An electron repulsion integral compression algorithm

A data compression algorithm for packing/unpacking floating point numbers is presented. The method has been used to compress large volumes of data commonly generated in ab initio quantum mechanical calculations. To retain an accuracy of 10^?6 Hartree on the final energy, the required file space needed is approximately half its original size whereas the CPU time required to solve the Hartree–Fock self-consistent field equations increases with 30–60%. © 1993 John Wiley & Sons, Inc.     

Potentiometric micro-titration of potassium

Summary The potentiometric micro titration of potassium tetraphenylborate in acetone/water mixtures using a silver nitrate solution gives a sharper end-point than with indicators. The silver nitrate titer obtained against K(Ph)₄B in acetone/water mixtures varies with the acetone concentration. This applies particularly for solutions which contain less than ca. 40 Vol.% acetone.

---

Zusammenfassung Die potentiometrische Mikrotitration von Kaliumtetraphenylborat in Aceton-Wasser-Gemischen mit Silbernitrat gibt einen schärferen Endpunkt als bei Verwendung eines Indikators. Der Silbernitrattiter gegen K(Ph)₄B in Aceton-Wasser-Gemischen variiert mit der Acetonkonzentration, besonders wenn der Acetongehalt der Lösungen geringer ist als 40 Vol.-%.

---

Résumé Le microtitrage potentiométrique du tétraphénylborate de potassium dans des mélanges d'eau et d'acétone à l'aide d'une solution titrante de nitrate d'argent donne un point final de titrage plus net que les indicateurs. Le titre du nitrate d'argent déterminé à l'aide de K(Ph)₄B dans des mélanges acétone-eau varie avec la concentration en acétone. Cette observation s'applique particulièrement aux solutions qui contiennent moins de 40% environ en volume d'acétone.

     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted Basis sets for the atoms H-Kr have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANO's are constructed by averaging over the most significant electronic states, the ground state of the cation, the ground state of the anion for some atoms and the homonuclear diatomic molecule at equilibrium distance for some atoms. The contracted basis sets yield excellent results for properties of molecules such as bond-strengths and-lengths, vibrational frequencies, and good results for valence spectra, ionization potentials and electron affinities of the atoms, considering the small size of these sets. The basis sets presented in this article constitute a balanced sequence of basis sets suitable for larger systems, where economy in basis set size is of importance.     

Solvent effects on the n-->pi* electronic transition in formaldehyde: a combined coupled cluster/molecular dynamics study

We present a study of the blueshift of the n-->pi* electronic transition in formaldehyde in aqueous solution using a combined coupled cluster/molecular mechanics model including mutual polarization effects in the Hamiltonian. In addition, we report ground and excited state dipole moments. Configurations are generated from molecular dynamics simulations with two different force fields, one with and one without an explicit polarization contribution. A statistical analysis using 1200 configurations is presented. Effects of explicit polarization contributions are found to be significant. It is found that the main difference in the effects on the excitation energies arises from the fact that the two force fields result in different liquid structures, and thus a different set of configurations is generated for the coupled cluster/molecular mechanics calculations.     

The viscosity and temperature dependence of X-band ESR lineshapes of Gd(III) aqueous complex

X-band ESR spectra of Gd-aqua complex in various weight concentration of glycerol have been recorded at four temperatures. The interpretation of the ESR linewidth is preformed using both the stochastic Liouville approach (SLA) and a perturbation theory. The SLA uses a one dynamic model of the zero-field splitting whereas the perturbation approach uses a two dynamic model. Both models can reproduce the variation of the linewidth with respect to viscosity. In the SLA model, both the zero-field splitting (ZFS) interaction and the correlation time vary with the glycerol content. In the two dynamic perturbation model, only the correlation times are viscosity dependent. The two models give different NMRD profiles.     

Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.     

Primitive roots of ideals in algebraic number-fields

Mathematische Annalen -