Temporal mapping of photochemical reactions and molecular excited states with carbon specificity

Easy computation of the Bayes factor to fully quantify Occam's razor in least-squares fitting and to guide actions

The Bayes factor is the gold-standard figure of merit for comparing fits of models to data, for hypothesis selection and parameter estimation. However, it is little-used because it has been considered to be subjective, and to be computationally very intensive. A simple computational method has been known for at least 30 years, but has been dismissed as an approximation. We show here that all three criticisms are misplaced. The method should be used to complement and augment all least-squares fitting, because it can give very different, and better outcomes than classical methods. It can discriminate between models with equal numbers of parameters and equally good fits to data. It quantifies the Occam’s Razor injunction against over-fitting, and it demands that physically-meaningful parameters rejected by classical significance testing be included in the fitting, to avoid spurious precision and incorrect values for the other parameters. It strongly discourages the use of physically-meaningless parameters, thereby satisfying the Occam’s Razor injunction to use existing entities for explanation rather than multiplying new ones. More generally, as a relative probability, the Bayes factor combines naturally with other quantitative information to guide action in the absence of certain knowledge.

Developing effective electronic-only coupled-cluster and Møller-Plesset perturbation theories for the muonic molecules

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the nuclear-electronic orbital theory [Phys. Chem. Chem. Phys., 2018, 20, 4466]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Møller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

Effective electronic-only Kohn-Sham equations for the muonic molecules

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

Photoexcited Muon Spin Spectroscopy: A New Method for Measuring Excess Carrier Lifetime in Bulk Silicon

We have measured excess carrier lifetime in silicon using photoexcited muon spin spectroscopy. Positive muons implanted deep in a wafer can interact with the optically injected excess carriers and directly probe the bulk carrier lifetime while minimizing the effect from surface recombination. The method is based on the relaxation rate of muon spin asymmetry, which depends on the excess carrier density. The underlying microscopic mechanism has been understood by simulating the four-state muonium model in Si under illumination. We apply the technique to different injection levels and temperatures, and demonstrate its ability for injection- and temperature-dependent lifetime spectroscopy.