2c - w (IR // vibrational spec)

Question 1

gross selection rule for vibrational spec

Answer 1

u need a fluctuating electric dipole during a vibration

Question 2

specific selection rule for vibrational spec

Answer 2

change v = +-1.

Question 3

what do we assume in vib // ir spec

Answer 3

that the molecule is vibrating and rotating simultaneously.

Question 4

v = what and its allowed values

Answer 4

vibrational quatum number
0,1,2,3,4 etc

Question 5

is vibrational energy or rotational energy larger

Answer 5

vibrational energy is larger than rotational energy.

rot, vib, electronic!!

each one has sublevels of the other.

Question 6

when we think of vibrational spec / IR spec,, what should we think about

Answer 6

harmonic oscillator!! an anharmonic oscillator.

Question 7

describe a harmonic oscillator

Answer 7

u shape.

energy on y axis (cm-1)

internuc distance // r on x axiS

Question 8

what is r eq in a simple harmonic oscillator

Answer 8

the equilibrium bond length// distance

aka the bond length

Question 9

what is a bond

Answer 9

a combo of attractive ( nuc and e-) and repulsive forces (e- and e-)

Question 10

when a bond is stretched // compressed what is disrupted

Answer 10

the attractive // repulsive forces

energy is needed to disrupt themmm

Question 11

compression and extention of bonds equation hooks law

Answer 11

f = - k (r - req)

restoring force = - force constant( bond distance - equilibrium force distance)

r - req = extent of distortion

Question 12

equation for energy of system related to distortion

Answer 12

E = 1/2 k ( r - req)^2

aka the larger the distortion,, the larger the enrgy of the system.

req = equilibrium bond length.

r=. bond length when its distorted.

Question 13

vibrational freq,, w is dependent on what

Answer 13

the force constant and reduced mass

Question 14

to go from Hz to cm-1 what do we do

Answer 14

divide by C ,, speed of light.

w (Hz) = 1/2pi root( k/ red mass) Hz

w (cm-1) = 1/2 pi c root( k / redmass) cm-1

aka a higher energy syste can still oscillate at the same freq,, w, , bc w depends on k and redmass. its independent to distortion.

Question 15

vibrational energy levels are whattt + the equation

Answer 15

theyre quantised according to the schrodinger equation

Ev = Ev/hc = (v+1/2) w(cm-1)

in cm-1

Question 16

energy of vibrational level 0 =

Answer 16

E0 = w(0+1/2) = 1/2w-(cm-1)

this tells us that even at the lowest vib energy level,, the molecule still vibrates!!!!

zero point energy: still has vib energy in the lowest vib state.

its always trying to balance the attractive and repulsive forces in a bond.

Question 17

energy of vib energy level 1

Answer 17

E1 = w(1+1/2) = 1.5w

Question 18

in rot spec: J = 0 has how much enrgy

Answer 18

J = 0 = 0 energy
its zero point energy = J=1

Question 19

simple harmonic specific selection rule

Answer 19

change v = +-1

Ev –> Ev+1
= w{(v+1) 1/2} - w{(v+1/2)}
= higher enrgy level bc v+1 - lower energy level bc just v

Question 20

vibrational energy levels are spaced out equally with what value

Answer 20

with w,, transition energy is the same for all harmonic oscillations.

position of allowed transition v- spec (cm-1) = w-(cm-1)

Question 21

what is needed for smt to be ir active aka have a vibrational spec

Answer 21

needs a dipole
so it must be a heteronuclear diatomic as these have dipoles

Question 22

in a simple harmonic oscillator,, describe the graph and how it changes + why this isnt a real representation of a bond

Answer 22

okay so simple harmonic is just the U graph however on the x axis we have r,, the centre of the U parabola is the req,, aka equilibrium bond length,, the sides of the parabola are said to distort further away from this as frequency// energy increases.

this isnt a real representation as bonds will break if the bond length is distorted too much

Question 23

whats a better way of describing a bond using a graph

Answer 23

anharmonic oscillator /// morse curve.

fancy v type shape
vibrational energy reaches a plateau at large ‘r’ value.

Question 24

whats Deq

Answer 24

Dissociation energy in a morse curve // anharmonic oscillator.

from plateau to very bottom of the graph (even tho no molecule are present here bc bc molecules are always cibrating and trying to balance repulsive and attractive forces).

Question 25

Deq equation

Answer 25

[1- exp(-a(r-req))] ^2

Question 26

in an anharmonic curve// as u increase frequency what happens + what equation do we use

Answer 26

the vibrational energy levels get closer together

due to the correction factor having ^2,,, this makes the gaps smaller as the correction factor has a larger influence on the vibrational energy level as u increase energy

Ev = (v+1/2)we - (v+1/2)^2 we xe

we = anharmonic equilibrium oscillating frequency

xe= anharmonicity constant no units

wexe = anharmonicity wavenumber

Question 27

whats Do

Answer 27

like Deq but better bc its the energy gap between the plateue of the morse curve and v=0 )where atoms accccc are)

from lowest vib state to plateau.

Question 28

is Deq accurate

Answer 28

nope it hypothetical bc zero point energy is v=0 not the bottom of the graph.

moelcules always have vibrational energy.

Question 29

what does oscillating frequency,, w.osc. depend on

Answer 29

depends on the vibrational level

larger vibrational level = larger oscillating frequency bc ur increasing energy

Question 30

selectrion rules for anharmonic oscillator

Answer 30

change in vibrational energy level = +- 1,2,3, etcccc

these are called overtones

Question 31

what is w.osc

Answer 31

the oscillating frequency

the frequency of the transition we see in spec

Question 32

what does w.osc equal to

Answer 32

w.osc= w.e {1-xe (v+1/2)}
in cm-1

Question 33

what is xe

Answer 33

the anharmonic constant aka correction factor low-key

Question 34

what is w.e

Answer 34

equilibrium oscillating frequency in anharmonic

Question 35

what’s E.v and what does it equal to

Answer 35

vibrational energy
= w.e(1-xe (v+1/2))(v+1/2)

Question 36

when does Ev=0 and w.osc = w.e

Answer 36

if the system is at the very bottom of the morse curve (anharmonic graph) not v=0 but at the bottom bottom of the curve

but this is a hypothetical scenario bc v cannot equal -1/2.

so we need to remember that w.osc is different to w.e

Question 37

what is we

Answer 37

anharmonic oscillating frequency

Question 38

simple harmonic selection rule (vibrational spec)

Answer 38

change is v = +- 1

Question 39

anharmonic curve selection rule

Answer 39

change in v = +-1, +-2, +-3

these are overtonesssss (there’s also hot bands allowed too)

Question 40

what is the first allowed transition called and which vib levels does if correspond to

Answer 40

first allowed transition = fundamental transition =
V0 —> V1

Ev1-Ev0 = change in energy = w.e(1-2xe)

Question 41

what is the wavenumber we observe for the fundamental transition :

Answer 41

w.e(1-2xe)

Question 42

what’s the vibrational energy of 1 vibrational level

Answer 42

[(v+1/2)we - (v+1/2)^2 we xe]

Question 43

what’s the first overtone and which vib levels does it occur between

Answer 43

V0–> V2

change E = EV2-EV0 (this is the vibrational wavenumber we would observe for that transition and answer is cm-1)

= 2we (1-3xe)

Question 44

2nd overtone

Answer 44

v0–>v3

E= Ev3-Ev0

= 3we (1-4xe)

Question 45

okay so for change in energy for a transition we use the longgg equation: 🔺E = [we(v+1/2) - we(v+1/2)^2 xe] so we put transition vib levels in the v,, but we do the first level for both. then do the other vibrational level,, then remove the smaller from the bigger. and this gives u the energy change between then. and what do we know about xe

Answer 45

xe is rlly small
so the 1st and 2nd overtone energy is very similar to the 2we , 3we respectively.
which we can work out using the long equation above

Question 46

okay so which transition will be more intense + which one will be weaker

Answer 46

the most intense transition is the one that is more likely to occur + we can see this by seeing which vibrational state the system will be in. (we use boltzman distribution to predict which vibrational state the molecule will be in)!!

Question 47

what is the boltzmann distribution

Answer 47

N v=1 // N v=0 = exp ( -hc 🔺E /// kT)

🔺E will be in J so we use hc to turn it into wavenumbers

Question 48

what if we get a super small value for the boltzman distribution,, what does that mean

Answer 48

it means that the nominator vibrational level has a very small population.

Question 49

how can we populate the higher energy level and get a larger boltzman distribution value N.higher//N.lower = exp(-hc🔺E// kT)

Answer 49

increase the temppppppp

increase in temp = smaller value for the boltzman distribution which means there’s similar populations in both vibrational levels. as the fraction value is closer to 1.

Question 50

the larger the boltzman distribution // the what???

Answer 50

the larger the valueeee,,,, the higher populated the higher vibrational levels,, the higher the temp,, the more transitions that can occur from higher energy levels,, the more vibrational spec transitions there are.

Question 51

IR stretch of CO is what

Answer 51

1700 cm-1

Question 52

what’s a hot band transition

Answer 52

it’s in the nameeeee.
hot transition. from V=1 to higher energy levels

u heat it up so u populate higher energy levels. and transitions can now occur from the higher energy levels.

🔺E = Ev=2 — Ev=1. = w.e(1- 4xe)

Question 53

what vib level do hot band transitions occur from

Answer 53

V=1
to higher energy levels.

and this is due to heating up the system + populating higher energy levels.

= we (1 - 4xe)

🔺E = Ev2 - Ev1

Question 54

selection rule for hot ban transition

Answer 54

🔺v = +-1

Question 55

what energy?? is the hot band transition at

Answer 55

we

but there’s a larger correction factor = 4xe

so like there’s a larger difference from we than a normal transition.

Question 56

RoVib spectrum description + what are they

Answer 56

2 humps,, both humps are the fundamental transition of a diatomic

Question 57

why are there so many lines in the ro vib spectrum

Answer 57

there’s 2 humps that correspond to the fundamental transition (V=0 —> V=1)

there’s a bunch of lines bc ur looking at IR (vib spec) but each vib level has corresponding rotational levels (lower energy) so molecules rotate and vibrate at the same time. rotational and vibrational transitions both give rise to resonances in spec.

Question 58

describe the energy diagram that describes the rotational and vibrational transitions

Answer 58

think of a U parabola with 2 groups of lines,, 1 group of lines being v=0 and one being v=1. each line has a value (0,1,2,3 etc) and there’s J’’(for v0) and J’ (for v1)

the y axis is energy and the x axis is r (inter nuclear distance)

E = Erot + Evib
increase in J = increase in gap for rotational levels. ( Ej,v = (BJ(J+1) - DJ^2(J+1)^2) + ((V+1/2)we - (v+1/2)^2 wexe)
first is rot energy + anharmonic vib energy

it looks like a simple harmonic oscillator bc we’re only taking the v0 and v1 which is before the plateau.

the distortion factor is rlly small bc we’re in a low vib level.

Question 59

selection rule for rot spec =

Answer 59

J = +-1

Question 60

vibrational spec selection rule ( anharmonic)

Answer 60

V = +-1, 2 , 3 etccccc

Question 61

okay so describe ro vib spec girlllll

Answer 61

2 humps
lhs = p branch (🔺j = -1) (toilet with lef)
rhs = r branch (🔺j = +1) (self explain)

going from v0 and J’’ to v1 and j’.

Question 62

ro vib selection rules

Answer 62

🔺v = +-1, 2 3 4 etc (anharmonic curve)

🔺J (p branch = -1)
🔺J (r branch = +1)

so basically 🔺J = +-1

Question 63

higher energy is r or p branch

Answer 63

r branchhhhh!!!

so 🔺J = +1

the higher energy branch bc y axis is diff vib (big) and rot levels

and x axis is wavenumberrrrr from small to big going to the right. rigght = larger wavenumber = r branch

Question 64

okay so the p branch cant have what transition,, and what does this mean

Answer 64

the p branch selection rule for rot spec = 🔺J = -1

so the transition cannot start at v0 j0 bc u cant go down to j-1!!

so the j value needs to start at j=1

so J’’ —–> J’

so we can tell what branch is p and which is r by looking at where the arrows start.

Question 65

in rro vib spec the vib levels,, rott,, and vib levels must change by how much

Answer 65

vib = +1
rot R = +1
rot P = -1

Question 66

okay so if theres no P0 but theres P1 and R0,, what is the gap between them and what is this called + explain what r0 and all of those are

Answer 66

okay so P1 is the transition that starts at P1 (v0 + j’‘1)

theres no P0 transition bc P branch selection rule is -1 for J. and normally the difference between resonance signals in rot spec = 2B,, so if theres a bigger gap this would be 4B!!

in the middle of 4B theres the wo line!!!!

Question 67

what is in the middle of the 4B energy gap between p1 and ro

Answer 67

the wo

the wo = we (1-2xe)

wo is said to be the bond origin!!!!

we(1-2xe) = equilibrium oscillating frequency. (anharmonic oscillator)

Question 68

energy difference between J and V for ro vib spec

Answer 68

🔺Ej,r = wo + B( J’-J’’) (J’+J’’ + 1) cm-1

Question 69

so the observed spectral line in vib spec = whatttt

Answer 69

Vspec = wavenumber of spec aka wavenumber aka position on the x axis

Vspec = wo + 2Bm

where m is the number of spectral lines wrt the bond origin!!

Question 70

okay so describe the transirion for P1

Answer 70

P1 :
p branch so lower energy
J’’ = 1 ——> J’ = 0

Question 71

okay so describe the transition for the R1 branch

Answer 71

R0:
so R branch so higher energy one

J’’ = 0 ——> J’ = 1