The neglected halogen dimer bands: Dimerization equilibrium constants from spectrophotometric data Joel Tellinghuisen Department of Chemistry Vanderbilt University Nashville, TN 37235

An old problem: Br 2 (g)Evans, JCP 23, 1426 (1955). Ogryzlo & Sanctuary, JPC 69, 4422 (1965). Passchier, Christian, & Gregory, JPC 71, 937 (1967). Wen & Noyes, JPC 76, 1017 (1972). I 2 (g)Tamres, Duerksen, & Goodenow, JPC 72, 966 (1968). Passchier & Gregory, JPC 72, 2697 (1968). I 2 (soln)Keefer & Allen, JCP 25, 1059 (1956). de Maine, et al., JCP 24, 1091; Can. JC 35, 573 (1957); JMS 4, 271 (1960).

Consider Br 2 (g) … * * J.Phys.Chem.A (ASAP).

Treat as sum of contributions: A = b (  1 [Br 2 ] +  2 K c [Br 2 ] 2 )  b (  1 c +  2 K c c 2 ) Ideal gas:c = P/RT = c 1 + c 2 c 1 = (2 K c ) –1 [(1 + 4 K c c) 1/2 – 1] Feasibility of analysis depends on extent to which c 1 ≠ c; if c 2 is too small, can estimate only  1 and  2 K c.

Analyze 18 spectra using simplified scheme dimer monomer Passchier, Christian, & Gregory Wen & Noyes Hubinger & Nee, (1995) Present — dimer slighty stronger, monomer weaker 23°C

For multispectrum analysis, need to weight data, because short- much less precise. Use preliminary analysis to estimate  2 (l).

Examine results from 4-parameter model at selected wavelength. (Parameters include constant A 0.) Differences between 3- and 4-parameter models appear only on blowup — suggests baseline important. 205 nm

Another question: Given subtle differences, are parameters and errors returned by 4-parameter model realistic? Address w/ Monte Carlo calculations. Key Results: Parameters not significantly biased and errors reasonable.  2 is ~35% smaller for 4-parameter model, when justified. Parameters K c,  1, A 0 near-normal;  2 grossly nonnormal — manifested as divergences in MC runs; none when 4th parameter defined as  2 K c.

Examine baseline by accumulating statistics on multiple scans. [Baseline is set by an instrumental routine run w/ solvent in sample cell.] Error bars = standard errors. Blue and red recorded for same baseline function; yellow after resetting. Conclusion: Need baseline data; include as zero-c spectra.

Global analysis — Fit to 3 A 0 parameters,  1, and  2 at each, plus K c valid at all —18 spectra + 6 baseline scans. Examine dependence of K c on data selection … From such considerations, K c = 2.5(4) L/mol. Results from analyzing 4 adjacent (1 nm) wavelengths at a time.

van’t Hoff plot for comparison with previous — present K c more than factor 2 larger. Lasater, et al., JACS, Kokovin, Russ. J. Inorg. C., (Both from ideal gas model of PVT deviations; correction for excluded V is in right direction but too small to resolve discrepancies.)

Discrete structure in spectra? Examine residuals. Statistically significant excursions attributed to subtle correlation effects. monomer dimer

Although K c is >2 times previous estimate, it,  H° (–9.5 kJ/mol), and  S° (–51 J mol –1 K –1 ) are commensurate with results for I 2 (g) (more below). Maximum [Br 4 ] < 2% at 23°C and 119 Torr; dimers should become much more prominent at lower T, e.g., in properly designed free-jet expansions. Dimer bands long attributed to charge-transfer transitions; nothing new there from this study. Monomer band factor of 4 weaker than weakest of well-known UV-visible bands, A  X. Factor of 7 weaker than corresponding band for I 2 (270 nm, below). For the dimer,  2 K c is a factor of 2 weaker than the same in I 2. So, on to I 2 (soln) …

A different baseline problem — cell replacement error.

Position and strength of monomer band depend strongly on medium; current CCl 4 results suggest more than one transition. I2I2

Quantitative consensus lacking, but T dependence does yield consistent estimates of  H° for dimerization. Prominent medium wavelength shift. Shape again suggests multiple transitions. I4I4

These dimerization equilibria are notoriously problematic, so it is reassuring to consider a related “slam dunk” — the BrCl formation reaction.* * J. Phys. Chem. A. 107, 753 (2003).

Analysis yields K = 9.1, with a nominal  of This translates into a remarkable ±0.4 cm –1 in D e for BrCl — a precision that rivals spectroscopic methods from essentially a thermochemical method. Consideration of possible model error leads to a more conservative ±0.2, and D e = ± 2 cm –1.