As one of the major carbon producers, data centers produce around 1% of global carbon emissions per year. Researchers are making significant effort to reduce the data center carbon emissions. However, the current carbon-neutral data center solutions seldom take the carbon quotas into account, nor do they integrate new emission reduction technologies like Carbon Capture (CC) and Power-to-Gas (P2G), etc. To bridge this gap, in this paper a novel carbon-neutral data center architecture is proposed based on which a holistic cost minimizing problem is formulated. We use the Variational Mode Decomposition (VMD) and the Long Short-Term Memory (LSTM) neural network to construct highly accurate prediction models, and develop a Model Predictive Control (MPC) algorithm for energy and carbon management. Finally, simulations on real-world data demonstrate that our approach reduces up to 19.19% overall cost compared with traditional solutions.