By Silmo J.

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Extra resources for A return mapping algorithm for plane stress in plasticity

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1 Basis Sets Gaussians and Slater Functions Having selected a specific electronic structure method the next choice is related to which basis set to use in order to represent the orbitals ψ i in terms of simple analytic functions fν with well–known properties. In general a linear combination of such basis functions ψi (r) = ν ciν fν (r; {RI }) 38 (97) is used, which represents exactly any reasonable function in the limit of using a complete set of basis functions. g. Ref. 292 for a concise overview–type presentation.

U. per picosecond, see solid line in Fig. 5(top). Increasing the 30 Table 1. u. / ps for Car–Parrinello (CP) and Born–Oppenheimer (BO) molecular dynamics simulations of a model system for 1 ps of trajectory on an IBM RS6000 / model 390 (Power2) workstation using the CPMD package 142 ; see Fig. 5 for corresponding energy plots. u. /ps and much larger energy fluctuations, see open circles in Fig. 5(top). The computer time needed in order to generate one picosecond of Car–Parrinello trajectory increases – to a good approximation – linearly with the increasing time step, see Table 1.

Car– Parrinello dynamics in advantageous cases. However, it has to be taken into account that in simulations 331 with such a large time step dynamical information is limited to about 10 THz, which corresponds to frequencies below roughly 500 cm −1 . In order to resolve vibrations in molecular systems with stiff covalent bonds the time step has to be decreased to less than a femtosecond (see the estimate given above) also in Born–Oppenheimer dynamics. The comparison of the overall performance of Car–Parrinello and Born– Oppenheimer molecular dynamics in terms of computer time is a delicate issue.

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