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Physical y3 term 1 > Topic 4 - Electronic structure of diatomic molecules > Flashcards

Topic 4 - Electronic structure of diatomic molecules Flashcards

1
Q

What is the shrodinger equation? (basic)

A

Hψ=Eψ

where y is the wavefunction letter

H is the hamiltonian and has a little hat
E is energy

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2
Q

What three parts is the hamiltonian for a two particle electron nucleus system made up of?

A

a term for
1) the electron kinetic energy
2) the nuclear kinetic energy
3) the coulomb potential energy

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3
Q

What are the lapacian operators?

A

the upside doen triangles with subtext e and n which acto on the electronic anf nuclear coordinates respectively.

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4
Q

what is r in the hamiltonian?

A

the distance of the electron from the nucleus

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5
Q

How can we express the hamiltonian for a two particle electron nucleus system in a word equation?

A

H = Ek electron + Ek nucleus + V(r)

note: H, E and V should have a hat

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6
Q

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?

A

Nuclear KE
Elecetron KE
Electron- nuclear PE
nuclear-nuclear PE

Kinetic and potential energy groups

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7
Q

which part of the hamiltonian for a one electron diatomic eg h2+ can we neglect and why?

A

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

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8
Q

How do we apply the born oppenheimer approximation?
what do we fix?

A

R(AB) —-> R

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9
Q

Schrodinger equation for electronic motion:

A

Heψe= Eeψe

H has a hat

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10
Q

solutions of EeYe depend on what?

A

The value of R

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11
Q

The spatial distributions of electrons in molecules are described by what?

A

1e wavefunction Molecular orbitals

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12
Q

1 e wavefunction molecular orbitals are —-??—– to atomic orbitals

A

analogous

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13
Q

Electronic energy comes from what

A

the solutions of the schrodinger equations

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14
Q

what do we use to account for the fact that exact solutions to the schrodinger eqn are not possible for multielectron molecules ?

A

we use approximations in the form of MOs LCAOs or AOs

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15
Q

LCAOS:

what does LCAO stand for?

A

linear combination of atomic orbitals

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16
Q

LCAOS:
An in phase LCAO has what sign?

A

positive (+)

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17
Q

LCAOS:
An out of phase LCAO has what sign?

A

negative (-)

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18
Q

LCAOS:
in phase means what type of interference?

A

constructive

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19
Q

LCAOS:
out of phase means what type of interference?

A

Destructive

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20
Q

Properties of ψ+

how does ψ+ behave at large R?

A

like two independent (in this case 1s) atomic orbitals (AOs)

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21
Q

Properties of ψ+

how does ψ+ behave at small R?

A

there is significant overlap between the atomic orbitals

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22
Q

Properties of ψ+

what does constructive interference between atomic orbitals lead to?

what does it do to the value of ψ?

A

an increase in e density between the nuclei

increases the value of ψ

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23
Q

Properties of ψ+

when R decreases ….
e density ……??
ψ, ψ2 …..?

A

R decreases
e density increases
ψ ψ2 increases

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24
Q

Properties of ψ-:

how does ψ- behave at large R?

A

Like two indepenent (in this case 1s) atomic orbitals (AOs)

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25
Q

Properties of ψ-

how does ψ- behave at small R?

A

there is significant overlap between the two AOs

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26
Q

Properties of ψ-:

what does destructive interference between atomic orbitals lead to?

what does it do to the value of ψ?

A

depleated e density between the two nuclei

decreases ψ and ψ2

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27
Q

Properties of ψ-:

what type of interference is associated with ψ-?

A

destructive

28
Q

Properties of ψ+:

what type of interference is associated with ψ+?

A

constructive

29
Q

Properties of ψ-:

depletion of electron density between nuclei leads to what?

A

decrease in electron-nucleus attraction
electrons react weakly with both nuclei

30
Q

Properties of ψ-:

how does lower e density between nuclei effect how the electrons interact with the nuclei ?

A

lower e density means the electrons react more weakly with both nuclei

31
Q

Properties of ψ+:

how does higher e density between nuclei effect how the electrons interact with the nuclei ?

A

the electrons interact strongly with both nuclei

32
Q

Properties of ψ+:

Accumulation of electron density between nuclei leads to what?

A

increased electron- nucleus attraction

this means the electrons strongly interact with both nuclei

33
Q

Properties of ψ+:

What type of symmetry does ψ+ have?
Description and symmetry label?

A

it is cylindrically symmetrical about the internuclear A-B axis
labelled sigma MO (σ)

34
Q

Properties of ψ-:

What type of symmetry does ψ- have?
Description and symmetry label?

A

it is cylindrically symmetrical about the internuclear A-B axis
labelled sigma star MO (σ*)

35
Q

Molecular orbital diagrams:

what does (ψ-)^1 tell us ?

A

that there is one electron in the antibonding orbital

36
Q

Molecular orbital diagrams:

what is the excited state configuration for H2+?

A

(ψ-)^1

37
Q

Molecular orbital diagrams:

What is the ground state configuration for H2+?

A

(ψ+)^1

38
Q

Molecular orbital diagrams:

what does (ψ+)^1 tell us ?

A

that there is one electron in the bonding orbital

39
Q

Comparing H2 and H2+:

Does H2 or H2+ have a shorter and stronger bond and why?

A

H2 because it has more bonding electrons

bond order = (bonding-antibonding)/2

40
Q

Comparing H2 and H2+:

Does H2 or H2+ have a higher vibrational frequency?

A

H2
shorter bond
higher vibrational frequency

41
Q

How does bond length relate to vibrational frequency?

A

shorter bond length
higher vibrational frequency

42
Q

Molecular orbital diagrams:
He2

what is the ground state configuration for He2?

A

(ψ+)^2(ψ-)^2

43
Q

Molecular orbital diagrams:
He2
Is there covalent bonding present?

A

No, there is no net covalent bonding as the bonding and antibonding contributions cancel eachother out

44
Q

Molecular orbital diagrams:
He2
What type of forces hold these atoms together?

A

only weak disperion forces hold these atoms together.

45
Q

Molecular orbital diagrams:
He2+
Is there covalent bonding present?

A

yes, there is net covalent bonding as the bonding and antibonding contributions do not cancel eachother out.

46
Q

Wave particle duality:

Energy of photons E=

A

hv

47
Q

Wave particle duality:

v (frequency)=

A

c/λ

c is speed of light

48
Q

Wave particle duality:

what is the speed of light ?

A

2.9979x10^8 m/s

49
Q

Wave particle duality:

wavenumber (v with squiggle)

A

v/c = 1/λ

50
Q

Wave particle duality:

true or false, all moving particles display this wave particle duality?

A

true as physics has no arbitrary boundaries

51
Q

Wave particle duality:

momentum p=

A

mv
mass x velocity

52
Q

Wave particle duality:

wavelength,λ, (in relation to momentum) =

A

h/p

53
Q

Wave particle duality:

the wavefunction:
what does the wavefunction describe?

A

the amplitude of the electron wave as a function of time and location.

54
Q

wave particle duality :

a stationary (standing wave) is known as

A

an eigenstate

55
Q

wave particle duality :

wavefunctions for an eigenstate are known as

A

eigenfunctions

56
Q

wave particle duality :

associated energies for an eigenstate are known as

A

eigenvalues

57
Q

wave particle duality :

the schrodinger equation describes the wavefunction for a —— in terms of its ——–?

A

wave particle duality :

the schrodinger equation describes the wavefunction for a quantum state in terms of its absolute energy.

58
Q

LCAO:

states that the wavefunction for a given molecular orbital (ψ) can be derived from what?

A

the sum of the wavefunctions of the atomic orbitals (Φ) (AOs) that contribute to it.

59
Q

LCAO:

how do we mathematically represent the wavefunction for a given molecular orbital ?

A

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

60
Q

LCAO?

What is Ci?

A

ci is a factor that depends on how far the wavefunction in from the nucleus of an atom.

61
Q

MOs:

Molecular orbitals are labelled according to the number of what?

A

nodal planes in the wavefunction

62
Q

MOs:

no nodal planes in the wavefunction - what label?

A

sigma

63
Q

MOs:
a nodal plane in the wavefunction - what label ?

A

pi

64
Q

MOs:
g/u parity

what type of diatomic molecule is this parity labelling useful for?

A

homonuclear diatomics

65
Q
A

Physical y3 term 1 (3 decks)

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