The mathematical expressions for the simulated spectra assume that the diatomic molecule is a rigid rotator, with a small anharmonicity constant (
, zero electronic angular momentum (
), and that the rotational constants of the upper and lower states in any given transition are essentially equal (
). It is also assumed that only the
vibrational state is thermally populated, in order to eliminate the presence of "hot bands" and simplify the spectra.
The first parameter control lets you vary the fundamental vibrational frequency, which will change the spectrum position along the
axis. The second control manipulates the rotational constant
, which increases or decreases line separation. The third control manipulates temperature, and consequently the number of lines observed and their intensities. The last parameter control manipulates the line width, allowing simulation of spectra at various resolutions.
Spectrum Display Controls
These controls should be used to change how the spectrum is viewed. Line color and background color can be chosen and filling under the line can be turned on. Enabling the peak height control allows for the height of the spectrum to be manually increased or decreased. The
axis upper and lower boundary controls function to set the range of the
Snapshot 1: spectra acquired at low temperatures are greatly simplified as a result of few populated rotational energy levels
Snapshot 2: spectra acquired at high temperatures have many populated rotational energy levels, resulting in more observed lines
Snapshot 3: spectra acquired of diatomic molecules with a large rotational constant will have larger line separation
Snapshot 4: an increase in line width causes the lines to overlap and resolution to be lost
Snapshot 5: the lines of the P and R branches are completely unresolved due to low resolution
Snapshot 6: with low resolution characteristic of that used in organic chemistry, the band for the vibrational transition is broad and no longer rotationally resolved
P. Atkins and J. de Paula, Physical Chemistry
, New York: Oxford University Press, 2006.
G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules
, New Jersey: D. Van Nostrand Company, Inc., 1967.