Anharmonic Oscillator (4)

Question 1

What are the limitations of the harmonic oscillator model for molecular vibrations?

Answer 1

need more realistic potential function; only good for tiny displacements and first approximation of real spectra

Question 2

Describe the characteristics of a more realistic anharmonic potential function that provides a better approximation to physical reality

Answer 2

Vx approaches infinity as x approaches 0; Vx - Vxe must asymptotically approach a constant value De as x approaches infinity ; Morse potential

Question 3

What happens to the potential energy function V(x) as x approaches 0 in the anharmonic case?

Answer 3

Approaches infinity

Question 4

What happens to the potential energy function V(x) as x approaches infinity in the anharmonic case?

Answer 4

Asymptotically approaches Dissociation Energy

Question 5

What is the morse potential?

Answer 5

Empirical function that satisfies criteria for realistic potential function

Question 6

What are the properties of the Morse potential that make it useful in describing an anharmonic oscillator?

Answer 6

Correctly depicts behavior and calculate bond energy. Higher energy states show greater shift on graph. Spacing between successive levels and bond break threshold more realistic than predicted graph shows

Question 7

What are the typical values of WeXe (anharmonicity constant)

Answer 7

1-50 cm^-1

Question 8

What is the quantum mechanical selection rule for the anharmonic oscillator?

Answer 8

Change in frequency = +-1, +-2, +-3…

Question 9

What is the energy difference between two states for the anharmonic oscillator?

Answer 9

Change in energy = observed oscillation frequency

Question 10

What is a fundamental vibrational frequency?

Answer 10

Transition from v=0 to v=1

Question 11

A transition between what two states gives rise to a fundamental vibrational frequency?

Answer 11

v=0 to v=1

Question 12

What is an overtone vibrational frequency?

Answer 12

Transitions that appear with change in frequency +-2, +-3 etc appear with decreasing intensity at ~2 we, ~3we

Question 13

A transition between what two states gives rise to an overtone vibrational frequency?

Answer 13

Above +-1

Question 14

What is a hotband frequency?

Answer 14

Transition from v=1 to higher v occurs more rapidly if temp is raised bc higher v states are more populated at higher temps

Question 15

A transition between what two states gives rise to a hot band vibrational frequency?

Answer 15

From v 1 to higher v

Question 16

What is the energy spacing between the various energy levels in the anharmonic oscillator?

Answer 16

Unequal