A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

HSAB principle applied to the time evolution of chemical reactions

Time evolution of various reactivity parameters such as electronegativity, hardness, and polarizability associated with a collision process between a proton and an X- atom/ion (X = He, Li(+), Be(2+), B(3+), C(4+)) in its ground ((1)S) and excited((1)P,(1)D,(1)F) electronic states as well as various complexions of a two-state ensemble is studied using time-dependent and excited-state density functional theory. This collision process may be considered to be a model mimicking the actual chemical reaction between an X-atom/ion and a proton to give rise to an XH(+) molecule. A favorable dynamical process is characterized by maximum hardness and minimum polarizability values according to the dynamical variants of the principles of maximum hardness and minimum polarizability. An electronic excitation or an increase in the excited-state contribution in a two-state ensemble makes the system softer and more polarizable, and the proton, being a hard acid, gradually prefers less to interact with X as has been discerned through the drop in maximum hardness value and the increase in the minimum polarizability value when the actual chemical process occurs. Among the noble gas elements, Xe is the most reactive. During the reaction: H(2) + H(+) --> H(3)(+) hardness maximizes and polarizability minimizes and H(2) is more reactive in its excited state. Regioselectivity of proton attack in the O-site of CO is clearly delineated wherein HOC(+) may eventually rearrange itself to go to the thermodynamically more stable HCO(+).     

Stability and reactivity of all-metal aromatic and antiaromatic systems in light of the principles of maximum hardness and minimum polarizability

It is demonstrated that among various possible isomers of all-metal aromatic compounds such as Al(4)(2-) and their complexes the most stable isomer with the minimum energy is the hardest and the least polarizable. A similar situation is observed for different isomers of all-metal antiaromatic compounds such as Al(4)(4-) and their complexes. It is shown that linear Al(4)(4-) is energetically more stable than its cyclic isomer. The reaction energies associated with the complexation processes highlight the stability of those complexes. The difference in energy, hardness, and polarizability between a cyclic molecule and its linear counterpart convincingly shows that an aromatic molecule exhibits negative changes in energy and polarizability but positive changes in hardness as expected from the principles of minimum energy, minimum polarizability, and maximum hardness. Although the aromaticity of Al(4)(2-) is unequivocally established through this study, the antiaromaticity picture in the case of Al(4)(4-) is shown to be poorly understood;however, the present analysis sheds light on this controversy.     

High temperature enthalpy increment and thermodynamic functions of U2Ti

This study investigated thermodynamic properties of uranium–titanium alloy to determine its suitability for storage of hydrogen isotopes. The enthalpy increments of U₂Ti were measured using a high temperature inverse drop calorimeter in the temperature range of 299–1,169 K. Temperature dependence of the molar enthalpy increment and molar heat capacity is expressed in the form $ H^\circ_{\text{m}} (T) - H^\circ_{\text{m}} (298.15\,{\text{K}})({\text{J }}\,{\text{mol}}^{ - 1} ) = 23.236(T/{\text{K}}) + 53.292 \times 10^{ - 3} (T/{\text{K}})^{2} - 21.294 \times 10^{5} ({\text{K}}/T) - 4523 $ and $ C^\circ_{\text{p,m}} ({\text{J}}\,{\text{K}}^{ - 1} \,{\text{g}}^{ - 1} ) = 23.236 + 10.6584 \times 10^{ - 2} (T/{\text{K}}) + 21.294 \times 10^{5} ({\text{K}}/T)^{2} (300 \le T/{\text{K}} \le 900) $ , respectively. A set of self consistent thermodynamic functions such as entropy, Gibbs energy function, heat capacity, and Gibbs energy and enthalpy values for U₂Ti have been computed using data obtained in this study and required data from the literature.     

Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 and NgBeSiN2 Clusters

The global minima of Be₂N₂, Be₃N₂ and BeSiN₂ clusters are identified using a modified stochastic kick methodology. The structure, stability and bonding nature of these clusters bound to noble gas (Ng) atoms are studied at the MP2/def2‐QZVPPD level of theory. Positive Be?Ng bond dissociation energy, which gradually increases down Group 18 from He to Rn, indicates the bound nature of Ng atoms. All of the Ng‐binding processes are exothermic in nature. The Xe and Rn binding to Be₂N₂ and Be₃N₂ clusters and Ar?Rn binding to BeSiN₂ are exergonic processes at room temperature; however, for the lighter Ng atoms, lower temperatures are needed. Natural population analysis, Wiberg bond index computations, electron density analysis, and energy decomposition analysis are performed to better understand the nature of Be?Ng bonds.