Theoretical Approach Using DFT Calculations of Novel Oxime Derivatives

This study used the density functional theory (DFT) methods to evaluate the geometrical properties, UV, the lowest unoccupied molecular orbital (LUMO), the highest occupied molecular orbital (HOMO) analysis, and the molecular electrostatic potential (MEP) of oxime ether derivatives containing a quinoxaline. In addition, the stability of the molecule resulting from hyper conjugative interactions charge delocalization was studied using a natural bond orbital (NBO) analysis. The HOMOLUMO energy gaps indicated different charge-transfer possibilities within the regarded molecules. Eventually, NBO analysis demonstrates the charge transfer between the lone pairs and the localized bonds.


Introduction
Synthesis of novel biologically active heterocyclic compounds is undertaken with the ultimate hope of the development of drugs [1]. Heterocyclic compounds containing nitrogen heteroatoms have recently attracted attention due to their considerable potential as pharmacotherapeutic agents [2]. The presence of a heterocyclic nitrogen nucleus in the framework of various pharmacologically active compounds representing antibacterial, antiasthmatic, antitumor, antimalarial, antileishmanial, antiplatelet, and anthelmintic properties justifies their synthesis [3,4]. Quinoxalines are important classes of nitrogen-containing heterocyclic compounds which have shown a wide variety of applications in pharmacology, so they have received special interest from synthetic chemists for many years. These invaluable heterocycles have shown different pharmacological activities [5]. Previously our group synthesized quinoxaline derivatives with good bactericide activity [6].
DFT methods have been widely used to verify experimental measurements for biological systems [7]. Several experimental and molecular modeling studies have been reported on the electronic structure of quinoxalines derivatives [8−11]. At the same time, there are not many theoretical studies on their electronic structures, quantum descriptors, and The optimized structures of all the considered compounds were studied by a comprehensive computational method, namely PBE1PBE/6-31+G * theoretical level discussed in this work.

Frontier molecule orbitals analysis.
As can be seen in Figure 1, the optimized molecular structures of compounds 1a−e were shown. LUMO and HOMO are known as the frontier molecule orbitals (FMOs), which participate in optical properties, UV spectrum, chemical reactions, and electronic properties [20,23]. We have calculated the HOMO-LUMO orbital energy and electronic properties of compounds 1a-e using PBE1PBE/6-31+G * theoretical level and summarized in Table 1. As can be seen in Figure 2, the HOMO orbitals of the molecules 1a, 1b, 1c, 1d, and 1e are mostly based on the double bonds (−C=C−) and the nitrogen atoms of quinoxaline and oxygen atom, the LUMO orbitals of the molecules 1a, and 1b are localized on double bonds (−C=C−) and the nitrogen atoms of quinoxaline, while for the molecules 1c, 1d, and 1e are localized on double bonds (−C=C−) of the phenyl rings and the N−O group. As a result, most of the charge transfer from HOMO to LUMO in the studied compounds is attributed to the contribution of lone pairs and π bonds. The negative and positive phases are in green and red colors, correspondingly. The energy gap is a significant parameter for determining the reactivity of the molecules and the properties of molecular electrical transport [24].
Molecules with a low gap have simpler electronic transport properties. The molecular system has high polarization, low kinetic stability, and high chemical reactivity; thus, the system is called a soft molecule [25]. The HOMO-LUMO energy gap values for compounds 1a, 1b, 1c, 1d, and 1e were measured around 3.21, 3.15, 2.16, 2.18, and 1.38 eV, respectively. The trend of the softness degree of the titled molecules is 1e > 1d > 1c > 1b > 1a. The molecules are converted to a softer system by the expansion of conjugation. Also, as can be seen from Figure 3, the total electronic density of states (DOS) plots [21] show the energy gaps of the studied molecules. While molecular interactions occur, the LUMO accepts the electrons and their energy associated with the electron affinity (A), whereas the HOMO denotes electrons donors, and its energy is associated with the ionization potential (I) [24,25]. The electronic chemical potential (µ), electronegativity (χ), global chemical hardness (η), chemical softness (S), and global electrophilicity (ω) parameters are calculated as follows [24,26] ; The global reactivity of the considered compounds is investigated in terms of the energy of the HOMO and LUMO and the HOMO-LUMO energy gap, which is a useful quantity for investigating kinetic stability and computed at the PBE1PBE/6-31+G * level (see Table 1). The HOMO-LUMO energy gap and defined as the resistance measurement of an atom or a group of atoms to charge transfer [1−3]. A molecule with a high Eg has a low chemical reactivity and high kinetic stability because it is energetically disadvantageous to add an electron to the highlying LUMO to remove electrons from the low-lying HOMO [3]. The global chemical hardness values of molecules 1a, 1b, 1c, 1d, and 1e are 1.60, 1.57, 1.08, 1.0 and 0.69 eV, respectively. The highest η value for compound 1a is observed; thus, it's the hardest molecule relative to other molecules. The absolute electronegativity parameter is applied to investigate the electron transfer direction, which is a good measure of the molecular ability to attract electrons.

MEP analysis of molecules 1a−e.
MEP maps display electronic density and are used to detect positive and negative electrostatic potential regions for nucleophilic reactions and electrophilic attacks, respectively [1,4]. The various values of the electrostatic potential are seen in different colors, and the potential reductions are: blue > green > yellow > orange > red. Negative (red, high electron density) regions are related to the electrophilic reactivity, while the positive (blue, low electron density) regions are associated with the electrophilic attack sites−the molecular electrostatic potential surfaces of molecules 1a−e are shown in Figure 4.
The negative sites of compounds 1a, 1b, 1c, 1d, and 1e are mostly focused on the phenyl ring of quinoxaline (ring a); therefore, these sites have a high electron density and are appropriate for electrophilic attack (Figure 4). The parts of molecules 1c, 1d, and 1e are pale red or orange colors that show regions with a partial negative charge, such as phenyl rings. The positive sites of the studied compounds are mostly focused on the Hb of the N−H bond in quinoxaline. Furthermore, green regions show zero potential and neutral sites, like hydrogen atoms in phenyl rings and saturated C−C bonds.

Natural bond orbital analysis.
The natural bond orbital analysis is important for determining intra-and intermolecular interactions and defining interactions between virtual and filled orbital spaces [5]. This analysis is an important method for the chemical understanding of hyper-conjugative interactions and electron density transfer from the filled lone pair orbital of one subsystem to the empty orbital of another subsystem. The filled NBOs and empty filled NBOs and the stabilization energy, E (2) estimated from the 2 nd order micro disturbance theory of compound 1d are reported in Table 2. The electron delocalization from the donor orbitals to the acceptor orbitals describes a conjugative electron transfer process. For each donor NBO(i) and acceptor NBO(j), the stabilization energy E (2) associated with electron delocalization between donor and acceptor [i→j] is estimated as [21]: where F(i,j) is the off-diagonal NBO Fock matrix elements, εi and εj represent diagonal elements (orbital energies), and qi denotes the i th donor orbital occupancy.
The higher value of E (2) , the more powerful the interaction between the donor and the acceptor orbitals, i.e., the greater the donation propensity of the electron donors to the electron acceptors and the greater the conjugation of the whole molecular structure. Delocalization of electron density between occupied Lewis-type (bond or lone pair) NBO orbitals and formally unoccupied (antibonding or Rydberg) non-Lewis NBO orbitals leads to the donor-acceptor stabilization relationship [4]. The NBO study was measured for molecule 1d using the PBE1PBE/6-31+G * theoretical level to elucidate the intramolecular, rehybridization, and delocalization of electron density. The intramolecular hyper-conjugative interactions of the studied molecule with different intensity (weak, moderate, and strong) comprising σ→σ * , π→π * , n→σ * , n→π * , and π * →π * transitions are summarized in Table 2.
As shown in Table 2, the intramolecular hyper-conjugative of the π→π * interactions have the most resonance energy relative to the σ→σ * interactions. The π→π * interaction in the quinoxaline ring, leads to strong delocalization energy, including πC4−C6→π * C2−C3 with the resonance energy of 15.46 kcal/mol. The other important π→π * interactions in the quinoxaline rings and the phenyl rings are such as πC1−C5→π *  Table 3 and Figure 1).
The size of the polarization coefficients indicates the contribution of the two hybrids in forming bonds in the molecular system [6]. The variations in electronegativity of the atoms involved in bond-forming are reflected in the larger differences in the polarization coefficients of the atoms (C−N, C−O, and C−H bonds) [7]. The σC4−C6 bonding orbital is equal to σ=0.7046(sp 1.90 )+0.7096(sp 1.89 ) with a high occupancy of 1.96715 a.u. and low energy of −0.62593 a.u. In the σC4−C6 bonding orbital, the polarization coefficients C4=0.7046 and C6=0.7096 suggest a low discrepancy in the polarization coefficients between the two atoms and the importance of the bond formation. The πC1−C5 bonding orbital in the quinoxaline ring, measured as σ=0.6973(sp 1.00 )+0.7168(sp 1.00 ) with an occupancy of 1.72464 a.u. and the energy of −0.22076 a.u.  (Table 2). NBO analysis indicates that the lone pair of the N7 atom [n(1)N7] has a pcharacter (93.77%) and high occupancy (1.77796 a.u.) in the studied molecules, leading to stronger stabilization interactions. Thus, the electron donation to the π * C4−C6 antibonding orbital for the LP(1)N7→π * C4−C6 interactions with a high resonance energy of 27.97 kcal/mol ( Table  2). The interaction of LP(2)O12→π * N13−C14 has higher stabilization energy of 16.10 kcal/mol when it has a p-character (99.58%) with occupation number (1.84458 a.u) in molecule 1d.

Electronic structure and excited states of the compounds 1a−e.
The theoretical absorption spectra of molecules 1a, 1b, 1c, 1d, and 1e were determined at the TDPBE1PBE/6-31+G * level in the water. We have computed numbers of excited states using TD-DFT calculations for studied molecules summarized in Tables 4−8. The highest signal in the electronic absorption spectrum of molecule 1a is detected at λmax=232 nm with oscillator strength f = 0.23 (Table 4) Table 4, the other excited states of molecule 1a have a very small intensity and do not play a critical role in forming the electron spectrum. Also, the electronic absorption spectrum of compound 1b reveals a high signal that belongs to λmax= 240 nm with f = 0.13 ( Table 5). The charge transfer at λmax= 240 is related to the excited state So→S17 and is defined by five configurations, including H→L+12 (6%), H−1→L+3 (18%), H−1→L+2 (21%), H−2→L+2 (21%), and H−1→L+4 (27%), that the highest transition is from HOMO−1 to LUMO+4. As can be seen in Table 5, the other excited states of compound 1b have a very minimal intensity that is almost prohibited by orbital symmetry considerations.
As shown in Table 6, the highest signal in the electronic absorption spectrum of compound 1c is revealed at λmax=296 nm with oscillator strength f = 0.44, that the charge transfer is important for the first excited state So→S9 with two electron configurations, namely H−2→L (88%) and H−2→L+1 (3%) that the main transition is from HOMO−2 to LUMO (H−2→L). The other excited states of molecule 1c have very small intensities and play little part in forming the electron spectrum.
The theoretical electronic absorption spectrum of 1c in the solvent water is shown in Figure 5. As can be seen from Table 7, electronic spectra absorption of compound 1d reveals a strong signal at λmax= 281 nm with f = 0.23. As can be seen from Table 7, the charge transfer at λmax= 281 is connected to the So→S20 excited state intensity that is almost restricted by orbital symmetry considerations. The UV spectrum obtained from molecule 1b in water is seen in Figure 5.      The other excited states of molecule 1e do not have a key role in the formation of the electron spectrum and have a very small intensity. The theoretical electronic absorption spectrum of molecule 1e in solvent water is seen in Figure 5.

Conclusions
The design of new oxime ether derivatives containing a quinoxaline moiety was investigated using the DFT/PBE1PBE/6-31+G * theoretical level. The calculated results showed that the highest global hardness value is observed for molecule 1a (R1=R2=CH3). According to NBO analysis of compound 1d, (R1=R2=Ph), the π-bonds and lone pairs with pcharacter participate in the electron donation to π * -bonds that lead to high stabilization energy. The global hardness values of molecules 1a, 1b, 1c, 1d, and 1e are 1.60, 1.57, 1.08, 1.01 and 0.69 eV, respectively. The highest global hardness value is observed for molecule 1a; thus, it is the hardest molecule compared to other molecules. The strongest signals in electronic absorption spectra of the molecules 1a, 1b, 1c, 1d, and 1e are observed at λ max = 232, 240, 296, 281, and 286 nm.

Funding
This research received no external funding.