原子力显微镜(AFM)实验上已经成功地直接观测到分子间的氢键作用，但是其成像机理在理论上并不清楚,缺乏完善的计算模拟进行验证。本文基于密度泛函理论(DFT)，利用第一性计算方法，采用vasp软件包，对水分子以及甲酸分子各自形成的氢键结构进行了DFT计算，并利用力谱、相互作用能谱、频移谱的形式对氢键进行了表征。计算表明力谱、频移谱是表征氢键最好的方式，分别对应着AFM的两种工作模式。要实现较高的分辨率，合适的高度是其中的关键，而高度的选择要使短程的化学力成为力的主要成分，频移谱的最佳测量高度比力谱的最佳测量高度要高一些。力谱比频移谱更好地识别分子间的氢键，而频移谱比力谱更好的识别分子内化学键。分子形成氢键的时候，电荷密度会发生重新分布，成像会有一定的失真。

Hydrogen bond has been successfully observed in the latest atomic force microscopy(AFM) experiment, but its atomistic mechanism is unclear ,neither it has been validated in simulat or quantum theory. This thesis is based on density functional theory, using first-principles calculations implemented in vasp packages. The hydrogen bond structures made by water molecules and formic acid molecules have been studied, and the force spectrum, the interaction energy spectrum, and frequency shift spectrum have been obtained to characterize hydrogen bonds. Calculation shows that force spectrum and the frequency shift spectrum are the best way for the characterization of hydrogen bond, which corresponds to two kinds of working mode of AFM,respectively. To achieve high resolution, appropriate height for the AFM tip is the key, by which the chemical force become dominant. Moreover,the optimal height for frequency shift spectrum is slightly higher than that for the force spectrum. Force spectrum is better than frequency shift spectrum in the identification of intermolecular hydrogen bonds, while frequency shift spectrum is better in the identification of intramolecular bonds.When the molecules form intermolecular hydrogen bonds, charge density redistributes, the resulted AFM image to distort to some extent.