A generalized solid-state nudged elastic band (G-SSNEB) method is presented for determining reaction pathways of solid-solid transformations involving both atomic and unit-cell degrees of freedom. We combine atomic and cell degrees of freedom into a unified description of the crystal structure so that calculated reaction paths are insensitive to the choice of periodic cell. For the rock-salt to...

The applicability of the recently developed PM6 method for modeling various properties of a wide range of organic and inorganic crystalline solids has been investigated. Although the geometries of most systems examined were reproduced with good accuracy, severe errors were found in the predicted structures of a small number of solids. The origin of these errors was investigated, and a strategy ...

We give a basic introduction to the properties of Gauss’ hypergeometric functions, with an emphasis on the determination of the monodromy group of the Gaussian hyperegeometric equation. Initially this document started as an informal introduction to Gauss’ hypergeometric functions for those who want to have a quick idea of some main facts on hypergeometric functions. It is the startig of a book ...

T h i s p a p e r p r e s e n t s a n e w t e x t u r e a n a l y s i s m e t h o d i n c o r p o r a t i n g w i t h t h e p r o p e r t i e s o f b o t h t h e g ray l eve l c o o c c u r r e n c e m a t r i x ( G L C M ) a n d t e x t u r e s p e c t r u m (TS) m e t h o d s . T h e c o o c c u r r e n c e f ea tu res e x t r a c t e d f r o m t h e c r o s s d i a g o n a l t e x t u r e m ...

The Kronig–Penney model serves to illustrate the formation of energy bands in a periodic solid and appears as a pedagogical example in many textbooks in elementary solid state physics. The model is generally solved either by matching the boundary conditions for the wave functions at the cell boundaries, by a plane-wave expansion of the wave function in the reciprocal lattice space, or even by t...