Geometry optimization of crystals by the quasi-independent curvilinear coordinate approximation

The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid under periodic boundary conditions, enabling simultaneous relaxation of the lattice and atomic coordinates, as illustrated by tight optimization of polyethylene, hexagonal boron nitride, a (10,0) carbon nanotube, hexagonal ice, quartz, and sulfur at the Gamma-point RPBE/STO-3G level of theory.     

Nonorthogonal density-matrix perturbation theory

Recursive density-matrix perturbation theory [A.M.N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of materials response properties [V. Weber, A.M.N. Niklasson, and M. Challacombe, Phys. Rev. Lett. 92, 193002 (2004)]. In this article, we generalize the density-matrix perturbation theory to include properties computed with a perturbation-dependent nonorthogonal basis. Such properties include analytic derivatives of the energy with respect to nuclear displacement, as well as magnetic response computed with a field-dependent basis. The theory is developed in the context of linear scaling purification methods, which are briefly reviewed.     

A Raman spectroscopic study of the uranyl phosphate mineral threadgoldite

Raman spectra of threadgoldite at 298 and 77K are measured and interpreted for the first time. Bands related the (UO(2))(2+) and (PO(4))(3-) stretching and bending vibrations are tenatively attributed together with the bands assigned to the stretching a and bending vibrations of water molecules and hydroxyls. Hydrogen-bonding network and H(2)O and (OH)(-1) libration modes are mentioned. U-O bond lengths in uranyls are calculated via empirical relations R(U-O)=f[nu(1) and nu(3)(UO(2))(2+)]A. They are comparable to the values inferred from the single crystal structure analysis of threadgoldite.     

A Raman and infrared spectroscopic study of the uranyl silicates--weeksite, soddyite and haiweeite

Raman spectroscopy has been used to study the molecular structure of a series of selected uranyl silicate minerals, including weeksite K2[(UO2)2(Si5O13)].H2O, soddyite [(UO2)2SiO4.2H2O] and haiweeite Ca[(UO2)2(Si5O12(OH)2](H2O)3 with UO2(2+)/SiO2 molar ratio 2:1 or 2:5. Raman spectra clearly show well resolved bands in the 750-800 cm-1 region and in the 950-1000 cm-1 region assigned to the nu1 modes of the (UO2)2+ units and to the (SiO4)4- tetrahedra. For example, soddyite is characterized by Raman bands at 828.0, 808.6 and 801.8 cm-1 (UO2)2+ (nu1), 909.6 and 898.0 cm-1 (UO2)2+ (nu3), 268.2, 257.8 and 246.9 cm-1 are assigned to the nu2 (delta) (UO2)2+. Coincidences of the nu1 (UO2)2+ and the nu1 (SiO4)4- is expected. Bands at 1082.2, 1071.2, 1036.3, 995.1 and 966.3 cm-1 are attributed to the nu3 (SiO4)4-. Sets of Raman bands in the 200-300 cm-1 region are assigned to nu2 (delta) (UO2)2+ and UO ligand vibrations. Multiple bands indicate the non-equivalence of the UO bonds and the lifting of the degeneracy of nu2 (delta) (UO2)2+ vibrations. The (SiO4)4- tetrahedral are characterized by bands in the 470-550 cm-1 and in the 390-420 cm-1 region. These bands are attributed to the nu4 and nu2 (SiO4)4- bending modes. The minerals show characteristic OH stretching bands in the 2900-3500 cm-1 and 3600-3700 cm-1.     

Mean Extinction Time in Predator-Prey Model

A basic predator-prey (Lotka-Volterra) system exhibits marginal stability on the deterministic level. Intrinsic demographic stochasticity destroys this stability and drives the system toward extinction of one or both species. We analytically calculate the mean extinction time of such a system and investigate its scaling with the system’s parameters. This mean extinction time, measured in number of population cycles, scales as the square root of the size of the smaller population and as the minus three halves power of the size of the larger population. The analytic results are fully confirmed by Monte-Carlo simulations.