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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne)
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The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne)

机译：双曲化学键：HX（X = H-Ne）的基态和第一激发态势能曲线的傅立叶分析

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摘要

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H-2 X (1)Sigma(+)(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-Cl 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 C, 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.
机译：RHF / aug-cc-pVnZ，UHF / aug-cc-pVnZ和QCISD / aug-cc-pVnZ，n = 2-5，H-2 X（1）Sigma（+）（g）的势能曲线为通过反双曲余弦坐标映射转换为新坐标系后，通过傅立叶变换方法进行分析。傅立叶频域频谱是根据潜在的数学行为进行解释的，从而产生了鲜明的特征。在HF和全Cl水平下计算出的势能曲线的基本数学性质之间存在明显差异。该方法特别适合于在最高理论水平上获得的势能曲线的分析，因为观察到傅立叶频谱具有紧凑的性质，傅立叶频率系数的包络以指数方式衰减幅度。描述CI曲线所需的有限数量的Fourier C，系数允许开发出最佳的采样策略，该策略对应于指数和几何收敛所需的策略。由于有限收敛准则而导致的潜在随机数字噪声也是傅立叶频谱中的一个明显可识别的特征。该方法适用于分析HX（X = H-Ne）的基态和第一激发态的MRCI势能曲线。所有势能曲线在傅立叶光谱中均显示出与共振一致的结构。逆双曲余弦坐标映射之后的傅立叶光谱的紧致性质强烈暗示，将化学键视为具有潜在的双曲性质具有一定优势。

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