IAVELEWOIH
IYLWOYETEOll
Figure 6. Effeet of Spectral Bard width ard Pen Period. At small MlWS fw SBW and PP. shot noise becomes apparent, Curve B. Table 2. Student Calculated Path Lengths of an Optlcal Cell lnshument Chem-Anal Coleman 124
Spectral Bandwidth
Calculated Path Length
nm
cm
20.0 1.0
0.800 1.002 1.010
0.5
1.024
2.0
The noise algorithm is more involved than the others used in the emulation. A test of user-specified pen period and spectral bandwidth values is made to determine if any of the onset of noise conditions are met. If the spectral bandwidth, a t a given pen period, is greater than the onset value, no noise is introduced into the spectrum. If the specified spectral handwidth is equal to or less than the onset value, noise is introduced into the spectrum. A random number for each spectrum is generated and is multiplied by an amplitude factor for a set of given pen period and spectral handwidths. The noise amplitude factor is directly proportional to the inverse of the spectral bandwidth and inversely proportional to the square root of the pen period. Care is taken in the plotting routine to force the noise-containing spectrum to follow the noiseless curve. This is done by forcing the total noise to he zero every 16 points. Example Outputs
Fieures 4 throueh 6 show actual terminal screen c o ~ i e of s the spectra generated by the program. Figure 4 showsihe effect of spectral bandwidth on resolution and absorbance accuracy; peaks are depressed and wider a t larger spectral handwidths. Peaks with more narrow natural bandwidths are more sensitive to spectral bandwidths than those with larger natural handwidths. Figure 5 shows depressed absorbances and spectrum shifts t o shorter wavelengths as a result of faster scan speeds. A similar set of curves are obtained at different pen period. Figure 6 shows the introduction of noise into the spectrum at a pen period of 0.5 second and spectral bandwidth of 0.03 nanometer. Student Use and Comments
The emulation is used in an instrumental methods laboratory by students who have completed work with a singlebeam spectrophotometer, e.g., Bausch & Lomb Spectronic 20 or Sargent-Welch Chem-Anal. Students study the effects of the wavelenzth dependence of detector sensitivitv and source radiaiivr ou.tput. in addition, they determine theerror in the nominal wnvelmath reading of deliberately misadiusted instrument and determine thk path length of an optical cell, using a potassium chromate solution of known concentration and National Bureau of Standards data from which the ahsorptivity of the chromate can be calculated. This latter ex-
ercise is repeated on other instruments a t a total of four different spectral handwidths. Typical results are given in Table 2. The dependence of the path length determination on spectral bandwidth is a lead-in to the emulation program. Students are directed to vary the spectrophotometer parameters of spectral bandwidth, scan speed, and pen period and relate how each one affects waveleneths of maximum absorbance, values of maximum absorbance, spectral handwidths compared to the natural bandwidths,. sianal - to noise ratios, and instrument time required to obtain spectra. After com~letinathe emulation exercise, students use a Beckman model 5270 absorption spectrophotometer to obtain an "optimized" spectrum of an unknown substance. Students report that the various spectrophotometer controls are readily understood and instructon observe that very little instruction need be given the students for them to operate the instrument. Students react very positively to the rapidity of learning with the graphics-emulator rather than the slower instrument itself. The rapidity of a graphics emulator is very important for this work as well as any extensions to other instruments. At 1200 baud a snectrum is eenerated and disolaved within 5 s. using a ~ e r o x ' ~ i ~6mtime a share system. hist time increases if the svstem resnonse time is ~ o o rA. microcom~uterstandalone system is not communication-rate limited, but the execution time to calculate and display a single spectrum with an %hit microprocessor may increase to 57 sec or longer. If a student must wait for more than 30 sec for a spectrum, the emulation may lose its effectiveness. Spectra have been generated with a 16-hit microprocessor system within 6 sec. I t is believed that screen resolution can he sacrificed to a greater extent than execution time and still have an effective emulation system.
A Program for the Synthesis of Mass Spectral Isotopic Abundances Marllyn L. Brownawell and Joseph San Fillppo, Jr. Rutgers University, New Brunswick, NJ 08903 Medium- and low-resolution mass spectrometers are capable of resolving ions with ma~s-to-ch&~e (mle) values that differ by 0.01-1 mass unit. Under such resolution, a molecular or fragment formula cannot be determined from m/e values alone. However, such formula assignment frequently can he accomplished by the method of isotopic ahundances as described below.' Since each ionic species produced in a mass sprctromrtrr is normally observed as a cluster of peaks, the intemitv ratlo of these peaks is uniquely characteristic of the iskopic abundance ratios of the elements that comprise the particular ionic species. Thus, for example, the stable carbon isotopes of natural abundance are 12C (98.9%) and 13C (1.1%). If the peak containing all 12Catoms is designated M+, then the peak in which one 12Catom is replaced by a '3C atom must he the ( M I)+ peak. In the absence of interference from isotones of othe; eiements, the intensity ratio of the M+I(M + i)+ peaks will depend on the abundance ratio of 12C/'3C and on the number of carbon atoms present. Using the isotopic abundance ratio and the peak intensity ratios, the numher of
+
' The computation of either the molecular or a frabment ion cluster Obsewed in the mass spectrum of a poiyisotopic substance has been stlldied fw some time. (See Sukharev, Yu. N., Sizoi. V. F.. and Nekrasov. Yu. S., Org. Mass Spec.. 16, 23 (1981)andreferencestherein.)Early anempts to address this problem had the disadvantage of being limited in scope and in particular did not permit the calculation of isotopically enriched substances. Volume 59 Number 8 August 1982
663
carbon atoms in the ion can he calculated. Likewise, the number of chlorine atoms in a moleculelfraement can also be determined from the isotopic abundance iatio of 35C1P7C1 (3:l) and the relative peak intensities in the mass spectrum. The relative peak intensities of an ion cluster may be calculated from the ionicor molrcular formula and the-isotopic abundance ratios of the constituenr elemenw. This calculation rnrnils successive expansion of polynumials, each polynomial representing 1111e element of the ion~cor molecular formula.'.3 The natural lor enriched) isou~uicabundanres of each element are designated by a p o l ~ o m i hrepresentation in which the exoonent of each oolvnomial is eaual to the number of atoms of'that element in the formula. The computation of relative mass spectral peak intensities is governed by a statistical distribution of the isotopes of each element in a compound. The peak intensities resulting from combinations of any number of atoms of the same element can be calculated from the polynomial expansion2.3
Table Collected Polynomlal Expanslon Terms for Carbon Dlsulfide
Mass
Polynomial Expansion Term
Value of Polynomial Expansion Term
Normalized Value of Polynomial Expansion Term
12C3ZS32S
a042
0.8925
10000
12c32s33S
2a04bf a,bo2
0.0100
isotopic Composition
76 = M 77=M+1
'3C32S3ZS
0.0143 0.0243
2.72
78=M+2 '2~32~3'~
2aobob2
'2C33S33S
gob?
'3C32S33S
2atbobl
0.0793 0.0001 0.0001 8.91
0.0795
( a o + a l + a z + . . .)m where the terms an, .. a,, .. a?, . etc.. reoresent either the natural or enriched relative isotopic ab"ndances of the element, and the value of the exponent is the number of atoms of that element found in themolecule. Combining all elements present in the molecule, the polynomial expansion becomes (ao
+ n l + az.. .Im(bo+ br + bz.. .)"(co + c1 + c 2 . . .)P .. .
where each polvnomial exoression corresoonds to a different element. ~ i c h t e r mprodiced by the expansion is collected according to its contribution to a oarticular mass within the cluster OFisotopes. A simple example will serve to illustrate the above description of the use of a polynomial expansion to calculate isotopic abundances in mass spectra. Carbon disulfide has six naturally occurring isotopes, 12C,W, 32S, 33.5, 34S, and 3%. Let a0 and a l represent the isotopic abundances of '2C and 13C, respectively, and let bo, bl, bz, b3, and b4 represent the abundances of the consecutive masses of the isotopes of sulfur. In the polynomial expression for each element, the natural isotopic shundances of' all mass units hetwwn the isotopes of lowest and highest mass must he represented. Since'"S does nut occur naturally, the value of b:, is set equal to zero. Using these desienntioni. the oolvnomial exoression from which mass spec&al peak'intekitiks of the molecular ion cluster of CS2 are computed is given by:
+ b l + bz + ba (a0 + a~)(bo
+ bd2
Expansion of this polynomial gives an isotope abundance proportional to the value of aob; for M, the peak of lowest mass (mle 76) in the molecular ion cluster of CS2arising solely from molecules of composition 12C32S32S.Both 12C32S33S (2anbob,)and '3C32S32S (a, bff)contribute to the intensitv of the.^ t 1 peak at m/e 77. These and the remaining makes that comprise the molecular ion cluster of carbon disulfide. together kith polynomial expansion terms representing the particular isotopic compositions which comprise each mass, are listed in the table. The values of the polynomial expansion terms were calculated using 0.9889 and 0.0111 for the natural abundances of 12C and '3C and 0.9500, 0.0076, 0.0422, and
Mclafferiy,F. W.. "Interpretation of Mass Spectra," 2nd Ed.. W. A. Beniamin. Inc.. Readina. MA. 1973. ~resweli.C.J.. ~un;;;ist.'o., and Campbell. M. M.. "Spectral Analysis of Organic Compounds," 2nd Ed., Burgess Pub. Co., Minne-
aoolis. MN.- 1972 - - - ~ , ~ ~ ~ , 'Weast. R. C.. (Editor)"CRC Handbook of Chemistry and Physics." 55th Ed.. Chemical Rubber Pub. Co., 1974. 664
Journal of Chemical Education
0.0002 for the natural abundances of 32S, 33S, 34S, and 3%. Terms containine bl eoual zero and are not included in the table, nor are te- ck&ibuting to mle 81 through 85, because their computed abundances are insignificant. The last column contains the relatiue total values of the collected polynomial exoansion terms which contribute to each mass value. These numbers, of course, are directly related to the relative intensity of each mass spectral peak.
The Program Polynomial expansion and collection of terms is accomplished in loops; two one-dimensional arrays are employed to handle the products of the polynomial expansion and the collection of the terms. Array 1holds a set of terms beloneing to the isotopic abundances of the first atom as they are m u c tiplied by the set of isotopic abundances belonging to the next atom. The product terms are entered into Array 2 where they are summed with those terms with which they have a common mass. Many organic and organometallic molecules contain large numhem of carbon and hydrogen atoms. In order tnsave array space, the terms corresponding to the binomial expansion of more than two carhoi and two hvdroeen ~"~atomsis accomplished prior to the main expansions by expanding (0.98893 0.01107)" for carbon and (0.99985 0.00015)" for hydrogen. These numbers derive from the fact that 0.98893 is the natural abundance of 1% and 0.01107 is the natural abundancce of I3C; 0.99985 and 0.00015 are the natural abundances of 'H and 2H, resoectivelv. The binomial for carbon is expanded only throuih the fourth term since further expansion produces terms that are statistically insignificant for a mass range up to 1000; the hydrogen binomial is expanded through the second term for the same reason. The tables of elements and isotopic ahundances are read in as pairs of card images a t the beginning of the promam. Each~elementcard contains the &omir'numhe;, aiomic symbol, lowest isotopic mass, and numher of isotopes. The atomic number is not read in, but rather serves to index the cards. Elements 1 through 83are included, excepting Pm and Tc. The isuwuicahundance cards contain the natural ahun~~dances of the e l e m e n t ~ The . ~ last three pairs of cards are dummy elements, XX, YY, and ZZ, which represent elements that are isotopically enriched.
.
+
~
~
~
+
~
~
~
~~~~~~
~~~~
Figure 2. The computed mass spechal peak intensities for the molecular ion cluster of iron pentacarbonyl with (a) naturally occurring isotopic abundances. (b) 100%-S7Fe. and (c)92%-S'Fe. Figure 1. A comparison of (a) the computedand (b) the observed highest m/e fragment ion cluster in the mass spectrum of tetraphenylgermane. (C&&Ge.
Natural isotopic abundances cannot be used for an isotopically enriched element. Thus. it is necessarv to calculate new ibundances, correcting for the amount of knrichment. T h e revised abundances are calculated in a subroutine of the program called ENRICH, and stored in the two-dimensional array for abundances (ABUND) a s the ahundances of the dummy element. These abundances are then the ones used for the enriched elements during.the . ~olvnomial ex~ansions . of the main program. T h e Fortran IV program presented here consists of 179 statements and 93 comments. T h e program was run via a Datamedia 1520 graphics terminal, on an IBM 370, using a WATFIV compiler; object code = 7272 hytes, array area = 7320 bytes. The program calculates the relative peak intensities of any molec~daror fragment ion and displays them graphically as a bar graph resetnhlinga mass spectrum. Data for the Drogram is given as a molecule. or fraement thereof. composed of any cimbination of elements & the periodic table, of which up to a maximum of three may be isotopically enriched. Available documentation includes listing, sample usage, and sample execution. Copies of the listing and documentation are available free of charge. Results T h e following examples briefly illustrate typical program output simulating mass spectral isotopic clusters; where
possible, comparisons have been made with published mass spectra. Tetraphenylgermane. The spectrum of tetraphenylgermane has a prominent cluster of peaks between mle 301 and 308. A comparison
of the authenti* spectrum of tetraphenylgermane with the computed spectrum of the fragment(PhsGe)+(Fig. 1) is consistent with the fragmentation of (PhrGe)+to (PhaGe)+. Iron Pentacarbonyl. Iron-57 is frequentlythe isotope of choice for studies requiring isotopically enriched iron. Shown in Figure 2 is the spectrum of iron pentacarbonyl in three stages of S7Fe-enrichment. Iron-56, with 91.66%natural abundance, is responsible for the principal peak (mle 196)in the molecular ion region of Fe(CO)s,while 57Fe makes a small contribution with 2.19% natural abundance. The small peak at mle 194 is due to the 5.82%natural abundance of MFe.Iron-55 does not occur naturallv: a contribution (too small to be revresented graphically)at mle 195-isdue partly to the contribution ofW2 to the (M I)+ oeak of mass 194. ~-~~~~~~ The contrihutinns nf 54Fe and SaFe m e seen to k bminished when FetCO)
