Structure and Bonding Flashcards
All 29 lectures of structure and bonding in term 1 year 1
1
Q
What is key about energy is quantum chemistry?
A
It is quantised (not continuous)
2
Q
How are electrons described?
A
Must be seen as both a wave and a particle
Cannot be conceived as a single granule of electricity
3
Q
Why must electrons be associated with a wave?
A
Wavelength can be measured and interference predicted
4
Q
What is the equation for energy involving h?
A
ΔE = hv
Change in energy = Planck’s Constant * Frequency
5
Q
How is frequency and wavelength affected by energy?
A
More energy = Higher frequency and shorter wavelength
6
Q
What is the photoelectric effect?
A
The emission of electrons when certain wavelengths of light strike a metal surface
7
Q
What are the observations of the photoelectric effect?
A
- Emission only occurs if wavelength of light is less than a specific value
- Emission occurs at very low intensities
- The KE of emitted electrons depends on frequency of the light, after threshold has been exceeded
8
Q
What is the graph that comes from the photoelectric effect?
A
Graph of KE of photoelectrons against frequency of light
Slope = h
Work function depends on the metal
9
Q
What is the main thing that the photoelectric effect tells us?
A
Light is made up of ‘photons’
- Energy transferred by light is directly related to its frequency
10
Q
What is the explanation of the photoelectric effect?
A
When a photon strikes the surface, all of its hv energy is transferred to a single electron
- Photons always carry the same energy regardless of intensity
11
Q
What are the equations linked to the photoelectric effect and what do they tell us?
A
hv = 1/2mv^2 + ϕ
1/2mv^2 = hv - ϕ
If a photon doesn’t have enough energy there is no emission
Ejection occurs with 1/2mv^2 KE
Electron is only removed if hv > ϕ
12
Q
What are electrostatics?
A
Interactions between charges due to their mutual arrangements - all molecules are described by this force
13
Q
What is electrodynamics?
A
Forces associated with motions of charges, magnetic effects
14
Q
What does the X-ray bombardment of graphite experiment tell us?
A
That there are scattering ‘collisions’ so photons have momentum and are particle like
15
Q
Even if photons are particle like what is the key thing they do not have?
A
No rest mass but they do have inertial mass due to E=mc^2
16
Q
What do you need to remember when calculating energy calculations?
A
You are actually calculating ΔE = E1-E2
17
Q
What wave and particle behaviour do photons have?
A
Diffraction - Wave behaviour
Collisions - Particle behaviour
18
Q
If light waves have particle properties can particles have wave properties?
A
Yes - however we can only see it for electrons and small particles (not macro scale) due to inverse relationship between mass and wavelength
19
Q
What is a wavefunction?
A
A mathematical function that when squared gives us the probability of finding an electron at any point
Affects where electrons can go
20
Q
What is the associated wave function for a single free electron?
A
Ψ(x) = Ae^(ikx)
21
Q
What is the reduced Planck constant?
A
ℏ=h/2π
22
Q
What is ‘k’ in the wave function?
A
Wave vector - related to the wavelength from either cos or sin part of the wavefunction
k=2π/λ
23
Q
What does k determine for the wavefunction?
A
If k is high the wave would repeat quicker
24
Q
What does a more curved wave function equal?
A
Greater kinetic energy
25
What are the key points about electrons and waves?
An electron is not a wave but it is 'guided' by waves
Electrons are so small that wave behaviour usually dominates
26
What is the physical significance of Ѱ?
Itself has no direct physical significance - not always real
However ѰѰ* is always real and relates to the probability of finding the associated particle in a particular region of space
27
If electron is confined what is the probability of the electron being in it?
1
28
What is the probability of finding a particle between x and x+dx?
Proportional to ѰѰ*dx=|Ѱ|^2dx
Wavefunction^2 * Bit of space we are in
Position is never certain
29
For a free particle what is the probability of finding the electron at a specific position on the x axis?
Constant (A^2)
30
What is important to understand about the position of a particle at any instant?
Position at any instant is completely undefined
31
What are the consequences of the probability interpretation of a wave function?
1. It is single valued - can only be one value at a particular point in space
2. It is continuous and continuously sloped - as dealing with waves
3. It is finite - sum of probabilities over all space is 1
32
What is quantisation a result of?
Quantisation is a result of confinement in space
33
What does confinement act as?
A filter: restricting the acceptable solutions leading to quantised energy levels
34
What are some things about the approximation of a particle in a 1D box?
Has discrete energy levels
Described as real wavefunctions
Found at different positions at different probabilities
35
What is the model of a particle in a 1D box?
Particle confined in a small region of the x axis from 0 to L
Inside the box the potential energy V=0
Outside, V is infinite so no wavefunction
36
What are the boundary conditions of a particle in a 1D box?
Value of the wave function at each end of the box is zero else it wouldn't be continuous
Values of k are restricted
37
What introduces the quantum number n and what does it represent in a particle in a 1D box?
The boundary condition of going to zero at end of box - represents the integer number of half wavelengths in the box
38
What is the wavefunction in a 1D box given by?
Ѱ=Bsin(nπx/L)
39
What is the most important physical idea in a particle in a 1D box?
We can choose sine waves that go to zero in two places and not just one
40
What is the energy inside the box?
E = (h^2n^2)/(8mL^2)
41
How do we now have quantised energy levels for a particle in a 1D box?
As energy is a function of n, which has specific allowed values
And only certain types of wave functions fit the boundary conditions
42
What does each value of n give? (particle in a 1D box)
Each n gives a different energy level - so no degeneracy
43
What happens when n=0/1 in particle in a 1D box?
n=0 gives no solution (particle disappears)
n=1 is lowest energy solution (zero point energy)
No upper limit on n
44
What do you need to see quantised energy levels?
Small masses and small distances (confinement)
45
What happens as m and L tend towards infinity?
Change in energy tends to 0 - hence why we don't care about quantisation all around us
46
What is the formula for ΔE in a particle in a 1D box?
ΔE = (2n+1)h^2/8mL^2
47
What is the correspondence principle?
In the limit of large or unconfined particles there is no apparent quantum behaviour
48
Why do you normalise a wavefunction and how do you do it?
To ensure the sum of probabilities over all space is 1 and therefore the particle must be found somewhere in the box
Integrate between limits of the box and set equal to 1
49
In a particle in a 1D box what do the values of n=1 and n=2 tell us about probability densities?
When n=1 - particle most likely to be in the middle of the box
When n=2 - there is a node in the middle - zero probability of being found in the middle
50
In quantum mechanics what leads to quantisation?
Boundary conditions and restrictions on acceptable wavefunctions
However this leads inescapably to uncertainty
51
What do we know about position and momentum for a free particle and particle in a 1D box?
Free particle - Position completely undefined, momentum precisely defined
1D box - Both are partly defined
52
What is Heisenberg's uncertainty principle?
It is impossible to specify simultaneously, with arbitrary precision, both the position and momentum of a particle along the same axis
53
What does Heisenberg's uncertainty principle tell us?
There is a fundamental limit on how well we can know both position and momentum at the same time
ΔxΔpx≥h/4π
54
Why can we not see electrons?
In order to see them we would need gamma rays but they would affect what we are trying to see too much
55
What is the Schrödinger Equation?
An equation that connects energies and wavefunctions
'Doing something to the wave function returns the wave function multiplied by the total energy'
There is a different equation for each quantum system and they have multiple solutions
56
What does the overall Schrödinger equation look like?
ĤѰ=EѰ
57
What does assuming the wave function allow you to do?
You can solve the equation to unlock its energy
58
What are key facts about the Schrödinger equation?
Essential to QM
Second order linear differential equation
Has many solutions, limited to boundary conditions
Rarely solvable exactly but can obtain an approximate solution
Time independent
59
What is Ĥ and what does it equal?
Hamiltonian operator for the total energy
Ĥ=T̂+V̂ (kinetic + potential)
60
What is an operator?
Any symbol that indicates an operation to be performed
61
In QM what do we make a distinction between?
A measurable quantity (observable) and the way its obtained (operator)
62
Why introduce operators in QM?
Given Ѱ we can obtain the value of any observable property by acting on Ѱ with the appropriate operator - Doing something to the wavefunction to get a value
63
What does the wavefunction contain?
Everything we need to know about the quantum particle
64
What form is the Schrödinger equation in?
Operator on function = Number * Same function
65
What is the Schrödinger equation also known as?
The eigenvalue equation
Ѱ is the eigenfunction
E is the eigenvalue
66
What is the special property of the Schrödinger equation?
That there is a well defined value E for a particular Ѱ
67
How do you show a certain wave function is a solution to the Schrödinger equation?
Differentiate the wavefunction and substitute into the equation
If get expected energy then it is a solution
68
What is the difference in a 1D box/2D box in terms of quantum numbers and degeneracy?
1D box has one qn n
2D box has two qn n1 and n2 and the possibility of degenerate energy levels
69
How can 2D/3D box problems be solved?
Can be solved by separating variables that are independent (terms that don't affect each other)
70
What is the Schrödinger equation for a 2D particle in a box?
A partial differential equation
- Differentiate only with respect to one variable treating all other variables as constants
71
What is the model of a 2D particle in a box?
2D box with V=0 inside and V=infinity outside
Essentially 'two lots of the 1D equation'
72
What is independent about a particle in a 2D box equation?
Each part of energy that comes from moving along each axis is independent
73
What is energy level degeneracy a result of?
It is a result of symmetry
- In a square 2D box two of the diagrams are equivalent just rotated so give the same energy
74
How do you start to solve a particle on a ring system?
By changing the coordinate system to polar coordinates (r,φ)
distance from origin and angle from positive horizontal direction
75
What is the key mathematical thing you need to use in a particle on a ring system?
Circular motion
76
What is fixed in a particle on a ring system?
r is fixed as always on the edge of the 'circle'
77
What can you use the 1D box and particle on a ring approximations to do?
To see where an electron is/the energy of an electron in
1D box - Conjugated straight chain pi system
Particle on a ring - Benzene ring
78
What are the cyclic boundary conditions? Why are they required?
Required so that the wavefunction is single valued at any point on the ring
Wave needs to be periodic every 2π - needs to have same value at 0 and 2π
Ψ does not have to be zero anywhere, just single valued
79
Where does the magnetic moment quantum number come from on a particle on a ring?
That the function has to be periodic - introduces QN ml
80
What do the boundary conditions for particle on a ring show?
That angular momentum is quantised
81
What values of ml are allowed?
0,±1,±2 etc
Negative is allowed as it could go either way around ring
82
What do boundary conditions correspond to for a particle on a ring?
Fitting a whole number of wavelengths around the ring
- must cross zero twice if crosses it at all
83
What are some things to know about ml?
ml can be 0 - as there is still a wavefunction when ml = 0
ml=1 is distinct to ml=-1
- All energy levels are doubly degenerate
84
What else is there to know about a particle on a ring?
There is well defined angular momentum
There is uniform probability distribution around the ring
85
What is the emission spectra of hot gases a result of?
Excitation of the hydrogen atom followed by falling back down and emitting energy
86
What do different gases emission spectra look like?
Different gases give different characteristic lines
87
What do the lines on the emission spectra of hot gases match?
The lines match the absorption spectra of cool gases
88
What do emission spectra show?
Distinct energy levels
89
What were the assumptions for the Bohr model for the H atom?
Certain allowed orbits are stable - called stationary states - i.e. angular momentum is quantised
For transitions between stationary states energies are given by ΔE = hv
90
What is true for wavefunction of the H atom?
The only atom for which electronic wavefunctions can be determined exactly
The same Schrödinger equation can be used as a starting point to approximate all other atoms and molecules
91
How do we solve the Schrödinger equation for the hydrogen atom?
Too complicated to solve in detail but the solutions are known
First we construct the hamiltonian for the energy and then solve the equation by -
- Changing coordinates in 3 dimensions
- Separating variables
92
What is the new approximation for the H atom?
Assume the proton is fixed in space
- Meaning we are looking at the relative motion of electron around nucleus
- So only electron has KE
93
What is true about potential energy in the H atom Schrödinger equation?
There is potential energy in the hamiltonian as it keeps the electron and proton apart
94
For the hydrogen atom what types of energy does the electron have?
Both kinetic and potential energy
95
What does changing the coordinate system in 3D mean for the wavefunction?
Meaning that the wavefunction becomes separable
96
What does the separation of the wavefunction in the H atom look like?
Ψ(r,θ,φ)=R(r)Y(θ,φ)
Separated out into distance and angle
97
What does the separation of the angular part of the wavefunction look like?
Ψ(θ,φ) = Θ(θ)Φ(φ)
98
What is the angular part of the wavefunction?
The Φ(φ) part is the solution to the particle on a ring - depends on the ml quantum number
The Θ(θ) part is more complicated and is the solution to a spherical harmonic - depends on two quantum numbers ml and l
99
What are all the different quantum numbers and what do they mean?
Principle quantum number n - designates the principle electron shell (e.g. 1 in 1s)
Angular quantum number l - designates the shape of the orbital (e.g. s in 1s)
Magnetic quantum number ml - designates the specific orbital and number of orbitals (e.g. which one of the 5 d orbitals)
Electron spin quantum number ms - designates the direction of the electron spin (+1/2 or -1/2)
100
What is the actual interpretation of each quantum number?
n = energy
l = magnitude of orbital angular momentum
ml = projection of orbital angular momentum
ms = projection of spin angular momentum
101
What does wavefunction shape depend on?
The quantum numbers
102
What is angular momentum connected to?
Both quantum numbers l and ml
- l determines ml
103
What QNs does the solution to the radial part of the wavefunction for the H atom contain?
Two quantum numbers n and l
104
How are n and l related?
n = 1,2,3,....
l = 0,1,2,....,n-1
105
What is the full one electron wavefunction for the electron in hydrogen?
A product of radial and angular part, depending on 3 quantum numbers n,l and ml
Ψ(r,θ,φ)=Rn,l(r)Yl,ml(θ,φ)
106
What is a node on the wavefunction?
Where the electron probability is zero - no chance of an electron being found there
107
What does higher energy mean for nodes?
Higher energy means more nodes (radial and angular) in the wavefunction
108
What happens for many electron atoms wavefunctions?
What must be included?
It is a function of both n and l quantum numbers
- Electron electron repulsion and electron spins must be included
- No exact solution
109
What is the chart of nuclides?
A two dimensional graph of all of the isotopes of the elements
x axis represents number of neutrons
y axis represents number of protons
110
What is the evolution of the structure of the atom?
Thomson - Rutherford - Bohr - Today
111
What are protons made up of?
Up and down quarks
112
What does the energy of electrons determine?
Electron configuration which then governs bonding and molecular structure/reactivity
113
What is the feature of the hydrogen atom emission spectra?
There are many different series - not just the visible light one (Balmer)
114
What are the important series in the hydrogen line spectra and what do they represent?
Lyman series (UV) - En to E1 - higher energy shorter wavelength
Balmer series (Vis) - En to E2
Paschen series (IR) - En to E3 - lower energy higher wavelength
115
What are the key things about the Balmer series?
It is the visible emission spectrum lines
H-ɑ is red line to the right
Four lines are formally in the visible range with line 5 and 6 actually in the UV range
116
What actually is the emission spectrum?
Spectrum of frequencies of electromagnetic radiation emitted due to electrons making a transition from a high energy state to a lower energy state
117
What does the Rydberg equation relate to?
Relating spectral lines to energy levels in hydrogenic atoms
118
What are hydrogenic atoms?
Atoms with a singular valence electron
119
What can each solution to the Schrödinger equation be thought of?
When can exact solutions be achieved?
As an atomic orbital
Exact solutions can be achieved for systems with z protons and a single electron
120
What is the allowed energy of an electron in a level dependent on?
The principle quantum number n
121
What do the line spectras of hydrogenic atoms look like?
Identical to the H atom but shifted to smaller wavelength
122
What are key things about line spectra of other elements?
Each element has a unique set of absorption/emission lines
Each element has a characteristic set of energy levels
As no of electrons increase, spectra become more complex
The patterns can be used to identify the elements
123
How do line spectra show quantisation?
All atomic line spectra show electron transitions between energy levels absorbing/emitting photons
As photons are at sharply defined energies energy levels must also have fixed values (so can absorb/emit photons)
Therefore quantisation
124
What can the Schrödinger equation be used to calculate?
Can be used to calculate the difference between atomic energy levels in both H and hydrogenic atoms
125
Why can we calculate the frequencies that an atom will absorb/emit?
As the energy and frequency are related
126
What does the wavefunction describe?
An electron in a specific energy level
Contains all the info relating to the electron - although has no physical meaning
127
What do Ψ^2 and Ψ^2dt represent?
Ψ^2 - probability density - probability of finding an electron at a certain location
Ψ^2dt - probability of finding the electron in the volume element
128
What are the symbols for the radial and angular function?
R = radial function
Y = angular function
129
What does a unique set of the 3 quantum numbers represent?
Describes one atomic orbital
130
How do you describe each orbital?
n is shell, l is letter, ml is specific orbital
131
What does the radial part of the H atom wavefunction determine?
The variation of the orbital with distance from the nucleus
- Different radial wavefunctions for different combinations of QN
132
What is a0?
Bohrs radius - 53pm
133
What are the key points about the radial wave functions of 1s,2s and 3s etc hydrogenic orbitals?
All s orbitals have a max amplitude when r=0 at the nucleus
All functions become zero when r=infinity
2s passes through zero once (one node)
3s passes through zero twice (two nodes)
134
What are the key points about the radial wave functions of 2p and 3p hydrogenic orbitals?
The p orbitals have zero amplitude when r=0 at the nucleus
All functions become zero when r=infinity
3p orbital plot passes through zero once
135
What do d orbital radial wave functions have that is similar to p orbital plots?
Also have zero amplitude when r=0
136
What are the axis of the radial wave function plot?
x axis is the radius
y axis is the radial wavefunction
137
What is the radial distribution function (RDF)?
Helps show the probability of finding an electron at any one place at a certain distance from the nucleus
138
What is the formula for the RDF?
P(r) = RDF = 4πr^2|Ψ(r)|^2
139
What are the features of the RDF of the 1s orbital?
RDF is zero when r=0 due to r^2 factor
As r increases probability increases to a max value
At large r values, probability decreases to zero
140
What can we use RDFs for?
Finding where the electron probability is at its greatest
Finding radial nodes
141
How do you calculate number of radial nodes?
Radial nodes = n-l-1
142
How do you schematically represent orbitals?
Using a surface plot - which normally represents the region of space within which there is a high probability of finding the electron (normally 95%)
143
For each principle orbital (1s,2p.3d,4f) where does the max electron density lie?
At n^2*a0
144
What is the trend in atomic orbitals related to the max of the RDF?
For a given l quantum number the max of the RDF moves to longer distances from the nucleus as n increases (e.g. 1s,2s,3s)
145
What is the trend in number of radial nodes?
Number of radial nodes increases with n
146
What is the trend in rmax (max peak) for a given n?
It follows the order ns>np>nd>nf
147
What is the trend in penetrating power of electrons towards the nucleus (r tends to 0)?
Follows the order ns>np>nd>nf
e.g. s orbitals of the same n value have a higher penetrating power than p orbitals
e.g. for 3s,3p,3d the total electron density within 300pm is s>p>d
148
When l=0 what is the value of the angular part of the wavefunction?
A constant
149
What are the three p orbitals?
px,py,pz
150
Where does the majority of p orbital electron density lie?
Along the corresponding cartesian axis
151
What is the shape of electron density in p orbitals?
Dumbbell shapes with two lobes of opposite phase
A nodal plane divides the lobes of the orbital
152
How do p orbitals differ?
In directionality although they are identical in shape
153
What is wavefunction shading and signs?
As angular part is not squared its relative sign is preserved
Shading indicates positive or negative
154
What is an alternative way of viewing the nodal planes in p orbitals?
Which angles θ and φ correspond to it
- Called an angular node and corresponds to a fixed value at which wavefunction is zero
155
What are the d orbitals? What are their shapes?
dxy,dxz,dyz,dx^2-y^2,dz^2
Shapes - Two p orbitals at 90 degrees to each other - has 4 lobes of electron density
156
Which d orbital isn't identical in appearance?
dz^2
157
What nodal planes does dz^2 have?
Two conical planes
158
What eliminates the directionality of d orbitals?
Sum of all orbitals of a subshell
159
When it comes to orbital shapes what does separation of radial and angular parts allow for?
The visualisation of orbitals
160
What does the angular part generate and what does the radial part generate in terms of orbitals?
Radial part is spherical so generates s orbitals
Angular part is directional so generates p and d orbitals with nodal planes
161
What are the energy eigenvalues of the hydrogen atom?
Only depend on n meaning they all have the same energy is have the same n
Therefore they are degenerate
162
What are the energy eigenvalues of polyelectronic atoms?
Depend on n and l so orbitals of the same n can have different energies
So only degenerate orbitals when same n and l
163
Why are polyelectronic atoms different to hydrogenic atoms?
They have electron electron repulsive interactions
Has a significant consequence for relative energies of orbitals and hence e- configs
Schrödinger equation cannot be solved analytically anymore
Can no longer readily visualise wavefunctions
164
What do we need for the wavefunctions of polyelectronic atoms?
Approximations
165
What are the approximations for wavefunctions of polyelectronic atoms?
1. Born-Oppenheimer approximation - assume motion of nuclei is independent of electron movement (static nuclei)
2. Orbital approximation - each electron occupies an AO that resembles those found in hydrogenic atoms (as exact solutions are known)
166
What does approximation 2 allow for in polyelectronic atoms?
The overall wavefunction can be split into multiple wavefunctions multiplied by each other. Where each one occupies its individual H atom like orbitals
167
How are the individual wavefunctions in polyelectronic atoms different to H atom?
The nuclear charge is modified to take into account of all other electrons repulsion
- Called effective nuclear charge (Zeff)
168
Why is approximation 2 needed for polyelectronic atoms?
Electron electron interactions influence orbital energies and shapes
169
What is Zeff? How do you calculate it?
A reduction in the actual charge of the nucleus (reducing the 'attractive' power)
Zeff = Z-σ (shielding constant)
170
What is Zeff a result of?
Shielding effect of electrons
171
What does the value of Zeff tell us?
How good the electrons are at screening each other
e.g. Zeff is reasonably high for He as the 1s electrons are bad at screening each other
172
What does a reasonably high value of Zeff tell you?
The electrons are held strongly which means it is unreactive and has high IE
173
What is the effect of Z on hydrogenic species?
Rapid contraction of orbital size as z increases
Most prominent for orbitals close to the nucleus - electrons are drawn closer and down in energy
174
When Z increases in hydrogenic orbitals what do the electrons become?
'Core like' - energetically inaccessible for reactions
175
What are the effects of Zeff for polyelectronic species? Not to do with physical properties
Contraction effect of orbital penetration
Max of same n get closer together as they attract
- In some cases they can switch around the order of Rmax
176
How do you compare 1s and 2s in terms of orbital penetration?
Despite 1s contracting, an electron in 2s still has a small probability of being found close to the nucleus - 2s can penetrate through
However 1s is still very good at shielding 2s
177
What is true, relating to Zeff, for atoms with one outer electron?
Inner core electrons tend to be very good at shielding the outer electrons
178
What does the energy of outer electrons depend on?
How much it penetrates the core region - depends on type of orbital
If an electrons spends much time close to the nucleus it will experience a larger nuclear attraction
179
Which electrons experience more electrostatic attraction?
Electrons in s orbitals
180
For a given n what is the order of penetration?
s>p>d>f
181
What is true for penetration and shielding?
The more penetrating the electron the better it shields the outer electrons
182
What is true when σ(shielding constant) is lower?
Zeff is higher
Worse screening
Deeper in energy
183
How does the value of Z affect the orbital energies of 3d vs 4s?
If Z<21 3d is higher in energy
If Z≥21 3d is lower in energy
184
What happens to the s-p gap from left to right of the periodic table?
s-p gap increases due to increasing Zeff and the effect that has on s and p orbitals - more impact on the s orbital so lowers the energy more
185
What is the Aufbau Principle?
Lowest energy orbitals are filled before electrons are placed in higher energy orbitals
186
For polyelectronic atoms what rule is used to decide order of filling of orbitals?
Using the Madelung rule - filled using the most stable one first
187
Why do you need to be careful around the Aufbau principle?
It rests on the assumption that order of energies in orbitals are fixed for a given element
Does not consider effects of other electrons in the atom
- Basically lots of exceptions!!!!!
188
What is the Madelung rule?
The order of orbital filling follows this rule
- Subshells are filled in order of increasing n+l values - if two subshells have identical n+l then filled in order of increasing n
189
How can you show the Madelung rule?
— 1 2 3 4 5 6
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
etc
Fill from diagonals
190
What is the Pauli exclusion principle?
No two electrons in any one atom are allowed to have the same set of quantum numbers
191
What is each orbital defined with?
Three QN : n,l and ml
192
Why do we need an extra quantum number and what is it?
As each orbital can fit two electrons an additional quantum number is needed to distinguish between them
Called ms
193
What does the Dirac equation describe?
Electrons intrinsic spin
Relativistic QM explains occurrence of particle spin
194
What are the allowed values of ms and what do they mean?
ms = ±1/2
Electrons can rotate clockwise or anticlockwise creating a magnetic moment
195
How do you represent electron configurations?
1s2,2s2,2p6,3s2,3p6 etc
196
What are the different configurations of the 1s orbitals?
1s0 - empty
1s1 - holding one electron of either spin
1s2 - holding two electrons one of either spin
197
Why can we not have for example 1s3?
The third electron wouldn't have a unique set of QNs
198
What can you use as shorthand electron configurations?
Noble gases
e.g. [Ar]4s2 = Ca
199
What principle do we use to fill electron configurations?
The Aufbau principle
200
What is Hund's rule of maximum multiplicity?
Degenerate orbital must be filled with one unpaired electron each (with parallel spins) before spin pairing occurs
201
Why do orbitals follow Hund's rule?
They are filled in a way to minimise overall potential energy of the atom
- Minimises electron electron repulsions
202
How do you explain Hund's rule?
1. Electron proximity - placing two electrons in same orbital decreasing energy between them - leading to greater overall repulsion - becomes less significant as size increases
2. Exchange energy - electrons with parallel spins are further apart than anti-parallel spins - experience lower overall repulsion
203
What comes from exchange energies?
Origin of stability of half and full degenerate orbitals
204
What do atoms always arrange electrons to accomplish?
The lowest possible energy - leads to ground state configurations
205
What are the first two odd exceptions to ground state electron configurations?
Cr [Ar]4s13d5
Cu [Ar]4s13d10
Extra stability
206
How do the RDFs of 3d and 4s explain the electron configurations for K and Ca?
4s penetrates through core shells so has higher Zeff
Meaning 4s is more stable so is filled first
207
What happens when you try to fill the 3d block?
4s fills before the 3d level however experimentally the 4s is above the 3d which contravenes the Aufbau principle
208
How do we achieve the lowest energy state?
Maximising coulombic attraction (Zeff)
Minimising electron electron repulsion
209
What three things are used for determining 4s vs 3d?
Orbital energies - Overall Zeff 4s > 3d
- However when 3d fills the electrons screen each other less well than 4s so it changes around
Interelectronic repulsions - 4s is a larger orbital so electron electron repulsions are lower in 4s2 - favours 4s
Exchange energies - Greater for 3d as has higher ml values
210
How do you calculate exchange energies?
EE = n(n-1)/2 where n = number of parallel spins
211
What are the two ways of writing electron configurations?
Order in which they are filled or energy order
Both correct
212
What happens when we ionise 3d atoms?
4s is more penetrating than 3d
Loss of 4s electrons removes screening creating a rapid increase in Zeff of 3d electrons
3d increases stability
So 4s electrons are removed before 3d
213
What are the different kinds of radius?
Metallic radius - half the experimentally determined distances between centre of atoms in a solid
Covalent radius - half the internuclear distance between atoms of the same element in a molecule
Atomic radius is joint of above two
Ionic radius - distance between centre of cations and anions in a compound
214
What are the periodic trends in atomic radii around the periodic table?
Down groups - Orbitals of increasing quantum number so larger radius
Increasing radius down a group
Across rows - Increasing Zeff means valence e- are increasingly close to nucleus so smaller radius
Decreases radius across a row
215
What is the Lanthanide contraction?
f subshells are bad at shielding
So there is a greater than expected decrease in atomic radii across the lanthanides
- caused by poor shielding effect of nuclear charge by 4f elements
216
What is ionisation energy?
Energy required to remove one electron from each atom in one mole of gaseous atoms to form one mole of gaseous +1 ions
217
What are the trends in ionisation energy?
Horizontal trend - first ionisation energy increases going to the right due to increase in Zeff and therefore attraction
Vertical trend - first ionisation energy decreases going down as n increases
218
How can the two drops in ionisation energy be explained across a period?
First drop - filling of the 2p level is higher in energy and benefits from screening of filled 2s - easier to remove
Second drop - electrons need to be paired in 2p sub shell and they repel each other - losing exchange energy and easier to remove
219
What is electron affinity?
Energy released when an atom gains an electron
220
What are the trends in electron affinity?
Increases from left to right and down to up
221
What do the values of electron affinity show?
Large positive value means there is an energy gain
Negative and low values show it is unfavourable for this to happen
- 2nd electron affinity will also be very unfavourable
222
What are key points about electron affinity?
Determined by the energy of the lowest unfilled orbital in the atoms
An element has a high value if electron enters a shell with a high Zeff
Subsequent Ea values are always negative (repulsion)
If an atom acquires an electron to achieve the configuration of an element with a high IE then it will have a high EA
223
What is a chemical bond?
A link between atoms that is formed if the resulting arrangement has a lower energy than the total energy of the separate atoms
224
What are the types of chemical bond?
Covalent bond - sharing of electrons between two atoms
Ionic bond - electrostatic forces between ions of opposite charge
Metallic bond - sharing of delocalised electrons between lots of positive ions
225
How does covalent bonding work?
Electrons are shared between elements to achieve the lowest possible energy arrangement
- Involves overlap of AOs on adjacent atoms
226
What is the 8 electron (octet) rule?
Electron configs of noble gases are particularly stable and other elements try to achieve this config
The ideal number of e- in the valence shell is 8 so electron deficient compounds result in higher reactive compounds
Only works for mainly period 2
227
What is Paulings electronegativity?
Tendency to attract electrons towards an atom in a covalent bond
228
What do deviations Δ from additivity of bond energies E give a measure of?
Strength of ionic character of the heteronuclear bond AB
229
How do you calculate deviations from additivity of bond energies?
ΔAB = EAB - 1/2(EAA-EBB)
sqrt(ΔAB) = χA-χB
230
What is absolute electronegativity (χ^m)?
1/2(IE + EA) in eV
231
What does a high IE and a high EA show?
High IE reveals desire to retain existing e-
High EA reveals a prosperity to gain further electrons
232
What is the difference between Pauling's scale and Mulliken scale?
Paulings scale - ranges from 0-4 and shows electronegativity
Mulliken scale - ranges from 0->10 and shows absolute electronegativity
233
What does a difference in electronegativity do?
Influences the polarity of the bond
And therefore determining the ionic and covalent contributions to a molecule
234
What are the rough Δχ values for different types of bond?
0 - homopolar (no dipole)
0-1.5 - polar covalent (dipoles)
>1.5 - ionic
235
What is special about the polarised covalent bond?
It has both ionic and covalent contributions
236
What are dipole moments and how do you calculate it?
The charge distribution results in a more positive/negative side which can be quantified by the dipole moment (μ)
μ=Qr (measured in D - debye)
Q is unit of electronic charge e
where two equal and opposite charges (Q+ and Q-) are separated by r
237
What is the basis of ionic bonding?
Combinations of elements with low IE and elements with high EA
Complete transfer of one or more electrons
238
What is lattice enthalpy?
ΔHl - energy required to completely separate one mole of a solid ionic compound to its gaseous ions
239
How can lattice enthalpy be calculated?
Cannot be calculated directly so needs to use other energy in a born hater cycle
240
What are isoelectric species?
Species with the same electron configuration
241
How can you roughly calculate the size of ions?
r ≈ n/Zeff
242
What do we know about the size of ions?
All anions are larger and all cations are smaller
Ionic radii decrease with increasing positive charge on the same ion
243
For a series of isoelectronic ions what happens to the size?
Size of ions increase with amount of negative charge
244
What is polarisability?
Measure of how readily e- density of atom/ion can be distorted by a field
Large ions with low electronegativities are generally highly polarisable
245
What is polarising power?
Measure of the ability of an ion to polarise/distort e- density of another atom/ion
Small and highly charged cations
Highly positive charge density - high polarising power
246
How does going down a group affect polarisability and polarising power?
Polarising power - going down a group polarising power of cation decreases
Polarisability - going down a group polarisability of anion increases
247
When must you take polarisation effects into account?
When determining extent of covalent contribution to ionic bonds
248
What happens to covalence as size and charge changes?
Larger anion - increasingly covalent
Smaller cation - increasingly covalent
Increasing charge - increasingly covalent
249
When does polarising power of cations increase?
With smaller radius and increasing positive charge
250
Are pure covalent and pure ionic bonds possible?
Pure covalent is possible but not pure ionic
251
What is the lewis theory of acids and bases?
Lewis acid - electron pair acceptor
Lewis base - electron pair donor
252
What can lewis acids and bases be quantitatively categorised as?
Hard or soft
253
What LA/LB interactions are preferred?
Hard/hard and soft/soft are preferred over hard/soft combinations
254
What dictates hard hard and soft soft reactions?
Electrostatics drive hard hard reactions
Covalency dictates soft soft reactions
255
What are hard and soft acids?
Hard acids - small highly charged cation of electropositive metal e.g. Al3+
Soft acids - large cations of less electropositive metals e.g. Cu+
256
What are hard and soft bases?
Hard bases - Non-polarisable highly electronegative donor atoms e.g. OH-
Soft bases - polarisable less electronegative atoms e.g. CN-
257
What impacts harder/softer character of acids/bases?
Increasing/decreasing cation oxidation state e.g. Fe2+ vs Fe3+
258
What does knowledge of hard/soft acids/bases allow for?
Allows for predictions of stable compounds
259
What is a molecule?
Aggregate of atoms that possesses distinct observable properties
260
What is identity of a molecule dependent on?
Chemical formula but also bonding connectivity and geometry
261
What are the different ways of illustrating molecules?
Molecular formula
Structural formula
Perspective drawing (3D structural)
Ball and stick
Space filling model
262
What are lewis symbols?
Simple way of representing electrons
Each valence electron is a dot arranged around the element symbol
One dot = one e- in orbital
Two dots = two e- in orbital
263
What is important to remember about lewis structures?
They do not see geometry and you must draw all valence electrons around the atoms
264
How do you draw lewis structures?
1. Count no of valence e- on each atom (adjust for ions)
2. Divide total number by two to get no of electron pairs
3. Decide on most likely arrangement (central atom usually least electronegative one unless H is involved)
4. Place an electron pair between each pair of bonded atoms
5. Complete octet (or equivalent) of each atom by adding remaining electron pairs
6. If not enough e- pairs try forming multiple bonds
7. Replace dots between atoms with bonds
265
How can you find the formal charge on each atom in a lewis structure?
Find valence electrons - 1/2(bonding e-)-all non bonding e-
Result is the formal charge
266
What is dative bonding?
When both electrons involved in the bond come from the same atom
Represented as an arrow but is indistinguishable from any other covalent bond
267
What is used if the lewis structure cannot accurately depict a molecule with one structure?
Resonance forms - indicated by double headed arrows
268
What is the actual molecule considered as?
A superposition or blending of resonance structures
269
What is important to know about resonance structures?
Hybrid structure is lower in energy than any single structure
Resonance averages bond characteristics (e.g. bond lengths)
270
What is the difference between resonance and isomerism?
Resonance describes only different electron locations
Isomerism describes different arrangement of atoms
271
What are the exceptions to the octet rule?
1. Ions or molecules with less than an octet e.g. BF3 (elements in 2nd period before C)
2. Ions or molecules with an odd number of e- (relatively rare and usually unstable)
3. Ions or molecules with more than 8e- e.g PCl5 (elements in period 3 or below can use d orbitals to make more than four bonds)
272
What theory determines molecular shape?
Valence Shell Electron Pair Repulsion Theory
273
What is the VSEPR?
Assuming electron pairs are arranged as far away from each other (as electron pairs repel each other) we can predict shape and angles
274
For a molecule with formula AXnEm how do X and E adopt positions?
In a way that minimises electrostatic repulsions
275
When deciding shape what is useful to do first?
Draw the lewis structure first
276
What is important in VSEPR?
Number of electron domains (lone pairs + bonds)
277
What is the difference between pseudostructure and structure?
Pseudostructure - Arrangement of electron domains and thus lone pairs - overall structure
Structure - Actual arrangement of atoms in a molecule
278
What is key to know about lone pairs, bonding pairs and multiple bonds in VSEPR?
Lone pairs occupy more space than bonding pairs
Multiple bonds occupy more space than single bonds
Bonding pairs on electronegative substituents occupy less space than those on more electropositive atoms
279
What is key to know about lone pairs on certain shapes?
Lone pairs adopt equatorial positions in trigonal bipyramidal
If all sites are equal lone pairs go trans (180 degrees) to each other (e.g. octahedral)
280
What are the shapes with two electron domains?
Linear AX₂ - 180°
PS/S: Linear
281
What are the shapes with three electron domains?
Pseudostructure - Trigonal Planar
Structures -
Trigonal Planar AX₃ - 120°
Bent/Angular AX₂E - <120°
282
What are the shapes with four electron domains?
Pseudostructure - Tetrahedral
Structures -
Tetrahedral AX₄ - 109.5°
Trigonal Pyramidal AX₃E - <109.5
Bent/Angular AX₂E₂ - <109.5
283
What are the shapes with five electron domains?
Pseudostructure - Trigonal Bipyramidal
Structures -
Trigonal Bipyramidal AX₅ - 90 and 120
See-Saw/Sawhorse AX₄E - <90 and <120
T-shaped AX₃E₂ - <90
Linear AX₂E₃ - 180
284
What are the shapes with six electron domains?
Pseudostructure - Octahedral
Structures -
Octahedral AX₆ - 90
Square based pyramidal AX₅E - <90
Square-planar AX₄E₂ - <90
285
What is different about trigonal bipyramidal?
Not all atoms are chemically equivalent
3 are equatorial and 2 are axial
Therefore they must be arranged to minimise repulsion and lone pairs go equatorial
286
For molecules with no central atom how do you decide shape?
Look at each atom geometry individually
287
How do you use VSEPR to determine shape?
1. Identify the central atom and determine no of valence electrons
2. Use a lewis diagram to identify how each atom is bonded (e.g. single/double etc)
- Can assume O/S always double bonded and N/P always triple bonded
3. Add one electron for each σ bond formed and subtract one for each π bond involving the central atom
4. Assume charge is on the central atom for calculations and adjust accordingly (+1 for negative charge, -1 for positive charge)
5. Divide total number by two to give no of electron pairs - that gives the pseudostructure
6. Based on number of atoms attached to central atoms determine no of lone pairs and finally structure
288
What does the molecular dipole moment depend on?
Polarity of individual bond dipoles and geometry
289
What are the limitations of VSEPR?
Will fail under following circumstances
- Molecules where bonding is largely ionic
- Transition metal complexes
- Compounds of metals at bottom of p block - lone pairs are stereochemically non-active
- Species that need to be flat to maximise π bond interactions
290
What are the two principle ways of explaining bonding in molecules?
Valence bond (VB) theory
- Consider bonds as localised interactions involving two e- between two atoms
Molecular orbital (MO) theory
- Delocalisation of electrons in MOs delocalised over some/all of the molecule
291
Which way of explains bonding in molecules is easier to visualise?
Valence bond theory as it is essentially QM version of electron dot model
292
What are the basics of Valence Bond Theory?
Electrons of two atoms begin to occupy some space
Called 'overlap' of orbitals
Sharing of space between two e- of opposite spin = covalent bond
293
What happens as orbital overlap increases in VB?
Increased overlap brings e- and nuclei closer together until balance is reached between like charge repulsions and electron-nucleus attraction
Atoms cannot get closer as repulsions too great
294
At the balance point in VB what is true?
The energy is at its lowest
295
What is a σ bond?
When the bond is symmetrical with respect to rotation about intramolecular axis (looking down the bond)
296
What is the problem with basic VB theory when looking at the water molecule?
Shows two p orbitals on oxygen overlapping with H s orbitals
- Suggesting bond angle is 90° as p orbitals are orthogonal
297
What is the problem with basic VB theory when looking at the BeH₂ molecule?
Be atom has e- config of 1s22s2 so has no single e- capable of pairing with H
298
What is hybridisation?
A way of deriving spatially directed orbitals which can be used within VB theory
- Not real - just a mathematical device for modelling
299
What is true about the new hybrid orbitals?
They are of equal energy (degenerate) and n orbitals mix to create n hybrid orbitals
300
What does the character of the hybrid orbitals depend on?
AOs used
Percentage contributions
301
How is hybridisation in linear systems shown?
One 2s and one 2p can be linearly combined to give two hybrid orbitals
Called sp hybrids and are 50% s and 50% p character
302
How does promotion of electrons help with hybridisation?
Solves the problem of no single e- being available for bonding
e.g. Promotion of an electron from 2s to 2p gives two unpaired electrons (requires energy)
Hybridisation can then be performed after promotion converting single e- into hybrid orbitals
303
How does hybridisation fix the problem with BeH₂?
The electron config is now 1s2(sp)2
Using these hybridised orbitals, Be can now form two sigma bonds
304
How is hybridisation in trigonal systems shown?
One 2s and two 2p can be linearly combined to give three hybrid orbitals
Gives sp2 hybrids that are 33% s and 66% p character
- Co planar and at 120° to each other
305
How is hybridisation in tetrahedral systems shown?
One 2s and 3 2p can be linearly combined to give four hybrid orbitals
Gives sp3 hybrids that are 25% s and 75% p character
306
What are the different hybridised orbitals?
sp linear
sp2 trigonal planar
sp3 tetrahedral
sp3d trigonal bipyramidal (using dz^2)
sp3d2 octahedral
307
How does hybridisation fix the problem with the water molecule?
It now predicts the V-shape - oxygen has two sigma bonds and two lone pairs and is sp3 hybridised
308
How does multiple bonding work in hybridisation?
Cannot form multiple bonds using just hybridised orbitals
However can by using ones that are not hybridised
- Possible to have a sideways overlap
309
What is a π bond?
Sideways overlap of orbitals with electron density above and below the axis
310
What happens to bond lengths and bond strengths with increasing s character?
Bond length decrease with increasing s character due to s orbitals being smaller than p orbitals
Bond strength increases with increases s character for the same reason
311
How does hybridisation work in benzene?
Contains six sp2 hybridised carbons and each carbon has a free p orbital that can form delocalised π bonds
312
How can MOs be constructed?
MOs can be constructed as a linear combination of atomic orbitals (LCAO)
MO = cᵦѰᵦ + cᵧѰᵧ+.....
313
What are the characteristics of MOs?
Max of two e- per orbital
e- in same orbital has opposite spin
Definite energy of orbital
314
What happens when two AOs overlap?
Two MOs are formed (one bonding and one anti bonding)
315
What is the difference between bonding and anti bonding orbitals?
Bonding MOs - constructive combinations of AOs
Anti-bonding MOs - destructive combinations of AOs
316
What do anti bonding MOs have?
Nodal plane
317
How do you apply symmetry labels σ and π?
If MO is unaffected by rotation about internuclear axis - given σ
If MO wavefunction changes sign on rotation of 180° about the internuclear axis - given π
318
What are parity labels and how do you assign them?
g (gerade - even) and u (ungerade - odd)
Consider the inversion operation - does wavefunction have same sign at same distance but opposite direction from centre of symmetry
Yes - g
No - u
Only apply to MOs with a centre of symmetry
319
What happens when two AOs are combined in terms of energy?
The bonding MO is stabilised so lower in energy
The anti bonding MO is destabilised so higher in energy
320
What is the bond order and how do we calculate it?
Helps us know the no of participating electrons in formation of bonds
Bond order = 1/2(no of bonding e- - no of anti bonding e-)
321
What does the value of bond order tell us?
High bond order
- Higher stability
- Shorter bond length
322
When can AOs mix to form MOs?
When symmetry requirements and size requirements are met
323
What is the procedure for constructing MO diagrams?
1. Find valence e- configs of each atom and plot AOs on a diagram
2. Identify reference coordinates and make sure locations of AO/MOs are consistent
3. Mix the appropriate AOs to give new MOs taking into account the following rules:
- AOs need correct symmetry to mic
- n AOs = n MOs
- Size of AOs must be compatible to give strong interaction for MOs
- AOs closer in energy to MOs contribute more
4. Check relative energies of MOs
- More nodes = more energetic = higher MO
- Antibonding MO > Bonding MO
- sigma bonds usually stronger than pi bonds
5. Add electrons to MOs starting with lowest energy
324
How do VB and MO theory differ when considering magnetism of O₂?
VB suggests all lone electrons are paired (diamagnetic)
MO suggests there are two lone electrons (unpaired) (paramagnetic)
- MO theory is true
325
What is the difference between diamagnetism and paramagnetism?
Paramagnetic molecules contain single unpaired electrons and are magnetic
326
How do some MO diagrams differ from others?
Some have s-p orbital mixing which leads to a change in the expected order of MO energies
327
What else, in addition to symmetry, needs to match in MO theory?
Energies of orbitals
328
What happens when you cross period 2 in terms of energy of orbitals?
Energies of 2s and 2p AOs decrease due to increased Zeff
- For O₂ to F₂ - energy gap is large and s-p mixing can effectively be ignored
For B₂ C₂ and N₂ - energy gap is much smaller so need to consider s-p mixing
329
How do you handle s-p mixing in homodiatomics?
Need to consider mixing of 2s and 2pz AOs on one atom with 2s and 2pz AOs on another atom
Hard to mix all 4 AOs in one step so
1. Mix matching pairs of AOs as before
2. Mix the resultant MOs to give new MOs
330
When can MOs mix?
When MOs are close in energy and have the same symmetry label
- Forms new bonding/antibonding combination
- Cannot be from the same pair
331
What does the mixing of two bonding MOs result in?
Two new bonding MOs
332
How do you draw an MO diagram that involves s-p mixing?
First decide if there will be s-p mixing
Then form MOs from AOs
Next form new MOs from old MOs and draw diagram
333
What happens when you mix bonding MOs?
One will stabilise and the other will destabilise
Similar for anti bonding MOs
334
What is the difference between mixing bonding MOs and mixing anti bonding MOs?
The energy gap between them is larger than for bonding MOs so mixing interaction isn't as pronounced
335
How does electronegativity affect MO diagrams?
Atoms with higher electronegativity have lower energy AOs
336
What is the experimental evidence for the σ-π crossover?
Photoelectron spec used to determine energies and ordering of orbitals by analysis is KE of ejected e-
Sample is irradiated with intense UV which causes ionisation of higher energy e-
Ionisation energy ≈ - Orbital energy
337
How do MO diagrams of heteronuclear diatomic differ?
Differ in having uneven distribution of electron density
- Due to differences in energy and electronegativites
338
What do the relative energies of AOs of X and Y dictate?
Dictate whether an interaction leads to efficient overlap or not - closer in energy the AOs are the stronger the interaction
339
In heteronuclear diatomics what happens to bonding and anti bonding e-?
Bonding e- tend to be closer to more e-neg atom
Antibonding e- tend to be closer to less e-neg atom
340
What happens in the MO diagram of HF?
As the AOs are so different in energy the F 2s has no corresponding AO in H to mix with so is non bonding
The F 2p and H 1s AOs combine to create one sigma combination and two non bonding p orbitals
341
Can you get s-p mixing in heteronuclear diatomics?
Yes you can and in compounds like CO it is large enough to cause σ-π crossover
342
When it comes to polynuclear molecules what can MO theory be used for?
Can be used to understand/rationalise electronic distribution
Resemble those of diatomics the only difference being MOs are built from a larger set of AOs
343
What do we need to do MO diagrams for triatomic molecules?
Ligand group orbitals (LGOs)
- Derived from suitable combos of AOs of all ligands
VSEPR theory in order to predict shape before considering overlap of orbitals
344
How do you draw MO diagrams for triatomic molecules?
1. Form LGOs from the ligands (atoms that are not the central atom)
2. Determine by symmetry which AOs on your central atom can interact with new LGOs
3. Draw mini MO diagrams to show the interaction of the central atom with both the in phase LGOs and out of phase LGOs
4. Then use this to draw your full MO diagram
345
What should you do when combining LGOs and AOs?
Assume starting orbitals are of similar energy
346
Why do we form LGOs?
So we only have two things combining to form MOs
347
When do you get non bonding orbitals?
When there are left over AOs that have not been combined
Means there is no net overlap between the AOs
348
What happens to energy of MOs with increasing number of nodal planes?
Energy of MOs increase with number of nodal planes
349
In a polynuclear molecule where are the electrons located in MO theory?
Spread over the entire framework
350
How to find bond order for an individual ligand?
Divide total bond order by a specific amount
351
What happens when you put electrons in anti bonding MOs?
It weakens the bond - if put too many the bond will break
352
How can the s-p gap help with drawing MO diagrams?
If s-p gap for outer atoms is large then sometimes you don't need to consider certain overlaps
353
How can you describe bonds in MO theory?
x-centre y-electron (xc-ye) bonds
x number of atoms and y electrons delocalised between them
354
How do linear and non linear triatomic molecules differ?
Basically in no way at all apart from the different ways LGOs could combine with AOs
355
If you can mix three LGOs and AOs together what happens?
Common to form one bonding, one anti bonding and one approximately non bonding MO
356
What are Walsh Diagrams?
They look at the effect of moving a linear triatomic molecule towards a bent molecule on the occupied MOs
- Can be used to know what order your MOs should be in
357
Why are some triatomics linear and some bent?
Geometry adopted by a AX₂ molecule minimises total energy for all e-
- In linear triatomics only two MOs are populated so minimum is at 180
- In bent triatomics 4 MOs cause the bond angle where energies are at a minimum to be 104.5
358
What are transition metals?
Elements in the centre block of the periodic table that have partially filled d orbitals (or can form cations with partially filled d orbitals)
359
What do transition metals form when bonding?
Coordination compounds consisting of a metals bonding to ligands (molecules/ions)
Structure and bonding models for s and p block elements can also be applied with some changes
360
What do ligands act as?
Lewis bases - donating pair of e- to form bond (coordination bond)
σ donors
361
What is the 18 electron rule when talking about transition metals?
Based on filling valence shell of TMs which consist of 9 orbitals
Total number of valence electrons around the TM should equal 18 - Metal d e- + e- from ligands
362
What is the 18 electron rule used for and what is the problem with it?
Used to predict and rationalise formula for TM complexes
However not helpful for non TM complexes and some TM don't obey the rule
363
How many electrons do each ligand add to the count?
Two
364
What do you need to remember when counting electrons for the 18 electron rule?
Include the oxidation state of the TM
365
What is the Kepert Model?
A model that rationalising shapes of d block metal complexes based on the number of ligands
- ignoring non bonding e- and is independent of e- config
366
What shapes does the Kepert model predict for coordination numbers 2-6?
2 - linear
3 - trigonal planar
4 - tetrahedral (can be square planar but model doesn't work as electronic effects are controlling factor)
5 - trigonal bipyramidal or square pyramidal
6 - octahedral
367
Can VB theory be used for metal complexes?
Yes but hybridisation not often used now with crystal field and MO preferred
368
What can some ligands act as?
pi donors or pi acceptors as well as sigma donors
369
Where do electron donation and electron acceptance come from in ligands?
Electron donation occurs from HOMO
Electron acceptance occurs into LUMO
370
What is synergic bonding?
'Working together'
Sigma donation to the metal causes more negative charge on the metal so there is a stronger pi back donation
Push-pull mechanism
371
What does donation of a pair of e- to the metal centre do?
Greatly increases negative charge on metal
372
What is true about the distribution of charge in a molecule or ion? Paulings electronegativity principle
Distribution is such that the charge of any single atom is ideally close to zero for it to be favourable
373
Due to the distribution of charge what happens when there is a donation of a pair of e- to the metal centre?
Makes the complex unfavourable so the ligand can act as a pi acceptor and e- can be transferred back
374
What causes a decrease in bond strength of CO?
Donation of e- from bonding orbital on ligand lowers bond order so decreases bond strength
Acceptance of e- into anti bonding orbital lowers bond order so decreases bond strength
375
How can the weakening of the CO bond in binding to a metal be seen?
By looking at bond length and IR stretch
376
What happens to M-C bonding as C-O bonding decreases?
M-C bonding increases
377
What are the trends in CO bond strength upon binding to a metal centre?
CO can stabilise metals in low oxidation states by acting as a pi acceptor
More negatively charged/electron rich the metal the greater the pi back donation
And therefore a weaker CO bond
378
What is true about the number of ligands a metal has and the amount of pi back donation?
Greater the number of ligands a metal has to share negative charge with the less there is pi back donation
379
How does dihydrogen bind to complexes?
What is special about dihydrogen bonding to complexes?
In a side on fashion
It can do the same as CO ligands
If sufficient e- den is transferred to σ* on H₂ then H-H will break
380
What is a singlet state?
When one orbital is full and the others empty
381
How do we know about solid state structure?
Using X-ray diffraction allows measurement of interatomic distances and bond length/angles
382
How are atoms and molecules arranged in a crystal?
Arranged in a repeating pattern in all 3 dimensions
383
What do identical atoms in a crystal form?
Planes within the crystal
384
Why can X-ray diffraction be used to probe the separation of layers in a crystal?
As the distance separating the planes is the same order of magnitude as wavelengths of X-rays (Å)
385
What do beams of rays diffract off of when analysing crystals?
Different planes in the crystal
386
What happens if you get the correct angle of beam in X-ray diffraction?
What happens if not?
Difference in distance between how far each beam travels is a whole number of wavelengths
- Greater constructive interference and beam that comes out is strong/bright
If not there is greater destructive interference and beam is weak/non-existent
387
What are diffraction patterns analysed to find?
Distance between planes and hence interatomic distances
388
What is a crystal structure?
A regular array of objects in space
389
What is one way of describing structure?
Using lattice + motif
Lattice - set of imaginary identical points in space
Motif - associated with each lattice point
390
What is important to remember about lattice points?
They are not real so shouldn't be in the final structure
391
Where do your lattice points have to go in a molecule?
Anywhere as long as constant throughout the lattice
392
How do you turn a motif and lattice into crystal structure?
1. Place one motif on each lattice point
2. Remove lattice points as are imaginary
393
What is another way you can describe crystal structure?
Using a repeat unit cell
- Part of space that can be tessellated to form the whole crystal
394
What are unit cell corners?
They are identical points in space
- Corners = Lattice points
395
Where can unit cell corners be put in a crystal?
Either at a point on the atom/molecule or in empty space
396
What are the two types of unit cell?
Primitive unit cell - lattice points only at the corners
Non primitive unit cell - lattice points in addition to those at the corners
- normally larger than need to be
397
What should you try and do when drawing unit cells?
Try to capture geometry
Try to use right angels
398
In 3D what do unit cells have?
Identical corners
Identical parallel edges
Identical parallel faces
399
What type of unit cell do we usually use in 3D and why?
Conventional unit cell - non primitive but still clearer than the primitive unit cell
Primitive unit cell can sometimes be confusing and oddly shaped
400
What are the parameters for a 3D unit cell?
Must be a parallelepiped (3D parallelogram)
- Parallel sides are the same length (a,b,c)
-Angles at the origin (ɑ,β,ɣ) are opposite a,b,c respectively
401
How do the axes in 3D unit cells differ from convention?
They follow the right hand rule but are not necessarily perpendicular
- Just aligned with the edges of the cell
402
How do we describe points in a 3D unit cell?
Using unit cell vectors
Origin is always back bottom left and point front top right is (1,1,1)
All other points are relative to this
403
What makes unit cell vectors different from normal vectors?
Each number is relative to the full length of the side
Meaning 1 down the a side could mean a different length to 1 down the b side
404
What are the 4 types of unit cell (1primitive/3 non primitive)?
Primitive, P (simple)
- Lattice points at corners
Face centred, F
- Additional lattice points at all face centres
Body centred, I
- Additional lattice points at (1/2,1/2,1/2) - in the middle of the unit cell
Side centred, A/B/C
- Additional lattice points at e.g. (1/2,1/2,0) if C - end up with two extra lattice points
- Normally use C
405
How do you explain lattice point equivalency?
For primitive all lattice points are equivalent so only need to label one at (0,0,0) - all others are therefore already there
For non primitive lattice points if you have one on the side you will also have one on the corresponding opposite side
406
How can you describe structure using unit cells?
Unit cell type and parameters + Motif
407
What do you need to be able to draw a unit cell?
Unit cell type - F,P etc
Parameters - angles/lengths
Motif - e.g. S: (0,0,0)
408
What must you do to ensure a complete structure is drawn?
Apply the motif at multiple different lattice points within the unit cell
409
In crystals with different atoms how do you know what type of unit cell it is?
Just look at the main set of atoms
e.g. if there is Au atoms at all corners and a Ag atom in the centre it is not body centred just primitive
410
How do we show the 3D structure of the unit cell on 2D?
Using unit cell projections
411
What do you need to remember to add when drawing unit cell projections?
A key to tell you which atom is which
412
What are the key factors about the unit cell projection?
- if a=b and ɣ=90° it is a square projection
- x and y coordinates are indicated by position on diagram
- z coordinates are indicated by writing
- more than one z coordinate indicates two atoms for that x and y
- absence of writing indicates atom at both 0 and 1
413
What can unit cell projections be used for and how are they described?
To draw the complete structure
'Unit cell projection along c' which means down the c vector
414
How do you count objects in a unit cell?
Objects at corners - Shared with 7 other cells so 8 in total
- count = 1/8
Objects on edges - Shared between 4
- count = 1/4
Objects on faces - Shared between 2
- count = 1/2
Objects within unit cell - Shared with none
- count = 1
415
What is the general rule for finding the count of a unit cell?
Count = 1/(no of unit cells that share the point/edge etc)
416
What can you use the count of a unit cell to find?
The empirical formula by comparing no of atoms involved by calculating separate counts for each atom
417
What is the most efficient space-filling arrangement and what is the packing efficiency?
Close-packed
74% packing efficiency
418
What are the types of close packed arrangements?
Hexagonal close packed (HCP)
Cubic close packed (CCP)
419
What is there to know about hexagonal close packed arrangement?
It has ABA layers
Packing efficiency = 74%
Atom coordination = 12
420
What is there to know about cubic close packed arrangement?
It has ABCA layers
Packing efficiency = 74%
Atom coordination = 12
421
What is important to remember about the unit cell projection of CCP?
It comes from slightly tilting the structure
422
What is packing efficiency?
The percentage volume of the unit cell occupied by atoms
423
How do you calculate packing efficiency?
Find total volume of unit cell and total volume of spheres both in terms of r
Divide total volume of spheres by total volume of unit cell x100
424
What is atom coordination?
Number and geometric arrangement of nearest atoms
'How many atoms each atom is in contact with' and 'what shape does this make'
425
What are the types of non-close packing?
Body centred cubic (BCC)
Primitive cubic
426
What are the atom coordination of the non-close packing arrangements?
BCC- 8 and cubic
primitive cubic - 6 and octahedral
427
How can you work out the geometry of a packing arrangement?
Look at how the atoms look in space e.g. octahedral would have four atoms in the plane with one above and one below
428
What are most metals/transition metals packed using?
One of HCP/CCP/BCC
429
What is the free electron theory in metallic bonding?
Nuclei are held together by a 'sea of electrons' formed from shared valence e-
430
What is the explanation for conductivity in the free electron theory?
e- can move unimpeded by 'cores' (nuclei and core e-) or by each other
431
By only considering one electron in the free electron theory what can you do?
Apply the particle in a box model
- can be refined by introducing periodic potential (modelling the nuclei)
432
What is band theory?
By considering the a solid to be a very, very large molecule and applying MO theory to it
433
What is band theory useful for?
Comparing metals and semiconductors
434
How does band theory work?
You combine AOs over and over again
As number of AOs combining increases the energy difference between the MOs formed decreases
Eventually the energy difference between MOs is negligible so the energy levels get grouped into bands
- Within which the energy can be varied continuously (effectively not quantised)
435
What are the features of band structure?
Band width - height of band
Band gap - can be gap between bands
- Both effected by the extent of orbital overlap
Strongly bonded MOs at bottom of band
Strongly antibonded MOs at top of band
Fermi level (at 0K) is where the levels stop being occupied by electrons
436
What happens within the band?
A certain level of it is occupied by electrons and then the rest of it isnt
437
What are the simple metals in G1,2,13?
High coordinate, metallic, conductors
438
What does the band theory in simple metals look like?
One single s/p band with no band gap
- due to small energy gap between atomic s and p orbitals which form the MOs
439
Do simple metals have effective metallic bonding?
Yes due to structures which place atoms in relatively high coordinate environments
- 1,2 or 3 valence e- per atom occupy bonding MOs at bottom of band
440
What is conductivity a consequence of?
Partially filled bands
- empty delocalised MOs are readily energetically accessible and their population creates partially filled MOs, allowing electrons to move through structure
441
What are the elements in group 14? (properties)
Lead/Tin (<286K) - high coordinate, metallic, conductors
Germanium/Silicon - extended covalent network, semi conductors
442
What happens in 4 coordinate tetrahedral atomic centres in band theory? (such as silicon)
Two separate bands as the s and p AOs are far apart in energy
443
What are the two bands called in tetrahedral atomic centres and why are they strong bonds?
Valence band - contains e-
Conduction band - doesn't contain e-
Strong bonds as 4 valence e- means valence band is completely filled and conduction band is completely empty (Bonding MOs filled/Antibonding MOs empty)
444
Why is there a small band gap in germanium and silicon and what does this do?
Comes from the overlap of relatively diffuse derived orbitals
Causes significant thermal population of the conduction band at raise temps - hence conductivity and that they are semi conductors
(can jump the band gap)
445
What are diamonds and what type of band gap do they have?
Extended covalent structure, insulator
Large band gap - effective overlap which stabilises/destabilises strongly creating a large gap between bonding and anti bonding
446
What are transition metals? (properties)
High coordinate structures, metallic, conductors
They have additional (n-1)d valence electrons and the radially contracted 3d orbitals cause a narrow band
447
What are important things to know about semi conductors?
They have a small band gap (0.5-3eV)
Intrinsic semi conductors - pure materials
- elements e.g. silicon
- III/V and II/VI compounds
Extrinsic (doped) semi conductors
- adding other elements
448
How can you tell the difference between conductors, semi conductors and insulators?
Conductors - no band gap
Semi conductors - small band gap
Insulators - large band gap
449
What affects band width and band gap?
Extent of orbital overlap
Band width - more overlap = wider band
Band gap - coordination: orbital size, orientation, energy separation
450
How does electrical conductivity change with temperature?
Conductors - increase in temperature decreases conductivity
Semi conductors - increase in temperature increases conductivity
Insulators - increase in temperature very slightly increases conductivity
451
What do close packed arrangements contain?
Holes - cavities between atoms
452
What are tetrahedral/octahedral holes?
Tetrahedral holes - centre of a tetrahedral arrangement of spheres
Octahedral holes - centre of a octahedral arrangement of spheres
453
What can structures of ionic solids be described as?
A close packed (or non close packed) arrangement of one type of ion, with other ions occupying some or all holes
454
What are structural archetypes?
Packing arrangement + holes occupation
There are a number of possible common configurations
Also called 'parent structures'
455
How can structures be described using coordination polyhedra?
In terms of -
- Polyhedral 'atom+coordination sphere' units
- How these units are connected
e.g. vertex sharing, edge sharing or face sharing of 3D polyhedra shapes
456
When will ions of the same charge pack together?
If the ensuing Coulombic repulsion is overcome by attraction to oppositely charged ion in holes
457
When is the attraction between ions maximised?
When both are in contact - ions fit will in holes
458
What is hole size a function of and what is the formula?
A function of the radius of the close packed ions
r(hole) = r(cp)((1/sinθ)-1)
459
What can be calculated with radius of ions and ions in holes, what is it for and how can you calculate it?
The critical ratio of radii for fitting each type of hole
Can be used to find the preferred coordination of a lattice
r(hole ion)/r(cp ion) = (1/sinθ) - 1
460
How can you use the critical ratio of radii?
Find value
If between two critical values then the preferred coordination is the lower one
461
Why can the critical ratio of radii only predict the correct structure sometimes?
As there are multiple archetypes with the same coordination it can only predict what holes are preferred
Sometimes doesn't predict the correct holes
- Assumes ions are hard spheres
- But they are polarising and have polarising power so a more directional covalent bonding component can influence structure
462
When can you be confident with your prediction of structure?
When ions are relatively small and have a high charge
- As these are hard ions so the hard sphere assumption is good
463
How can you test the structure you found using critical radii?
X ray diffraction
464
What is the lattice energy?
Sum across the crystal of Coulombic attractions between oppositely charged ions and repulsions between similarly charged ion
- A function of arrangements of ions in space - structure
465
What is the Madelung constant (A)?
A constant that depends only on the geometric arrangements of charges and is different for different structural types
466
What is the (1-ρ/r) term for?
To prevent packing of ions after a certain distance
- There is short range repulsion between ions irrespective of charge
- ρ = 34.5pm
467
How do you find the internuclear separation for lattice energy?
Approximated by sum of ionic radii
468
What is accurate/not accurate about lattice energy?
Based on experimental r values (XRD)
But considers only electrostatic interactions and ions are hard spheres with fixed radii
469
What is lattice enthalpy?
Energy required to dissociate a crystalline solid into gaseous ions
NaCl(s)→Na+(g) + Cl-(g)
470
How is lattice enthalpy derived?
From thermochemical cycles (sum of all contributions to bonding)
- Born-Haber cycle
471
What can be use the Born-haber cycle to do?
Find experimental lattice enthalpy
Estimation of other data where lattice enthalpy is known or estimated (e.g. electron affinities)
Estimation of enthalpy of formation for hypothetical compounds based on lattice energy
472
What can we do when working with Born Haber cycles?
Estimate that lattice enthalpy ≈ lattice energy
473
How do you calculate number of radial nodes
n-l-1
474
How do you calculate angular nodes?
l
475
How do you calculate total number of nodes?
n-1
