Topic 4 - Electronic structure of diatomic molecules

Question 1

What is the shrodinger equation? (basic)

Answer 1

Hψ=Eψ

where y is the wavefunction letter

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

Question 2

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

Answer 2

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

Question 3

What are the lapacian operators?

Answer 3

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

Question 4

what is r in the hamiltonian?

Answer 4

the distance of the electron from the nucleus

Question 5

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

Answer 5

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

note: H, E and V should have a hat

Question 6

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?

Answer 6

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

Kinetic and potential energy groups

Question 7

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

Answer 7

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

Question 8

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

Answer 8

R(AB) —-> R

Question 9

Schrodinger equation for electronic motion:

Answer 9

Heψe= Eeψe

H has a hat

Question 10

solutions of EeYe depend on what?

Answer 10

The value of R

Question 11

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

Answer 11

1e wavefunction Molecular orbitals

Question 12

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

Answer 12

analogous

Question 13

Electronic energy comes from what

Answer 13

the solutions of the schrodinger equations

Question 14

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

Answer 14

we use approximations in the form of MOs LCAOs or AOs

Question 15

LCAOS:

what does LCAO stand for?

Answer 15

linear combination of atomic orbitals

Question 16

LCAOS:
An in phase LCAO has what sign?

Answer 16

positive (+)

Question 17

LCAOS:
An out of phase LCAO has what sign?

Answer 17

negative (-)

Question 18

LCAOS:
in phase means what type of interference?

Answer 18

constructive

Question 19

LCAOS:
out of phase means what type of interference?

Answer 19

Destructive

Question 20

Properties of ψ+

how does ψ+ behave at large R?

Answer 20

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

Question 21

Properties of ψ+

how does ψ+ behave at small R?

Answer 21

there is significant overlap between the atomic orbitals

Question 22

Properties of ψ+

what does constructive interference between atomic orbitals lead to?

what does it do to the value of ψ?

Answer 22

an increase in e density between the nuclei

increases the value of ψ

Question 23

Properties of ψ+

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

Answer 23

R decreases
e density increases
ψ ψ2 increases

Question 24

Properties of ψ-:

how does ψ- behave at large R?

Answer 24

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

Question 25

Properties of ψ- how does ψ- behave at small R?

Answer 25

there is significant overlap between the two AOs

Question 26

Properties of ψ-: what does destructive interference between atomic orbitals lead to? what does it do to the value of ψ?

Answer 26

depleated e density between the two nuclei decreases ψ and ψ2

Question 27

Properties of ψ-: what type of interference is associated with ψ-?

Answer 27

destructive

Question 28

Properties of ψ+: what type of interference is associated with ψ+?

Answer 28

constructive

Question 29

Properties of ψ-: depletion of electron density between nuclei leads to what?

Answer 29

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

Question 30

Properties of ψ-: how does lower e density between nuclei effect how the electrons interact with the nuclei ?

Answer 30

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

Question 31

Properties of ψ+: how does higher e density between nuclei effect how the electrons interact with the nuclei ?

Answer 31

the electrons interact strongly with both nuclei

Question 32

Properties of ψ+: Accumulation of electron density between nuclei leads to what?

Answer 32

increased electron- nucleus attraction this means the electrons strongly interact with both nuclei

Question 33

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

Answer 33

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

Question 34

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

Answer 34

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

Question 35

Molecular orbital diagrams: what does (ψ-)^1 tell us ?

Answer 35

that there is one electron in the antibonding orbital

Question 36

Molecular orbital diagrams: what is the excited state configuration for H2+?

Answer 36

(ψ-)^1

Question 37

Molecular orbital diagrams: What is the ground state configuration for H2+?

Answer 37

(ψ+)^1

Question 38

Molecular orbital diagrams: what does (ψ+)^1 tell us ?

Answer 38

that there is one electron in the bonding orbital

Question 39

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

Answer 39

H2 because it has more bonding electrons bond order = (bonding-antibonding)/2

Question 40

Comparing H2 and H2+: Does H2 or H2+ have a higher vibrational frequency?

Answer 40

H2 shorter bond higher vibrational frequency

Question 41

How does bond length relate to vibrational frequency?

Answer 41

shorter bond length higher vibrational frequency

Question 42

Molecular orbital diagrams: He2 what is the ground state configuration for He2?

Answer 42

(ψ+)^2(ψ-)^2

Question 43

Molecular orbital diagrams: He2 Is there covalent bonding present?

Answer 43

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

Question 44

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

Answer 44

only weak disperion forces hold these atoms together.

Question 45

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

Answer 45

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

Question 46

Wave particle duality: Energy of photons E=

Answer 46

hv

Question 47

Wave particle duality: v (frequency)=

Answer 47

c/λ c is speed of light

Question 48

Wave particle duality: what is the speed of light ?

Answer 48

2.9979x10^8 m/s

Question 49

Wave particle duality: wavenumber (v with squiggle)

Answer 49

v/c = 1/λ

Question 50

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

Answer 50

true as physics has no arbitrary boundaries

Question 51

Wave particle duality: momentum p=

Answer 51

mv mass x velocity

Question 52

Wave particle duality: wavelength,λ, (in relation to momentum) =

Answer 52

h/p

Question 53

Wave particle duality: the wavefunction: what does the wavefunction describe?

Answer 53

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

Question 54

wave particle duality : a stationary (standing wave) is known as

Answer 54

an eigenstate

Question 55

wave particle duality : wavefunctions for an eigenstate are known as

Answer 55

eigenfunctions

Question 56

wave particle duality : associated energies for an eigenstate are known as

Answer 56

eigenvalues

Question 57

wave particle duality : the schrodinger equation describes the wavefunction for a ------ in terms of its --------?

Answer 57

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

Question 58

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

Answer 58

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

Question 59

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

Answer 59

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

Question 60

LCAO? What is Ci?

Answer 60

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

Question 61

MOs: Molecular orbitals are labelled according to the number of what?

Answer 61

nodal planes in the wavefunction

Question 62

MOs: no nodal planes in the wavefunction - what label?

Answer 62

sigma

Question 63

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

Answer 63

pi

Question 64

MOs: g/u parity what type of diatomic molecule is this parity labelling useful for?

Answer 64

homonuclear diatomics