Molecular Orbital Theory PDF

Molecular Orbitals An approach to bonding in which orbitals encompass the entire molecule, rather than being localized between atoms.  Molecular Orbitals Molecular orbitals result from the combination of atomic orbitals. Since orbitals are wave functions, they can combine eithe...

Molecular Orbitals An approach to bonding in which orbitals encompass the entire molecule, rather than being localized between atoms.  Molecular Orbitals Molecular orbitals result from the combination of atomic orbitals. Since orbitals are wave functions, they can combine either constructively (forming a bonding molecular orbital), or destructively (forming an antibonding molecular orbital).  Molecular Orbitals Molecular orbitals form when atomic orbitals with similar energies and proper symmetry can overlap. Atomic orbitals with differing energies or the wrong spatial orientation (orthogonal) do not combine, and are called non-bonding orbitals.  Molecular Orbital Theory In order to simplify things, we’ll consider the interaction of the orbitals containing valence electrons to create molecular orbitals. The wave functions of hydrogen atom A and hydrogen atom B can interact either constructively or destructively.  Linear combination of atomic orbitals Rules for linear combination 1. Atomic orbitals must be roughly of the same energy. 2. The orbital must overlap one another as much as possible- atoms must be close enough for effective overlap. 3. In order to produce bonding and antibonding MOs, either the symmetry of two atomic orbital must remain unchanged when rotated about the internuclear line or both atomic orbitals must change symmetry in identical manner. Typical molecular energy levels diagram of an octahedral complex showing the frontier orbitals in the tinted box a Singly degenerate s 1g t Triply degenerate p 1u Doubly degenerate d eg t Triply degenerate d 2g  g- identical B under inversion A u- not identical  Rules for the use of MOs * When two AOs mix, two MOs will be produced * Each orbital can have a total of two electrons (Pauli principle) * Lowest energy orbitals are filled first (Aufbau principle) * Unpaired electrons have parallel spin (Hund’s rule) Bond order = ½ (bonding electrons – antibonding electrons)  Molecular Orbital Theory Constructively: Ψ(σ) or Ψ+ = (1/√2 ) [φ(1sa) + φ(1sb) ] Destructively: Ψ(σ*) or Ψ- = (1/√2 ) [φ(1sa) - φ(1sb) ]  Constructive interference + +. +... g bonding cA = cB = 1  g = N [A + B] Amplitudes of wave functions added The accumulation of electron density between the nuclei put the electron in a position where it interacts strongly with both nuclei. Nuclei are shielded from each other The energy of the molecule is lower  node +. -. +..- cA = +1, cB = -1 u antibonding u = N [A - B] Destructive interference Nodal plane perpendicular to the H-H bond axis (en density = 0) Energy of the en in this orbital is higher. A-B Amplitudes of wave functions subtracted.  The electron is excluded from internuclear region destabilizing Antibonding  When 2 atomic orbitals combine there are 2 resultant orbitals. Eg. s orbitals * 1 s E high energy antibonding orbital 1sb 1sa  1s Molecular orbitals low energy bonding orbital  Molecular Orbital Theory The bonding orbital is + - sometimes given the notation σg, where the g stands for gerade, or + symmetric with respect to a center of inversion. The signs on the molecular orbitals indicate the sign of the wave function, not ionic charge.  Molecular Orbital Theory The anti-bonding orbital + - is sometimes given the notation σu, where the u stands for ungerade, or + asymmetric with respect to a center of inversion. The signs on the molecular orbitals indicate the sign of the wave function, not ionic charge.  H2 11.4 eV LCAO of n A.O Þ n M.O. 109 nm Location of Bonding orbital 4.5 eV  Period 2 Diatomic Molecules For the second period, assume that, due to a better energy match, s orbitals combine with s orbitals, and p orbitals combine with p orbitals. The symmetry of p orbitals permits end-on- end overlap along the bond axis, or side-by-side overlap around, but not along, the internuclear axis.  2 2 dx -dy and dxy 2- Cl4Re ReCl4  g- identical B under inversion A u- not identical  MOs using p orbitals σ + - + - u - + - σg Some texts will use the symmetry designations of g (gerade) or u (ungerade) instead of indicating bonding or anti-bonding. For these orbitals, the anti-bonding orbital is asymmetric about the bond axis, and is designated as σu. Note that the designations of u or g do not correlate with bonding or anti-bonding.  π Molecular Orbitals + - - + + side-by-side - overlap The orbital overlap side-by-side is less than that of overlap along the bond axis (end-on- end). As a result, the bonding orbital will be higher in energy than the previous example.  Molecular Orbital Diagram This is a molecular orbital energy level σu diagram for the p πg orbitals. Note that the σ bonding orbital is 2p πu 2p lowest in energy due to σg the greater overlap end-on-end. Place labels g or u in this diagram u g u g  Molecular Orbital Diagrams 1. Electrons preferentially occupy molecular orbitals that are lower in energy. 2. Molecular orbitals may be empty, or contain one or two electrons. 3. If two electrons occupy the same molecular orbital, they must be spin paired. 4. When occupying degenerate molecular orbitals, electrons occupy separate orbitals with parallel spins before pairing.  Molecular Orbital Diagrams Although molecular orbitals form from inner (core) electrons as well as valence electrons, many molecular orbital diagrams include only the valence level.  First period diatomic molecules H H2 H 1s2 u* Bond order: 1 Energy 1s 1s g Bond order = ½ (bonding electrons – antibonding electrons)  Diatomic molecules: The bonding in He2 He He2 He 1s2, *1s2 u* Bond order: 0 Energy 1s 1s g Molecular Orbital theory is powerful because it allows us to predict whether molecules should exist or not and it gives us a clear picture of the of the electronic structure of any hypothetical molecule that we can imagine.  Second period diatomic molecules Li Li2 Li 1s2, *1s2, 2s2 2u* Bond order: 1 2s 2s Energy 2g 1u* 1s 1s 1g Diatomic molecules: Homonuclear Molecules of the Second Period Be Be2 Be 2u* 1s2, *1s2, 2s2, 2s 2s *2s2 Energy 2g Bond order: 0 1u* 1s 1s 1g Simplified Simplified MO diagram for B2 3u* 1g* 1u 3g Diamagnetic?? * 2u 2g Li : 200 kJ/mol F: 2500 kJ/mol  Same symmetry, energy mix- the one with higher energy moves higher and the one with lower energy moves lower  MO diagram for B2 B B2 B 3u* 3u* 1g* 1g* 1u 2p (px,py) 3g 2p LUMO 3g * 2u HOMO 1u 2u* 2s 2s 2g 2g Paramagnetic C2 1g 1 g 1u 1u 1 1g g ParamagneticX ? Diamagnetic  General MO diagrams 1 1 g g 1u 1u 1g 1g Li2 to N2 O2 and F2 Distance between b-MO and AO  Heteronuclear Diatomics…. The energy level diagram is not symmetrical. The bonding MOs are closer to the atomic orbitals which are lower in energy. The antibonding MOs are closer to those higher in energy. c – extent to which each atomic orbitals contribute to MO If cAcB the MO is composed principally of A  Rules for Combining Atomic Orbitals For heteronuclear molecules: 1. The bonding orbital(s) will reside predominantly on the atom of lower orbital energy (the more electronegative atom). 2. The anti-bonding orbital(s) will reside predominantly on the atom with greater orbital energy (the less electronegative atom). HF The 2s and 2px orbitals on fluorine interact with the 1s orbital on hydrogen. The py and pz orbitals on fluorine lack proper symmetry to interact with hydrogen, and remain as non-bonding orbitals. HF The anti-bonding orbital resides primarily on the less electronegative atom (H). Note that the subscripts g and u are not used, as the molecule no longer has a center of symmetry. Carbon monoxide In carbon monoxide, the bonding orbitals reside more on the oxygen atom, and the anti-bonding orbitals reside more on the carbon atom. Carbon monoxide CO is a highly reactive molecule with transition metals. Reactivity typically arises from the highest occupied molecular orbital (HOMO), when donating electrons. Carbon monoxide When acting as an electron pair acceptor, the lowest unoccupied molecular orbital (LUMO), is significant. Carbon monoxide When acting as an electron pair donor, the highest occupied molecular orbital (HOMO), is significant.  The highest occupied molecular orbital of CO is a molecular orbital which puts significant electron density on the carbon atom.  The lowest unoccupied molecular orbital of CO is the π* orbitals. The lobes of the LUMO are larger on the carbon atom than on the oxygen atom.  CO as a Ligand Carbon monoxide is known as a σ donor and a π acceptor ligand. It donates electrons from its HOMO to form a sigma bond with the metal.  CO as a Ligand Carbon monoxide accepts electrons from filled d orbitals on the metal into its antibonding (LUMO) orbital.  CO as a Ligand This phenomenon is called back bonding. The increased electron density in the antibonding orbitals of CO causes an increase in the C-O bond length and a decrease in its stretching frequency.  MOs for Larger Molecules Group theory is usually used to develop molecular orbital diagrams and drawings of more complicated molecules. When a central atom is bonded to several atoms of the same element (H2O, BF3, or PtCl42-], group theory can be used to analyze the symmetry of the orbitals of the non-central atoms, and then combine them with the appropriate orbitals of the central atom.  MOs for Larger Molecules The orbitals of the non-central atoms are called group orbitals. In considering a simple example, H2O, we obtain group orbitals using the two 1s orbitals on the hydrogen atoms.  Group Orbitals of Water The A1 representation has both 1s orbitals with positive wave functions: Ha+Hb. The B1 representations is Ha+Hb.  Molecular Orbitals of Water Since the 2py orbital on oxygen doesn’t match the symmetry of the group orbitals of hydrogen, it will remain non-bonding. The other orbitals on oxygen will combine with the appropriate group orbitals to form bonding and antibonding molecular orbitals. Oh σ bonding Antibonding MOs 4p 4s  Six donor orbitals 6NH3 each donating - 3d 2es xy xz yz 2 x2-y2 z NB MOs Bonding MOs Atomic orbitals in metal ion Molecular orbitals Atomic orbitals in ligand ion III Molecular Orbital diagram for [Co (NH ) ]3+ 36  Oh σ bonding Antibonding MOs 4p 4s  Six donor orbitals - 6 F each donating 3d - 2es xy xz yz 2 2 NB MOs x -y 2 z Clearly good σ donor ligand Result in good M-L overlap Bonding MOs Strongly antibonding eg set Atomic orbitals in metal ion Molecular orbitals Atomic orbitals in ligand ion 3- Molecular Orbital diagram for CoF6  - Case 1 (CN , CO, C2H4) empty π-orbitals on the ligands ML π-bonding (π-back bonding) t2g (π*) t 2g eg eg o ’o o has increased t 2g Stabilization t2g (π) ML6 ML6 (empty π-orbitals on ligands) -only +π Case 2 (Cl-, F-) filled π-orbitals on the ligands L M π-bonding eg eg ’o t2g (π*) o has decreased o Destabilization t 2g t 2g Stabilization t2g (π) ML6 ML6 -only (filled π-orbitals) +π  Putting it all on one diagram. Strong field Weak field Or π acceptor ligands π donor ligands lower higher in E than t2g. in E than t2g. Summary: strong σ- or π-donor weak field ligands. π-acceptors strong field ligands.