2c - w (IR // vibrational spec) Flashcards
gross selection rule for vibrational spec
u need a fluctuating electric dipole during a vibration
specific selection rule for vibrational spec
change v = +-1.
what do we assume in vib // ir spec
that the molecule is vibrating and rotating simultaneously.
v = what and its allowed values
vibrational quatum number
0,1,2,3,4 etc
is vibrational energy or rotational energy larger
vibrational energy is larger than rotational energy.
rot, vib, electronic!!
each one has sublevels of the other.
when we think of vibrational spec / IR spec,, what should we think about
harmonic oscillator!! an anharmonic oscillator.
describe a harmonic oscillator
u shape.
energy on y axis (cm-1)
internuc distance // r on x axiS
what is r eq in a simple harmonic oscillator
the equilibrium bond length// distance
aka the bond length
what is a bond
a combo of attractive ( nuc and e-) and repulsive forces (e- and e-)
when a bond is stretched // compressed what is disrupted
the attractive // repulsive forces
energy is needed to disrupt themmm
compression and extention of bonds equation hooks law
f = - k (r - req)
restoring force = - force constant( bond distance - equilibrium force distance)
r - req = extent of distortion
equation for energy of system related to distortion
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.
vibrational freq,, w is dependent on what
the force constant and reduced mass
to go from Hz to cm-1 what do we do
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.
vibrational energy levels are whattt + the equation
theyre quantised according to the schrodinger equation
Ev = Ev/hc = (v+1/2) w(cm-1)
in cm-1
energy of vibrational level 0 =
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.
energy of vib energy level 1
E1 = w(1+1/2) = 1.5w
in rot spec: J = 0 has how much enrgy
J = 0 = 0 energy
its zero point energy = J=1
simple harmonic specific selection rule
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
vibrational energy levels are spaced out equally with what value
with w,, transition energy is the same for all harmonic oscillations.
position of allowed transition v- spec (cm-1) = w-(cm-1)
what is needed for smt to be ir active aka have a vibrational spec
needs a dipole
so it must be a heteronuclear diatomic as these have dipoles
in a simple harmonic oscillator,, describe the graph and how it changes + why this isnt a real representation of a bond
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
whats a better way of describing a bond using a graph
anharmonic oscillator /// morse curve.
fancy v type shape
vibrational energy reaches a plateau at large ‘r’ value.
whats Deq
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).
Deq equation
[1- exp(-a(r-req))] ^2
in an anharmonic curve// as u increase frequency what happens + what equation do we use
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
whats Do
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.
is Deq accurate
nope it hypothetical bc zero point energy is v=0 not the bottom of the graph.
moelcules always have vibrational energy.
what does oscillating frequency,, w.osc. depend on
depends on the vibrational level
larger vibrational level = larger oscillating frequency bc ur increasing energy
selectrion rules for anharmonic oscillator
change in vibrational energy level = +- 1,2,3, etcccc
these are called overtones
what is w.osc
the oscillating frequency
the frequency of the transition we see in spec
what does w.osc equal to
w.osc= w.e {1-xe (v+1/2)}
in cm-1
what is xe
the anharmonic constant aka correction factor low-key
what is w.e
equilibrium oscillating frequency in anharmonic
what’s E.v and what does it equal to
vibrational energy
= w.e(1-xe (v+1/2))(v+1/2)
when does Ev=0 and w.osc = w.e
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
what is we
anharmonic oscillating frequency
simple harmonic selection rule (vibrational spec)
change is v = +- 1
anharmonic curve selection rule
change in v = +-1, +-2, +-3
these are overtonesssss (there’s also hot bands allowed too)
what is the first allowed transition called and which vib levels does if correspond to
first allowed transition = fundamental transition =
V0 —> V1
Ev1-Ev0 = change in energy = w.e(1-2xe)
what is the wavenumber we observe for the fundamental transition :
w.e(1-2xe)
what’s the vibrational energy of 1 vibrational level
[(v+1/2)we - (v+1/2)^2 we xe]
what’s the first overtone and which vib levels does it occur between
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)
2nd overtone
v0–>v3
E= Ev3-Ev0
= 3we (1-4xe)
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
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
okay so which transition will be more intense + which one will be weaker
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)!!
what is the boltzmann distribution
N v=1 // N v=0 = exp ( -hc 🔺E /// kT)
🔺E will be in J so we use hc to turn it into wavenumbers
what if we get a super small value for the boltzman distribution,, what does that mean
it means that the nominator vibrational level has a very small population.
how can we populate the higher energy level and get a larger boltzman distribution value N.higher//N.lower = exp(-hc🔺E// kT)
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.
the larger the boltzman distribution // the what???
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.
IR stretch of CO is what
1700 cm-1
what’s a hot band transition
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)
what vib level do hot band transitions occur from
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
selection rule for hot ban transition
🔺v = +-1
what energy?? is the hot band transition at
we
but there’s a larger correction factor = 4xe
so like there’s a larger difference from we than a normal transition.
RoVib spectrum description + what are they
2 humps,, both humps are the fundamental transition of a diatomic
why are there so many lines in the ro vib spectrum
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.
describe the energy diagram that describes the rotational and vibrational transitions
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.
selection rule for rot spec =
J = +-1
vibrational spec selection rule ( anharmonic)
V = +-1, 2 , 3 etccccc
okay so describe ro vib spec girlllll
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’.
ro vib selection rules
🔺v = +-1, 2 3 4 etc (anharmonic curve)
🔺J (p branch = -1)
🔺J (r branch = +1)
so basically 🔺J = +-1
higher energy is r or p branch
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
okay so the p branch cant have what transition,, and what does this mean
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.
in rro vib spec the vib levels,, rott,, and vib levels must change by how much
vib = +1
rot R = +1
rot P = -1
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
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!!!!
what is in the middle of the 4B energy gap between p1 and ro
the wo
the wo = we (1-2xe)
wo is said to be the bond origin!!!!
we(1-2xe) = equilibrium oscillating frequency. (anharmonic oscillator)
energy difference between J and V for ro vib spec
🔺Ej,r = wo + B( J’-J’’) (J’+J’’ + 1) cm-1
so the observed spectral line in vib spec = whatttt
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!!
okay so describe the transirion for P1
P1 :
p branch so lower energy
J’’ = 1 ——> J’ = 0
okay so describe the transition for the R1 branch
R0:
so R branch so higher energy one
J’’ = 0 ——> J’ = 1
