This work presents the quantum mechanics calculation based on density functional theory ( DFT ) for the design of new asymmetric diphosphine ligands. Complexex of this ligand can be expected to combine high catalytic activity with thermal stability under the mind conditions of methanol carbonylation process. Chapter 1 introduces quantum mechanics asymmetric/unsymmertric diphosphine ligand , methanol carbonylation cycle and homogeneous catalysis. Chapter 2 provides the literature review. Chapter 3 presents scope, aim , methodology and apparatus. Chapter 4 presents the design and study of new asymmetric diphosphine ligands , which contain thiis asymmetric diphosphine ligand 1.1 which can be a promoter for methanol carbonylation. Because 1.1 has a chiral center with electron withdrawing group and electron donating group. This would be the reason that the different trans-influence and trans effect or complex type “ Rh(L)L’(1.1) “ would favor the formation of different isomers. Complex 1.5 is the most stable isomer among its four isomers. It cans notices notices that the stereochemistry at rhodium in which the P(Me)2 irans to the CO and the PF2 fies trans to the Me group are preferred. The presence of strong electronegativity atoms in PF2 makes them weak ?-donors but much stronger ?-acceptors and the presence of Me groups in P(Me)2 makes them stronger ?-donors but much weaker ?-acceptors , with confirming by the Rh-P bond distances. The electronic property is in a good agreement. All considered complexes adopt a square-planar geometry. The molecular orbital confirmed that the dZ2 orbital is lower energy than dX2-y2 orbital as expected for a low-spin d8 orbital Rh ( 1 ) configuration. In a homogeneous methanol carbonylation process as developed by Forster, the outer processes involve organometallic compounds. The process made up of some four separation stoichiometric reactions, namely the oxidative addition , migratory insertion , CO ligand insertion and feductive elimination. The full catalytic cycle of asymmetric diphosphine rhodium complex 1.5 methanol carbonylation process are investigated. The investigation involves consideration of many possible structures of reaction intermediate. Isomer 1.5 is formed to be the initial catalytically active species. The interaction with the substrate CH3I results in the formation of the six coordinated complexes N1 and N2. Later, they transform into the isomeric five coordinated acetyl complexes O3 and O4 , as the results of migratory insertion process. Isomers O3 and O4 react rapidly, with CO to form the six coordinated dicarbonyl complexes P5 and P6. Finally, the acetyl iodide hydrolysis leads to the formation of the target product, acetic acid. By consideration of the difference of energy ( ?E )values, the calculated equilibrium constant confirmed the possibility to make this model 1.5. Chapter 5 presents the investigation of asymmetric rhodium catalysis 1.3 as the starting material for the methanol carbonylation cycle. Again, the outer four process are investigated. From the optimization data, the methyl iodide oxidative addition to the four coordinated reactant 1.3 is six coordinated isomers B5. The Co migratory insertion of octahedral isomers B5 yield the square pyramidal structures C2 and C3. The product of CO ligand addition to the five coordinated isomers C2 and C3 are six coordinated acetyl structures D5 and D6 which also are the precursor of the last reaction step, acetlyiodide elimination. In this last reaction, the six coordinated isomers D5 and D6 transform into square planar isomer 1.3. As regard the optimization energy , the methanol carbonylation process can separate into 2 routes. The first one is 1.3 + Me B5C3+COD6.The second route is 1.3+MelB5C2+COD5. The reaction energy of these two steps is about the same. This is confirmed that the oxidative addition of methyl iodide to 1.3 may have only isomer B5. Form the enthalpy energy, the product from oxidative to migratory insertion change repidly, indicating from the similar energy. Once again , the difference of energy ( ?E 0 values are used to calculated equilibrium constant and confirmed the possibility to make this model 1.3.