Electronic Structure , Nonlinear Optical Properties , and Vibrational Analysis of Gemifloxacin by Density Functional Theory

Shamoon Ahmad Siddiqui,1 Tabish Rasheed,2 Mohd Faisal,1 Anoop Kumar Pandey,3 and Sher Bahadar Khan4 1Centre for Advanced Materials and Nanoengineering, Najran University, P.O. Box 1988, Najran 11001, Saudi Arabia 2Department of Applied Sciences, School of Engineering and Technology, Sharda University, Plot No. 32–34, Knowledge Park III, Greater Noida 201306, India 3Department of Physics, University of Lucknow, Lucknow 226001, India 4Center of Excellence for Advanced Materials Research and Chemistry Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia


Introduction
Gemifloxacin (7-[(4E)-3-(aminomethyl)-4-methoxyiminopyrrolidin-1-yl]-1-cyclopropyl-6-fluoro-4-oxo-1,8-naphthyridine-3-carboxylic acid) is an oral broad-spectrum quinolone antibacterial agent widely used in the treatment of acute bacterial exacerbation of chronic bronchitis and mild-to-moderate pneumonia [1][2][3].Gemifloxacin acts by inhibiting DNA synthesis through the inhibition of both DNA gyrase and topoisomerase IV enzymes, which are essential for bacterial growth.Notably this drug has about 100 times higher affinity for bacterial DNA gyrase than for mammalian ones.Gemifloxacin is a broad-spectrum antibiotic that is highly active against both Gram-positive and Gram-negative bacteria Figure 1: Molecular structure and numbering scheme of gemifloxacin.[4,5].Gemifloxacin is globally used for the treatment of bacterial infection caused by susceptible strains like S. pneumoniae, H. influenzae, H. parainfluenzae, or M. catarrhalis, S. pneumoniae (including multidrug-resistant strains (MDRSP)), M. pneumoniae, C. pneumonia; K. pneumoniae.Gemifloxacin rapidly absorbed from the gastrointestinal tract and the absolute bioavailability averages approximately 71%.Gemifloxacin is metabolized to a certain extent by the liver.All metabolites formed are minor (<10% of the administered oral dose); the principal ones are N-acetyl gemifloxacin, the E-isomer of gemifloxacin and the carbamyl glucuronide of gemifloxacin [6,7].
The aim of the present communication is to investigate the molecular structure, vibrational spectra, and energetic data analysis of the molecule under study, in gas phase, due to biological and pharmaceutical importance of the title molecule.The structure and the ground-state energy of the drug under investigation have been analyzed employing density functional theory with B3LYP method.In order to obtain a more complete description of molecular vibration, vibrational frequency calculation has been carried out.The vibrational analysis also provides the detailed information about the intramolecular vibrations in the fingerprint region.The reported optimized geometries, molecular properties such as equilibrium energy, HOMO-LUMO gap, dipole moment, polarizability as well as first static hyperpolarizability components along with the electrostatic potential contours and surfaces have also been used to understand the activity of the molecules.

Experimental: Structure and Spectra
The fourier transform infrared spectrum was recorded with FT-IR Perkin Elmer spectrometer in KBr dispersion in the range of 400 to 4000 cm −1 .The optical properties of the gemifloxacin were examined using UV-visible spectrophotometer at room temperature.UV-visible spectrum was recorded in the range of 190-800 nm with Perkin Elmer-Lambda 950-UV-visible spectrometer.To measure the UVvisible absorption, the gemifloxacin particles were dispersed in distilled DI water and measured.The model molecular structure of gemifloxacin has been given in Figure 1.The experimental and calculated FT-IR spectra is given in Figure 2, and the experimental UV-visible spectrum is given in Figure 3.

Computational Details
In the present communication the density functional theory (DFT) [8] has been employed using Becke's three-parameter hybrid exchange functionals [9] with the Lee-Yang-Parr correlation functionals [10,11] to optimize the molecular structure and to calculate the electronic structure properties of the drug molecule.The Gaussian 03W program [12] was used to calculate the vibrational spectra, dipole moment (μ), polarizability (α), and the first static hyperpolarizability (β) of the title molecule, based on the finite field approach.The vibrational frequencies are calculated and scaled down by the appropriate factor [13,14].The vibrational wavenumber assignments and PED calculation have been carried out by combining the result of the GaussView 4.1 and the VEDA program [15,16] with symmetry considerations.The comparative experimental and calculated FTIR spectrum plotted using the pure Lorentzian band shape is shown in Figure 2.

Analysis of Conformers of Gemifloxacin
Theoretical calculations for conformers of gemifloxacin were carried out using the B3LYP/6-31G(d,p) method.The plots of the potential energy surface (PES) scans for this molecule are shown in Figures 4 and 5.The dihedral angles N 9 -O 3 -C 28 -H 46 and C 18 -C 23 -C 27 -O 5 are the relevant coordinates for conformational calculations within the molecule.In these calculations, all the geometrical parameters were simultaneously relaxed during the calculations while the dihedral angles were varied in steps of 10  3884 Hartree, which implies that the obtained structure was a global minimum.This structure is shown in Figure 1 and was used for performing frequency calculations.

Molecular Geometry Optimization
The equilibrium geometry optimization of lowest energy conformer has been achieved by energy minimization.The optimized geometry of the molecule under study is confirmed to be located at the global minima on PES, as the calculated vibrational spectrum contains no imaginary wavenumber.The given molecule has three rings.Out of these two are six membered and one five membered.Ring R1 and R2 are in a plane while ring R3 deviates from the given plane due to two bulky groups, one attached at 6N of ring R1 and the other attached at 19C.The optimized bond length of C-C in six-membered pyridine ring R1 ranges between 1.367 Å and 1.475 Å, while, for another pyridine ring R2, this ranges  between 1.366 Å and 1.401 Å.For five-membered pyrrole ring R3, C-C bond lengths are quite high and range between 1.510 Å and 1.536 Å.The optimized value of C23-C27 bond length adjacent to pyridine ring R1 is found to be 1.496 Å, which is also high in comparison to the C-C bond length in R1.The optimized value of C15-C22 bond length adjacent to pyrrole ring R3 is found to be 1.546 Å, which is also high in comparison to the C-C bond length in R3.Another important C-C bond length in cyclopropane attached to pyridine ring R1 is found in the range 1.501 Å-1.508 Å.The optimized C-N bond lengths in pyridine ring R1 are found to be 1.367 Å and 1.401 Å, while, in pyridine ring R2, the optimized C-N bond lengths are found to be 1.337 Å and 1.341 Å.On the other hand the optimized C-N bond lengths in pyrrole ring R3 are calculated as 1.473 Å and 1.469 Å, which is quite high in comparison to C-N bond length in both pyridine ring R1 and R2 because C-N bond in R2 is double bond while C-N bond in ring R1 has just double bond character due to delocalization of lone pair electrons of nitrogen in R1.C11-N6 bond length adjacent to ring R1 is found to be 1.451 Å, while C20-N7 bond length between ring R2 and R3 is calculated as 1.365 Å, which is quite small in comparison to C11-N6 bond length.The length of C19=N9 bond adjacent to ring R3 is found to be 1.276 Å, while C22-N10 bond length is found to be 1.465 Å.The length of C28-O3 bond adjacent to pyrrole ring R3 is found to be 1.425 Å.Values of all the bond angles are given in Table 1, and all are in accordance with previous experimental and theoretical studies on different biomolecules [17][18][19].
In five-membered ring, torsional strain also arises from the fact that, as the lateral distance between the bonds on two adjacent carbon atoms decreases, the repulsive interaction between the electrons of the bonds increases which cause decrease in bond angle.The double bond is sp 2 hybridized and forms bonds with bond angles of about 120 • .In such cases the unsaturated double bond has two electron pairs, one of the sigma bond and the other of the pi bond.Repulsion by these two electron pairs, the other bond pair is greater than that between two single bond pairs.This leads to deviations from exact trigonal geometry.The same is the reason for R1 and R2 which shows lower bond angles as compared to true trigonal geometry.According to Buckingham's definitions [20], DFT has also been used to calculate the dipole moment (μ), polarizability (α), and the first static hyperpolarizability (β).The total intrinsic hyperpolarizability β TOTAL [21] and a component of the first hyperpolarizability along the direction of the dipole moment are represented by β [21,22].The β components of the Gaussian output are reported in atomic units, where 1 a.u.= 8.3693 * 10 −33 e.s.u.. Table 3 clearly shows that molecule has major component of polarizability along axial direction; however, perpendicular components of polarizability have negligible contribution.Thus the polarization ellipsoid nearly planar is stretched along Y axis and contracted along Z axis.Thus dipole formed along XY Z axis and less stretched along perpendicular direction.The plane contains XX and XY having major part of hyperpolarizability.It means ellipsoids flattered along this plane.This means that this molecule is optically reactive in X direction.

Electronic Properties
HOMOs and LUMOs determine the way the molecule interacts with other species.The frontier orbital gap helps characterize the chemical reactivity of molecule.A molecule which have more orbital gap is more less polarized and less chemically reactive [23].According to the present DFT calculations, the frontier orbital gap in case of given molecule is 4.30 eV.The 3D and 2D plots of the HOMO, LUMO, and electrostatic potential for the molecule are shown in Figures (6)(7)(8).HOMO is located at ring R1 and R2, however, half R3 and F atom part of pentagon ring.If we see 2D plot of HOMO (Figure 6) a negative equipotential concentric line appears around N atom (ring R1) and F atom (adjacent to ring R2).However, a surface of positive line is closely concentrated around O atom adjacent to ring R1.It clearly indicates that delocalized electrons are confined at negative region of given molecule, however, shifted from positive part.This type of delocalized electron takes part in reaction and behaves as active part for binding to the receptor.LUMOs are located (Figure 7) at same place as HOMOs, except to those two carbon which are adjoint to ring R1 and R2.In the case of given molecule, the electronegative region (red) is towards the outer part and near the oxygen which is adjacent to ring R1, and moderate positive region (green) is located nearly over whole molecule.
The importance of MESP lies in the fact that it simultaneously displays size as well as shape and with the help of colour grading (shown in Figure 8) defined positive, negative, and neutral electrostatic potential regions, which are very useful in investigation of molecular structure with its physiochemical property relationship [24][25][26][27][28].As we see from 2D molecular electrostatic potential plot (Figure 8), negative equipotential surface lines are passing near to O atom which is adjacent to ring R1, and other negative potential regions are found near to N atom of ring R2 (where negative lines closely form a concentric circle).Negative potential surface line near to O atom is passing through F atom.This indicates that it is suitable place for nucleophilic substitution reaction.The energy equal to the shielded PES is required for any substitution reaction near the oxygen.The electronegative lines (between −0.08.u. and −0.04.u.) form a closed contour which clearly indicates that the total flux passing in between these curves is not equal to zero.It generates a negative electric field region near the oxygen atom which opposes the electrophilic substitution.The molecule acts as a dipole in which the area near the oxygen atom acts as the negative pole (better site for positive radicals in human bodies), however, the remaining part of the molecule is suitable for electrophilic substitution reaction.Out of these, all regions are surrounded by the positive potential surface line over whole molecule.

Vibrational Assignments
The molecule gemifloxacin contains 48 atoms, and it has 138 normal modes of vibration.All the 138 fundamental vibrations are IR active.The harmonic-vibrational frequencies calculated for gemifloxacin and experimental frequencies (FTIR) have been compared in Table 4. Vibrational assignments are based on the observation of the animated modes in GaussView and assignments reported in the literature.
In gemifloxacin, the C-H functional group is present at a number of positions.The stretching vibration, ν(C-H), is expected to occur in the region 3010-3120 cm −1 .The calculated values of the ν(C-H) vibration lie within this spectral range.The other important stretching vibration corresponds to the C=O moieties at the C 24 and C 27 positions.The region 1650-1750 cm −1 is generally considered as the double bond stretching region for C=O, C=C, and C=N bonds [29][30][31][32].The C=O stretching vibration, ν(C=O) appears as a prominent mode in the FTIR spectra at 1716 cm −1 .Another important stretching vibration in gemifloxacin is the O-H stretching vibration.The O-H group vibrations are likely to be most sensitive to the environment, so they show pronounced shifts in the spectra of the hydrogen-bonded species.In the subject molecule, the ν(O-H) vibration appears at 3439 cm −1 in the FTIR spectrum.The calculated (scaled) and experimental frequencies are deviated by large amount, which may be explained by the presence of hydrogen bondings in the solid sample.
The -NH 2 , and -CH 2 , functional groups are important constituents of gemifloxacin and vibrations corresponding to these groups are present in a number of modes.The stretching vibrations of these groups appear in a number of modes.The wagging vibrations ω(CH 2 ) and ω(NH 2 ) are also present in a number of modes.Mode 39 shows a pure ω(CH 2 ) vibration, and there is excellent correspondence between calculated (scaled) and experimental FTIR wavenumber as can been seen in Table 4.The twisting (τ ) and rocking (ρ) vibrations for both the functional groups are present mixed with other vibrations.
The other important functional group in gemifloxacin is the -CH 3 group.There are nine modes of vibration of methyl group, which are distributed as follows: one symmetric stretching (ν s ), two antisymmetric stretching (ν as ), one symmetrical deformation (δ s ), two asymmetrical deformation (δ as ), one in-plane rocking (ρ i ), one out-of-plane rocking (ρ o ), and one twisting (τ ) vibration modes [30].The ν s (CH 3 ) and ν as (CH 3 ) vibrations, are present in higher frequency modes as pure vibrations, and the other vibrations are mixed with other vibrations.The H 2 C-CH 2 functional group which is attached to the C 11 atom in gemifloxacin has unique vibrational fingerprints.It shows a number of vibrations, and these are distributed throughout the spectrum.
In gemifloxacin, a very important vibration corresponds to the modes involving the vibrations of the ring atoms.For the purpose of easing the analysis, we have classified the structure of gemifloxacin into three rings R1, R2, and R3 as shown in Figure 1.The ring stretching vibrations ν(Ring) are complicated combinations of stretchings of C-N, C=C, and C-C bonds.The most important ring stretching vibration is the ring breathing vibration at mode 90.In this mode, all bonds of the rings appear to stretch and contract in-phase with each other [33].In the experimental infrared spectrum of gemifloxacin, this mode appears at 649 cm −1 .Other ring vibration modes present a mixed profile.

Conclusion
In the present work we have calculated the geometric parameters, vibrational frequencies, frontier molecular orbitals, molecular electrostatic potential contours, and surfaces and the nonlinear optical properties of gemifloxacin using DFT/B3LYP method.Optimized geometry clearly shows that the skeleton of the title molecule is nonplanar.The higher frontier orbital gap of 4.30 eV shows that gemifloxacin has high kinetic stability and can be termed as hard molecule.However, the higher value of dipole moment shows that gemifloxacin molecule is highly polar.Nonlinear optical behavior of title molecule was investigated by the determination of the dipole moment, the polarizability, and the first static hyperpolarizability using density functional B3LYP method.In general, a good agreement between experimental and calculated normal modes of vibrations has been observed.The molecular electrostatic potential contours and surfaces have also been drawn to explain the activity of gemifloxacin molecule.The present quantum chemical study may further play an important role in understanding of the structure, activity, and dynamics of the molecule.