The Sigma Program - Algorithm and Software Package Description

    The algorithm for the cross section calculations has been described in the literature.[3,4] It is sometimes referred to as the "projection model" and can be summarized as in the last paragraph of the Model section of ref. 4:

"The molecule is projected onto a randomly chosen plane in space, and a circle with the corresponding collision radius is drawn in that plane at the position of each projected atom. Then points in the plane are randomly picked within a square of area A that encloses the projected molecule. If a selected point is inside one or more circles, it is counted as a hit. The ratio of hits to the number of tries multiplied by A is the collision cross section of that particular projection. The procedure is repeated for many different randomly selected projections..."

The radius of the circle drawn around each atom is either taken from a parameter file (hard sphere mode) or is calculated from Lennard-Jones parameters supplied by a second parameter file (Lennard-Jones mode). In the latter case the radii are temperature dependent.

Files
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Included are 8 files:

1 FORTRAN source file
1 C source file used when compiled on SGIs
4 parameter files
1 coordinate file of fullerene C₆₀
1 README file (this file)

Compiling
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The code is intended to be compiled under a UNIX platform.

1.) Make a copy of the source file and edit it, following the instructions mentioned in the head of the source file.

2.) Modify the call for the random number generation to match your system. This call is the only system-dependent call. The routine used in this version is for an IBM risc/6000. (SGI Indigo2 version available)

3.) Compile source code using a FORTRAN compiler. Use highest possible optimization to speed up execution.

Running
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For a list of options, run the programs by typing the name of the executable, e.g. sigma

sigma

The program will return the following information:

Usage: sigma

-i input_filename
-f filetype [mol2 xyz crd trj pdb cssr lis] (mol2 default)
-a amber_prm_file_name (crd trj filetypes only)
-l number of datasets in trj file
-p parameter file (hard sphere)
-s parameter file (Lennard-Jones)
-h parameter file (Lennard-Jones scaled by size)
-b bufferradius (hard sphere only, 1.09 default)
-t temperature (300K default)
-n accuracy (average deviation in %)
2% default, less than 1% is expensive!

Results are unpredictable when more than one of the flags -p, -s, and -h are used!
Files of type oldxyz, cssr, or lis are read by an old subroutine for backwards compatibility.

To run the program type the name of the executable (e.g. sigma) and specify the coordinate file with the -i flag (default format is "mol2") and one of the flags -p, -s or -h with a parameter file name following:

sigma -i coord.mol2 -p parameters.dat

Other formats for the coordinate file are supported and can be specified by the -f flag. If AMBER crd- or trj-files are used the topology file is indicated by -a and the number of structures per file by -l

sigma -i coord.xyz -f xyz -p parameters.dat

sigma -i coord.crd -f crd -a prmtop -l 100 -p parameters.dat

The accuracy (average deviation in %) can be given by -n (default 2)

sigma -i coord.mol2 -n 0.5 -p parameters.dat

There are 3 modes of operation: hard sphere mode, Lennard-Jones mode, and ion size scaled Lennard-Jones mode.

In the hard sphere mode the atomic radii are supplied in the file specified by the -p flag. A parameter file supplied for this mode is called "parameters.dat". The buffer gas radius can be given by -b

sigma -i coord.mol2 -p parameters.dat -b 1.11

In the Lennard-Jones mode the parameters used are specified by the -s flag which automatically triggers the Lennard-Jones mode. Parameter files supplied and used with -s are "mm3.pot" and "adj.pot". The temperature is set in Kelvin by -t and is by default 300 K.

sigma -i coord.mol2 -s adj.pot -t 400

Two Lennard-Jones parameter files are provided. One (mm3.pot) contains parameters that are used in Molecular Mechanics (MM3), the other one (adj.pot) those that have been optimized to fit the experimental temperature dependence of the cross section.

Before using any parameters please read and understand the following paper:

Wyttenbach, T.; von Helden, G.; Batka, J. J., Jr.; Carlat, D.; Bowers, M. T. J. Am. Soc. Mass Spectrom. 1997, 8, 275-282.

The third mode of operation, the "ion size scaled Lennard-Jones mode", is used in manner very similar to that described above. The only difference is that the L-J potential parameters are scaled to the size (number of atoms) of the polyatomic ion: the fewer atoms, the less buffer gas-ion interaction (the less deep the potential well). This mode is selected by the -h flag and the parameter file following. The parameter file supplied with the software package is called "sca.par".

sigma -i coord.mol2 -h sca.par

The formats for the parameter files are different for each mode of operation and are described in the source code.