tailieunhanh - Carbon Alloys part 2

Tham khảo tài liệu 'carbon alloys part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Hybrid Orbital Control in Carbon Alloys 19 Fig. hybridization. The shading denotes the positive amplitude of the wave function. 12s 2p. is elongated in the positive direction . negative direction of X. Thus when nearest-neighbor atoms are in the direction of the X axis the overlap of xpj with the wave function at X 0 becomes larger compared with the original 2p function so giving rise to a larger binding energy. If 12pv for 12px is selected the wave function shows a valence in the direction of they axis. It is important to emphasize that the solution of Eq. 3 is not a unique solution of Eq. 2 . Below we give a general solution of Eq. 2 . Generality is not lost when 6 I sin0 c COS0 c sin 02 and C4 COS02 and use the orthogonal condition c c C C4 0 which becomes sinO sinO cosOj cosO cos 0 - 0 0 4 and gives 0 -0 Tt 2 so that we obtain sinO2 - COS0 andcosO sin0 .Thus a general solution of sp hybridization is given by denoting 0 simply by 0 in the relations sin6 2 cos0 2pv ISP1 cos 6 2x sin 0 2px where the sign is taken so that Isp2 is elongated in the opposite direction to Ispị . This general sp solution is a two-dimensional unitary transformation which belongs to the special orthogonal group SO 2 of 12s and 2pr . The angle 0 and the signs in Eq. 5 are determined for each molecular orbital so as to minimize the total energy of the molecule. The elongation and the asymmetric shape of the sp hybridized orbital become maxima for 0 rt 4 which corresponds to Eq. 3 . When the two nearest neighbor atoms are different elements the coefficients are shifted from 0 rt 4. When an asymmetric shape of the charge density see Fig. 2 is needed to form a chemical bond then a mixing of 2p orbitals with 2s orbitals occurs. The mixing of 2p orbitals only with each other gives rise to the rotation of 2p orbitals because the 2px 2p _ and 2p. orbitals behave as a vector x y . The wave function Cx 12px Cv I 2ạ. c. 2p. where c2 Cy C2Z 1 is the 2p wave function whose direction of .