## 1 Introduction  
A fascinating feature of metamaterials is their ability to manipulate and enhance chiral fields, leading to peculiar interactions with chiral matter systems. Several metamaterial structures have been proposed and have demonstrated large circular dichroism (CD) [1; 2; 3; 4]. Interestingly, the superchiral fields originated by such metamaterials boost the molecular CD signals and enable highly sensitive enantioselective detection of chiral molecules [5; 6; 7; 8]. These results indicate that the elucidation of the interaction between metamaterials and molecular systems is an important factor for the future development of metamaterials for relevant applications. Although in [5; 6; 7; 8], the authors have shown that near-field interactions of metallic surfaces and molecules should play an essential role in the above-mentioned metamaterial effects, it is still challenging to reveal the spatial structures of the near-field around a single molecule because of the limited resolution of existing photo-assisted microscopic techniques.  
Photoinduced force microscopy (PiFM), which detects photoinduced force (gradient force) using atomic force microscopy, is a promising approach to address this problem [9; 10]. To observe the optical response of single molecules, various types of scanning microscopic techniques have been developed, such as scanning tunneling microscopy luminescence (STML) [11; 12], tip-enhanced Raman spectroscopy (TERS) [13; 14], and the atomic force microscopy (AFM) with CO-terminated tip [15]. PiFM can be used as a complement to these microscopic techniques because unlike these methods, PiFM does not detect propagating light but directly obtains information of the localized near-field associated with molecules as the force. In particular, PiFM has the advantages of proving vertical polarization of the near-field, detection of buried objects, and no propagation loss [16; 17; 18; 19]. Recently,heterodyne frequency modulation, an innovative measurement technique that enables high-precision and high-resolution PiFM measurements to eliminate photothermal oscillations, has been developed [20; 21]. Further development is expected for atomic resolution PiFM measurements of single molecules. By utilizing such properties of PiFM, we can elucidate the near-field interaction between metamaterials and single molecules. For this purpose, it is important to theoretically clarify how the intrinsic optical response of each molecule can be \"seen\" by PiFM.  
Thus, in this study, we theoretically propose PiFM measurements for a single molecule with a size smaller than 1 nm. In the PiFM system, because the molecules strongly interact with the localized plasmon enhanced at the gap between the tip and substrate, the interaction between the total field created by the entire system, including the molecule, and the polarization of all materials, must be treated self-consistently. By using the discrete dipole approximation (DDA) method, we numerically analyzed the total response field in the PiFM measurements and evaluated the radiation force acting on the tip. We show PiFM images for molecular excitation, including the optical forbidden transition beyond the long-wavelength approximation, and provide an interpretation in terms of the microscopic interaction between the molecule and the localized plasmon. In particular, under the electronic resonance, experimentally obtained images of PiFM become complicated, and hence, the theoretical simulations will be useful for interpreting the images. We also investigated how atomic-scale structures on the tip surface, picocavity [22], play an important role in the atomic resolution measurement of PiFM, which detects the field gradient of localized plasmons.