COMPUTATIONAL APPROACH ON QUANTUM CHEMICAL ANALYSIS OF 2-BROMO-2-METHYL- 1-PHENYLPROPAN-1-ONE

1. Assistant Professor, Department of Physics, SCSVMV, Kanchipuram. 2. Associate Professor, Department of Mechanical Engineering.,SCSVMV, Kanchipurnam. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 05 April 2020 Final Accepted: 07 May 2020 Published: June 2020

The molecular geometry of 2-bromo-2-methyl-1-phenylpropan-1-one was optimized by DFT quantum chemical calculations and used to determine various molecular parameters theoretically. The HOMO and LUMO energy gap reveals that the energy gap reflects the chemical activity of the molecule. Global reactivity descriptors values are determined for the title molecule. Determination and visualization of molecule sites prone to electrophilic attack and nucleophilic attack performed by mapping of total density to the electron density surface is done by MESP Map analysis. Also, electron localization function (ELF) and localized orbital locator (LOL), determination of possible reactive centres of the title molecule realized by calculation of Fukui function analysis were carried out. Stability of the molecule arising from hype conjugative interactions, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The possibility of being NLO active were studied by investigating the linear polarizability (α) and first-order hyperpolarizability(β) values computed using DFT quantum mechanical calculations. UV absorption spectra (in gas phase and in different solutions) were investigated by TD-DFT using B3LYP/6-311 +G(d,p) basis set and electronic properties such as excitation energies, oscillator strength and wavelength were tabulated.

Molecular Geometry
The title compound has 23 atoms. A molecule consisting of N atoms has a total of 3N degrees of freedom, corresponding to the Cartesian coordinates of each atom in the molecule. In a nonlinear molecule, 3 of these degrees belong to the rotational, 3 of these degrees belong to the translational motions of the molecule and so the remaining corresponds to its vibrational motions. The net number of the vibrational modes is 3N-6. Therefore, for the title compound, three Cartesian displacements of 23 atoms provide 63 normal vibration modes. The molecular structure of the molecule with atom numbering is shown in Fig.1.

Topological analysis Frontier molecular orbitals
The frontier molecular orbitals and their properties are important for predicting the most reactive position inelectron system and several types of reactions in conjugated systems. [9][10]. The energy of the highest occupied molecular orbital (HOMO) is directly proportional to the ionization potential and characterizes the susceptibility of the molecule towards the attack of the electrophiles and the lowest unoccupied molecular orbital (LUMO) is related to the electron affinity and characterizes the susceptibility of the molecule towards the attack by nucleophiles [11]. The HOMO and LUMO values of the title compound are 7.254559 eV and 2.2705191eV respectively. The value of the energy gap is calculated to be 4.984040 eV which clearly indicates that charge transfer occur within the molecule and increasing the molecular activity. The HOMO-LUMO molecular orbitals are shown in Fig.2. It is clear from the HOMO-LUMO figure that HOMO is mainly situated over oxygen, bromine and ring atoms attached to oxygen atom while LUMO is mainly localized on atoms attached to oxygen and bromine atoms.

Molecular electrostatic potential analysis
The molecular electrostatic potential (MEP) is related to electronic density and a very useful descriptor for determining the sites for nucleophilic and electrophilic reactions [13]. The different values of electrostatic potential are represented by different colours and the potential increases in the order of red<orange<yellow<green<blue. From this surface, we can interpret that the most residing areas of electron density (denoted by more red areas) and least electron density residing areas (denoted by deep blue areas). The color code of the map was found to be in the range -4.417e-2 (deepest red color has negative extreme) to 4.417e-2 (deepest blue color has positive extreme).In the present MEP map, the maximum negative represents the site for electrophilic attack indicated by red colour while the maximum positive region represents the nucleophilic attack indicated by blue colour. The MEP map of the investigated compound ( Fig.3 (a)) shows the regions of negative potential over the electronegative oxygen atom of the carbonyl group and less negative indicated by yellowish blob over the bromine atom and the regions having the positive potential are over the hydrogen atoms.   [14] for this molecule tabulated in Table.2. 0.15272 C 5 -0.09154 C 6 -0.08723 428 C 7 -0.01449 C 8 -0.02459 C 9 -0.03068 C 10 -0.03449 C 11 -0.03563 C 12 -0.02557

Electron Localization function analysis
The modern method for investigating electronic structure of molecules free from arbitrary choice of molecular orbitals used in this study is the topological analysis of ELF as proposed by Silvi and Savin [15][16] belonging to quantum chemical topology [17]. The analysis such as ELF, LOL, Hole-Electron distribution Figures and Fukui Functions figures were performed using Multiwfn 3.7. [14] which is a multifunctional wave function analysis program. An electronic structure of a molecule described by ELF is represented by maxima (attractors) and its localization basin of η (r) field, which characterize covalent bonds, lone pairs, core regions and valence shells in atoms. Calculated electron populations on chemical bonds, , is related to integration electron density over localization basins. results represent average values with quantum uncertainty. The topological analyses of the Electron Localization function (ELF) and Localized orbital locator (LOL) are tools used for performing covalent bonding analysis as they reveal regions of molecular space where the probability of finding an electron pair is high [18][19].
The topological analysis has been carried out for ELF for the title compound. The 2D map of ELF of the title compound shown in

NBO analysis
Natural Bond Orbital (NBO) calculations were performed using NBO 3.1 program [21] as implemented in the Gaussian 09 package at DFT/B3LYP levels. The second order Fock-matrix was carried out to evaluate the donor (i) and acceptor (j) interaction in the NBO basis [22]. For each donor (i) and acceptor (j), the stabilization energy E (2) is associated as: The electron transfers from filled bonding orbital (donor) to empty antibonding orbitals (acceptor) [23][24][25] leading to hyperconjugative interactions can be examined by employing NBO analysis. The donor-acceptor interactions in NBO basis were evaluated using the second order Fock matrix. [26][27]. The larger the E (2) value, the more intensive is the interaction between electron donor and electron acceptor which means more donating tendency from electron donors to acceptors and a greater extent of conjugation of the whole system and the possible intensive interactions and the perturbation energies obtained by NBO analysis are listed in Table.3.  .60 and 15.11 (Kcal/mol) respectively and hence they give stronger stabilization to the structure. The stabilization of some of the ring is due to the interaction between C-C to anti bond of C-C in the ring as evident from the Table. 3.

Condensed Fukui Function
The Fukui function describes the electron density after adding or removing some amount of electrons. R.G.Parr and W.Yang [28] reported condensed Fukui function and frontier function. The local reactivity descriptor like Fukui function indicates the preferred regions where a molecule will alter its density or indicates its natural tendency to deform at a given position on accepting or donating electron HUMO or LUMO [29]. The theoretical tool Fukui function was performed by UCA-FUKUI software to understand the chemical reactivity , the condensed Fukui function and related local and global parameters were calculated [30]. In order to find the chemical reactivity and selectivity of the specific atomic site in a molecule, condensed Fukui function and local softness are used [30][31]. The Fukui functions at the atom k result to be: The sub-indexes "H" and "L" refers to HOMO and LUMO orbitals. When a molecule gains electrons, it has the reactivity site of electrophilic attack f k -, when the molecule losses electrons, it has reactivity site for nucleophilic attack f k + , and when the molecule has neutral electrons, they are in radical attack. Local electrophilicity, Local Nucleophilicity, Hardness and second order Fukui functions are called Dual-Descriptor ∆f r and by using finite difference approximation [31][32][33] The condensed Fukui functions using FMO theory were calculated and listed in Table.4.It is observed that maximum electrophilic attack order are C 8 > C 10 > C 7 > C 9 > C 11 > C 12 > C 4 > C 3 > C 6 > O 2 >C 5 and the maximum nucleophilic attack order are C 4 > O 2 > C 3 > C 7 > C 8 > C 10 > C 6 > C 9 >Br 1 > C 12 > C 11 . The highest radical attack order was found to be C 4 > C 8 > C 10 > O 2 > C 7 > C 9 atoms [34].
The Fukui function of the system defines the most reactive regions in a molecule. The individual atomic charges deliberated by Frontier Molecular Orbital and Natural Population analysis (NPA) have been used to calculate the Condensed Fukui function (CFF). Kolandaivel et al. [35] introduced the atomic descriptor to determine the local reactive sites of the molecular structure. The reactivity indices are directly concerned with the selectivity of the molecule. Using the NPA charges of neutral(radical),negative (cation) and positive(anion) state of a present molecule, Fukui function + ( ), − ( ), 0 ( ) are calculated. Fukui function are calculated using the following solutions: + ( ) = q r (N+1) -q r (N) for nucleophilic attack − ( ) = q r (N) -q r (N-1) for electrophilic attack 0 ( ) = q r (N+1) -q r (N-1) for radical attack where +,-and 0 show the nucleophilic, electrophilic and radical attack respectively. The condensed Fukui function (f k + , f k -, f k 0 ) and Dual-descriptor (Δf k ) evaluated by NPA listed in Table.5. It is found that dual descriptor (Δf k ) value is highly positive for Br 1 having tendency to acquire electron and C 5 is electrophilic [36] and Condensed Fukui function figures ( − , 0 , ∆f k ) for the title compound is presented in Fig.6.

Nonlinear optical (NLO) property analysis
The first order hyperpolarizability (β), polarizability (α) and dipole moment (µ) were calculated using B3LYP/6-311 +G(d,p) level of the finite field approach. The complete equations for calculating the magnitude of totla static dipole moment, polarizability and first-order polarizability using the x,y,z components from Gaussian '09 output are as follows: µ tot = (µ x 2 + µ y 2 + µ z 2 ) 1/2 α tot = 1 3 (α xx + α yy + α zz ) β tot = [(β xxx +β xyy +β xzz ) 2 + (β yyy +β yzz +β yxx ) 2 + (β zzz +β zxx +β zyy ) 2 ] 1/2 The calculated values of dipole moment, polarizability and hyper-polarizability are given in Table.6. The calculated dipole moment is 3.0516 Debye, polarizability α tot is equal to 5.265370x10 -24 e.s.u and have non-zero values and was dominated by diagonal components. The first-order polarizability is found to be 2.9002 X 10 -30 e.s.u which is nearly 5 times that of urea [37]. Our title compound with greater dipole moment and hyperpolarizability value shows that the compound has large NLO optical property. Theoretically, the first hyperpolarizability of the title compound is 4.779 times magnitude of urea. Domination of particular component indicates on a substantial delocalization of charges in that direction. In the present study, the biggest value of hyperpolarizability is noticed in β yyy direction and subsequently delocalization of electron cloud is more in that direction. The maximum β value may be due to -electron cloud movement from donor to acceptor which makes the molecule highly polarized and intramolecular charge transfer possible. So, from the magnitude of first hyperpolarizability, the title compound may be a potential applicant in the development of NLO materials.

Electronic excitation analysis
The electronic excitation analysis of the title compound has been carried out using TD-DFT method using B3LYP/6-311 +G(d,p) basis sets. The comparative theoretical UV absorption spectra in gas phase and in three solvents ethanol, water and DMSO is presented in Fig.7. Due to specific solute-solute and solute-solvent interaction in form of hydrogen bonding, the intensities, positions and shapes of the electronic absorption bands are usually altered when the absorption spectra are recorded in solvents of different polarity. The calculated results involving vertical excitation energies, oscillator strengths (f) and wavelength are tabulated inn Table.7. According to Frank-Condon principle, the maximum absorption ( max ) correspond to vertical excitation in UV spectrum [38]. It is observed the very intense electronic transition occur at 333.87, 333.69, 333.52 with oscillator strength 0.0028,0.0029 and 0.0028 for Ethanol, DMSO and water. Moreover, the theoretical wavelength in gas phase is found to be higher ie.339.92 nm than the wavelength in different solvents.  The distribution of hole, electron and both simultaneously are shown in Fig.8. It can be observed that there is a spatial separation between the hole-electron distribution thus indicating the charge transfer. values of electron localization is observed from 2D map of ELF. It is clear from NBO analysis that most of transitions with stabilization energies correspond to only three pairs of orbitals (C7-C9),(C8-C10) and (C11-C12) and interaction between LP(2) O2 σ* (C3-C4) and LP(2) O2 σ* (C4-C7) leads to stabilization of 21.13 and 18.37kcal/mol. The sites of electrophilic and nucleophilic were determined using Fukui functions. UV absorption spectra (in gas phase and in different solutions) were investigated by TD-DFT using B3LYP/6-311 +G(d,p) basis set and electronic properties such as excitation energies, oscillator strength and wavelength were tabulated. NLO calculations showed that the first hyperpolarizability of the title compound is 4.779 times magnitude of urea suggesting that the title compound is NLO active.