Quiz 4 Slides Flashcards
Each mass will experience a restoring force that is proportional to its displacement from equilibrium
Hooke’s Law
Does harmonic oscillator obey hooke’s law?
yes
force constant of the bond is equivalent to the ___ of the potential energy function
curvature
masses m1 and m2 each have
displacements x1 x2 assuming simple harmonic motion oscillating as a cosine function of time
since both standard differential equations have to be true simultaneously, they also show
that each mass oscillates with the same frequency and phase constant; each mass goes through its equilibrium position simultaneously
transition spacings are all what frequency of oscillation
v0
resulting spectrum from harmonic oscillator has how many bands
1 abs band
fundamental vibrational frequency
transition v = 0 to v=1
harmonic oscillator approach is good for
very small displacements about equilibrium; first approximation to real spectra; not much else
a better approximation to physical reality from harmonic oscillator needs what
a more realistic potential function
morse potential
empirical function where Vx approaches infinity as x approaches 0, is asymptotically approaching a constant value De
correction factor that lowers each energy level relative to the harmonic energy levels
anharmonicity constant
result of anharmicity constant
energy levels of oscillatornot evenly spaced
transitions that appear with decreasing intensity at fundamental vibrational frequencies 2, 3, etc
overtones
transition that occurs more rapidly if temp is raised
hot bands
what causes hot bands
higher v states are more populated at higher temp
anharmonic oscillator equation overestimates De by 20% because…
it assumes a linear estimates – change in energy constant with v, which is not true, especially at higher v
energy levels equally spaced on the ladder
harmonic oscillator
energy levels get closer as energy increases; near dissociation, energy becomes continuous
real molecule
degrees of freedom also refers to
number of possible fundamental vibrations in a molecule
three of the possible fundamental vibrations are simply…
simultaneous, in phase translations of each atom together along one of the directional coordinates
do translations correspond to real molecular vibrations?
nope
three more possible fundamental vibrations exist that simply refer to…
rotation of each atom about 3 principle axes of rotation
does rotation correspond to real molecular vibration
no
to find translational movements for non-linear molecules
subtract 3 degrees freedom
for rotational movements of nonlinear molecules
subtract 3 degrees of freedom around its principle axes
for linear molecule’s translational movements
subtract three degrees of freedom
for a linear molecules rotational movement
subtract 2 degrees of freedom
do linear molecules have rotation around long axis?
no real discernable rotation along major axis
linear polyatomic fundamental molecular vibration
3N-5
nonlinear polyatomic fundamental molecular vibrations
3N-6
of the possible fundamental molecular vibrations, how many are caused by bond stretching?
N-1
of the possible fundamental molecular vibrations, how many will be caused by bond bending
2N-5 nonlinear, 2N-4 linear
molecular motion in which all atoms move in phase and with the same frequency
normal modes of vibration
types of normal mode molecular vibrations: stretching
symmetric and asymmetric
types of normal mode molecular vibrations: bending
in plane rocking, in plane scissoring, out of plane wagging, out of plane twisting
strength of polarity in chemical bond described by
the dipole moment
chemical bonds and vibrations can be described on the basis of
molecular symmetry relative to a symmetry element in the molecule
in order to absorb IR radiation, molecular vibration must
cause a change in the permanent dipole moment either parallel or perpendicular to a symmetry element in molecule
is symmetric stretching vibration ir active
no
IR activity requires
change in permanent dipole moment of the chemical bond
very strong in IR spectrum
polar bonds with large dipole moments
non polar bonds in IR spectrum
weak or absent
when harmonic oscillator condition is relaxed
overtone vibrations become permissible
also appear due to anharmonicity
combination and difference bands
in addition to overtone vibrations, these bands also appear due to anharmonicity
combination and difference
appear at the value due to the sum of 2+ fundamental molecular vibrations
combination bands
arise from ground vibrational levels
combination bands
binary combination level involves
2 different normal coordinates with nonzero quantum numbers
1 photon excites 2 different vibrations simultaneously if
that photon has an energy approx. equal to the sum of energies needed to excite them separately
do not arise from fundamental molecular vibrations
difference bands
difference bands vs combination band strength
difference are weaker
difference bands at low temps
disappear
difference transition occurs from
excited level of one transition to that of another
intensity of difference transition varies with
the population of the excited state
when the energy of an overtone or combo band happens to have the same value as the energy of a fundamental vibration
accidental degeneracy
Fermi resonance
accidental degeneracy results in sometimes 2 relatively strong bands where only one fundamental was expected; two observed occur at higher and lower energies than the expected
two energy levels in fermi resonance interact
on quantum mechanical level due to anharmonic terms in potential energy
does fermi resonance energy difference have to be big
no
vibrations in fermi resonance should be
able to couple via anharmonic terms, with overtone and fundamental of same symmetry
vibrations which involve large amplitudes of isotopically labelled atom should
shift by the greatest amount
isotopic mass difference vs wavenumber shift
larger IMD greater WNS
For H-D substitution new vibrational wavenumber of D substituted bond will always
be shifted to lower energy relative to H sub species by factor of 1/sqrt2
certain sub molecular groups of atoms consistently produce vibrational bands in characteristic frequency regions of vibrational spectrum
group frequencies
what causes group frequencies
coupling of oscillating dipole moments
group frequencies can be very sensitive to
both config and conformation of local molecular groupings
very sensitive probe for molecular structure
IR spectroscopy
