Quantum Chemistry Flashcards
Why was quantum theory developed?
Developed to explain various experimental observations that couldn’t be understood by prevailing ‘classical’ theories of physics
What is quantum theory?
It is based on several principles such as wave particle duality and quantisation.
What were 3 issues which puzzled classical physicists which led to the development of quantum theory?
Black body radiation
Photoelectric effect
Spectroscopic lines
What is a black body?
A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It does not reflect or transmit any radiation; instead, it absorbs all incoming radiation and re-emits it.
What was the issue with black body radiation?
The issue with understanding black body radiation in the late 19th and early 20th centuries was the failure of classical physics to explain the observed spectral distribution of the emitted radiation. According to classical electromagnetic theory, it was expected that the energy emitted by a black body would increase without bound as the wavelength of the radiation became shorter (known as the ultraviolet catastrophe).
The ultraviolet catastrophe problem arose because classical physics predicted that the intensity of radiation would increase without limit as the wavelength approached zero, leading to an infinite amount of energy. However, experimental observations, particularly the detailed measurements of black body radiation depicted a different behaviour.
Thus, physicists had to find a solution to the black body radiation
What was Planck’s solution to black body radiation?
He proposed that energy is quantised. This means that electroncs can only possess certain discrete energy values, and values between these quantised values aren’t permitted
He suggested that energy is emitted or absorbed in discrete packets or ‘quanta’, which is proportional to the frequency of radiation.
What was the formula to calculate the energy of a system / electron by Planck?
E = hv
E = energy
h = Planck’s constant
v = frequency of oscillation
What is planck’s constant
6.62607015×10^−34 Js-
What is the photoelectric effect? WHat was the issue with it?
Light / electromagnetic radiation can eject electrons from a metal, but only if its frequency is above a threshold frequency which is characteristic for every different metal. The emission of electrons occurs instantaneously and energy of the emitted electrons depends on the frequency of the incident light rather than intensity
However, this contradicted classical wave theories of light, which predicted a gradual increase in the emission of electrons with increasing light intensity, however intensity of light doesnt affect the energy of the emitted electrons.
What did EInstein propose in 1905?
That light has a particle nature as well as a wave nature. Light is quantised.
What is the formula that EInstein developed from Placnk’s formula? (energy of a photon)
E = hv = h x c /λ –> v = c / λ
E = energy
where v = frequency
c = speed of light = 3.0 x 10^8 ms^01
λ = wavelength
h = Planck’s constant
How did Louis de Broglie build on Einstein’s findings of the photoelectric effect
De Broglie built on this to further propose that if light can behave as a wave and a particle, why can’t matter such as electrons also have wave properties –> idea that electrons act as a wave-particle duality
He further suggested that the momentum (mv) of a particle should be related to its wavelength in the same way as a photon
What is the equation of momentum?
Stems from Einsteins special theory of relativity
p = E / c
Where p is momentum, E is energy and c is the speed of light
How can we combine both the equation of momentum and quantum theory?
To form the equation of :
λ = n / p = n / mv
where m = mass
v = velocity
h = planck’s constant
λ = wavelength
What were spectroscopic lines? WHat was the issue with it?
Spectroscopic lines refer to the discrete, well defined lines observed in a spectrum when light is dispersed. These lines represent specific wavelengths or frequencies of light emitted or absorbed by atoms or molecules.
The issue with spectroscopic lines for classical physicists arose when they attempted to explain the observed patterns using classical electromagnetic theory, which treats light as a continuous wave. This means that a heated object would emit radiation continuously across all wavelengths, forming a smooth and continuous spectrum. However, experimental observations showed distinct and well defined lines instead of a continuous spectrum
How did Bohr address the issue of spectroscopic lines
He further developed the quantum model of the atom through using the knowledge of both Einstein (quantised packets of energy for light) and Planck (quantisation of energy).
He suggested that electrons then exist in discrete energies with quantised electron orbits. The electrons in atoms could only exist in certain allowed energy levels, and transitions between these levels resulted in the emission or absorption of photons with specific energies corresponding to the observed spectral lines. This successfully addressed the issue of the defined spectroscopic lines
What was the Bohr model?
Bohr postulates that there is a set of circular orbits for electrons with specific, discrete radii, and energy (quantised) and that electrons could move in each orbit without radiating energy
What was the formula derived for the energy of an orbit ‘n’ in Bohr’s model?
This was derived by looking at the atomic spectra for hydrogen.
En = - (me^4) / (2h^2n^2) = - Er x 1/n^2
En = energy of a particular orbit ‘n’
h = planck’s constant
n is an integer 1,2,3… corresponding to Bohr’s discrete orbitals
Er = Rydberg’s constant - 2.18 x 10^-18 J
This means that only specifc values of E are allowed. Values between Er (n= 1) and Er (n=2) can’t be observed, etc. Has to be only these integers
What’s wrong with Bohr’s model?
According to classical physics, revolving charged particles radiate energy. Thus, electrons should continually lose energy and spiral into the nucleus
Bohr’s model could only explain the emission spectra of single electron atoms such as Hydrogen. It failed to predict the spectra of multielectron atoms
Bohr couldn’t offer a reason as to why an electron should actually have a discrete orbit or energy
How are changes in energy levels achieved?
They are done through the absorption or emission of photons.
Absorption involves increasing an energy level
Emission involves decreasing an energy level
What can electrons be thought of as?
As 3d standing waves, with an amplitude characterised by a wavefunction (𝚿)
A standing wave is also known as a stationary wave, its a combination of two waves moving in opposite directions, each having the same amplitude and frequency.
What is the lowest energy level of any standing wave called?
The fundamental
What are the energy levels after the fundamental called?
They are called ‘harmonics’ in order of how many waves it is after the fundamental
I.e. n= 1 –> fundamental –> 1 half wavelength
n = 2 –> First Harmonic –> 2 half wavelengths
n = 3 –> Second Harmonic –> 3 half wavelengths
n = 4 –> Third Harmonic –> 4 half wavelengths
And then the pattern continues
Each harmonic adds a half wavelength
WHat is a half wavelength
It is the distance between each node
What is a node defined by when graphing?
It is defined by the intersections of the standing wave with the x axis
What is the energy of the fundamental of a standing wave dependent on?
Depends on the degree of confinement
WHat confines an electron wave in an atom?
Electrostatic attraction to nucleus
Why does the energy of the electron increase as it gets further away from the nucleus. (I THINK)
(I THINK) This is apparently because of potential energies. It takes more energy to take an electron away when it is close to the nucleus, however the electron only releases a set amount of energy, which is ultimately less than the energy it takes to take it away –> more negative energy, however as it becomes easier to tear the electron away, the amount of ‘potential energy’ increases (?)
Another explain by chatgpt:
So, the basic idea is that electrons have more energy when they’re further from the nucleus because they’ve had to work against the attractive force from the positively charged nucleus to get there.
What is electron density?
It describes an area where the electron is most likely to be in
What is Born’s interpretation?
The probability of finding an electron (i.e. electron density) is given by the square of the wavefunction 𝚿
Because 𝚿^2 is always positive, the probability of finding an electron is always positive regardless of the sign of the wave
WHat is a node?
A node is a point where the probability of finding an electron is zero
How do you determine the number of nodes from the principal quantum number ; n ?
There are n-1 nodes. This means that for n = 1, there are no nodes
WHat is the lobe representation of s orbitals?
It is a sphere around the centre (sphere around the nucleus)
Why does orbital size increase with energy?
This is because electrons with higher energy are found further away from the nucleus. As a result of an increase in energy of electrons, thus, the orbital size also increases (distance to the furthest electron)
How do you identify the principal quantum number, n?
It is the number in front of the letter when listing orbitals, i.e. for 1s, the principle quantum number is 1
What is the equation for energy of an electron?
E = Er (Z^2 / n^2)
WHere E = energy of electron
Er = Rydberg’s constant
Z = Charge (which is normally always 1)
n = principle quantum number
What does the radial probability look at?
Probability of finding a radial/ spherical node
What is a planar/angular node?
Angular node is also referred to as the nodal plane. Angular node refers to a plane that passes through the nucleus.
Does energy increase with the number of nodes?
Yes
WHat does the lobe representation of a p orbital look like?
A dumbbell
How can the 2p orbital exist?
It can exist across 3 planes; x, y and z axis (2px, 2py, 2pz)
What is the angular momentum quantum number , ‘L’, What is its significance
This arises because principal number cant differentiate between 2p and 2s. Thus, the angular moment quantum number determines the shape of the orbital.
L is quantised into different discrete values
S orbital : L =0
p orbital : L = 1
d orbital: L = 2
f orbital: L = 3
L also equals the number of planar/angular nodes. I.e. the p orbital will have 1 planar/angular node, and a 3p orbital would have 1 radial node as well
What is the magnetic quantum number, mL?
mL = -L…, 0,…+L
For example, when L = 1 (i.e. p orbital), mL = -1, 0, 1 –> hence when we see a p orbital it can exist on 3 different planes (x, y, z), and if they’re all used, the 3 different planes are used all together, however if not, it could just be expressed on the x axis or the y axis or the z axis, same continues for others.
Thus, for example, a d orbital will have 5 different orbitals as part of it
It determines the number of orbitals and their orientation
What does the pauli exclusion principle mean?
States that no two electrons in an atom can be in the same quantum state (n, L, mL, and ms)
as a result, electrons in the same orbital must have opposite spins (ms)(application)
What does the Aufbau principle mean?
States that electrons in atoms generally exist in their lowest possible energy state. (Ground state)
Thus, electrons fill lower energy atomic orbitals before filling higher energy ones
What does Hund’s rule state
States that the lowest energy electron configuration in orbitals equals energy t
Thus, before the double occupation of any orbital, every orbital in the sub level must be singly occupied first.
This works because we need to keep electrons as far apart from each other as possible to account for repulsive potential energy between electrons. Thus, the number of unpaid electrons in degenerate orbitals is maximised
What is the significance of Hund’s rule?
What is a degenerate orbital
Electron orbitals having the same energy levels are called degenerate orbitals.
What is the spin quantum number, ms?
Describes the ‘spin’ of an electron which is form of angular momentum of electrons. This arises because an electron behaves like a magnet, so they can be deflected in an inhomogenous magnetic field. A famous example is the Stern - Gerlach experiment demonstration of spin
It states that ms has a spin of +1/2 or -1/2
What are the 2 things we need to consider in a multi electron system?
Electron - electron repulsion
Orbital shielding
What is electron -electron repulsion
When we have more than one electron, the electrons within an orbital will repel each other –> want to maximise distance between electrons
What is orbital shielding and its effects?
This is when an orbital is occupied, it shields the interaction of the outer orbital with the nucleus. This alters the energy levels of the orbital. Orbital shielding depends on the shape of the orbital
s<p<d<f in terms of orbital shielding
Explain further the significance of orbital shielding
For an atom with more than 1 electron, electrons in orbitals closer to the nucleus shield electrons that are further away. This decreases positive attraction from nucleus, thereby raising energy. Thus lower shells have less shielding
What is the main difference between hydrogen like atoms and multi electron atoms
In hydrogen like atoms (one electron), Energy of electron is the same for a single principal quantum number –> quantum number determines energy, whereas in multi electron atoms due to orbital shielding and electron repulsion, the energies of different orbitals might be different due to these factors –> specific order
What are valence electrons?
These are electrons on the outermost shell of an atom. They are the ones which are important in forming chemical bonds.
What is SPDF notation, and how can we use noble gas configuration
stating how many electrons are in each orbital such as 1s2 2s2 2p3 etc.
However, we could use noble gas configuration, which uses the closest noble gas and then doing the spdf notation afterwards to identify a certain atom:
[He] 2s2 2p2 = Carbon
How many electrons per orbital?
2
What is nuclear charge(z)?
Number of protons in nucleus
WHat is effective nuclear charge (Zeff)
Positive charge felt by an electron in a multi electron atom
Is the effective nuclear charge higher or lower than the nuclear charge? Provide a reason.
Electrons in outer orbitals are partially shielded from the nuclear charge, resulting in weaker attraction between the valence electrons and the protons –> lower Zeff.
Electrons close to a nucleus (i.e. in 1s orbital) feel a nuclear charge close to Z
Outer electrons are considerably shifted from nucleus so Zeff is much lower than Z
What is the trend in atomic radius charge across a period and down a group?
Across a period: effective nuclear charge increases, because number of protons increase and there aren’t that many more electron orbitals being formed –> electrons more tightly held by nucleus –> smaller radius
Down a group: Electrons are added to orbitals further from nucleus –> larger radius. There is also a weaker attraction between the positive nucleus and outside electrons
What is atomic radii?
Distance between nucleus and the furthest electron
Describe anionic radii and the trends associated with it
When forming an anion, electrons are usually added to the same orbital. Because there are more electrons –> more electronic repulsion. Thus, size of anion (how many extra electrons are added), will result in a increase in size of atom because of idea of repulsion
The anion thus has a higher atomic radii compared to the parent atom
Describe cationic radii and the trends associated with it
When forming a cation, electrons are removed from the outer orbital. This reduces electron repulsion, and also allows valence orbitals to be closer to the nucleus (allowing for greater attraction) –> cation is smaller than the atom
The cation thus has a smaller atomic radii compared to the parent atom
What is ionisation energy
It is the amount of energy required to remove an electron completely from an electron
It requires the input of energy. Thus ironisation energy will always be positive
How does effective nuclear charge influence ionisation energy?
Larger Zeff = electrons held more tightly to nucleus –> electrons harder to remove due to increased electrostatic attraction –> higher ionisation energy
What is the trend in ionisation energy across a period?
Across a period Zeff increases. This is because as Zeff increases across a period, electrons are more attracted to the nucleus –> more energy required to pull an electron away –> higher ionisation energy
What is the trend in ionisation energy down a group?
Down a group, electrons are added to orbitals that are further away from the nucleus, and also form electron repulsion with each other. This indicates weaker nuclear attraction –> easier to pull apart this attraction –> lower ionisation energy
What is Electron affinity?
Electron affinity is the energy when an electron is added to an atom in the gas phase
If energy is released when an electron is added, the atom has an affinity for electrons, and it has a negative electron affinity
When energy is required to add an electron, it does not have an affinity for electrons and we cannot directly measure an electron affinity value.
What is the trend for electron affinity?
Periodic trends for electron affinity aren’t too clear.
CHeck books on equilibrium bond distance and covalent bonds
What is bond length?
Separation distance at which the molecule has the maximum energetic advantage
What is bond energy?
Energy required to break the covalent bond
What is the unit for bond length?
Angstrom (Å) = 0.1nm
What is the bohr radius
Most probable distance between the nucleus and electron in a H atom. The Bohr radius is 0.53 Å
What is the total number of atomic orbitals in the component atoms equal to?
Equal to the number of molecular orbitals
Overlap of N atomic orbitals = formation of N molecular orbitals
What is molecular orbital theory
Considers the formation of molecular orbitals from the overlap of atomic orbitals on all of the individual atoms in the molecule
What are the 2 ways that atomic orbitals can overlap?
Through in-phase overlapping (both orbitals having the same phase (wave function)), or out of phase overlapping (both orbitals having opposite phases)
In-phase overlapping is constructive overlaps and gives a bonding molecular orbital, in which electron density is maximised –> minimises internuclear repulsion. (This has lower energy)
Out-of-phase overlapping is destructive overlaps, and gives an antibonding molecular orbital, in which electron density is minimised between the nuclei and is zero at the node between the nuclei (it forms a node). (This has higher energy due to presence of node)
LOOK AT EXAMPLES OF MOLECULAR ORBITAL DIAGRAMS IN BOOK
LOOK AT EXAMPLES OF MOLECULAR ORBITAL DIAGRAMS IN BOOK
LOOK AT EXAMPLES OF MOLECULAR ORBITAL DIAGRAMS IN BOOK
CHECK WHAT bonding and antibonding SIGMA AND PI MO BONDS LOOK LIKE
What are paramagnetic molecules?
Paramagnetic molecules have unpaired electrons and a net magnetic moment. Such substances will be drawn into magnetic fields
What are diamagnetic molecules?
Diamagnetic molecules do not have unpaired electrons, and have no magnetic moment. They are weakly repelled by magnetic fields
WHat is HOMO?
Refers to the ‘Highest Occupied Molecular Orbital’–> highest orbital which has an electron
What is LUMO?
Lowest Unoccupied Molecular orbital –> lowest orbital which doesn’t have an electron
What is the lowest energy electronic transition of a molecule?
The lowest energy electronic transition of a molecule is the HOMO-LUMO transition
CHECK BOOKS AND TEXTBOOK AND THE SLIDES
What are core electrons?
These are electrons not affected by the presence of neighbouring atomic nuclei
