采用密度泛函理论计算了两种类胡萝卜素(β-胡萝卜素和叶黄素) 和几种短链(n=2~5)多烯烃的Raman光谱, 用波数线性校正（WLS）方法对计算频率进行了校正, 并与常用的几种校正方法作了比较。 最常用的单一参数校正（UFS）方法只适用于个别频率的校正, 对于所有振动频率的综合校正效果并不理想。 WLS方法对于多烯烃和类胡萝卜素的校正结果明显优于UFS方法, 校正公式分别为νobs／νcalc=0.999 9－0.000 027 4νcalc和νobs／νcalc=0.993 8－0.000 024 8νcalc, 这些结果说明WLS方法可以用于类胡萝卜素这样的大分子的频率校正。 WLS方法对多烯烃和类胡萝卜素的校正参数非常接近, 证明WLS方法对多烯烃的校正结果可以用于类胡萝卜素的频率校正, 这为类胡萝卜素频率校正提供了一种新的方法。

Raman spectra of two typical carotenoids(β-carotene and lutein) and some short(n=2~5) polyenes were calculated using density functional theory. The wavenumber-linear scaling (WLS) and other frequency scaling methods were used to calibrate the calculated frequencies. It was found that the most commonly used uniform scaling (UFS) method can only calibrate several individual frequencies perfectly, and the systematic result of this method is not very good. The fitting parameters obtained by the WLS method are νobs／νcalc=0.999 9－0.000 027 4νcalc and νobs／νcalc=0.993 8－0.000 024 8νcalc for short polyenes and carotenoids, respectively. The calibration results of the WLS method are much better than the UFS method. This result suggests that the WLS method can be used for the frequency scaling of the molecules as large as carotenoids. The similar fitting parameters for short polyenes and carotenoids indicate that the fitting parameters obtained by WLS for short polyenes can be used for calibrating the calculated vibrational frequencies of carotenoids. This presents a new frequency scaling method for vibrational spectroscopic analysis of carotenoids.