**4.3 Asymmetric nucleation by one-handed CPL**

Solid CO is formed via CO deposition from the vapor phase in molecular clouds. The crystallinity of solid CO, either amorphous or crystalline, can be determined by the CO flux in a molecular cloud [5]. Because the CO flux in a molecular cloud is much smaller than the critical flux in which amorphous CO (a-CO) is formed, α-CO should be formed. When one-handed CPL is irradiated during the nucleation of α-CO, the formed crystals might have an enantiomeric excess (**Figure 7**). When there are no metal or high-index nanoparticles on icy grains, α-CO can absorb UV-CPL, which may result in excess enantiomeric crystals. In this case, the formation of one-handed α-CO would only occur in the shallow part of the molecular cloud because the UV-ray penetration depth is not so large (see **Figure 6**). However, when there are metal or high-index nanoparticles on the icy grains, the peak absorption wavelength could be transferred to the visible wavelength region, and the peak could be enhanced compared to that of the UV region [65–67], resulting in excess enantiomeric crystals, possibly up to several tens of percent. This could be supported by laboratory experiments on chiral crystallization [68, 69] and theoretical work [70–72]. In this case, the

formation of one-handed α-CO would occur not only in shallow parts of a molecular cloud but also in deeper parts because the penetration depth of visible rays is considerably deep (see **Figure 6**).

A similar process might occur during the crystallization of a-H2O to form chiral ice crystals and hydrogen-ordered cubic and hexagonal ices (see **Table 2**) in protosolar nebula, as shown in **Figure 1**. The crystallization temperature of a-H2O under a 10<sup>5</sup> -years' timescale is 90 K [12]. The penetration depth of UV to visible CPL in protoplanetary disks is smaller than that in molecular clouds. However, icy grains could be moved to the surface of the disk by turbulent motion [73] and irradiated with CPL, resulting in the formation of one-handed, hydrogen-ordered H2O crystals. When ice crystals were recondensed during the cooling of the solar nebula (**Figure 1**), one-handed, hydrogen-ordered H2O crystals might be formed by the same mechanism.

The crystallization of a-CH3OH and a-NH3 also occurred in the protoplanetary disk. Crystallization temperatures of a-CH3OH and a-NH3 under a 10<sup>5</sup> -years' timescale can be estimated from those in the laboratory (a-CH3OH: 100 K [14, 42] and a-NH3: 80 K [15, 45]) and from the assumption that the slopes of a-CH3OH and a-NH3 in the plot of the timescale of crystallization vs. the inverse of the temperature lie between those of H2O [12] and CO2 [6]. We found that the crystallization temperatures of a-CH3OH and a-NH3 under the 10<sup>5</sup> -years' timescale were 40–60 K and 20–40 K, respectively. The formation of one-handed α-CH3OH, NH3 I, and NH3 hydrates might also occur, as in the crystallization of a-H2O. In this way, various kinds of homochiral ice crystals could be formed in protoplanetary disks.

## **5. Conclusion and outlook**

The results of this study indicate the possibility that there were/are many chiral ice crystals in space and that homochiral ice crystals might form by the irradiation of CPL in the star-forming region. These findings have important implications for the origin of the homochirality of organic molecules in space, and the pursuit of the following three suggested areas of study would further our understanding of this.

The crystallinity of CH3OH and NH3 in space and the formation mechanism of α-CH3OH, NH3 I, and their hydrates in protoplanetary disks are still unclear. Therefore, astronomical observations of the crystallinity of these ices are highly desirable.

For chemical reactions on icy grains, only a-H2O ice has been considered as a substrate. The adsorption and subsequent surface diffusion of atoms (H, C, N, and O), small molecules (e.g., CO, CO2, and H2CO), and radicals (e.g., OH, HCO, and NH), followed by surface two-body reactions to form larger molecules on a-H2O at low temperatures have been calculated using astrochemical reaction network models [74]. However, this study indicated the possibility of the growth of single ice crystals on grains. On the surface of α-CO, the adsorption behavior of atoms differs greatly from that on a-H2O [6]. Therefore, it is expected that atoms, except for C and small molecules/radicals, are not adsorbed on the surface of singe-crystalline H2O ice I. Instead, larger molecules/radicals diffuse easily on the surface of singe-crystalline H2O ice I, which leads to the formation of more complex organic molecules. Furthermore, the asymmetric adsorption/synthesis of organic molecules on homochiral ice crystals might also proceed.

The search for enantiomeric surfaces on achiral ice crystals, as investigated in minerals [2, 4], is another important subject that should be explored.
