Herein, a new series of bowl-shaped quadridentate ligands with a Si-N-Si-C-Si-C six-membered ring core and their manganese catalysts were designed using the density functional theory (DFT) method for the hydrogenation of unsaturated CX (XN, O) bonds. The frameworks of these ligands named by LYG (LYG = P(R1)2CH2Si(CH2)(CH3)NSi(CH3)(CH2Si(CH3)CH2P(R3)2)CH2P(R2)2) have a Si-N-Si-C-Si-C six-membered ring core at the bottom of the bowl structure and each Si atom links with one phosphorus arm (-CH2PR2). The Mn catalyst Mn(CO)-LYG was constructed to catalyze the hydrogenation of CO/CN bonds. The calculated results indicate that due to the bowl-shaped structure of LYG quadridentate ligands, these Mn catalysts could be advantageous not only in the tuneup of catalytic activity and stereoselectivity by modifying three phosphorus arms but also in the homogeneous catalyst immobilization by linking with the Si-N-Si-C-Si-C six-membered ring core using different supports. This work might provide theoretical insights to design new framework transition-metal catalysts for the hydrogenation of CX bonds.