Calculating the rate constant for the photoisomerization of retinal to the all-trans configuration in the Rhodopsin protein using ab initio calculations of excited state dynamics is a complex task that requires specialized software and computational resources. As an AI language model, I am unable to perform these calculations directly.However, I can provide you with some general information on the process. The photoisomerization of retinal in the Rhodopsin protein is a key step in the process of vision. Upon absorption of a photon, the 11-cis-retinal chromophore undergoes an ultrafast isomerization to the all-trans configuration. This process occurs on a timescale of femtoseconds to picoseconds.To calculate the rate constant for this process, you would need to perform ab initio calculations of the excited state dynamics, which typically involve solving the time-dependent Schrödinger equation for the system. This can be done using quantum chemistry software packages like Gaussian, ORCA, or Q-Chem, among others.Once you have obtained the excited state potential energy surfaces and the corresponding wave functions, you can use various methods to estimate the rate constant, such as the fewest switches surface hopping FSSH algorithm or the direct quantum dynamics approach.Keep in mind that these calculations can be computationally demanding and may require significant computational resources and expertise in quantum chemistry.