SimEPR Manual

5.0 - SIMEPR - Isotropic Simulation program

This program is intended for simple EPR simulations of isotropic EPR spectra. It will simulate either the CW or FT spectrum in the zeroth, first, or second harmonics and will optimize the values to match the simulated spectrum to an imported experimental spectrum. Up to 10 species may be included in each simulation with varying concentrations and in each species up to 16 nuclear spin sites.

5.0.1 The data screen

These features are all the same as in the Ftepr.exe program.

5.0.2 Function keys

No function keys are active in this program.

5.0.3 Calculations

All calculations are first order isotropic for X-band configuration. Therefore, the exact frequency and field position values are not important. The field position is set by the g-shift parameter by specifying the distance in Gauss from center of the scan. A simulation centered in the display has a zero g-shift. A simulation sited 10 Gauss to the right of center has a positive 10G g-shift while one sited 10 Gauss to the left of center has a negative 10G g-shift A Nitroxide option has been added that will compute a spectrum with quantum number dependent linewidths. If you select this option, for each species you must enter a Nitroxide coupling and separate linewidths for each of the three spin 1 lines. This program also includes calculations of the modulation amplitude and time constant, which affect the measured linewidth. More accurate linewidth and lineshape calculations should be possible by using this feature. Note that the spectrum file modulation amplitude and time constant values are neither converted to nor from the simulation mod. amp and time constant values. The two sets of values are independent. The spectral file values displayed are text representations and may contain non-numeric characters while the simulation values are numeric. Check the spectral file parameters with the Parameters option and edit the simulation parameters with the Edit_scan option. Spectral simulations are generated by calculating Fourier coefficients. If a CW (continuous wave) simulation is specified, then an inverse FFT is executed. Obviously, an FT simulation is faster than a CW simulation since no inverse FFT is needed. However, one cannot look at even a simple FT spectrum and easily guess the spin and coupling constant values. An FT spectrum must include both the Real and Imaginary components; however, because of the Nyquist frequency relationship, the total number of data points remains constant. For EPR spectra of relatively few lines such as spin trap data, FT simulations are usually more difficult to examine. For EPR spectra of numerous lines such as large molecule direct data, FT simulations are usually less difficult to examine. This is our first program to allow you to optimize in either FT or CW space. FT simulations and optimizations are obviously much faster than CW optimizations. The CW optimization seems to be equivalent to if not better than the single and composite Tune.exe routines on our HP computer The FT optimization appears to allow a greater range of parameter adjustment. This program to works equivalently for both single and multiple species simulations. No additional work is required to optimize multiple species parameters.

5.0.4 Parameter storage

The simulation parameters for all 10 species are stored in a single file, \lab\eprdata\simdata.sdf , after each simulation and are recalled when the program is started; the file is binary and cannot be edited or printed. If your simulation program is suddenly unusable then maybe your should delete this file and start over. You may also save simulation parameters into individual files and recall them later, all from the Edit_Species menu.. These files all have the .sdf extension and are found in the \lab\eprdata directory. This file format is subject to change so it should not be relied upon for long term storage of parameters.

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5.1.0 The Simepr.exe menu

The main menu has the following choices:

Each function is described in more detail below.

Import

Loads an exported data file. Enter the clipboard page number ( 1-99 ) to load experimental data into the Simepr.exe program. The import is loaded into the experimental data space.

Export

Saves data to a file. You will be prompted for R or I if the display is Real and Imaginary, or prompted with E or S if the display is Experimental and Simulation. After that, you will be prompted for the clipboard page number ( 1-99 ).

Parameters

Displays the current spectral parameters on screen. These parameters are imported with the experimental spectrum.

Edit Scan

Enables editing of the simulation scan parameters: These values default to the values of the Imported spectrum, if any.

Now, to enter the simulation parameters for an individual species:

A Nitroxide simulation does not use the constant Linewidth parameter since it has three linewidth parameters of its own. To include a non-Nitroxide species in an otherwise Nitroxide type calculation, enter 0.0 for that species' Nitroxide coupling and enter the constant linewidth for each of the three linewidths.

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Calculate

Calculates the simulation. After the calculation, the display will be Real and Imaginary data. A CW simulation always shows up as Real data with no intensity in the Imaginary data. An FT calculation with combined Imaginary and Real data will show up in the Imaginary display. The imported experimental display will not be shown immediately after the simulation until a compare is executed.

Display

Switches the display from Real and Imaginary data to Experimental and Simulation data and back again.

X-Y-scale

Use the arrow keys to change the X and Y display scale parameters. Press ESC or Backspace to return to the menu.

Zoom

To show either the upper or lower display full screen. If the Real and Imaginary data are displayed, you will be prompted for R, I, or [ESC]. If the Experimental and Simulation data are displayed, the display will overlay the two spectra in different colors.

Residual

Subtracts the simulation data from the experimental data and displays the results.

Compare

Calculate and display the Sum of Squared Residuals and the Spearman's Rank Correlation Constant between the current simulation and experimental spectral data.

Write

This option will output the current experimental filename and simulation parameters to a formatted text file suitable for printing named \lab\eprdata\simdata.epr. Use the DOS command "type filename" or "more < filename" to print the contents of the file to the screen. In MS-Windows, use the Reporter program to view and print the contents of the file.

Tune_prep

This option prepares data for input to the Tune.exe and Tunex.exe programs. The tune programs are character mode versions of the Optimization routine and are available for many different computers. Follow the same process as you would with Optimize. You will then be prompted twice for data:

• Choose the experimental file type to create. Enter B for Binary or A for ASCII spectrum data files. Choose Binary for the PC versions of tune and ASCII for non-PC versions of the tune program.
• Enter a filename prefix (1-8 characters) for the tune input files.

Two files will then be created for input to the Tune program for fitting the experiment to the simulation.

Optimize

This feature will attempt to fit the simulation parameters to produce a simulation that best matches the experimental spectrum. An entire manual section follows and is dedicated to Optimizations. Follow this general procedure:

• Import the experimental data file
• Enter your simulation parameters
• Calculate a simulation
• Compare the simulation with the experimental. If it is 'good enough' ( a subjective analysis ), then proceed.
• Choose Optimize from the menu and enter the optimization options.
• The optimization will begin. Press F10 to stop the process.

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5.2.0 Optimizations

This program uses an algorithm developed here at LMB to fit the simulation to the experiment. The experimental spectrum must first be imported into the Simepr.exe program. The routine loops over the parameters generating perturbations, simulations, and error calculations until no successive better simulations are found. The current best simulation is displayed on screen with the experimental. The iteration then stops and the final simulation is displayed. Simulations are compared to the experiment by a Sum of Squared Residuals : SSR= S ( Expi - Simi )2 , i=1 .. n. A short series of inputs is necessary to begin the optimization.

Optimization inputs

The following inputs are necessary to start a simulation Optimization. The default values are usually acceptable, permitting a large search space across the entire spectral range.

LMB1 fit parameters:

Conventional Hyperfine Analysis ? [ Y / N ] Y perform a conventional hyperfine analysis by varying each coupling constant individually. This is the usual way of fitting data.

Parametric Hyperfine Analysis ? [ Y / N ] Y

perform a parametric hyperfine analysis by varying all possible pairs of coupling constants with a constant sum. That is, if a spin 1 hyperfine is perturbed by +1.0, then a spin 1/2 hyperfine is perturbed by -2.0 so that the total spectral length remains unchanged. This option is significantly more time consuming and tedious. This is a more exotic way of fitting data and should be tried when the Conventional Hyperfine Analysis is unsuccessful.

Step type: [ 0, 1, 2 ] 0

The optimization refines the parameter values by decreasing the perturbation size between levels

where i is the step (level) number and resolution= ( scan_range / data_points), the accuracy of the experiment. For the non field parameters, the resolution of lineshape and relative intensity is defined as 1.0. The binary (0) method should be used. If it is unsuccessful, you may at your own risk try the other methods.

Number of Levels n

This value controls the starting perturbation size and the time of the optimization. For binary steps, the max. value is 7; for quadratic and linear steps the max. value is 256. The program will decrement the level number from this value to one in in units of one. With binary steps, a value of 7 permits quite large initial perturbations; if the simulation is already close to acceptable, you should use a smaller value such as 3 to save time and eliminate very wrong answers,

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SIMPLEX fit parameters:

Number of restarts [ 1 - 10 ] The number of times to restart the simplex algorithm after an apparent error surface minimum has been found.

Iterations/restart [ i < 5000 ]

The maximum number of algorithm iterations permitted within a single restart. This parameter prevents infinite wandering.

Fractional tolerance [ 0.0 - 1.0 ]

(ftol) This parameter defines the criteria for ending the algorithm, when the difference between the n (=Number of parameters+1) error values satisfies: ( max. - min. ) / (max. + min. ) < ftol. A typical value is 0.1.

Common fit parameters:

Select Parameters to Optimize ? [ Y & N ] Y allow the user to select whether or not each individual parameter is to be varied or kept constant. If so, then after this input screen will follow an edit session for flagging each parameter as vary or keep constant.

CW fit range : from _____ to _____.

With a CW simulation, you may choose to fit only a sub-region of the magnetic field, thus excluding unwanted features of the spectrum. Enter the starting and ending data point values of the region needed.

Selecting Parameters to Optimize

If you have chosen to "select parameters to optimize", then you will now be prompted with an edit session for flagging each parameter as vary or keep constant. The edit session is analogous to the Edit_Species session except that you must enter not the parameter value but rather a Y or N for each parameter; Y= vary the value, N= keep the value constant.

Final input

After you have competed the Optimization inputs, a test simulation is calculated and compared to the experimental by calculating the Sum of Squared Residuals, SSR. You will the be prompted with something like this: Trial SSR= 1.543E+6, Continue the optimization ? Enter Y or N > ____. Enter Y to continue the process, N to return to the Simepr.exe menu.

Observing the process

The Optimization proceeds by decrementing the level when no further perturbations produce a simulation with a lower SSR. Each simulation is matched to the experimental in overall intensity before the SSR calculation. The screen display will update the simulation data once a species is completed within each step. A panel on the left of the screen will continuously show the starting SSR, the current SSR, the total number of simulations calculated, the current Level, the current Species number, and the current Parameter number.

Optimization output

Once finished, the program will display the final simulated spectrum and prompt the user with a completion message. This message will include the run time and the Spearman's rank correlation coefficient (r). Also, a file will be output as \lab\eprdata\simdata.epr which will include the experimental filename, the job time and rate, r, and the final simulation parameters. This file may be viewed and printed using the Reporter.exe program for Windows or with the DOS command more < \lab\eprdata\simdata.epr . In addition, the final values may be viewed within the simepr.exe program by selecting the edit_species option.

5.3.0 The Tune program for simulation optimizations

Tune is character mode version of the optimization program. This program has been compiled and executed on IBM/AT, DEC VAX, and on UNIX machines using the standard cc compiler. Tune.exe allows execution of an optimization to work in the background in a multitasking environment and can easily be ported to faster computers.

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