Study Of Asymmetric Frequency Shift Of The Fermi Resonance In The Raman Spectra

Fermi resonance is a common phenomenon that widely exits in vibration coupling and energy transfer of Intramolecular and intermolecular.Fermi resonance can occur when a fundamental vibrational level F0+ is close to an overtone (or combination)vibrational level F0-.The investigation of Fermi resonance not only has great theoretical significance in some physics field, such as molecular electronic state, vibration and dynamic interaction,but also has important applications in biology,material,and assignation of spectra.This is mainly because the simple small molecules and the complex are involved in these fileds. Fermi resonance is a common phenomenon that not only exits in Simple small molecules,but also exits in complex.Fermi resonance makes the spectrum frequency shift.Because of Fermi resonance ,some overtone (or combination) that not exists in theory appear.These phenomenon lead to a great deal of difficulty for the assignment of spectrum and the analysis of material composition.The explanation to Fermi resonance is not perfect until now and the common Bertran theory can not explain all the phenomenon of Fermi Resonance. The research to Fermi resonance has just began and the theory to Fermi resonance is not perfect,so there are lots of things worthy of our study in this area.The study to Fermi resonance is a new topics that worth to studying. The Raman spectra of CS2 in C6H6 is meassured and the Fermi resonance ofν1-2ν2 in solution and in pure CS2 is discrepant in this report.The characteristic parameters are calculated by Berttern equation.In conclusion,with the concentration of CS2 decline,the ratio of the spectral intensity (R=I655/I796) decreases and the coupling coefficient (W) raises and also the other parameters change correspondingly.The analyse shows that dissipation coefficient of V10 of CS2 is affected by the concentration ofC6H6 . Asymmetric frequency shift of V1O and 2V20 are observed in experiment,which is explained by the amended Bertran theory. This report provides positive reference value for the molecule spectrum certification and the understanding and using of Fermi resonance theory.There are three parts in this paper,as follow:1.The experimental results and the analysis of it from Bertran theoryIn the experiment,we find that Fermi resonance spectrum have a obvious frequency shift with the concentration change in the mixture of CS2 and C6H6.We calculated coupling coefficient W(cm-1)and anharmonic constant K122(cm-1)with Bertran theory. 2.The relationship between the Raman scattering coefficient and the changing of Fermi resonance of the liquid CS2 at different concentrations Table 1 showed that theν1-2ν2 Fermi resonance Raman spectra of the pure liquid CS2 and the liquid CS2 in C6H6 at different concentrations are different from each other . Especially , in the solution of CS2 and C6H6 , the values of R decrease with the volume concentration of solution from 10% to 100% , but the values of K,Δ,W increase , which has been rational explained using the theory of solvent effects .In C6H6 ,the CS2 spectrum intensity of stretching vibration V10 is very strong ,and it is effected by C6H6.The CS2 spectrum intensity of Bending vibration V20 is very weak, and it is effected by C6H6,so compared with the intensity I2V20 of 2V20, the intensity IV10 of V10 has a big change.The changed of intensity of the Raman spectrum in binary mixtures with the concentration changed are explained by G. Fini , et al. ,derived from Onsager's theory of dielectric polarization . Theν1(656cm-1) fundamental Raman scattering coefficient of CS2 changed with theconcentration in C6H6 is presented in Fig.1 .we obtained the scattering coefficients ss/Si of CS2 in different concentration of C6H6 from Fig.1 and Table 1. The scattering coefficients Ss/Sl are listed against the Fermi coupling coefficient W in Table 2 . With the coupling coefficient W increases , the scattering coefficient Ss/Sl decreases .3,The explanation of the Fermi resonance with the modified Bertran theoryWith concentration of decreases, the coupling coefficient W increases,so it lead to the frequency differenceΔbecome more large after Fermi resonance. Bertran advised the basic Fermi resonance theory that based on the symmetrical movement of enery level after Fermi resonance compared with natural frequency.But we find that when CS2 mixed with C6H6 with different concentration, the Raman shift of V1 has a small change ,the Raman shift of 2V2 has a large change.We believe that the main reason is that When the two spectrum intensity and frequency of Fermi resonance have a big difference,the anharmonic potential will make the center of the two energy levels shift. The bigger the concentration is, the bigger the anharmonic potential is, so the side-play amount of center of the energy level will be swelled. That resulted in the frequency shift of the 655cm-1 spectrum does not happen, and the Raman spectrum 796cm-1 with the lower concentration will be moved to high wavenumber . The theoretical model shows in Figure 2.We can see that the change of the anharmonic potential' H++ and'H_ will result in movement of center of the energy level from Figure 2,so the natural energy vel E0+and E0_ have a frequency shift. The energy level move to the opposite direction compared with the natural frequency after Fermi resonance. The change of H++ may result in no frequency shift of energy level E+,but energy level E_ does. The paper assume that H++ and H'_ is the same,if the spectrum V1(E+) does not have a frequency shift,H'++ will be the half of the frequency shift of spectrum V2(E_). H'++ is calculated in Table 3. We find that the spectrum 655cm-1 have no frequency shift and the spectrum 2V2 have frequency shift from formula4,The v1+v4 and V3 bands of ccl1 at Fermi resonance are studied.It is shown that the frequency V1 is the major factor that impacts the characteristic parameters of infrared and Raman spectra at Fermi resonance and the intensity has no direct relation with these parameters.The results are interpreted from group theory and the Berttan's theory.This report provides reference value for the understanding of Fermi resonance and the band assignment in the study of molecular structures.