Chemical BondingChemical BondingHydrogen atom based atomic Hydrogen atom based atomic orbitalsorbitals a.k.a. hydrogen atom a.k.a. hydrogen atom wavefunctionswavefunctions: 1s, 2s, 2p, 3s, 3p, 3d, : 1s, 2s, 2p, 3s, 3p, 3d, …………..yy1s1s = 1/( = 1/(pp))1/21/2(1/a(1/a00))3/23/2 exp[-r/a exp[-r/a00], a], a00=Bohr Radius = 0.529 Angstroms=Bohr Radius = 0.529 Angstroms••xxyyzzNucleusNucleus••rrElectronElectron((xx,,yy,,zz))rr22==xx22++yy22++zz22OrbitalsOrbitals, , Wavefunctions Wavefunctions and Probabilitiesand ProbabilitiesThe orbital or The orbital or wavefunction wavefunction is just a mathematical function is just a mathematical function that can have a that can have a magnitudemagnitude and and signsign (e.g. + 0.1 or -0.2) at a (e.g. + 0.1 or -0.2) at a given point r in space.given point r in space.Probability of finding a 1s electron at a particular point in Probability of finding a 1s electron at a particular point in space is often not as interesting as finding the electron space is often not as interesting as finding the electron in a thin shell between r and r+in a thin shell between r and r+drdr..OrbitalsOrbitals, , Wavefunctions Wavefunctions and Probabilitiesand ProbabilitiesProbability of finding a 1s electron in thin shell Probability of finding a 1s electron in thin shell between r and r+between r and r+drdr::ProbProb(r,r+(r,r+drdr) ~ ) ~ yy1s1s yy1s1s [r [r22]]drdr•rrr+r+drdrVolume of shell of thickness Volume of shell of thickness drdr::[r>>>dr Æ 3r2dr>>> 3r(dr)2+(dr)3 ]dV = (4/3)p [(r)3+3r2dr+ 3r(dr)2+(dr)3 - r3]dVdV≈≈(4(4p)[r2dr]Bonding in Diatomic Molecules such as HBonding in Diatomic Molecules such as H22••••••••rr11rr22H Nucleus AH Nucleus AH Nucleus BH Nucleus Byy1s1s(A) = 1/((A) = 1/(pp))1/21/2(1/a(1/a00))3/23/2 exp[-r exp[-r11/a/a00], 1s orbital for atom A], 1s orbital for atom ANote the two Note the two orbitals orbitals are centered at different points in space.are centered at different points in space.zz11xx11zz22xx22yy11yy22Bonding Bonding AxisAxisss1s1s = C = C11[[yy1s1s(A) + (A) + yy1s1s(B)], Sigma 1s (B)], Sigma 1s Bonding MolecularBonding Molecular orbital. Corbital. C11 is a constant. is a constant. Note that probabilities for finding electron at some position in Note that probabilities for finding electron at some position in space scale like [space scale like [ss1s1s]]22 and [ and [ss1s1s*]*]22::[[ss1s1s]]22 = {C = {C11[[yy1s1s(A) + (A) + yy1s1s(B)]}(B)]}2 2 = = (C(C11))22{[{[yy1s1s(A)](A)]2 2 + [+ [yy1s1s(B)](B)]2 2 + 2[+ 2[yy1s1s(A)][(A)][yy1s1s(B)](B)]} } [[ss1s1s*]*]22 = {C = {C22[[yy1s1s(A) - (A) - yy1s1s(B)]}(B)]}22 = = (C(C22))22{[{[yy1s1s(A)](A)]2 2 + [+ [yy1s1s(B)](B)]2 2 - 2[- 2[yy1s1s(A)][(A)][yy1s1s(B)](B)]}}““Non-interactingNon-interacting”” part is result for large part is result for large separation between nucleus A and Bseparation between nucleus A and BNotational DetailNotational DetailOxtoby Oxtoby uses two different notations for uses two different notations for orbitals orbitals in the 4th and 5th editions of the class text:in the 4th and 5th editions of the class text:ss1s1s* i* in the 4th edition becomes ssu1su1s* in the 5th editionss1s1s i in the 4th edition becomes ssg1sg1s in the 5th editionThe addition of g and u provides some extra identificationof the orbitals and is the one encountered in the professionalliterature.g and u are from the German “gerade” and “ungerade”ANTIBONDINGANTIBONDINGBONDINGBONDINGNON-INTERACTINGNON-INTERACTINGWave FunctionsWave FunctionsElectron DensitiesElectron Densities[y - y ]1s21s 1ss*= CA B1s 1s 1s[y + y ]1s= CA BABA BBA+++++-AA BB1s[ s *]21s[ s ]21s1s1s1syy22(n.i.) (n.i.) ~~[(y ) + (y ) ][(y ) + (y ) ]2222AABBH2+--yy1s1s(B)(B)yy1s1s(A)(A)- 2[y1s(A)][y1s(B)]+ 2[y1s(A)][y1s(B)]Pushes e- away fromregion betweennuclei A and BPushes ePushes e-- between betweennuclei A and Bnuclei A and Byy1s1s(A)(A)yy1s1s(B)(B)A BPotential Energy of H2+V(R)RR1.07 1.07 ÅÅ ∆∆EEdd==255 kJ mol255 kJ mol-1-1H + HH + H++0HRR HSingle electronholds H2+ togetherSeparated H, H+s1ss**1sEss11ss**HH22 Molecular Molecular OrbitalsOrbitalsss11ss1s(H Atom A)Atomic Orbital1s(H Atom B)Atomic OrbitalCORRELATION DIAGRAMCORRELATION DIAGRAMHH22Energy Ordering:ss11ss < 1s < ss11ss**Ess11ss**HeHe22 Molecular Molecular OrbitalsOrbitalsss11ss1s(He Atom A)Atomic Orbital1s(He Atom B)Atomic OrbitalCORRELATION DIAGRAMCORRELATION DIAGRAMHeHe22Z for He =2Ess22ss**LiLi22 Molecular Molecular OrbitalsOrbitalsss22ss2s(Li Atom A)Atomic Orbital2s(Li Atom B)Atomic OrbitalCORRELATION DIAGRAMCORRELATION DIAGRAMLiLi22For LiFor Li22 ( (ss2s2s))22, Bond order =, Bond order =(1/2)(2-0) = 1(1/2)(2-0) = 1Bonding for Second Row Bonding for Second Row DiatomicsDiatomicsInvolves the n=2 Atomic ShellInvolves the n=2 Atomic ShellLithium atomic configuration is 1s22s1(Only the 2s electron is a valence electron.)Li2 dimer has the configuration:[([(ss1s1s))22((ss1s1s*)*)22] (] (ss2s2s))22= [KK]((ss2s2s))22Bonding for Second Row Diatomics: the Role of 2p OrbitalsOnce the s2s, s2s* molecular orbitals formed from the2s atomic orbitals on each atom are filled (4 electrons, Be2),we must consider the role of the 2p electrons (B2 is firstdiatomic using 2p electrons).There are 3 different sets of p orbitals (2px, 2py, and 2pz), allmutually perpendicular. If we choose the molecular diatomic axis to be the z axis (this is arbitrary), we have a picture like this:••Nucleus A Nucleus Bx1y1x2y2zz11zz22Bonding Axis+2p2pzz obital on atom 1 and atom 2+- -2p2pzz orbitals orbitals point point atat each other.each other.••Nucleus A Nucleus Bx1y1x2y2zz11zz22Bonding Axis++- -2p2pxx orbital on orbital onatom 1 and atom 2atom 1 and atom 22px orbitalsare parallel to each