257 research outputs found
Using molecular similarity to construct accurate semiempirical electron structure theories
Ab initio electronic structure methods give accurate results for small
systems, but do not scale well to large systems. Chemical insight tells us that
molecular functional groups will behave approximately the same way in all
molecules, large or small. This molecular similarity is exploited in
semiempirical methods, which couple simple electronic structure theories with
parameters for the transferable characteristics of functional groups. We propse
that high-level calculations on small molecules provide a rich source of
parametrization data. In principle, we can select a functional group, generate
a large amount of ab initio data on the group in various small-molecule
environments, and "mine" this data to build a sophisticated model for the
group's behavior in large molecules. This work details such a model for
electron correlation: a semiempirical, subsystem-based correlation functional
that predicts a subsystem's two-electron density as a functional of its
one-electron density. This model is demonstrated on two small systems: chains
of linear, minimal-basis (H-H)5, treated as a sum of four overlapping (H-H)2
subsystems; and the aldehyde group of a set of HOC-R molecules. The results
provide an initial demonstration of the feasibility of this approach.Comment: The following article appeared in the Journal of Chemical Physics,
121 (12), 5635-5645 (2004) and may be found at http://jcp.aip.org
O(N) methods in electronic structure calculations
Linear scaling methods, or O(N) methods, have computational and memory
requirements which scale linearly with the number of atoms in the system, N, in
contrast to standard approaches which scale with the cube of the number of
atoms. These methods, which rely on the short-ranged nature of electronic
structure, will allow accurate, ab initio simulations of systems of
unprecedented size. The theory behind the locality of electronic structure is
described and related to physical properties of systems to be modelled, along
with a survey of recent developments in real-space methods which are important
for efficient use of high performance computers. The linear scaling methods
proposed to date can be divided into seven different areas, and the
applicability, efficiency and advantages of the methods proposed in these areas
is then discussed. The applications of linear scaling methods, as well as the
implementations available as computer programs, are considered. Finally, the
prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys
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Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics
We develop and validate a density functional, XYG3, based on the adiabatic connection formalism and the Görling–Levy coupling-constant perturbation expansion to the second order (PT2). XYG3 is a doubly hybrid functional, containing 3 mixing parameters. It has a nonlocal orbital-dependent component in the exchange term (exact exchange) plus information about the unoccupied Kohn–Sham orbitals in the correlation part (PT2 double excitation). XYG3 is remarkably accurate for thermochemistry, reaction barrier heights, and nonbond interactions of main group molecules. In addition, the accuracy remains nearly constant with system size
Fragmentation Methods: A Route to Accurate Calculations on Large Systems
Theoretical chemists have always strived to perform quantum mechanics (QM) calculations on larger and larger molecules and molecular systems, as well as condensed phase species, that are frequently much larger than the current state-of-the-art would suggest is possible. The desire to study species (with acceptable accuracy) that are larger than appears to be feasible has naturally led to the development of novel methods, including semiempirical approaches, reduced scaling methods, and fragmentation methods. The focus of the present review is on fragmentation methods, in which a large molecule or molecular system is made more computationally tractable by explicitly considering only one part (fragment) of the whole in any particular calculation. If one can divide a species of interest into fragments, employ some level of ab initio QM to calculate the wave function, energy, and properties of each fragment, and then combine the results from the fragment calculations to predict the same properties for the whole, the possibility exists that the accuracy of the outcome can approach that which would be obtained from a full (nonfragmented) calculation. It is this goal that drives the development of fragmentation methods
Complexity Reduction in Density Functional Theory: Locality in Space and Energy
We present recent developments of the NTChem program for performing large
scale hybrid Density Functional Theory calculations on the supercomputer
Fugaku. We combine these developments with our recently proposed Complexity
Reduction Framework to assess the impact of basis set and functional choice on
its measures of fragment quality and interaction. We further exploit the all
electron representation to study system fragmentation in various energy
envelopes. Building off this analysis, we propose two algorithms for computing
the orbital energies of the Kohn-Sham Hamiltonian. We demonstrate these
algorithms can efficiently be applied to systems composed of thousands of atoms
and as an analysis tool that reveals the origin of spectral properties.Comment: Accepted Manuscrip
Efficient Algorithms for Solving Structured Eigenvalue Problems Arising in the Description of Electronic Excitations
Matrices arising in linear-response time-dependent density functional theory and many-body perturbation theory, in particular in the Bethe-Salpeter approach, show a 2 × 2 block structure. The motivation to devise new algorithms, instead of using general purpose eigenvalue solvers, comes from the need to solve large problems on high performance computers. This requires parallelizable and communication-avoiding algorithms and implementations. We point out various novel directions for diagonalizing structured matrices. These include the solution of skew-symmetric eigenvalue problems in ELPA, as well as structure preserving spectral divide-and-conquer schemes employing generalized polar decompostions
Implementation and benchmark of a long-range corrected functional in the density functional based tight-binding method
Bridging the gap between first principles methods and empirical schemes, the
density functional based tight-binding method (DFTB) has become a versatile
tool in predictive atomistic simulations over the past years. One of the major
restrictions of this method is the limitation to local or gradient corrected
exchange-correlation functionals. This excludes the important class of hybrid
or long-range corrected functionals, which are advantageous in thermochemistry,
as well as in the computation of vibrational, photoelectron and optical
spectra. The present work provides a detailed account of the implementation of
DFTB for a long-range corrected functional in generalized Kohn-Sham theory. We
apply the method to a set of organic molecules and compare ionization
potentials and electron affinities with the original DFTB method and higher
level theory. The new scheme cures the significant overpolarization in electric
fields found for local DFTB, which parallels the functional dependence in first
principles density functional theory (DFT). At the same time the computational
savings with respect to full DFT calculations are not compromised as evidenced
by numerical benchmark data
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