b. sp2hybridization (trigonal planar)One s and two p (px and py) AOs mix to form a set of threehybrid orbitalsO-Equivalentsp?2px2s0pxO+2px2s2p1PJh32pJ2px2s2p30Ssp2, D3h, 0-120°, trigonalα = 1/3 (component of s-orbital)
• One s and two p (px and py ) AOs mix to form a set of three hybrid orbitals. b. sp2 hybridization (trigonal planar) sp2 , D3h, =120º, trigonal = 1/3 (component of s-orbital) h s p x p y h s p x p y h s p x 3 2 2 2 2 2 1 2 2 1 6 1 3 1 2 1 6 1 3 1 3 2 3 1 • Equivalent sp2 :
In general, an sp? hybrid orbital can be expressed as.pm = a,Φ, + b,d2px + C,p2pyFor equivalent hybridization: the weighting of s orbital in eachhybrid orbital is α = a;?=1/3, and therefore a, = 3-1/2= pm: = (1 / /3 )Φ, + b,d2px + Cc,d2i2pySupposing Φh, is parallel to the x-axis, but perpendicular to the y-axis,thenwehave中h = /1 / 3g, + b,d22pxNormalization中h = /1/30, +/2/3gpx
hi i s i px i py a b c 2 2 For equivalent hybridization: the weighting of s orbital in each hybrid orbital is = ai 2=1/3, and therefore ai = 3 -1/2 Supposing h1 is parallel to the x-axis, but perpendicular to the yaxis, then we have h1 1 3s bi 2 p x / Normalization h i s i p x i p y b c 1 3 2 2 ( / ) h1 1 3s 2 32 p x / / In general, an sp2 hybrid orbital can be expressed as
gh = /1/3g, + /2/3p2px中n: = /1/30, +b,Φ2 px +c,02py(i = 2 or 3)Normalization and orthogonality→1/3+/2/3b2 +0.C2=0ajaz +b,b, +c,C2 = 0-→ 1/3+b,2+c2 =1a2 +b, +c2 =1→b, =-/1/6C =±/1/2pm2 =/1/30,-/1/602px+V1/20p2pypn3=/1/3g,-V1/6g2px-V1/202py
h i s i p x i p y b c 3 2 2 1/ h1 s 3 2 p x 1/ 3 2 / Normalization and orthogonality 1/ 3 1 1/ 3 2 / 3 0 0 2 2 2 2 2 2 b c b c 1 0 2 2 2 2 2 2 1 2 1 2 1 2 a b c a a b b c c b2 1/ 6 c2 1/ 2 h2 s 2 p x 2 2 p y 1/ 3 1/ 6 1/ h3 s 2 p x 2 2 p y 1/ 3 1/ 6 1/ (i = 2 or 3)
c.sp3hybridization(tetrahedral)One s and 3 p AO's mix to form a set of four hybrid sp3 orbitals: For equivalent sp3 hybridization (α=1/4), e.g, CH4X[s+px+p,+p.]PhiH:C:H2HΦn2ZLSs-px-p,+p.J2@n1dh ==[s- px + P,- p.]VXdh4 =s+px-p,-p.]Spn3dn42CH4, SiH4, GeH4, PX4, S-, PO
H C H H H h1 h2 h4 h3 z [ ] 2 1 h2 px py pz s [ ] 2 1 h1 px py pz s [ ] 2 1 h4 px py pz s [ ] 2 1 h3 px py pz s • One s and 3 p AO’s mix to form a set of four hybrid sp3 orbitals. • For equivalent sp3 hybridization (=1/4), e.g, CH4 c. sp3 hybridization (tetrahedral) 3 4 2 4 4 4 4 4 CH ,SiH ,GeH ,PX ,SO ,PO x y
Xd. dsp3 (sp3d) hybridization (bipyramidal)dn32pΦn4FpF中n2Ph5P:F[p, +d_ ];dFThe bond lengths will not be the same because there is mored contribution to the axial hybrid orbitalsFor dsp3, the axial bonds are shorter.For sp3d, the axial bonds are longer, e.g., in PF5(But mostly exaggerating the contribution of d orbitals!)
P F F F F F h x y h x y h x s p p s p p s p 2 1 6 1 3 1 2 1 6 1 3 1 3 2 3 1 3 2 1 h1 h2 x y h3 [ ] 2 1 [ ]; 2 1 4 2 5 2 z h z z h pz d p d h4 h5 z d. dsp3 (sp3d) hybridization (bipyramidal) The bond lengths will not be the same because there is more d contribution to the axial hybrid orbitals. • For dsp3 , the axial bonds are shorter. • For sp3d, the axial bonds are longer, e.g., in PF5 . (But mostly exaggerating the contribution of d orbitals!) S F F F F