## 3 Molecular Force Field Description and Modeling
\[l_{0}=\lambda_{0}(\lambda_{1}-\lambda_{2}\Delta v-\lambda_{3}\Delta a)v_{n} \tag{2}\]  
In the equation, \(l_{0}\) represents the equilibrium distance between vehicles; \(\Delta v\) denotes the speed difference between the target vehicle and the interacting vehicle; \(\Delta a\) signifies the acceleration difference between the target vehicle and the interacting vehicle; \(v_{n}\) indicates the speed of the target vehicle; and \(\lambda_{0}\), \(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\) represent the comprehensive influence parameters of speed, speed difference, and acceleration difference. By integrating Equations (1) and (2), we constructed the vehicle interaction field as follows:  
\[U(l)=l_{m}\Big{\{}\{1-\exp[-\beta l+\lambda_{0}v_{n}(\lambda_{1}-\lambda_{2} \Delta v-\lambda_{3}\Delta a)]\}^{2}-1\Big{\}} \tag{3}\]  
Figure 1: Trends in the Morse potential field. In the equation, \(l_{m}\) denotes the maximum interaction distance between vehicles, \(l\) represents the distance between vehicles, and \(\beta\) is the field parameter. Building upon this, we applied the gradient descent method to derive the force function acting on the target vehicle as follows:  
\[F(l)=-\frac{dU(l)}{dl}=-2\beta l_{m}\{1-\exp[-\beta(l-l_{0})]\}\exp[-\beta(l-l_{ 0})] \tag{4}\]  
Furthermore, we can derive the acceleration of the target vehicle induced by the interaction force field as follows:  
\[a=\frac{2\beta l_{m}\{\exp[-\beta(l-l_{0})]-1\}\exp[-\beta(l-l_{0})]}{M} \tag{5}\]  
In the equation, \(M\) represents the mass of the target vehicle. Based on the vehicle interaction force field, we can derive the potential risk field associated with vehicle interactions as follows:  
\[U_{V}=l_{m}\Big{\langle}\{1-\exp[-\beta l+\lambda_{0}v_{n}(\lambda_{1}-\lambda _{2}\Delta v-\lambda_{3}\Delta a)]\}^{2}-1\Big{\rangle}\cdot\omega\cdot\exp( \cos\theta) \tag{6}\]  
In the equation, \(\theta\) denotes the angle between the vehicle's velocity direction and the road's centerline, while \(\omega\) represents the field parameter. To integrate spatial and temporal risks, while distinguishing the impact of varying future time on the risk field, we introduced the discount function \(\gamma(t)\). This discount function adheres to the principle of half-life, exhibiting an exponential decay in its value as the future time unit progresses. \[\gamma(t)=(0.5)^{t/t_{1/2}} \tag{7}\]  
In the equation, \(t_{1/2}\) represents the half-life, indicating the driver's level of concern regarding future risks. A larger value of A signifies a slower decay of the risk field across spatial dimensions, reflecting a heightened awareness of long-term future risks by the driver; \(t\) denotes the future time variable. From Equations (6) and (7), we can derive the potential spatiotemporal risk field of vehicle interactions as follows:  
\[U_{r}=l_{m}\Big{\{}\{1-\exp[-\beta l+\lambda_{0}v_{n}(\lambda_{1}-\lambda_{2} \Delta v-\lambda_{3}\Delta a)]\}^{2}-1\Big{\}}\cdot\omega\cdot\exp(\cos\theta )\cdot(0.5)^{t/t_{1/2}} \tag{8}\]  
In order to more accurately describe the risk zone, it is essential to consider the actual occupied area of each vehicle. The actual occupied area refers not only to the physical space occupied by the vehicle on the road, but also its safety margin. [PERSON] [19] describes the safety margin as the \"distance that causes a perceived threat to the driver\", which represents the vehicle dimensions as perceived by the driver. It is the additional space allocated to the vehicle, providing the driver with a greater sense of safety and comfort during operation. Furthermore, it helps compensate for measurement errors in onboard and road-based sensors to some extent, thereby aiding in making more conservative risk predictions. Therefore, the safety margin is expressed as the maximum interaction distance (\(l_{m}\)) between the target vehicle and the interacting vehicle, as follows:  
Figure 1.0  
In the equation, \(V_{R}\) represents the speed of the target vehicle, while \(V_{F}\) denotes the speed of the interactive vehicle.