ARTICLE

Density functional theory study of electric field effects on theisomerization of a photochromic molecular switch based on1,2-dithienyletheneEhsan Zahedi, Majid Mozaffari, Fereshteh-Sadat Karimi, and Azita Nouri

Abstract: Structural and electronic properties of 1,2-bis(5-methyl-[2,2=-bithiophen]-4-yl)cyclopent-1-ene in closed form and openform under various external electric field with strengths, 0, 10 × 10−4, 20 × 10−4, 30 × 10−4, 40 × 10−4, and 50 × 10−4 a.u., were studiedusing the DFT-B3LYP/6-31G* method. As a positive index, structural parameters, length of the photoisomers, and the electronicspatial extents are almost stable at different external electric fields. The UV-Vis electronic spectrum based on time-dependentdensity functional theory indicated that the HOMO ¡ LUMO transition in the closed form under different electric field strengthsis strongly allowed, whereas is very weak in the open form. Electronic response parameters such as the HOMO−LUMO gap,electric dipole moment, and polarizability showed that electric conductivity of the closed form at different field strengths isgreater than in the open form. Results of electronic density of states show that at high external electric field, the conductivity ofthe open form and closed form will be probably equal and switching behavior cannot be observed. Isomerization of the closedform to the open form at different external electric fields can be considered as exothermic and spontaneous.

Key words: TD-DFT, photoisomerization, DOS, external field effect.

Résumé : Les propriétés électroniques et structurales du 1,2-bis(5-methyl-[2,2=-bithiophen]-4-yl)cyclopent-1-ene, sous ses formesouverte et fermée, lorsque celui-ci est soumis a un champ électrique externe variable de force égale a 0, 10 × 10−4, 20 × 10−4, 30 ×10−4, 40 × 10−4 et 50 × 10−4 u.a., ont été étudiées a l’aide de la méthode DFT-B3LYP/6-31G*. Un signe positif est que les paramètresstructuraux, la longueur des photoisomères et les extensions spatiales des électrons sont quasiment stables lorsque le composéest soumis a des champs électriques de forces différentes. Le spectre électronique UV-Vis, combiné a la théorie de la fonctionnellede la densité dépendante du temps, a indiqué que la transition HOMO ¡ LUMO est fortement permise lorsque le composé,soumis a des champs électriques de forces différentes, est sous sa forme fermée tandis qu’elle est très faiblement permise lorsquece même composé est sous sa forme ouverte. Les paramètres liés au comportement des électrons, tels que l’écart HOMO−LUMO(HLG), le moment dipolaire électrique et la polarisabilité ont montré que la conductivité électrique de la forme fermée ducomposé soumis a des champs électriques de forces différentes est plus grande que celle de sa forme ouverte. Les résultats ducalcul de la densité des états électroniques montrent que, lorsque le champ électrique externe est élevé, les conductivités desformes ouverte et fermée soumises sont susceptibles d’être égales et le phénomène de permutation ne peut pas être observé. Laréaction d’isomérisation transformant la forme fermée en forme ouverte, lorsque le composé est soumis a différents champsélectrique externes, peut être considérée comme exothermique et spontanée. [Traduit par la Rédaction]

Mots-clés : TD-DFT, photoisomérisation, DOS, effet de champ externe.

IntroductionMolecular-scale electronics is a field of nanotechnology that

uses single molecules, or nanoscale collections of single mole-cules, as electronic devices. This is conceptually different fromconventional solid-state semiconductor electronics and allows en-gineering of organic molecules with specific special physical andelectronic properties.1–4 Molecular electronics systems can playthe role of wires, switches, diodes, Zener diodes, capacitors, field-effect transistors, thyristors, electrochromic devices, etc.5–8 Aninteresting class of molecular electronics is molecular photo-chromic switches. Conformation and molecular structure of thephotochromic molecular switches can be controlled with UV orvisible light and classified as light-responsive switches.9,10 A pho-tochromic molecular switch is an assembly of two or more (meta)-stable states that can be interconverted reversibly via cis−transphotoisomerization, photocyclization, or the combination of the

two. A useful photochromic molecular switch should have someimportant properties: (1) it should be thermally stable, (2) thegeometry structure, dipole moment, HOMO−LUMO gap, densityof states (DOS), UV-Vis absorption, polarizability, etc., shouldshow significant differences between the states, (3) the statesshould be separately addressable, (4) the amount of the inactiveform should be negligible in comparison with the activating form,and (5) synthesis and purification of the photochromic molecularswitch should be simple.11 There are various classes of photochro-mic molecular switches, but among them, 1,2-dithienylethenederivatives are very important because they have two excellentproperties; firstly, they are fatigue resistant and secondly, varia-tion of their length upon photoconversion is negligible. There-fore, 1,2-dithienylethene derivatives have been studied in muchof the literature.12–23 1,2-Dithienylethene derivatives are P-type(photoisomerization only) dyes that have colored and noncoloredforms. In the 1,2-dithienylethenes, conjugated units are connected

Received 7 January 2014. Accepted 27 January 2014.

E. Zahedi, M. Mozaffari, and F.-S. Karimi. Chemistry Department, Shahrood Branch, Islamic Azad University, Shahrood, Iran.A. Nouri. Chemistry Department, Shahr-e Qods Branch, Islamic Azad University, Tehran, Iran.Corresponding author: Ehsan Zahedi (e-mails: e_zahedi1357@yahoo.com; e_zahedi@iau-shahrood.ac.ir).

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Can. J. Chem. 92: 317–323 (2014) dx.doi.org/10.1139/cjc-2013-0589 Published at www.nrcresearchpress.com/cjc on 4 February 2014.

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by a switching element. By irradiation of the molecule at specificfrequencies, the covalent bonds in the switching element rear-range, and this molecule can be photoconverted between conju-gated (on state or closed form) and cross-conjugated (off state oropen form) forms. The conjugated and cross-conjugated formsare different in various physical and chemical properties, such astheir absorption, luminescence, refractive indices, oxidation/reduction potentials, chiral properties, magnetic properties, elec-tronic properties, and so on.23 Recently, various theoretical stud-ies have been done on the switching of 1,2-dithienylethenederivatives. Patel et al.24 applied several exchange-correlationfunctionals in combination with time-dependent density func-tional theory (DFT) to find the best theory level to predict themaximum wavelengths in the absorption spectra for diarylethenederivatives in the solvent media. They suggested the TD-M05/6-31G*/PCM//M05-2X/6-31G*/PCM theory level for prediction of thestructural and spectral parameters of diarylethene derivatives.

Furthermore, Patel and co-workers have extensively worked ongeometrical and optical properties,24 thermal stability,25 mecha-nisms of fatigue resistance,26 and photodegradation of diarylethenederivatives. In parallel to above theoretical studies, some researchhas been done on the design and examination of new molecularswitches based on diarylethene.27,28 The effects of the externalelectric fields on the geometric and electronic structure of someconjugated molecules have been investigated extensively29–32 butswitching behavior of diarylethenes at an external field effect isstill an unresolved issue and a fundamental question for re-searchers.

Consequently, a detailed study of the external electric field ef-fect with variable strengths has been done on the 1,2-bis(5-methyl-[2,2=-bithiophen]-4-yl)cyclopent-1-ene (Fig. 1) photochromic switchby performing quantum chemical calculations.

Computational detailsPrevious theoretical studies on molecular switches showed that

the methods including gradient corrections and hybrid function-als for exchange and correlation, such as DFT/B3LYP, togetherwith the nondiffused 6-31G* basis set33,34 is sufficiently accuratefor the present theoretical study.30–32,35 Thus, in the presentstudy, quantum chemical calculations have been performed usingthis methodology. To confirm the nature of the stationary speciesand evaluate the polarizability and thermodynamic functions, fre-quency calculations were carried out at the same level of theory.To predict the UV-Vis spectrum of the studied photochromic mo-lecular switch, excited state calculations using the time-dependentDFT (TD-DFT) calculation36,37 were done using the “IOP(9/40=2)”keyword to output information on smaller contributions to eachelectronic transition. The static electric field was applied in thepositive X direction (Fig. 1). The numerical values of the appliedfield intensities are 10 × 10−4, 20 × 10−4, 30 × 10−4, 40 × 10−4, and 50 ×10−4 a.u. (1 a.u. = 514.224 V/nm). Under a specific field strength (E),the voltage difference (V) applied on the two ends of the switchdepends on the length (l) of the switch: V = El.30 For all quantumchemical computations, the Gaussian 03 program package hasbeen used.38

Results and discussionOptimized values of bond lengths, bond angles, and dihedral

angles at different external electric fields referenced to the corre-sponding values at zero field (E = 0) are tabulated in Tables 1–6 ofthe supplementary data (see “Supplementary material” section).The switching of the closed form to the open form leads to thecleavage of the C5–C17 bond and change in the nature of C–C bondsin the switching element. Due to the switching of the closed form,the C4–C5, C7–C8, and C12–C17 bonds change from single to double;therefore, C4–C5, C7–C8, and C12–C17 bonds are shortened from1.540, 1.448, and 1.541 Å in the closed form to 1.381, 1.355, and

1.381 Å in the open form, respectively. On the other hand, as aresult of switching, C4–C7 and C8–C12 bonds change from doubleto single. Consequently, C4–C7 and C8–C12 bonds are elongatedfrom 1.364 Å to 1.475 and 1.473 Å, respectively. Cleavage of theC5–C17 bond and opening of the ring leads to significant changesin the D5,4,7,8, D4,7,8,12, and D7,8,12,17 dihedral angles. These molec-ular torsions may effectively block the molecular conjugation (seeFig. 1 of the supplementary data), separate the whole moleculeinto two separate � systems, and reduce the conductivity of themolecule.

As can be seen from Tables 1–6 of the supplementary data,geometric parameters of the studied molecular switch are notchanged significantly under external electric field. The largestchanges in the bond length are observed at the field strength of50 × 10−4 a.u. for C7–C8 (−0.008 Å) and C26–C27 (+0.003 Å) in theclosed form and open form, respectively. Changes in the bondangles in all field strengths compared with zero field are negligi-ble and lower than ±0.4°. The largest changes in the dihedralangles are observed at the field strength of 40 × 10−4 a.u. forD16,15,18,20 (+2.8°) and D14,15,18,20 (−6.1°) in the closed form and openform, respectively. Length of the molecular switch (l) and elec-tronic spatial extent (ESE) are other geometric parameters thatreflect the response of the molecular switch to the external elec-tric field. The ESE is a single number that attempts to describe thesize of a molecule and computed as the expectation value of elec-tron density times the distance from the center of mass of a mol-ecule.39 The l and ESE of the studied photochromic molecularswitch with the criteria of 0.001 electrons/bohr3 are reported inTable 1. The overall changes of l and ESE at different external fieldstrengths with respect to zero field are less than 0.1% and 0.5% forthe closed form and open form, respectively. This resistanceagainst the structural changes is a positive index because whenthe molecule is inserted between two electrodes, the mechanicalstress is minimal.

Electronic spectra of the studied photochromic molecular switchwere predicted using the TD-DFT formalism. TD-DFT is a quantummechanical method to investigate the excited state proprieties ofmany-body systems. Absorption wavelengths with the maximaloscillator strength and major contributors (>20%) of excitationsare tabulated in Table 2 and the visualized molecular orbitals arepresented in Figs. 1–6 of the supplementary data for the closedform and open form at different external field strengths. Also,absorption spectra for the closed form and open form at differentexternal field strengths are depicted in Fig. 2 by convoluting theelectronic transition information with Gaussian curves of unitheight and full width at half maximum of 2000 cm−1.40 For the closedform at zero external field, the HOMO ¡ LUMO transition isstrongly allowed and a band appeared at 602.7 nm. At higherexternal fields, this band shifted to the larger wavelengths. One ofthe possible explanations is destabilization of the HOMO and sta-bilization of the LUMO under external fields (see Table 3), whichleads to the red spectra shift and intensity enhancement. This isdue to an increase in the conjugation property of the closed form.The band maxima and band intensity increase with increasingexternal electric field and the strongest red shift (about 64.9 nm)appears at 50 × 10−4 a.u. The �max values indicate that the closedform at the 0, 10 × 10−4, 20 × 10−4, and 30 × 10−4 a.u. external electricfields is orange and at the 40 × 10−4, 50 × 10−4 a.u. external electricfield is red. The nature of �max shows that in the closed form, theoptical gap and conduction gap coincide. Figures 1–6 of the sup-plementary data show that the polarization of HOMO and LUMOof the closed form at different external electric fields is negligible.Consequently, the nature of electronic transition in the absenceand presence of an external electric field is similar and electronictransition with the lowest excitation energy is favored. In the caseof the open form, the HOMO ¡ LUMO transition is very weak andthe band maxima at zero external field occur at 313.4 nm throughthe H − 1¡ L + 1 transition, but at 10–50 × 10−4 a.u. external electric

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fields, other transitions appear. The adsorption maximum shiftedto other wavelengths and the strongest shift is a red shift that isabout 16 nm at 20 × 10−4 a.u. The �max values indicate that the openform at zero electric field and under electric fields is colorless.Consequently, based on the nature of �max in the open form, theoptical gap and conduction gap do not coincide. Changes in theelectronic spectra, band maxima, and oscillator strength are dueto the reoptimization of the open/closed structures, changes inthe excitation energies, the nature of transition, and the shapesand extent of frontier molecular orbitals. For example, in theopen form at field strength 10 × 10−4 and 20 × 10−4 a.u., delocalized� orbitals of HOMO and LUMO are observable at the left and rightsections of the open isomer, respectively. Therefore, orientationof � orbitals is contradictory and electronic transition betweenHOMO and LUMO is improbable. In this condition, two electronictransitions are favored from the shapes and extent of the frontiermolecular orbital viewpoint, HOMO ¡ LUMO + 1 and HOMO − 1 ¡LUMO. The excitation energy of HOMO ¡ LUMO + 1 at fieldstrength 10 × 10−4 a.u. and of HOMO − 1 ¡ LUMO at field strength20 × 10−4 a.u. are lower than the other. Consequently, electrontransition of HOMO ¡ LUMO + 1 at field strength 10 × 10−4 a.u. andof HOMO − 1 ¡ LUMO at field strength 20 × 10−4 a.u.occur. Otherelectronic transitions at different external electric fields can bejustified in this manner. Polarization of HOMO and LUMO of theopen form at different external electric fields is clear (Figs. 1–6 ofthe supplementary data).

Energy levels of the frontier molecular orbitals, includingHOMO and LUMO, and HOMO−LUMO gap (HLG = ELUMO − EHOMO)

are important parameters in the determination of molecular elec-trical transport properties. In addition, variation of the frontiermolecular orbital energy levels with the static external electricfield is a valuable viewpoint to study the electron conductivity ofthe molecular-scale electronic device in nanocircuits.

Consideration of only the HOMO and LUMO may not yield arealistic description of the frontier orbitals because in the bound-ary region, neighboring orbitals may show quasi-degenerate en-ergy levels. For this reason, DOS values,40 in terms of Mullikenpopulation analysis, were calculated and created by convolutingthe molecular orbital information with Gaussian curves of unitheight and full width at half maximum of 0.3 eV. DOS analysis canprovide basic information on the effects of the external electricfield on the electronic properties of the studied photochromicmolecular switch. In addition, the conductivity and energy gapalteration of studied photochromic molecular switch can be in-vestigated from the viewpoint of DOS. Values of the seven frontiermolecular orbital energies and the electronic DOS spectra at var-ious electric field strengths are shown in Table 3 and Fig. 3, re-spectively. In the studied photochromic molecular switch, theHLG value increases in going from the closed form to the openform. In fact, the gap between HOMO and LUMO in the closedform is smaller than in the open form; consequently, electricalconductivity of the closed form is greater than that of the openform. The reported data in Table 3 illustrate that for the closedform, the values of EHOMO increase gradually from −4.41 to −4.33 eVbut the values of ELUMO decrease gradually from −2.12 to −2.28 eVfrom zero field strength to 50 × 10−4 a.u., respectively. Similarly,for the open form, the values of EHOMO increase gradually from−5.18 to −4.57 eV and the values of ELUMO decrease gradually from−1.18 to −2.01 eV from zero field strength to 50 × 10−4 a.u., respec-tively. Therefore, HLG values decrease from 2.29 to 2.05 eV for theclosed form and similarly from 4.00 to 2.56 eV for the open form.This trend shows that the sensitivity of frontier molecular orbitalenergies, especially HOMO and LUMO, of the open form to theexternal electric field is greater than of the closed form. The gen-eral shifts in the frontier molecular orbital energy levels can berelated to the polarization effects of the electric fields. Calculatedvalues of the Fermi level energies (midway between HOMO andLUMO energy levels30) decrease with increasing electric fieldstrength. The behavior of electrons near the Fermi level is a criti-cal parameter in determining the electrical behavior of materials.Figure 3 shows that the electronic DOS values near the Fermi level

Fig. 1. Numbered molecular structures of 1,2-bis(5-methyl-[2,2=-bithiophen]-4-yl)cyclopent-1-ene in the closed form (conjugated) and open form(cross-conjugated). The frame of the axes is given to show the direction of the molecule.

Table 1. Optimized length (l) and electronic spatial extent (ESE) of theclosed form and open form of the studied photochromic molecularswitch at various external field strengths.

Closed form Open form

Fieldstrength (a.u.) l (Å) ESE (a�

2) l (Å) ESE (a�2)

0 16.26 15894.5 16.67 17342.210×10−4 16.26 15895.1 16.67 17347.720×10−4 16.26 15897.0 16.68 17366.230×10−4 16.27 15900.3 16.70 17397.140×10−4 16.27 15904.9 16.72 17441.350×10−4 16.27 15909.9 16.62 17420.1

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for the closed form and open form are different. It is clearly seenthat the conductivity of the closed form is greater than that of theopen form. From DOS results, an important point can be ob-served. With an increase in the external electric field, electroniclevels of the open form in the valence band and conduction band(near the Fermi level) come closer to the electronic levels of theclosed form. Therefore, at higher external field, conductivity ofthe open form and closed form will be equal and switching behav-ior cannot be observed in all probability.

The size and direction of the electric dipole moment vectorsand values of the electric polarizability tensor elements charac-terize the dependence of a molecule on an external electric field.

The calculated values of the size and components of the electricdipole moment vectors and diagonal components and isotropicpart of the electric polarizability tensor elements at different elec-tric field strengths are listed in Table 4.

Under the applied external electric field, the electric charges oforganic molecules with extended � systems are easily changed,and consequently, electric dipole moments can be changed. It canbe seen from Table 4 that �y and �z are almost steady under anexternal electric field, whereas �x increases from 0.0 Debye at zeroelectric field to −10.0 and −6.9 Debye at a field strength of 50 ×10−4 a.u. for the closed form and open form, respectively. Also,values of �t increase from 0.0 and 1.3 Debye at zero electric field to

Table 2. Oscillator strength and major contributors of absorption maxima (�max) in the closed form andopen form of the studied photochromic molecular switch at various external field strengths.

Closed form Open form

Fieldstrength (a.u.) �max (nm)a

Majorcontributors (>20%) �max (nm)a

Majorcontributors (>20%)

0 602.7 (0.531) H ¡ L (74%) 313.4 (0.751) H − 1 ¡ L + 1 (77%)10×10−4 605.7 (0.532) H ¡ L (74%) 325.9 (0.499) H ¡ L + 1 (68%)20×10−4 613.7 (0.538) H ¡ L (74%) 329.4 (0.365) H − 1 ¡ L (76%)30×10−4 625.6 (0.550) H ¡ L (73%) 318.0 (0.802) H ¡ L + 2 (36%)

H ¡ L + 1 (33%)40×10−4 640.6 (0.568) H ¡ L (72%) 320.2 (0.757) H ¡ L + 2 (41%)

H − 3 ¡ L (22%)50×10−4 657.6 (0.591) H ¡ L (71%) 324.7 (0.765) H − 3 ¡ L (51%)

H ¡ L + 2 (28%)aNumbers in the parentheses are the oscillator strengths.

Fig. 2. Absorption spectra of the studied photochromic molecular switch in the closed form (red) and the open form (blue) at different fieldstrengths. Color in the online version only.

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10.1 and 6.9 Debye at a field strength of 50 × 10−4 a.u. for the closedform and open form, respectively. It is obvious that the dipolemoments for the closed form are higher than for the open form atvarious electric field strengths, meaning that the conductivity ofthe closed form is higher than that of the open form.

Electric polarizability is the relative tendency of a charge distri-bution, like the electron density of an atom or molecule, to bedistorted from its normal shape in the presence of an infinitesi-mal electric field.41,42 Table 4 shows that �yy and �zz for the openform and closed form do not differ remarkably and are almoststeady under an external electric field, with the exception of the

open form at 50 × 10−4 a.u. On the other hand, �xx for the closedform and open form is much greater than other components andis very sensitive to the external electric field. It is noteworthy that�xx is the primary characterizing component of the polarizabilitytensors. Table 4 shows that �xx for the closed form is larger thanfor open form and increases with increasing external electricfield. Therefore, conductivity of the closed form is higher thanthat of the open form and conductivity of the studied photochro-mic switch increases with increasing external electric field.

Finally, the thermodynamic functions Gibbs free energy, en-thalpy, and equilibrium constant corresponding to the isomeriza-

Table 3. Values of seven frontier molecular orbital energies, HLG, and Fermi level (all in eV) of the closed form and open formof the studied photochromic molecular switch at various external field strengths.

Fieldstrength (a.u.) HOMO − 3 HOMO − 2 HOMO − 1 HOMO LUMO LUMO + 1 LUMO + 2 HLG EF

0 Closed −6.37 −6.32 −5.69 −4.41 −2.12 −1.07 −0.07 2.29 −3.26Open −6.73 −6.02 −5.45 −5.18 −1.18 −1.12 −0.42 4.00 −3.18

10×10−4 Closed −6.45 −6.24 −5.69 −4.40 −2.13 −1.07 −0.07 2.27 −3.26Open −6.60 −6.01 −5.51 −5.11 −1.32 −0.99 −0.42 3.79 −3.21

20×10−4 Closed −6.54 −6.15 −5.69 −4.39 −2.15 −1.08 −0.07 2.24 −3.27Open −6.39 −6.02 −5.59 −4.99 −1.48 −0.85 −0.44 3.51 −3.23

30×10−4 Closed −6.48 −6.06 −5.68 −4.38 −2.19 −1.09 −0.08 2.19 −3.28Open −6.18 −6.04 −5.64 −4.84 −1.65 −0.73 −0.47 3.19 −3.24

40×10−4 Closed −6.35 −5.99 −5.66 −4.35 −2.23 −1.11 −0.09 2.12 −3.29Open −6.12 −5.93 −5.66 −4.69 −1.83 −0.66 −0.46 2.86 −3.26

50×10−4 Closed −6.22 −5.94 −5.63 −4.33 −2.28 −1.13 −0.15 2.05 −3.30Open −6.18 −5.74 −5.61 −4.57 −2.01 −0.68 −0.42 2.56 −3.29

Fig. 3. Electronic density of states of the studied photochromic molecular switch in the closed form (red) and open form (blue) at differentfield strengths. Color in the online version only.

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tion of the closed form to the open form were calculated atdifferent electric field strengths and tabulated in Table 5. Theresults show that the photoisomerization at zero electric field andunder an external electric field is exothermic and spontaneous.Additionally, with increasing external electric field, the exother-micity of the isomerization and thermodynamic stability of theopen form decrease.

ConclusionsIn this paper, the DFT-B3LYP/6-31G* method has been used to

study 1,2-bis(5-methyl-[2,2=-bithiophen]-4-yl)cyclopent-1-ene. Thissystem is a bistable photochromic molecular switch that can showa remarkable switching property via making/breaking of theC−C bond. By breaking of the C−C bond, the structural form of theswitching element is changed and the � conjugated system will beseparated into two independent fragments. Therefore, molecularconjugation is blocked and finally electrical conductivity of themolecule is reduced. Structural analysis showed that ESE andlength of the studied photochromic molecular switch in theclosed form and open form do not change significantly and struc-turally are stable under different electric field strengths. Analysisof the UV-Vis electronic spectrum indicated that the HOMO ¡

LUMO transition in the closed form under different electric fieldstrengths is strongly allowed and band maxima occur at the col-ored wavelengths between 602.7 and 657.6 nm, whereas theHOMO¡ LUMO transition in the open form is very weak and bandmaxima occur at near-UV wavelengths. The nature of transitions,excitation of energies, and shapes of the frontier molecular orbit-als are effective factors on the electronic spectra, band maxima,and oscillator strength of the studied photochromic molecularswitch. From HLG values, it is concluded that the conductivity ofthe closed form at different electric field strengths is greater thanthat of the open form. On the other hand, numerical HLG valuesfor the closed form and open form decrease with increasing fieldstrengths. DOS results showed that in the high external field, the

conductivity of the open form and closed form will be equal andswitching behavior can not be observed in all probability. Otherelectronic response parameters such as electric dipole momentand polarizability show that �x and �xx are key components andthe conductivity of the closed form is greater than that of the openform at various external electric fields. Finally, thermodynamicfunctions indicate that isomerization of the closed form to theopen form at different external electric fields is exothermic andspontaneous and thermodynamic stability of the open form de-creases with increasing external electric field strength.

Supplementary materialSupplementary material is available with the article through

the journal Web site at http://nrcresearchpress.com/doi/suppl/10.1139/cjc-2013-0589.

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Table 4. Values of the electric dipole moment (�t), components of the electric dipole moment (�x, �y, and �z)(in Debye), and diagonal elements (�xx, �yy, and �zz) and isotropic part (�iso) of the electric polarizability tensor(in bohr3) for the closed form and open form of the studied photochromic molecular switch at various externalfield strengths.

Fieldstrength (a.u.) �x �y �z �t �xx �yy �zz �iso

0 Closed 0.0 1.3 0.0 1.3 722.5 361.6 152.3 412.1Open 0.0 0.0 0.0 0.0 515.6 299.2 186.5 333.8

10×10−4 Closed −1.8 1.3 0.0 2.2 726.5 361.6 152.3 413.5Open −1.3 0.0 0.1 1.3 516.2 299.1 186.5 334.0

20×10−4 Closed −3.8 1.3 0.0 4.0 738.2 361.8 152.3 417.4Open −2.6 0.0 0.2 2.6 518.3 298.9 186.6 334.6

30×10−4 Closed −5.7 1.3 0.0 5.9 757.7 362.1 152.2 424.0Open −4.0 0.0 0.3 4.0 521.8 298.4 186.7 335.7

40×10−4 Closed −7.8 1.3 0.0 7.9 785.1 362.3 152.2 433.2Open −5.4 0.0 0.4 5.4 527.2 297.6 187.0 337.3

50×10−4 Closed −10.0 1.3 0.0 10.1 818.8 362.6 152.2 444.5Open −6.9 0.0 0.1 6.9 529.0 281.2 204.3 338.2

Table 5. Thermodynamic functions Gibbs free energy (�G), enthalpy (�H), and equilibrium constant (K) corre-sponding to the photoisomerization of the closed form to the open form of the studied photochromic molec-ular switch at various external field strengths.

Field strength (a.u.)

Thermodynamicproperty 0 10×10−4 20×10−4 30×10−4 40×10−4 50×10−4

�G (kcal/mol) −12.83 −12.76 −12.55 −12.20 −11.77 −10.68�H (kcal/mol) −8.92 −8.85 −8.64 −8.26 −7.72 −7.12K 2.5×109 2.3×109 1.6×109 1.0×109 5.0×108 7.1×107

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