Forecasted sales of China sports lottery through 2035.

Forecasted sales of China sports lottery through 2035.</p

Sales of China sports lottery between 2011 and 2022.

The pink line indicates the trend between 2011 and 2019, the red line indicates the trend between 2020 and 2022, and the blue line indicates the overall trend within the data set. The confidence level (shaded region) for the overall data is set at 90%.</p

Fig 2 -

Worm plot of the model residual: (A) stable model; (B) shock model.</p

Sales of China sports lottery modeled with GAMLSS distributions.

Sales of China sports lottery modeled with GAMLSS distributions.</p

On the Nature of Support Effects of Metal Dioxides MO₂ (M = Ti, Zr, Hf, Ce, Th) in Single-Atom Gold Catalysts: Importance of Quantum Primogenic Effect

Fundamental understanding of support effects and metal–support interaction is critical in heterogeneous catalysis. In this work, theoretical investigations are carried out to study the nature of support effects of different tetravalent-metal dioxides of MO₂ (M = Ti, Zr, Ce, Hf, Th) in single-atom gold catalysts using density functional theory with on-site Coulomb interactions (DFT+U). The properties of gold adatom on the stoichiometric (MO₂) and reduced (MO_2–<i>x</i>) surfaces as well as CO adsorption on Au₁/MO₂ and Au₁/MO_2–<i>x</i> have been investigated systematically. Our calculations indicate that the fundamental <i>quantum primogenic effect</i> that causes the radial contraction and low orbital energies of 3d and 4f orbitals in these MO₂ oxides plays a vital role in determining the valence states and charge distribution of single-atom gold as well as the adsorption modes of CO on various MO₂ supports. We find that gold atoms supported on different surfaces exhibit oxidation states from Au­(−I) to Au(0) to Au­(I), depending on the nature of the metal oxide supports. The support-dependent oxidation states and charge distribution of Au can further influence the adsorption mode of CO. While CO adsorbs strongly on Au­(I) in Au₁/MO₂ (M = Ti, Ce) via Au–C σ-bonding, weaker adsorption occurs on Au(0) in Au₁/MO₂ (M = Zr, Hf, Th) with charge back-donation to CO 2π* antibonding orbitals. In contrast, at Au₁/MO_2–<i>x</i> of reduced support, CO adsorption is stronger for M = Zr, Hf, and Th than for M = Ce. These results provide essential understanding on the nature of support effects of metal oxides in heterogeneous catalysis

Geometries from The influences of ammonia on aerosol formation in the ozonolysis of styrene: roles of Criegee intermediate reactions

Geometries optimized at the B3LYP/6-311G++(2d,2p)

How Much Can Density Functional Approximations (DFA) Fail? The Extreme Case of the FeO₄ Species

A thorough theoretical study of the relative energies of various molecular Fe·4O isomers with different oxidation states of both Fe and O atoms is presented, comparing simple Hartree–Fock through many Kohn–Sham approximations up to extended coupled cluster and DMRG multiconfiguration benchmark methods. The ground state of Fe·4O is a singlet, hexavalent iron­(VI) complex ¹<i>C</i>_2v-[Fe­(VI)­O₂]²⁺(O₂)^2–, with isomers of oxidation states Fe­(II), Fe­(III), Fe­(IV), Fe­(V), and Fe­(VIII) all lying slightly higher within the range of 1 eV. The disputed existence of oxidation state Fe­(VIII) is discussed for isolated FeO₄ molecules. Density functional theory (DFT) at various DF approximation (DFA) levels of local and gradient approaches, Hartree–Fock exchange and meta hybrids, range dependent, DFT–D and DFT+U models do not perform better for the relative stabilities of the geometric and electronic Fe·4O isomers than within 1–5 eV. The Fe·4O isomeric species are an excellent testing and validation ground for the development of density functional and wave function methods for strongly correlated multireference states, which do not seem to always follow chemical intuition

Rate constants from The influences of ammonia on aerosol formation in the ozonolysis of styrene: roles of Criegee intermediate reactions

The rate constants for bimolecular reactions