Theoretical chemists and physicists have been consumed during the 1990’s with reducing the expense of various numerical solutions to solving the Schrödinger equation, so that larger numbers of atoms can be treated “from first principles”. In particular, there are instances in which collective effects ranging over thousands of atoms may be important to include in models of the behavior of, e.g., proteins or metal surfaces, and where empirical potential molecular dynamics methods simply fail to capture the essential phenomenon.
The strategy for reducing the expense has taken the form of reducing the “scaling” or the power law dependence on the number of electrons/size of basis set included in the model. While conventional numerical approaches scale anywhere from cubically to the eighth (!) power in the size of the system, new strategies have reduced this scaling to linear in many instances. These methods, however, are generally not globally applicable. For example, one strategy involving localization of orbitals (one-electron wave functions) to construct a banded density matrix works only for insulators or semiconductors. Another approach has been shown thus far to work well only for metals. The purpose of this workshop is to bring together chemists, physicists, and mathematicians interested in developing new linear scaling algorithms that will have global applicability, and will reach out to applied mathematicians interested in the challenge described above. The desired outcome will be some fresh ideas on possible approaches, which will further this exciting field.
Roi Baer (Hebrew University, Jerusalem, Israel)
Gregory Beylkin (University of Colorado)
Achi Brandt (Weizmann Institute of Science)
Emily Carter (UCLA)
Yousef Saad (Minnesota)