Grand Canonical Adaptive Resolution Simulation for Molecules with Electrons: A Theoretical Framework based on Physical Consistency

A theoretical scheme for the treatment of an open molecular system with electrons and nuclei is proposed. The idea is based on the Grand Canonical description of a quantum region embedded in a classical reservoir of molecules. Electronic properties of the quantum region are calculated at constant electronic chemical potential equal to that of the corresponding (large) bulk system treated at full quantum level. Instead, the exchange of molecules between the quantum region and the classical environment occurs at the chemical potential of the macroscopic thermodynamic conditions. T he Grand Canonical Adaptive Resolution Scheme is proposed for the treatment of the classical environment; such an approach can treat the exchange of molecules according to first principles of statistical mechanics and thermodynamic. The overall scheme is build on the basis of physical consistency, with the corresponding definition of numerical criteria of control of the approximations implied by the coupling. Given the wide range of expertise required, this work has the intention of providing guiding principles for the construction of a well founded computational protocol for actual multiscale simulations from the electronic to the mesoscopic scale.Comment: Computer Physics Communications (2017), in pres

Innovation Contests with Entry Auction

We consider procurement of an innovation from heterogeneous sellers. Innovations are random but depend on unobservable effort and private information. We compare two procurement mechanisms where potential sellers first bid in an auction for admission to an innovation contest. After the contest, an innovation is procured employing either a fixed prize or a first-price auction. We characterize Bayesian Nash equilibria such that both mechanisms are payoff-equivalent and induce the same efforts and innovations. In these equilibria, signaling in the entry auction does not occur since contestants play a simple strategy that does not depend on rivals' private information

catena-Poly[[(1,10-phenanthroline)cobalt(II)]-di-μ-azido]

In the crystal structure of the binuclear title complex, [Co(N3)2(C12H8N2)]n, each CoII cation is coordinated by two N atoms from one chelating 1,10-phenanthroline ligand and four azide ligands in a slightly distorted octa­hedral coordination. The two CoII cations of the binuclear complex are related by an inversion centre and are bridged by two symmetry-related azide ligands in both μ1,1 and μ1,3 modes. The μ1,3 bridging mode gives rise to an infinite one-dimensional chain along the a axis, whereas the μ1,1 bridging mode is responsible for the formation of the binuclear CoII complex

catena-Poly[[(pyrimidine-2-carb­oxy­lic acid)iron(II)]-μ-oxalato]

In the title complex, [Fe(C2O4)(C5H4N2O4)]n, the FeII ion is coordinated by two oxalate anions and a pyrimidine-2-carb­oxy­lic acid ligand in a slightly distorted octa­hedral geometry. Each oxalate anion chelates to two FeII ions, forming chains along the a axis. The chains are further connected by O—H⋯O and C—H⋯O hydrogen bonds, stabilizing the structure. An intra­molecular O—H⋯N inter­action results in a five-membered ring

Bis[N,N-bis­(2-hy­droxy­eth­yl)glycinato]cobalt(II)

The asymmetric unit of the title compound, [Co(C6H12NO4)2], contains one half-mol­ecule with the CoII ion situated on an inversion center. Inter­molecular O—H⋯O hydrogen bonds generate a three-dimensional hydrogen-bonding network, which consolidates the crystal packing

Poly[(μ4-1,2,3-benzothia­diazole-7-carboxyl­ato)silver(I)]

In the crystal structure of the title compound, [Ag(C7H3N2O2S)]n, the AgI atom is coordinated by two N atoms and three O atoms of four organic ligands forming a distorted square pyramid. The carboxyl­ate group acts as a bidentate ligand on one AgI atom and as a bridging group for a symmetry-related AgI atom, forming a dimer. Futhermore, the two N atoms of two thia­diazole rings bridge a third symmetry-related AgI atom, forming a six-membered ring. These two frameworks, AgO2Ag and AgN4Ag, extend in three directions, forming a three-dimensionnal polymer. The whole polymer is organized around inversion centers

Poly[tetra-μ1,1-azido-bis­(μ2-pyrimidine-2-carboxyl­ato)tricopper(II)]

In the title compound, [Cu3(C5H3N2O2)2(N3)4]n, one of the CuII atoms lies on an inversion centre and is octa­hedrally coordinated by two bidentate chelating pyrimidine-2-carboxyl­ate ligands and two azide anions, each of which gives an N:N-bridge to the second inversion-related CuII centre in the formula unit. The second CuII atom is five-coordinated with a distorted square-pyramidal coordination sphere comprising a single bidentate chelating pyrimidine-2-carboxyl­ate anion and three azide N anions, two of which doubly bridge centrosymmetric CuII centres, giving a two-dimensional network structure extending parallel to (010)