Linear Scaling with Cluster Size for Calculations of NMR Properties in Liquids

2003 ◽  
Vol 68 (12) ◽  
pp. 2292-2296 ◽  
Author(s):  
Markus G. Müller ◽  
Hanspeter Huber
Keyword(s):  
Cluster Size ◽  
Pair Potential ◽  
Extreme Case ◽  
Time Correlation ◽  
Computational Effort ◽  
Cluster Method ◽  
Linear Scaling ◽  
Chemical Shielding ◽  
Solvent Molecules ◽  
Nmr Properties

It is shown for liquid water that the contributions of the solvent molecules to the NMR chemical shielding of a proton in the solute molecule is approximately pair-additive. This leads to linear scaling in the computational effort with cluster size if the cluster method is applied. Alternatively, a pair chemical shielding surface, in analogy to the pair potential surface, can be calculated in advance of the simulation. Its analytical fit can be coded into the simulation program to be easily evaluated any time during the simulation, e.g. to get time correlation functions. As water is an extreme case, it is assumed that for other systems an even better additivity might be found.

scholarly journals Calculation of chemical-shift tensors of heavy nuclei: a DFT/ZORA investigation of 199Hg chemical-shift tensors in solids, and the effects of cluster size and electronic-state approximations

2014 ◽  
Vol 16 (27) ◽  
pp. 14298-14308 ◽  
Author(s):  
Fahri Alkan ◽  
C. Dybowski
Keyword(s):  
Chemical Shift ◽  
Electronic State ◽  
Cluster Size ◽  
Cluster Method ◽  
Molecular Cluster ◽  
Heavy Nuclei ◽  
Chemical Shielding ◽  
Solid Materials ◽  
Chemical Shift Tensors

A ZORA/DFT investigation of the NMR chemical shielding of a suite of 199Hg-containing solid materials shows the importance of calculations with the molecular-cluster method.

Recent Advances in Graph Matching

1997 ◽  
Vol 11 (01) ◽  
pp. 169-203 ◽  
Author(s):  
H. Bunke ◽  
B. T. Messmer
Keyword(s):  
Decision Tree ◽  
Graph Matching ◽  
Extreme Case ◽  
Input Image ◽  
Computational Effort ◽  
Compact Representation ◽  
Subgraph Isomorphism ◽  
Input Graph ◽  
Matching Problem ◽  
Tree Traversal

A powerful and universal data structure with applications invarious subfields of science and engineering is graphs. In computer vision and image analysis, graphs are often used for the representation of structured objects. For example, if the problem is to recognize instances of known objects in an image, then often models, or prototypes, of the known objects are represented by means of graphs and stored in a database. The unknown objects in the input image are extracted by means of suitable preprocessing and segmentation algorithms, and represented by graphs that are analogous to the model graphs. Thus, the problem of object recognition is transformed into a graph matching problem. In this paper, it is assumed that there is an input graph that is given on-line, and a number of model, or prototype, graphs that are known a priori. We present a new approach to subgraph isomorphism detection which is based on a compact representation of the model graphs that is computed off-line. Subgraphs that appear multiple times within the same or within different model graphs are represented only once, thus reducing the computational effort to detect them in an input graph. In the extreme case where all model graphs are highly similar, the run time of the new algorithm becomes independent of the number of model graphs. We also describe an extension of this method to error-correcting graph matching. Furthermore, an approach to subgraph isomorphism detection based on decision trees is proposed. A decision tree is generated from the models in an off-line phase. This decision tree can be used for subgraph isomorphism detection. The time needed for decision tree traversal is only polynomial in terms of the number of nodes of the input graph. Moreover, the time complexity of the decision tree traversal is completely independent on the number of model graphs, regardless of their similarity. However, the size of the decision tree is exponential in the number of nodes of the models. To cut down the space complexity of the decision tree, some pruning strategies are discussed.

Linear scaling coupled cluster method with correlation energy based error control

2010 ◽  
Vol 133 (1) ◽  
pp. 014107 ◽  
Author(s):  
Marcin Ziółkowski ◽  
Branislav Jansík ◽  
Thomas Kjærgaard ◽  
Poul Jørgensen
Keyword(s):  
Error Control ◽  
Correlation Energy ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Linear Scaling ◽  
Coupled Cluster Method

Monte Carlo Simulations with an Improved Potential Function for Cu(II)-Water Including Neighbour Ligand Corrections

1991 ◽  
Vol 46 (4) ◽  
pp. 357-362 ◽  
Author(s):  
Bernd M. Rode ◽  
Saiful M. Islam
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Potential Function ◽  
Hydration Shell ◽  
Pair Potential ◽  
Computational Effort ◽  
Direct Construction ◽  
Simple Method ◽  
Dilute Aqueous Solution ◽  
Simple Pair

Abstract Monte Carlo simulations for a Cu2+ ion in infinitely dilute aqueous solution were performed on the basis of a simple pair potential function leading to a first-shell coordination number of 8, in contrast to experimental data. A simple method was introduced therefore, which allows the direct construction of a pair potential containing the most relevant 3-body interactions by means of a correction for the nearest neighbour ligands in the ion's first hydration shell. This procedure leads to much improved results, without significant increase in computational effort during potential construction and simulation

A near-linear scaling equation of motion coupled cluster method for ionized states

2018 ◽  
Vol 148 (24) ◽  
pp. 244101 ◽  
Author(s):  
Achintya Kumar Dutta ◽  
Masaaki Saitow ◽  
Christoph Riplinger ◽  
Frank Neese ◽  
Róbert Izsák
Keyword(s):  
Equation Of Motion ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Linear Scaling ◽  
Coupled Cluster Method ◽  
Scaling Equation

Chloride Ion in Liquid Hydroxylamine: Pair Potential Function and Monte Carlo Simulation

1994 ◽  
Vol 49 (7-8) ◽  
pp. 797-801
Author(s):  
Pornthep Sompornpisut ◽  
Sirirat Kokpol ◽  
Bernd M. Rode
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Potential Function ◽  
Energy Surface ◽  
Pair Potential ◽  
Chloride Ion ◽  
Solvation Shell ◽  
Basis Set ◽  
Basis Set Superposition Error ◽  
Solvent Molecules

Abstract An analytical pair potential function for the Cl--NH2OH interaction energy surface has been constructed based on basis set superposition error corrected ECP/DZP ab initio calculations. The potential has been tested by Monte Carlo simulation of a solution of one chloride ion in liquid hydroxylamine at 32 °C, leading to the conclusion that under these conditions Cl-forms a solvation shell of eight solvent molecules, coordinated via OH hydrogens.

A natural linear scaling coupled-cluster method

2004 ◽  
Vol 121 (22) ◽  
pp. 10935 ◽  
Author(s):  
N. Flocke ◽  
Rodney J. Bartlett
Keyword(s):  
Cluster Method ◽  
Coupled Cluster ◽  
Linear Scaling ◽  
Coupled Cluster Method
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