Thermal properties of nanofluids using hydrophilic and hydrophobic LiYF4:Yb/Er upconverting nanoparticles.

Luminescent nanoparticles have shown great potential for thermal sensing in bio-applications. Nonetheless, these materials lack water dispersibility that can be overcome by modifying their surface properties with water dispersible molecules such as cysteine. Herein, we employ LiYF4:Er3+/Yb3+ upconverting nanoparticles (UCNPs) capped with oleate or modified with cysteine dispersed in cyclohexane or in water, respectively, as thermal probes. Upconversion emission was used to sense temperature with a relative thermal sensitivity of ∼1.24% K-1 (at 300 K) and a temperature uncertainty of 0.8 K for the oleate capped and of 0.5 K for cysteine modified NPs. To study the effect of the cysteine modification in the heat transfer processes, the thermal conductivity of the nanofluids was determined, yielding 0.123(6) W m-1 K-1 for the oleate capped UCNPs dispersed in cyclohexane and 0.50(7) W m-1 K-1 for the cysteine modified UCNPs dispersed in water. Moreover, through the heating curves, the nanofluids' thermal resistances were estimated, showing that the cysteine modification partially prevents heat transfer.

A combined experimental-molecular modeling study of crown ether europium complexes: Effects of the coordinated anion on structural and luminescence properties.

It is reported the synthesis, characterization by elemental analysis, thermogravimetry; electronic absorption, infrared, excitation, and emission spectroscopies of the [Eu(12C4)(phen)2(X)n]X2 complexes, where 12C4 = 12-crown-4, phen = 1,10-phenanthroline, and X  = F-, Cl-, Br-, SCN-, ClO4-, and NO3-. It is verified that the polarizability of the anion X- exerts remarkable effects on the emission process. As a general trend, lower wavenumbers for the 7F0→5L6, 7F0→5D2 and 7F0→5D1 transitions are associated with the anions with higher volumes and, consequently, higher polarizability. The molecular modeling results performed with quantum methods (RHF and DFT) suggest some relationships between the calculated structures, electronic, and luminescence properties with the presence of the LMCT (ligand-to-metal charge transfer) states, which explains the differences in the emission spectra of these complexes due to the coordinated anion.

Exploring the intra-4f and the bright white light upconversion emissions of Gd2O3:Yb3+,Er3+-based materials for thermometry.

Upconversion broadband white light emission driven by low-power near-infrared (NIR) lasers has been reported for many materials, but the mechanisms and effects related to this phenomenon remain unclear. Herein, we investigate the origin of laser-induced continuous white light emission in synthesized nanoparticles (Gd0.89Yb0.10Er0.01)2O3 and a mechanical mixture of commercial oxides with the same composition 89% Gd2O3, 10% Yb2O3, and 1% Er2O3. We report their photophysical features with respect to sample compactness, laser irradiation (wavelength, power density, excitation cycles), pressure, temperature, and temporal dynamics. Despite the sensitizer (Yb3+) and activator (Er3+) being in different particles for the mechanical mixture, efficient discrete and continuous upconversion emissions were observed. Furthermore, the synthesized nanoparticles were developed as primary luminescent thermometers (upon excitation at NIR) in the 299-363 K range, using the Er3+ upconversion 2H11/2 → 4I15/2/4S3/2 → 4I15/2 intensity ratio. They were also operating as secondary ones in the 1949-3086 K, based on the blackbody distribution of the observed white light emission. Our findings provide important insights into the mechanisms and effects related to the transition from discrete to continuous upconversion emissions with potential applications in remote temperature sensing.

Temperature Dependence of Hydrogen Bond Networks of Liquid Water: Thermodynamic Properties and Structural Heterogeneity from Topological Descriptors.

Topological analyses of hydrogen bond networks were performed based on the complex network and island statistics of liquid water at different temperatures. The influence of temperature on the liquid water structures and the topological properties of the hydrogen bond networks was investigated by Metropolis Monte Carlo simulations with the TIP4P/2005 potential model. The bilinear behavior of the second peak in the radial distribution function with the temperature was properly reproduced by these simulations. The average connectivity also displayed a bilinear behavior consistent with being a local descriptor. The semiglobal average path length (or geodesic distance) descriptor showed an unprecedented trimodal distribution, whose areas were dependent on the temperature. Considering equilibrium between these three sets of networks, standard enthalpy and entropy of equilibrium were determined for the first time, providing new insights into the structural heterogeneities of liquid water with interesting perspectives for modeling these quantitative properties of hydrogen bond networks.

Surface Plasmon-Photon Coupling in Lanthanide-Doped Nanoparticles.

Lanthanide-doped nanoparticles have great potential for energy conversion applications, as their optical properties can be precisely controlled by varying the doping composition, concentration, and surface structures, as well as through plasmonic coupling. In this Perspective we highlight recent advances in upconversion emission modulation enabled by coupling upconversion nanoparticles with well-defined plasmonic nanostructures. We emphasize fundamental understanding of luminescence enhancement, monochromatic emission amplification, lifetime tuning, and polarization control at nanoscale. The interplay between localized surface plasmons and absorbed photons at the plasmonic metal-lanthanide interface substantially enriches the interpretation of plasmon-coupled nonlinear photophysical processes. These studies will enable novel functional nanomaterials or nanostructures to be designed for a multitude of technological applications, including biomedicine, lasing, optogenetics, super-resolution imaging, photovoltaics, and photocatalysis.

Thermal properties of lipid bilayers derived from the transient heating regime of upconverting nanoparticles.

Heat transfer and thermal properties at the nanoscale can be challenging to obtain experimentally. These are potentially relevant for understanding thermoregulation in cells. Experimental data from the transient heating regime in conjunction with a model based on the energy conservation enable the determination of the specific heat capacities for all components of a nanoconstruct, namely an upconverting nanoparticle and its conformal lipid bilayer coating. This approach benefits from a very simple, cost-effective and non-invasive optical setup to measure the thermal parameters at the nanoscale. The time-dependent model developed herein lays the foundation to describe the dynamics of heat transfer at the nanoscale and were used to understand the heat dissipation by lipid bilayers.

Overlap properties of chemical bonds in generic systems including unusual bonding situations.

Chemical bond is a ubiquitous and fundamental concept in chemistry, in which the overlap plays a defining role. By using a new approach based on localized molecular orbitals, the overlap properties, e.g., polarizability [Formula: see text], population pOP, intra [Formula: see text], and inter [Formula: see text] repulsions, and density ρOP, of polyatomic systems were calculated, analyzed, and correlated. Several trends are shown for these properties, which are rationalized by the balance of some well-known effects, such as, electron donor/withdrawing character and electronegativity. The overlap properties of unusual bonds are also analyzed, revealing an OZn4(OOCH)6 structure with four equivalent Zn-O chemical bonds with overlap properties like the O-O bond in H2O2, while in protonated methane [Formula: see text], it is observed that a CH3⋯[Formula: see text] bond pattern at the equilibrium structure changes to a [Formula: see text]⋯H2 pattern upon dissociation. Charge-shift resonance energies, atom-in-molecule properties, and the lone-pair-bond-weakening effects are related to the overlap properties, which can provide alternative views and insights into chemical bonds. Graphical abstract A chemical bond analysis approach based on its overlap properties is presented for the first time. The model was applied directly to 25 diatomics and for 28 bonds in polytomics employing localized molecular orbitals. Correlations of the overlap properties with the charge-shift resonance energies and with atom-in-molecule (AIM) properties were uncovered. In addition, it provided insights into the Zn-O bonds in the unusual OZn4(OOCH)6 system as well as in the bonding patterns of [Formula: see text] at equilibrium and upon dissociation.

Simulation of the Adsorption and Release of Large Drugs by ZIF-8.

The adsorption and release of two drugs 5FU (5-fluorouracil) and CAF (caffeine) into and from the ZIF-8 framework were simulated by the Gibbs-ensemble Monte Carlo approach employing two models for representing the sorbent: one without surface (ZIF-8P) and another with surface (ZIF-8S). The inner pores of ZIF-8S were inaccessible to the drugs, but accessible to the solvents (methanol or water). The ZIF-8P model is not recommended to describe the actual sorption processes because it lacks surface and solvent effects, which are reflected in the poor quantitative agreement with experimental results. The ZIF-8S model yielded results for the sorption of CAF in very close agreement with the experimental loading from methanol solution and release of the drug into water. For 5FU, the computer simulations provided qualitative agreements, which suggests that the sorbent-5FU interaction potentials should be improved. The excellent performance of the ZIF-8S model is due to its adequate description of the surface and by exposing adsorption sites such as undercoordinated zinc ions to interactions with large molecules. This was achieved by applying periodic conditions to a ZIF-8 nanocrystal, instead of an elementary cell, which is easy to generalize and used to describe several surface defects. Furthermore, the combination of this ZIF-8S model with the Monte Carlo method provides a very simple and efficient approach to simulate the inaccessibility of the ZIF-8 inner porosity to large molecules. Namely, any trial moves that inserted the drug within the pore were disregarded. This is a quite simple and general approach that can be promptly applied to a large number of MOF sorbents and of drugs that cannot access the inner pores.

A thermo-responsive adsorbent-heater-thermometer nanomaterial for controlled drug release: (ZIF-8,EuxTby)@AuNP core-shell.

An adsorbent-heater-thermometer nanomaterial, (ZIF-8,EuxTby)@AuNP, based on ZIF-8 (adsorbent), containing Eu3+ and/or Tb3+ ions (thermometer) and gold nanoparticles (AuNPs, heater) was designed, synthetized, characterized, and applied to controlled drug release. These composite materials were characterized as core-shell nanocrystals with the AuNPs being the core, around which the crystalline ZIF-8 has grown (shell) and onto which the lanthanide ions have been incorporated or chemosorbed. This shell of ZIF-8 acts as adsorbent of the drugs, the AuNPs act as heaters, while the luminescence intensities of the ligand and the lanthanide ions are used for temperature monitoring. This thermo-responsive material can be activated by visible irradiation to release small molecules in a controlled manner as established for the model pharmaceutical compounds 5-fluorouracil and caffeine. Computer simulations and transition state theory calculations shown that the diffusion of small molecules between neighboring pores in ZIF-8 is severely restricted and involves high-energy barriers. These findings imply that these molecules are uploaded onto and released from the ZIF-8 surface instead of being inside the cavities. This is the first report of ZIF-8 nanocrystals (adsorbents) containing simultaneously lanthanide ions as sensitive nanothermometers and AuNPs as heaters for controlled drug release in a physiological temperature range. These results provide a proof-of-concept that can be applied to other classes of materials, and offer a novel perspective on the design of self-assembly multifunctional thermo-responsive adsorbing materials that are easily prepared and promptly controllable.

Modeling zigzag CNT: dependence of structural and electronic properties on length, and application to encapsulation of HCN and C2H2.

Density functional theory (B3LYP, B3LYP-D2 and wB97XD functionals) was used in finite models of zigzag carbon nanotubes (CNT), (n,0)×k with n = 6-9 and k = 2-4, to systematically investigate the effects of size on their structural and electronic properties. We found that the ratio between the length (L t) and the diameter (d t) of the pristine CNT has to be larger than 2, i.e., L t/d t > 2, in order to provide the observed experimental trends of C=C bond distances, as well as to maintain the atomic charges nearly constant and zero around the center of the tube. Therefore, the concepts of useful length and volume were developed and tested for the encapsulation process of HCN and C2H2 into CNTs. The energies involved in these processes, as well as the changes in molecular structure and electronic properties of the dopants and the CNTs are discussed and rationalized by the amount of charge transferred between dopant and CNT. Graphical Abstract Illustration of zigzag CNT length and diameter ratio in order to represent C=C bond experimental trend.

Benchmark, DFT assessments, cooperativity, and energy decomposition analysis of the hydrogen bonds in HCN/HNC oligomeric complexes.

Hydrogen cyanide (HCN) and its tautomer hydrogen isocyanide (HNC) are relevant for extraterrestrial chemistry and possible relation to the origin of biomolecules. Several processes and reactions involving these molecules depend on their intermolecular interactions that can lead to aggregates and liquids especially due to the hydrogen bonds. It is thus important to comprehend, to describe, and to quantify their hydrogen bonds, mainly their nature and the cooperativity effects. A systematic study of all linear complexes up to pentamers of HCN and HNC is presented. CCSD(T)/CBS energy calculations, with and without basis set superposition error (BSSE) corrections for energies and geometries, provided a suitable set of benchmarks. Approximated methods based on the density functional theory (DFT) such as BP86, PBE, TPSS, B3LYP, CAM-B3LYP with and without dispersion corrections and long-range corrections, were assessed to describe the interaction energies and cooperativity effects. These assessments are relevant to select DFT functionals for liquid simulations. Energy decomposition analysis was performed at the PBE/STO-TZ2P level and provided insights into the nature of the hydrogen bonds, which are dominated by the electrostatic component. In addition, several linear relationships between the various energy components and the interaction energy were obtained. The cooperativity energy was also found to be practically linear with respect to the interaction energy, which may be relevant for designing and/or correcting empirical force fields. Graphical Abstract Hydrogen bonds in HCN/HNC oligomeric complexesᅟ.

A Green Approach for Allylations of Aldehydes and Ketones: Combining Allylborate, Mechanochemistry and Lanthanide Catalyst.

Secondary and tertiary alcohols synthesized via allylation of aldehydes and ketones are important compounds in bioactive natural products and industry, including pharmaceuticals. Development of a mechanochemical method using potassium allyltrifluoroborate salt and water, to successfully perform the allylation of aromatic and aliphatic carbonyl compounds is reported for the first time. By controlling the grinding parameters, the methodology can be selective, namely, very efficient for aldehydes and ineffective for ketones, but by employing lanthanide catalysts, the reactions with ketones can become practically quantitative. The catalyzed reactions can also be performed under mild aqueous stirring conditions. Considering the allylation agent and its by-products, aqueous media, energy efficiency and use of catalyst, the methodology meets most of the green chemistry principles.

Dynamical Bifurcation in Gas-Phase XH- + CH3 Y SN 2 Reactions: The Role of Energy Flow and Redistribution in Avoiding the Minimum Energy Path.

The gas-phase reactions of XH- (X=O, S) + CH3 Y (Y=F, Cl, Br) span nearly the whole range of SN 2 pathways, and show an intrinsic reaction coordinate (IRC) (minimum energy path) with a deep well owing to the CH3 XH⋅⋅⋅Y- (or CH3 S- ⋅⋅⋅HF) hydrogen-bonded postreaction complex. MP2 quasiclassical-type direct dynamics starting at the [HX⋅⋅⋅CH3 ⋅⋅⋅Y]- transition-state (TS) structure reveal distinct mechanistic behaviors. Trajectories that yield the separated CH3 XH+Y- (or CH3 S- +HF) products directly are non-IRC, whereas those that sample the CH3 XH⋅⋅⋅Y- (or CH3 S- ⋅⋅⋅HF) complex are IRC. The IRCIRC/non-IRC ratios of 90:10, 40:60, 25:75, 2:98, 0:100, and 0:100 are obtained for (X, Y)=(S, F), (O, F), (S, Cl), (S, Br), (O, Cl), and (O, Br), respectively. The properties of the energy profiles after the TS cannot provide a rationalization of these results. Analysis of the energy flow in dynamics shows that the trajectories cross a dynamical bifurcation, and that the inability to follow the minimum energy path arises from long vibration periods of the X-C⋅⋅⋅Y bending mode. The partition of the available energy to the products into vibrational, rotational, and translational energies reveals that if the vibrational contribution is more than 80 %, non-IRC behavior dominates, unless the relative fraction of the rotational and translational components is similar, in which case a richer dynamical mechanism is shown, with an IRC/non-IRC ratio that correlates to this relative fraction.

Structural and relative energy assessments of DFT functionals and the MP2 method to describe the gas phase methylation of nitronates: [R(1)R(2)CNO2](-) + CH3I.

The performances of 26 combinations of density-functional theory (DFT) functionals or second-order Møller-Plesset (MP2) methods and basis sets were evaluated for the calculation of the activation energy (Δ(‡)E), the energy available (ΔRCE) to the reactant complex, the energy of reaction (ΔrE), and rotational constants of the main structures involved in the methylation reactions of nitronates, [R(1)R(2)CNO2](-) + CH3I, in the gas phase, where R(1) = R(2) = H, R(1) = H and R(2) = CH3, R(1) = R(2) = CH3, and R(1) + R(2) = c-(CH2)2. The separated reactants and products, the reactant and product complexes, and the transition states were considered, leading to 43 data points for the statistical analysis for each method under assessment. Five statistical quantifiers: the mean signed error (MSE), the mean unsigned error (MUE), the percent mean relative error (% MRE), best and worse (BW), and the confidence interval (CI) were used to assess the performance of methods relative to the CCSD(T)/CBS//MP2/aug-cc-pVTZ reference method. The DFT functionals included the widely applied B3LYP and M06-2X global-hybrids and the recently available DSD-PBEP86, DSD-PBEP86-D3BJ and PWPB95 double-hybrids. The basis sets involved an effective core potential (ECP) for describing the inner electrons of iodine such as LANL2DZdp and aug-cc-pVXZ-PP (X = D, T, and Q), and all-electron basis sets for the remaining atoms. The energy available to the reactant complex is described quite well by all methods, however, only the MP2/aug-cc-pVTZ-PP method provided values within 2 kcal mol(-1) (8.4 kJ mol(-1)) from the reference method for Δ(‡)E and ΔrE. Amongst the DFT methods, the global-hybrid M06-2X functional produced the best overall results including BW and CI. Notice that all methods yielded the smallest Δ(‡)E for the C-methylation pathway. The rotational constants of the reactant complexes and the transition state structures were compared, for which the MP2 method and the M06-2X functional provided the most accurate results. Thus, unlike previous assessments of DFT functionals for describing SN2 reactions, M06-2X was the most accurate for these methylation reactions of nitronates, followed closely by the DSD-PBEP86 double-hybrid functional. The inclusion of dispersion effects with DSD-PBEP86-D3BJ does not improve the accuracy. Whereas MP2/aug-cc-pVTZ was the most accurate and nearly provided results with chemical accuracy.

Molecular Dynamics Simulations of Specific Anion Adsorption on Sulfobetaine (SB3-14) Micelles.

Structures of zwitterionic micelles of 61 sulfobetaine SB3-14, CH3(CH2)13[N(+)(CH3)2](CH2)3SO3(-), molecules in water and in 0.15 and 0.015 mol L(-1) NaX (X = F(-), Cl(-), Br(-), I(-), and ClO4(-)) aqueous solutions were investigated by atomistic molecular dynamics simulations. The micelle presents a near-spherical shape and an average angle of 110° between the zwitterionic headgroup and the alkyl tail that provides an L-type shape for the surfactants and exposes the positive charged ammonium groups to the solution. This allows anions to adsorb at the surface of the micelle and the amount of adsorbed anions follows the Hofmeister series F(-) < Cl(-) < Br(-) < I(-) < ClO4(-), which directly correlates to the measured values of the zeta-potential. The size and shape of the micelle are not affected by the salt, except the solvent accessible surface area that decreases for strongly adsorbing anions such as ClO4(-) due to the approximation of the headgroups between adjacent surfactants. Indeed, the ion distribution shows the formation of ion-pair-type species between ammonium and perchlorate, which indicates that the adsorption is directly related to the easiness of the anion to partially lose its hydration shell.

Revisiting the concept of the (a)synchronicity of Diels-Alder reactions based on the dynamics of quasiclassical trajectories.

A number of model Diels-Alder (D-A) cycloaddition reactions (H2C=CH2 + cyclopentadiene and H2C=CHX + 1,3-butadiene, with X = H, F, CH3, OH, CN, NH2, and NO) were studied by static (transition state - TS and IRC) and dynamics (quasiclassical trajectories) approaches to establish the (a)synchronous character of the concerted mechanism. The use of static criteria, such as the asymmetry of the TS geometry, for classifying and quantifying the (a)synchronicity of the concerted D-A reaction mechanism is shown to be severely limited and to provide contradictory results and conclusions when compared to the dynamics approach. The time elapsed between the events is shown to be a more reliable and unbiased criterion and all the studied D-A reactions, except for the case of H2C=CHNO, are classified as synchronous, despite the gradual and quite distinct degrees of (a)symmetry of the TS structures.

Understanding the Reactivity and Regioselectivity of Methylation of Nitronates [R(1)R(2)CNO2](-) by CH3I in the Gas Phase.

Methylation of [R(1)R(2)CNO2](-), where R(1) = R(2) = H (1), R(1) = CH3 and R(2) = H (2), R(1) = R(2) = CH3 (3), and R(1) + R(2) = c-(CH2)2 (4), by CH3I was studied by an ab initio MP2/CBS method, RRKM theory, and kinetic simulations. Contrary to a previous proposal for the reaction mechanism, C-methylation is the preferred pathway of thermodynamics and kinetics. This is corroborated by the agreement between the calculated and experimental reactivity trend 4 ≫ 3 > 2 > 1. The regioselectivity toward C-alkylation is explained by the much larger exothermicity of this reaction channel compared to that of O-alkylation. The increase in reactivity with an increase in the crowdedness of the central carbon atom is explained by differences in sp(3) character at this atom and the decrease in the vibrational frequency associated with pyramidalization around this carbon atom.

Features of chemical bonds based on the overlap polarizabilities: diatomic and solid-state systems with the frozen-density embedding approach.

The chemical bond overlap properties were obtained for alkali halides NaY (Y = F, Cl, Br), alkaline-earth chalcogenides MX (M = Ca, Mg and X = O, S, Se) and alkali and alkali-earth metals (Li, Na, and Mg) in diatomic and solid-state systems using an embedding approach based on the frozen density functional theory to simulate the crystalline effects. The computational protocol established provides errors for bond distances smaller than 1%. The results indicate that larger chemical bond covalency leads to larger absorption or scattering by the overlap region. The ionic specific valence and overlap polarizability are closely related to the valence orbital compactness measured by the sum of Mulliken electronegativities. The embedding approach used in this work makes it possible to quantify the effects of the crystalline environment on the chemical bond overlap properties. In the solid-state, the bond overlap charges are less polarizable, in cases of well-known ionic systems (provided by electronegativity differences), leading to smaller chemical bond covalency in solids than in diatomics. The spectroscopic properties of the polarizability of the electron density in the overlap region of a chemical bond could be measured in the 1-20 eV spectral region and could be used to characterize some bands in several spectra whose assignments are ambiguous or not available.

Efficient and tuneable photoluminescent boehmite hybrid nanoplates lacking metal activator centres for single-phase white LEDs.

White light-emitting diodes (WLEDs) are candidates to revolutionize the lighting industry towards energy efficient and environmental friendly lighting and displays. The current challenges in WLEDs encompass high luminous efficiency, chromatic stability, high colour-rending index and price competitiveness. Recently, the development of efficient and low-cost downconverting photoluminescent phosphors for ultraviolet/blue to white light conversion was highly investigated. Here we report a simple route to design high-efficient WLEDs by combining a commercial ultraviolet LED chip (InGaAsN, 390 nm) and boehmite (γ-AlOOH) hybrid nanoplates. Unusually high quantum yields (ηyield=38-58%) result from a synergic energy transfer between the boehmite-related states and the triplet states of the benzoate ligands bound to the surface of the nanoplates. The nanoplates with ηyield=38% are able to emit white light with Commission International de l'Eclairage coordinates, colour-rendering index and correlated colour temperature values of (0.32, 0.33), 85.5 and 6,111 K, respectively; overwhelming state-of-the-art single-phase ultraviolet-pumped WLEDs phosphors.

Assessment of density-functionals for describing the X(-) + CH3ONO2 gas-phase reactions with X = F, OH, CH2CN.

The energetics of the ECO2, SN2@C and SN2@N channels of X(-) + CH3ONO2 (X = F, OH, CH2CN) gas-phase reactions were computed using the CCSD(T)/CBS method. This benchmark extends a previous study with X = OH [M. A. F. de Souza et al., J. Am. Chem. Soc., 2012, 134, 19004] and was used to ascertain the accuracy and robustness of nineteen density-functionals for describing these potential energy profiles (PEP) as well as the kinetic product distributions obtained from RRKM calculations. Assessments were based on the mean unsigned error (MUE), the mean signed error (MSE), the #best : #worst (BW) criterion and the statistical confidence interval (CI) for the MSE. In general, double-hybrid (DH) functionals perform better than the range-separated ones, and both are better than the global-hybrid functionals. Based on the MUE and CI criteria the B2GPPLYP, B2PLYP, M08-SO, BMK, ωB97X-D, CAM-B3LYP, M06, M08-HX, ωB97X and B97-K functionals show the best performance in the description of these PEPs. Within this set, the B2GPPLYP functional is the most accurate and robust. The RRKM results indicate that the DHs are the best for describing the selectivities of these reactions. Compared to CCSD(T), the B2PLYP method has a relative error of only ca. 1% for the selectivity and the accuracy to provide the correct conclusion concerning the nonstatistical behavior of these reactions.