All highly deformable materials (soft matter) including polymers, collides and surfactant solutions are studied in liquid-crystal physics and have novel technological applications [ 1,2]. Liquid crystalline behaviors of materials depend on chemical structure and physical properties of structural unit [ 3]. At present theoretical conclusions are available, based on extensive experimental data regarding mesomorphism of low molecular weight mesophases, depending on the structure of molecules, particularly on the nature of terminal groups and linkages [ 4]. This enables to synthesize new compounds with desired liquid crystalline properties. p-Azoxyanisole (PAA) is an organic compound. In a solid state, it appears as a white powder, but when heated it forms a liquid crystal. As one of the first known and most readily prepared liquid crystals, PAA has been played an important role in the development of liquid crystal displays [ 5,6]. Presently, a number of azoxy based liquid crystals are well known. Some of azoxybenzene-based liquid crystals, listed in Table-1, belonging to nematic class are p-azoxyanisole, p-azoxyphenetole, ethyl-p-azoxybenzoate, ethyl-p-azoxycinnamate and n-octyl-p-azoxycinnamate. In our previous work, we have described some behavior of these liquid crystals based on (i) partial atomic charges [ 7], (ii) frontier orbital densities [ 8] and (iii) bond properties viz., bond length, bond order and bond angle [ 9]. In this work, we present geometry and electronic structure of above liquid crystals based on molecular properties: total energy, ionization potential, electron affinity, HOMO energy, LUMO energy, electronegativity, hardness and dipole moment.

The study materials of this work are listed inTable 1. For present study the three dimensional modeling and geometry optimization of all the compounds have been done in DGauss using the DFT B88-PW91 GGA functional with the DZVP basis sets [ 10,11]. The application of DFT has given a new concept to chemical system [ 12]. The DFT based calculations of above parameters were performed with CAChe software and results are tabulated inTable 2 toTable 10.

If p-azoxyanisole is treated as reference compound (RC) then the study shows that replacement of –OCH₃ group of RC by –OC₂H_5, –COOC₂H₅, –CH=CH–COOC₂H₅ and –CH=CH–COOC₈H₁₇ groups formed p-azoxyphenetole, ethyl-p-azoxybenzoate, ethyl-p-azoxycinnamate and n-octyl-p-azoxycinnamate, respectively. Molecular properties provide essential information of a molecule with respect to its physical, chemical and electronic performance. For sake of simplicity the study of above liquid crystals with respect each molecular property is described in different heads as given below.

The structure and stability of a molecule is determined by the total energy E of the molecule [ 13]. Total energy can be partitioned as follows.

where T_n is the kinetic energy of all nuclei, T_e is the kinetic energy of all electrons, V_nn the potential energy of all Coulomb interactions between the nuclei, V_ne the potential energy of Coulomb interactions between the nuclei and the electrons, and V_ee the potential energy of all Coulomb interactions between the electrons. The total energies of the above LCs were evaluated and are reported inTable 2. A reference to theTable table indicates that the total energy of RC is -877.067 hartree. On replacement of –OCH₃ group of RC by –OC₂H₅, there is a decrease of 78.635 hartree energy of the resulted compound, p-azoxyphenetole. Similarly, replacement of –OCH₃ group of RC by–COOC₂H₅, –CH=CH–COOC₂H₅ and –CH=CH–COOC₈H₁₇ groups decreases successively the E of the resulting compounds. This is also demonstrated byFigure 1.

Energies of the highest occupied molecular orbital (εHOMO) and lowest unoccupied molecular orbital (εLUMO) are very popular quantum chemical descriptors. It has been shown that these orbitals play a major role in governing many chemical reactions and determining electronic band gaps in solids; they are also responsible for the formation of many charge transfer complexes [ 14]. According to the frontier molecular orbital theory (FMO) of chemical reactivity, the formation of a transition state is due to an interaction between the frontier orbitals (HOMO and LUMO) of reacting species. Thus, the treatment of the frontier molecular orbitals separately from the other orbitals is based on the general principles governing the nature of chemical reactions. The HOMO energies of the above LCs were evaluated and are reported inTable 3. A reference to thisTable table indicates that the HOMO energy of RC is -4.994. On replacement of –OCH₃ group of RC by –OC₂H₅, there is an increase of 0.053 eV value of HOMO energy of the resulted compound, p-azoxyphenetole. Similarly, replacement of –OCH₃ group by –COOC₂H₅ (compd. no. 3) shows a decrease (0.969 eV) in the value of HOMO energy. Thus, ethyl-p-azoxybenzoate has lower value of HOMO energy of 1.022 eV than the former compounds (compd. no. 2). On further replacement of –OCH₃ group by –CH=CH–COOC₂H₅ (ethyl-p-azoxycinnamate) shows a decrease in the value of HOMO energy with respect to compd. no. 1 and 2 but an increment in respect to 3. Finally, replacement of –OCH₃ group by CH=CH–COOC₈H₁₇ (n-octyl-p-azoxycinnamate) shows an abnormal decrease in the HOMO energy. The decreasing order of HOMO energy of above LCs for electrophilic attack is p-azoxyphenetole > p-azoxyanisole > ethyl-p-azoxycinnamate > ethyl-p-azoxybenzoate > n-octyl-p-azoxycinnamate (Figure 2).

The LUMO energies of the above LCs were evaluated and are also reported inTable 4. A reference to thisTable table indicates that the LUMO energy of RC is -2.718 eV. On replacement of –OCH₃ group of RC by –OC₂H₅, there is an increase of 0.05 eV value of LUMO energy of the resulted compound, p-azoxyphenetole. Similarly, replacement of –OCH₃ group by –COOC₂H₅ (compd. no. 3) shows a decrease (0.922 eV) in the value of LUMO energy. Thus, ethyl-p-azoxybenzoate has lower value of LUMO energy than the former compounds (compd. no. 2). On further replacement of –OCH₃ group by –CH=CH–COOC₂H₅ (ethyl-p-azoxycinnamate) shows a decrease in the 2.058 eV and 2.108 eV value of LUMO energy with respect to compd. no. 1 and 2 but an increment of 0.026 in respect to 3. Finally, replacement of –OCH₃ group by –CH=CH–COOC₈H₁₇ (n-octyl-p-azoxycinnamate) shows an abnormal decrease of 75.397 eV in the LUMO energy. The decreasing order of LUMO energy of above LCs for nucleophilic interaction shows trend similar to the HOMO energy, p-azoxyphenetole > p-azoxyanisole > ethyl-p-azoxycinnamate > ethyl-p-azoxybenzoate > n-octyl-p-azoxycinnamate (Figure 3).

The HOMO-LUMO gap, i.e. the difference in energy between the HOMO and LUMO, is an important stability index [ 14]. A large HOMO-LUMO gap implies high stability for the molecule in the sense of its lower reactivity in chemical reactions. The HOMO-LUMO gaps of the above LCs were calculated and are also reported inTable 5. A reference to the data shows the following sequence of above LCs with respect to their stability: Ethyl-p-azoxycinnamate > p-Azoxyphenetole > p-Azoxyanisole > Ethyl-p-azoxybenzoate > n-Octyl-p-azoxycinnamate. The trend of HOMO-LUMO gap is also demonstrated byFigure 4.

The minimal energy needed for the detachment of an electron for an atom or a molecule [ 15]. According to Koopman&#x02019;s theorem [ 16], the EA is simply the eigenvalue of HOMO with change in sign (IP = -&#x003b5;HOMO) and characterizes the susceptibility of the molecule toward attack by electrophiles. The IP of the above LCs were calculated directly from the structure of the compound and are reported inTable 6. A reference to theTable table indicates that the IE of RC is 4.994. On replacement of &#x02013;OCH₃ group of RC by &#x02013;OC₂H₅, there is a decrease of 0.053 eV value of ionization energy of the resulted compound, p-azoxyphenetole. Similarly, replacement of &#x02013;OCH₃ group by &#x02013;COOC₂H₅ (compd. no. 3) shows an increase (0.969 eV) in the value of ionization energy. Thus, ethyl-p-azoxybenzoate has larger value of ionization energy of 1.022 eV than the former compounds (compd. no. 2). On further replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₂H₅ (ethyl-p-azoxycinnamate) shows an increase in the value of ionization energy with respect to compd. no. 1 and 2 and decrease in respect to 3. Finally, replacement of &#x02013;OCH₃ group by CH=CH&#x02013;COOC₈H₁₇ (n-octyl-p-azoxycinnamate) shows an abnormal increase in the ionization energy. The increasing order of IE of above LCs shows trend opposite to the HOMO energy (IE = -&#x003b5;HOMO), p-azoxyphenetole < p-azoxyanisole < ethyl-p-azoxycinnamate < ethyl-p-azoxybenzoate < n-octyl-p-azoxycinnamate and is good agreement to the Koopman&#x02019;s theorem (Figure 5).

The energy difference between an uncharged species and its negative ion, referred to as an electron affinity, is an important property of atoms and molecules [ 15]. A survey of examples illustrates the diversity of areas in which electron affinities play a role: silicon and quantum dot (nanocrystal) semiconductor chemistry, Schottky diodes, molecular clusters, fullerene chemistry, interstellar chemistry, polymer photoluminescence, microelectronics, flat panel displays, and even hypotheses regarding the shuttle glow phenomenon. The EA of the above LCs were calculated directly from the structure of the compound and are reported inTable 7. A reference to thisTable table indicates that the EA of RC is 2.718 eV. On replacement of &#x02013;OCH₃ group of RC by &#x02013;OC₂H₅, there is a decrease of 0.05 eV value of EA of the resulted compound, p-azoxyphenetole. Similarly, replacement of &#x02013;OCH₃ group by &#x02013;COOC₂H₅ (compd. no. 3) shows an increase (0.922 eV) in the value of EA. Thus, ethyl-p-azoxybenzoate has larger value of EA than the former compounds (compd. no. 2). On further replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₂H₅ (ethyl-p-azoxycinnamate) shows an increase in the 1.088, 0.138 and 0.166 eV value of LUMO energy with respect to compd. no. 1, 2 and 3. Finally, replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₈H₁₇ (n-octyl-p-azoxycinnamate) shows an abnormal increase of 75.397 eV in the EA. The increasing order of EA of above LCs shows trend opposite to the LUMO energy (EA = -&#x003b5;LUMO), n-octyl-p-azoxycinnamate > ethyl-p-azoxycinnamate > ethyl-p-azoxybenzoate > p-azoxyanisole > p-azoxyphenetole (Figure 6). It is good agreement of the Koopman&#x02019;s theorem, according to which the EA is simply the eigenvalue of LUMO with change in sign and characterizes the susceptibility of the molecule toward nucleophilic interaction.

In DFT, the electronegativity, commonly known to a chemist, is defined as the negative of a partial derivative of energy E of an atomic or molecular system with respect to the number of electrons N with a constant external potential v(r) [ 15].

When assuming a quadratic relationship between E and N a finite difference approximation Eq. 2 may be rewritten as

where IP and EA are the vertical ionization energy and electron affinity, respectively, thereby recovering the electronegativity definition of Mulliken [ 17]. Moreover, a theoretical justification was provided for Sanderson&#x02019;s principle of electronegativity equalization, which states that when two or more atoms come together to form a molecule, their electronegativities become adjusted to the same intermediate value. According to Koopman&#x02019;s theorem [ 16], the IP or IE is simply the eigenvalue of HOMO with change in sign and EA is the eigenvalue of LUMO with change of sign; hence Eq. 3 may be written as

The &#x003c7; of the above LCs were calculated by solving the Eq. 4 and are reported inTable 8. A reference to thisTable table indicates that the &#x003c7; of RC is -3.856 eV. On replacement of &#x02013;OCH₃ group of RC by &#x02013;OC₂H₅, there is an increase of 0.051 eV value of &#x003c7; of the resulted compound, p-azoxyphenetole. Similarly, replacement of &#x02013;OCH₃ group by &#x02013;COOC₂H₅ (compd. no. 3) shows a decrease (0.946 eV) in the value of &#x003c7;. Thus, ethyl-p-azoxybenzoate has lower value of &#x003c7; than the former compounds (compd. no. 2). On further replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₂H₅ (ethyl-p-azoxycinnamate) shows a decrease in the 0.92 eV and 0.971 eV value of &#x003c7; with respect to compd. no. 1 and 2 but an increment of 0.026 in respect to 3. Finally, replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₈H₁₇ (n-octyl-p-azoxycinnamate) shows an abnormal decrease of 72.968 eV in the &#x003c7;. The decreasing order of &#x003c7; of above LCs is: p-azoxyphenetole > p-azoxyanisole > ethyl-p-azoxybenzoate > ethyl-p-azoxycinnamate > n-octyl-p-azoxycinnamate (Figure 7).

The absolute hardness &#x003b7; is defined as

where E is the total energy, N is the number of electrons of the chemical species, and v(r) is the external potential [ 15]. The operational definition of absolute hardness is given as

where IP and EA are the vertical ionization energy and electron affinity, respectively, of the chemical species. According to Koopman&#x02019;s theorem [ 16], the IP or IE is simply the eigenvalue of HOMO with change in sign and EA is the eigenvalue of LUMO with change of sign; hence Eq. 6 may be written as

The &#x003b7; of the above LCs were calculated by solving the Eq. 7 and are reported inTable 9. A reference to thisTable table indicates that the &#x003b7; of RC is 1.138 eV. On replacement of &#x02013;OCH₃ group of RC by &#x02013;OC₂H₅, there is a decrease of 0.001 eV value of &#x003b7; of the resulted compound, p-azoxyphenetole. Similarly, replacement of &#x02013;OCH₃ group by &#x02013;COOC₂H₅ (compd. no. 3) shows an increase of 0.024 eV in the value of &#x003b7;. Thus, ethyl-p-azoxybenzoate has higher value of &#x003b7; than the former compounds (compd. no. 2). On further replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₂H₅ (ethyl-p-azoxycinnamate) shows a decrease of 0.168 eV, 0.167 eV and 0.192 eV in the value of &#x003b7; with respect to compd. no. 1, 2 and 3. Finally, replacement of &#x02013;OCH₃ group by &#x02013;CH=CH&#x02013;COOC₈H₁₇ shows a negative value of &#x003b7;, -1.292 eV. The decreasing order of &#x003b7; of above LCs is: ethyl-p-azoxybenzoate > p-azoxyanisole > p-azoxyphenetole > ethyl-p-azoxycinnamate > n-octyl-p-azoxycinnamate (Figure 8).

The dipole moments of polyatomic molecules depend on the nature of the atoms and on their arrangement. The dipole moment of a molecule is the vector sum of the dipole moments of the bonds and is calculated according to the rule of vector addition [ 18]. If two bonds with the dipole moments P and Q are at an angle &#x003b8; the total dipole moment is given by

For instance two identical bonds with the opposite directions (&#x003b8; = 180&#x002da;) have &#x003bc; = 0. For identical bonds (P = Q) Eq. 8 yields

The dipole moments of the above LCs were computed directly from the optimized structure and are reported inTable 10. A reference to the data shows that the dipole moment of RC is 1.343 D. On replacement of &#x02013;OCH₃ group of RC by &#x02013;OC₂H₅, there is a decrease of 0.146 D of the resulted compound, p-azoxyphenetole. Further, replacement of &#x02013;OCH₃ group of RC by&#x02013;COOC₂H₅, &#x02013;CH=CH&#x02013;COOC₂H₅ and &#x02013;CH=CH&#x02013;COOC₈H₁₇ groups increases the dipole moments of the resulting compounds. This is also demonstrated byFigure 9.

Above study concluded that

Total energy increases in sequence &#x02013;OCH₃ < &#x02013;OC₂H₅ < &#x02013;COOC₂H₅ < &#x02013;CH=CH&#x02013;COOC₂H₅ < &#x02013;CH=CH&#x02013;COOC₈H₁₇ showing the stability of LCs.

The decreasing order of HOMO energy of above LCs for electrophilic interaction is p-azoxyphenetole > p-azoxyanisole > ethyl-p-azoxycinnamate > ethyl-p-azoxybenzoate > n-octyl-p-azoxycinnamate.

The decreasing order of LUMO energy of above LCs for nucleophilic interaction shows trend similar to the HOMO energy.

The increasing order of IE of above LCs show trend opposite to the HOMO energy and the increasing order of EA of above LCs shows trend opposite to the LUMO energy that are good agreement to the Koopman&#x02019;s theorem.

The decreasing order of &#x003c7; of above LCs is: p-azoxyphenetole > p-azoxyanisole > ethyl-p-azoxybenzoate > ethyl-p-azoxycinnamate > n-octyl-p-azoxycinnamate.

The decreasing order of &#x003b7; of above LCs show trend similar to the &#x003c7;.

The dipole moment increases in sequence &#x02013;OCH₃ < &#x02013;OC₂H₅ < &#x02013;COOC₂H₅ < &#x02013;CH=CH&#x02013;COOC₂H₅ < &#x02013;CH=CH&#x02013;COOC₈H₁₇ showing polar interaction behavior.