Quantum Chem All

What is quantum mechanics?

Quantum mechanics is the framework for explaining the behavior of matter and energy at the atomic and subatomic levels, where classical mechanics fails.

Why is quantum mechanics important?

Understanding the structure of atoms, properties of solids, interactions with light, nuclear fission and fusion, semiconductors, LEDs, microscopy, and computing.

What did classical physics explain?

Newton’s laws explained motion and matter. Maxwell’s equations explained radiant energy (electromagnetism).

What is the UV Catastrophe?

The UV catastrophe refers to the contradiction between classical physics predictions (continuous emission of energy at shorter wavelengths) and experimental observations of black body radiation.

What was Planck's Quantum Theory about?

Planck proposed that electromagnetic waves are quantized, meaning energy is emitted and absorbed in discrete packets (quanta) rather than continuously.

According to Planck's Quantum Theory, how does matter absorb light?

Matter can only absorb light of frequency in discrete quanta, which we now call photons. E=hv

What is the Photoelectric Effect?

When light of variable frequency is shone on a metal surface, electrons are only emitted at particular frequencies. This is the photoelectric effect.

According to classical theory, what should control light energy in the photoelectric effect?

Classical theory suggested that light intensity should control light energy, meaning electron emission should occur irrespective of frequency.

What was observed in the Photoelectric Effect experiment?

Electron emission depended on the frequency rather than intensity. A certain threshold frequency was required for emission.

How does light behave in the Photoelectric Effect?

Light behaves as a particle (photons), transferring energy to electrons. The work function is the minimum energy required to release an electron.

How is kinetic energy and threshold frequency related in the Photoelectric Effect?

The electron released has a kinetic energy = 1/2mv^2. The threshold frequency (v0), must be exceeded to give photons enough energy to enable electrons to escape from the surface: hv0 = (M), so 0 = (M)/h

How is the Photoelectric Effect experiment performed?

Variable frequency light source, shine light onto a metal surface. Determine the light frequency which causes electrons to be emitted. Measure the energy of the emitted electrons.

What happens during Photoelectron Spectroscopy?

EM radiation (typically X-Ray) is directed onto a molecule/material, and the energy of the electrons emitted is measured: ½ mev2 = h - I (where I is the ionisation energy, instead of the work function).

What is XPS used for?

It can determine composition, and chemical properties of surfaces. Can be used for molecules!

What happens during Compton Scattering?

If light can be described as photons, if they collide with other particles, there should be a change in their momentum (= mass x velocity).

What were Compton's results?

The incident wavelength peak was always present, but also observed a peak at different wavelengths. The shift in 𝝀 varies with the angle

How can the photon model explain Compton Scattering?

The photon model explains the change in energy/momentum of photons scattered by individual electrons. ∆ = (2h/mec) sin2 (½)

What do electrons act like, in addition to particles?

Electrons can also act like waves.

What do diffraction and interference patterns indicate about electrons?

Diffraction and interference patterns indicate wave-like behavior.

What does it mean to say that ligh and electrons exhibit wave-particle duality?

Light behaves as a particle at the atomic scale. The electron can also behave like a wave. This leads to the concept of wave-particle duality

What is wave particle duality?

That subatomic molecules behave in both ways as waves, but also as particles at the same time.

What scale is classical mechanics good at describing?

Macroscale. So understanding how big objects move.

What is quantum chemistry important for?

Understanding what an atom looks like. Understanding how bonding works and understanding how molecules interact with each other.

Who derived a mathematical explanation for some phenomena that were previously unknown, marking the beginning of quantum theory?

Max Planck in the 1900s.

What work did Einstein win the Nobel prize for?

Einstein's explanation of the photoelectric effect.

Who derived mathematical descriptions of quantum applied to an electron in atoms?

Heisenberg and Schrodinger.

What do the Schrodinger and Heisenberg equations do?

They encompass everything that can possibly happen to an atom or to a subatomic molecule.

What did Maxwell accurately describe?

Electromagnetic radiation works.

How does quantum theory explain the blackbody radiation spectrum?

It treats the system as quantised states rather than a continuum, explaining the UV catastrophe.

What is threshold frequency in the context of the photoelectric effect?

The minimum energy required to remove an electron from a metal surface.

How does the photoelectric effect experiment work with a detector or photocell?

Bombarding a metal with light and measuring the emitted electrons to understand surface properties, with a voltmeter indicating electron velocity and energy.

What did Compton observe in his scattering experiment?

The change in wavelength of scattered X-rays varies with the scattering angle, indicating a change in momentum.

What did Davisson and Girmer's experiment demonstrate?

Electrons, when diffracted through nickel foil, create concentric rings, indicating they behave as waves.

How do electrons behave at the atomic level?

Electrons behave as waves at an atomic level; their wavelength is comparable to the distances between atoms in a crystal.

What information can be obtained from the distances between rings in electron diffraction?

The distances between the rings in the diffraction pattern can provide structural information, and they can reveal surface information because they do not penetrate far into the crystal.

What is Low Energy Electron Diffraction (LEED) used for?

Low Energy Electron Diffraction (LEED) is used to detect surface features like adsorbed molecules when the energies are low enough (20-200 eV).

According to wave-particle duality, how do electrons behave?

Electrons behave as both waves and particles.

What is the de Broglie equation?

λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.

What does Heisenberg's Uncertainty Principle state?

The more precisely you know the position of a quantum particle, the less precisely you can know its momentum, and vice versa.

What is Zero Point Energy?

There is never a state with zero energy at the atomic level due to the uncertainty principle.

Why does the Bohr electron model not work with quantum theory?

Because it would be possible to know the trajectory (position and momentum), which is not allowed by the uncertainty principle.

What do orbitals describe?

Orbitals describe the location of electrons.

What is a wavefunction (Ψ)?

The mathematical function that, when plotted, gives the shape of the orbital (e.g., 1s orbital).

What is the Schrödinger equation?

HΨ = EΨ, where H is an operator, Ψ is the wavefunction, and E is the energy.

Give the general form of the equation used to represent orbitals

Ψ = exp (-ζr) Y (θ, φ), where r, θ, φ are coordinates.

Schrodinger Equation

An equation used to define the energy of a system using a wave function, containing all the information about that system.

Hamiltonian Operator

An operator that acts on a wave function to alter it, containing all the information that can be applied to the wave function to get the result (energy operating on the wave function).

Splitting the Hamiltonian

Dividing the Hamiltonian into kinetic and potential energy terms, applying classical concepts to quantum mechanics.

Heisenberg's Uncertainty Principle

We cannot know both position and momentum at the same time, but we can apply a wave function to understand how momentum is changing as the wave function moves.

Particle in a Box

A conceptual and mathematical way of showing how the Schrodinger equation works, involving a particle trapped in a confined area.

Harmonic Oscillator

A model showing how energy is quantized, applying to diatomic molecules and atoms in molecules with restoring force.

Boundary Conditions

At the edges of the box, the wave function equals zero, leading to the understanding of how wavelengths change as energy increases.

Permitted Wavelengths

The permitted wavelengths for a particle in a box, defined by the equation lambda = 2L/n.

Permitted Energies

The energy of a wave function within a particle in a box, defined by the equation E = n^2h^2 / 8mL^2.

Quantum Dots

Semiconducting nanoparticles that behave like particles in a box due to their small size, allowing for tuning of absorption properties.

Conjugated Molecules

Molecules with delocalized electrons across the molecule, creating a 'box' the length of the chain, allowing for calculation of energy levels

Potential Energy (Harmonic Oscillator)

The potential energy term in the harmonic oscillator, defined as potential energy equals 1/2 kx^2.

Zero Point Energy

The non-zero energy that a quantum system always has, even at absolute zero.

Hydrogen Atom

Simplified system with one proton and one electron, to which the Schrodinger equation is applied to calculate its properties.

Born-Oppenheimer Approximation

Approximation stating that the mass of the proton is so big that we can ignore the kinetic energy, focusing on the kinetic energy of the electron.

Applying Schrodinger Equation to Molecules

Considering the interactions between each electron and the nuclei, including attraction and repulsion forces.

Fixed Nuclei

Nuclei are frozen in space, simplifying the interactions considered in molecular calculations.

Quantization of Energy

Energy is always quantized, whether treated as a particle in a box or a harmonic oscillator.

What is wave-particle duality?

The concept that subatomic particles and light can exhibit properties of both waves and particles.

What is the electron diffraction experiment?

An experiment demonstrating the wavelike behavior of electrons by firing them at a nickel foil and observing interference patterns.

What information can be obtained from electron diffraction patterns?

Structure information about the distance between atoms on the surface of the material.

What is Low Energy Electron Diffraction (LEED)?

A technique using low energy electrons (20-200 eV) to probe the surface of a material.

What is reciprocal space in the context of LEED?

A representation showing what's between the atoms in a material, useful for analyzing surface structures.

What is the significance of momentum in relation to wavelength?

Momentum is linked to wavelength, meaning any moving matter has an associated wavelength.

What is the de Broglie wavelength equation used for?

Calculating the wavelength of any moving object based on its momentum.

Why is it important to pay attention to units when using the de Broglie equation?

Because the constants used in the equation are in specific units (e.g., meters per second), and conversions may be necessary.

What is Heisenberg's uncertainty principle?

The principle stating that it is impossible to know both the position and momentum of a quantum particle with perfect accuracy.

What is zero-point energy?

The non-zero energy that a quantum system has even at absolute zero due to the uncertainty principle.

Why does helium stay liquid at very low temperatures?

Because of its zero-point energy, it has energy even at its lowest energy state.

What are orbitals?

A way of understanding where the electron position is and how the electron moves around a nucleus using probability of an electron being located in a certain place.

What is used to describe the movement of a wave?

A wave function.

What is the Schrodinger equation used for?

To determine the energy of a particle or quantum species.

What is a Hamiltonian?

An operator that, when applied to a wave function, gives the energy times the wave function.

What is the Schrödinger equation?

HΨ = EΨ, where H is an operator, Ψ is the wavefunction, and E is the energy.

Give the general form of the equation used to represent orbitals

Ψ = exp (-ζr) Y (θ, φ), where r, θ, φ are coordinates.

What equation relates angular wavenumber, k, to wavelength?

k = 2π / 𝜆

What is the general form of a wavefunction?

(x) = Asin(kx) + Bcos(kx)

What is the value of B in the general wavefunction form given the boundary conditions?

B = 0

What is the condition for kL based on the boundary condition (L) = 0?

kL = nπ

How are quantum dots related to the particle in a box model?

Electrons in bands behave like particles in a box, and emission is tuned by size.

In conjugated molecules, what are the delocalized 𝜋 electrons free to do?

Move over the length of the molecule chain.

What kind of force does a diatomic molecule experience when one atom is displaced from its position in the harmonic oscillator model?

A restoring force, opposite to the displacement (F = -kx).

What is the potential energy V(x) for a harmonic oscillator?

V(x) = (1/2)kx^2

What is the formula for allowed energies En for a harmonic oscillator?

En = (n + 1/2)ℏω, where n = 0, 1, 2, 3, 4…

What is the zero point energy?

The energy when n=0 E0 = 1/2 ℏω

Where are energy levels seen?

Vibrational spectroscopy and photochemistry

What terms are included in the Hamiltonian for the Hydrogen atom?

Kinetic energy of the electron and potential energy of attraction between the proton and the electron

What is the Born-Oppenheimer approximation?

The mass of the proton is so large that its kinetic energy can be ignored.

What is the formula of the potential energy term in the Hydrogen atom Hamiltonian?

Vne = −𝑒2 / (4𝜋𝜀0r)

What are the two terms included in the molecule Hamiltonian for H2+?

kinetic energy of the electron and the potential energy for the attraction for each proton

Why is the potential energy negative?

Due to the attraction between the electron and proton.

What is the formula of the potential energy term in the Hydrogen atom Hamiltonian?

H2 molecule includes an electron repulsion term.