Harrison John A
Institute of Fundamental Sciences, Massey University, Private Bag 102-904 NSMSC, Auckland, New Zealand.
J Phys Chem A. 2008 Sep 4;112(35):8070-85. doi: 10.1021/jp804945z. Epub 2008 Aug 13.
RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.
通过反双曲余弦坐标映射转换到新坐标系后，利用傅里叶变换方法分析了RHF/aug-cc-pVnZ、UHF/aug-cc-pVnZ和QCISD/aug-cc-pVnZ（n = 2 - 5）下H₂ X (¹Σg⁺)的势能曲线。傅里叶频域光谱根据产生独特特征的潜在数学行为进行解释。在HF和全CI水平计算的势能曲线的潜在数学性质之间存在明显差异。该方法特别适用于分析在最高理论水平获得的势能曲线，因为观察到傅里叶光谱具有紧凑的性质，傅里叶频率系数的包络在幅度上呈指数衰减。描述CI曲线所需的有限数量的傅里叶系数允许开发一种最佳采样策略，这与指数和几何收敛所需的策略相对应。由于有限收敛标准导致的潜在随机数值噪声在傅里叶光谱中也是一个明显可识别的特征。该方法应用于分析HX（X = H - Ne）基态和第一激发态的MRCI势能曲线。所有势能曲线在傅里叶光谱中都表现出与共振存在一致的结构。反双曲余弦坐标映射后的傅里叶光谱的紧凑性质强烈表明，将化学键视为具有潜在双曲性质有一些优势。
