Department of Chemistry, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2011 Aug 21;135(7):074502. doi: 10.1063/1.3625278.
The center line slope (CLS) method is often used to extract the frequency-frequency correlation function (FFCF) from 2D IR spectra to delineate dynamics and to identify homogeneous and inhomogeneous contributions to the absorption line shape of a system. While the CLS method is extremely efficient, quite accurate, and immune to many experimental artifacts, it has only been developed and properly applied to systems that have a single vibrational band, or to systems of two species that have spectrally resolved absorption bands. In many cases, the constituent spectra of multiple component systems overlap and cannot be distinguished from each other. This situation creates ambiguity when analyzing 2D IR spectra because dynamics for different species cannot be separated. Here a mathematical formulation is presented that extends the CLS method for a system consisting of two components (chemically distinct uncoupled oscillators). In a single component system, the CLS corresponds to the time-dependent portion of the normalized FFCF. This is not the case for a two component system, as a much more complicated expression arises. The CLS method yields a series of peak locations originating from slices taken through the 2D spectra. The slope through these peak locations yields the CLS value for the 2D spectra at a given T(w). We derive analytically that for two component systems, the peak location of the system can be decomposed into a weighted combination of the peak locations of the constituent spectra. The weighting depends upon the fractional contribution of each species at each wavelength and also on the vibrational lifetimes of both components. It is found that an unknown FFCF for one species can be determined as long as the peak locations (referred to as center line data) of one of the components are known, as well as the vibrational lifetimes, absorption spectra, and other spectral information for both components. This situation can arise when a second species is introduced into a well characterized single species system. An example is a system in which water exists in bulk form and also as water interacting with an interface. An algorithm is presented for back-calculating the unknown FFCF of the second component. The accuracy of the algorithm is tested with a variety of model cases in which all components are initially known. The algorithm successfully reproduces the FFCF for the second component within a reasonable degree of error.
中心线斜率（CLS）方法常用于从 2D IR 光谱中提取频率-频率相关函数（FFCF），以描绘动力学并识别系统吸收线形状的均匀和非均匀贡献。虽然 CLS 方法非常高效、准确且能抵抗许多实验伪影，但它仅被开发并适用于具有单一振动带的系统，或具有光谱分辨吸收带的两种物质的系统。在许多情况下，多组分系统的组成光谱重叠，彼此无法区分。这种情况在分析 2D IR 光谱时会产生歧义，因为不同物质的动力学无法分离。本文提出了一种数学公式，将 CLS 方法扩展到由两个组分（化学上不同的非耦合振荡器）组成的系统。在单一组分系统中，CLS 对应于归一化 FFCF 的时间相关部分。对于两个组分系统，情况并非如此，因为会出现更复杂的表达式。CLS 方法产生一系列源自通过 2D 光谱切片的峰位置。通过这些峰位置的斜率可得出给定 T(w)下 2D 光谱的 CLS 值。我们推导出解析表达式，对于两个组分系统，系统的峰位置可以分解为组成光谱的峰位置的加权组合。权重取决于每个物种在每个波长的分数贡献，以及两个组分的振动寿命。结果发现，只要已知一个组分的峰位置（称为中心线数据）以及两个组分的振动寿命、吸收光谱和其他光谱信息，就可以确定一个未知物种的 FFCF。这种情况可能会出现在将第二种物质引入特征良好的单一组分系统中时。例如，一种系统中，水以块状形式存在，也与界面相互作用。提出了一种用于反向计算第二个未知 FFCF 的算法。通过对所有初始已知组分的各种模型案例进行测试，验证了该算法的准确性。该算法成功地在合理的误差范围内再现了第二个组分的 FFCF。
