efforts to build devices with molecular-scale components. Among those molecular electronic devices, the molecular wire [1], switch [2], diode/rectifier [3], resonant tunneling diodes (RTD) [4], and field effect transistor (FET) [5] have attracted much attention. Molecular wire is the basis of all the other components of such electronic systems. Examples of the most promising families of molecular wires are conjugated hydrocarbons, porphyrin oligomers, carbon nanotubes, and so on, all of which have the same key requirements. For instance, they have to be electron or hole conducting in order to carry a current through the circuit. Thus, the wire provides a pathway for transport of the electrons from one reservoir to another, which is more efficient than electron transport through space. Conjugated molecules com*

Corresponding author. Tel.:/fax: +86 25 83596523. E-mail address: [email protected] (J. Zhao).

0166-1280/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2007.07.007

prising alternating single and double (or triple) carbon– carbon bonds can conduct electrons through their p-system, and this has been the basis of many wires. The wire must also be linear in most cases and of a defined length to bridge the gap between two leads in the circuit. Polyacetylene (PA) is the prototype of the conjugated structure, and many other conjugated molecules can, in principle, be derived by the structural modification. Therefore, it has received intensive study both experimentally [6–8] and theoretically [9–11]. Among the four isomers of PA (trans-transoid (Tt-PA), cis-transoid (Ct-PA), transcisoid (Tc-PA), and cis–gauche forms) [12], the former three are stable and easy to be modified, so we focus on them in the present work. Many molecular properties, such as optical [13] and electrical properties [14] are dominated by the structure of the conjugation path. Therefore, a detailed investigation on their structural and electric characters of the three isomers with different conjugation styles is of great importance for not only understanding the molecular electrical properties but also other physical or chemical properties of the conjugated systems.

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20

Theoretical investigations on the molecular wires so far can be roughly classified into two categories: the static research focusing on the geometric and electronic structures [15,16], and the dynamic study showing the transportation behavior based on non-equilibrium Green’s function (NEGF) formulism [17,18]. It is well known that the surroundings may interact with the functional molecules through such as van der Waals force, electrostatic force, hydrophobic interaction and solvated effect. Among these molecular-scale refined interactions, the one from the external electric field (EF) is of considerable importance, because it is fairly large when a bias of several volts is applied on a molecule [19–21]. Under the EF interaction, the molecule may resume a new geometric equilibrium or even undergo a dielectric breakdown [21,22], therefore, both the molecular geometry and electronic structure are doubted to be the same as in the zero-EF case [23–26]. Since many of previous theoretical studies did not take the EF effect into account, they look rather ex-situ [15,16]. Recently, we have proposed a more likely in-situ theoretical approach to the determination of molecular geometry and electronic structures of a given molecular wire in the electronic device [23–26]. Although the structure of molecular wire can be various, most of them can be summarized as the derivatives of the isomers of polyacetylene. The purpose of this paper is to study on the EF-dependence of Tt-PA, Tc-PA, and Ct-PA, with ab initio HF calculations. Since the molecular chain length is an important factor determining the molecular electronic transportation [27], the chain length effect has been considered as well. 2. Methodology Recent studies have demonstrated that the performance of a molecular wire is predominated by many factors, such as the nature of the molecule itself [28], the interface between the molecule and the electrode [29], the electrode material [30], and the electrode shape [31]. Considering all these factors seems impossible. In addition, all effects from the electrode and interface can be reasonably eliminated by an introduction of methenes to the end of conjugated molecule. Therefore, we give a simplified model that a PA molecule (HA(CH@CH)nAH, referred to as n-PA, n = 4, 6, 8, 10, 12, 14, and 16) bridges two chemically inert electrodes as shown in Fig. 1 (applied here with the positive pole on the left side and the negative pole on the right side). Theoretical approach to this model has been realized as follows. Prior to the introduction of EF, all molecules were fully optimized at HF/6-31G* level of theory. Then, two terminal carbon atoms were fixed in the space to simulate the connection to the electrodes, and others were optimized at the same level of theory in the applied series of EF. A uniform EF ranging from zero to 2.57 · 109 V/m and aligned along the two terminal carbon–carbon inter-atomic vector was applied to the model molecules, which may reasonably represent the working condition of the molecular devices [32]. On the other hand, fixing of the terminal car-

13

External Electric Field

+ + + + + + + + + + +

2 1

4 3

5

3

1

1

3

12 11

8

6 6

5

10 9

7

5

4

8 7

4

2 2

6

13

11 12

9 10 7

10

8

14

9

16 15

13 14 11

12

14

13

19 20 17 18 18 19 17 20 17

15 16

15

16

20 -

18

Tt-PA

19

Ct-PA

Tc-PA

Fig. 1. Schematic descriptions of the representative molecular wire, 10TtPA, 10Ct-PA, and 10Tc-PA which are connected with two chemically inert metal electrodes. In fact the Tc-PA is non-planar and shows a helical structure. The external EF is aligned along the two terminal carbon– carbon inter-atomic vector with positive potential at the left side.

bon atoms is also effective to remove the field-induced rotation [33]. All calculations were performed using Gaussian 03 program [34]. In our previous works [22,35,36] comprehensive tests have been performed at the HF and DFT levels with a wide variety of basis sets, showing that 6-31G* basis set is the relatively ‘‘good’’ one which can be used with sufficient accuracy and sustainable computing time. Since DFT method takes the electron correlation into account, it may more accurately predict molecular geometry as well as the energy when a proper basis set is used. However, HF method may give the molecular orbital with clearer physical meaning than the Kohn–Sham molecular orbital in the DFT methods. Considering the importance of molecular orbital in the molecular device, the connection to electrode, the transportation behavior and so on, we select the HF/6-31G* method for the present systems in this work. 3. Results and discussion 3.1. EF effect on the geometric structures Generally, the configuration of the series of model molecules is the balance of the steric repulsion that distorts the molecule and the conjugation effect that favors a planar conformation. At zero-EF Tt-PA and Ct-PA show planar structures as expected, but Tc-PA favors a helical configuration due to the strong steric repulsion of the two adjacent double bonds. By comparing the values of a series of dihedral angles, we find that in the middle of the molecule it is smallest while at the two ends they are bigger. This demonstrates that the conjugation of molecular center is stronger. After the EF has been introduced the configurations of Tt-PA and Ct-PA keep planar while Tc-PA remains nonplanar but the distorted degree decreases, i.e. the molecule becomes more planar. Fig. 2 gives the relationship between the variation of dihedral angles and the applied EF from which we can see that all the dihedral angles decrease with

14

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20 37 D1-2-3-4 D3-4-5-6 D5-6-7-8 D7-8-9-10 D9-10-11-12 D11-12-13-14 D13-14-15-16 D15-16-17-18 D17-18-19-20

35

34 34.5

33

32

31

Dihedral angle / Degree

Dihedral angle / Degree

36

D5-6-7-8 D7-8-9-10 D9-10-11-12 D11-12-13-14 D13-14-15-16

34.0 33.5 33.0 32.5 32.0 31.5 31.0

0

1x109 2x109 3x109 4x109 5x109 6x109 7x109

(Electric field)2 / (V2m2)

30 0.0

0.5

1.0

1.5

2.0

2.5

Electric field / (Vm-1) Fig. 2. The dihedral angles of 10-Tc-PA under the external electric field.

the increase of the EF except the D17-18-19-20. This is because it is located in the terminal position where the potential is low and the end effect is strong. It is obvious that the dihedral angles in the middle of molecule show more sensitive to the EF for its stronger conjugation. Another point to be noted is that these dihedral angles in the middle of molecule change almost linearly with the square of EF (shown in the inset). This can be explained by the same reason with the change of torsional angle of bithiophene [35]. It is known that the bond length alternation (BLA, defined as the average difference between the adjacent single and double bonds) along the backbone of a conjugated system is a crucial parameter for tuning the transportation behavior [37,41,42]. Many other properties, for example non-linear optical properties and spectrum, are also strongly dependent on the degree of bond length alternation [38]. Considering the structure of three PA’s isomers consists of similar single and double bonds, a detailed study of the bond length variation under the EF interaction is instructive for understanding the molecular structure– property relationship. Fig. 3a shows the bond length evolutions of three representative examples, 10Tt-PA, 10Tc-PA, and 10Ct-PA under the external EF. At zero-field the TcPA have longer single bonds and shorter double bonds which results in larger BLA than 10Tt-PA and 10Ct-PA. With the EF increasing, the carbon–carbon single bonds of all PAs become shorter and the double bonds become longer, resulting in a higher conjugation. However, the EF-dependence of the bond length evolution is not identical for all the bonds. In the three molecule models the maximum variations all occur in the central parts due to the better overlap of p-orbitals which gives higher p-conjugation as compared with those toward the end of the molecule. This can be also proven by the analysis of Mulliken atomic charges (in Fig. 4). Similar bond length evolution

is also observed for other PA molecules located in the external EF. Fig. 3b shows that the variations of double bonds are different especially in the higher EF for three PA models: Tt-PA > Ct-PA > Tc-PA. Obviously this originates from the difference of conjugations of three isomers: the stronger the molecule changes the better the conjugation is. In our previous studies a linear relationship between the double bonds variation of Tt-PA and the square of EF was given [26]. This character is also found for the other two isomers of PA. In Fig. 5a–c we can see this linear dependence varies depending on the location of the double bonds. The largest slope corresponding to that is in the central part of the molecular chain where the conjugation effect is strongest and it also shows obvious chain length dependence. Fig. 5d shows that the value of slope increases linearly with the chain length (denoted by the number of double bond N) for Tt-PA and the others slightly deviate from linearity. The slope of three isomers follows in the order: Tt-PA > Ct-PA > Tc-PA which means the difference of conjugation will be more obvious with the chain length’s increase. The same research was carried on the single bonds but regrettably there is no simple relationship between the single bond and the external electric field which has been proven in our previous work for Tt-PA [26]. Another important feature is that the molecular wire bends down from the original straight configuration in the same p-conjugation surface with the increase of the electric field. This behavior has been found for all Tt-PA molecules [26]. Although the bended arc is not so intense for the shorter ones, the longer the molecular chain is the more obviously the molecule bents. But this phenomenon is not observed for Tc-PA and Ct-PA, although we applied an electric field as high as 2.57 · 109 V/m. This behavior can be interpreted by the interaction between the external EF and the induced dipole moment. Due to the molecular

0.06

1.46

1.34

1.33

Tc-PA

C2 C4 C6 C8 C10 C12 C14 C16 C18 C20

0.02 0.00 -0.02 -0.04

EF=0 EF=1.44x109 V/m 9 EF=2.57x10 V/m

C2-3 C4-5 C6-7 C8-9 C10-11 C12-13 C14-15 C16-17 C18-19 C2-3 C4-5 C6-7 C8-9 C10-11 C12-13 C14-15 C16-17 C18-19 C2-3 C4-5 C6-7 C8-9 C10-11 C12-13 C14-15 C16-17 C18-19

C1 C3 C5 C7 C9 C11 C13 C15 C17 C19

Position of carbon atoms Fig. 4. EF effect on the deviation of the Mulliken atomic charge of 10TtPA, 10Ct-PA, and 10Tc-PA (see chemical structures in Fig. 1 for atom codes and bond codes). The Mulliken atomic charges of the PA under zero EF are referred to as zero.

9

EF=1.44x10 V/m 9

EF=2.57x10 V/m

0.004

0.000

-0.004

Tt-PA

Ct-PA

Tc-PA

C1-2 C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18 C19-20 C1-2 C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18 C19-20 C1-2 C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18 C19-20

Deviation of bond length / Angstrom

0.04

EF=0

0.008

-0.008

Tc-PA

-0.06

Bond position

b

Ct-PA

C1 C3 C5 C7 C9 C11 C13 C15 C17 C19

1.32

Ct-PA

C1-2 C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18 C19-20 C1-2 C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18 C19-20 C1-2 C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18 C19-20

Tt-PA

Tt-PA

C1 C3 C5 C7 C9 C11 C13 C15 C17 C19

Bond length / Angstrom

1.48

Deviation of Mulliken atomic charge

EF=0 9 EF=1.44x10 V/m 9 EF=2.57x10 V/m

15

C2 C4 C6 C8 C10 C12 C14 C16 C18 C20

C2 C4 C6 C8 C10 C12 C14 C16 C18 C20

C2-3 C4-5 C6-7 C8-9 C10-11 C12-13 C14-15 C16-17 C18-19

C2-3 C4-5 C6-7 C8-9 C10-11 C12-13 C14-15 C16-17 C18-19

C2-3 C4-5 C6-7 C8-9 C10-11 C12-13 C14-15 C16-17 C18-19

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20

Bond position Fig. 3. (a) The bond lengths of 10Tt-PA, 10Ct-PA, and 10Tc-PA under the electric field (bond codes of chemical structures are shown in Fig. 1). (b) Deviation of the bond lengths of 10Tt-PA, 10Ct-PA, and 10Tc-PA under various external electric fields. The bond lengths under zero EF are referred to as zero.

symmetry, the molecule does not have dipole moment in the zero-EF. When bias is applied, the nucleus is displaced in the direction of the field and the electrons are redistributed accordingly. Since the induced dipole moment of double bond is much higher than that of the molecule itself [26], we can roughly analyze the molecular tension caused by the interaction of the electric field and induced dipole moment of double bond by summing up the dipole moment vectors. 3.2. EF effect on dipole moment As we know when an external electric field is applied, the delocalization of p-electron of the conjugated organic molecules results in a new charge distribution of the molecular

chain and consequently leads to the change of the dipole moment. The better the conjugation is the more obviously the molecule’s dipole moment changes. So it is significant to research the responses of dipole moment to the electric field through which the ability of electron transport can further be explored. In another word we can roughly estimate the ability of electron transport by simply comparing the variety of their dipole moments. The Fig. 6a gives the evolution of the dipole moment of Ct-PA to the electric field. The other two isomers also obey the similar evolution. As expected, the dipole moments vary linearly with the electric field and are affected by the chain length effect: the longer the chain length the greater the dipole moment. Kirtman’s work shows the relationship between the electric field and dipole moment is non-linear when the electric field is larger (as high as 2.57 · 1010 V/m) [39]. It should be noted such high voltage can hardly be obtained for the molecular electronic devices [32]. So we use a comparatively moderate electric field ranging from zero to 2.57 · 109 V/m, which is comparable to the realistic laboratory field [32]. The comparison of dipole moment for three isomers of PA having the same double bond number under the electric field is shown in Table 1. It can be seen that the values of three PAs’ dipole moments follow this order: Tt-PA > Ct-PA > Tc-PA which is in accord with the order of conjugation discussed above. We also see the values of Tc-PAs’ are obviously smaller than the other two which can be explained by the Tc-PAs’ torsional molecular chain. According to Taylor’s expansion, the molecular induced dipole moment under the electric field (E) can be expressed as: lðEÞ ¼ aE þ bE2 þ cE3 þ    where a, b, and c are the first-order, second-order, and third-order derivatives of the dipole moment, respectively.

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20

Double bond length / Angstrom

1.341

C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18

1.340 1.339 1.338 1.337 1.336 1.335 1.334 1.333 1.332 1.331

1.340 1.339 1.338

Ct-PA

1.337 1.336 1.335 1.334

0

1x1018 2x1018 3x1018 4x1018 5x1018 6x1018 7x1018

(Electric field

1.332

strength)2

/

1x1018 2x1018 3x1018 4x1018 5x1018 6x1018 7x1018

0

(Electric field strength)2 / V2m-2

V2m-2

Tc-PA

2.0

Tt-PA

1.8

Ct-PA Tc-PA

1.6

Slope / m3V-2

C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18

1.333

Double bond length / Angstrom

C3-4 C5-6 C7-8 C9-10 C11-12 C13-14 C15-16 C17-18

1.341

Tt-PA

Double bond length /Angstrom

16

1.331

1.330

1.4 1.2 1.0 0.8 0.6 0.4

1.329

0.2

0

1x1018 2x1018 3x1018 4x1018 5x1018 6x1018 7x1018

(Electric field strength)2 / V2m-2

0.0

4

6

8

10

12

14

16

N

Fig. 5. Linear relationship between the double bond lengths and the square of EF for (a) 10Tt-PA, (b) 10Ct-PA, and (c) 10Tc-PA. (d) Correlation of the largest slopes and the number of double bonds (N) for three isomers of PA.

Champagne’s research shows that it is incorrect to describe the polarization of conjugated systems when the polarization is due to donor/acceptor substitution or an external field or both [40]. So it must be pointed out that a, b, and c do not directly mean the polarizability and first and second hyperpolarizabilities. However we can simply use the expansion to research the change of dipole induced by the external EF. Since the effect of higher order polynomials is negligible, we focus on the value of a. The chain length-dependent of a is given in Fig. 6b. As expected, the first-order derivatives of three PA models enhance with the increase of the chain length and the values of Ct-PA and Tc-PA have a good linear relationship with the number of double bond. The deviation of Tt-PA maybe roots in its bent molecular structure mentioned above. 3.3. EF effect on the electronic structures The energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), known as energy gap (HLG), is a key parameter determining the conductance of molecular wire [37,41,42]. Thereby, in order to study, and eventually to be able to predict the electrical conduction of

molecular wire, it is important to understand the nature of the HOMO–LUMO gap getting response to the external EF. Fig. 7 shows the evolutions of the LUMO and HOMO energy levels of the series of Ct-PAs as functions of the applied EF. For short conjugated molecular wires, 4CtPA and 6Ct-PA for example, the EF-dependence of HOMO and LUMO is insensible. When the conjugation chain is 8Ct-PA or longer, an obvious EF-dependence is observed. With the EF increasing, the LUMO decreases, whereas the HOMO increases. Both of them move toward each other almost symmetrically, leading to a decrease of HOMO–LUMO gap. The same tendencies also happen to the Tt-PA and Tc-PA molecules. When EF increases from zero to 2.57 · 109 V/m, the HOMO–LUMO gap of Ct-PA is decreased by 0.1, 0.33, 0.78, 1.46, 2.29, 3.22, and 4.21 eV for 4Ct-PA, 6Ct-PA, 8Ct-PA, 10Ct-PA, 12Ct-PA, 14Ct-PA, and 16Ct-PA, respectively. Nearly 42-fold difference has been found between 16Ct-PA and 4Ct-PA. The differences for Tt-PA and Tc-PA are 80 and 50 times. So the HOMO–LUMO gap of Tt-PA shows the stronger sensitivity to chain length increasing than the others. In the most cases of previous studies, the absolute value of the electron tunneling barrier height of a molecular

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20 4-Ct-PA 6-Ct-PA 8-Ct-PA 10-Ct-PA 12-Ct-PA 14-Ct-PA 16-Ct-PA

20 16

4Ct-PA

2

Molecular orbits Energy / eV

Dipole moment / Debye

24

12 8 4 0 0.0

8

5.0x10

9

1.0x10

9

1.5x10

9

2.0x10

9

2.5x10

LUMO

3.0x10

14Ct-PA 16Ct-PA 16Ct-PA

4Ct-PA

5.0x108 1.0x109 1.5x109 2.0x109 2.5x109 3.0x109

Electric field / Vm-1 Fig. 7. EF-dependence of the HOMOs and LUMOs of Ct-PA.

1800 Tt-PA Ct-PA Tc-PA

1600 1400

The value of α

14Ct-PA 12Ct-PA 10Ct-PA 8Ct-PA 6Ct-PA

-6 HOMO

-8 0.0

9

6Ct-PA 8Ct-PA 10Ct-PA 12Ct-PA

0

Electric field strength / Vm-1

In our published paper [26], a HOMO–LUMO gap expression of Tt-PA considering the effects of chain length and electric field has been gotten:

1200 1000

HLG ¼ k 1 =n þ ðHLGÞ1  k 2  n2  ðEFÞ

800 600 400 200 0

17

4

6

8

10

12

14

16

N Fig. 6. (a) EF-dependence of the dipole moments of Ct-PA. (b) Correlation of the first-order derivatives of the dipole moment and the number of double bonds (N) for three isomers of PA.

bridge has been treated as a constant for a wide variety of materials [43,44]. These can be true for some kinds of molecules such as the saturated alkyl chains, because the EFdependence of their HOMO–LUMO gap looks insensible. For short conjugated molecules, 4Tc-PA, 4Ct-PA, and 4TtPA for example, the EF-dependence of HOMO–LUMO gaps are also not considerable. However, as proven in present study, this rule can not be valid for the long conjugated molecular wire, the longer the chain length is, the more pronounced the HOMO–LUMO gap variation is.

2

Fig. 8 illustrates the evolution of HOMO–LUMO gap for the series of PA as functions of EF (Fig. 8a) and chain length (Fig. 8b) from which the constants k1, k2 and (HLG)1 can be received. We find that the HOMO–LUMO gap of the other two isomers of PA: Ct-PA and Tc-PA also can be expressed by this formula although the constants k1, k2, and (HLG)1 are different. Comparing the HOMO– LUMO gap of three different isomers we also find whether there is electric field or not the value of them always follow this order: Tt-PA < Ct-PA < Tc-PA. Because the larger the HOMO–LUMO gap is, the more stable the molecule is, and therefore the harder it is to rearrange its electron density under the presence of an external EF. So we predict the conductivity of three molecular wires consisting of three PA’s isomers which have same repeated units should follow this order: Tt-PA > Ct-PA > Tc-PA. Furthermore the molecules derived by the structural modification basing on the Tt-PA’s skeleton should also have better conductivity than the other two. Another note should be pointed is that the trends of HLG variation is similar with the double bond discussed in the geometric structure section, but the effort to find a more quantitative correlation between the

Table 1 The dipole moments of three PA models with different chain lengths under various electric fields (the unit is V/m) PA

4-Tt-PA 10-Tt-PA 16-Tt-PA 4-Ct-PA 10-Ct-PA 16-Ct-PA 4-Tc-PA 10-Tc-PA 16-Tc-PA

EF 0

0.51 · 109

1.03 · 109

1.44 · 109

1.80 · 109

2.06 · 109

2.32 · 109

2.57 · 109

0 0 0 0 0 0 0.05 0.06 0.01

0.60 2.59 4.84 0.57 2.33 4.42 0.39 1.40 2.52

1.20 5.18 9.87 1.14 4.68 8.93 0.78 2.82 5.08

1.68 7.31 14.08 1.60 6.59 12.65 1.09 3.99 7.05

2.10 9.25 18.12 2.00 8.30 16.07 1.37 5.05 9.19

2.40 10.70 21.38 2.29 9.54 18.63 1.57 5.84 10.67

2.71 12.23 25.18 2.58 10.84 21.35 1.77 6.66 12.24

3.02 13.85 30.14 2.87 12.16 24.28 1.97 7.51 13.85

18

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20 9.6

8-Tt-PA 8-Ct-PA 8-Tc-PA

9.4

LUMO-HOMO gap / eV

9.2 9.0 8.8 8.6 8.4 8.2 8.0 7.8 7.6 7.4 0

1x1018 2x1018 3x1018 4x1018 5x1018 6x1018 7x1018

(Electric field strength)2 / (V2 m-2) 11.0

LUMO-HOMO gap / eV

10.5 10.0 9.5 9.0 8.5 8.0

Tt-PA Ct-PA Tc-PA

7.5 0.05

0.10

0.15

0.20

0.25

1/N

Changes in the spatial distribution of molecular orbitals, especially the frontier molecular orbitals (HOMO and LUMO), are excellent indicators of many molecular properties [15]. Without knowing the spatial distribution of LUMO and HOMO, we are unable to understand, at least intuitively, various EF-correlated molecular electrical properties. As representative examples, the spatial distribution of the HOMOs and LUMOs of 16Tt-PA, 16Ct-PA, and 16Tc-PA is illustrated in Table 2. At zero-EF, both LUMOs and HOMOs are delocalized over the whole molecular backbone symmetrically. However, with the increase of EF, LUMOs and HOMOs shift from fully delocalized to partially localized configuration and separate to positive potential and negative potential, respectively. This feature also exhibits great chain length dependence, showing the longer the chain length is, the more obvious the shifts of the spatial distribution of LUMO and HOMO are. As is known, if the frontier molecular orbitals are delocalized over the molecule, it can be assumed to have high molecular admittance (LUMO) or high electronic emission to the electrode (HOMO) and therefore can facilitate electronic transportation. Detailed analyses of these features are very instructive for understanding not only the conductance of the molecular wire, but also the photoemission that depends on the vertical electron transmission and the injections of either hole or electron in the light emitting diodes (LEDs) in the existence of the external EF. Moreover, this EFdependent spatial distribution may also provide us a new avenue to tune the molecular electrical properties.

Fig. 8. (a) HOMO–LUMO gaps as functions of square of EF for 8-PA. (b) HOMO–LUMO gaps as functions of the reciprocal of the number of the double bonds (1/N) at zero-EF.

4. Conclusion

variations of these two types of quantities with the electric field has not succeeded. We will keep eyes on this issue in our further research.

In summary, we have performed the theoretical investigation on the geometric and electronic structures of PA molecular wires at ab initio HF level by considering the interaction from a uniform external EF. It demonstrates that both the geometry and electronic structures of the

Table 2 EF-dependence of the spatial distributions of HOMO and LUMO for 16-PAs

Y. Ye et al. / Journal of Molecular Structure: THEOCHEM 822 (2007) 12–20

PA are very sensitive to the external EF. The variations of several properties are shown to be linear in the square of the electric field. This perhaps is related to the fact that the permanent dipole moment is zero and that the first non-zero term in the field expansion is second-order in the field and proportional to the polarizability. One of the three isomers, Tt-PA, bends down for an arc with a slight degree and Tc-PA becomes more planar. In particular, the external EF decreases HOMO–LUMO gap and increases the conjugation and the dipole moment. The spatial distributions of frontier molecular orbitals change from the fully delocalized form to the partly localized with the increase of the external EF. Furthermore, chain length dependence of all these properties is remarkable. The three isomers of PA show different variation to the interaction of electric field that is for their different bond structures. The molecules derived by the structural modification basing on the TtPA’s skeleton show the more potential to be the molecular wires. The evidences provided in present study also remind us that the device formed by the soft molecular materials can be greatly influenced by the electric field or others. Some experience or rules obtained in the silicon-based electronics are questionable for the molecular electronics. Acknowledgements The authors thank The National Natural Science Foundation of China (NSFC) (Nos. 20503012 and 20435010) and Natural Science Foundation of Jiangsu (BK2005413) for financial supports. Mr. Y. Ye thanks Mrs. Danmin. Ye for the help in preparation of the manuscript. References [1] (a) L.A. Bumm, J.J. Arnold, M.T. Cygan, T.D. Dunbar, T.P. Burgin, L. Jones II., D.L. Allara, J.M. Tour, P.S. Weiss, Science 271 (1996) 1705; (b) M.T. Cygan, T.D. Dunbar, J.J. Arnold, L.A. Bumm, N.F. Shedlock, T.P. Burgin, L. Jones II., D.L. Allara, J.M. Tour, P.S. Weiss, J. Am. Chem. Soc. 120 (1998) 2721; (c) S. Jalili, H. Rafii-Tabar, Phys. Rev. B 71 (2005) 165410. [2] (a) R. McCreery, J. Dieringer, A.O. Solak, B. Snyder, A.M. Nowak, W.R. McGovern, S. DuVall, J. Am. Chem. Soc. 125 (2003) 10748; (b) F. Chen, J. He, C. Nuckolls, T. Roberts, J.E. Klare, S. Lindsay, Nano Lett. 5 (2005) 503. [3] (a) A. Dhirani, P.-H. Lin, P. Guyot-Sionnest, R.W. Zehner, L.R. Sita, J. Chem. Phys. 106 (1997) 5249; (b) M.-K. Ng, D.-C. Lee, L. Yu, J. Am. Chem. Soc. (Commun.) 124 (2002) 11862; (c) A. Troisi, M.A. Ratner, Nano Lett. 4 (2004) 591; (d) J. Zhao, J.J. Davis, Colloids Surf. B Biointerfaces 40 (2005) 189. [4] (a) J. Chen, M.A. Reed, A.M. Rawlett, J.M. Tour, Science 286 (1999) 1550; (b) Y. Karzazi, J. Cornil, J.L. Bre´das, J. Am. Chem. Soc. 123 (2001) 10076. [5] (a) C. Joachim, J.K. Gimzewski, A. Aviram, Nature (Lond.) 408 (2000) 541; (b) M.A. Reed, J. Chen, A.M. Rawlett, D.W. Price, J.M. Tour, Appl. Phys. Lett. 78 (2001) 3735. [6] D.B. Tanner, G.L. Doll, A.M. Rao, P.C. Eklund, G.A. Arbuckle, A.G. MacDiarmid, Synth. Met. 141 (2004) 75.

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