Quantum Chemistry 3

Flashcards based on Quantum Chemistry Lecture Notes

What does the Schrodinger equation relate?

The wave function to the energy of any system.

What information does the wave function contain?

All the available information about what it is describing, e.g. a 1s electron in hydrogen.

What two energy terms does the Schrodinger equation divide energy into?

Kinetic and potential energy.

What is the Hamiltonian operator?

The sum of kinetic and potential energy operators that acts on the wavefunction.

How is kinetic energy altered in the context of the Schrodinger equation?

It must account for quantum effects on momentum.

What is the condition for a particle trapped in a box at the edges of the box?

The wavefunction must equal zero (the particle cannot escape).

What do the solutions for a particle in a box represent?

Standing waves, where more energy equals more nodes.

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 main difference between the Hamiltonian of the H2+ and H2 molecules?

H2 molecule includes an electron repulsion term.

(r,,) = R(r) Y(, ) represent?

Expression for the wavefunction

State the expression for En in terms of the Rydberg constant.

En = −RH/n2