Orbitals & hybridisation

Question 1

atomic orbital definition:

Answer 1

regions of space where electrons of particular energies are most likely to be found.

Each orbital can hold up to 2 electrons of opposite spin (Pauli exclusion principle)

Question 2

What is an orbital?

Answer 2

a mathematical function (a wavefunction) that describes the 3-dimensional wave-like behaviour of either one electron or a pair of electrons in an atom. It shows us the probability density of the electron (i.e. the region it is most likely to be found).

Question 3

What does the shape of atomic orbital relate to?

Answer 3

angular wavefunction, Y(θ, ϕ).

Question 4

Describe the 1s hydrogen angular wavefunction and orbital

Answer 4

neither angles, θ or ϕ, appear in the angular wavefunction for the hydrogen 1s orbital.

1s orbital – angular wavefunction = constant, and is the same in all directions from the nucleus.

1s orbital = spherical - same for all s orbitals except size is bigger and they get more radial nodes.

The probability of finding an electron in a 1s AO is greatest in the vicinity of the nucleus and then decreases exponentially at the distance from the nucleus increases – represented by a spherical “cloud” of charge.

Question 5

Describe the 2s orbital:

Answer 5

The 2s AO is spherical, but is larger than the 1s AO – on average an electron in a 2s AO is further from the nucleus than in a 1s AO.

The 2s AO also has a nodal sphere – where the probability density is 0.

Question 6

describe the angular wavefunction and the orbitals of the 3 2p orbitals:

Answer 6

angular wavefunctions for the 3 2p orbitals are dependent on θ and/or ϕ.

for example, angular wavefunction for 2pz orbital is dependent on cos θ.

means the wavefunction depends on the direction from the nucleus.

so in some directions, cos θ will be +ve and others it will be –ve.

Each 2p AO has a nodal plane – where the probability of finding an electron is 0.

Question 7

What is an angular node?

Answer 7

a nodal plane which arises from the angular wavefunction.

Question 8

What are the orientations of the 3 2p orbitals?

Answer 8

2px orbital is aligned along the x-axis
2py orbital along the y-axis
2pz orbital along the z-axis

Question 9

What is a boundary surface?

Answer 9

a boundary surface contains a certain proportion of the wavefunction, usually 95%.

it represents the shape of the orbital.

Question 10

What shape are the 5 3d orbitals?

Answer 10

four of the five orbitals have a ‘clover-leaf’ shape with four lobes and two nodal planes

The dz2 orbital has a different shape with two lobes of the same phase directed along the z-axis and a torus (ring) of the opposite phase around the centre.

Question 11

Where are the lobes located in the dxy, dxz, and dyz orbitals?

Answer 11

the dxy, dxz, and dyz orbitals are oriented with their lobes directed between two of the 3 Cartesian axes (x, y, z)

Question 12

Where does the dx2–y2 orbital have its lobes located?

Answer 12

the dx2–y2 orbital has its lobes directed along the x and y axes.

Question 13

Where is electron density concentrated?

Answer 13

Electron density is most concentrated in the region in between the two nuclei – where the AO overlap most.

Question 14

how to generate the in-phase combination (bonding MO) ?

Answer 14

In mathematical terms, we take linear combinations of atomic orbitals (LCAO), in which we add the two AOs to generate two new MOs: the bonding MOs.

Question 15

how to generate the out-of-phase combination (antibonding MO)?

Answer 15

In mathematical terms, we take linear combinations of atomic orbitals (LCAO), in which we subtract the two AOs to generate two new MOs: the anti bonding MOs.

Question 16

What leads to the general conclusion that 4 electron bonding between two atoms is repulsive?

Answer 16

antibonding orbitals are always more antibonding than bonding orbitals are bonding.

Question 17

What are the 5 general feature of MOs?

Answer 17

1. AOs must have the appropriate symmetry to interact, and they cannot do so if they are orthogonal (at 90 °) to one another.
2. Better overlap leads to a stronger interaction, and vice versa. - Head-on ( σ -type) overlap is always better than sideways-on ( π-type) overlap.
3. Energies of valence AOs are lower for elements of higher electronegativity.
4. When two orbitals of unequal energy interact, the interaction is less than when two orbitals of very similar energy interact.
5. There are mathematical rules that must be maintained for orbital coefficients in MOs. One result of this is that a bonding MO polarised towards one atom (based on EN) must be polarised in the opposite sense in the antibonding orbital.
   - The sum of the squares of the coefficients within a single MO must be normalised to 1 (because only 1 electron in each spin state can be in the orbital).
   - The sum of the squares of the coefficients on a single atom, across all MOs, must be normalised to 1 (because if all MOs were filled, there would have to be one electron in each spin state on each atom).

Question 18

How can we determine the electron density of an atom?

Answer 18

X-ray crystallography allows the determination of the structure of a crystalline material.

The X-rays are diffracted by the interactions with electrons in the molecule, producing electron density maps.

The sum of the electron densities of each of the electrons in each AOs gives the total electron density of an atom .

Question 19

What is hybridisation?

Answer 19

Atoms in molecules are not the same as free atoms – they can change shapes and energies of their AOs to provide for the best overlap and the maximum bonding with other atoms, this is known as hybridisation.

bonding electrons are spread (delocalised) over the entire structure and not confined to 2-centre-two-electron (2c-2e) bonds.

Question 20

What shape does methane take due to VSEPR and why?

Answer 20

Due to VSEPR , the shape that provides the least amount of repulsive interactions between pairs of electrons in the 4 bonds is tetrahedral, with a bond angle of 109.5°.

Question 21

What is sp3 hybridisation?

Answer 21

The term “sp3 hybridization” refers to the mixing character of one 2s-orbital and three 2p-orbitals to create four hybrid orbitals with similar characteristics. In order for an atom to be sp3 hybridized, it must have an s orbital and three p orbitals.

Question 22

Features of the 4 sp3 hybrids in methane are?

Answer 22

identical in energy

directional – they point towards the corners of a tetrahedron.

Well suited for good overlap with the 4 1s AOs of H atoms.

Question 23

Who came up with the valence bond theory?

Answer 23

Linus Pauling.

Question 24

What is the valence bond theory?

Answer 24

an alternative approach to describing covalent bonding that has the distinct advantage of bonding electron pairs being treated as localised between two atoms.

This notion of a covalent bond consisting of two electrons shared between two nuclei (i.e., a 2c-2e bond) is the basis for valence bond theory - an older theory of bonding that underpins the drawing of molecules as Lewis structures.

Question 25

Describe what happens with sp hybridisation for a molecule like ethyne:

Answer 25

• hybridisation required to construct a triple bond via head-on overlap of the sp hybrids on two different carbons (sigma bonding) and side-on overlap of the unchanged p orbitals (pi bonding).
  
  • each carbon forming 1 C-H σ-bond and 2 C-C π-bonds to form a triple bond.
• geometry of the sp hybridised carbon atom is described as digonal, with two other atoms bound to the central carbon.

Question 26

Describe what happens with sp2 hybridisation for a molecule like ethene:

Answer 26

• this is the hybridisation required to construct a double bond via head-on overlap of the sp2 hybrids on 2 different carbons (sigma bonding) and side-on overlap of the unchanged p orbitals (pi bonding):
• Planar geometry with each carbon forming 2 equivalent C-H σ-bonds and 1 C-C π-bond.
• Each carbon is approximately trigonal ( C-H-C = 117.8°)
  
  • to minimise the repulsions between these 3 bonds.

-Each carbon is approximately sp2 hybridised.

• The C=C bond compromises of:
  
  • One σ-bond.
  • One π-bond

Question 27

How do you know if a heteroatom is sp3 hybridised?

Answer 27

If a heteroatom has only σ -bonds to its neighbours, and no unoccupied (empty) orbitals, it is sp3 hybridised.

Question 28

How do you know if a heteroatom is sp2 hybridised?

Answer 28

If a heteroatom has one π-bond to its neighbours, or an unoccupied (empty) orbital, it is sp2 hybridised.

Question 29

How do you know if a heteroatom is sp hybridised?

Answer 29

If a heteroatom has two π-bonds to its neighbour(s), it is sp-hybridised.

Question 30

What does a curly arrow represent?

Answer 30

Curly Arrows: represent the formal movement of an electron pair in a covalent bond-formation or cleavage

Question 31

Why do most chemical reactions involve simultaneous bond-formation and cleavage?

Answer 31

because making a new bond to a first-row element like carbon must necessarily break an existing bond, in order to avoid violating the octet rule

Question 32

Is the nucleophile the HOMO or LUMO?

Answer 32

HOMO

Question 33

Is the electrophile the HOMO or LUMO?

Answer 33

LUMO

Question 34

What amount of energy separation dominates between the HOMO-LUMO interaction?

Answer 34

Of the 2 HOMO-LUMO interactions, the one with the smallest energy separation dominates out of the two.

Question 35

Things that affect the extent of interaction include:

Answer 35

the energy difference between two interacting orbitals (e.g., HOMO-LUMO).

effective orbital overlap.

relative symmetry.

Question 36

What is stereoelectronics?

Answer 36

the study of how the spatial relationship between interacting orbitals affects the structure/energy of a molecule (or a transition state).

Question 37

What is the Born-Oppenheimer approximation?

Answer 37

• it states that:
• nuclei are heavier than electrons – therefore they move slower.
• this approximation allows the nuclei to be regarded as stationary – with only electrons moving – so the Schrödinger equation can be solved for the wavefunctions of the electrons.

Question 38

Why do we need both VBT and MOT?

Answer 38

• VBT provides a qualitative picture of bonding – also useful in infrared spectra of large molecules (vibrations between bonds).
• MOT useful in computational chemistry (more qualitative) - useful for looking at excited states of molecules + for interpreting electronic spectra – provides simple explanation of paramagnetism of O2.

Question 39

What is the Valence Bond Approach?

Answer 39

• linked to Lewis’s idea of bonding – with shared pairs of electrons forming bonds between atoms.
• bond arises from interaction of AOs on 2 atoms to form a bonding orbital between the atoms – bonding orbital contains 2 electrons.

Question 40

What is the Molecular Orbital Approach?

Answer 40

• atomic orbitals of atoms in a molecule combine to form molecular orbitals which are spread over the molecule.
• these orbitals are delocalised.

Question 41

Why is resonance used in the VBT?

Answer 41

resonance is used in VBT when no single Lewis-type structure accurately represents the observed bonding in a molecule
- the actual structure is the average of several resonance forms – resonance forms don’t contribute equally.

Question 42

Symbol used to denote the wavefunctions of atoms:

Answer 42

ϕ (phi)

Question 43

Symbol used to denote the wavefunctions of molecules:

Answer 43

ψ (psi)

Question 44

Basic definition of hybridisation:

Answer 44

a way of mixing atomic orbitals on an atom as it interacts with another atom.

Question 45

What is the evidence for the hybridisation in N2?

Answer 45

if there was 0 interaction between nitrogen’s s and p orbitals – the l.p of electrons would lie in the 2s orbitals and wouldn’t be directional.

l.p of electrons = observed in x-ray diffraction experiments.

Question 46

What type of hybridisation occurs in N2?

Answer 46

sp hybridisation

Question 47

What is different about the valence bond treatment of heteronuclear diatomics?

Answer 47

ionic contributions aren’t equal in heteronuclear diatomics.

Question 48

What occurs in the hybridisation of heteroatoms?

Answer 48

Hybridisation is equally applicable to heteroatoms – only difference is that AOs for X and Y aren’t of the same energy.

treat lone pairs spatially as if they are bonding pairs

Question 49

Molecular orbital basic definition:

Answer 49

a single-electron wavefunction on a molecule.

Question 50

What is the orbital approximation?

Answer 50

this approximation allows the overall wavefunction for an atom, containing n electrons, to be written as a product of n single-electron wavefunctions.

Question 51

How can we calculate single-electron wavefunctions?

Answer 51

single-electron wavefunctions can be calculated from the Schrödinger wave equation.

Question 52

What is constructive interference?

Answer 52

results from the in-phase combinations of wavefunctions, where you add the wavefunctions.

Question 53

What is deconstructive interference?

Answer 53

results from the out-of-phase combinations of wavefunctions, where you subtract one wavefunction from the other

Question 54

What does the Normalisation constant do?

Answer 54

Ensures the wavefunction remains a single-electron wavefunction.

Question 55

What is Diamagnetism?

Answer 55

Any electron in the same orbital, the spin quantum numbers have to be different.

So when a pair of electrons are in an orbital, their total spin = 0.

This is means the atom or molecule = diamagnetic.

Diamagnetic atoms or molecules are not attracted to a magnetic field but are slightly repelled.

Question 56

What is Paramagnetism?

Answer 56

Single electrons in an orbital = paramagnetic electron.

If the electron is alone in the orbital, then the orbital will have a net spin which means the whole atom will have a net spin.

Paramagnetic atoms and molecules are attracted to a magnetic field.

Paramagnetic properties are caused by the realignment of the electron paths caused by the externa magnetic field.

Question 57

What is general procedure for simple molecules containing a central atom? MO approach with polyatomic molecules.

Answer 57

Build group orbitals using outer atoms.

Interact group orbitals with central atom to make MOs.

Question 58

When does covalent bonding occur?

Answer 58

Covalent bonding occurs when AOs on different orbitals overlap and electrons with opposite spins pair up.

The electrons in a molecule experience mutual repulsions among themselves and attraction to the nuclei of all the atoms, under these conditions the electrons arrange themselves so that they occupy molecular orbitals.

Question 59

What 2 types of MOs are generated from using the LCAO approach?

Answer 59

an in-phase combination (bonding MO) 

an out-of-phase combination (antibonding MO)

Question 60

What does a g type parity label represent?

Answer 60

it comes from the word gerade meaning even – if the orbital is identical after inversion.

The sign on the σ-bonding orbital stays the same with inversion.

Question 61

What does a u type parity label represent?

Answer 61

it comes from the word ungerade meaning odd – if the orbital keeps the same shape.

Th sign on the σ-antibonding orbital changes on inversion.

Question 62

symbol for electron density:

Answer 62

ψ^2

Question 63

How are ionisation energies measured?

Answer 63

measured using Photoelectron spectroscopy

Question 64

What happens during Photoelectron spectroscopy?

Answer 64

The sample is bombarded with protons and the kinetic energy of the expelled electrons is measured.

Question 65

the in-phase combo of pz orbitals gives rise to:

Answer 65

in-phase combination of pz orbitals give rise to a σg bonding orbital – with increased electron density between the nuclei.

Question 66

the out-of-phase combo of pz orbitals gives rise to:

Answer 66

out-of phase combination of pz orbitals give rise to a σu* antibonding orbital – with reduced electron density between the nuclei.

Question 67

the in-phase combination of 2 px orbitals gives rise to:

Answer 67

in-phase combination of 2 px orbitals gives rise to a bonding orbital, with increased electron density between the nuclei - orbital does not have cylindrical symmetry, as a rotation of 180° around the X–X axis maps the orbital onto itself, but with a change in phase = called a π orbital, and the symmetry label = πu as, on inversion, the phase of the orbital changes.

Question 68

the out-of-phase combination of 2 px orbitals gives rise to:

Answer 68

the out-of-phase combination of 2 px orbitals gives an antibonding orbital, with reduced electron density between the nuclei - orbital is also a π orbital, but it does not change its phase on inversion, so the antibonding orbital has the symmetry label πg*.

Question 69

What does the degree of interaction between the orbitals depends on?

Answer 69

degree of interaction between the orbitals depends on the energy gap between them - orbitals that are close in energy give a large interaction, orbitals that are far apart in energy give a small interaction.

Question 70

What is sp mixing?

Answer 70

With B, C and N a degree of “s and p orbital interaction” occurs – where a change of the relative MO occurs. This is known as sp mixing.

Question 71

Describe the bonding in N2:

Answer 71

s–p mixing leads to the stabilization of the 2σg and 2σu* orbitals and the destabilization of the 3σg and 3σu* orbitals.

destabilization of the 3σg orbital is important for N2 as this pushes the 3σg orbital above the 1πu orbitals in energy.

Question 72

Why do S and p orbitals become stabilised across the PTE?

Answer 72

Increased nuclear charge pulls orbitals closer to the nucleus but increased electron-electron repulsion pushes them further out.

Increased attraction is more important.

Electrons with the same PQN don’t shield each other very well.

Effective nuclear charge increases across a row:

S orbital is more stabilised then p orbitals with increasing nuclear charge as it is more penetrating.

Question 73

How to know the relative energies of the AOs in heteronuclear diatomics?

Answer 73

• can look the relative energy up.
• or can use electronegativities: more electronegative an atom, the more it holds its valence electrons tightly, so that its highest occupied AO is lower in energy.