AN ANALYSIS OF OPTICAL AND ELECTRON SPIN RESONANCE SPECTRA OF METAL-MINE SOLUTIONS Thesis for the Degree 0% M. S. MICHIGAN STATE UNIVERSITY Jay Dean Rynbrandf I 966 L1Le chemical Species (9,1o). for this re" on the chemistry oi'tne peeies will be fire con red ind' " three with 3 Table I. Absorption Laxima of Retals in Amine Solvents. Temperature Absorption Cell Path Solvent hetal OC tax. mp Absorbance Length mm Reference NH3 Li -70 1300 2.h3 0.1 (11) Na ~62 thO 2.57 1.0 (ll) K -71 1&80 0.1 (11) CS 1530 (51) 01131113 Li -55 1320 0.73 0.1 (11) Na -h0 650a (3) Na -30 650 0.15 1.0 (11) Na 690 (12 ) +20;;NH3 Na 690b (12) 1320 +u0zNH3 Na 1250 (12) K -67 660 1.0 (ll) 800 K 650a (0) Us 650a (8) Ca ~60 1280 0.3 0.1 (8) CH3CH2NH2 Li ~u0 1u20 2.11 0.1 (11) Li RT 1300 1.3 0.2 (10) 700 Na 680 (12) +301NH3 Na 700 (12) 1300 +50%KH Na 1250 (12) 3 Table I. Continued. Temperature Absorption Cell Path Solvent Metal OC flax. mp Absorbance Icngth mm Reference tH30H2112 h ~6u 650 1.66 (11) K RT 675 1.2 10 (10) Rb RT 930 1.6 10 (10) 630 Rb ~80 650C 0 10 (10) Cs RT 10h0 0.8 10 (10) 710 1300 Cs ~80 675C (10) 9b0 NH2(CH2)ONH2 Li RT 660 0.9 (13) ° 1280 1.2 Na. RT 660 2.0 (13) 1280 0.03 Na RT 670d (1h) Na 650 1.5 1.0 (15) K RT 8h; 0.1 (13) 650 1300 K RT 660 1.0 (13) 8&0 1300 K 670d (1h) K 650 1.0 0.1 (15) 800C 0.8 Rb RT 890 1.0 (13) 1280 0.5 6506 Table I. Continued. Temperature Absorption Cell Path Solvent ketal ‘C flax. mp Absorbance Length mm Reference NH (CH ) NR Rb ' 700 1.3 0.1 (15) Rb 700f 0.7 0.1 (15) 900 0.1 Cs RT 1030 1.35 0.1 (13) 1250 Cs RT 1280f 0.1 (13) NH20H(Me)CH2NH2 Na RT 600d (11) K RT 670d (11) 870 (la) a Limited to visible region b Absorption maxima listed in order of decreasing magnitude unless otherwise noted c Samples diluted by decomposition d Limited to below 1000 mp e Seen only after some decouposition f After some decomposition emphasis on the trends among the various metals and solvents. l. The IR band. This is the only Optical absorption seen in metal- ammonia and metal-deuteroammonia solution (16). This absorption has been shown to obey Beer's law (17-19) and to have a temperature dependence of --1}_L.3cm"']-deg"l (16) in deuteroammonia and aslightly lower value in ammonia (18,11,20). However Burrow and Lagowski point out that ammonia possesses an intense absorption band at 1532 mp which may cause the ammonia results to be somewhat ambiguous (16). An IR absorbing species is produced when pure ammonia, ethylamine, prepylamine, ethylenediamine and 1,3 propanediamine are exposed to short pulses of high energy electrons (21). This IR absorption in ethykenediamine has the same shape in the region studied as the IR band for metal solutions in this solvent (22,13). When fresh or faded metal solutions in ethylamine were flashed with pulses of high intensity light, an immediate increase of the IR absorption was noted (23,2h,10). The IR band tends to become more predominant relative to the V and R band absorptions in better solvents for ionic Species. The ESR hyperfine splitting appears to correlate with solubility in the larger alkyl amines showing the greatest hyperfine Splitting, lowest IR absorption, and lowest solubility (25-27). The metal used also affects the relative size of the IR band. It is predominant in fresh lithium solutions and becomes less predominant as the metal solubility decreases in the order Li) Cs) Rb) K) Na. Dewald's work with cesium and lithium in ethylenediamine indicated that the cesium IR band decomposes more slowly than the R band, and that the lithium IR band is less stable than the V band (22,13). The IR absorption band is attributed to the solvated electron. ESR results indicate that in fresh, saturated solutions of the larger alkyl amines the electrons probably exist primarily as the paired species (28,29). A possible pairing reaction is 28- 3 -- o (2) The low dielectric constants of the amines would also tend to favor ion pairing of the electrons with metal cations (9) according to 82-.- + 2II+ = 114.082-- 4- In? 3 bid-082--.}? O (3) Alternatively, the paired species might exist as ion triples and quadrupoles. The presence of different absorption bands indicates that the electrons can also interact in other ways with the metal to give rise to species not present in ammonia. 2. The R band. This absorption is observed only in amine solutions of potassium, rubidium and cesium. The absorption maxima for these metals in ethylenediamine at room temperature occur at 8&0, 890 and 1020 my respectively and at 910, 930 and th0 mp in ethylamine (22,10). The similarity in temperature dependence of the band maximum, -ll.3 chl deg”l for cesium and rubidium in ethylamine supports assignment of the R band to the same chemical species for the different metals (10,9). It is generally agreed that this species is dimeric (9,10). The peak positions of potassium, rubidium and cesium in ethylenediame correlate well with the intense IZIu‘“ 12:g transitions of gaseous dimers listed in Herzberg (30,9). However the potassium R band absorption in ethylenediamine occurs at a higher energy (8&0 mp at room temperature) than the dimer transition in the gas phase (860 mp) (30,9). Solvation would be ex- pected to lower the energy of this transition. The position of maximum absorption shifts to even higher energies as the temperature is lowered (10). 'work in this laboratory (31), indicates that the absorption should probably be assigned to the 11T‘*‘1£Ig transition. In the gas phase dimers, this is a comparatively narrow absorption occurring near 660 my in rubidium and 770 mp in cesium. This absorption is presumed to broaden and shift to longer wavelengths as a result of solvation. Dye and Dewald,using thermodynamic arguments, have predicted the concentrations of metal dimers in ethylenediamine using the rubidium concentration and absorbance as a standard (9). These calculations agree well with the observed absorbances and indicate that lithium and sodium solutions should have no R band absorption, in agreement with experiment. Less polar amines seem to favor this band. It is also more predominant at high metal concentrations. The cesium R species sppears to be the least stable of those giving Optical absorption; in decomposing cesium solutions in ethylenediamine, this band decays most rapidly (l3). 3. The V band. The behavior of this band (650-750 mp) is somewhat paradoxical. Its presence or absence is dependent upon the metal used but the position of its maximum absorbance is only slightly - if at all - metal dependent. It is not observed in metal-ammonia spectra but is more prominent in strongly solvating amines than in the less polar amines. When compared to the relative intensity of the R band, the V band is favored by low temperatures and by dilute solutions where these tests have been made (13,22,10). Under similar conditions, the lighter alkali metals 10 favor the V band in comparison with the R band. Tuttle and coaworkers found that in decomposing solution, the ratio of the square of the V band absorption to that of the R band was constant for solutions of both potassium and rubidium in ethylamine (32,2h). The relative intensities of the V and R band were not however, reproduced in regenerated solutions (32). A graph of lOg absorbance at 650 mp versus the lOg absorbance at 850 mp for the data of Tuttle and coaworkers showed a SIOpe slightly greater than l/2. Data obtained in this laboratory, when plotted on the same graph, had a lepe of nearly one (25,29). The non- reproducibility of the decomposition data indicates mainly that these results are not good criteria on which to base prOposed models. The quali- tative dilution observations remain useful however. A correlation between the V band Optical absorption and the ESR signal in a decomposing potassium ethylamino solution, along with other ESE studies in mixtures of amines and the Optical decomposition results, have led Tuttle and co-workers to con- clude that this absorption is due to a Becker-Lindquist-Adler monomer (33,32,28). In this laboratory, using reference standards of known spin concentration, it has been shown that there is no correlation between the number of spins in the potassium hyperfine pattern and the V band Optical absorption (25,29). h. Interconversion studies. Studies of the interconversion of different Optically absorbing species have given interesting results. The absorptions at 660 mp and at 1280 mp in lithium ethylenediamine solutions decayed at different rates.CL3). The IR absorption decayed more rapidly and, when it had disappeared, the decay rate of the V band increased (22,13). The decomposition rate of the sum of the V and IR band absorbances was continuous implying that the IR absorbing species acts as a buffering agent for the V Species (13). In another study, a lithium ethylenediamine solution showing only V band absorption was removed from contact with its decomposition products. Tne V band continued to decay but as it did an IR absorption slowly built up and finally both peaks decayed (22,13). The slow interconversion of the lithium V and IR bands implied the breaking of a covalent bond. On this basis, an H2+.e', molecule-ion was prOposed as the V species (9). Recent flash photolysis studies by Linschitz and CO-workers (10,2h,23) of metal-ethylamine solutions over a range of temperatures and concentrations seem pertinent to the understanding of the interconversion of the V, R and IR bands, briefly these investigators flashed the solutions with light of known wavelength and then Observed the change in absorbance at various wavelengths as a function of time. Flashing at wavelengths below hBO mp initially gave rise to an increased absorbance in the IR region and a bleaching of both the V and R bands. Following photobleaching of the V band, a rapid second order build-up of the R species was noted. No ab- sorbance was observed in the region scanned (th—1000 mp) whose decrease matched the rapid build-up of the R absorbance. The increased IR absorption from this flash decayed at about the same first order rate as a second, slower, first order build-up of the R band noted in cesium solutions. The R species then decayed in a first order reaction to give the V species. The rate constant of the first order build-up of the V band (except for a fast initial build-up amounting to 10% of the total 12 recovery) is the same as that of the R band decay. The IR Species obtained when the R band in rubidium solutions was flashed behaved differently from that resulting from flash photolysis of the V band. This IR species decays in a rapid second order process which matches the build-up of the R band, implying that the two IR Species undergo different reactions as the system returns to equilibrium (10). III. EXPTQIHEHTAL Ah) RESULTS "a A. Optical and Electron Spin Resonance spectra. Lany data have recently been obtained in this laboratory from 33R and Optical studies of potassium solutions in ethylamine-ammonia mixtures and frnm s milar studies on other metal-amine systems. In order to extract additional information from these data and to process data in different ways, computer techniques were required. This section provides a background for the theories and methods used in these calcu- lations. While the author has participated in all phases of solution preparation, and in some of the measurements, this thesis deals primarily with the treatment of the ESR and Optical spectra. In addition, the construction of a new spectrOphotometer is described. Earlier publica- tions have described in detail the preparation of the solutions used (31:13:29). 1. Optical spectra of potassium solutions in ethylamine-ammonia mixtures. These spectra are strongly dependent upon the ammonia concentration. In agreement with the observation of Kraus (3S) potassium formed no blue solution in high purity ethylamine. At ammonia concentrations up to h.S mole percent, the V band is predominant with a temperature shift of ~11 cm"l deg"l. At higher temperaturesenki? to]1; mole percent ammonia, all three absorption bands were observed. The IR band is present in all solutions in this concentration range and the ratio of R to V band ab- sorption was very temperature dependent, again favoring the R band at higher temperatures. For example, at 15 mole percent ammonia and 25°C the 13 1h visible absorption appeared only as a shoulder on an intense R absorption and the solution showed strong IR absorption. However, at -38°C and below, the V band was the strongest absorption, the R band was not observed and only a small IR absorption was apparent. For the same temperatures, the position of the V band shifted to longer wavelengths with increased ammonia concentration. Comparing the sample containing h.5% ammonia with that containing 9.9% ammonia, this change was approximately h00 cm'l. The IR band became more predominant with higher ammonia content until in a sample containing 32.5% ammonia, both the V and R bands were absent (29). 2. ESR studies of metal-amine solutions. These studies have pro- duced much new information pertaining to these systems. Metal-ammonia solutions Show only a single narrow 33R absorption. host metal-amine solutions however give hyperfine splitting. Hyperfine splitting of an electron by a nucleus is related to the fraction of the time the electron spends at this nucleus. The change in hyperfine splitting with temperature and solvent composition provides valuable information regarding the nature of the hyperfine Species. ESR linewidths, g values and spin concentrations are also useful because they relate respectively to the relaxation time, the orbital angular momentum and the concentration of the unpaired electrons in question. Some ESR spectra of metal-amine solutions indicate that two or more species with unpaired electrons are simultaneously present in the solutions (29,36). The structure of the hyperfine pattern observed in lithium-ethyl- amine solutions is different from that seen for the other metals in this solvent. At room temperature a single ESR absorption is seen which at 15 -h000 converts to a nine line pattern with peak intensities suggesting Splitting by four nitrOgen nuclei (I = 1) (37,27). This pattern becomes clearer as the temperature is lowered and is well resolved at the freezing point of the solvent. Below the freezing point the nine line pattern converts back to a single absOrption (27). This nitrogen splitting in lithium solutions was first observed by Tuttle (28), but the low signal- to—noise ratio made it advisablet>o confirm this observation. In all other metal-amine solutions showing hyperfine structure, the splitting is attributed to a metal nucleus. Potassium solutions have been most extensively studied, particularly solutions of potassium in ethylamine-ammonia mixtures. At room temperature, fresh potassium-ethylamine solutions with low ammonia content give a well-resolved four line potassium hyperfine splitting pattern as seen in Figure 1. This observation was first reported by Tuttle and has since been confirmed by other investigators (28,29). The hyperfine Splitting value decreases markedly with increased ammonia concentration as illus- trated in Figures 2 and 3. A striking change in hyperfine splitting also resulted from changes in the temperature of given:samples. Between -60°C and 20°C the hyperfine splitting increased moderately with temperature but above hOOC the temperature dependence of the hyperfine splitting changed markedly as shown in Figure h. Extrapolation of 10g contact density versus l/T to infinite temperature gives a value close to that of the free atom (29). By considering the hyperfine splitting to‘arise from a rapid equilibrium between a species with the magnetic prOperties of free atoms and one or more species having a lifetime greater than the rotation time of a solvent molecule, the temperature and ammonia dependence of the hyperfine splitting 16 . n c . . .. e...u « - .moHMH firm nmmw xmm mom mtw repflm damp newsflem oEom cw hamper HHmkrm mo manomom mam .H masmmm genie... 633.70 6.3 .35. no 62.37.... 6.3 .263"... . Eamon"... 6.3. iii. it: i c 3 65.8 no 638.. u a 6.2 emcee. . .mmmmms us 6.8 .083"... 6mg? . a 6.3 all? 4? 3 7 i% a .0031... .8683 6.2 600.9,... 6309..."... 6.09 otoomue 69mm / wz_2domd mz_2<._>I._.m wz:>_<...>I._.ms_ 17 2.7% 9.6% 14% 24 k %\j 1 Figure 2. Qualitative ammonia dependence of the ESR spectra. (GAUSS) h.f.s. l8 h- r- p .- l l 1 1 l l 1 4 6 8 IO 12‘ J4 l6 I8 20 22 24 MOLE % NH, Figure 3. Dependence of the hyperfine splitting upon ammonia concentration. Triangles are for a temperature of 25°C; circles, for -h0°C. H.F.S. (GAUSS) l9 20 I 1 T l l Ifi O O - Figure 14. Temperature dependence of the hyperfine splitting. O , 1.2; , 2.7; , 5.8; , 9.6 mole % ammonia. O - 20 0 l6 - O O A 0 A ' o O. A O - I5 :2 - o . A D .69 M a O A . A W ‘ A If 019 A.“ _' 6? AAA - - IO 8 _ 0 AAA 0 plane E] 0 AA 0 AA . 0 AA fig .. 0 D o 0 AA mafia? O U > A D [@1965] 60': A A D D 69° " 5 4 ’ . D D - 990° ’ DD 0 w E] U D as - o . . o l l i l l I l 0 . 'IBO 'I40 'IOO '60 ’20 20 50 IOO TEMPERATURE (’0) HFS (°/. FREE ATOM) 20 could be quantitatively described. The prOgram used to separate the con- tributions to hyperfine splitting from an atom and monomer is described later. Along with the four line potassium hyperfine splitting pattern, at least one additional single line absorption was noted. In older potassium solutions with low ammonia concentration, the single line was quite narrow, centered near the free electron g value and related to the degree of decomposition. Symons and co-workers have observed an extra absorption in unsaturated solutions. The absorption of the Species they describe correlates with the intensity of the four line species and implies the equilibrium (36) h = h* + e“ . (h) This may well be the same species observed in this laboratory in saturated solutions of higher ammonia content. In solutions with 9.6 to lh.2 mole percent ammonia, a broad extra line was observed underlying the four line hyperfine pattern (29). Two prOgrams, (ESE FT and uBN.LS), were written to separate the observed spectra into contributions from the 39K and th hyperfine patterns and these from a broad single absorption. These prOgrams are described later in this section. At 33 mole percent ammonia, the hyperfine structure is no longer discernable. ESR spectra of rubidium-amine solutions are a superposition of hyperfine patterns from 85Rb and 87Rb as can be seen in Figure l. A narrow single absorption was also noted in these solutions. The hyperfine Splitting in many Rb amine solutions was large enough to warrant perform- ing second and third order corrections in order to Obtain the g value and hyperfine Splitting more accurately. 21 Amine solutions of cesium have the largest ESR hyperfine splitting and therefore also require second order corrections. As will be noted in Figure l, the linewidth of the eight line cesium hyperfine pattern shows marked dependence upon the nuclear spin, ml (26). Recent results in this laboratory indicate that the variation of linewidth with nuclear spin is greater in l, 2 prOpanediamine than in ethylamine whereas the hyperfine splitting value is smaller in l, 2 prOpanediamine than in ethylamine (27). An explanation and treatment of the variation of line- width is described later in this section. In addition to the hyperfine pattern, a single line was noted with a g value near that of the free electron. The magnitude of this line seemed related to the degree of decomposition as in the potassium solutions. B. PrOgrams and Results. All prOgrams described in this section were % itten in Fortran 3600 for use with the Hichigan State University Control Data 3600 computer. 1. PrOgram A M EQ. This prOgram was used to separate the hyperfine D splitting oi potassium ethylamine-ammonia solutions iito contributions from the atom, A, and two solvated monomeric species, B and C, which are considered to be :1 (sneak and M (stqu) 13:33). The fOllowing scheme XI. describes the equilibra involved: A ll EU I): ll (13)/(A) (5) B + NH3 3 C + EtNH2 Kl‘c) = ((0) / (and ~x> / x). in which X is the mole fraction of ammonia. The measured hyperfine splitting 22 A? is related to the concentration of these species and their reSpective .L splittings by .. O O O L- (nXA +niA +nA )/n (6) r I A D 5 n C U in which n - n + n“ + n . A s C If the solutions are assumed to be saturated, the concentration of atoms would be expected to vary according to ln (.1) = -AHO + A30 RT R x7) in which.AAH° and.‘ASO are the molar enthalpy and molar entrOpy of solution of the metal to give atoms. The strong dependence of AF upon temperature 00 indicates that the temperature variation of atom concentration above hO is much greater than that of the other two species. This permits an approximate separation of the Splitting due to atoms from that due to the species B and C by extrapolation of the low temperature behavior. The separation is accomplished by using the approximation 0 P. n.-\ = n (A1," 4140) / (A; - A110) , (o) I}, in which AVG represents the splitting expected to be observed in the .L'. absence of atoms and includes the contributions from species B and C 0 _ O Q r,‘ on L, + g . g ‘ AVG was obtained for the low temperature region by calculating a least squares line through the AF values as a function of temperature assuming no contribution from atoms to the observed splitting. The high temperature 23 value of Auo'was then estimated from a linear extrapolation into this r region. Using n calculated from Equation (3) as a measure of the A concentration of atoms, a least squares line was calculated through a g 1'70 .. "VO ' i1 ' plot of ln (nA) vs. 1 / T to eJaluate An and. AD in equation (7) with a standard state of one mole per liter. The points on this line were weighted to place greater emphasis on those for higher temperature which are less affected by errors resulting from the extrapolation of o . ,. . . . into this region. The atom concentrations in the low temperature A, l'l region were then calculated from the extrapolation of the high tempera- ture ln (nx) vs. 1 / T plot. These calculated atom concentrations were I then combined with the experimental splitting to give new values of AF0 J. using the expression A»? = (“A-:9 " “A AA) / (n - HA) (10) in the low temperature region. These new values of Aho'were extrapolated into the high temperature region and new values of nA were calculated. This procedure was repeated five times to give consistent results. These results are reported in Table II. Calculated and experimental Splittings are compared in FigureSa for a 2.7 mole percent ammonia solution. It is seen from Table III that the value of [50° is reasonably independent of ammonia concentration as are A H0 and 45° at lower con- centrations. This lends support to the treatment used, eSpecially in light of the large variation of AF and n with ammonia concentration. The average value of 130°, combined with the free energy of formation of the gaseous atom yields 1500 = ~S.2 kcal mole'l for the solvation process K (g) B K (solution) (11) Table II. Least-Squares 510pes and Intercepts from Computer Analysis of Atom-Lonomer dquilibria. Hole percent lucnomera Monomera Atomb Atomb ammonia SlOpe intercept lepe intercept 1.2 0.00277 9.5337 -hl92.3 h2.9h0 2.? 0.00765 7.7905 ~h928.2 h5.079 5.8 ~0.000u2 b.9918 -h601.9 uh.22h 9.6 0.00588 3.7188 -6512.h 50.663 11.8 0.01093 2.8h33 -7326.3 5h.285 lh.2 0.00709 3.0h27 ~7607.6 55.607 aThe lepes and intercepts given are for the linear function used to evaluate the contribution to the total hyperfine splitting arising from the concentration of monomers in solution. t is well to remember that the intrinsic splittings of the monomer and atom units may or may not be temperature dependent. bSlOpe and intercept of the exponential function used to evaluate the contribution arising from atoms in concentration units of spins per cc. The lepe and intercept must be multiplied by R to obtain the correct units. (GAUSS) H.F. S. TEMPERATURE (’0) Figure 5a.Separation of hyperfine sglitting into atomic and monomeric contributions, experimental; ‘ , , C81C'ilflt0d; __ _, monomer contr.; ----, atom contr. '5 I I I I I I 0 I4 .— . l2 ... O C C ‘ e C .. IO 0 C I .. o . o e .0 ”______ _ 8 ... .' . ———-'—"——— ~~~ .0 ’ - I I I, - 6 ’. I . I I I I I, " 4 ' I ’I X. I” 2 I” ’/ I ”” ” o I ....ai-g-fl‘” I I I 1 '50 '30 'IO ' I0 30 5O 8 .70 9O Table II . ThUI'IIlOdynaflllC Parameters for Solvation of the Gaseous Potassium Atom. Parameters of Eq. 7 hole percent A H0 A S0 AGO (25°C) ammonia (kc a1) (cal/degree) (kcal) 1.2 8.3 ~9.3 11.2 2.7 9.8 ~S.S 11.1.1 5.8 9.1 -7.2 11.9 9.6 12.9 5.6 11.3 11.8 lu.6 12.8 10.8 111.2 15.1 15.11 10.5 26 27 using standard states of 1 mole / liter for both the gas and the solution. Results for the three lowest ammonia concentrations yield AHO = -l2.LI kcal mole ‘1 and A80 = -2h.2 cal mole"1 deg‘l for this process. Because of the limited studies above ambient temperatures at higher ammonia con~ centrations and possible unsaturation of the solutions, the values of A110 and A30 especially in the high ammonia region, are subject to con— siderable uncertainty (29). 2. PrOgram K 35R. The ESE spectra of potassium in ethylamine-ammonia mixtures between 9.9 and lh.5 mole percent in ammonia were difficult to interpret because of overlap of a four line hyperfine pattern with a broad extra line (29). To be certain that the pattern did not simply result from broadening of the hyperfine lines, a prOgram was written to calculate and plot the expected spectra for a given splitting value as the lines broadened. This prOgram could use both Gaussian and Lorentzian line shapes and in- cluded the pattern from both 33K and th. Neither line shape could give spectra similar to those observed. The problem was then one of separating the observed spectra into contributions from a single and a four line pattern. A prOgram, K ESE, was written to generate a spectrum which would duplicate as closely as possible those observed and is described and listed in the appendix. An observed spectrum was read into the computer as a series of X - Y points. Using initial estimates for splitting, g value, linewidth and intensity parameters, the computer calculated a com- posite spectrum. The parameters were then adjusted individually until the sum of squares of the deviations from the observed spectrum was minimized. Each time a parameter other than intensity was changed, the intensity was adjusted to give the best fit. During adjustment of one parameter the 28 contribution of the other pattern was kept constant. The relative in- tensities of the two patterns depended on which was adjusted first. After approximately fifteen iterations however, the relative intensities reached values which were in most cases nearly independent of the order of adjust- ment. Table IV lists the results obtained when various spectra were fit using this pregram with Gaussian shape functions; FigureSb illustrates the type of pattern fit and the degree of fit obtained. If more spectra were fitted.‘ by this method, a new pregram should be written similar to IR, FIT, to be described later. This shorter and more flexible prOgram has the advantage of permitting independent adjustment of intensities. By adjusting the intensities of both patterns from the start, the other para- meters would not be forced to compensate for the initial absence of one pattern. The other parameters could then be adjusted and, would presumably converge more quickly to the best value. 3. Program GEN LS. many of the problems resulting when the parameters were individually adjusted, were eliminated by using the method of generalized least squares (38,39) to fit the Spectra. This method is more rigorous, more accurate and requires less computer time. The prOgram, GEN LS, utilizing this method requires the same kind of information described pre- viously. The pr0gram,described in detail inthe appendix, uses matrix techniques to find corrections to the estimated parameters. The matrices are generated from partial derivatives of the spectral function evaluated at each point being considered. The corrected parameters are then used as new estimates in repeated cycles. Usually constancy better than the precision of the data is reached after three iterations. There are, Table IV. EPR Parameters of hfs Pattern and Extra Absorption as Obtained by Computer Analysisa, Using PrOgram K ESE. Temp . AF A H (hf s ) A H (extra nextra/ r1hfs absorption) (00 (gauss) (gauss) (gauss) Sample K-l2 5.8 hole percent ammonia ~38 5.08b 1.25b -72 b.2hb 1.17b Sample K—ll 9.6 mole percent ammonia ~7 3.76b 2.11b 2.1b 2.31b ~15 3.66 2.18 10.3 1.28 3.66b 2.18b 10.2b 1.27b -hl 3.2h 1.76 12.7 h.9h 3.23b 1.8LIb 11.8b 3.35b Sample K-25 9.9 Role percent ammonia -8 3.52 2.63 9.27 1.7h 3.52b 2.6hb 9.2ub 1.70b -35 3.39 2.5h 8.83 1.78 ~68 2.97 2.2h 7.87 1.88 2.97b 2.2LIb 7.85b 1.73b Sample K~10 11.8 hole percent ammonia ~12 2.7h 2.31 6.83 h.81 ~h2 2.36 1.97 5.9 6.h5 -75 1.89 1.h8 n.69 7.78 29a PO \ C Table IV. (continued) Temp. AF A H (hfs) A H (extra ne)r_1‘.ra/n}'-.fs absorption) (00) (gauss) (gauss) (gauss) Sample K-9 lh.2 hole percent ammonia -10 2.9L; 2.50 7.85 14.77 '11]. 20514 2.16 6051 1‘03]. -69 2021 1077 5068 3.19 3Spectra were fit by the superposition of two absorption patterns. One of these was the Gaussian hyperfine pattern arising from electrOnic interaction . 39 __ 141 . , , A . , . . _. . With the K and K nuclei. Tne other Was a Single absorption 01 Gaussian shape. The routine alternately adjusted the parameters for both of these patterns. Except as noted, initial adjustment was made on the single absorption. 0The hyperfine pattern was adjusted first. 3O I I 1 I I I 1 I I p — O Q ." ‘\ I \‘ I. I" ‘~" I I \ ’0 \ I \\ i \ ' x .' \ ' \ I- I ‘ 1 \ l \ l \\ l I \\ f ‘ - I \ ' \ >4 1 \ ’ g: l .\ E:- l \ "J I E: I ‘s‘ .4 -.. _ I ‘ H I “~ £2“ “ g 5 _ a; Ho 3/ an. A) Computer analysis of BBB pattern. Observed spectrum at -h2°C for l‘.8 mole 1monia is the solid line. The calculated superposition of a hyperfine pattern and a single line is given (displaced vertically) by the dotted line. The difference (obs - calc.) is shown by the solid line in the center. 31 however, two disadvantages involved in using this method with a computer. First, it requires that one take the partial derivatives of the function representing the spectrum with respect to each parameter being adjusted. This makes it difficult to adapt the pregram to new functions. Second, the initial parameters must be known more accurately than for the prOgram which adjusts each parameter individually. The parameters obtained for each spectrum using the prOgram K ESE were used as the initial estimates for pregram GEN.LS. The results using this method generally agreed well with those obtained earlier. Those cases which had yielded two sets of parameters depending upon which pattern had been adjusted first now converged on the same set of parameters from either starting point as seen in Table V. These parameters are considered to be more accurate than those given in the previous Table. A striking correlation was found between the linewidth of the extra line and the hyperfine splitting of the four line potassium pattern as illustrated in Figure 6. The correlation was much better than that between the linewidths of the two patterns shown in Figure 7. The linewidths and Splittings in these Figures are in arbitrary units. The implications of this correlation are not yet fully understood. h. PrOgram POLY FT. A detailed theoretical treatment based upon the McConnell model (50) of an asymmetric species has been derived by Kivelson (h?) and co-workers to describe the variation of linewidth with nuclear spin, mI. On the basis of this model, the variation of linewidth with mI seen in Table V. EOE Parameters of hfs Pattern and Extra Absorption as Obtained by Computer Analysis, Using PrOgram GAE IS. Temp. AF A H (hfs) A H (extra nextra I1hfs . absorption) (“0) (gauss) (gauss) (gauss) Sample K-ll 9.6 Lolegpercent emkonia -7 3.76 2.36 10.13 1.03 ~15 3.66 2.32 9.65 0.90 -31 302h 2003 ‘073 1.61 ‘67 2058 1065 6.7b 1.50 oample K~LS 9.9 Role percent ammonia ‘35 3.39 2°58 8.59 1.67 ~68 2.97 2.25 7.73 1.61 osnple K-lO 11.8 hole percent ammonia "12 207 2036 6079 h.b8 ~L2 2.36 2.01 5.96 6.27 ~h6 2.h5 2.1L 6.07 b.92 ~75 1.89 1.116 mm 8.52 ~36 1.81; 1.38 h.50 3.71; Sample K-9 lh.2 hole percent ammonia ~10 2.96 2.55 7A5 11.63 --'.;1 2.511 2.18 6.116 11.21 ~69 ' 2.21 1.79 5.611 3.05 32 ”PM _,. -1 03 I I l l l l l .— Q A o - <:> _- O p. _ Q ~.. 0 ‘9. O O -‘Q 00 ' c) 55 r _ ’ A _ O U Qq O l . (3 ZS ‘; 1 I 1 l l l 1 l 37. 4J 4&5 4&9 53 I/T XIO" jFigure 8. variation of the coefficient of m1, (CO) with l/T: Cs in ethyiamine, Results are shown for three different sample preparations. (GAUSS) CI 0.5 0.4 - 0.0 l l 5.3 3.7 Figllre 90 4.l Variation of the coefficient of mI, Dnenl is are shown 1‘ 1 4.5 l/T x lo“3 I '31—- three different 9 .~ ...1 - 21mm"; nrenaratiOnS. (Cl) with l/T: Cs in ethylamine. A Md .7 ..- Iii < anV C2 (GAUSS) OLSC) 38 (Df46 0.42 1 0.38 _ 0.34 - 0.30 _ DL 1 1 J l l 1 1 3.5 3.9 4.3 . 4.7 an l/T x|0+3 Figure 10. Variation of the coefficient of mi, (02) with 1/1‘: Cs in ethylamine. Results are shown for three different sample preparations. C3(GA USS) rz9 J (100 . . . . 1 u r . E 2 -4101- E] I E] -0.02 2 O E] C) _ 8 A A D O . A “0.03 "" 8 z; -C> ' A -()()4. 1 1 1 A} 1 1 1 I ' . 37 41 45 was I/Txlo+3 Figure 11. Variation of the co ffioient of mi, (C ) with l/T: Cs in ethylamine. - ‘ .1. Results are shown fir three different sample preparations. pregram has been used to find a function capable of fitting the IR peak with the minimal number of parameters. It seems to require at least four parameters to describe this absorption; they relate to the center (C), the intensity (I), the width (J) and the asymmetry (S) of the peak in question. Approximately ten Gaussian or Lorentzian functions with different asymmetry preperties have been used in attempting to fit the curve representing the absorption. This curve was plotted on the basis of either a wave length or wave number scale. In both cases the function Absorption ( A or'g ) = I (l + 3°R) / ( l + (R/WZ) in which R = ( A or'5 ) - C, gave the most satisfactory results. The degree of fit in the region of interest is nearly identical for the wave length and wave number fit, with agreement within 0.02 of an absorption unit for a peak with a maximum.absorption of one. Of course the constants required in the two representations are different. 6. Pro rem 600 00. Perturbation methods are usually used to treat the hyperfine Splitting of electronic energy levels resulting from contact with atomic nuclei (L0). The magnetic field, H , at which the transition 0 would occur in the absence of the perturbation is given by (hl) H = w + Aom + A2 '(I ’I + l) - m2) / 2F + i3 / hH 2 (13) ‘ ‘Hn ' \ fin ‘ In in which Hm is the observed field position for the hyperfine component with nuclear spin quantum number m, I is the total nuclear spin, and A is the hyperfine splitting. In this Equation, the perturbation treatment is carried through third order. Because of the large values of A for rubidium and cesium in amines, these higher order corrections are required and the hl hyperfine splittings cannot be taken directly from the spectra. A pregram, 858 00, described and listed in the appendix, was written to make second and third order corrections to the peak positions and from these to calculate hyperfine splittings and g values. This pregram cal- culates the quantity HO - Am by subtracting the second and third order contributions from the observed field position. This calculation for various values of m can be used to evaluate Ho and A. The process is repeated until constant values are obtained. The center of the spectrum, H0, is taken as the average Of values calculated for each peak using Equation (2). Finally the g value is calculated from the expression (LE) 5 = hV/flHo (it) where h is Planck's constant, ‘9 the klystron frequency and ,6 the electronic Bohr magnetono, C. A New Variable-Temperature SpectrOphotometer. The desirability of measuring Optical spectra under conditions used for ESR measurements prompted the construction Of a temperature controlled Optical cell compartment. Previously it was necessary to attach an .ainco Optical cell to the ESR tube. Difficulty in cleaning the sample tubes, the large surface to voane ration of the Optical cells and the cumbersome temperature control unit restricted the measurements which could be made. Obviously, if the ESR tubes themselves could be used for Optical measure- ments over the entire ESR temperature range, some Of these problems would be eliminated. The stopped—flow system assembled in this laboratory (h3) employing h2 a Perkin-Elmer model 108 rapid scanning monochromator was adapted to take static spectra by replacing the flow cell with a temperature controlled cell compartment which held the ESR cells in a fixed position. The mono- chromator, using a fused quartz prism, is able to scan the spectral region from 0.2 to 12.5 p.with apprepriate light sources. TO date this instrument has been used over a range of 0.h to 1.1 p with a Bausch.and Lomb tung- sten-iodine source. A stacked mirror beam splitter, with apprOpriate focusing mirrors, divides the emergent light from the monochromator into twO beams and focuses the slit image approximately 8 cm from the mono- chromatcr. After passing through the sample and reference cells, the two light beams strike photomultipliers whose anode current output is fed into a Philbrick differential amplifier and leg circuit rendering output voltages hich are prOportional to absorbance from 0.01 to 2.0 absorbance units. A Textronix type 56h storage Oscillosc0pe, with types 2A63 differ- ential amplifier and 35h time base plug-in units, recorded the spectra. The spectra were photOgraphed with a C-12 camera attachment using Polaroid type lhé-L red sensitive film to give transparancies with good contrast between the spectrum and background. In order to insure that the horizontal positions on the screen during successive scans would represent the same wavelength, a triggering circuit was devised which fired each time a slot in a rotating sector disc within the monochromator allowed light from a small neon lamp to strike a cadmium sulfide photocell. The principle difference between this spectrOphotometer and that used in the flow system is the temperature-controlled cell compartment. This unit employs a Varian V-LSS? Variable temperature accessory as the temperature controller. It Operates by heating a stream of precooled LLB nitrogen to the desired temperature with s ability sufficient to maintain a4: 100 maximum temperature variation at the sensor. Two thermocouples were placed at the bottom Of the cell compartments as a added check on the temperatures. This was necessary because the sensor is approximately two inches from the samples and because of the comparatively large spaces which required cooling. The sample and reference cell compartments can accommodate either conventional one centimeter Optical cells or round ESE cells. In order to position the round ESE-Optical cells reproducibLy, the cell holder illustrated in the appendix was designed. A point, groove and plane locating system for the cell holders proved to be quite functional. When the cells were in these holders, their position could be adjusted to allow prOper alignment in the light beam. Quartz rods were used to connect the cell holder to the adjustment system. The low coefficient of thermal expansion of quartz minimizes changes in the cell position with changing temperature. The quartz rods were attached to the upper and lower cell holder plates with epoxy cement. The point, groove and plane of the locating system for the cell holder were set as far as possible from the cell compartments to lessen the effect of any distortions in their positions as the temperature changed. The cell compartments and light tubes were constructed Of black Plexiglas to reduce light and heat leaks. Double windows were required to keep the cold nitrogen gas in the cell compartment and to prevent frosting. The centers of thick pieces of black plastic were drilled out to make the light tubes. Originally quartz flats (American Thermal Fused Quartz CO.) were sealed with epoxy cement to the ends Of the light tubes. Upon cooling, the inner quartz flats cracked because Of the difference in the thermal expansion coefficient of the quartz and Plexiglas. Next a plastic bracket screwed to the main body bl; of the light tube was used to press the quartz flats and a thin Teflon gasket to the tube body. When this unit cooled, the windows frosted even though dry nitrOgen was blown into the light tubes during assembly. The moisture may have entered the light tubes when the cooling lowered the pressure inside the tubes and impaired the sealing quality of the Teflon. The frost was eliminated by blowing a small stream Of dry nitrogen through the light tubes while the temperature controlling unit was in Operation. If this unit were to be rebuilt, it would be advisable to substitute evacuated one-piece quartz or quartz faced light tubes for those now in use. When conventional one centimeter Optical cells were used in the spectrometer, good spectra were Obtained. However when the solutions used in the one centimeter cells were transferred to round ESE-Optical cells, certain anomalies in their spectra became Obvious. The problem was elimin- ated by carefully masking the fron side Of the cell holder to prevent light from striking the side Of the round cell and being refracted around it without having passed through the sample. A one millimeter slit positioned in front Of and very near the sample provided the desired masking effect. IV. CONCLUoICES The computer prOgram, A M 3Q, has permitted the equilibrium model to be tested quantitatively. A satisfactory description Of the dependence of the hyperfine splitting and spin concentration on temperature and ammonia content has resulted. Although stationary—state models can qualitatively describe the nature Of this dependence, they have not yet permitted a quantitative description Of the ESR results. Symons and co—workers have recently prOposed an additionalenuilibrium.with dia- magnetic species to explain the broadening Of the four-line potassium pattern with increased cation concentration (36). The appearance Of a broad extra absorption underlying the potassium four line hyperfine pattern in ethylamine-ammonia mixtures between 9.9 and lh.S mole percent ammonia has been confirmed by a quantitative fit of the spectra. The surprising correlation between the linewidth Of this extra absorption and the hyperfine splitting Of the four line pattern strongLy suggests that the species giving rise to the broad extra absorption is also interacting with one or more metal nuclei. It should be noted that the spectra analyzed by the computer were in the low-temperature range. At these temperatures atom concentration predicted by the equilibrium model is negligible. The factors which influence the width Of the extra line are therefore those which also influence the monomer hyperfine splitting. The change of the linewidth Of the extra line into the higher temperature reiion Should be examined to see whether the presence of atoms destrors b i 1:5 L‘ " 0\ this correlation. both of the fitting prOgrams devclOped are useful in synthesizing spectra for comparison with experiment. The IR FIT type which adjusts each parameter individually is very easily modified for use with different functions. It can be used effectively to develOp and test fitting functions or in cases where only a few spectra are to be analyzed. Where many "imilar spectra are to be treated, prOgrams Of'fhe GEN LS type take less computer time and are probably more accurate. If some of the parameters to be used in fitting the Spectra are not reasonably well known, the generalized least—squares method may not converge. In such cases a combination of the two types Of prOgrams Should be a pow rful technique. The least well known parameters couldbe adjusted individually before they were all simultaneously corrected. The ability to Obtain data not otne~wise accessible suggests that this method would be useful for other systems where merger Of several patterns makes analysis difficult. The second order correction program, 533 CC, illrstrates the use Of .\ computers in efficiently treating large quantities of information. Over _¢ ( two hundred sgectra have been treated with this prOgram. It is difficult at this time to draw any definite conclusions from the dependence of the cesium linewidth on ml. It can only be said that the major contributions to the linewidth come from the coefficients Of the zero and second-power terms in the polynomial and that these co- efficients showed more consistency from one sample to another than did the other two coefficients. The new temperature-controlled spectOphotometer enables us to measure Optical Sp ctra on all solutions used for ESE measurements, pro- vided the absorbance is small enough. The conditions present when doR meaSurements are made can be duplicated in this instrument. As the description of netal—amine s lutions becomes more quantitative it will be increasingly necessary to correlate results from different areas Of Stddy. This instrument sdould prove to be a valuable asset in Obtaining data for "orrelation of optical and d3“ spectra. LI- ‘ I THE V QAKD F# C.) V. A LODJL There is general agre ment among workers in this field on the assignment Of the species giving rise to the IR and R absorption bands as has been discrssed in the historical Section. The temperature de- pendence of the hyperfine Splitting is adequately explained by an equilibrium between atoms and monomers. This section will deal with the species givinv rise to the broad single ESR absorption and the V species. The absorption in the region of 650 mp (V band) is assigned to e2" species whose potential has been lowered by a partially solvated metal cation at the cavity center giving a species Of stoichiometry hf. This is a symmetrical species to be differentiated from h? in ammonia (hh-hé) which is assumed to exist mainly in an ion pair between e2-‘ and h+. The assignment Of the V species is based primarily on the flash photolysis results Of Linschitz and is supported by the changes in intensity relative to the R band which occur upon dilution and cooling (10,13,22). The species which result from photo bleaching Of the V band must be capable of combining in a rapid second order reaction tO form dimers (R species). The prOposed reactions are 1:"(v) ~—> 15+ e“(IR) (15) 2M «—> 1420?.) The increased IR absorption Observed immediately following V band photolysis is attributed by the author to electrons, implying their £8 h? removal from the V species. The R species can then produce the V species by the reaction 112 (a) = LTCJ) + If . (16) This reaction will also occurupon dilution. The increased relative intensity of the V band at low temperatures implies a species favored by low concentrations and/or by a more highly structured solvent, both of which support this ass‘gnment. The apparent low V band absorption for rubidium.and cesium may arise because they are too large to fit easily within the cavity. The explanation of the slow interconversion of the lithium ‘ species to the IR band (22) according to this model is admittedly weak. It is attributed to the high activation energy brought about by the required solvent reorganization since a symmetric species h? goes to species with the charges separated. The broad extra 33R absorption observed in certain solutions of potassium in ethylamine-ammonia mixtures is attributed to an unpaired electron. The high metal concentrations present when this phenomenon is observed would allow the solvated electron to pair with and separate from a number of metal cations rapidly enough to give a single lihe. It is believed that simultaneous interaction with several nuclei occurs since a single metal nucleus would not be capable of broadening the electron ESE line to a width greater than the splitting observed for the monomer. The greater asymmetry of the cesium hyperfine pattern compared with potassium and rubidium could result from a slower atom-monomer equilibrium and/or the increased hyperfine Splitting by the cesium nucleus. Although 50 the former may be true, the major effect appears to be the increased hyperfine splitting. Clearly much work remains before models are develOped which are capable of quantitatively describing all facets of the behavior of metal solutions. The instrumentation and computer programs described in this thesis should help to develOp and test such models. 1. H. J. Hart, "Solvated filectron" in Advances in Chemistry Series 50, R. F. Could, fid., American Chemical society Pub., vii (1205). 2. h. fibert and A. J. Swallow, "Solvated Electron" in Advances in Chemistry Series 50, R. F. dould, fid., American Chemical society Pub., 28) (1965). 3. 3... Kraus, J. Am. Chem. 300.,‘2é, 86h (lth). he 30 A. Kraus, Jo 1km. Chis}... SOCO, 2;), 155? (1)07). o, 1197 (1908 . K» 50 Co A. Kraus, J. A}... Child. SOC.) , 653 (1903 3. Co A. RIVELALJ, Jo 155:3}. Chem. 800., ha ~J > \x) C) , 1323 {1908). . Co “- Kraus, J. AK. C-em. 600., 8. G. 3. Gibson,and'£. L. Argo, J. Am. Chem. Soc., hO, 1327 {1918). ‘. J. L. Dye and R. R. Dewald, J. Phys. Chem., 8, 135 (196L). 10. E. Cttolenghi, K. bar-Eli and H. Linschitz, J. Chem. Phys., D}, 206 (1965). l]. 5. blades and J V ”od ins Can 7 Chem 93 211 ”lQRS) .... . i. .5 . I. . ..- b , (AL 0 U C LVuL.’ '\-J_’ Jun- \ / O 12. G. Hollstein and V. Wannagat, Z. Anorg. Chem., 288, 193 (1)56 13. R R. Dewald, Ph.D.dissertation, Lichigan State University, (1963). lb. C I. A. Fowles, M. R. hedregor and h. C. R. Symons, J. Chem. Soc., 1957, 332). 15. S. Hindwer and B. Sundheim, J. Phys. Chem., éé, lZSh {1962). 16. D. F. Burow and J. J. Lagowski, "solvated filectron" in Advances in Chemistry Series 50, R. F. Gould, Ed., American Chemical Society Pub., 125, (1965). 17. N L. Jolly, C J. Hallada and h. dold, Letal Armenia solutions, . . - - - r1 - - -.- - , '7 . G. Le Poutre and L. J. oienko, ud., sehJamin, new iork, 11E (1)6h). m \n I‘D (7\ re —\1 O [‘3 CO I\) L) (D o T) 1'... ‘H l‘.) C, Douthit and J. L. Dye, J. Am. Chem. 500., E2, LL72 (1)60). Gold,'¥. L. Jolly and H. S. Pitzer, J. Am. Chem. Soc., Eh, 226L (1962). Gold and H. L. Jolly, Inorg. Chem., 1, 818 (1962). R. Dalton, J. L. Dye, J. h. Fielden and S. J. Kart, J. Phys. Chem., in press. R. Dewald and J. L. Dye, J. Phys. Chem., 68, 121 \lj6h). Ottolenghi, h. bar—Ali and H. Linschitz, J. Am. Chem. 500., 87, 1302 (1265 ). Cttolen; -1 and u. Linschitz, "solvated Electron" in Ad inces in Chemistry bories 50, R. F. Gould, Ed., American Chemical Society Pub., 1&9 (1)657; 1 L. Dye, L. R. Dalton and m. V. Kansen, Abstracts, lh,th national heating of the American Chemical Society, April 1965, L55. L. Dye and L. R. Dalton, Symposium on Clectron Spin Resonance, East Lansing, nichigan, August 1266. R. Dalton and J. L. Dye, results to be published. Ear-Eli and T. R. Tuttle,Jr., J. Chem. Phys., L0, 2508 (196L). R.Dalton, J. D. Rynbra ndt, E. h. I—Iansen and J. L. Dye, J. Chem. Phys., LL, 3269 (126;). Herzber g, Spectra of Diatomic holecules, D. Van Nostrad CO., New York (1,50). Hess and J. L. Dye, unpublished results. Ottolenghi, K. bar-111 and h. Linschitz, J. Chem. Phys., L0, 3729 (1)6h). Becker, R. R. Lindquist and B. Alder, J.Chem. Phys. 25, 971 (1956). L, Dye, R, F. dankuer and G. E. Smith, J. Am. Chem. 500., 82, f r‘ \ * ’47 97 \l)?6U ) - P. Kraus, Letal Ammonia Solutions, G. Le Poutre and M. J. Sienke, au., Benja 111n, New Yark, 9 (iych). 36° 37. R. R. H‘I H. . Catterall, h. C. R. Symons and J. W. Tipping, private communication. 1. Ca P. Ramsey, Kuclear homents, John Wiley and Sons, Inc., New York, 39 (1:53). 13. Wentworth, J. Chem. 1311., L2, (2), 96 (1,765). E.flentworth, J. Chem. Rd., L2,(3), 162 (1965). P. Kohin, Ph. D. dissertation, university of Liaryland (1961). A. fuska, Ph. D. dissertation, Lichigan State University (1965). 0 <5 ’1 (4. O :3 ‘0 Chem. Rev., 6%, L53 (196D). L. Dye and L. Feldman, Rev. Scientific lnstr., 31, (2), 15h (1966). Arnold and A. J. Patterson, J. Chem. Phys., Q1, 308) (196L). 3. R. dymons, h. J. Blandamer, R. Catterall and L. Shields, J. Chem. 500., 196h, L357. R. Brendly and E. C. dvers, "Solvated Electron" in Advances in Chemistry Series 50, R. F.30uld, 3d., American Chemical Society m L. Clark, A. Horsfield and h. C R. Symons, J. Chem. Soc. 1359, 2L78. Catterall, J. Carset and n. C. R. Symons, J. Chem. Phys. 38, 272 (1)63). ‘dilson and D. Kivelson, J. Chem. Phys., Lg, 15L (1966). h. thonnell, J. Chem. Phys., 25, 709 (1956). ‘ -"- T *7 n‘m ' ' (J . -: 1“: ’1 f 1‘ - a 01. dduu’ .1. 1... JOlIJ‘ 0.11.111. --'O 34.13331“, J. .131. v1". .‘wllo UVL’O’ U4, Ar. / . géb‘h \17‘612) o APPENDICES 5h IDSJT' Title: APPSNDIX A 1. ATOl-L-lZOIIOiER SQUILISRIUI-i Category: PrOgrammer: Date: PURPOSE 3IJATION ' L Atom-Monomer Equilibrium Separation of effects Jay D. Rynbrandt July 29, 1966 Given‘the variation of potassium hyperfine Splitting in ethylamine- ammonia mixtures with temperature, calculate the contributions of atoms and monomers to this splitting. :5 A t‘ ‘ UuAJZ: l. Arguments JL, KL are integers definin" the low field region for each data set. JH. D H are integers defining the high field region for each data set. PC is the mole percent ammonia. n U A is the is the is the is the is the array array array array array name of the temperature in degrees centigrade. name for the hyperfine Splitting in Gauss. name for the total number of spins. name for the temperature in degrees Kelvin. name stored in common and used to transfer the independent variables into the least squares subroutine. Y is the same as X but for dependent variables. AT is the array name for the calculated number of atom spins. NA is the array name for the weighting factors. (NOTE: A more 55 (3‘. scent least squares subroutine than that used with this pregram is listed. This subroutine can use non-integer weighting values.) KA, JA are the integers defining the first and last points to be used in the least squares subroutine. SAC, SLC are the calculated contributions to the Splitting of the atom and monomer. SPA, SPE are the atom and monomer Splittings calculated an- other way. PA, PE are the percent atom and monomer contributions to the splitting. TS, DS are the total Splitting and its difference from the observed value. Ah is the calculated monomer Splitting. YB is the Splitting from atoms. IA is the number of spins due to atoms. 2. Print-Cuts: All arrays on each iteration. 3. Output Formats: See listing. h. Timing: Roughly one minute for all Operations described here. 5. Accuracy: Depending on data and number of iterations. 6. References: L. R. Dalton, J. D. Rynbrandt, E, h. fiansen and J. L. Dye, Journal of Chemical Physics ha, 3969, 1966 and J. D. Rynbrandt, k3 Thesis, Michigan State University. RETROD The contributions of either of we species to the total hyperfine Splitting are calculated in one temperature range and extrapolated 57 into another, to be used in the calculation of the contribution from the other species. An iterative procedure is then applied to reach constant contributions from each. For the details of the calculation see the references. A So \ Program A M EQ Read-in all temperature, hfs, and spins: C(l), A(I), and 8(1). {D Define beginning and end of high and low temperature region of each data set along with percent ammonia. l l IPrint percent ammoniaT] Calculate Kelvin temperatures. Define for low temperature region: Y(I) = A(I), X(I) = C(I). Call LINE ‘ #42) I Calculate atom and monomer contributions to splitting, percent contributions, and concentrations. i Y Print temperatures observed A and informat.ui from previous statement. Extrapolate Low temperature (monomer) splitting into high temperature - region. 1 Define weighting factor, NA(I), favoring points with largest splitting from atoms. a l Calculate number of atom spins, YA. Define Y(I) 1n (YA) x(1) = 1/P(I). [Cali LiNE.j Extrapolate atom spins to low. temperature region. Calculate atom and monomer contributions to splitting, percent contribution, and concentrations. Print information from previous statement. Calculate monomer contribution in low temperature region by sub- tracting extrapolated atom Contribution. I Define Y(I) : monomer contribution, \.(l) “7 C(l). ...-...— (Has data set been treated 5 times? ' No-*<:> Yes (_Have all data sets been used?#)--*No-*<:> Yes 1 End ._\_ 1 PROGRAM A M 50 COMMON JAOKAONAOSYOCYOXOY DIMENSION T(200)o AIZOOIo 5(200Io XIZOO). ATI200) 1 FORMAT (ZFIOoO oEIOoZI 2 FORMAT (*IPERCENT NH3 8 *FQoI I 3 FORMAT (*0 TEMP A MON A C 1 AT A C AT A P AT T S 4 FORMAT (*0 TEMP SPINS MON 5 I P AT */) 5 FORMAT (IOFIIQSI 6 FORMAT (F110502E11030Filo50 EIIO3OF1105’ 20 21 22 23 24 25 NB 8 165 DEAD 19 (C(I)o A(I)o 5(1). I 8 IONS) DO 15 MB 3 1.6 BM 8 MB IE (BM-1.0) 20020021 CONTINUE JL I I KL 8 17 JH s 18 KH 8 35 PC 3 106 GO TO 32 CONTINUE IF (BM-2.0) 220 22023 CONTINUE JL 8 36 KL 8 54 JH u 55 KH 8 66 PC 8 207 GO TO 32 CONTINUE IE (BM-3.0) 24924025 CONTINUE JL867 KLIBS JH I 86 KH I 107 PC I 508 GO TO 32 CONTINUE Y(200)o C(2OO)0 NA(200I MON A OBS-CALC*/I P MON P MON AT 5 C 26 27 28 29 3O 31 32 II IF (BM-4.0) 26026.27 CONTINUE JL 8 108 KL 8 118 JH c 122 KH 8 130 pc I 906 GO TO 32 CONTINUE IE (BM-5.01 28028.29 CONTINUE JL 8 131 KL 8 140 JH s 143 KH 8 148 PC 8 1402 GO TO 32 CONTINUE IF (BM - 6.0) 30.30.31 CONTINUE JL 8 149 KL t 156 JH 8 159 KH 8 165 PC I 11.8 60 TO 32 CONTINUE CONTINUE PRINT 20 PC 00 II II JLoKH TI!) 3 CIII + 273oI5 XII) 3 CI!) YIII ' A(II ATIII 3 OOO NAII) 8 I CONTINUE JA 8 JL KA a KL CX I 0.0 Sx I 0.0 DO 14 MA 8 195 61 I6 12 I? I3 14 15 (j\ m CALL LINE PRINT 3 DO 16 I I JL.KH SAC I AT11) *82o4/S1I) SMC 31C11)§SY + CY)§1S11) - AT(I)) / S11) SPA 8 A11) - SMC SPM I A11) - SAC PA I IO0.0*SAC/A1I) PM a IO0.0*SMC/A1I) TS I SAC + SMC DS 2 A11) - TS PRINTS. C11). A11). SMC. SPM. PM. SAC. SPA. PA. TS.DS CONTINUE JA 3 JH KA I KH DO 12 I I JA.KA AM I SY*C1I) + CY YB I A11) - AM NACI) I YB + 1.0 YA I YB*S1I) / 182.4 - AM) Y1I) I LOGF1YA) X11) = 11.0 / T1I)) CONTINUE CALL LINE PRINT 4 DO 17 I I JL.KH ATIIIIEXPFISY/TII) + CY) SAC I AT1I) SPM a S11) - SAC PA I IO0.0*SAC/S1I) PM I IO0.0*SPM/S1I) TS I SAC + SMC OS I 511) - TS PRINT 6. C11). S11). SPM. PM. SAC. PA CONTINUE KA I KL JA I JL DO 13 I I JA.KA Y11) I 1S1I)*A(I) - AT1I)*82.4) / 1S1!) ‘ AT11)) X11) I C11) NA1I) I I CONTINUE CONTINUE CONTINUE END A. B. C. APPBHDIXIA 2. 1.1211151“ S¢JJXRJJQ Liiflto Title: Least Squares Line Category: Line calculating PrOgrammer: Jay D. Rynbrandt Date: July 29, 1966 PORPG'JE 1. Calling sequence: ALLLS" (Largo 133,3,SDB,SIJA,TIcs,n-I,I:) 2. Arguments: X is he array name of the independent variable. Y is the array name of the dependent variable. i is the array nine of the calculated dependent variable. DY is the array name for the difference between Y and XX. 8 is the slope. C is the intercept. BBB is the standard deviation of the slope. SBA is the standard deviation of the intercept. TIGS is the total sum of the squares of DY. 'W is the array name of the weighting factors. N is the number of data points. 3. Print-Outs: All values listed in calling sequences . Out—put formats: See listing. 5. Timing: Less than a second for 50 data points. 0\ \u D. ‘I on ’3\ 0 Accuracy: Floating point, single precision. 7. References: 5. H, Lindgren and G. W; KcElrath, Introduction to Probability and Statistics, The Fac hillan CO., New York (1359). 13TH C3 zit-xix. gust? - 21-:..Y..X.Zw..x, l 1 .1. l l l l l C 2 O . O T. - 1‘! o — "' I T" 04' ‘- ZJlEixi \Zfi‘ci) 21 . f o .‘r - 1." a ‘P O s g “£21.11 xi ii 2 «1x12214111 2 . 2 1' T. ‘{ - 2' . .X. 2 hi 2.1.1.th \ 2 J1 1) See reference for standard deviation evaluation. 1 2 3 4 5 6 10 11 13 6C SUBROUTINE LINE (X. Y. YY. DY. S. C. SUB. SDA. DIMENSION X1100).YIIOO).W1IOO).YYIIOO).DYIIOO) FORMAT 1*0SLOPE I*EI4.6) FORMAT 1* INTERCEPT I*EIA.6) FORMAT (*0 X Y Y CALC W*/) FORMAT (5F14.7) FORMAT 1*OSTD DEV SLOPE I*E14.6) FORMAT 1* STD DEV INTCPT I*E14.6) P I N SSI000 US I 0.0 XSI0.O YPIOQO YSIOoO DO 10 I P I.N U11) I ABSF1W1II) SS I SS + W11)*X11)**2 US I US + W11) XSIXS+X1I)*W1I) YP I YP +X11)*Y11)*U11) YSIYS+Y1I)*W1I) CONTINUE C I 11XS*YP) - (SS*YS))/11XS**2) ‘ US*SS) S I 11XS*YS) ~WS*YP) / 11XS**2) - US*SS) AVX I XS / P TIGS I 0.0 TXS I 000 PRINT 3 DO 11 I I I.N YY1I) I S {X11) + C DYII) I Y1!) ' YYII) 5165 I OY1I)**2 SXS I X11)*1X1I) - AVX) TIGS I TIGS + $165 TXS I TXS + SXS PRINT 4. X11). YCI). YY1I). DY1I). W11) CONTINUE STIGS I TIGS/P STXS I TXS/P VARA I STIGS * 11.0 + AVX**2/STXS)/P VARB I STIGS / 1P*STXS) VARA I ABSF1VARA) VARB I ABSF1VARB) SDA I SORTF1VARA) $08 I SORTF1VARB) PRINT 1.5 PRINT 2.C PRINT 5. 508 PRINT 6. SDA RETURN END T165. 6. N) RESIDUE O . AFPJHDIK B IDJKTIFiCi-qu Title: Least Squares Spectra Synthesizing. Category: Curve fittins. Programmer: Jay D. Rynbrandt Date: July 29, 1966 a series of X - Y coordinates, a shape function 9" 0) C (L C (+— "I I; .3 m U) diven capable of fitting the curve and estimates of the parameters involved, more precise values of the parameters are obtained by adjusting them in an iterative process to obtain a best fit as judged by the sum of ‘. the squares of the deviation from the observed spectra. This specific pregram vas used to reproduce an ptical spectrum consisting of three peaks vita feur parameters used to descrile each peak. T" ‘ .‘ VUJ;L§A.‘J l. Callin; sequence: Terms are stored and transferred through common. mane of the independent variable. The second sub- >4 H t: st a Q1 t'5 H p a ‘1 "3 script, I, is a running index over all points used. The first subscript denotes : l. the wavelength in mu, 2. the wave number and 3. is an extra array in the event that X must be read in some different units and converted to one of the prior two. I is the array name of the dependent variable. The second sub- script, I, is a running index over all points used. The first subscript, l - 6, desiénates: l. the contribution from the IR band 66 47 at the point in the spectrum being corsidered, 2. the contribu- tion from the 3 band, 3. that from the V band, h. the observed spectra, 5. the calculated Spectra and 6. the difference of the vectra. .r. L .I. observed and calculated 5 U is the array name of the weighting factor which enables certain ‘ions of the spectrum to be eapiasized, The first subscriot, H I \A) 9 representing the peak; the second subscript, the point in question. P is the array name of the paraueters used for each peak. The first subscript, l - 3, designates the IR, R and V band, respec- tively; the second subscript, l - 3, relates to the skew factor, the linewidth and‘the peak center respectively. B is the array nape of the parameters related to the maénitude of the three peaks. 9 C is the arrar name oi , the adjustment increments with subscripts corresponding c those of P. 50 is the sum of the deviation square". TRIS is the number of attempts allowed to obtain a best fit oy adjusting any pa icular parameter. N is the number of points used to represent the spectrum. J is the integer designating the particular band. K is the inteder ranging over three of the parameters describing L represents the fitting function used. TB is the number of times the pregram passed through a given point in subroutine SIZE. 3. h. 7. ‘ .\ CL) Storage: 1390 Input, Output formats: See listi-g. Timing: a. Compile 20 sec. b. Execution 10 sec for 10 iterations over three peaks. Accuracy: Limited by the capacity of the shape function and the number of iterations. hanual, Control Data References: 3heO/3éCO Fortran Referenc (D Corporation, Palo Alto, Calif. (1965). C?“ \«J ' U F: O ’1 so ..3 Fl L0 '71 F4 F3 Read estimates of parameters, P. 1 mead one X-Y data point. F“ Convert to cm'l. f Lgero arrays used. \ C Have 11 data points been read?j———No——' [ Define adjustment increnente:] ! F3231 A135,}: Have all peaks been treated? ‘\ No (one in this case). _,/ 'Yes \ / l 7O Y ( Have all parameters been adjusted?j—No—§@ Yes \ Chas adjustment been made 10 times? No—a® Yes C Have all shape functions been used'a-No-—@ Yes Y C all DRAW . Proposed Flow Chart fot IR FIT Read all spectra. \ Y Read all parameters of all peaks to be used in fitting a specific spectrwn. V Hake corrections for missing data points in given spectrum. v Make conversions and definitions required. Has adjustnv o~.ks ._ V Have all peaks been treated a \ orescribed number of tines?z ‘1] No P) 4 1’ C Have all “.".“:.‘;"18 ‘bcen treated? )" ICC-Q Yes \ C Have all par-meters hem adjusted? >-—I=Io_@ Yes V "as this '13-'32". ‘cne a prescribed No—)@. nurfer of times? 4, C Have all sweetrn. been treated? : I-Jo-)@ Yes “DUN” PROGRAM IR FIT COMMON X0 Y9 We Po C. 80 SO. TRYSO N9 JO K0 L9 TR. 80 DIMENSION X(39100)0 Y(69100)c W(30100)o 9(303)0 C(393). 8(3) FORMAT (IZOAB) FORMAT (251003) FORMAT (3510-0) FORMAT (*IDATA OF SPECTRUM *AB, FORMAT (*0 ~ L 3*12) READ 10 NQRECORD READ 39 P(lol)c 9(192)o P(lo3) DO I! I 8 ION READzo X(19I)o Y(4OI) X¢20I) ‘ IODOOOOOoO/XCIOI) X(39') 3 000 Y(291) 3 0.0 Y(3oI, 8 000 "(101’ 3 100 U(Zo!’ 0 100 "(301) 8 !00 CONTINUE 50 8 100 TRYS 3 2500 DO 15 L 3 108 PRINT 4. PECORD PRINT 5. L 8(1) ' 100 HO 8 0.4 C(10133031 S C(102)800005 S C(lo3)800002 DO 14 NB 8 1010 DO 14 J B 101 DO 14 K 8 103 CALL ADJ CONTINUE CALL DRAW CONTTNUE END 7h APPjfiDIX“ r.n.v.nz - . r 2. ADJuoTilgla i‘f‘leITOR \ADJ.) Title: Adjustment honitor Category: Curve Fitting Pregrammer: Jay D. Rynbrandt fl 3 ‘. v ’36/ Date. Joly 29, l/‘o Given a set of parameters of which one is being adjusted, obtain the best value of that parameter. C. USAGE See Least Squares Spectra Synthesizing (IR FIT). 75 fl¥8ubroutino ADJ [:grint heading—l Define: TRIALS = 0 T - large number V = l + adj. increment L L Call 512E] ; T0 - old sum of sq. T - sum of sq. from SIZE 'TRIALS = TRIALS + l I you. (Does TRIALS - 25 7) A‘ no [frint current information] . Is fit bet : *ec Continue parameter this time? adjustment no .0 Reverse direction of adjustment *7 [adjust parameterl Has parameter been adjusted no this way before? . J lye. ARedefine adjustment increment l a l_} . -‘Print current information AR SUBROUTINE ADJ COMMON X0 Y0 We Po CO 80 SO. TRYSO No JO K. Le TR. BO DIMENSION X(30100,0 YI6QIOOI9 WIBOIOO). PI303). C(303). 8(3) I FORMAT (I60 I109 4X0 4E120492F7013 2 FORMAT(/* PK NO CONST NO CONST ADJ INT I 50 TR TRIALS*/) PRINT 2 TRIALS 8 000 T 8 99999909 V 8 100 + C(JOK) DO 8 N1 8 102 3 CONTINUE CALL SIZE TOIT T350 TRIALS 8 TRIALS + 100 IF (TRIALS - TRYS) 50909 5 CONTINUE PRINT 10 J0 K9 P(J0K)o C(JoK). B(J)o SO. TRoTRIALS IF IT - TO)69707 6 CONTINUE PIJQK) 8 PIJoK)*V GO TO 3 7 CONTINUE C(JoK) 8 -C(J9K) V 3 1.0 + C(JOK) PCJQK) I PIJQK)*V 8 CONTINUE 9 CONTINUE C(JQK) I C(JoK)*TRIAL$/I0.0 PRINT 10 J0 K0 P(JOK)O C(JOK)0 BIJIO SO. TPQTRIALS RETURN END (3 77 APPEIDIX B 3. IAGILIT' . s ADJUSTEEET (31313) IDJIIIFICATION Title: Catego ': Size Curve Fitting Proérammer: Jay D. Fynbrandt Date: July 29, 1966 UP 033 Give: a spectrum as a series of I.- Y coordinates, a shape function capable of fitting the curve and a set of parameters other than magnitude, adjust the ma nitude to give the lowest sum of squares of the deviation from the observed spectra. See Least Squares Spectra Synthesizing (IR FIT). subroutine SIZE Define direction of adjustment, V, using magnitude of two previous times through subroutine. Calculate size of peak, Y(J,I), . at specific point, x(2,I). uare difference of calculated, Y 5,1), and observed, Y(b, I), spectra. a 1 i[fiAdd square, SQ, to previous ‘ sum of sq., S. < Have all points, I, been \ 'no considered? 1 ' yes [_Qefine counts; TR - 0.]. l Define fracti 'onal ad jus fluent}, : increment. ' ;fi I Change magnitude, B(J), by - adjustment increment, A. d) I ‘ 50 = previous sum of sq. S - 0 TR - TR + l 1 ' Change size of peak, Y(J,I), by adjustment increment, A. . A S uare difference of observed - r h,I), and calculated, Y(S,15, spectra. [Add square, SQ, to previofl sum of sq., S. ‘ Have all.points been no , considered? _ Is sum of sq., 8, better you than previous SO? 4/ no — Decrease and change magnitude of adjustment increment, V. l Lila: this been done 7 tinwflH‘ 10 11 12 13 14 15 16 r J O SUBROUTINE SIZE DIMENSION X(3.100)9 Y(6oIOO)o W(30100)o P(303)o C(3o3)o COMMON X0 Y0 We P. C0 80 SO. TRYSO No Jo K0 L9 TPO BO 5 I 000 V I 0.025*(B(J)‘BO)/ABSF(B(J)‘BO) 80 I B(J) GO TO (10012014.16018020922024) L CONTINUE DO 11 I = I.N R I X(201) - P(J03) PX I P(J91)*X(ZOI) Y(J.t) : B(J)*(1.+Px )/(1.+(P(J02)*R)**2) Y(50I) I Y(101) + Y(201) + Y(30I) Y(6oI) I Y(401) - Y(SQI) SO I W(J01)*Y(6011**2 S I S + 50 CONTINUE GO TO 4 CONTINUE DO 13 I 8 I.N R I X(201) - P(J03) PX I R(J91)*X(20I) Y(JoI) I B(J)*(1.+PX*§2)/(1.+(P(J02)*P)**2) Y(501) I Y(101) + Y(201) + Y(3oI) Y(601) I Y(40I) ‘ Y(501) SO I W(JoI)*Y(6oI)**2 S I S + $0 CONTINUE GO TO 4 CONTINUE DO 15 I = I.N p a x¢2.1) — PtJoa) PX I P(J01)*X(ZOI) Y(JOII I B(J)*(I.+PX**3)/(1.+(P(J02)*R)**2) Y(59!) I Y(191) + Y(291) + Y(301) Y(691) I Y(401) - Y(SoI) SO I W(JoI)*Y(6oI)**2 S 8 S + $0 CONTINUE GO TO 4 CONTINUE DO 17 I I I.N R I X(201) - P(J93) PX I P(J01)*X(201) Y(J0I) I B(J)*(1o+PX**4)/(I.+(P(J02)*R)**P) YtSoI) I Y(IOI) + Y(201) + Y(3oI) Y(601) I Y(4oI) - Y(501) SO I W(J01)*Y(60I)**2 S I S + 50 8(3) 17 18 19 20 21 22 23 24 25 CONTINUE GO TO 4 CONTINUE DO 19 I I I.N R I X(201) - P(J03) RR I P¢J01)*P Y(JoI) I B(J)*(1.+PR )/(Io+(P(Jo2)*R)**2) Y(BoI) I Y(IOI) + Y(2oI) + Y(39I) Y(6oI) I Y(4OII - Y(SoI) SO I W(JoI)*Y(6oI)**2 S I S + $0 CONTINUE GO TO 4 CONTINUE DO 21 I I ION R I X(201) - P(J.3) PR I P(J01)*R AR I ABSF(PR) Y(JoI) I B(J)*(1.+PR*AR)/(Io+(P(Jo2)*R)**2) Y(50I) I Y(1¢I) + Y(201) + Y(3oI) Y(601) I Y(4vI) - Y(501) SO I W(JOI)*Y(69I)**2 S I S + $0 CONTINUE GO TO 4 CONTINUE DO 23 I I I.N R I X(2OI) - P(J03) RR I(P(J01)*P)**3 Y(JQI) I B(J)*(1.+PR )/(Io+(P(J02)*P)**2) Ytfigt) I YIIoI) + Y(201) + Y(301) Y(601) I Y(401) - Y(501) SO I V(J01)*Y(601)**2 S I S + $0 CONTINUE GO TO 4 CONTINUE DO 25 I I I.N R I X(291) - P(J03) PR I(P(J01)*R)**3 AR I ABSF(P(J01)*P) Y(JoI) I B(J)*(1.+PR*AR)/(1.+(P(J02)*P)**2) Y(SoI) I Y(101) + Y(2QI) + Y(3OII Y(6oI) I Yt401) - Y(5¢I) SO I W(JoI)*Y(6oI)**2 S I S + SG CONTINUE GO TO 4 CD I‘D 4 CONTINUE TR I 0.0 DO 8 N2 I 1.7 A I 100 + V 5 CONTINUE B(J) I B(J) *A $0 I S S I 000 TR I TR+IoO DO 6 I I ION Y(JoI) I Y(J01)*A Y(591) I Y(101) + Y(201) + Y(3OII Y(601) I Y(491) - Y(501) SO I U(J01)*Y(601)**2 S I S + 50 6 CONTINUE IF (5 - 50) 5.7.7 7 CONTINUE V I -V*O.25 8 CONTINUE RETURN END APPJNDIX u. I‘EFQRi-ATIOI-I PRLJTQQT (oat-I) A. IDEXTIFICATILN Title: Information Printout PrOgrammer: Jay D. Rynbrandt Date: July 29, 1966 s. 1332:3052 Printout information obtained previously. LL; SUBROUTINE DRAW DIMENSION X(3oIOO)o Y(69100)o W(30100)o P(303)o C(303)o 8(3) COMMON X9 Y0 We Po Co Be 50. TRYSO No Jo K0 Lo TR. 80 1 FORMAT (*1 X 085 LAMDA CM-I ABS CALC ABS OBS RESIDU 1E Y IR WT IR Y R WT R Y V WT V*/) 2 FORMAT (3F100109F1005) PRINT 1 DO 12 I I ION PRINT 20X(39I)0X(1QI)OX(?OI)QY(SQI)OYIQOI)0Y(6OI)0Y(10IIOW(IOI)O IY(291)9W(291)9Y(301)0W(3011 12 CONTINUE RETURN END l. IDELTIFICATIOH Pregrammcr: Date: APPTQIDIX C Gfiifll‘a‘xLIZfl) LEAD‘ “T SQUMLQ‘T” Generalized Least squares Parameter adjustment J ay D. Rgmbrandt July 29, 1966 PJRrUSS Given F (x,, y,, do, b0, co), find the corrections to so, b0, and c0 a i so as to minimize the weighted deviations, - 7' Tr ‘ 2 fl 2 D " z J.) i (yobs - foalc) + ”xi (XODS xcalc) UEHUEJ 1. Arguments: X is the array name of the independent variable. Y is the array name of the dependent variable. is the array name of the parameters to be adjusted. C) RQCORD is the array name used to store and print the date set identification. C‘ o is the array name for the nuclear Spins. P is the array name for the partial derivatives (partials) cal- culated at each point. 55 is the array name for some sums of partials going into sub- routine SQRTMET and that for the corrections to the parameters which it calculates. ST is the array name used to sum the products hf partial de- rivatives calculated. CO (_}\ NY is the array name of the weibhts. Y1, Yll are the array names for the calculated single line con- tribution (Yll being that obtained with weighing factors of l). Yh, Ylh are the array names for the calculated four line patterns. YC, YlC are the array names for the calculated spectrum. YD, YlD are the array names for the difference of the observed and calculated spectra. N is the number of points in a particular data set. 2. Print Outs: All parameters with each adjustment and all observed and calculated spectra. 3. Input and Output Formats: See listing. '. Timing: Less than one second for each complete adjustment with 50 data points. 5. Accuracy: Single precision, adjustment completed in three cycles. O\ . References: M 3 Hentworth, J. Chem. Ed., kg, (2), 96 (1965) ‘N. E. Uentworth, J. Chem. Ed., h2, (3),162 (1965). D . I-‘JETHOD Given: 1‘1 - “I“ I - - 1‘. - ". . ', a C '- 1 *1 \213 J1: : b: ) O a, b and c are the least squares estimate of these parameters. ri ‘ 3i (Xi: yi: a 3 D 1 C ) Xi, yi, are the observed variables; a0, b0, 00 are the estimated parameters. then A, B and C can be found by solving the synaetric *3: Fai ai Fa F‘o Li Fb lFai Foi Li U3 FC. lFai _—j-]-FCEE.;AZ in which 2 2 in Eyi L_ 2 + 1 h , Jxl Jyl and Wx., my. are the weighting factors of x- l i and i - 0 O O le (xi,yi,a,b,c Fa = CylFi o/ .000 a (xi: yi’ d 3 b : C ): 3 Fatii Li C) Fb.Fc. 1 i C Li lc-Pc l C Li 1 and yi, ), etc. (+- Prov" u‘; (11%! [S ( l ‘r-e 1 'Read record cant] H .‘I Read estimatcn parameters and number of cards in data set, N. <:><-Yes-4:_Iave all data sets been read? > No Read spectrum (X(1), Y(I), I = 1,N). I Convert parameters, C(J), for use in this program. r Define cvzatants used. I Define weightinu Factor, WY(I) = 1. Redefine WY(I) = {(slope).‘ 3 \ Store calculated peaks and residues obtaiwed With WY(I) = 1. v Calculate peak area ratio and ‘____<:> line widths. r Print perinent information. K5 8) C? hero matrix to be used. ‘J Calculate partial derivatives with respect to each parameter for each point, P(l-10). \ Take sums of products of partials, SP(J,K), to form matrix. J9 H Cal! Calculate new estimates of parameters, C(J). V Have 12 fits been tried with ---No--%(:) WY(I) = 1 ? Yes I [gas this the 13th fit? No Y Yes-—-#<:> Have 5 fits been tried with «Y(l) : f(slopc)? sow I I {Yes Cabulate peak ...;Lios and line ‘\“ 'llfho ‘s informationf] [ Print pertinext \ .Print observed and calculated spectra. I x PROGRAM GEN L S DIMENSION X(100)0Y(100)0C(103oRECORD(!O)oS(IO ST(10010)0 UY(100)0 YD‘IOO)OYC(100)0Y1C(100)9Y11(100)oY (85500015) (251000) ( IZFIIQS) FORMAT (HlolOAB) FORMAT (*0 914/911 1 CEN 4 R! 1 2 SUM SG*/) 6 FORMAT (IOAB’ 7 FORMAT (*0 X‘l) Y OBS IY RES I RES WYsl 9 FORMAT (7F100501504F1005) IO FORMAT (9514.4) 18 CONTINUE READ 60 (RECORD(I)9 I 8 1010) READ !OC(I)0C(2)0C(3)9W49W10C(6)0C(7)0C(8)0N IF (N-l)33033019 CONTINUE READ 20 (X(I)oY(I)oIIloN) '4 I W4*200 WI 3 Wl*200 SRT 8 1.414214 C(3) = C(3)/300 C(4) 8 SRT/WA C(S) 3 SRT/Ul C(131 C(13/C(4)/C(4) C(7) * C(7)/C(5)/C(5) AR 8 0.0691/009308 SR 8 9.07477/16053766 SC]’8‘!05$SCZ)=‘OO5SS(3)=OOS$S(4) 3 105 PRINT ‘0 (RECORD(I)01 3 1910) DO 99 L 3 102 GO TO (34035) L CONTINUE NADJ ' 12 DO 20 I 8 I.N UYCI’ ' 100 GO TO 39 CONTINUE NADJ 8 5 NM 8 N -1 SW 8 000 DO 36 I * EONM IR 2 I + 1 I" I I -1 NYC!) I 1.0/(ABSF(YCIP) SW 8 SW + WY(!) 1 2 FORMAT FORMAT FORMAT RI J INT 1 INT 4 W 1 Y CALC Y C Y 1 I9 34 20 35 -Y(IM)) + leO) 36 )OP(!O)QSB(!O)0 Yl(!00)oY4(100)o 14(100)0YID(100) W 4 CEN AVY Y ALN Y lLN Y 4*/) W 37 38 39 22 23 24 )1 DO 37 I I ZONM HYII) IWYII)*NM/SW HYII) I 1.0 WYIN) I 100 DO 38 I I I.N YIC(I) I YCII) YIIII) I YIII) YI4II) I Y4II) YIDII) I YD(I) CONTINUE PRINT 5 SO I 0.0 DO 99 NTIMES I I.NADJ '4 I SRT/CI4) WI I SRT/CIS) RI4 I 400*(IOO+AR)*C(I)/C(4) RII I CI7)/C(5) RAT I RII / RI4 PRINT SCRATQRIQOCII)0CI3)9W40C(2)0RII0C(7)9UIOC(6)oCI8)oSO DO 22 J I 109 DO 22 K I J09 STIJOK) I 000 $0 I 000 DC 26 I I I.N DO 23 J I 1010 PIJ) I 0.0 DO 24 M = 104 RK I XII) + SIM)*C(3) - C(2) RI I XII) + SIM)*C¢3)*SR - C(2) PK I CII)*CI4)*CI4)*RK*EXPFI-ICI4)*RK)**2) PI I CII)*C(4)*CI4)*RI*FXPF(‘ICI4)*RI)**2)*AR PI!) I P(I) + (PK + PI)/C(I) PC I -PK/RK-PI/RI+PK*C(4)*C(4)*200*RK + PI*C(4)*C(4)*2. 0*RI PIE) 3 pIZ) + PC 9(3) I P(3)+$(M)*(PK/RK+PI*SR/Rt-PK*c(4)*c(4)*2,*pK-pl*sn*c¢4, *CI4)*2Q*RII PI4) I 9(4) + (PK +PI)*2oO/C(4) -PK*RK*RK*200*CI4)-PI*RI*RI*2*C(4) P(9) I 9(9) + PK + PI PIIO) I PIIO) - PC CONTINUE RS I XII) - C(6) PS I C(7)*C(5)*C(5)*RS*FXPF(-(C(5)*RS)**2) PIS) I PS*2oO/C(S) - PS*RS*RS*C(5)*2.0 P(6) c ~PS/RS + PS*C(5)*C(5)*RS*ZOO PI7) I PS/CI7) PIE) 8 100 YQII) I PI9) P(9) n P(9) + PS + CIR) - YII) PIIO) IIPIIO) - P(6))**2 + IoO/WY(I) YCII) I P(9) + YII) YICI) I PS YOU) . 9(9) 50 I 50 + P(9)*P(9) DO 25 J I 109 DO 25 K I J09 25 STIJOKI I STCJQK) + PCJ)*P(K)/P(IO) 26 CONTINUE NXIB DO 98 J I IONX SBIJ) I STIJ09) 98 CONTINUE CALL SORTMETCSTQSBONX) DO 3! J I I.NX 31 C(J) I C(J)-SB(J) 99 CONTINUE U4 I SRT/C(4) HI I SRT/CIS) RI4 I 400*(IoO+AR)*C(I)/C(4) RII I C(7)/C(5) RAT I RII / R14 PRINT 30RAT0RI4¢CII)0C(3)cW40C(2)oRIIoC(7)oWIoC(6)oC(8)oSQ PRINT 40 (RECORD(I)OI I 1910) PRINT 7 DO 32 I I ION 32 PRINT 9. XII)0Y(I)0YC(I)0Y4(I)0YI(I)9WY(I)9YD(I)oIoYID(I)oYIC(+)¢ 1 Y11(1)0YI4(I) GO TO I8 33 CONTINUE END TWO BLANK CARDS SHOULD BE AT END OF DATA DFCK at. '\ .00 APPENDIX C 2. SlJARE-ROOT LETEOD r'm‘rr‘v‘fl. m“: ‘3 IDnuiiriolith Title: Square-Root hethod Category: ‘ymmetric Linear Systems Solving Fragrammer: Dr. R. H. Schwendenan, Department of Chemistry, hichigan State University Date: January 1, 1966 PURPOSE W Given: AX = b in which A is a symmetric matrix and X and B are column matrices, find the values of X. 5’11 U Sii‘u‘fl 1. Calling sequence: CALL 3; mm (P, w, N) Arguments: P is the array name of the symmetric matrix. 'W is the array name of the column.matrix read in and the solutions to the linear system after execution. N is the order of the matrix. Print-Outs: None. Timing: Fast. Accuracy: Single precision, to accuracy of input values. Reference: V. N. Faddeeva Computational Methods of Lineal Alrebra 3 4 Q ’ Translator C. D. Benster, Dover Publications Inc., New York. \\0 \« LETHQD The symmetric matrix, A, is resolved into tne product of a triangular matrix and its transpose A 3 8'5 then S'K = B 5X = K This subroutine calculates the triangular matrix S. From the tri- angular matrix it is a simple matter to calculate K and from K to calculate X. IO 20 30 40 5O 60 7O SUBROUTINE SORTMET (PoUoN) DIMENSION P(109)O)o WIIO) NNIN+1 NMIN-l DO 50 I'ION PCI.NN)IW(I) JMII-I SUMIPIIOI) DO 20 J'IOJM SUM:SUM-W¢J)*P(J.I)**2 VII)ISUM/ABSF(SUM) SUM ISORTF¢ABSF(SUM)) PIIOI)ISUM JPII+1 DO ‘0 J-JPONN TUMIPIIOJ) DO 30 KIIQJM TUMITUM-P(KoI)*P(K9J)*W(K) PIIoJ)ITUM/SUM CONTINUE "(N)IW(N)*P(N0NN)/P(N0N) DO 70 IIIONM SUMIP(N-IONN) JPIN-I+I DO 60 JIJPQN SUM25UM-P(N-IoJ)*W(J) VtN-I)IW(N-I)*SUM/P(N-IoN-I) END U1 0 C. APPJNDIX D l. IJHEJIDTH ANALYSIS IDSJTIFICATIOH Title: Polynomial Linewidth Fit Category: Curve Fitting PrOgrammer: Jay D. Rynbrandt Date: July 2), 1966 PURPCSD Given the heishts of a series of BBB hyperfine lines, obtain the linewidths and from them, the polynomial describing their dependency on the nuclear spin quantum number m I. USAGE 1. Calling sequence: 2. Rain prOgram. Arguments: S is the array name of the nuclear spins. ii is the array name of the linewidths. NC is the array name of the linewidths calculated from the coefficients of the least squares polynomial. B is the arra" name of the coefficients. SB is the array representing the estimated errors in B. TT is the array name of the temperatures of all the samples. C is the array name of the coefficients calculated for all samples. L”, n o is the array name of the estimated errors in o for all samples. t. TB is the array name of l / Kelvin temperature. H is tie array name of the heights. 96 V'jf‘ he is the array name of the Spectra identifications. ‘H3 is the width of the standard line. IS is the number of the standard line. h is the number of data sets for a particular Spectrum. 3. Output—Input Formats: see listing. h. Timing: 1 minute for lhO spectra. 5. References: Jay D. Rynerandt, he Thesis, Lichigan State university, {1366). Los Alamos Subroutine Description K—OSO. The heights, HCI), of the various hyperfine lines are read-in, along with the linewidths of a standard line, HS, which has been accurately determined. The linewidth of all of the lines are then determined from the expression / I 1‘ W 'V' - 1."? "T W: r 2 N K...) "' II.) {n (4-D) / n KL) ) in which IS represents the number or the standard line. The polynomial describing the linewidth as a function of ml is then calculated in subroutine LSQPOL. )8 PROGRAM POLY LU DIMENSION 5(100)9W(!OO)OWC(IOO)OSB(10)OB(10)9TT(200)0C(50200)o 1 EC¢50200)0TR(200)0H(100)0RE(200) FORMAT (A802X92E10020215) FORMAT (SE 502) FORMAT (1H1030X9* DATA OF SPECTRUM NO. *A8* L 8*!3, FORMAT (//* DEG CENT I§F90495X0*STANDARD L W 8*F803’ FORMAT (*OSPINS *BFIOOBY FORMAT (§ HEXGHTS *BFIOQB) FORMAT (* WIDTHS *BFIOOa) FORMAT (*1 L T l/K C l E 1 C 2 1 E 2 C 3 E 3 C A E 4 2 E 5*/) 9 FORMAT C'40F4000F90692X04(EI2.40E1I03’02X0A8) IO FORMAT ( * DEG KELV niFQQQOSXQ *NO OF STD L W 8*!4’ 11 FORMAT C * l/D KELV 8*F90695Xo *NO OF DATA PTS 3*14) malO‘UIbUNfl 12 FORMAT (*0 L T 1/K C 1 E l C 2 I E 2 C 3 E 3 C 4 E 4 2 E 5*/) 13 FORMAT (150F50004E140702X0A8) L 8 O 100 READ IORECOWSQTOISOM IF(M)12001200110 110 READ 20 (H¢I)o! 8 10M) L c L+1 SH I 4.5 00 20 I 8 19M SH 8 SH - 10 20 SC!) 8 SH DO 19 I 8 10M IF (HCI’) 17017019 17 M 8 M-1 IF (IS-1915015916 16 IS 8 15-1 15 CONTINUE DO 18 I! 8 10M 19 8 11+! H‘II’ . H(IP) D8 5(11) 8 SCIP) I a [-1 I9 CONTINUE 9) DO 21 I 8 19M 21 U(I)s US*SGRTF(H(ISI/H(I)) PRINT JORECOL DK 8 273.15+T RK I IoO/DK PRINT 40T 0W5 PRINT IOODKOIS PRINT IIORKOM PRINT 50(S(IIOI 8 IOMI PRINT 60(H(IIOI 8 IOM’ PRINT 79(U(IIOI 8 IOM) KM a 4 CALL LSOPOL (MoKMoSoWoUCoBoSBoSIG) PUNCH ISoLoToB(I)oBC2)oB(3)oB(4)OREC DO 22 Lp 8 IOKM C(LPOL) 8 B(LP) 22 EC(LPOLI 8 SBCLPI TTCL) 8 T TRCLI 8 RK RE‘L) 8 REC PRINT 12 PRINT 9. L 0TT(L )9TR(L )0(C(LPOL )oEC(LPoL )0LP8IQKM)0RE(L) GO TO 100 120 CONTINUE PRINT 8 PRINT 9. (LSQTT(LS)9TR(LS)0(C(LPOLS)QECILPQLS)OLPOIoKM)oRE(LS)o 1 L5 8 IQLI END APPLIDIX D we Wm "M VP [N -fi"‘ 2 0 T'H.-I:).L Qs‘JALsLJ; FLT—LAIU; ..LILIJ J. -‘..L.L “r" ' 71" 'VY‘NAm'f'u-r “Jinn; 4.; .1.J;..l.LU-. :17‘r‘1‘1"‘“" Auk} Title: Least Squares £el;ncri,‘ IL’: .; J Op .LLU‘JALtO 32 CSD LSQPC'L Cateéoiy: CurVe littlng Pro; an.e : T. L. Jord'm and R, D. Vogel, Los $.lamos 5134x1134“: 1C 1:" .V Kodified and t George A. sake Date: September 19, :RPODM Given X: observed Pix; m .L . max UeASD l. Sallin Sequence‘ 2. AI‘" data points, ested on L x‘mum degree of fit, oratorg, Jew Lexico. A.-. / the VUU loOh by I“, JI‘. 911d 19-51 (1, Yr), 00.... )‘There 1 is the a m 5 die observed independent variable, ”(km is fitted + 2.11 degrees 113-; Bkm+l D‘ H b 33 SIGLA : 2 : h 100. IE 10. A is the array name of ouserved inde130nuent vai iaoles. Y is the array name of observed dencndent variables. ICAL is the output array name of the estimated dependent variable. BELT is the output array name for the difference between Y and YCAIH ~ UT .4. L) the output array nane for the coefficients of the powers of X. DD is the output array name of the estimates of'the errors in B. SIGLA is the standard deviation corrected for the order of fit used. 3. Output Formats: See listing. h. Timing: Roughly 0.2 sec. per derree of fit for 30 data points. ,. Accuracy: Floating point, single precision. 6. References: Los Alanos Subroutine Description h—OSO. ZLDLQJ V" l - ‘W ‘V' " Pfizl $331. "" .01 + 32...». + o o 0 3161+]. X H is obtained by collecting the powers of X in a set of orthOgonal polvnonials which are generated by this subroutine. ’f‘Y’fi‘, 534“}le = \ 1: - (n: + 1) 102 SUBROUTINE LSQPOL(MoKMoXoYoYCALoBoSBcsIGMA) DIMENSION 5(IO’OX(IOOIOY(IOOIQST(IOIO$B(IOIOP(IOOIOB(IOIO IDELY(IOO)9A(IOOIO)oT(10)oYCAL(100)oPM(IOO) 10 20 60 65 70 80 81 82 83 9O A(Iol)8IoO A(292381.O YBARlooO XBAR8OOO DO 10 1810M leIIF’OO YBAROYBAR+YIII X8AR¢XBAR+XCII XBARIXBAR/M T(I)IYBAn/M A(Zol)8-XBAR PXF8O¢O pXPI0.0 DO 20 I8IoM P(I$8X(I)-XBAR PXF:PXF+P(I)*Y(I) PXP:PXP+P(I)*P¢I) TfZIOPXF/PXP PMXPM8M SCIIIPMXPM BCI)8T(I)*A(191)+T¢2)*A(201I 8(2)8T(2)*A(202) DO 190 KSZQKM L8K-I IF(K-2)I90ol65065 prpaogo XPXPMPOQO BIK’8OOO DO 70 J810M XP0X(J)*P(J) XPXPIXPXP+XP*P(J) xpxpM.xpxpM+XP*PM¢J) ALPHAIXPXP/PXP BETAIXPXPM/PMXPM FFXF8O¢O PPXPP'OQO DO 90 1810M PTIP¢I) P(I)-X(I)*PT-ALPHA*PT-BETA*PMCI) PPXF-PPXF+P¢I)*Y(I) PPXPPtPPXPP+p(II*P(II PM(I)8PT 103 TIK1IPPXF/PPXPP PMXPMIPXP PXPcPPXPP AIKOI)8~ALPHA*A(K-101I-BETA*A(K-ZOII A(KoK-1):A(K-19K-2)-A(K-1oK-|)*ALPHA A(K9K)8IQO IF(K-3)150015091!0 110 KlsK-Z DO 120 1820K1 120 A(Kot)3A(K-101~11-ALPHA*AIK‘1OI)-BETA*A(K-20I) 150 DO 160 1810K 160 B(II=B(I)+T(K)*A(K01) 165 516280o0 DO 180 I810M YCAL¢11881K1 KK-K-l DO 40 J810KK IKIK-J 40 YCAL(1)8X(I)*YCAL(I)+B(IK) 175 DELY1118YCAL(I)~Y(1) 180 516285162+DELY(11*DELY(11 AMK8M‘K IF1AMK118101810182 181 AMKBIOO 182 SIGMAOSORTF15162/AMK) S(K) 8 PXP DO 499 1810K 499 5T(1)aSIGMA/$QRTF(S¢I)) DO 501 1810K SB‘II‘OOO DO 500 J810K 500 SB!I18SB(I)+(A(J01)AST(J)1**2 501 58(118SORTF(SB(I)) K'JaK 190 CONTINUE WRITE OUTPUT TAPE 6103000L DO 183 I810KJ 183 WRITE OUTPUT TAPE 6103040198(110$B(1) 135 "RITE OUTPUT TAPE 6103019516MA 670 WRITE OUTPUT TAPE 6103020(10X(I)0Y(I).YCAL(I)QDFLY¢II01810", 300 FORMAT151HOCOEFF1CIENTS OF Y881+BZ*X+ETC AND ERRORS FOR ORDEROIBQ/ 1) 301 FORMAT18HOSIGMA =El6oB) 302 FORMAT‘AHO 19X04HX11)14X94HY(I113X07HYCALC1111X07HDELY¢I)//(I4¢ 1451808)) 304 FORMAT(3X02HB(1292H)8E15.805X05HERR88E10031 RETURN END C) APPnZTD Ei E " . ---’ rx- 1 ’ "“ W , “W"? .I‘ I " SECOn-L) 0.20mi C haRiCTiuJ \SDC 00) TISLTIFIJATION Title: Second Order Correction Category: Iterative Data Treatment Pregrammer: Jay D. Rynbrandt Date: January 1, 1966 PURPOSE Given the chart position of ESE hyperfine absorption peaks, the nuclear spin quantum number of these peaks and the chart position of two frequency markers, calculate the field positions of the peaks, make second order corrections and calculate the g value. v ‘i ‘ "1" UDauil: l. 2. ”ailing Sequence: Rein prOgram with no subroutines. Arguments: Hh is the array name for the observed magnetic field positions. 3 is the array name of the nuclear Spin quantum number. XE is the array name of the chart positions of the peaks, H0 is the array name of the field position calculated in the absence of interaction with nuclear moments. HOB is the average value of HO. SHO is the swm of HO. FL, FH are the low and high field frequency markers. FK is the klystron frequency. lob, ...; 0 \fl XL XH are the lov and hirh field chart positions of the ) V i frequency markers. ~I is the nuclear spin. (I) SPECEO identifies the spectrum. 8L, 3 are the lepe and intercept of the magnetic field as a function of chart position. is the number of peaks in a specific spectrum. A is the hyperfine Splitting. Al, A2, A3 are the hyperfine splitting calculated between different pairs of 30R lines. value. 6 is the f- b 3. Output and Input Formats: See listing. h. Timinrz 6.3 sec per spectra. 5. Accurac*: Consistent results after three iterations. 6. References: H. A. Kuska, Ph. D. dissertation, hichigan State University (1965), Jay D. Egnbrandt, LS dissertation, hichisan State University (1966). LETHOJ The magnetic field, HO (I), at which an electronic transition would occur in the absence of interaction vith atomic nuclei is \ sou) = 1111(1) + A~S(I) 4- A2 / (2-m~<1(1))- (13) ,3 (31(SI+1) - s(:)(—) + A3 / h-I:--:{I)2 in which the terms have been previously described. This pro— gram calculates the quantity HO(I) - A03(I) by subtracting the 106 seCund and third order contributions from the observed field position. This calculation for various values of 5(I) can be useu to evaluate HO(I) and A. T.e process is re- peated until constant values are obtained. The Center of the spectrum, H0, is taken a“ the average of 'alues cal- culated for each peak using Equation (13). Finally the g value is calculated from the expression g = hoFK /,6 ones where h is Planck's constant, PK is the klystron frequency and [9 the electronic 30hr magneton. 63—) -) E. H , P" 91 \~ dead ngcrnxcion about 5- . w spectrum are '~xnouru. I l <::fi&-Ies-—<:_§ave all spectra been treated? > ‘7 5-00 I Read chart posi ions and spins Of p9 3153 o V . . Print roan-in information about spectra. Calculate field as function of incles on snectrum. A -- 3 u .. ;\/ a. 1 § ‘x/ I .L,‘ .0: ‘ -L ...-v I. a ..7, Calculao.. s. . , .1. a. 1“” 3.1-30 '1 w . ‘ Calculate c: o 77 'f' O ..., " .“.. '. nCCi), in ahtqwce Ol -aCLsrs ' .' .2 ,. - 3 .- . giving r.re :ccnr 1:3 01"181“ errtw 103 Calculate Al between outer two peaks; A = A1. No-4:_§re there two more peaks?i) Yes f Calculate A2 between first two inner peaks: A = (A1 + A2)/2. No——{;¥ére there two more peaks? Yes Calculate AI sctween two inner most peaks: A = (A1 + A2 + A3)/3. Calculate new H‘. y Print ll 0' A, A1. A2, and A3. f < Has this spectrum been treated \ No 10 times? ‘J/ Yes oe—J (9—1, . ’\ in: DUN" ~C)O(D~IOLI 5 5 22 21 10 f4 (3 \0 PROGRAM SEC 0 C DIMENSION HMIZO). S(20)0 HC(20)0 XM(20)9 HO(20) FORMAT (* G VALUE 8*F1106I FORMAT (GEIOoIOIIOoABI FORMAT (ZEIOoI) FORMATI/*O HO A AI A2 A3*/) FORMAT (5FI407) FORMAT(/*O SPIN X VAL H 085 H CALC*/) FORMAT (2F9.202FI406) FORMAT (*1 DATA OF SPECTRUM NO. *OABI FORMAT (*OSLOPE I*FII.5/* INTERCEPT 8 *F1003I FORMAT (3F120403F9030I6) FORMAT(/*0 FREQ H FREQ L FREQ K X VAL L X VAL H I SPIN PEAKS*/) CONTINUE READ ZoFLoFHoFKoXLoXHoSIo NoSPECNO IF (FL) 20020021 CONTINUE READ 39 (XM‘IIOSIIIOI 3 ION) PRINT 80 SPECNO PRINT 51 PRINT SOOFLOFHOFKQXLOXHOSIO N PRINT 4 A1=0.0 s A2=OoO S ABSOoO BL 8 2.3486855iFL BH 3 203486855iFH 5L 8 (EH-BLI/(XH-XL) C 8 BH ~SL*XH A 8 SL*IXM(NI‘XMIIII/(S(I)‘S(N)I A a ABSF(A) SHO 8 000 DO 10 I 8 I.N HMII) 85L*XM(II + C HOII) I HM(II + S(I)*A SHO I SHO + HOCI) CONTINUE HOB I 5H0 / N Al 8 A PRINT 5. HOBQAOAIOAZOAB 113 DO I9 KB I 1910 DO I2 I 3 ION HCII) I HMII) + Aiiz/(200§HM(III*(SI*(SI+IQOI‘5(II**2I +A**3/I4* I HM(II**2) I2 CONTINUE AI .- (HC(N) - HC(!H/(S(1)- 5 (NH AI 8 ABSF(AII A 2 A1 IF (NoGToB) 13015 13 CONTINUE J 8 N - I A2 8 (HCIJ) ‘ HCIZII/(SIZI ‘ S (JII A2 : ABSF(A2I A 8 (AI + A2I/2oO IF (NoGToSI I4915 I4 CONTINUE J 8 N - 2 A3 I (HCIJ) ‘ HCIBII/(SIB) “ S (J), A3 I ABSF(A3I A 2 (AI + A2 + A3)/3oO IS CONTINUE SHO 8 000 D0 II I ' ION . HOII) I HM(I) + (A*S(I) + A**2/(2¢O*HM(I))*(SI*(SI+I00I -S(I)**2) I + A**3/( 4oO*HM(I)**2)) 5H0 I 5H0 + HOIII II CONTINUE HOB! SHO / N PRINT So HOBOAOAIOAZOAB I9 CONTINUE PRINT 6 DO IT I ' I.N PRINT 7. 5(1). XM(I)0 HM(I)9 HCIII 17 CONTINUE G 8 Oo?I4489*FK/HOB PRINT 9. SLOC PRINT Io G 60 TO 22 2O CONTINUE END ‘RUNQIQZOOOOOM fl. Ad'ust a set of parameters to synthesizing ESRS sp APP); ”‘31:; 1' LIST smug smwm SLTJ’.;I;SIZJZIG (I: 3:521 1:13.: TfiribA.’ .LL/u Title: Least Squares Spectra Synthesizing onto 0 ': CurVe flttlflg Pr03rarJ1er: Jay D. RJnJrandt D te: Auoust l, l}SS PJITOJE (I; O (+- "S m o {Lote: Pro rem I? FIT uses this same method and is more general. This listing is presented for the sake of ccwoleteness.) L 111 C SAMPLE 5 TEMP. ~41 30 PROGRAM K FSR 112 SPLIT 4.82 LINE WD 0603 CFN 9.75 CARDS 39 COMMON XoYoJAoKAoA080ToARoTRoAVXoAVYoAVXRoCoHcTRYSoPoPIQPISQ DIMENSION X(90100)0Y(7q100) FORMAT (2(FIOoOII READ Io ( X(19I)o Y(IOI)¢ C I I00 8 I 4071 UL I 0.43 AVX I 9073 AVXR I 908 JA I 1 KA I 39 SUM Y I 0.0 XJ I JA XK I KA TI I XK - XJ + IoO DO 30 I I JAoKA SUM Y I SUM Y + vclot) Y( BOI) I 0.0 CONTINUE AVY I SUM Y/ TI A I C AR I C AVXR I AVX C2 I ‘ IoO/ZOO C3 I - IoO/6eO C4 I + IoO/6eO C5 I + 1.0/200 T I 1.0 /(Io41‘214*UL) TR I 0039 PI I 30I4IS926536 PIS I (2oO*PI)**2 J8 I 4 TRYS I 2000 CB I-IOOO CT I 1000 I JAOKAI I C29C30C40C50$W0TRIALSQTIoJBoCToCBQCXoDTQDX CALL CALL CB I CT I CX I CALL CALL CALL OT I CALL DT I CALL OX 3 CALL CB I CT 3 CALL CALL CALL DT I DO 7 CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL 113 SEP4 WDTH4 I00 100 I00 SEP4 WDTH4 CEN4 IOoO WDTHEX IoO WDTHEX I00 CENEX 200 2.0 SEP4 UDTH4 CEN4 200 LA I I96 WDTHEX SEP4 WDTH4 WDTHEX SEP4 WDTH4 WDTHEX CENEX SEP4 WDTH4 CENQ CONTINUE CALL CALL CALL CALL CALL CALL CALL CALL CALL END WDTHEX CENEX SEP4 WDTH4 CEN4 PRINTI WDTHEX CENEX PRINTI 11h SUBROUTINE WDTH4 COMMON XQYQJAoKAvoBoToARQTRoAVXoAVYoAVXRoC0H0TRYSQPQPIQPISO I C20C3OC4OCSOSWQTRIALSOTI.JBOCTICBOCXODTOOX DIMENSION XI9OIOOIQYITQIOO) 5 FORMAT ( 9(FII05)) 6 FORMAT (////* T A ST B I RI TRIALS TRYS C */) PRINT 6 TRIALS I 000 ST I 999999999909 DO 14 I I JAoKA XI20II I AVX + B*C2 - X(IoI) XISQI) I AVX + 8*C3 - XIIOII XIIQII I AVX + 8*C4 - XIIQI) XI5OII I AVX + 8*C5 - XIIOII XIGOI) I AVX +BI*C2 - XIIQI) XITOII I AVX +BI*C3 ~ XIIOI) XIBOII I AVX +BI*C4 - XIIoI) XI90II I AVX +BI*C5 - XIIQI) I4 CONTINUE DO 25 NT I 102 26 CONTINUE STO I ST A8 I A A I C BI I B * (9.07477 / 16.53766, H I A * (000691 / 009308) SA I 0.0 V I C DO 3I I I JAoKA Y2 I ‘A*X(20II*EXPF('IT*X(20III**2I Y3 8 ~A*X(3OII*EXPF(~(T*X(30II)**2) VI 8 ~A*X(4013*EXPFI-(T*X(4OIII**2I VS 8 -A*X(59I)*EXPF(-(T*X(50II)**2) Y6 s -H*X(69II*EXPF(-(T*X(60III**2) Y7 I -H*XITOII*EXPF(-IT*X(79II)**2) Y8 I -H*XIBOI)*EXPFI’IT*X(80II)**2) Y9 a ~H*X(9o!)*EXPF(-(T*X(9o!))**2) Y(40II I Y2+Y3+Y4+Y5+Y6+Y7+YB+Y9 YI7OI, I Y(IOI) - Y(40II - AVY - YISoI) so I v¢7.r)**2 SA I SA + 50 3! CONTINUE 27 I3 34 18 23 24 DO I8 MD I I.JB CONTINUE SAO I SA SA I 0.0 AAIA+V AC I AA/A A.IAA DO I3 I I JA.KA Y(4.II I Y(4.I)*AC Y(2.I) I Y(I.I) - Y(4.I) Y(7.I) I Y(I.II - Y(4.II SQ I Y(7.II**2 SA I SA + SQ CONTINUE IF (SA ~ SAO I 27.34.34 CONTINUE V'I‘V*O.I CONTINUE ST I SAO TRIALS I TRIALS + I.O IF (TRIALS - TRYS) 2.2.3 CONTINUE 115 * AVY - AVY - YI3.II RI I (A*4.0*I.7724539) * (I.O + 0.069I/Oo9308) UL I 1.0 / (1.4142I4*T) PRINT 5. T. A. ST . 8. UL. IF (ST - STO I 23.24.24 CONTINUE T I T + CT*0.0I GO TO 26 CONTINUE CT I -CT T I T + CT*0.0I CONTINUE A I A8 + V*10.0 CONTINUE CT I TRIALS * CT/ IOIO PRINT 5. T. A. ST. 8. WL. RETURN END PI. PI. TRIALS. TRIALS. TRYS. TRYS. CT CT / (2.0*T**3I 116 SUBROUTINE SEP4 COMMON X.Y.JA.KA.A.B.T.AR.TR.AVX.AVY.AVXR.C.H.TRYS.P.PI.pIS. I C2.C3.C4.C5.SU.TRIALS.TI.JB.CT.CB.CX.DT.DX DIMENSION X(9.IOO).Y(7.IOO) 5 FORMAT I 9(FII.5)) 6 FORMAT (////* B A ST T I RI TRIALS TRYS C */) PRINT 6 TRIALS I 0.0 SD I 9999999999o9 DO 43 NB I 1.2 47 CONTINUE $80 I 58 AB I A A I C BI I B * (9.07477 / I6.53766) H I A I (0.069I / 0.9308) SA I 0.0 V I C 00 49 I I JA.KA X(2.I) I Avx + BICE - XII.I) X(3.I) I AVX + B*C3 - X(1.I) x(4.1) . AVX + BICA - x¢1.!) x(5.1) . Avx + 3*c5 - x(1.!) X(6.I) - Avx +BI*C2 - X(lot) x(7.1) a Avx +BI*C3 - xt1.1) X(8.I) I AVX +BIIC4 - X(1.I) X(9.I) I AVX +B!*C5 - X(1.I) Y2 I -A*X(2.I)IEXPF(-(T*X(2.I))**2) Y3 I IA*X(3.I)*EXPF(-(T*X(3.I))**2) Y4 I ‘A*X(4.I)*EXPF(-(T*X(4.I))**2) YS I -A*X(S.I)*EXPF(-(T*X(S.I))**2) Y6 I -H*X(6.I)IEXPFI-(T*X(6.I))**2) Y7 I -H§X(7.I)IEXPF(°(T*X(7.I))**2) Y8 I -H*X(8.I)*EXPF(-(T*X(8.I))**2) Y9 n -H*X(9.I)*EXPF(‘(T*X(9.I))**2) Y(4.I) I Y2+Y3+Y4+Y5+Y6+Y7+Y8+Y9 Y(7.I) I Ytlo!) - Y(4.I) - AVY - Y(3.!) so - Y¢7ot)**2 SA I SA + so 49 CONTINUE 29 57 SB 48 43 44 45 DO 48 MD I IOJB CONTINUE SAO I SA SA I 000 AA I A + V AC I AA/A A I AA 00 57 I I JAOKA Y(40I) I Y(40I)*AC Y‘ZOI) I Y(19I) - Y(40I) Y(79I) I Y(IQI) - YCAOI) SO I Y(70I)**2 SA I SA + $0 CONTINUE IF (SA - SAO I 29058058 CONTINUE V .‘V*OOI CONTINUE $8 I SAO TRIALS I TRIALS + 100 IF (TRIALS - TRYS) 20203 CONTINUE RI I (A*4.0*1.7724539) * (1.0 + 000691/009308) / (200*T**3) IL I 1.0 / (10414214IT) PRINT 5. Bo A. SB 0 To WLQ IF (SB - 580 I 43044044 CONTINUE B I B + CB*OOOI GO TO 47 CONTINUE CB I -CB B I B + CB*OOOI CONTINUE A I AB + V*IOOO CONTINUE CB I TRIALS * CB/ 1000 PRINT 5. Be A. $80 To UL. RETURN END - AVY - AVY - Y(30I) RIO RIO TRIALS. TRYS. TRIALS. TRYSo C8 C8 SUBROUTINE CEN4 COMMON XQYQJAIKAQAOBOTOAROTRIAVXQAVYQAVXRoCoHoTRYSoPoPIQPISQ I C20C3oC4oCS-SW0TRIAL50TIOJBOCTOCBOCXODTODX DIMENSION XI9OIOO)0Y(7OIOO) 4 FORMAT (*OAVY I *F9o6) 5 FORMAT (IO(FIIISI) 7 FORMAT(////* AVX T B A I WL RI , TRYS TRIALS C*/) PRINT 7 TRIALS I 0.0 BI I 8 fl (9.07477 / 16053766) H I A I (000691 / 009308) SX I 999999999909 DO 55 NX I 192 66 CONTINUE SXO I 5X SUMDY I 000 S" I 0.0 S! I 0.0 00 SI I I JAOKA X(20I) I AVX + 8*C2 - X(!0I) X(39I) I AVX + B*C3 - X(IoI) X(40I) I AVX + B*C4 - X(IoI) X(50I) I AVX + 8*C5 - X(IoI) X(6.t) I AVX +BI*C2 - X(1¢I) X(70I) I AVX +BI*C3 - X(10II X(89I) I AVX +BI*C4 - X(IQII X(90I) I AVX +BI*C5 - X(10I) Y2 -A*X(20II*EXPF(-(T*X(20I))**2) Y3 I -A*X(30IIIEXPF(I(T*X(39III**Z) Y4 -A*X(40II*EXPF(-(T*X(40I))**2) Y5 -A*X(SQI)*EXPF(-(T*X(59I)I**2) Y6 -H*X(60I)IEXPF(-(T*X(60III**2I Y7 -H*X(70I)*EXPF(-(T*X(70II)**2) Y8 -H*X(BOI)*EXPF(-(T*X(80II)**2) Y9 I -H*X(90I)IEXPF(-(T*X(90II)**2I Y(49II I Y2+Y3+Y4+Y5+Y6+Y7+Y8+Y9 Y(29II I Y(19I) - Y(4OI) - AVY Y(79I) I Y(10I) - Y(49I) - AVY - Y(39I) SO I Y(7OII**2 SUMDY I SUMDY + Y(70II Y(SOI) I Y(40I) + AVY Y(20I) I Y(le) - Y(50II SO" I Y(20I)**2 SX I 5X + SG SH I SW + saw 51 CONTINUE AVY I AVY + SUMDY/TI 53 54 119 RI I (A*400*Io7724539) * (1.0 + 000691/009308I / (200*T**3I UL I 1.0 / (II4I4214IT) PRINT 5. AVX. T! 89 A0 SXQ WLO RIO TRYSO TRIALS! CX TRIALS I TRIALS + I00 IF (TRIALS - TRYS) 20293 CONTINUE IF (SX - SXO I 53054054 CONTINUE AVX I AVX + CX*OOOOI GO TO 66 CONTINUE CX I -CX AVX I AVX + CXIOoOOI CONTINUE CONTINUE CX I TRIALS * CX/ 1000 PRINT 5. AVX. To Bo A. 5X00 WLO RIO TRYSI TRIALS. CX PRINT 4. AVY RETURN END 5 6 I5 70 71 75 I6 SUBROUTINE WDTHEX COMMON XOYQJAOKAOAOBOTQAROTRQAVXOAVYOAVXROCOHOTRYSOPOPIOPISO I C20C30C49C595W9TRIALSoTIcJBoCTQCBocxooToDX DIMENSION XIQQIOOIOYI7OIOOI FORMAT ( 9(FIIQSII FORMAT (////* TR AR STR AVXR RIR TRIALS TRYS C*/I PRINT 6 TRIALS I 0.0 STRI 999999999909 DO I5 I I JAQKA XI69II I AVXR - XIIOI) CONTINUE DO 65 NTR I I02 CONTINUE STOR I STR ABR I AR AR I C SARI 0.0 V I C DO TI I I JAQKA YI39II I -AR*X(60II’EXPFI-ITR*X(60III**EI Y(70II I Y(20I) - YCSQII SO I Y(70I)**2 SARI SAR+ SO CONTINUE OO 73 KKI IOJB CONTINUE SAOR I SAR SAR I 000 AA I AR + V AC I AA / AR ARI AA DO I6 I I JAoKA YI30II I AC * Y(30II YIToII I Y(291) - Y(30II SO I YC7OII**2 SAR I SAR + $0 CONTINUE WLR 74 73 63 64 65 IF (SAR - SAOR) 75.74.74 CONTINUE V I-V*O.I CONTINUE STR I SAOR RIR I AR*I.7724539 / I2.0*TR**3I WLR. 1.0 / (I.4I42I4*TRI PRINT 5. TR. AR. STR. AVXR. TRIALS I TRIALS + 1.0 IF (TRIALS - TRYS) 2.2.3 CONTINUE IF (STR - STOR) 63.64.64 CONTINUE TR I TR + OT*0.0I GO TO 70 CONTINUE DT I ~DT TR I TR + DT*0.0I CONTINUE AR I ABR + V*I0.0 CONTINUE OT I TRIALS * DT/ PRINT 5. RETURN END TR. AR. 12.0 STOR.AVXR. f—J WLR. WLR. RIR. RIR. TRIALS. TRIALS. TRYS.DT TRYS.DT 5 6 80 BI 83 84 00 Ct. SUBROUTINE CENEX COMMON X.Y.JA.KA.A.B.T.AR.TR.AVX.AVY.AVXR.C.H.TRYS.PIPI.PIS. I C2.C3.C4.C5.SW.TRIALS.TI.JB.CT.CB.CX.DT.DX DIMENSION XC9.IOOI.Y(7.IOO) FORMAT IIOCFII.5)I FORMAT (////‘l AVXR AR STR TR WLR RIR TRIALS ~TRYS C*/I PRINT 6 TRIALS 3 COO SXRI 999999999909 DO 85 NXR I 1.2 CONTINUE SXOR I SXR SXR I 0.0 DO 8I I I JA.KA X(6.II I AVXR - X(I.I) YI3.II I ‘AR*X(6.II*EXRF(IITR*XI6.III**2I YC7.I) I Y(2.II - Y(3.I) SO I Y(7.II**2 SXRI SXR+ SO CONTINUE RIR I AR*I.7724539 / I2.0*TR**3) HLRI 1.0 / (1.4I4EIAITRI PRINT 5.AVXR. AR. SXR. TR. WLR. RIR. TRIALS. TRYS. DX TRIALS I TRIALS + 1.0 IF (TRIALS - TRYS) 2.2.3 CONTINUE IF (SXR - SXOR) 83.84.84 CONTINUE AVXR I AVXR + DXi0.00I GO TO 80 CONTINUE DX I -DX AVXR I AVXR + DX*0.00I CONTINUE CONTINUE DX I TRIALS * DX/ 1000 PRINT 5.AVXR. AR. SXOR.TR. WLR. RIR. TRIALS. TRYS.DX RETURN END l23 SUBROUTINE RRINTA COMMON X.Y.JA.KA.A.B.T.AR.TR.AVX.AVY.AVXR.C.H.TRYS.R.RI.pIS. I C2.C3.C4.C5.SW.TRIALS.TI.JB.CT.CH.CX.DT.DX DIMENSION XI9.IOOI.Y¢7.IOOI 6 FORMAT (*O X AXIS 5 LINE OBS SP 4 LINE RES*/) 9 FORMAT (5F12.6) PRINT 6 DO IO I I JA.KA YI6.II I Y(4.I) + Y(3.I) RRINT 9. XIIOI). YI6.I). YII.I). Y(5.I). YITOII IO CONTINUE RETURN END SUBROUTINE PRINTI COMMON X.Y.JA.KA.A.8.T.AR.TR.AVX.AVY.AVXR.C.H.TRYS.P.PI.RIS. I C2.C3.C4.C5.SW.TRIALS.TI.JB.CT.CB.CX.DT.DX DIMENSION X(9.IOOI.Y(7.IOO) 4 FORMAT (4FI2.6I 8 FORMAT I *O X AXIS CALC EX RK DIFF EX pK RES*/I PRINT 8 DO 91 I I JA.KA PRINT 4. XII.II.Y(3.II.Y(2.II. Y(7.II 9I'CONTINUE RETURN END P-D . AI’PJID EC \3 {-.ALJIM-‘L‘LLLJIJL J: 4.1 uPdVLMAJP IOLU- 4;:st LL. _ ‘ L‘ .Lburdi) . C. I”) I .— O i. Temgerature-ccntrollcd cell costar tnent (F ib ure 12). Coolant delivery ojstem (Figmre 13). Hooslng of cell compartment constructed of l/h" I . \ a . 4 ~ ‘ ~ ‘ 1’) “.13.... ...L L8. 1 \L' 4.53 3.qu f- I! . PolfurethaLe foam used as lieulation. 3141*;gm cuanLero sLIF orting Dewar connected to hCLoLnC O 5 my a threaded ring which presses againsf a sh‘ulue- at the end of the 0Tlinder (Ligure 12). LexL 133 used fo l’LPt tuoes and cell comLartrcnt (jiéore 13). Quartz windows useo Ln light tubes (Figure 13). Teflon washers used to prevent glass from touching metal. seal tnc Dewar to the 13s: T and F3 (L l' *3 VJ P ,3 0: 9.) (J) v .0 t 3 c4. [,3 g: C k“ C I" O C‘s to seal quartz Il-ts to light tubes {FiDLre 13). lower section of cell holder can be reim1a ed with urit to hold standard 1 cn‘. Optica 01 cells {Figure 1h). Point, groove and plane locating system used for all componets of s ctrowhcfometer requiring alignment. A. j. h. A polyurethane plug with a thermocouple seals the tottons of cell compartments (Figure 13). Kitrogen blown through light tubes to prevent frosting of the windows (Figure 13). 126 4 7l/2 r/ 5/ A L; 0 a v / 4b2 £0) V TEMPERATURE- CONTROLLED ' CELL COMPARTMENT Figure 12. COOLANT DELIVERY SYSTEM 7k 1/ 41 l CELL HOLDER Figure 1b, ' 1mm WWII/W Mum ll 17m ' 31293 01750 6548