We propose and implement an alternative approach to the original Carâ€“Parrinello method where the density matrix elements ~instead of the molecular orbitals! are propagated together with the nuclear degrees of freedom. Our new approach has the advantage of leading to an O(N) computational scheme in the large system limit. Our implementation is based onâ€¦ (More)

A generalization is presented here for a newly developed approach to ab initio molecular dynamics, where the density matrix is propagated with Gaussian orbitals. Including a tensorial fictitious mass facilitates the use of larger time steps for the dynamics process. A rigorous analysis of energy conservation is presented and used to control the deviation ofâ€¦ (More)

Sixteen rats were initially exposed for 50 sessions to either a fixed-ratio 40 or an interresponse-time-greater-than-11-second food reinforcement schedule, then shifted to a fixed-interval 15-second food reinforcement schedule. Animals with fixed-ratio 40 histories lever pressed at much higher rates under the fixed-interval schedule than did animals withâ€¦ (More)

In Ref. 1 the authors discuss the curvy-extendedLagrangian molecular dynamics curvy-ELMD approach to ab initio molecular dynamics, which is similar to our atomcentered density-matrix propagation ADMP , but differs in not requiring the idempotency constraints to be numerically enforced. In this Comment, we address several misleading remarks in Refs. 1 and 7.â€¦ (More)

When we look up into the sky, it is hard not to think about how vast the universe is. Our universe is estimated to contain around 100 billion galaxies with each galaxy having around 100 billion stars. And most of those stars are expected to harbor planets. That is a mind-boggling number of stars and possible planets. This leads inevitably to questions aboutâ€¦ (More)