ABSTRACT
A position-dependent transformation is introduced for mapping a system of atomistic particles to a system of coarse-grained (CG) variables, which under some circumstances might be considered particles. This CG mapping allows atomistic particles to simultaneously contribute to more than a single CG particle and to change in time the CG particle they are associated with. That is, the CG mapping is dynamic. Mori-Zwanzig theory is then used to obtain the equations of motion for this CG mapping, resulting in conservative, dissipative, and random force terms in generalized, non-Markovian Langevin equations. In addition to the usual forces arising from the effective CG potential derived from atomistic interactions, new forces arise from the dynamic changes in the CG mapping itself. These new forces effectively account for changes arising from fluxes of atomistic particles into and out of CG ones as time progresses. Several examples are given showing the range of problems that can be addressed with this new CG mapping. These range from the usual case where atomistic particles are grouped into large molecular-like chunks, with mappings that remain fixed in time and for which an atomistic particle is part of only a single CG one, to the case where CG particles resemble fluid elements, containing many hundreds of independent atomistic particles. The new CG mapping also allows for hybrid descriptions, in which a part of the system remains atomistic or molecular-like and a part is highly coarse-grained to mesoscopic fluid element-like particles, for example. In the latter case, the equations of motion then provide the correct formalism for determining the forces, beyond the usual conservative ones. This provides a theoretical foundation upon which approximate equations of motion can be formulated to thus build numerical algorithms for expanded applications of accurate CG molecular dynamics.
ABSTRACT
Luminescence spectra of isoelectronic square-planar d8 complexes with 3d, 4d, and 5d metal centers show d-d luminescence with an energetic order different from that of the spectrochemical series, indicating that additional structural effects, such as different ligand-metal-ligand angles, are important factors. Variable-pressure luminescence spectra of square-planar nickel(II), palladium(II), and platinum(II) complexes with dimethyldithiocarbamate ({CH3}2DTC) ligands and their deuterated analogues show unexpected variations of the shifts of their maxima. High-resolution crystal structures and crystal structures at variable pressure for [Pt{(CH3)2DTC}2] indicate that intermolecular M···H-C interactions are at the origin of these different shifts.
ABSTRACT
We present the variable-pressure d-d luminescence spectra of crystalline bis-dimethyldithiocarbamate palladium(ii) and its deuterated analog. The energies and shifts of the band maxima provide evidence for intermolecular PdH-C interactions, with quantitative differences observed for the deuterated complex. Shifts show distinct interactions in three pressure ranges between 1 bar and 85 kbar.
