Comparison of conjugate gradient density matrix search and Chebyshev expansion methods for avoiding diagonalization in large-scale electronic structure calculations

1998 ◽  
Vol 109 (9) ◽  
pp. 3308-3312 ◽  
Author(s):  
Kevin R. Bates ◽  
Andrew D. Daniels ◽  
Gustavo E. Scuseria
Keyword(s):  
Electronic Structure ◽  
Density Matrix ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Electronic Structure Calculations ◽  
Chebyshev Expansion ◽  
Gradient Density ◽  
Structure Calculations

scholarly journals The Linearly Scaling 3D Fragment Method for Large Scale Electronic Structure Calculations

2009 ◽  
Author(s):  
Zhengji Zhao ◽  
Juan Meza ◽  
Byounghak Lee ◽  
Hongzhang Shan ◽  
Erich Strohmaier ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Large Scale ◽  
Electronic Structure Calculations ◽  
Fragment Method ◽  
Structure Calculations

scholarly journals The linearly scaling 3D fragment method for large scale electronic structure calculations

2009 ◽  
Author(s):  
Zhengji Zhao ◽  
Juan Meza ◽  
Byounghak Lee ◽  
Hongzhang Shan ◽  
Erich Strohmaier ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Large Scale ◽  
Electronic Structure Calculations ◽  
Fragment Method ◽  
Structure Calculations

Electronic Structure Calculations on a Real-Space Mesh with Multigrid Acceleration

1995 ◽  
Vol 408 ◽  
Author(s):  
D. J. Sullivan ◽  
E. L. Briggs ◽  
C. J. Brabec ◽  
J. Bernholc
Keyword(s):  
Electronic Structure ◽  
Ab Initio ◽  
Large Scale ◽  
Electronic Structure Calculations ◽  
High Energy ◽  
Real Space ◽  
Parallel Architectures ◽  
Wurtzite Phase ◽  
Ongoing Work ◽  
Structure Calculations

AbstractWe have developed a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods permit efficient calculations on ill-conditioned systems with long length scales or high energy cutoffs. We discuss the design of pseudopotentials for real-space grids, and the computation of ionic forces. The technique has been applied to several systems, including an isolated C60 molecule, the wurtzite phase of GaN, a 64-atom cell of GaN with the Ga d-states in valence, and a 443-atom protein. The method has been implemented on both vector and parallel architectures. We also discuss ongoing work on O(N) implementations and solvated biomolecules.

State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems

2008 ◽  
Vol 227 (15) ◽  
pp. 7113-7124 ◽  
Author(s):  
Christof Vömel ◽  
Stanimire Z. Tomov ◽  
Osni A. Marques ◽  
A. Canning ◽  
Lin-Wang Wang ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Large Scale ◽  
State Of The Art ◽  
Electronic Structure Calculations ◽  
Structure Calculations

Summary, Conclusions, and Future Trends

2012 ◽  
Author(s):  
Lionel Raff ◽  
Ranga Komanduri ◽  
Martin Hagan ◽  
Satish Bukkapatnam
Keyword(s):  
Electronic Structure ◽  
Complex Systems ◽  
Human Brain ◽  
Ab Initio ◽  
Large Scale ◽  
Dimensional Space ◽  
Electronic Structure Calculations ◽  
Potential Surfaces ◽  
The 1960S ◽  
Structure Calculations

Since the introduction of classical and semiclassical molecular dynamics (MD) methods in the 1960s and Gaussian procedures to conduct electronic structure calculations in the 1970s, a principal objective of theoretical chemistry has been to combine the two methods so that MD and quantum mechanical studies can be conducted on ab initio potential surfaces. Although numerous procedures have been attempted, the goal of first principles, ab initio dynamics calculations has proven to be elusive when the system contains five or more atoms moving in unrestricted three-dimensional space. For many years, the conventional wisdom has been that ab initio MD calculations for complex systems containing five or more atoms with several open reaction channels are presently beyond our computational capabilities. The rationale for this view are (a) the inherent difficulty of high level ab initio quantum calculations on complex systems that may take numerous, large-scale computations impossible, (b) the large dimensionality of the configuration space for such systems that makes it necessary to examine prohibitively large numbers of nuclear configurations, and (c) the extreme difficulty associated with obtaining sufficiently converged results to permit accurate interpolation of numerical data obtained from electronic structure calculations when the dimensionality of the system is nine or greater. Neural networks (NN) derive their name from the fact that their interlocking structure superficially resembles the neural network of a human brain and from the fact that NNs can sense the underlying correlations that exist in a database and properly map them in a manner analogous to the way a human brain can execute pattern recognition. Artificial neurons were first proposed in 1943 by Warren McCulloch, a neurophysiologist, and Walter Pitts, an MIT logician. NNs have been employed by engineers for decades to assist in the solution of a multitude of problems. Nevertheless, the power of NNs to assist in the solution of numerous problems that occur in chemical reaction dynamics is just now being realized by the chemistry community.

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