3CHAPTER 11 THEORIES OF MOLECULAR BONDING II In order to achieve agreement with observed molecular structures the atomic orbitals used to create the molecular bonds are hybridized Happens before creating the overlap of atomic orbitals to form the molecular orbital Valence Bond Theory Orbital Overlap and the Name of the Chemical Bond Electron rearrangement of atomic structure that results in the minimum potential energy of the molecular structure molecular structure For each wavefunction there is a corresponding energy representing the energy of that electron in the specific orbital Lewis structures way to find molecular structures of the lowest potential energies Wavefunction for the molecule some resemblance to the wavefunction for the atom o Formal charges good in cases of ambiguity o 2 dimensional use VSEPR 3D o Equation with normalization term This equation also puts emphasis on overlap of atomic orbitals o Orbital overlap S sum over all of the volume elements within the overlap region in the limit of small V Of key importance in understanding the structure and strength of the chemical bond With increasing the overlap of two orbitals the strength of the bond formed the decrease in potential energy increases until the proton proton repulsion at very small internuclear distance begins to dominate the attraction of the two atoms that form the molecular bond Valence Bond Theory based on the development of combinations of atomic orbitals that combine to form orbital overlap between 2 atoms Molecular Shape and the Concept on Bond Hybridization Wavefunctions can mix in any manner that will reduce the potential energy of the ensemble of electrons and nuclei of the molecule sp3 Hybridization and the Structure of Methane Combine 1 s orbital and 3 p orbitals o Result 4 hybridized orbitals of carbon in the molecular structure of methane o All 4 resulting hybridized orbitals are of equal energy o Each 25 s and 75 p character This mixing of atomic orbitals of the separated atoms to form hybrid orbitals in the molecule formed from those atoms shows the wave nature of the electron o Wave nature shown in its ability to combine spatially in whatever manner is required to lower the potential energy of the assembled molecule Electrons masters of energy minimization o Only takes 10 15 seconds to switch from an unhybridized orbital to a hybridized one sp2 Hybridization and the Formation of and double bonds One sp2 sp2 bond is formed first Then the unhybridized p orbitals form a bond that locks the remaining sp2 orbitals into a common plane o Forms a double bond Pi bond is the weaker of the 2 bonds sp Hybridization and the Formation of Triple Bonds Can mix orbitals with any combination of coefficients that minimize the energy of the molecular structure Mix one s orbital with one p sp orbital Triple bond 1 bond 2 bonds Trigonal Bipyramidal and Octahedral Geometry sp3d and sp3d2 Hybrid Orbitals VB theory formed with quantum mechanics wavefunction addition Lewis structures and VSEPR Need one d atomic orbital to make sp3d Molecular Orbital Theory and Electron Delocalization It is the tendency of electrons to delocalize from the confinement of atomic orbitals to the geometrical flexibility of extended molecular orbitals Electrons will employ the full spatial dimension of a molecular structure to spread out over when given the opportunity delocalize o In order to minimize the potential energy of the ensemble of electrons and nuclei When the schr dinger equation is solved for a molecule a molecular orbital results Must add 2 wavefunctions by correctly combining both the amplitude and phase of those individual waves to find the resulting multi electron wavefunction of the molecule o Electron density what controls the forces and thus the potential energy surface that defines the strength and character of a chemical bond New molecular orbital H2 A B Total MO molecular orbital Linear combination of atomic orbitals use of atomic orbitals of the separated atoms to form the molecular orbitals of the molecule formed Bonding and Antibonding Orbitals Atomic orbitals can add destructively as well as constructively Destructive union of 2 atomic orbitals destructive interference Combining mixing two electron wavefunctions destructively the resultant MO will increase in potential energy with decreasing internuclear distance o Antibonding orbitals o Antibonding orbitals have a higher energy than bonding orbitals Two ways to combine mix wavefunctions of 2 separated hydrogen atoms o 1 Constructive o 2 Destructive leading to an increase in electron density between the two atoms that comprise the molecule and a decrease in potential energy created by the net attraction between the two atoms decrease in electron density between the two atoms and an increase in potential energy potential energy created by the net repulsion between the atoms Nodal plane plane of zero electron density between two nuclei o Greater the number of nodal planes higher the energy MO has both an amplitude and a phase MO s are filled I their order of increasing energy A MO can be occupied by max of 2 electrons one spin up one spin down Molecular Orbital Structure of Molecular Oxygen P orbitals also experience bonding and Antibonding 2py must combine with 2py same with 2px and 2pz Molecular Orbital Structure and the Potential Energy Structure Potential energy diagram shows o The geometry of the atomic orbitals as they form the MO s w decreasing internuclear distance o Molecular orbital diagram that defines the energy ordering and spacing of the MO s as a function of decreasing internuclear distance as the molecular bonds form o Potential energy surface of bound molecules Basic LCAO MO Theory o MO s are added together by mixing atomic orbitals Must be added constructively or destructively o May be more molecular orbitals than electrons available but electrons always fill into the lowest orbital o Bond order e s in bonding e s in Antibonding 2 Each electron that enters a bonding molecule strengthens the molecular bond each electron that enters an antibonding orbital weakens or destabilizes the molecular bond Molecular Orbital Structure of Homonuclear Diatomics Order of pi and sigma orbitals switches after O2 o B c electrons will do whatever is necessary to lower the potential energy of the ensemble of electrons Has to do with energy of 2px orbital Molecular Orbital Structure of Heteronuclear Molecules MO drawn at lower energy than the more