The molecule carbon monoxide is a simple diatomic molecule with an even number of electrons. Its ground electronic state "X", has no unpaired electrons, so is a singlet state. Many of its excited electronic states are also singlet states, where the first of these is the "A" state.
This demonstration can be used to illustrate the different types of vibration and rotation transitions within the "X" state, within the "A" state, and between the "X" and "A" states, where in all cases transitions are from a lower to an upper state, and correspond to absorption. In addition to the default 12C16O isotopic version of CO, bands can be shown for other isotopic versions of CO.
On entering information in the form below, a display of the types of transitions is shown in the large display area, with the smaller display area to the lower left being used as a key to the types of transitions involved. More details are given below the form, and by mousing over the components in the form tool-tips are used to explain their functionalities.
|Initial Electronic State||X:||A:||Initial Vibrational Level v":|
|Final Electronic State||X:||A:||Final Vibrational Level v':|
|Automatic Scaling:||Carbon Isotope:|
|Manual Scaling:||Oxygen Isotope:|
|Calculated Wavenumber in cm-1||Isotopic Shift of||Minimum||Maximum||Number of|
|Minimum||Maximum||Band Origin||Band Origin in cm-1||Scaled||Scaled||Intervals|
|Input Values in cm-1||Number of||Maximum||Number of|
On loading/reloading the page, clicking "Submit" or "Reset", the width of the main display area is adjusted to fit in the window. By default the main display area is blank, the caption window showing the key is replaced by the "Show Caption" button, the initial and final electronic states are both "X", the initial vibrational level v" is set to 0 and the final vibrational level v' is set to 1, the 12C16O isotopic version of CO is selected, and automatic scaling is set. Also all inputs are cleared. When suitable input is specified and there are no errors, then when "Submit" is clicked, a band is plotted, together with a title on the plot specifying the band system and the isotopic version of CO, expressed in parentheses as the mass number of carbon and oxygen, respectively. By clicking "Reset" the page is set back to its default state.
As an experiment, the capability of downloaded a GIF image file is added. After creating an image, you can enter a filename without the ".gif" extension in the input field then click "Download", then a file with the ".gif" extention should be downloaded. Note that at the moment only the lines are saved in the image, without the axes, background, labels and other text. Also note that only GIF files are currently supported, and the browser you are using may not support this feature.
If manual scaling input is required, the manual scaling radio button should be selected, then the scaling input fields are enabled with a green background. Realistic values should be entered in the first three input fields using the automatic scaling as a guide, thus automatic scaling should be initially selected. The number of intervals selected should match the limits in order to get useful divisions and labelling of the x-axis. After clicking "Submit", the newly scaled plot will be displayed, and the minimum scaled, maximum scaled, and number of intervals will be printed with a yellow background to show that these are the input values and have not been calculated. If at least one of the last two input fields are left blank, the default vertical scaling will be used. Note that the default maximum strength in 1.1 with 11 intervals to allow space for the title. If other scaling is required, a maximum strength of less than 1.1 with a suitable number of divisions should be used, but note that the plotted lines may run over the title. If a bad choice is made and no lines are drawn in the plotting range, a message is displayed in red in place of the information on the lines.
To select transitions between the "X" and "A" states, leave "X" as the initial state and select the "A" as the final state with the radio buttons below the display. Note that the form will not allow you to select the "A" as the initial state and the "X" as the final state. The X → A electronic transition is called the 4th Positive System and is in the UV. There are no restrictions of v" and v', as they are in different electronic states, but limits are set on their maximum values. Unlike the "X" state, the "A" state has an orbital angular momentum quantum number Λ = 1, and when ΔΛ ± 1, in addition to the P-branch with ΔJ = −1, and the R-branch with ΔJ = +1, there is strong Q-branch with ΔJ = 0, except that the transition J' = J" = 0 is always absent. Also note that for Λ > 0, the smallest value J can take for that state is Λ.
On clicking "Submit" with automatic scaling and the X → A electronic transition selected, a strong Q-branch is also plotted, and the caption is larger to show the Q-branch and any overlapping involving the Q-branch. The Q-branch alone is drawn in magenta, overlapping P and Q-branches are drawn in in blue, overlapping Q and R-branches are drawn in red, and all three overlapping branches are drawn in black. This in a way simulates absorption, as the three branches are drawn in the primary complementary colors of cyan, magenta and yellow, when added together for overlapping, the colors are in fact subtracted, yielding black if all three are subtracted. The user can of course select manual scaling as above, after using automatic scaling.
The final type of transitions are those within the excited "A" state. These are of academic interest as they have probably never been observed due to the very high excitation energies. Like the transitions within the "X" state, they should have vibration-rotations absorption in the IR. Also, like transitions within the "X" state, ΔΛ = 0, however, because Λ > 1 in both states, there will in fact be a weak Q-branch. The Boltzmann cut-off factor is based on the Boltzmann factor of the initial rotational level in the current vibrational level, regardless of how high the excitation energy is above the lowest rotational (J = 0) of the lowest vibrational level (v = 0) of the "X" state. The spectroscopic constants of the "X" and "A" states of CO were obtained from the book "Molecular Spectra and Molecular Structure - IV. Constants of Diatomic Molecules" by K .P. Huber and G. Herzber, Van Nostrand Reinhold Company (1979).
By default the bands of 12C16O are calculated. Other isotopes of carbon and oxygen can be selected from the number input fields as "spinners". As IE10 at least shows them as regular text inputs, the mass numbers of carbon and oxygen isotopes have to be entered by hand. For carbon only 12 and 13 are allowed, and for oxygen 16, 17, and 18 are only allowed. Any isotopic version other than 12C16O will cause an additional column to be displayed in the output table which will show the shift of the isotopically substituted band head in cm-1. After clicking "Submit" for a specified transition, the band will be shown as before, except that in addition to the band head, a fainter dashed line, or fainter gray line for IE10, will be displayed in the position corresponding to the band head of the 12C16O isotopic version, which gives an indication of the isotopic shift. The output table will show the shift, which will be positive when the band origin of the isotopically substituted molecule has a higher wavenumber than the corresponding 12C16O band origin, i.e. the latter will be drawn to the left, and negative when the wavenumber is lower than the corresponding 12C16O band origin, i.e. the latter will be drawn to the right. If the band origin of the 12C16O version is outside the plot, an arrow is displayed with the shift to indicate whether this is off to the left or right. By manually scaling, this can be displayed.
The demonstration application here has the spectroscopic constants of the "X" and "A" electronic states of CO "hard-wired" into the code. Improvements could be made by putting the spectroscopic constants of several electronic states of a number of diatomic molecules into a file or a database, then the user could select which transitions of which molecule he wants to display from a menu. When writing text to the <canvas> tag, unfortunately the HTML <sup> and <sub> tags do not work. The superscripts used here for the state designation were obtained from a Unicode list, but they do not work properly for prefixing the mass numbers of isotopes, so the numbers are given in parentheses.