摘要:
1980 205The Electronic Spectra of the Mixed Mercury Dihalides. Part I. Com-putational Procedures for calculating Spectra, for a New Route toEquilibrium and Formation Constants, and the Resolved SpectraBy Trevor R. Griffiths and Richard A. Anderson, Department of Inorganic and Structural Chemistry, TheUniversity, Leeds LS2 9JTThree possible methods for computing the spectra of the mixed mercury dihalides, HgCII, HgBrl, and HgBrCI, freefrom contributions of other species, are described and discussed as to their general applicability. The spectrastudied are either those of equimolar mixtures of HgX, and HgY,, or of HgX, with added halide Y-. A newprocedure is described for computing the formation constants of these species and the spectra have been resolvedinto their component bands.Each species is shown to contain three bands, even though this is not alwaysapparent from inspection of the calculated spectra. Peak maxima have been found at 37 800, 46 600, and 53 400for HgCII, 37 800,43 200, and 51 21 0 for HgBrl, and 43 500, 47 400, and 57 200 cm-l for HgBrCI. The otherparameters of the resolved bands are given.THE halide complexes of mercury(r1) have been extensi-vely studied by many workers using a variety of tech-niques. Several reviews have been written, that ofDeacon 1 being the most comprehensive, but now ratherout-of-date. Other reviewers have discussed the halo-genomercurates as part of the general chemistry ofmercury 2,3 or of the halogen^,^ or certain particularaspects, for example, the mixed halides5 This lastincludes complexes of the type HgXY, [HgX2Y2I2-, and[HgX3YI2-, where X is one halogen atom and Y isanother (but neither is fluorine). The neutral mixedhalides have been investigated by Delwaulle 6 9 7 whodetected new lines in the Raman spectrum of an equi-molar mixture of HgX, and HgY, and attributed them toHgXY.The formation constants of all the unchargedspecies have been measured in water and a few othersolvents.10-l2 However, the values for HgBrCl andHgClI agree in benzene and in a mixture of phenyls,12but that for HgBrI is reportedly seven times greater inthe polyphenyl mixture.12 No explanation has beenadvanced.The electronic spectra of the mixed mercury dihalidesin water have been calculated by Spiro and H ~ m e .~Recent work in our laboratory has involved the directdigitizing of absorption spectra and its subsequentprocessing in a computer to yield, for example, thespectra of species which are impossible to measureexperimentally free from the contributions of otherabsorbing species, their formation constants, and, fromtemperature-dependent equilibria, thermodynamicdata.13-17 We have therefore sought to apply thesetechniques to the mixed mercury dihalides, to obtainmore definitive spectra, and hence formation constants.As a result of our studies we now conclude that theprevious data9 are inaccurate and we therefore in thisfirst paper discuss the various new computing approacheswe employed.EXPERIMENTALDigitizing of Spectra.-Spectra were recorded 011 anApplied Physics Cary 14 H spectrophotometer, modified toyield spectra in digitized form on paper tape.Details ofthe system have been published.l** l 5 r l 7Smoothing of Spectra.-Calculated spectra are normallyvery noisy because the absorbances increased by extra-polation contain the original noise contribution enhancedby the same factor. In all our earlier papers we used theoriginal ‘ raw ’ data in order t o justify the technique un-ambiguously: now we smooth our original data. Wherepossible the spectra were recorded several times, usuallyfive, and averaged in the computer; otherwise we smoothedthe data mathematically, using the procedure of Savitskyand Golay l 8 (as corrected by Steinier et ul.lS). The spectrain this study were digitized at 1 nm intervals and smoothedusing a five-point convolution.This reduced the noisebut did not degrade the broad charge-transfer bandsobserved. The subsequently calculated spectra were morenoisy than recorded spectra and thus larger convolutingarrays were used to smooth them. Figure 1 shows theeffect of a 15-point smoothing convolution on the calculatedspectrum of HgClI in water.Calculation of the Spectra of Mixed Mercury DihaZides.-The mixed neutral halides of mercury(II), HgBrI, HgClI,and HgBrCl, may be formed in two ways [equations (i) and(ii)], where Y- is the more strongly co-ordinating, andHgX, + HgY, --t 2HgXY (i)HgX, + Y- + HgXY + X-electronegative, ligand. Here, three methods have beenderived to calculate the spectrum of HgXY from both theabove systems, and we therefore also discuss their variousmerits.If a large excess of HgX, is usedin the reaction between HgX, and HgY,, all the HgY, willbe converted into HgXY and the solution will containonly HgX, and HgXY, i.e.the final concentrations will be(a - b) and 2b, respectively, where a and b are the initialconcentrations of HgX, and HgY,, respectively. If E,and Eab are the molar absorbances of HgX, and HgXY, thenwe obtain equation (1) where A is the observed absorbance.(ii)Displaced equilibvium.Eab = [ A - (a - b)~,]/Zb (1)Thus, from the known molar absorbance of HgX, and asample spectrum of a solution containing a large excess ofHgX,, the molar absorbance of HgXY may be found a tany wavelength.A simple coniputer program was writtento implement this method over the complete wavelengthrange used.First, if a very The method has two disadvantages206 J.C.S. Daltonlarge excess of a given mercury halide is used, only part ofthe desired spectrum is observable, the remainder beinghidden under the absorbance of the species in excess.Thus, low concentrations of HgY, must be used, and thehalide in excess must be the one that absorbs a t lowestwavelength, e.g., excess of HgC1, for the determination ofHgClI and HgBrCl spectra. Secondly, as a consequence of20 I-15 n10 i\.I n mFIGURE 1 Effect of smoothing the calculated spectrum ofHgClI in water: (a), calculated spectrum before smoothing ;( b ) , after smoothing with a 15-point convolutionlow HgY, concentrations, the contribution of HgXY to theobserved spectrum is small, and any noise is magnified inthe calculation, by fluctuations in the low values of 2b[equation (I)].The calculated spectrum of HgXY thusrequired smoothing (see Figure 1).Reference-point method. ( a ) For a system containingthree absorbing species in solution, the molar absorbanceis given by equation (2), where x is the mol fraction andE = XaEu f XbEb XubEaI, (2)xu + %b + xab = 1. If the mol fractions of HgX, andHgY, are equal then equation (2) becomes (3). If data areE = Xa(Eu + ~ b ) + ( 1 - 2 x u ) ~ u b (3)obtained for solutions containing different mol fractions,Lab can be evaluated as in (4). ~ , + b is the reference spec-Eu6 = E $- [xu/(o.5 - X n ) ] ( E -- % + h ) (4)trum, and is the mean of the molar absorbances of HgX,and HgY,, and equation (4) only holds for a sample solutioncontaining equal quantities of HgX, and HgY, ; E,+ b wastherefore calculated from the known spectra of HgX, andA reference point is also needed to calculate the mixedmercury dihalide spectrum, and was obtained from theabove displaced-equilibrium method [equation ( l)] .Themolar absorbance of the mixed species was determined a ta wavelength where there was as low a slope in the spectrumas possible, and the difference between the calculatedspectrum and the mean of the molar absorbances of theHgX, and HgY, spectra was greatest. The spectracalculated by this method were noisy and needed smoothing.( b ) For reaction (ii), with added halide ion, but insuffi-cient to form [HgX,Y]- or [HgX2Y2I2-, a two-speciessystem pertains, and based on the above system i t is foundthat expression (5) is applicable.However, this assumesHgY,.Eab = E -k [Xu/Xab(E - %)I ( 5 )that the reference cell contains exactly the same amount ofthe added halide (Y-) as there is, after reaction, in thesample cell, otherwise an absorbance imbalance will occur.The same concentration of Y- was added t o both sampleand reference cells and the observed spectrum of the solutioncontaining the mercury species HgY, and HgXY of reaction(ii) is thus altered by the absorbance of Y- which hasdisplaced X-. If the absorbance of X-- is in the far u.v.,and negligible over the wavelength range studied (as is thecase for C1- and for most of the range with Br-), thenequation (1) may be used to determine the spectrum ofHgXY, on applying a halide-imbalance correction, asfollows.Using first the measured spectrum, the spectrum ofHgXY was calculated over the whole wavelength rangeemployed.The concentration of HgXY was then cal-culated using this spectrum, from a knowledge of the totalmercury content of the solution. The concentration ofreacted halide was thus known and, from the known molarabsorbance of free Y- ions, the absorbance imbalance of theoriginal sample spectrum was calculated, and a new cor-rected sample spectrum derived. This iterative processwas repeated until the difference between successivelyamended spectra in the region where Y - absorbed, usuallybelow 250 nm, was less than a predetermined amount,normally set at 0.01 yo.If the concentration of the added halide (Y-) is less thanthat of HgX,, and i t is all used in displacing X-, then theonly absorbing species in solution would be HgX,, HgXY,and X-.If the spectrum of this solution is recorded usingonly solvent in the reference cell, the reference-pointmethod ( a ) may be used without applying the halide-imbalance correction, so long as the additional absorbanceof X- is negligible, as is the case of C1- and Br-. Unfortun-ately this method was found to be inapplicable as only aproportion of the added halide reacted with HgX, whenthe latter was in excess.Calculation of Equilibrium and Formation Constants.-The term equilibrium constant is used t o refer t o reaction (i) ,and the term formation constant to reaction (ii).The con-stants are stoicheiometric constants since in this caseactivities cannot be measured, but the conditions are suchthat activity coefficients will be close to unity.Potentiometric, polarographic, and radioactive tracerstudies involving solvent extraction have all been appliedto the mercury(I1) halide system for the determination ofequilibrium constants, as well as spectroscopic methods.Direct measurement of the concentration of individuaspecies, and curve fitting for various equations, are amongthe methods used t o yield equilibrium constants undervarious conditions of solvent type, ionic strength, andtemperature.If the molar absorbances of all the species in a solution areknown, then the equilibrium (formation) constants may becalculated from a series of solutions of different ligandconcentrations, but constant ionic strength, using equation(6) where Kab is the equilibrium (formation) constant forA/CT = (&a + KabCL&b)/(l + KabCL) (6)HgXY, c~ is the total molar concentration of mercury, andCL is the free ligand concentration.In this study the mercury(1r) halides in water a t constantionic strength did not yield reliable results on applyingequation (6).It was found, as has been noted by others,20?2'that equilibrium (formation) constants calculated in thisway are very dependent on the values of the molar absorb-ance used.Instead, therefore, the concentrations of theindividual species were calculated as follows.At any given wavelength, the absorbance A of a solutionwill be given by (7) where ci and ci are the molar concen-tration and molar absorption coefficient, respectively, of theith species in solution. This equation holds true for allwavelengths, and hence if A is measured for n differentwavelengths, then n linear equations of i unknowns may bederived. For n > i these equations may be accuratelysolved for ci by means of multiple linear regression analysis.A library computer program was amended to perform this.The output of the program consisted of the requiredconcentrations, with their standard error, and variousparameters indicating the accuracy of the main comput-ation and the precision of the fitted data. These were theresidual and the regression sum of squares, F ratio, multiplecorrelation coefficient, and degrees of freedom of the F ratio.A table of residuals and standardized residuals was alsooutput.Equilibrium (formation) constants, with theirstandard error, were computed from the regression co-efficients.This method has the advantage that conditions ofconstant ionic strength were not necessary and hence thevariation of equilibrium (formation) constant with ionicstrength could be studied. Another advantage was theuse of complete spectra in the calculation. Equation (7)is wavelength independent and hence so should be thecalculated equilibrium (formation) constants. If they arenot, in a certain wavelength region, it may be assumed thatone of the reference spectra is inaccurate over part of thespectrum.For example, in reference-point method ( b ) ,the use of the spectrum of HgXY, calculated withoutallowing for halide imbalance below 250 nm, gives formationconstants in the 250-300 nm range that are significantlydifferent from those calculated in the 200-250 nm range.No such difference was found after corrections for halideimbalance. The use of a correct spectrum is also reflectedin the accuracy of the computation, as indicated by theimprovement in the correlation coefficient and the standarderrors.These properties were also utilized when comparing thespectrum of a species calculated by different methods, orusing different data, in order to determine the best spectrumpossible, particularly when the computation required anaccurate reference-point absorbance, since this was some-times difficult to obtain.An additional independent check on this method ofcalculating formation constants is that the total metalconcentration may be computed, and must be the same as,within experimental error, the known experimental quan-tity of metal in the sample solution.All three methods gave essentially identical calculatedspectra.Resolution of the Calculated Spectra of the Mixed MercuryDiha1ides.-The calculated spectra of the neutral mixeddihalide species in water were analyzed for their componentbands.It is first necessary to determine the number ofbands under a profile, and this may be obtained definitivelyby careful second and fourth differentiation of thespectra.1s,22 The presence or absence of a high-energy tailis not evidenced in this way but unless the spectrum exhibitszero absorbance a t both wavelength extrenia its presencemust normally be included in subsequent curve fitting.Derivative analysis.In this study the earlier pro-cedures 16,22 were not suitable because of the magnitude ofthe residual noise in the smoothed calculated spectra. Ahigher-order differentiating procedure l9 was theref oreemployed. Several second and fourth differentiations wereperformed on each calculated spectrum, with various sizesets of convoluting space elements, since the use of too largesets may result in a loss of resolution of closely overlappingbands, ancl small sets may not enable unambiguous itlenti-fication of peak maxima from noise.This procedureallowed the authoritative conclusion that all the spectra.contained hidden bands not always obvious on visualinspection.For resolving a spectrum the conventionalleast-squares method of fitting a set of component bandsrequires an assumption concerning the type of band distri-bution involved. The usual functions considered areGaussian, Cauchy (Lorentzian), or the product or sumfunctions of both.23 Charge-transfer-to-solvent (c.t.t.s.)spectra require the latter combination for proper resolu-tion; 24 for the intramolecular c.t. transitions describedhere the commonly employed Gaussian function was foundmost suitable.The program was based on the least-squares minimization procedure of Fletcher andand included matrix inversion 26 to increase the rate ofconvergence of fit.Rand shape.Absorption-band parameters for HgXY in water a t 20 "CObserved peaks-7Species Em,,. Ern Emax.HgClI 37.44 2 080 37.8046.6053.40HgBrI 51.28 26 370 37.8043.2051.21HgBrCl 46.95 3 400 43.5047.4057.20Resolved bandsEm2 0004 70020 0002 2002 55026 3002 1002 30035 000W5.885.007.426.065.256.516.514.607.42A2.505.012.842.862.912.2531.636.555.47 0s.1.082.161.231.241.260.9713.715.823.9E~ = molar absorbance (dm3 mol-' cm-l) ; E,,,.= peak max-imum ( lo3 cm-l) ; w = band width at half-height ( lo3 cm-l) ; A =band area (cm3 mol-l cm-l x ; O.S. = oscillator strength.RESULTSThe smoothed calculated spectra, and their resolutions,are given in Figure 2 and the computed band constants inthe Table. (The experimental details and justification foJ.C.S. Daltonthe calculated spectra are given in the following paper.)The resolved peak maxima were close to those indicatedby the derivative spectra. The difference plot given inFigure 2 also shows that a good fit to the data was obtained.20 -'E'i0EU\UJ0mc10 c II -. I , / 1 ,30 34 38 42 46 50IO-~P / cm-1FIGURE 2 Gaussian analysis of the spectra of the mixed neutralhalogenomercurates in water a t 20 OC: (a) HgClI, (b) HgBrI,and (c) HgBrC1; (- - -), resolved bands; (- - .), differencebetween sum of resolved bands and HgXY profileConclusion.-The application of three different comput-ational approaches to the problem of separating the spectraof HgXY from the ever-present spectral contributions ofneutral dihalide and/or halide ion has been successful.Consequently, accurate equilibrium and formation con-stants may now be obtained, and the spectra have beenresolved into their component bands.I t is howeverrecommended that for future similar applications morethan one route to a calculated spectrum should be followedwhenever possible.We thank the S.R.C. for the provision of the Cary 14 Hspectrophotometer. The digitizing attachment was pur-chased on Harwell Contract EMR 1913.We thank theUniversity of Leeds Computing Service for assistance andR. A. A. acknowledges a postgraduate research grant fromLeeds University. T. R. G. thanks the Royal Society for atravel grant and the Chemistry Department, MichiganState University, East Lansing, Michigan 48824, U.S.A. forhospitality and facilities during the preparation of thispaper.[8/1692 Received, 25th Se+tember, 19781REFERENCESG. B. Deacon, Rev. Pure Appl. Chem., 1963, 18, 189.D. Grdenic, Quart. Rev., 1965, 19, 303.L. H. Roberts, Adv. Inorg. Chem. Radiochem., 1968, 11, 309.V. Gutmann, ' Halogen Chemistry,' Academic Press,15 Y. Marcus and I. Eliezer, Co-ordination Chem. Rev., 1969, 4,(I M. L. Delwaulle, Spectrochim. Acta Suppl., 1957, 565.M. L. Delwaulle, Bull. Soc. chim. France, 1955, 1294 andY . Marcus, Acta Chem. Scand., 1957, 11, 329, 599, 610, andO T. G. Spiro and D. N. Hume, J . Amer. Chem. Soc., 1961, 88,lo R. E. Dessy and Y. K. Lee, J . Amer. Chem. Soc., 1960, 82,l1 M. L. Delwaulle and F. Francois, Compt. rend., 1939, 208,la M. Zangen and Y. Marcus, Israel J . 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Comput.London, 1967, vols. 1-111.273.refs. therein.811.4305.689.999,1002.1.Nuclear Chem., 1975, 87, 511.87, 521.1627.1972, 44, 1906.11, 2860.1970, 12, 439.Machinery, 1970, 6, 445
ISSN:1477-9226
DOI:10.1039/DT9800000205
出版商:RSC
年代:1980
数据来源: RSC