Spin polarization effect for Cr2 molecule

Density functional theory (DFT) (B3P86) of Gaussian 03 has been usedto optimize the structure of the CrCrCr$_{2}$, spin polarization,density functional theory, potential functionProject supportedby the National Natural Science Foundation of China (Grant No10647136).3420, 3420B, 3520D, 3520GDensity functional theory (DFT) (B3P86) of Gaussian 03 has been usedto optimize the structure of the Cr$_{2}$ molecule, a transitionmetal element molecule. The result shows that the ground state forthe Cr$_{2}$ molecule is a 13-multiple state, indicating that thereexists a spin polarization effect in the Cr$_{2}$ molecule.Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wave functions ofhigher-energy states. So the ground state for Cr$_{2}$ moleculebeing a 13-multiple state is indicative of spin polarization effectof the Cr$_{2}$ molecule among transition metal elements, that is,there are 12 parallel spin electrons in the Cr$_{2}$ molecule. Thenumber of non-conjugated electrons is greatest. These electronsoccupy different spatial orbitals so that the energy of the Cr$_{2}$molecule is minimized. It can be concluded that the effect ofparallel spin in the Cr$_{2}$ molecule is larger than the effect ofthe conjugated molecule, which is obviously related to the effect ofelectron d delocalization. In addition, the Murrell--Sorbie potentialfunctions with the parameters for the ground state and other statesof the Cr$_{2}$ molecule are derived. The dissociation energy {itD}e for the ground state of the Cr$_{2}$ molecule is 0.1034,eV,equilibrium bond length {it R}e is 0.3396,nm, and vibrationfrequency $omega_{rm e}$ is 73.81,cm$^{-1}$. Its force constants$f_2$, $f_3$ and $f_4$ are 0.0835, $-$0.2831 and0.3535,aJ,$cdot$,nm$^{- 4}$ respectively. The otherspectroscopic data for the ground state of the Cr$_{2}$ molecule$omega_{rm e}chi _{rm e}$, $B_{rm e}$ and $alpha_{rm e}$ are1.2105, 0.0562 and 7.2938,$times10^{-4}$cm$^{-1}$ respectively.