Quantum Mechanics Unit 12 Key Terms

translational, rotational, vibrational degrees of freedom

monoatomic: 3 translational.

diatomic: 3 translational, 2 rotational, 1 vibrational. 6 total

polyatomic: linear - 3 translational, 2 rotational, 3N-5 vibrational, 3N total

nonlinear - 3 translational, 2 rotational, 3N-6 vibrational, 3N total

rotational term

Rotational energy of a molecule in wavenumbers F(J), predicted by the rigid rotator model and dependent on the rotational constant B. Add more

nonrigid rotator model

Actual energy levels are slightly different (lower) from rigid rotator model, as nonrigid rotator model factors in centrifugal distortion, or the way molecules move further apart as rotation gets faster, molecule distortion as it rotates Add more

centrifugal distortion constant

As molecules distort or move further apart as they rotate, the centrifugal distortion constant is subtracted from the rotational term to lower the overall energy level.

vibrational term

The vibrational energy of a molecule in wavenumbers, G(n)

overtones

A series of less intense lines (frequencies at lower intensities), almost integral multiples of the fundamental resulting from transitions from n = 0 to n = 2 (first overtone) and from n = 0 to n = 3 (second overtone).

anharmonic oscillator

Considers and accurately represents the potential energy far from the equilibrium distance, energy results lower than predicted by the harmonic-oscillator model. Energy levels are not evenly spaced, and the energy difference between levels gets smaller as quantum number n increases.

anharmonicity constant

quantifies how a molecule's actual vibrational energy levels deviate from those of an ideal harmonic oscillator. Much smaller than the harmonic term

R , P, and Q branches

Absorption in IR regions of spectra, R branch at high frequency (where lines get closer together as J increases), P branch at low frequencies (lines get farther apart as quantum number (J?) increases, and Q branch, where the lines are very close in the spectra (what does this mean) due to vibration-rotation interactions

vibration-rotation interaction

The dependence of the rotational constant on the vibrational state n, explains the unequal spacing between lines in vibration-rotation spectra

dissociation energies: De and D0

D_e - the difference between the minimum of the potential energy curve and the dissociated atoms

D₀ - the difference between the ground vibrational level and the dissociated atoms

n’ progression

Series of lines with different vibrational states, shows transitions between energies of lower and upper electronic states. Can be used to get information about vibrational parameters of excited electronic states

Franck-Condon principle

Electronic transitions are vertical; because the motion of the electrons is almost instantaneous relative to the motion of nuclei, when the molecule makes a transition from one electronic state (electron transition), the nuclei do not move appreciably during the transition. The intensity of a vibronic transition is proportional to the overlap between the wave function in the upper and lower vibronic states.

Allows for the estimation of relative intensity of vibronic transitions

principal axes

3 axes i.e. X, Y, and Z, that are chosen so I_xy, I_yz, and I_xz vanish. In molecules with some degree of symmetry i.e. one principal axis is perpendicular per molecular plane in planar molecules, while the C₃ axis is one principal axis in CH₃Cl

principal moments of inertia

I_xx, I_yy, and I_zz

linear, spherical, symmetric, or asymmetric rotor

oblate/prolate symmetric top

centrifugal distortion

normal modes or normal coordinates

stretching (symmetric/antisymmetric), bending, and torsion

parallel/perpendicular band

IR/Raman activity

transition dipole moment

deexcitation processes

radiative/nonradiative transitions

fluorescence

internal conversion

intersystem crossing

phosphorescence

vibrational relaxation

0–0 transition

LASER

stimulated emission

spontaneous emission

Einstein coefficient

fluorescence lifetime

population inversion

pump light

gain medium

pumping source

coherence