Efficient implementation of the interacting quantum atoms energy partition of the second-order Møller–Plesset energy

We describe an efficient implementation of the partition of the second-order Møller–Plesset (MP2) correlation energy within the interacting quantum atoms (IQA) energy decomposition. We simplify the IQA integration bottleneck by considering only the occupied to virtual elements of the second order reduced density matrix, a procedure that reduces substantially the size of the two-electron matrix, which has to be addressed. The algorithmic improvements described herein allow to perform the decomposition of the MP2 correlation energy for medium size molecular systems using moderate computational resources. We expect that the methods developed in this investigation will prove useful to understand electron correlation effects through a real space perspective.     

Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $\omega _e x_e $ ω e x e and $\omega _e y_e $ ω e y e .     

Parsing of the free energy of aromatic–aromatic stacking interactions in solution

We report an analysis of the energetics of aromatic–aromatic stacking interactions for 39 non-covalent reactions of self- and hetero-association of 12 aromatic molecules with different structures and charge states. A protocol for computation of the contributions to the total energy from various energetic terms has been developed and the results are consistent with experiment in 92% of all the systems studied. It is found that the contributions from hydrogen bonds and entropic factors are always unfavorable, whereas contributions from van-der-Waals, electrostatic and/or hydrophobic effects may lead to stabilizing or destabilizing factors depending on the system studied. The analysis carried out in this work provides an answer to the questions “What forces stabilize/destabilize the stacking of aromatic molecules in aqueous-salt solution and what are their relative importance?”     

Adiabatic integration formula for the correlation energy functional of the Hartree–Fock density

An adiabatic integration formula for the quantum chemistry correlation energy functional of the Hartree–Fock density, E _c ^QC[n], is presented. The functional E _c ^QC[n] is meant to be added to the completed Hartree–Fock energy to produce the exact ground-state energy of the system under consideration. The initial slope of the integrand in this connection formula is identified as a second-order energy and an explicit expression for the initial slope of the integrand is presented. Our expression should be useful for arriving at new improved approximations to E _c ^QC[n]. Previous numerical results by Huang and Umrigar (1997) Phys Rev A 56:290, for two-electron densities are proved, and a generalization to more than two electrons is presented. Results obtained by means of the present density functional theory correlation energy functionals, when used to approximate the initial slope in our adiabatic integration formula for E _c ^QC[n], are compared against exact numbers. Received: 10 September 1998 / Accepted: 3 February 1999 / Published online: 21 June 1999     

Determination of the equilibrium melting point of the β-form of polypropylene

The melting behavior of the -form of isotactic polypropylene (-iPP) was investigated as a function of crystallization time and temperature. Calcium suberate, a selective -nucleating agent was used to produce samples that consist entirely of -form i-PP. The experimental melting points were recorded at different crystallization times and were extrapolated to the start of the crystallization process in order to eliminate the effect of lamellar thickening. Using the non-linear Hoffman—Weeks approach to correlate these extrapolated experimental melting temperatures with the corresponding crystallization temperatures, an equilibrium melting point of 209°C was obtained for -iPP. The equilibrium melting point estimated through the non-linear Hoffman—Weeks analysis is about 30°C higher than that (T _m ⁰=177°C) obtained on the basis of the linear extrapolation. These results are consistent with earlier claims that a linear extrapolation of T _m–T _c data leads to an underestimation of the equilibrium melting point. The results obtained for -iPP exemplify the importance of accounting for both the isothermal lamellar thickening effects and the non-linearity in the T _m–T _c correlation, when the determination of an equilibrium melting point is carried out using a procedure based on the predictions of the Lauritzen—Hoffman secondary nucleation theory.This revised version was published online in November 2005 with corrections to the Cover Date.     

Solutions of the Klein–Gordon equation with the improved Tietz potential energy model

We present the relativistic rotation–vibrational energy equation of a diatomic molecule which moves under the improved Tietz potential energy model in higher spatial dimensions. The nonrelativistic limits of the bound state solutions of the Klein–Gordon equation are the bound state solutions of the Schrödinger equation with the same potential energy function. Numerical analysis results show that there exists a critical point around which the solution behaviors bifurcate into two extreme cases. Below the critical point, the behavior of the relativistic vibrational energies for the ground electronic state of carbon monoxide in higher dimensions keeps similar to that of the three-dimensional system, while this symmetry phenomenon breaks and the Klein–Gordon equation has no stability solution upon the critical point.     

Do vectors point the way to understanding energy transfer in molecular collisions?

This tutorial review examines the proposition that vector properties reveal more about the underlying potential energy surfaces controlling the inelastic exchange of energy in intermolecular collisions than conventional scalar measurements. Exciting recent experimental progress is summarized in the form of six selected cases studies. The new information that has been extracted is compared with the predictions of complementary theory. Likely future prospects and promising avenues for further progress are discussed. The treatment should appeal to all those with interests in the forces governing intermolecular interactions, especially in gas-phase collisions.     

On the nature of the Møller-Plesset critical point

It has been suggested [F. H. Stillinger, J. Chem. Phys. 112, 9711 (2000)] that the convergence or divergence of M?ller-Plesset perturbation theory is determined by a critical point at a negative value of the perturbation parameter z at which an electron cluster dissociates from the nuclei. This conjecture is examined using configuration-interaction computations as a function of z and using a quadratic approximant analysis of the high-order perturbation series. Results are presented for the He, Ne, and Ar atoms and the hydrogen fluoride molecule. The original theoretical analysis used the true Hamiltonian without the approximation of a finite basis set. In practice, the singularity structure depends strongly on the choice of basis set. Standard basis sets cannot model dissociation to an electron cluster, but if the basis includes diffuse functions then it can model another critical point corresponding to complete dissociation of all the valence electrons. This point is farther from the origin of the z plane than is the critical point for the electron cluster, but it is still close enough to cause divergence of the perturbation series. For the hydrogen fluoride molecule a critical point is present even without diffuse functions. The basis functions centered on the H atom are far enough from the F atom to model the escape of electrons away from the fluorine end of the molecule. For the Ar atom a critical point for a one-electron ionization, which was not previously predicted, seems to be present at a positive value of the perturbation parameter. Implications of the existence of critical points for quantum-chemical applications are discussed.     

On the Reaction Path Hamiltonian

A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.     

Performance of CdTe detector in the 13–1333 keV energy range

The photopeak efficiency, peak to valley ratio and energy resolution of a 3×3×1 mm³ CdTe detector were determined experimentally for 13–1333 keV photon energy by using polyester coated radioisotopes ²⁴¹Am, ²²Na, ⁵⁴Mn, ⁵⁷Co, ⁶⁰Co, ¹⁰⁹Cd, ¹³⁷Cs and ¹³³Ba. The data were analyzed by using PX4 from Amptek. The experimental values were fitted to an analytical function of photon energy, and an agreement was observed for the entire range of the studied energies. The results have shown that the CdTe detector has a high performance due to both the improved charge collection efficiency comparable with that of SI GaAs detectors (Vittone et al., 1999), and the low leakage current. Also, CdTe detector is very attractive for field application as it works at room temperature.     

The Isoelectric Point and the Points of Zero Charge of Fe-Al-Mg Hydrotalcite-like Compounds

The relation of the isoelectric point (IEP) and the point of zero net charge (PZNC) of the hydrotalcite-like compounds was discussed. It was found that the IEP does not equal to the PZNC and the IEP is higher than the PZNC. The structural positive charges existing in the HTlc,which cause the difference between the IEP and the PZNC. The effects of the structural positive charges of the HTlc on its IEP and PZNC are the same as the specific adsorption of metal cations.     

Connection between the Ogilvie and the Murrell–Sorbie potential energy functions

Formulas for relating the parameters of the Murrell–Sorbie and the Ogilvie potentials are developed herein. Unlike the Simons–Parr–Finlan function, the Ogilvie potential is more easily connected with the Murrell–Sorbie potential, as evident from the longer range of agreement. The relationship is useful for generating high order Ogilvie potentials that exhibit the dissociation energy without experimentation, and for using the Murrell–Sorbie parameters in molecular softwares that adopt the Ogilvie function in their algorithms. The relations are invertible so that Ogilvie parameters from spectroscopic data can be applied in molecular softwares that employ Murrell–Sorbie potentials.      

Hamiltonian for the problem on the ground and excited electron–nuclear states of nano-objects of finite size with periodic structure: Oligomers

A Hamiltonian has been proposed to study ground and excited states of nano-objects with a periodic structure, which makes it possible to find a general solution as a linear combination of basis functions in the form of normal waves. Terms that allow obtaining easily the solution with varying degrees of accuracy are explicitly defined. The method is suitable for the analysis of both finite and infinitely extended objects, including segments with a periodic structure.     

Absolute yields in the fission of 239Pu by mono-energetic neutrons of energy 130–1700 keV

Absolute fission yields of ⁹⁹Mo, ¹¹¹Ag, ¹⁴⁰Ba, ¹⁴⁷Nd and ¹⁵³Sm have been measured for fission of ²³⁹Py by neutrons of energies 130, 300, 700, 900, 1300 and 1700 keV. While yields of ⁹⁹Mo and ¹⁴⁰Ba are constant, those of the other three nuclides increase with energy. This result has implications both for fission theory and for practical applications of fission yields in fast reactors.     

Thermal conductivity and interfacial energy of solid Bi solution in the Bi–Al–Zn eutectic system

The equilibrated grain boundary groove shapes for solid Bi solution (Bi–6.1 at.%Zn–0.38 at.%Al) in equilibrium with the Bi–Al–Zn eutectic liquid have been observed from quenched sample with a radial heat flow apparatus. The Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy of solid Bi solution have been determined from the observed grain boundary groove shapes. The variations of thermal conductivity with temperature for solid Bi solution (Bi–6.1 at.%Zn–0.38 at.%Al) has been measured up to five degree below the melting temperature by using radial heat flow technique. The ratio of thermal conductivity of equilibrated Bi–Al–Zn eutectic liquid phase to solid Bi solution (Bi–6.1 at.%Zn–0.38 at.%Al) phase has also been measured with a Bridgman type growth apparatus at the melting temperature.     

New approach to simplify the equation for the excess Gibbs free energy of aqueous solutions of electrolytes applied to the modelling of the NH3–CO2–H2O vapour–liquid equilibria

A new, simple, empirical equation for G^E (excess Gibbs free energy) of electrolyte solutions is proposed in which, contrary to the commonly used Pitzer equation, binary and ternary interaction parameters relate to the interactions of electrolytes in a solution rather than to the interactions of real species in a solution (i.e., anions, cations and nondissociated molecules). Such an approach radically reduces the number of parameters in the new equation for G^E as compared with the Pitzer equation and consequently significantly simplifies their calculation. The efficiency of the new approach is demonstrated on the example of modelling the vapour–liquid equilibria of the industrially important and widely investigated NH₃–CO₂–H₂O system.     

The excitation spectrum of pure liquid mesitylene in the energy range 4.5–21 eV

The fluorescence of pure liquid mesitylene at -50°C is investigated as function of excitation energy in the range 4.5–21 eV when the open surface of the liquid is excited. The normalized intensity is constant for excitation in the first two electronic absorption bands and increases significantly for excitation in the third absorption band. This increase in fluorescent quantum yield is explained as a result of reduced non-radiative transitions due to a decrease in the van der Waals interactions between the molecules at the surface of the liquid, and also by a decrease in the efficiency of excimer formation there. With increasing energy of the exciting photon photoelectrons are released which produce secondary excitations and hence cause the observed increase in fluorescent yield.     

Influence of Ag additions on the activation energy for the reverse eutectoid reaction in Cu–Al alloys

The eutectoid transformation may be defined as a solid-state diffusion-controlled decomposition process of a high-temperature phase into a two-phase lamellar aggregate behind a migrating boundary on cooling below the eutectoid temperature. In substitutional solid solutions, the eutectoid reaction involves diffusion of the solute atoms either through the matrix or along the boundaries or ledges. The effect of Ag on the non-isothermal kinetics of the reverse eutectoid reaction in the Cu–9 mass%Al, Cu–10 mass%Al, and Cu–11 mass%Al alloys were studied using differential scanning calorimetry (DSC), X-ray diffraction (XRD), and scanning electron microscopy (SEM). The activation energy for this reaction was obtained using the Kissinger and Ozawa methods. The results indicated that Ag additions to Cu–Al alloys interfere on the reverse eutectoid reaction, increasing the activation energy values for the Cu–9 mass%Al and Cu–10 mass%Al alloys and decreasing these values for the Cu–11 mass%Al alloy for additions up to 6 mass%Ag. The changes in the activation energy were attributed to changes in the reaction solute and in Ag solubility due to the increase in Al content.