In many practices, the classical Smoluchowski rate is often used as the initial guess for the diffusion-controlled reaction rate, e.g., in protein-protein interactions. Unfortunately, this rate is often several orders of magnitude different from the experimental results, and has difficulties to explain the concentration dependence of the rate constant. An effective reaction cross-section is often introduced for a given condition to replace the simple summation of the radii. Further justifications such as steric, geometry, rotation, long-range interaction, and activation energy effects are introduced to bring this initial guess to more realistic values. However, complications have been observed in simulations and experiments that are challenging the foundation of this rate equation in the reaction order of 2. Updating the calculations on collision frequency with diffusion is essential to us. There are more relevant problems of reactions that happened in the diluted conditions than in the neat gas phase, such as reactions in all biological systems, in the ocean, in the air, or in most industrial processes. Even if there is no solvent exist, often the products of the reaction will eventually dilute the system into the region where the original collision theory has difficulty to calculate the collision frequencies. To predict the rate of a reaction under such conditions, one must calculate the collision frequencies and the reaction probabilities of each collision in a different way than the classical collision theory.