Overall, our results demonstrate the good performance of the CT-TSH method and its potential for simulating excited-state processes, making it a promising tool for broader utilization in the future, for medium-to-large systems. Moreover, these findings suggest that the CT-TSH method has great potential for integration with other electronic structure methods, such as ab initio approaches. A RK4 method for the numerical integration of the electronic coefficients propagations in CT-TSH using the LD algorithm.