Topic 4 - Electronic structure of diatomic molecules Flashcards
What is the shrodinger equation? (basic)
Hψ=Eψ
where y is the wavefunction letter
H is the hamiltonian and has a little hat
E is energy
What three parts is the hamiltonian for a two particle electron nucleus system made up of?
a term for
1) the electron kinetic energy
2) the nuclear kinetic energy
3) the coulomb potential energy
What are the lapacian operators?
the upside doen triangles with subtext e and n which acto on the electronic anf nuclear coordinates respectively.
what is r in the hamiltonian?
the distance of the electron from the nucleus
How can we express the hamiltonian for a two particle electron nucleus system in a word equation?
H = Ek electron + Ek nucleus + V(r)
note: H, E and V should have a hat
What four parts is the hamiltonian for a one electron diatomic eg h2+ made up of?
what two groups can we make from these parts?
Nuclear KE
Elecetron KE
Electron- nuclear PE
nuclear-nuclear PE
Kinetic and potential energy groups
which part of the hamiltonian for a one electron diatomic eg h2+ can we neglect and why?
nuclear KE due to the Born oppenheimer approximation.
this is because the mass of the proton is so much greater than the mass of the electron
How do we apply the born oppenheimer approximation?
what do we fix?
R(AB) —-> R
Schrodinger equation for electronic motion:
Heψe= Eeψe
H has a hat
solutions of EeYe depend on what?
The value of R
The spatial distributions of electrons in molecules are described by what?
1e wavefunction Molecular orbitals
1 e wavefunction molecular orbitals are —-??—– to atomic orbitals
analogous
Electronic energy comes from what
the solutions of the schrodinger equations
what do we use to account for the fact that exact solutions to the schrodinger eqn are not possible for multielectron molecules ?
we use approximations in the form of MOs LCAOs or AOs
LCAOS:
what does LCAO stand for?
linear combination of atomic orbitals
LCAOS:
An in phase LCAO has what sign?
positive (+)
LCAOS:
An out of phase LCAO has what sign?
negative (-)
LCAOS:
in phase means what type of interference?
constructive
LCAOS:
out of phase means what type of interference?
Destructive
Properties of ψ+
how does ψ+ behave at large R?
like two independent (in this case 1s) atomic orbitals (AOs)
Properties of ψ+
how does ψ+ behave at small R?
there is significant overlap between the atomic orbitals
Properties of ψ+
what does constructive interference between atomic orbitals lead to?
what does it do to the value of ψ?
an increase in e density between the nuclei
increases the value of ψ
Properties of ψ+
when R decreases ….
e density ……??
ψ, ψ2 …..?
R decreases
e density increases
ψ ψ2 increases
Properties of ψ-:
how does ψ- behave at large R?
Like two indepenent (in this case 1s) atomic orbitals (AOs)
Properties of ψ-
how does ψ- behave at small R?
there is significant overlap between the two AOs
Properties of ψ-:
what does destructive interference between atomic orbitals lead to?
what does it do to the value of ψ?
depleated e density between the two nuclei
decreases ψ and ψ2
Properties of ψ-:
what type of interference is associated with ψ-?
destructive
Properties of ψ+:
what type of interference is associated with ψ+?
constructive
Properties of ψ-:
depletion of electron density between nuclei leads to what?
decrease in electron-nucleus attraction
electrons react weakly with both nuclei
Properties of ψ-:
how does lower e density between nuclei effect how the electrons interact with the nuclei ?
lower e density means the electrons react more weakly with both nuclei
Properties of ψ+:
how does higher e density between nuclei effect how the electrons interact with the nuclei ?
the electrons interact strongly with both nuclei
Properties of ψ+:
Accumulation of electron density between nuclei leads to what?
increased electron- nucleus attraction
this means the electrons strongly interact with both nuclei
Properties of ψ+:
What type of symmetry does ψ+ have?
Description and symmetry label?
it is cylindrically symmetrical about the internuclear A-B axis
labelled sigma MO (σ)
Properties of ψ-:
What type of symmetry does ψ- have?
Description and symmetry label?
it is cylindrically symmetrical about the internuclear A-B axis
labelled sigma star MO (σ*)
Molecular orbital diagrams:
what does (ψ-)^1 tell us ?
that there is one electron in the antibonding orbital
Molecular orbital diagrams:
what is the excited state configuration for H2+?
(ψ-)^1
Molecular orbital diagrams:
What is the ground state configuration for H2+?
(ψ+)^1
Molecular orbital diagrams:
what does (ψ+)^1 tell us ?
that there is one electron in the bonding orbital
Comparing H2 and H2+:
Does H2 or H2+ have a shorter and stronger bond and why?
H2 because it has more bonding electrons
bond order = (bonding-antibonding)/2
Comparing H2 and H2+:
Does H2 or H2+ have a higher vibrational frequency?
H2
shorter bond
higher vibrational frequency
How does bond length relate to vibrational frequency?
shorter bond length
higher vibrational frequency
Molecular orbital diagrams:
He2
what is the ground state configuration for He2?
(ψ+)^2(ψ-)^2
Molecular orbital diagrams:
He2
Is there covalent bonding present?
No, there is no net covalent bonding as the bonding and antibonding contributions cancel eachother out
Molecular orbital diagrams:
He2
What type of forces hold these atoms together?
only weak disperion forces hold these atoms together.
Molecular orbital diagrams:
He2+
Is there covalent bonding present?
yes, there is net covalent bonding as the bonding and antibonding contributions do not cancel eachother out.
Wave particle duality:
Energy of photons E=
hv
Wave particle duality:
v (frequency)=
c/λ
c is speed of light
Wave particle duality:
what is the speed of light ?
2.9979x10^8 m/s
Wave particle duality:
wavenumber (v with squiggle)
v/c = 1/λ
Wave particle duality:
true or false, all moving particles display this wave particle duality?
true as physics has no arbitrary boundaries
Wave particle duality:
momentum p=
mv
mass x velocity
Wave particle duality:
wavelength,λ, (in relation to momentum) =
h/p
Wave particle duality:
the wavefunction:
what does the wavefunction describe?
the amplitude of the electron wave as a function of time and location.
wave particle duality :
a stationary (standing wave) is known as
an eigenstate
wave particle duality :
wavefunctions for an eigenstate are known as
eigenfunctions
wave particle duality :
associated energies for an eigenstate are known as
eigenvalues
wave particle duality :
the schrodinger equation describes the wavefunction for a —— in terms of its ——–?
wave particle duality :
the schrodinger equation describes the wavefunction for a quantum state in terms of its absolute energy.
LCAO:
states that the wavefunction for a given molecular orbital (ψ) can be derived from what?
the sum of the wavefunctions of the atomic orbitals (Φ) (AOs) that contribute to it.
LCAO:
how do we mathematically represent the wavefunction for a given molecular orbital ?
ψ = Σ ciΦi
ci is a factor that depends on how far the wavefunction in from the nucleus of an atom.
Φi is the wavefunction of each atomic orbital
LCAO?
What is Ci?
ci is a factor that depends on how far the wavefunction in from the nucleus of an atom.
MOs:
Molecular orbitals are labelled according to the number of what?
nodal planes in the wavefunction
MOs:
no nodal planes in the wavefunction - what label?
sigma
MOs:
a nodal plane in the wavefunction - what label ?
pi
MOs:
g/u parity
what type of diatomic molecule is this parity labelling useful for?
homonuclear diatomics
