Charge Density Analysis and Transport Properties of TTF Based Molecular Nanowires: A DFT Approach

Thepresent study has been performed to understand the charge density distribution and the electrical characteristics of Au and thiol substituted tetrathiafulvalene (TTF) based molecular nanowire. A quantum chemical calculation has been carried out using DFT method (B3LYP)with the LANL2DZbasis set under various applied electric fields (EFs).Thebond topological analysis characterizes the terminal Au–S and S–C bonds as well as all the bonds of central TTF unit of the molecule. The variation of electron density and Laplacian of electron density at the bond critical point of bonds for zero and different applied fields reveal the electron density distribution of the molecule. The molecular conformation, the variation of atomic charges and energy density distribution of the molecule have been analyzed for the various levels of applied EFs. The HOMO-LUMO gap calculated from quantum chemical calculations has been compared with the value calculated from the density of states. The variation of dipole moment due to the polarization effect and the I-V characteristics of the molecule for the various applied EFs have been well discussed.


Introduction
Molecular scale electronics is known as single molecule electronics and it is a branch of nanotechnology.Mostly, it deals with single molecules or nanoscale collections of single molecules, which can be used as basic electronic components for fabricating molecular level devices.The ultimate aim of molecular electronics is miniaturization of electrical circuits.This can be done by using single molecules, which constitute the smallest stable structures [1][2][3][4].In the recent years, large efforts have been made to understand structural and electron transport properties of such molecules [5][6][7], which are currently being used in electronics as interconnects, diodes, switches, rectifiers, transistors, nonlinear components, dielectrics, and memories [8][9][10][11].Generally, higher conductivities originate from highly conjugated molecular systems [12][13][14].Tetrathiafulvalene (TTF) is a heterocyclic organosulfur compound which has distinctive electrical properties; notably, it exhibits a high anisotropic electrical conductivity.In addition, TTF is a well-known -electron donor in the field of organic metals [15][16][17].Studies on this compound contribute to the development of molecular electronics.Bulk TTF itself has unremarkable electrical properties.Distinctive properties are, however, associated with salts of its oxidized derivatives [15][16][17][18][19].The high electrical conductivity of TTF salts can be attributed to its high symmetry, which promotes charge delocalization, thereby minimizing columbic repulsions.So far, several scientific reports have discussed the TTF and its derivatives [20][21][22].However, this is the first report exploring the charge density distribution, bond topological, electrostatic, and transport properties of Au and thiol substituted TTF based molecule (Figure 1) under zero bias, and various levels of external applied EFs.Numerous theoretical ideas have been used to understand the conductivity of molecular wires (onedimensional systems).The charge density distribution and electrostatic properties along with the structural information give an accurate outline to design highly conducting new molecules.The wave function obtained from high level ab initio/DFT calculations coupled with Bader's Quantum theory of atoms in molecules (AIM) [23,24] makes it possible to determine the above properties for zero bias and various applied EFs.

Computational Details
Understanding the effect of applied electric field on the structural and electronic properties of the Au and thiol substituted TTF based molecule has been analyzed by optimizing it for the zero and applied fields for both directions [five biasing steps ±0.04, ±0.08, ±0.12, ±0.16 and ±0.20 V Å −1 ].All calculations in this study have been carried out using density functional theory (DFT) [23][24][25][26][27]. Gaussian03 program [28] is used throughout all computations.Here, we have used LANL2DZ basis set [29] for whole DFT calculation with B3LYP hybrid function to obtain effective core potential and the detailed description of the effect of heavy metal atoms in the molecule [29][30][31].All geometric optimizations have been performed via Berny algorithm in redundant internal coordinates.The self-consistency of noninteractive wave function has been performed with a requested convergence on the density matrix of 10 −8 and 10 −6 for the RMS and maximum density matrix error between the iterations [32].The wave function obtained from each calculation has been analyzed with the theory of "atoms in molecules" (AIM) and the atomic property has been calculated using AIMPAC program [33].
By using EXT94b routine incorporated to the AIMPAC software, the electron density  bcp (), Laplacian of electron density ∇ 2  bcp (), and bond ellipticity  have been calculated for various applied fields.The programs wfn2plots and DENPROP have been used to plot the deformation and the Laplacian of electron density maps.The electrostatic potential of the molecule has been plotted with Gview [34] to visualize the isosurface of positive and negative ESP regions of the molecule.The density of states (DOS) at various EFs has been determined by using GuassSum program [35].For the various applied electric fields (), the bias voltage () across the molecule of length  has been calculated from the expression  = .Further, using Ohm's law ( = /), the current () flows through the wire has been calculated for each biasing step.

Structural Aspects.
The geometric parameters, especially bond lengths, are important parameters for adjusting the electrical properties of molecular wires.Also, the average difference between the adjacent single and double bonds known as the bond length alternation along the backbone of a conjugated system plays a vital role for tuning the transport properties.Therefore, a detailed study of bond length variation under the EF interaction is instructive for understanding the relationship between molecular structure and property.The optimized geometry of Au and S substituted TTF based molecular wire for the zero bias and the maximum applied EF (0.20) is illustrated in Table 6.(Optimized geometries for various EFs are given in supplementary Figure S1 (see Figure S1 in Supplementary Material available online at http://dx.doi.org/10.1155/2015/806181)).This molecular wire has two aromatic rings with central TTF group and the Au atoms attached at both ends of the molecule through thiol atoms.The thiol atom forms an excellent link [36] between the conjugated TTF molecule and the Au atom.
For the zero field, the C−C bond distances of two aromatic rings and the C≡C bonds that link the rings in the molecule are ∼1.41 and ∼1.22 Å, respectively.When the field is applied, these distances are slightly modified; however, the EF dependence of bond length evolution is not identical for all the bonds.That is, the maximum observed variation in C−C bonds is 0.009 whereas C≡C bonds are 0.003 Å.Also, in most cases it is found that the C−C single bonds become shorter and the double and triple bonds become longer resulting in higher conjugation, which is pertinent to reported results [37,38].The zero field distance of S−C bonds in the TTF unit is ∼1.83Å; as the field increases, the maximum variation observed is 0.013 Å.Similarly, the applied EF alters the bond distances of terminal S−C bonds, which are found to be unequal on both ends.In the left-end (Lend), the distance increases from 1.838 to 1.842 Å, while in the right-end (R-end), the distance decreases from 1.837 to 1.828 Å; notably, the variation in the R-end is slightly greater than the L-end and the value is ∼0.009Å.Hence, it is found that the S−C bond distances increase in the high potential side while they decrease in low potential side.As the field increases, the distance of Au−S bond in the L-end decreases from 2.401 to 2.388 Å, while in the R-end, the distance increases from 2.401 to 2.463 Å; however, the variations in both ends are unequal.And, for the maximum applied field (0.20 V Å−1 ) the variations at L-and R-ends are 0.013 and 0.038 Å, respectively.This large difference attributes, the applied field lengthening the Au−S bond through by shrinking the S−C bond distance in the wire (Table 1) and these bond distances [S−C and Au−S bonds] are very close to the previously reported values [36,[38][39][40][41].Even though almost all bond distances vary by the application of external field, specifically, the S−C and Au−S bonds have uniform and systematic variation.Hence, we plot the variation of S−C and Au−S bond lengths for different applied EFs with reference to zero fields (Figure 2).The selected values of bond lengths are presented in   that the chemical bonds [42,43] exist in the molecule.We have also found that the interaction between Au and S atoms in Au-S bond of TTF based molecular wire is not a covalent interaction; hence, the Au-S bond is a very weak coordination bond.Also, the positive Laplacian of electron density of Au-S bond (Table 3) shows the existence of closed shell interaction between the S and Au atoms; this confirms the noncovalent interaction of Au-S bonds which is applicable to the reported results [44][45][46].
The zero field electron density [ bcp ()] at the bcp of all aromatic C−C bonds ranges from ∼1.884 to ∼1.949 e Å−3 , whereas for the applied field these values are slightly varied, and the maximum variation is 0.037 e Å−3 .Similarly, the zero field electron density  bcp () of the C−C bonds connecting the two thiophene rings in the TTF unit is ∼2.092 e Å−3 ; as the field increases, this value decreases and the observed maximum electron density variation of the bond is 0.019 e Å−3 .The zero field density of C−H bond is ∼1.8 e Å−3 ; this value is not much altered in the presence of electric field.The S−C bond electron density of thiophene rings for the zero field ranges from ∼0.996 to 1.084 e Å−3 and for the applied field, it decreases; the maximum variation observed is 0.024 e Å−3 .The C≡C bonds exhibit high electron density for the zero bias (2.477 e Å−3 ), and for the applied field, the variation is found to be very small.On comparing the  bcp () values of C−C, C−H, and S−C bonds, the density of S−C bond is notably small.This indicates that the charges of these bonds are moving away from the internuclear axis, which confirms its dominant -bond nature [40].Also, this can be well understood from the Laplacian of electron density of the molecule compared with the Cremer and Kraka's work [42,43].The Au−S bond density at zero field is ∼ 0.52 e Å−3 , whereas for the applied field the density increases to 0.538 e Å−3 in the L-end, but in R-end it decreases to 0.476 e Å−3 ; Although the electron density of Au−S bond is very small, the observed variation (0.055 e Å−3 ) is greater than all other bonds.The effect of electric field in the molecule is not much altered the electron densities of the bond in the molecule.Relatively, the variations are small for the applied field and are found to be very systematic (Supplementary Table S2).The increase or decrease of applied field in the molecule did not make any significant change in the bond charge accumulation of the molecule.
The Laplacian of the electron density [∇ 2  bcp ()] allows to understand the charge concentration or depletion at the bcp [42].It plays significant role in the study of the charge density [47,48].In this work, the Laplacian values for all bonds in the molecule have been calculated to realize whether the charges at the bcp of the bonds are concentrated or depleted when the molecules is exposed to external EFs.The selected Laplacian of electron density for the various applied EFs is shown in Table 3. Table 8 shows the Laplacian of electron density maps for zero and the maximum applied field (0.20 V Å−1 ).For the zero field, the predicted Laplacian of electron density for the aromatic C−C bonds ranges from −17.3 to −18.5 e Å−5 , whereas for the applied field these values become little less negative, indicating the charges of these bonds are slightly depleted (Supplementary Figure S2).Similar trend is found in the C−C bonds, which are connecting the rings in the molecule, in which Laplacian for zero field ranges from −16.3 to −19.9 e Å−5 , whereas for the applied field, the maximum variation observed is 0.314 e Å−5 .The zero field Laplacian of electron density for the C−H bonds is ∼ −20.5 e Å−5 , the high negative value of Laplacian, which indicates the charge concentration, and the applied field slightly alters this charge concentration.The Laplacian for the terminal S−C bonds of L-end and R-end is −4.207 and −4.217 e Å−5 , respectively.As the field increases, the Laplacian value in the L-end decreases to −4.101 e Å−5 and in the R-end, it increases to −4.387 e Å−5 .For the zero field, the Laplacian of Au−S bond is ∼2.95 e Å−5 ; when the field increases, this value slightly increases to 3.409 e Å−5 at the L-end, but at the R-end it decreases to 2.925 e Å−5 .Overall, the Laplacian of electron density distribution in the Au substituted molecular wire (Au−S-molecule-S−Au system) reveals that the applied field depletes the charges at the bcps of C−C bonds, whereas this effect is found little more in the terminal bonds (Supplementary Figure S3); specifically it is high at the R-end.The complete values of Laplacian of electron density for the various applied EFs are shown in supplementary Table S3.

Energy Density.
Bond energy density is the measure of bond strength in a chemical bond.The chemical bond is a fundamental concept, which provides an important basis for rationalizing the structural properties, stability, and reactivity for a host of materials.In addition to the bond critical point properties, the calculated energy density distributions provide important information about the local energy density properties for the bonded interactions [49].Further, the energy density distribution of TTF based molecule is directly related to Laplacian of electron density [40,42,43].When the Laplacian of electron density is positive, the kinetic energy density is dominant, which leads to the depletion of bond charge; if it is negative, the potential energy density dominates, and the accumulation of charge is expected to happen [25,42,43].Also, the kinetic energy density analysis of TTF identifies patterns within its electronic structure, which are linked to familiar concepts of chemical bonding [50].The total energy density in the bonding region (r) is expressed as (r) = (r) + (r), where (r) is the potential energy density and (r) is the local kinetic energy ) Å Position of bonds The small values are due to the nature of bonds.Further, for the applied field, the variation between both types of bonds is found to be opposite.However, the variations of S−C and Au−S bonds are significant and systematic.Figure 3 shows the energy density variations of the molecule.The calculated values of energy density distribution of the terminal bonds of the molecule for zero and various The Chelpg charges of all C-atoms except those which are linked to S atoms possess negative charge and vary with the increase of field.The linker S(1)-atom possesses negative Chelpg charge, which decreases from −0.333 to −0.331 e with increase of field, while the charge of S(2)-atom increases from −0.333 to −0.348 e.As the field increases, the charges of Au atom at L-end slightly increase from 0.175 to 0.183 e, but the same at the R-end almost remains the same (0.177, 0.176 e).For the zero field, the MK charge for all C-atoms is found almost negative, and the H-atoms are positive; when the field increases, the charge of the atoms also found increases.
For the applied field, the MK charges of S-atom at the Lend decrease gradually from −0.302 to −0.293 e, while at the R-end this effect is opposite and increases from −0.303 to −0.310 e.As the field increases, the charge of Au(1) atom increases from 0.156 to 0.165 e, but the same for Au(2) slightly decreases from 0.159 to 0.155 e (Table 5).The differences of charge distribution for zero and various applied EFs are presented in supplementary Table S5.

Molecular Orbital Analysis.
Generally, for any molecular level device, the charge transport characteristics are mainly controlled by the nature of the molecular orbitals.The spatial distribution and the energy level of a molecular orbital (MO) determine its contribution to the conductivity [56,57].The charge transfer through a particular MO gradually decreases as we go away from the Fermi level of the electrode.Further, the MOs, which are fully delocalized, contribute more to conduction channel [58][59][60][61].The frontier molecular orbitals are the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) and the difference between them is known as HOMO-LUMO gap (HLG).Recently, several theoretical studies report the influence of HOMO-LUMO gaps and the spatial distributions of molecular orbitals on the electronic transport through the molecular device [62,63].Further, the charge transport properties of the molecule [64] are determined by the difference of energy between HOMO and LUMO.Hence, it is essential to examine the variations of HLG and molecular orbital energy levels [64][65][66] for the various applied EFs.Table 9 shows the spatial redistribution of molecular orbital of TTF for the zero bias and the maximum applied EF (0.20 V Å−1 ).The applied EFs partially localize the frontier orbitals (HOMO−2, HOMO−1, HOMO, LUMO, LUMO+1, and LUMO+2) of the molecules, which are opposite to each other; this can be well understood from Table 9.
For the applied fields (0-0.20 V Å−1 ), the HLG decreases from 1.486 to 0.218 eV.This variation is also confirmed from the spectrum of density of states (DOS).Figures 4(a) and 4(b) show the DOS of Au substituted molecule, in which the HOMO (green lines) and the LUMO (blue lines) and the HLG are shown.Notably, the presence of gold atoms in the molecule broadens the DOS peaks.Seemingly, the significant decrease of HLG may facilitate large electron conduction [67,68] through the molecule; hence, the Au substituted TTF based molecule can perform as an efficient molecular nanowire.Figure 5 represents the energy levels of the molecule for various applied EFs.

Electrostatic Potential. Molecular electrostatic surface potential (ESP
) is another piece of information which is required to understand the electronic properties of molecules [69,70].Areas of the molecule with specific properties such as electron donation or electron-withdrawing capabilities and their stabilities can be easily evaluated from an ESP map [71]; this information is extremely useful in understanding molecular interactions, which helps to design molecular electronic devices [72,73]  the various applied EFs is shown in Table 10.The Au-S bond regions exhibit high negative ESP, which are the negative charged regions (red) of the molecule, and it explicitly reflects the opposing contributions from the nuclei and the electrons.
For the zero bias, the negative ESP is concentrated around the S-atoms, which are present at either ends of the molecule and also S atoms in the TTF unit.The rest of the molecule carries positive ESP.For the increase of positive field from 0-0.20 V Å−1 , the negative ESP at the L-end of the molecule gradually decreases for each biasing step and it disappears, while the same at the R-end gradually increases and finally spreads around the right edge of the molecule (Table 10); this shows that when the field increases the charges seem to drift from left to right.Similarly, the negative ESP regions are moved from R-to L-end of the molecule when the field is reversed.The ESP map clearly shows the effect of substitution and the applied EFs in molecule.

Molecular Dipole Moment.
When the molecule is subjected to an external EF, the delocalization of -electron of the conjugated organic molecules leads to redistribution of charges of the molecular chain, and consequently, the dipole moment of the molecule changes [38,74,75].Hence, we can roughly estimate the ability of electron transport by simply comparing the dipole moments of the molecule for various applied EFs.The variations of molecular dipole moment for the various applied EFs were analyzed by Kirtman et al. [76] and found a linear character.However, this linearity no longer exists beyond certain applied field and it is unimportant since no molecular electronic device works under such high voltages [77].Here, we have calculated the dipole moment of the molecule for zero bias as well as various applied EFs.The resultant molecular dipole moment () for zero bias is 1.31 D, which increases almost linearly with the increase of field.The molecule becomes highly polarized for the higher field (0.20 V Å−1 ) and the dipole moment becomes 35.9 D. Figure 6 shows the variation of , , and  components of dipole moment (  ,   , and   ) and the resultant molecular H( 6) H( 5) C( 1) C( 6) C( 7) C( 8) C( 4) C( 10) C( 11) C( 12) C( 13) C( 14) C( 16) C( 20) C( 21) C( 22) C( 18) C( 17) C( 15) Au (2) 0.20 S( 4) S( 6) S( 5) H( 10) H( 13) H( 21) H( 6) H( 5) C( 6) C( 7) C( 5) C( 4) C( 10) C( 11)C( 12) C( 13) C( 14) C( 20) C( 21) C( 22) C( 18) C( 17 dipole moment () for various applied EFs, the large variation of -component [68], may be due to the application of field along -direction.
3.8.- Characteristic Curve.As a preliminary approach for calculating the - characteristic of single molecules, a purely ab initio approach was developed [78].This method uses molecular calculations to estimate the - through a molecule.Thus formulating a new prescription, one can obtain current-voltage characteristics via the use of precise quantum chemistry techniques.Here, we have evaluated the - characteristics of the TTF based molecular wire using where   and   are the charge transport efficiency across the left and right contacts,   is the electron transmission through the molecule itself, and (ℎ/2 2 ) = 12.91 KΩ is the quantum of resistance [80][81][82][83].The left and right contacts electron transmission   and   can be neglected since there is no charge injection barrier in the molecule.  can be approximated by the expression where  is the potential barrier width which is equivalent to molecular length and  is the tunneling decay parameter which can be determined by where,  * is the effective mass of electron ( * = 0.16 0 ),  0 is the free electron mass,  is the symmetry parameter of potential profile which is equal to unity for symmetric molecule [80][81][82][83], and  is the potential barrier height for tunneling through the HOMO or the LUMO level.For a particular external applied EF,  is half of the HLG of the molecular wire.Hence, the resistance of the molecular wire has been calculated using expression (1).Further, the bias voltage () has been calculated from the expression  = .Using these parameters, the - characteristics of the TTF based molecule have been studied.Figure 7 illustrates the - characteristics of TTF based molecule for the various applied EFs, which reveals that as the bias voltage increases, the current increases gradually showing the nonlinear behavior of the molecule.Since the molecule is symmetric, the characteristic curve is also almost symmetric for both directions of the applied EFs.

Conclusion
The present quantum chemical study on TTF based molecular wire describes the bond topological parameters and the electrical characteristics for zero and various external applied fields.The bond topological analysis shows the variation of electron density  bcp () and Laplacian of electron density ∇ 2  bcp () for zero bias and the various applied fields of the molecule.Systematic and almost uniform redistribution of charge density as well as energy density have been observed for all bonds of the central TTF unit and terminal bonds of the molecule for various applied EFs.When the field increases, the hybridization of molecular levels broadens the DOS and decreases the HLG.The large decrease of band gap from 1.486 to 0.218 eV, at the high field, is facilitated to have high electrical conductivity.Also, the EF polarizes the molecule; in consequence the dipole moment of the molecule increases from 1.31 to 35.9 D. The - characteristic curve is found very symmetric for both directions of applied EFs; it explicitly shows the nonlinear behavior of TTF based molecule.Further, the significant - characteristic details of the molecule give an idea to tune the molecule for appropriate biasing voltages for the operation of molecular devices.Over all, the terminal groups and the central redox group of TTF unit of the molecular wire are found to be very sensitive to applied EF compared with the molecular region.The structural confirmation, charge density distribution, and electrostatic properties of TTF obtained in the study may support design of several kinds of molecular wires based on TTF and its derivatives.

1 Figure 3 :
Figure 3: Energy density variations of Au and S substituted TTF based molecule for various applied EFs with reference to zero field.

1 Figure 4 :
Figure 4: DOS of Au and S substituted TTF based molecule for (a) zero and (b) maximum applied EF (0.20 V Å−1 ).

Figure 5 :
Figure 5: Energy level diagram of Au and S substituted TTF based molecule for the zero and various applied EFs.

Figure 6 :
Figure 6: Molecular dipole moment of Au and S substituted TTF based molecule for the zero and various applied EFs.

Table 7 :
Deformation density maps of Au and S substituted TTF based molecule for the zero and maximum applied EF 0.20 V Å−1 .Solid lines represent positive contours, dotted lines are negative contours, and dashed lines are zero contours.The contours are drawn at 0.05 e Å−3 intervals.

Table 8 :the
Laplacian of electron density maps of Au and S substituted TTF based molecule for the zero and maximum applied EF 0.20 V Å−1 .The contours are drawn in logarithmic scale, 3.0 × 2  e Å−5 , where  = 2, 4 and 8 × 10  ,  = −2, −1, 0, 1, 2. Solid lines are positive contours and dotted lines are negative contours.Landauer formula [79].The tunneling electric current () has been calculated for various applied electric fields () and the bias voltage () across the molecule of length .The linear conductance () and the resistance () of the electrode-molecule-electrode junctions can be expressed as

Table 9 :Figure 7 :
Figure 7: - Characteristics of Au and S substituted TTF based molecule for various applied EFs.

Table 10 :
Molecular electrostatic potential of Au and S substituted TTF based molecule for the zero and various applied EFs.Blue: positive potential (0.5 e Å−1 ), red: negative potential (−0.04 e Å−1 Table 1 and the complete values of bond lengths are listed in supplementary Table S1.3.2.Charge Density Distribution.The selected bond electron density values of TTF based molecular wire for zero and various levels of applied EF are listed in Table 2. Table 7

Table 2 :
Electron density [23]() (e Å−3 ) values of terminal bonds of Au and S substituted TTF based molecule for zero and various applied EFs (V Å−1 ).displays the deformation density maps of TTF based molecular wire, showing the charge accumulation for zero bias and maximum applied field and the differences.The relation between the topology of electron density and the chemical concepts of molecules can be accurately quantified[23]by using Quantum theory of atoms in molecules (QTAIM).The critical point search in the molecule found a (3, −1) type of bond critical point (bcp) for all bonds, which implies

Table 3 :
Laplacian of electron density ∇ 2  bcp () (e Å−5 ) values of terminal bonds of Au and S substituted TTF based molecule for zero and various applied EFs (V Å−1 ).

Table 4 :
Bond energy density (H Å−3 ) values of terminal bonds of Au and S substituted TTF based molecule for the zero and various applied EFs (V Å−1 ).

Table 5 :
Atomic charges (e) of terminal atoms for the zero and various applied electric fields (first line CHELPG charges, second line MK charges).

Table 6 :
Optimized geometry of Au and S substituted TTF based molecule for the zero and maximum applied EF 0.20 V Å−1 .