### Fluorescence Quantum Yield

The fluorescence quantum yield (QY) of a dye is the fraction of photons absorbed resulting in emission of fluorescence. It can be shown that this definition leads to

where kf is the fluorescence rate constant and ki denotes the rate constants of all the decay processes from the first excited state of the fluorophore.

#### Measuring Fluorescence Quantum Yields

The QY of a fluorophore is determined relative to a reference compound of known QY. If the same excitation wavelength, gain and slit bandwidths are applied for the two samples then the QY is calculated as

where QYref is the quantum yield of the reference compound, h is the refractive index of the solvent, I is the integrated fluorescence intensity and A is the absorbance at the excitation wavelength. The absorbances at the wavelength of excitation is optimally kept in between A = 0.02-0.05 in order to avoid inner filter effects and ensure linear response on the intensity.

#### Reference standards for quantum yield measurements

It is advantageous to have a reference compound resembling your dye. Think of the following when choosing your reference compound:
• The lowest energy absorption band of your reference and dye should overlap as much as possible.
• The QY of the reference should match the expected QY of your dye.

#### Practical considerations when measuring quantum yields

• The excitation wavelength should be at the absorption maximum of the lowest energy transition of both your dye and reference.
• The full fluorescence spectrum must be acquired.
• Set the excitation slit bandwidth as small as possible. To compensate for loss in signal, increase the emission slit bandwidth instead.
• Use three to five different excitation wavelengths across the lowest energy absorption band. This provides a means to test the absorbance baseline used. If the calculated QYs show a tendency, e.g. decreasing towards lower excitation wavelengths, this is likely because the absorbance baseline is not perfect.

### Calculate fluorescence quantum yields in a|e

The a|e freeware provides a shortcut for calculating quantum yields of multiple samples at multiple excitation wavelengths.

1. Activate the 'Quantum yield table' toggle button in the toolbar. This will activate a table for the automatic calculation of QY's.

2. The table can either be edited manually or you can press the 'QY assistance' button located above the table to automate the process.

Pressing the 'QY assistance' button will open a dialog box for specifying the spectra in the QY determination.

3. In the top two listboxes the absorption and emission spectra of the sample are selected.

Note: It is possible to select one absorption spectrum and multiple emission spectra. Each selected emission spectrum corresponds to different excitation wavelengths specified in the excitation wavelength editbox (specified in identical order as the spectra appears in the listbox). Different excitation wavelengths are separated by space.

4. In the bottom two listboxes the absorption and emission spectra of the reference sample is selected. The number of selected emission spectra must be the same as the number of selected emission spectra in the top listbox and corresponds to different excitation wavelengths.

5. The fluorescence spectrum integration range is specified to the right in the dialog box. If the range is set to 0 the integration will be performed over the entire emission spectrum.

6. The excitation wavelengths is specified in the bottom of the box. Multiple excitation wavelengths can be specified (by spaces) but the number must equal the number of specified emission spectra.

7. The QY of the reference dye and the refractive index of the solvent is specified in the bottom right of the box.

8. Press OK to insert the values into the QY table, which automatically calculates the QY of the sample in the right column. A new row will be inserted for each specified excitation wavelength.

Note: The QY table can also be edited manually. Use the integration tool and the data cursor tool to assist with determining the parameters needed for the calculation of the QY. It is also possible to extract the absorbance values of all spectra at a certain wavelength by going to Tools -> Quantum yields -> Get all abs values.