Molecular Symmetry and Molecular Orbital Theory
Why does s-p mixing occur for the beginning of the second period?
- 2s orbitals are close in energy to the 2p orbital - Can't treat them separately - Makes 1σg more bonding and 2σg less bonding - Only s and pz as they have the same symmetry relative to molecular axis
What is the orbital energy order?
- 2σg < 2πu < 2πg < 2σu - As the best overlap would be in pz as they are directly facing each other
How do we know how good a wavefunction is?
- Calculate E from ∫φHφdτ - Variation principle, lower energy E, closer the φ is to the true solution - Better solutions when AO is contracted
What are the MO diagrams for heteronuclear atoms like?
- Depends on εε - If εa>>εb then cb>>ca and the bonding MO is concentrated entirely on the more electronegative atom - Closer the two orbitals in energy the greater the mixing
What are the Aufbau building up principles?
- Electrons in ground state of a molecule occupy MO of lowest energy so total electronic energy is minimised - No more than 2 e- may occupy a given orbital, spins must be paired - e- occupy the different degenerate orbitals before doublin g - e- occupy different degenerate orbitals, lower e is obtained w/ parallel spins - Hund's rule
What is required for atomic orbitals to combine effectively?
- Energies of the atomic orbitals should be similar - Atomic orbitals should overlap well - Atomic orbitals should have the same symmetry relative to the molecular axis
What is the molecular orbital diagram for BH?
- H 1s orbital lies close in energy to both B 2s and 2p orbital so there is s-p mixing - 1σ = c₁1sH + c₂2sB + c₃2pzB
What forms is the MO diagram for period 2 elements?
- Include p orbitals - Internuclear axis as z direction - pz orbitals combine to give bonding and antibonding σ orbitals
What is the molecular orbital diagram for HF?
- Internuclear axis is on z axis than only H 1s, F 2s and F 2pz can overlap - F 2pπ orbitals are non-bonding and F 2s is too low in energy - 1σ = 2sf - 2σ = c₁1sH + c₂2pzF where c₁<c₂
Why does CO have a stronger bond than N₂?
- Isoelectronic - N₂ formed from 6 unpaired electrons have to have their spins paired - CO only 4 spins have to be paired - Ionic contributions in CO, paired up leading to repulsions
What are general rules for AXn molecules?
- Outer atoms more electronegative than central one - Central atom from period 3 and lower - Large size of central atom facilitates the high coordination number - Somd d contribution possible but not full hybridisation
What is the bonding in diborane?
- Tetrahedral structure suggests there is sp³ hybrids on B - Terminal B-H shorter, ordinary 2 electron bonds - Bridging B-H longer, as each B-H-B bridge use two sp³ hybrids one from B and 1 H 1s - 3 centre - 2 electron bonds
Why does F₂ have a weaker bond than Cl₂?
- The π overlap is repulsive - Small size which reduces the bond dissociation enthalpy - Why F is so reactive
Why does O₂ experience paramagnetism?
- Two unpaired electrons w/ parallel spins in the 2pπg orbitals - Diradical species
What are the different symmetry elements?
- Which axis, plane, line or point the symmetry operation is carried out - E → whole space - Cₙ → n-fold axis of rotation - σ → mirror plane - i → centre of inversion - Sₙ → n-fold axis of improper rotation
What happens to the electron density in antibonding MO?
- ca=-cb, out of phase - electron density 0 in internuclear region with a node
What happens to the electron density in bonding MO?
- ca=cb, in phase - electron density is increased in the inter-nuclear region
What are the trends for MO down the group?
- n increases and core orbital differ - As atoms get larger the overlap between orbitals decreases
What is the identity operation?
Mathematically operation of 'doing nothing', the corresponding symmetry element is the entire molecule
What is the C₁ point group?
When molecules contain only E (CHFClBr) and either a mirror plane (Cs) (BHFCl) or a centre of inversion (Ci) (staggered ethane)
What is the Born-Oppenheimer approximation?
Assumed nuclear and electron positions can be treated independently, calculate electron energies for fixed nuclear positions
What is the orbital approximation?
Assumes that the wavefunction of the N electrons in a molecule can be written as the product of N one electron wavefunctions
What are the cubic point groups?
Totally symmetrical tetrahedral and octahedral molecules belong to the cubic point groups Td and Oh, all substitutions are the same, also Ih which corresponds to a regular isoahedron
What is the n-fold axis of rotation?
When a molecule possesses an n-fold rotation axis if the molecule appears unchanged after rotation by 360°/n about the axis
what is the Cn point group?
When molecules contain only E and an n-fold axis of rotation 1. Cnv - would have n vertical mirror planes σv 2. Cnh - a horizontal plane σh 3. S₂n - an S₂n improper axis coincident with the Cn axis
What is the principle axis?
When more than one rotation is present, highest order (maximum n) would be the principle axis ex. BF₃
How do the px orbitals combine?
- Combine to give bonding πu and antibonding πg orbitals - Bonding πu formed by px/y(A) + px/y(B), vice versa with -ve sign for antibonding πg
What experimental data do we want to understand?
1. Bond length 2. Molecular shape 3. Bond strengths 4. Reactivity 5. Spectroscopy 6. Magnetism
What are the principle types of hybridisation?
1. Combining s with 1 p to give 2 sp hybrids 2. Combine s with 2 p orbitals to give three sp² hybrids 3. Combine s with 3 p orbitals to give four sp³ hybrids
How do we treat electrons in molecules?
1. Described by a wavefunction φ₁ called molecular orbital 2. φ² gives probability distribution of the electron 3. Each orbital associated with definite energy value, ε, energy is quantised 4. Each e⁻ has a spin, and the aufbau principle is used in filling MOs
How can we draw Lewis structures?
1. Identify total number of valence electrons in each contributing atom 2. If charged add e⁻ to account for +ve or -ve charge 3. Distribute electrons in structure so that there is an electron pair forming a single bond between each pair of atoms bonded together, extras are LP or multiple bonds
What are some examples of bonding phenomenon that Lewis structures can't explain?
1. O₂ being paramagnetic - unpaired e⁻ which does not appear on structure 2. B₂H₆ - 12 e⁻ but 8 bonds, electron deficient molecule
How can we make a VSEPR prediction?
1. Write down Lewis structure, iden. central atom 2. Count number of bonding e pairs and LP around central, achieves lowest energy by being the furthest apart 3. Refine by recognising that repulsion are LP-LP > LP-BP > BP-BP with multiple bonds
What are some exceptions to VSEPR?
1. XeF₆ - 6 BP and 1 LP, distorted octahedral as LP takes less space than expected 2. SbPh₅ and InCl₅⁻ - 5 BP adopt square pyramidal structures 3. SeCl₆ and TeCl₆⁻ - 6 BP and 1 LP adopt regular octahedral, LP has no stereochemical role
What is the bond order?
1/2(n - n*)
What is photoelectron spectroscopy?
A method for experimentally probing the energies of electrons in different molecular orbitals in a molecule
What is a symmetry operation?
An action that leaves a molecule apparently unchanged
What is a point group?
Collection of symmetry elements, named by a Schönflies point group symbol
What is an improper rotation?
Consists of 1. Rotating through an angle of 360°/n about an axis 2. Reflecting in a plane perpendicular to the axis Axis is called an n-fold axis of improper rotation
What does the σ label refer to?
Cylindrical symmetry about the internuclear axis
What are the linear high symmetry point groups?
C∞v - C∞ axis , ∞σv D∞h - C∞ axis, ∞σv, i, σh and ∞C₂ perpendicular to principal axis
What did Lewis describe about covalent bonds?
Described as shared pairs of electrons, using dot and cross diagrams (inner kernel and outer electrons to represent them
What is the octet rule?
Each atom shares electrons with neighbouring atoms to achieve 8 valence electrons
What happens for three centre bonds?
Forms one bonding, one non-bonding and one anti-bonding molecular orbital
What is the general case for A-B heteronuclear diatomics?
If B is more electronegative than A, then more electron density will be on B than A so the bonding orbital will be concentrated on B - φ₁ = caχa + cbχb where cb > ca antibonding orbital will be concentrated on A - φ₁ = caχa - cbχb where ca > cb
What determines if a molecule possesses a plane of symmetry?
If reflection in the plane leaves the molecule looking the same, denoted by σ
What is the relationship between bond order and bond dissociation energy?
Increases as bond order increases, as the bond length typically decreases
What does paramagnetic mean?
Molecules are attracted into a magnetic field, happened when there are unpaired electrons
What does diamagnetic mean?
Molecules are repelled from a magnetic field
What are the dihedral point groups?
Molecules that contain more than 1 rotation axis, in addition to a principal axis Cn these molecules also contain nC₂ axes at right angles to this axis 1.Dn - only E, Cn, nC₂ 2. Dnh - contains a horizontal mirror plane σh 3. Dnd - additionally contains n vertical mirror planes which bisect the C₂ axes
What are hypervalent molecules?
Molecules that exert a higher valency than expected from the inert gas rule
What is the equation for formal charge?
No. of valence electrons in neutral atom - No. of LP electrons - 1/2 No. of e- in bonds formed
What does the π label refer to?
Nodal plane passing along the internuclear axis
What are electron deficient molecules?
Not enough electrons for the bonding to be described in terms of a Lewis structure with 2 centre-2 electron bonds
What determines optical activity?
Only if they have no improper rotation axes Sn
What is hybridisation?
Simplified model of bonding which has atomic orbitals overlap which then combine with others to make molecular orbitals
What is a formal charge?
The charge on an atom would have if all the covalent bonds in a molecule were broken and the electrons assigned equally to the atoms involved
What does the u subscript indicate?
The orbital changes sign on inversion
What does the g subscript indicate?
The orbital is identical after inversion through the centre of inversion
What does the g subscript refer to?
The orbital is identical after inversion through the centre of symmetry of the molecule
What does the u subscript refer to?
The sign changes on inversion through the centre of symmetry of the molecule
What is the inversion operation?
With respect to a centre of inversion i, every atom is projected in a straight line through the centre of inversion and then an equal distance on the other side, centrosymmetric (doesn't have to be an atom benzene has it in centre)
What are the different molecular orbitals?
s → σ p → π d → 𝛿
How do pz orbitals combine?
σg - bonding orbital, pz(A) - pz(B) σu - antibonding orbital, pz(A) + pz(B)
What are the mirror planes?
σv (vertical) - contains the principle axis σh (horizontal) - perpendicular to the principal axis σh (dihedral) - bisect C₂ axes perpendicular to the principle axis
What would the electron density be for H₂⁺?
φ²=c²aχ²a + c²bχ²b + 2cacbχaχb - Close to Ha the wavefunction will resemble χa (H1s orbital) and vice versa - Indistinguishable so electron density must be equal hence ca=cb or ca=-cb