Auto matic Assembly of Matrices for Mass Spectrometric Calculations SIR: Calculations for determining the composition of a gas mixture by mass spectrometric analysis consist primarily of the solution of a system of simultaneous linear equations (1). This is a standard mathematical problem for which existing machine programs are readily available ( 2 ) . Before such a program is started, hon ever, the matrix of the coefficientsof the system of equations must be in storage in the required locations in the machine. The manual execution of this matrix formulation is by far the most time consuming and burdensome part of obtaining the solution. This is particularly true for samples of a nonrepetitive type for which individual matrices are required to be formulated. One method of reducing the labor involved is to store a library of inverted matrices as for repetitive samples. For research work, however, a large library of these matrices must be stored, and the time required to search for the correct one could nullify the time saved by having the matrix preinverted. Furthermore, each recalibration of the mass spectrometer requires the whole library of matrices t o be reassembled and reinverted. As an alternative, a method has been developed for the automatic assembly of the required matrices. It can be adapted to any electronic digital computing system subject only to the limitations that the system be capable of alphabetic input and output, and the
system have sufficient storage for the particular application. The chemical formula of each gas or liquid, along with the m/e values of the ion masses and the corresponding pattern coefficients and the sensitivity coefficient of the base peak, forms the necessary dictionary of calibration data. As long as sufficient storage space is available, this dictionary is indefinitely expansible. Data for more gases can be added to it easily a t any time. Similarly, it can be updated readily to accommodate recalibrations. Calibrations from several mass spectrometers can be stored and used with the same program by using a prefix or a suffix to indicate the particular instrument for which the set of calibrations is applicable. The same thing can be done to designate isomers, for example :n-C4Hio for normal butane and Z’SO-C~H~~ for isobutane. The digitized output from the Consolidated 21-103 mass spectrometer furnishes the information which is necessary to formulate the matrix: a listing of all the mass to charge values in the mixture, and the ion intensities a t each mass. Once the identification of the components in the mixture and the m/e values and peak heights to be used have been established by the spectrometrist, this information is written in its usual form (combined alphabetic and decimal) and is given to computer personnel for conversion into machine input. An executive program stored in the
machine accepts this input, decodes the formulas, selects the proper calibration data from the dictionary, assembles the matrix, scales the digitized peak heights, and then continues automatically with the solution of the resulting system of simultaneous linear equations. At the end of the calculations, the results are reported in terms of chemical formulas and percentage composition. This program allows complete freedom to use any combination of gases from the library of calibration data. It permits the spectrometrist to select the best system of equations to be solved for the particular sample being analyzed. A detailed description of the system appears in the Proceedings of the Mass Spectrometer Conference, ASTbI Committee E-14, June 1961. The program in use was written for the Burroughs Datatron 205 equipped with a Datafile (magnetic tape). ItJaccommodates matrices of orders up to and including twenty (20). Copies of the coding may be obtained from the authors. LITERATURE CITED
(1) Barnard, G. P., “Modern Mass Spectrometry,’] Institute of Physics, London,
1953.
(2) Warga, J., Report (R-83),Electrodata
Division, Burroughs Corp., 1956. MARYH. LOEFFLER RUTHGOODMAN Westinghouse Research Laboratories Pittsburgh 35, Pa.
Mass Spectrometric Analysis. A Small Computer Program for the Analysis of Mass Spectra SIR: h program has been written for a Royal-LIcBee LGP-30 computer which makes possible the semi-automatic computation of nonroutine mass spectra. The calculation method used is the so-called “successive subtraction” technique and is limited only in that the calculations involved must be carried out within a mass range of 1 to 546 and that no provision has been made for the utilization of matrix algebra techniques for the resolution of compounds of identical mass. From raw spectral data, the program prepares a normalized mass spectrum and punches it on paper tape for future use. The program provides for the
automatic subtraction of background from the raw data. Ion peaks occurring a t fractional mass do not interfere with the calculation procedure. The computer subtracts standard patterns from the unknown pattern in such a manner that trial or incorrect subtractions have no effect upon the final outcome. When a sufficient number of standard spectra have been subtracted to reduce the residual unknown spectral peaks to essentially zero, the computer asks for the relative sensitivity of the various components which have contributed to the unknown spectrum. Upon receipt of these values, the computer calculates, quantitatively, the
amount of each component comprising the original unknown mixture. A copy of a more lengthy report describing this technique and illustrating an example of its use, as well as a report detailing the program coding commands, is available from one of UI (M.A.E.). M. A. EASH R. S. GOHLKE~ Chemical Physics Research Laboratory The Dow Chemical Co. Midland, Mich. 1 Present address, Eastern Research Laboratory, The Dow Chemical Co., Framingham, Mass.
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