An official website of the United States government
The molar absorptivity curves for [NiLn(MeOH)6-n]2+ L = pyridine, 3-methylpyridine, 4-methylpyridine, n = 1 – 4, have been simultaneously deduced by modeling composite absorbance data of a series of equilibrium solutions in dry methanol using equilibrium-restricted factor analysis, a technique for obtaining spectral and thermodynamic information for component species involved in solution equilibria. Furthermore, the stepwise formation constants at 296 K have been determined with a high degree of accuracy. For pyridine, logK1-4 = 1.272(6), 0.669(9), 0.14(2), -0.32(2), respectively. For 3-methylpyridine, logK1-4 = 1.802(9), 1.16 (1), 0.32(1), -0.46(1), respectively. For 4-methylpyridine, logK1-4 = 2.808(9), 1.114(4), 0.411(4), -0.421(9), respectively. Unrestricted factor analysis was used to confirm the precise number of unique complexes in each case. The only additional complex for which some evidence was found was the pentakis version of the pyridine complex.
more »
« less
Properly handling negative values in the calculation of binding constants by physicochemical modeling of spectroscopic titration data
Abstract To implement equilibrium hard‐modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high‐throughput Monte Carlo simulations, root‐mean‐square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant despite its ability to address spectrometer noise. Second, both truncation of negative molar absorptivity values and the fast nonnegative least squares algorithms are superior to unconstrained regression because they avoid local minima; however, they introduce bias into the calculated binding constants in the presence of negative baseline offsets. Finally, we establish two theorems showing that negative values are best addressed when all the chemical solutions leading to the raw absorbance data are the result of mixing exactly two distinct stock solutions. This allows the raw absorbance data to be shifted up, eliminating negative baseline offsets, without affecting the concentration matrix, residual matrix, or calculated binding constants. Otherwise, the data cannot be safely upshifted. A comprehensive protocol for analyzing experimental absorbance datasets with is included.
more »
« less
- Award ID(s):
- 2004005
- PAR ID:
- 10459182
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Chemometrics
- Volume:
- 33
- Issue:
- 11
- ISSN:
- 0886-9383
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Computation of binding constants from spectrophotometric titration data is a very popular application of chemometric hard modeling. However, the calculated values are misleading if the correct binding model is not used. Given that many supramolecular systems of interest feature unknown speciation, a priori determination of binding stoichiometry constitutes an important unsolved problem in chemometrics. We present a new and reliable algorithm for accomplishing this task, implemented using a hybrid particle swarm optimization technique. Simultaneous optimization of stoichiometry ratios and binding constants allows the optimal binding model to be calculated in just a few minutes for systems with up to four reactions. Simulated data studies demonstrate that the algorithm finds the correct stoichiometry with up to nine reactions in the absence of noise, including accurately determining species with unusual stoichiometry, such as H2G5. Application to four experimental datasets shows the algorithm is robust to experimental errors for a variety of chemical systems and binding models. This algorithm will facilitate the discovery of complex binding models, increase efficiency in titration analysis, and avert incorrect stoichiometry models, thereby improving the reliability of binding constant information in spectrophotometric titrations.more » « less
-
This paper portrays the solution-phase dynamics as copper(II) and ethylenediamine explore a multitude of different complexes. The data from five spectrophotometric titrations were globally analysed, evidencing four predominant species ([Cu]2+, [Cu(en-N,N’)]2+, [Cu(en-N,N’)2]2+, [Cu(en-N)4]2+) along with their molar absorptivity curves and associative binding constants. The data also seem to support a fifth species, [Cu2(µ-en-N,N’)]4+, in which ethylenediamine bridges two Cu(II) centres. The thermodynamic stability of all five species is corroborated by ab initio computational calculations. The potential existence of [Cu(en-N)4]2+ highlights the suprachelate effect – going beyond the chelate effect – where multidenticity is overtaken by monodenticity. Such dangling multidentate ligands are available to bind to additional metal centres and thus build towards self-assembling supramolecules.more » « less
-
Abstract. Photochemical reactions of contaminants in snow and ice can be importantsinks for organic and inorganic compounds deposited onto snow from theatmosphere and sources for photoproducts released from snowpacks into theatmosphere. Snow contaminants can be found in the bulk ice matrix, ininternal liquid-like regions (LLRs), or in quasi-liquid layers (QLLs) at theair–ice interface, where they can readily exchange with the firn air. Somestudies have reported that direct photochemical reactions occur faster inLLRs and QLLs than in aqueous solution, while others have found similarrates. Here, we measure the photodegradation rate constants for loss of thethree dimethoxybenzene isomers under varying experimental conditions,including in aqueous solution, in LLRs, and at the air–ice interface ofnature-identical snow. Relative to aqueous solution, we find modestphotodegradation enhancements (3- and 6-fold) in LLRs for two of theisomers and larger enhancements (15- to 30-fold) at the air–ice interfacefor all three isomers. We use computational modeling to assess the impact oflight absorbance changes on photodegradation rate enhancements at theinterface. We find small (2–5 nm) bathochromic (red) absorbance shifts atthe interface relative to in solution, which increases light absorption, butthis factor only accounts for less than 50 % of the measured rate constantenhancements. The major factor responsible for photodegradation rateenhancements at the air–ice interface appears to be more efficientphotodecay: estimated dimethoxybenzene quantum yields are 6- to 24-foldlarger at the interface compared to in aqueous solution and account for themajority (51 %–96 %) of the observed enhancements. Using a hypotheticalmodel compound with an assumed Gaussian-shaped absorbance peak, we find thata shift in the peak to higher or lower wavelengths can have a minor tosubstantial impact on photodecay rate constants, depending on the originallocation of the peak and the magnitude of the shift. Changes in other peakproperties at the air–ice interface, such as peak width and height (i.e.,molar absorption coefficient), can also impact rates of light absorption anddirect photodecay. Our results suggest our current understanding ofphotodegradation processes underestimates the rate at which some compoundsare broken down, as well as the release of photoproducts into theatmosphere.more » « less
-
Density functional theory (DFT) calculations are performed to compute the lattice constants, formation energies and vacancy formation energies of transition metal nitrides (TMNs) for transition metals (TM) ranging from 3d–5d series. The results obtained using six different DFT exchange and correlation potentials (LDA, AM05, BLYP, PBE, rPBE, and PBEsol) show that the experimental lattice constants are best predicted by rPBE, while the values obtained using AM05, PBE, rPBE and PBEsol lie between the LDA and BLYP calculated values. A linear relationship is observed between the lattice constants and formation energies with the mean radii of TM and the difference in the electronegativity of TM and N in TMNs, respectively. Our calculated vacancy formation energies, in general, show that N-vacancies are more favorable than TM-vacancies in most TMNs. We observe that N-vacancy formation energies are linearly correlated with the calculated bulk formation energies indicating that TMNs with large negative formation energies are less susceptible to the formation of N-vacancies. Thus, our results from this extensive DFT study not only provide a systematic comparison of various DFT functionals in calculating the properties of TMNs but also serve as reference data for the computation-driven experimental design of materials.more » « less
