Quantum Chemistry

Question 1

What is black body radiation?
Why does this not fit with classical physics?

Answer 1

a black body is an object which absorbs and emits radiation of all wavelengths uniformly
not accurate with classical physics as suggests energy density is infinite at high wavelengths.
can be solved with quantum physics

Question 2

What’s the difference between classical physics and quantum physics?

Answer 2

in classical physics, all energies are allowed, in quantum physics, energy levels are quantised

Question 3

What is wave particle duality?

Answer 3

concept that particles can show wave and particle properties for quantum scale objects

Question 4

What is the photoelectronic effect?

Answer 4

emission of electrons from a material caused by electromagnetic radiation.
electrons emitted are called photoelectrons

Question 5

is electromagnetic radiation a wave?

Answer 5

photoelectric effect suggests EM radiation behaves like a particle

Question 6

are electrons particles?

Answer 6

diffraction demonstrates that electrons show properties of waves

Question 7

What are 3 observations made from photoelectric effect?

Answer 7

-no electron ejected regardless of intensity unless frequency exceeds threshold value
-kinetic energy of ejected electrons increases linearly with frequency of radiation but is independent of intensity
-even at low intensities electrons ejected if frequency above threshold value

Question 8

What is PHI?

Answer 8

work function of the metal which is defined as minimum amount of energy needed to remove electron from a solid metal

Question 9

What does the photoelectric effect suggest?

Answer 9

shows that electromagnetic radiation which is considered a wave, shows particle-like properties

Question 10

What is the equation for kinetic energy, proved by the photoelectric effect?

Answer 10

Ek=1/2 x me x v^2=hv -PHI

Question 11

What does electron diffraction show?

Answer 11

shows electrons, which are considered particles, show wave-like properties

Question 12

What is the quotient rule?

Answer 12

(uxdv/dx -vxdu/dx) / v^2

Question 13

What is the product rule?

Answer 13

uxdv/dx + vxdu/dx

Question 14

What is the imaginary number i defined as?

Answer 14

i^2=-1

Question 15

How is the complex conjugate of a complex number found?

Answer 15

C*, complex conjugate, found by exchanging i with -i

Question 16

What is a wavefunction?
give 4 properties a wavefunction should have

Answer 16

contains all information about a system
should be single values, continuous, not infinite and have a continuous gradient

Question 17

What is the energy operator?

Answer 17

Hamiltonian, H
is a Hermitian operators so the eigenvalues are real and the eigenfunctions are orthogonal
compromised of kinetic energy and potential energy contributions
H=T+V

Question 18

How do we normalise a wavefunction?

Answer 18

when the integral of eigenfunction x eigenfunction* =1
*=complex conjugate

Question 19

What does it mean if two wavefunctions are orthogonal?

Answer 19

integral of eigenfunction* (i) x eigenfunction(j) =0
i is not equal to j

Question 20

what is the Heisenberg uncertainty principle?

Answer 20

it is not possible to measure position and momentum of a particle with absolute precision simultaneously
change in P x change in q> 1/2hbar

Question 21

what is hbar?

Answer 21

hbar=h/2pi

Question 22

What is the Schrödinger equation?

Answer 22

a time-independent eigenequation
HPsi=EPsi where E is total energy of system and H is Hamiltonian

Question 23

Describe particle in infinite well model problem

Answer 23

consider particle of mass m confined to region between two impenetrable walls
V=0

Question 24

what is the one-dimension, time-independent Schrodinger equation?

Answer 24

-hbar/2 x 2nd deriv of psi(x) +V(x)psi(x)= Epsi(x)

Question 25

How can energy be quantised?

Answer 25

by imposing boundary conditions where particle is found

Question 26

how can a particle at finite barrier be described?

Answer 26

V=0 and the wavefunction= Ae^ikx + Be^-ikx Ae^ikx represents the particle incident on barrier, BE^-ikx represents particle reflected from barrier

Question 27

How can a particle within finite barrier be descried?

Answer 27

V(x)=v and wavefunction=Ce^Kappax where kappa=[2m(V-E)]^1/2 / hbar wf is not 0 wf decays exponentially decay is faster as mass increases

Question 28

What calculations can be carried out for the transmission probability through a given barrier

Answer 28

transmission prob= probability that particle can tunnel through barrier T increases as E(energy) approaches V(height) epsilon=E/V so denominator will be larger so probability of tunnelling increases

Question 29

What happens to the transmission probability as the thickness of barrier increases?

Answer 29

transmission probability decreases exponentially with the thickness of the barrier

Question 30

What are some practical applications of tunneling?

Answer 30

important as leads to faster reaction rates enzymes use tunneling to transfer electrons long distances STM images objects at the atomic level by using air gap as potential barrier, surface mapped by change in tunnelling current

Question 31

What is the tunnel effect?

Answer 31

where particles pass through barrier they classically shouldnt be able to. particles act like waves which allows this

Question 32

Describe harmonic oscillator model, how are allowed energy levels given?

Answer 32

V=1/2kfx^2 kf is force constant which varies how steep parabola is allowed energy levels given by Ev=(v+1/2)hbarw where w=(kf/m)^1/2 reduced mass used for m in diatomics energy levels separated by hbarw

Question 33

What is the Hamiltonian for harmonic oscillator model?

Answer 33

wfv(y)=NvHv(y)e^-y^2/2 where y=x/a Nv is normalisation constant Hv(y) is a Hermite polynomial

Question 34

What are the basic features of ground state wave function of harmonic oscillator?

Answer 34

given by wf0(x)=N0e^x^2/2a^2 for the lowest energy state particle most likely to have 0 displacement

Question 35

What are the basic features of the 1st excited wave function of harmonic oscillator?

Answer 35

wf1(x)= N1(2/a)xe^-x^2/2a^2 has a node, as v increases number of nodes increases and probability density changed, more likely to be at extrema of vibrations

Question 36

What is the Hamiltonian for hydrogenic atom?

Answer 36

only can be solved for systems with 1 e- using atomic units; me=1, e=1, hbar=1, coulombs constant=1 so Schrödinger's eq can be rewritten

Question 37

What are hydrogenic wave functions in terms of their radial and angular contributions?

Answer 37

wf=Rn,l(r) x Yl,ml(theta, phi) Rn,l(r) is radial wavefunction and depends on n and l quantum numbers determines how spread out the wf is Yl,ml(Theta,Phi) is angular wf which determines shape and orientation

Question 38

How do you calculate energy levels for a hydrogenic atom? what happens to E levels as n increaes? what is n?

Answer 38

using E(n)=-Z^2/2n^2Eh ns,np and nd orbitals are degenerate(same E) as n increases the energy levels get closer together

Question 39

What are the fundamentals of Huckel theory?

Answer 39

can be applied to planar conjugated molecules, can be used to solve Schrödinger eq for multiple electron systems

Question 40

What is the variation theorem?

Answer 40

the energy of an arbitrary wave function will never be less than the true energy if wf is approximate wf and H s exact Hamiltonian, then approx energy, E can be found approx energy is not below ground state energy E0

Question 41

What is the best wavefunction given by?

Answer 41

variation theorem says best wf will be one with lowest energy, so coefficients Ca and Cb need to be minimised to find lowest Energy wf=Ca(PhiA)+Cb(PhiB)

Question 42

how do you solve huckel problems for small conjugates hydrocarbons using secular equations?

Answer 42

differentiating the energy equation and finding stationary points with respect to Ca and Cb to form secular equations. by factorising you can find secular determinant which is equal to 0.

Question 43

What are the 4 Huckel approximations?

Answer 43

-all overlap integrals(S) between p-orbitals on diff atoms are set to 0, selfoverlaps=1 -all resonance integrals(Beta) involving non-neighbouring atoms set to 0 -all remaining resonance integrals set to Beta (all equivalent) -all coulomb integrals set to alpha (all equivalent)

Question 44

what is the equation involving alpha, beta and x?

Answer 44

x=(alpha-energy)/beta

Question 45

how do you use the normalisation of the associated wavefunctions?

Answer 45

allows you to find the coefficients the integral of the wf times by wf complex conjugate =1

Question 46

how do you calculate electron populations and bond orders from Huckel solutions?

Answer 46

-electron pop found by using sum of number of electrons in an orbital multiplied by its MO coefficient -bond order found from sum of electron in orbital multiplied by MO coefficient of A for orbital A and coefficient B for orbital a

Question 47

Write down the Huckel theory determinant for Benzene and butadiene

Answer 47

check notes

Question 48

What do you do with the Huckel determinant?

Answer 48

can expand the Huckel determinant and solve it to get solutions. you should get 4 solutions for a 4 carbon molecule

Question 49

What are the limitatios to Huckel Theory?

Answer 49

limited to planar conjugated molecules, only treats pi MOs, severe approximations to simplify equations, integrals are set to parameters

Question 50

How can non-carbon atoms be included in Huckel theory?

Answer 50

theyll have different coulomb and resonance integrals, alphax=alphac + hxBetacc Betacx=KcxBetacc