Chemistry Reference
In-Depth Information
less computational work. These techniques have been incorporated in the
PARSEC and HARES codes. High-order evolution operator forms and collec-
tive approximations for response can enhance the convergence to the exact
numerical solution in DFT calculations significantly;
203,204
these new methods
lead to at least one order-of-magnitude improvement in convergence rates
relative to second-order schemes.
Several groups have developed linear-scaling approaches that generally
rely on the spatial localization of the density matrix. Some of those algorithms
have been discussed above in relation to particular applications: CON-
QUEST,
112
MGMol (Fattebert),
128,174
our own FAS solver,
127
MIKA,
73
Hoshi
and Fujiwara's code,
177
FEMTECK,
197
andOno andHirose's code.
158
Vashishta
and co-workers
205,206
have developed a divide-and-conquer/cellular decomposi-
tion algorithm for large-scale, linear-scaling DFT. Other linear-scaling codes
include the SIESTA
191-193
and ONETEP
207
programs. SIESTA utilizes a loca-
lized, numerical atomic-orbital basis, as do the Seijo-Barandiaran Mosaico
208
and Ozaki OpenMX codes,
209,210
while ONETEP employs plane-wave ideas to
generatea localizedpsincbasis. Thesemethods incorporatemixturesof real-space
and alternative representations. Other real-space representations based on
Lagrange functions
71,72
or discrete variable representations (DVRs)
68-70,211,212
appear to offer advantages over the FD and FEmethods. Linear-scaling Gaussian
codes have also been developed.
123-125
Earlier linear-scaling developments are
thoroughly summarized by Goedecker.
92
Applications of linear-scaling codes to
very large problems have appeared recently.
206
Real-space methods have found recent application in QM/MM methods,
which couple central quantum regions with more distant molecular mechanics
domains.
213,214
Wavelet applications to electronic structure are at an earlier
stage of development than are the methods discussed here, but they continue
to hold a great deal of promise due to their inherent multiscale nature. Several
recent studies suggest that wavelets will find wide application in future electro-
nic structure codes.
73-80,82,83
Electrostatics
Real-space numerical solutions to problems in electrostatics have
been a predominant theme in biochemistry and biophysics for some
time.
129-131,133,215
In condensed-matter physics, on the other hand, FFT
methods for periodic systems have dominated electrostatic calculations.
56
One reason for this difference is that computations in chemical and biophy-
sical electrostatics typically focus on large, but finite, molecules bathed in a
solution. Thus, periodic boundary conditions are often not appropriate.
Also, increased resolution near molecularsurfacesismucheasiertoenact
with a real-space approach. The early biophysics computational work
focused on solving the PB equation for solvation free energies of molecules
and ions. Recent efforts have been directed at more efficient solvers and
