LCAO Procedure LCAO 2nd Period LCAO constructs approximate MO s from Hartree AO s Li2 1s2 2s1 1s and 2s differ by 52 eV unlikely that 1s and 2 s interact here Homonuclear second period diatomic molecules Mixing of AO s mixing of different orbitals occurs if energy states are close 1Rydberg 1Ry 13 6 eV Mixing occurs when orbitals of similar symmetry overlap Overlap of 2s and 2 p orbitals creating and bonds radial nodes visible Fig 6 13 p 255 formation of bonding and antibonding g2pz u2pz MO s from 2pz AO s NODE Fig 6 14 p 256 2px and 2py AO s forming g2p u2p MO s contain nodal plane in internuclear axis momentum Fig 6 15 p 257 MO s and their constituent AO s g u omitted 1sA 1sB 1 s 1sA 1sB 1 s 2sA 2sB 2 s 2sA 2sB 2 s 2px A 2px B 2p 2px A 2px B 2p 2py A 2py B 2p 2py A 2py B 2p 2pz A 2pz B 2p 2pz A 2pz B 2p For Z 7 atoms and ions the degenerate 2p MO s are lower in energy than correlation diagram changes between N and O O 2p MO s are lower than 2s N 2p MO s are higher than 2s Fig 6 16 p 258 Drawing the Correlation Diagram 2nd period Li Be B C N O F Ne 2s and 2p mixing confirmed by photoelectron spectroscopy F F bond order 1 What correlation diagrams can tell us Bond order Correlation with Lewis diagram Paramagnetic or diamagnetic O2 6 valence electrons electrons O2 pick the correlation diagram Z 7 get the electron configuration plug them in the AO s Fill in the MO s Bond order 8 bonding 2 4 antibonding 2 2 Paramagentic or diamagnetic Has two unpaired electrons Hunds rule therefore paramagnetic Lewis predicts opposite liquid oxygen attracted by magnetic poles paramagentic Fig 6 18a p 260 N2 5 valence electrons liquid nirogen repelled by magnetic poles diamagentic Fig 6 18b p 260 Table 6 3 p 261 Fig 6 19 p 261 Heteronuclear Diatomic Molecules we drop the u g notation as symmetry changes no inversion symmetry in fact we can forget u and g in the exams now the energy levels of atom A and B differ energy of 1s 2s 2p are different in A and B Heteronuclear Diatomic Molecules 2s CA2sA CB2sB A B molecule 2s C A2sA C B2sB homonuclear CA CB C A C B heteronuclear CA CB C A C B If B is more electronegative than A CB CA for bonding and CB CA for antibonding resembles more a 2sA AO mixing of different orbitals occurs if energy states are close 1Ry 13 6 eV and symmetry is similar NO N 2 3 2s 2p focus on 2 p electrons paramagnetic free radical bond order 2 5 Nitric oxide also known as nitrogen monoxide O 2 4 2s 2p Correlation Diagram for a Heteronuclear diatomic molecule AB B Fig 6 20 p 263 Fig 6 21 p 264 wierd Fig 6 21a p 264 Fig 6 21b p 264 Fig 6 21c p 264 Fig 6 21d p 264 Fig 6 22 p 265 HCl HF En 13 6 2 Zeff 2 n eV Zeff effective atomic charge for the nucleus For approximate values one may use Z directly The 1s orbital energy level is 13 6 eV for hydrogen atoms measured as the ionization energy of H Thus for the quantum number n 1 the energy level for 1s of He is approximately 54 eV 24 6eV Similarly the 1s energy level for F is 1101 eV 696 7 eV Photoelectron spectroscopy H 2 H 2 e IE 15 5 eV h photon 1 2 mv2 Eivib Vibrational excitation approaches dissociation limit A photoemission from bonding orbital bond order decreases vibrational mode is softer B antibonding orbital bond order increases vibrational mode higher stiffer bond C non bonding orbital no change in vibrational frequency p 266 N1s N2 p 267 O1s O2 p 267 O1s N1s NO core electrons fairly insensitive to bonding except chemical shift CORE ELECTRONS p 267 MO theory MO theory Molecular orbital theory atomic orbitals no longer have no significant meaning after atoms form molecules Electrons no longer belong to a particular atom but to the molecule as a whole In MO theory electrons reside in molecular orbitals that are delocalized over the entire molecule The complexity of the full MO model increases exponentially with the size of the molecule Valence Bond VB Valence bond VB theory is a simple and useful framework through which we may understand covalent bonding VB has several drawbacks First when using this model it is difficult to say anything about the energies of electrons A more serious drawback of the VB model is its assumption that electrons are localized to specific atoms Lewis dot for ozone In fact electrons are commonly delocalized to several atoms as described by resonance structures MO theory we studied overcomes both those limitations Valence Bond VB theory O H C C C H don t vary much in bond length polarity bond energy form compound to compound LCAO assumes delocalization of electrons all over the molecule in form of MO s VB theory developed to justify Lewis dot method views QM of bonds bond is the product of two one electron AO s Pauli exclusion spin pairing is applied Can link with VSEPR method Valence bond theory VB is a straightforward extension of Lewis structures Valence bond theory says that electrons in a covalent bond reside in a region that is the overlap of individual atomic orbitals the covalent bond in molecular hydrogen can be thought of as result of the overlap of two hydrogen 1 s orbitals Molecular Geometry Valence Bond model runs into problems for molecular geometry Tetrahedral geometry of methane is clearly impossible if carbon uses its 2s and 2p orbitals to form the C H bonds which should yield bond angles of 90 degrees H2 VB theory isolated atoms RAB large atoms interact electron 1 associated with nucleus A or B so we write the sum of two terms symmetry requires c1 c2 and c1 c2 gerade g and u ungerade two electron wave functions to calculate prob density of electron 1 need to square function and average over positions for electron 2 and do reverse for electron 2 next we add both results can calculate for a series of RAB results show elg is lower in energy than isolated atoms elu is higher for all separations RAB Fig 6 24a p 269 Shorthand form 1 2 electron 1 and 2 s coordinates 1sA 1sB one electron AO wave function of nucleus A and B c1 is a normalization constant F2 1s2 2s2 2pX2 2pY2 2pZ1 similar in shape 2 overlapping 2pz orbitals provides no information on remaining 12 e s Heteronuclear HF drop u g notation c1 c2 H1s and F2p overlap 1s 1s 2pz 2pz 2s 2pz cylindrical symmetry bond VB theory bond wave functions are not MO s not delocalized and not single electron wave functions spins in bond …
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