Molecular orbitals (Pike) Flashcards
compare and contrast atomic and molecular orbitals
atomic orbitals
- is a wavefunction describing behaviour of an electron in an atom
- electron influenced by the nucleus and other electrons present
- Aos are the solution to Schrodingers equation for the atom
- core electrons are low energy orbitals close to the nucleus
- valence electrons are in high energy orbitals
molecular orbitals
- is a wavefunction describing the behaviour of an electron in a molecule
- each electron is influenced by all the nuclei and other electrons
- MO are the solutions to Schrodinger equation for the molecule
- each atoms has its own core electrons that are not shared with other atoms
- valence electrons are shared amongst atoms and occupy molecular orbitals rather than atomic ones
- each molecular orbital extends over the whole molecule not just 2 atoms
how are molecular orbitals formed
when bringing the 2 nuclei together the 1s orbitals begin to overlap, the electron can be shared by the 2 nuclei. the electron density is spread between the first nucleus, the second nucleus and the region in between, this sheilds the positive nuclei from each other. Tje overall energy is reduced this represents a bonding effect and the electron is now in a molecular orbital not an atomic one
what happens if the electron is near the left or right nucleus
the influence of one nuclei is greater than the other
the behaviour of the electron would be very similar to that in a 1s atomic orbital of the nucleus
what happens if the electron is between the two nuclei
it feels the influence of both nuclei
what is LCAO
the linear combination of atomic orbitals
wavefunction describing the molecular orbitals
mathematically this means adding together the atomic orbitals with appropriate coefficents to create the molecular ones
the cannot add up to more than one as a square as probability cannot be more than 1
when are interactions between atomic orbitals allowed
- if the symmetries of the atomic orbitals are comparable
- efficient if the region of overlap between the atomic orbitals is significant
- if the atomic orbitals are relatively close in energy
the size of the overlap depends on how well these criteria are met
what happens when two atoms overlap in terms of electron density
extra electron density built by constructive interference (as electrons are behaving like waves) of the two wavefunctions. the integral of this extra electron density is a measure of the bonding effect obtained by combining the two atomic orbitals
what is a bonding molecular orbital
a molecular orbital with a positive overlap of the atomic orbitals
the energy of bonding molecular orbitals is lower than the energies of the atomic orbitals from which it is formes
why are overlap integrals not always positive
the sign and value of an overlap integral depends on the size, shape, orientation and phase of atomic orbitals, the value of these can be positive, negative or zero
what is positive overlap
atomic orbitals with lobes of the same phase come together, bonding contribution. the energy of the molecular orbital is lower than that of the atomic orbital
what is negative overlap
atomic orbitals with lobes of different phase come together. A negative overlap integral represents an antibonding contribution. the energy of the molecular orbital formed is higher than that of atomic orbitals
what is zero overlap
atomic orbitals give positive overlap in some regions and negative in others. these cancel each other out by symmetry
zero orbitals overlap means there is no bonding contribution.
atomic orbitals are remained unchanged in form and energy
explain atomic orbitals of the same atoms in terms of orthogonality
orthogonal means they are perpendicular to each other, this implies they do not overlap with each other
- the overlap integral of any antomic orbital with itself is 1
- the overlap integral of any two different atomic orbitals on the same atom is 0
explain the atomic orbitals from different atoms in terms of orthogonality
the overlap integral of two atomic orbitals on different atoms is a measure of their bonding interaction.
if this is zero there is no contribution to bonding from the pair of orbitals
(non-bonding)
what is the number of molecular orbitals we get when we combine atomic orbitals
when combining atomic orbitals to form molecular orbitals the number of molecular orbitals will be equal to the number of atomic orbitals
what are the properties of energy level diagrams
energy level diagrams show which molecular orbitals have a lower or higher energy
the number of electron in this molecule will be the sum of electrons of the atoms.
what are the rules in energy level diagrams
Pauli exclusion principle each orbital can host a maxium of 2 electrons
Aufbau principle - orbitals are filled in order of increasing energy
Hunds rule - degenerate orbitals will be filled with the maximum number of spin paired electrons
how do we know if a molecular orbital is energetically favourable
the total energy of the molecule is lower than the energy of the separate atoms/ ions. meaning the formation of the molecule is more favourable than having the individual atoms or ions
how do we calculate bond order
1/2( number of bonding electrons - number of antibonding )
what are the different bonds that p orbitals can produce
p atomic orbitals can interact in different ways depending on their orientation. P orbitals are degenerate but this is lost when two atoms form a bond.
2 pz overlap to give sigma and sigma star
2 px or 2 py overlap to give a pie bond
we start with 6p atomic orbitals 3 from each atom and we obtain 6 molecular orbitals
why is sigma s* lower in energy than sigma p
some bonding MO are higher in energy than antibonding molecular orbitals
the term bonding an none bonding are relative to the contributing AOs and 2p orbitals have a higher energy than 2s
what does a higher bond order mean
shorter and stronger bond
what is the importance of unpaired electrons
unpaired electrons have their own spin and their own magnetic field. a substance which has unpaired electrons are called paramagnetic
what is s-p mixed orbitals
so far we have assumed that the s and p atomic orbitals behave independently
for B2, C2 and N2 mixing becomes important, orbitals with the same symmetry interact for example 2s and 2pz both for sigma bonds will combine with each other. they will generate new orbitals
MIXING MOLECULAR ORBITALS NOT ATOMIC ONES
the sigma p bonding orbital has swapped with the pie bonding orbital
what are the differences in the energy level diagrams for the following
[O2]+
O2
[O2]-
[O2]2
the energy level diagram is mostly the same
the exact energies of each level is different due to different number of electrons repelling each other
the number of antibonding electrons is different
bond strength decreases whereas bond length increases
how do energy level diagrams change with heteronuclear diatomic molecules
atomic orbitals of the two atoms will have different energies, the energies of atomic orbitals a lower for the more electronegative atom. the energy level diagrams are not symmetrical
what does isoelectronic mean
same/ similar amounts of electrons
examples of heteronuclear diatomics
CO, NO, [CN]-, [NO]+
what happens if the hetero atoms are far apart in energy
if AO1 and AO2 have very different energies there is essentially no overlap even though geometry allows it. The resulting MO is almost unaltered AO.
unequal coefficients when constructing the wave functions of MO
what makes a molecule more stable
if the bonding and non-bonding MOs are filled while the antibonding is empty the molecule is often more stable
what are the most important orbitals
HOMO - highest occupied molecular orbital
LUMO - lowest unoccupied molecular orbital
describe features of the HOMO
the HOMO has got electrons which it can give away, donating electrons is therefore a lewis base
describe features of the LUMO
the LUMO is empty there for it tends to act as a lewis acid accepting electron density
why are NO+, CN- and CO know as sigma donor pie acceptors
donates electron density from the sigma 3
accepts electron density into pie*
how does water being bend effect its energy level diagram
the most important change is that the px orbital can overlap with H 1s orbitals when the molecule is bent
the px orbital can contribute to the bonding/antibonding effect instead of being non-bonding
the overlap integral of the pz orbital becomes less good when the molecule is bent resulting in a change in energy of the MO.
why is the energy level diagram of CO2 more complicates
CO2 is known to be a linear molecule and it has more valence orbitals on the outer atoms
how are the antibonding/bonding MO with a sigma symmetry formed for CO2
2s and 2pz orbitals from the C atom
2s and 2pz orbitals from the O atoms
how can we simplify the energy level diagram for CO2
oxygen is more electronegative than carbon so the AO of O are much lower in energy. To simplify we will use an approximation: O 2s orbitals dont combine with C2s or C2pz
describe the energy level diagram of CO2
oxygens 2s AOs can form bonding and antibonding MO they do not combine with C 2s or 2Pz due to a difference in energy
- oxygens 2pz AOS form bonding and antibonding MOs with C 2s and 2pz AOS
- O 2px AOSs can form bonding and antibonding MOs with C 2px AOS the same thing happens to 2py
- one O 2px and one 2py remains none bonding
- there are 16 valence electrons
how would a metal complex for an octahedral geometry be produced
if all ligands are symmetrical the complex has an octahedral symmetry, symmetry dictates which orbital from the metal and the ligands can overlap
only the AOs with an eg geometry will be able to overlap with the AOs of the ligands
what symmetry labels are appropriate for octahedral symmetry
a1g, eg, t1u, t2g
what are hybrid orbitals
linear combinations of the primary atomic orbitals of the same atom
why do we use hybrid orbitals
they are a simple approximate way of showing which orbitals contribute effectively to the LCAO
which of the d orbitals have eg geometry
dz^2 and dx^2-y^2
which of the d orbitals have t2g geometry
dxy, dxz, dyz
Draw the CO2 energy level diagram with mixing
See sheet
Draw the HF energy level diagram
See sheet
Draw the NO energy level diagram with mixing
Draw the CN- energy level with mixing
Draw the BeH2 energy diagram
Draw the H2O energy diagram
Draw the B2 energy level with mixing
Draw the C2 energy level diagram with mixing
Draw the N2 energy level diagram with mixing
Draw the CO energy level diagram with mixing
