Theoretical study of the electric and the magnetic dipole in UV-Vis and ECD of fluralaner: the folded conformation and the extended conformation

: Through our contribution, we have carried out the theoretical study of the transition characteristics of one-photon absorption (OPA) spectra of the folded conformation and the extended conformation of fluralaner. The electronic transitions in OPA are visualized with charge difference density (CDD) and transition density matrix (TDM) to explain the charge transfer via hole-electron distribution. We’ve also analyzed the transition dipole electric/ magnetic moment by using the iso surface (real space) and TDM diagram in order to determine the portions of molecules, which have the most contribution in ECD spectra.


Introduction
Fluralaner [1][2][3] In quantum chemistry, the description of the electronic structure induced by light, from the fundamental state to the excited one, is habitually involved in researching electronic transitions of molecule. In fact, it has previously been shown that the accurate and the best methodology for describeing the light-induced electronic structure reorganization is the most important for the improvement of new theoretical methods or new experimental techniques. In this field, a considerable attention has been drawn in the literature [4][5][6][7][8][9][10][11]. The Time Dependent Density Functional Theory (TDDFT) is a really successful theory of electronic structure of matter, where the TDDFT has drawn a considerable attention in the literature [7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24] for calculating the transitions energy with relative intensity. According to this computation, many of objects are resulting such as: the difference in density matrix, which is known as the difference between the excited and ground states density matrix expressed on the basis set of atomic functions. In the transition process, charge density difference (CDD) analysis is prevalently used and commonly accepted method for studying the difference in charge distribution between two-electron states of a system. Our work admits a variety of analysis methods, according to the density difference between the excited state and the ground one. for unveiling the basic nature of an electron excitation, The transition density matrix (TDM) is very useful. TDM falls into two forms: i) the three-dimensional real space form, which can be expressed through drawing an isosurface map. A large value at a position corresponds to a large overlap of hole and electron, this reflect the contribution at this place taken into consideration. ii) The matrix form, in 2D, this TDM form can be exhibited as heat map, namely color-filled matrix map, which may be atom-based (our work) or fragment-based. This approach (TDM) is also considered as the best performing method for determining all of the one-electron properties such as: the transition dipole moment and the atomic transition charge [25][26][27][28][29][30][31].
Through TDM map, much information can be obtained, and different transition types can be distinguished (local excitation and charge transfer excitation) [27,30,32]. In this paper, we've begun with defining the theoretical background of the electronic transition in UV-Vis and ECD spectra. After that, we've studied charge transfer, by using method of charge density difference (CDD) to illustrate the distinction in electron density during excitement state (electron−hole coherence) through i) the transition density matrix using 2D visualization, where an increase in electron density is described at the level of the electrons, and a decrease in electron density is described at the level of the holes ii) the charge difference densities using 3D visualization (iso surface). Finally, we've visualized the transition electric dipole moment density and the transition magnetic dipole moment density of the excited states that have the strongest rotator strength using TDM in 2D and in real space 3D.

Oscillator strength f:
For occurring, an oscillating dipole must be induced by interaction of the molecules electric field with the electromagnetic radiation. For an electronic transition in theoretical chemistry filed, the oscillator strength f is always used for representing transition strength in UV-Vis spectrum, and is defined as: where ∆ denotes the transition energy between the two electronic states. The three Cartesian components of transition electric dipole moment between ground state and an excited state can be calculated as follows [27][28][29][30][31]: Where is the transition density matrix in basis set.

Transition density matrix TDM
To evaluate the electronic excitation, the TDM between ground and an excited state can be calculated as [27][28][29][30][31] = ∑ ∑ 3 corresponds to coefficient of the configurations involved in the excitation, denotes the expansion coefficient of basis set function in orbital molecule i. This permits to calculate the atomic contribution of the transition electric dipole moment. It should be noted that the TDM is in real representation, which can be constructed via TDM in basis function representations The excitation can be absolutely represented as I → j molecule orbital transition and suppose that there are only two basis set functions, the TDM could explicitly be written as below form: Where and denote the basic functions centered at atom A and on B.
If off-diagonal element has a big magnitude, we can say that, during the excitation, the atom A and the atom B have large contribution to hole and electron, respectively. The transition density is contributed by different basic functions (different atomic), that can be considered as the transition visualized by this transition density as a charge transfer excitation. If on-diagonal element , has a large magnitude, it implies that basis function must have large contribution to both hole and electron. This reflects the local excitation characteristics.

Electronic circular Dichroism ECD
Theoretically [33], the rotatory strength of an ECD (ECD spectroscopy characterizes the chiral molecules) is the imaginary part of the scalar of the scalar product of the transition electric dipole moment 0 and the transition magnetic dipole moment 0 The transition electric dipole moment 0 = 0 = 0 * , whereas the transition magnetic dipole The transition electric dipole moments of different Cartesian components is defined as follows Knowing that the operator for magnetic dipole moment, due to movement of electrons, is the angular momentum operator L, where = − .

Computational details
The ab initio calculations of UV-Vis and ECD of folded conformer extended conformer of fluralaner molecules using the time-dependent density function theory (TDDFT) methodology have first been reported. The geometry optimizations have been carried out using Gaussian9 program [34] at the B3LYP/6-31G* level to make sure of the minimum energy of molecular geometry. The excitation analysis has been predicted using the CAM-B3LYP functional and 6-31G* basis sets [35]. The CAM-B3LYP [36] has been utilized, in our work, since it is suitable to study charge transfer excitations. The transition density matrix (TMD), the charge difference densities (CDD) presented by heat maps (electron hole), and the transition electric dipole/ magnetic moment have been carried out by the Multiwfn 3.8 program [37]. Density in real space (3D iso surface) is designed by means of VMD software [38] to obtain preferable visualization effect. corresponds to the excitation states S1, S2 and S5 for conformer1 and S1, S2 and S3 for conformer2.

Electronic Transition and ECD Spectrum
Compared with the first part of excited state, the oscillator strength of the second part of excited state is considerably weaker. Concerning ECD spectra, we can observe that ECD intensity of conformer2 is stronger than conformer1. According to the ECD spectrum of conformer1 in figure 3, the S2 and S4 are characterized by big peaks, strong rotator strength, and opposite directions. According to the ECD spectra of conformer2 in figure 3, the excited states S1 and S2 have the strongest intensity in the rotator strength peaks of the absorption spectrum, hence the four excited states S1, S2 (two peaks) and S4 are chosen in our study. According to Eq. (6), it can be observed that the difference of the absorption spectrum in the ECD spectra is due to the different electric-magnetic interactions within the molecule, when it is excited by light. According to Eq. (6), the calculations of the moment tensor product are shown in table 1. According to the results of tensor product, we've checked that S2 is positive and S4 is negative. concerning the conformer2, the calculations have also shown the sing of both S1 and S2, where we can observe that S1 is negative and S2 is positive, which is consistent with the ECD spectrum in figure 3.

Charge difference density (CDD) via electron-hole
According to the results of UV-Vis spectra in section above, it should be very interesting to study charge transfer via electron hole analysis in S1, S2, and S5 exited state of conformer1 and S1, S2, and  The magnitude of diagonal element in the all TDM is quite little, but in some cases, the diagonal terms has a large magnitude, which means that the present electron excitation does not principally occur in the electron transfer between different atoms or groups. The main feature of this excitation is the local excitation like: the regions that are near to (26,26) are shown in a very red color in almost excitation.
According to the first preliminary analysis of electron-hole distribution and transition density matrix (TDM) in Fig. 4 and 5 of one-photon excited states, we conclude that all excitations occur in the half of the molecules i.e. between O13-O30 ( Conformers 1) and O13-O26 ( Conformers 1) Through studying the transition density matrix of electronic transition, we will be able to know how electrons transfer is among different sites. In figure 4-S1, concerning the first excitation S1 of

Electric and magnetic in ECD spectrum
To study the contribution of the transition electric/magnetic dipole moment, we've carried out the visualization of their densities (dipole/ magnetic) for the (S2, S4) for conformer1 and the (S1, S2) and   (27,27) and (26,26) show a very red color).

Figure. 8.
Transition electric dipole moment density (above) and transition magnetic dipole moment density (below) for excited state S1 in ECD of conformer2.
According to the figure 9, it can be remarked that the contribution of transition electric dipole moment is mainly contributed by with an acceptable contribution of both and . We can observe that the most areas of (X-and Y-component) of the heat map are red, so the red matrix element contributes more positively to the transition dipole moment of X-and Y-component. The transition electric dipole X Y Z S1 of D X Y Z S1 of M moment of the X-component is almost distributed in the all molecule and has the biggest intensity, except for dichlorophenyl group and trifluoromethyl group, that show only weak interactions. Figure.9. Transition electric dipole moment density (above) and transition magnetic dipole moment density (below) for excited state S2 in ECD of conformer2.
According to transition magnetic dipole moment density, it can be found that the strength of X, Y and Z component is very similar (the X component is only a little smaller), and the positive and negative isosurface strength of S1 excited state distribution in oxazol and benzamide location is bigger than that of S2.

Acknowledgment
The authors are grateful to the DGRSDT at the MESRS (Algerian Ministry of higher Education and Scientific Research) for financial supports.

Funding:
The DGRSDT at the MESRS (Algerian Ministry of higher Education and Scientific Research) for financial supports.

Conflicts of interest/Competing interests:
I did this work on my own, so there was no conflict of interest.

Availability of data and material
My work is a theoretical study.