27 research outputs found
Linear scaling computation of the Fock matrix. IX. Parallel computation of the Coulomb matrix
We present parallelization of a quantum-chemical tree-code [J. Chem. Phys.
{\bf 106}, 5526 (1997)] for linear scaling computation of the Coulomb matrix.
Equal time partition [J. Chem. Phys. {\bf 118}, 9128 (2003)] is used to load
balance computation of the Coulomb matrix. Equal time partition is a
measurement based algorithm for domain decomposition that exploits small
variation of the density between self-consistent-field cycles to achieve load
balance. Efficiency of the equal time partition is illustrated by several tests
involving both finite and periodic systems. It is found that equal time
partition is able to deliver 91 -- 98 % efficiency with 128 processors in the
most time consuming part of the Coulomb matrix calculation. The current
parallel quantum chemical tree code is able to deliver 63 -- 81% overall
efficiency on 128 processors with fine grained parallelism (less than two heavy
atoms per processor).Comment: 7 pages, 6 figure
Self-Similar Graphs
For any graph on vertices and for any {\em symmetric} subgraph of
, we construct an infinite sequence of graphs based on the pair
. The First graph in the sequence is , then at each stage replacing
every vertex of the previous graph by a copy of and every edge of the
previous graph by a copy of the new graph is constructed. We call these
graphs {\em self-similar} graphs. We are interested in delineating those pairs
for which the chromatic numbers of the graphs in the sequence are
bounded. Here we have some partial results. When is a complete graph and
is a special matching we show that every graph in the resulting sequence is
an {\em expander} graph.Comment: 13 pages, 1 tabl
Time-reversible Born-Oppenheimer molecular dynamics
We present a time-reversible Born-Oppenheimer molecular dynamics scheme,
based on self-consistent Hartree-Fock or density functional theory, where both
the nuclear and the electronic degrees of freedom are propagated in time. We
show how a time-reversible adiabatic propagation of the electronic degrees of
freedom is possible despite the non-linearity and incompleteness of the
self-consistent field procedure. Time-reversal symmetry excludes a systematic
long-term energy drift for a microcanonical ensemble and the number of
self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time
step) thanks to a good initial guess given by the adiabatic propagation of the
electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular
dynamics scheme therefore combines a low computational cost with a physically
correct time-reversible representation of the dynamics, which preserves a
detailed balance between propagation forwards and backwards in time.Comment: 4 pages, 4 figure
Linear scaling computation of the Fock matrix VII. Periodic Density Functional Theory at the -point
Linear scaling quantum chemical methods for Density Functional Theory are
extended to the condensed phase at the -point. For the two-electron
Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb
summation [J. Chem. Phys. {\bf 106}, 5526 (1997)], together with multipole
representation of the crystal field [J. Chem. Phys. {\bf 107}, 10131 (1997)]. A
periodic version of the hierarchical cubature algorithm [J. Chem. Phys. {\bf
113}, 10037 (2000)], which builds a telescoping adaptive grid for numerical
integration of the exchange-correlation matrix, is shown to be efficient when
the problem is posed as integration over the unit cell. Commonalities between
the Coulomb and exchange-correlation algorithms are discussed, with an emphasis
on achieving linear scaling through the use of modern data structures. With
these developments, convergence of the -point supercell approximation
to the -space integration limit is demonstrated for MgO and NaCl.
Linear scaling construction of the Fockian and control of error is demonstrated
for RBLYP/6-21G* diamond up to 512 atoms
Measuring kinetic coefficients by molecular dynamics simulation of zone melting
Molecular dynamics simulations are performed to measure the kinetic
coefficient at the solid-liquid interface in pure gold. Results are obtained
for the (111), (100) and (110) orientations. Both Au(100) and Au(110) are in
reasonable agreement with the law proposed for collision-limited growth. For
Au(111), stacking fault domains form, as first reported by Burke, Broughton and
Gilmer [J. Chem. Phys. {\bf 89}, 1030 (1988)]. The consequence on the kinetics
of this interface is dramatic: the measured kinetic coefficient is three times
smaller than that predicted by collision-limited growth. Finally,
crystallization and melting are found to be always asymmetrical but here again
the effect is much more pronounced for the (111) orientation.Comment: 8 pages, 9 figures (for fig. 8 : [email protected]). Accepted for
publication in Phys. Rev.