A topological approach to some cluster methods

2005 ◽  
pp. 479-487
Author(s):  
J. Jacas ◽  
J. Recasens
Keyword(s):  
Topological Approach ◽  
Cluster Methods

The X40x10 Halogen Bonding Benchmark Revisited: Surprising Importance of (n-1)d Subvalence Correlation

2017 ◽  
Author(s):  
Manoj Kumar Kesharwani ◽  
Nitai Sylvetsky ◽  
Debashree Manna ◽  
Jan M.L. Martin
Keyword(s):  
Dissociation Energy ◽  
Noncovalent Interactions ◽  
Halogen Bonding ◽  
Coupled Cluster ◽  
Dissociation Energies ◽  
Iodine Species ◽  
Explicitly Correlated ◽  
High Level ◽  
Cluster Methods ◽  
Small Separation

<p>We have re-evaluated the X40x10 benchmark for halogen bonding using conventional and explicitly correlated coupled cluster methods. For the aromatic dimers at small separation, improved CCSD(T)–MP2 “high-level corrections” (HLCs) cause substantial reductions in the dissociation energy. For the bromine and iodine species, (n-1)d subvalence correlation increases dissociation energies, and turns out to be more important for noncovalent interactions than is generally realized. As in previous studies, we find that the most efficient way to obtain HLCs is to combine (T) from conventional CCSD(T) calculations with explicitly correlated CCSD-F12–MP2-F12 differences.</p>

Double Precision Is Not Needed for Many-Body Calculations: New Conventional Wisdom

2018 ◽  
Author(s):  
Pavel Pokhilko ◽  
Evgeny Epifanovsky ◽  
Anna I. Krylov
Keyword(s):  
Large Scale ◽  
Computation Time ◽  
Coupled Cluster ◽  
Double Precision ◽  
Many Body ◽  
Single Precision ◽  
Parallel Performance ◽  
Point Representation ◽  
Electron Repulsion Integrals ◽  
Cluster Methods

Using single precision floating point representation reduces the size of data and computation time by a factor of two relative to double precision conventionally used in electronic structure programs. For large-scale calculations, such as those encountered in many-body theories, reduced memory footprint alleviates memory and input/output bottlenecks. Reduced size of data can lead to additional gains due to improved parallel performance on CPUs and various accelerators. However, using single precision can potentially reduce the accuracy of computed observables. Here we report an implementation of coupled-cluster and equation-of-motion coupled-cluster methods with single and double excitations in single precision. We consider both standard implementation and one using Cholesky decomposition or resolution-of-the-identity of electron-repulsion integrals. Numerical tests illustrate that when single precision is used in correlated calculations, the loss of accuracy is insignificant and pure single-precision implementation can be used for computing energies, analytic gradients, excited states, and molecular properties. In addition to pure single-precision calculations, our implementation allows one to follow a single-precision calculation by clean-up iterations, fully recovering double-precision results while retaining significant savings.

A topological approach to the strain-rate pattern of ice sheets

1993 ◽  
Vol 39 (131) ◽  
pp. 10-14 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Strain Rate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Point Of View ◽  
Principal Strain ◽  
Topological Approach ◽  
Contour Maps ◽  
Isotropic Point ◽  
Horizontal Strain

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

A TOPOLOGICAL APPROACH IN CORDIAL GRAPHS

2020 ◽  
Vol 9 (4) ◽  
pp. 1585-1595
Author(s):  
A. Divya ◽  
D. Sasikala
Keyword(s):  
Topological Approach

scholarly journals The “Emerging” Reality from “Hidden” Spaces

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 75
Author(s):  
Richard Pincak ◽  
Alexander Pigazzini ◽  
Saeid Jafari ◽  
Cenap Ozel
Keyword(s):  
Dark Matter ◽  
String Theory ◽  
Topological Approach ◽  
New Approach ◽  
Topological Interpretation ◽  
New Interpretation ◽  
M Theory

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole, but mainly we provide a topological interpretation, using this new approach, to M-Theory and String Theory in 10 dimensions. Further, we present some conclusions which this new interpretation suggests, and also some remarks considering a unifying approach between strings and dark matter. The approach shown in the paper considers that reality, as it appears to us, can be the “emerging” part of a more complex hidden structure. Pacs numbers: 11.25.Yb; 11.25.-w; 02.40.Ky; 02.40.-k; 04.50.-h; 95.35.+d.

scholarly journals A computational study for the reaction mechanism of metal-free cyanomethylation of aryl alkynoates with acetonitrile

RSC Advances ◽  
2021 ◽  
Vol 11 (30) ◽  
pp. 18246-18251
Author(s):  
Selçuk Eşsiz
Keyword(s):  
Density Functional Theory ◽  
Reaction Mechanism ◽  
Density Functional ◽  
Computational Study ◽  
Coupled Cluster ◽  
Functional Theory ◽  
Metal Free ◽  
Coupled Cluster Methods ◽  
High Level ◽  
Cluster Methods

A computational study of metal-free cyanomethylation and cyclization of aryl alkynoates with acetonitrile is carried out employing density functional theory and high-level coupled-cluster methods, such as [CCSD(T)].

Active-space coupled-cluster methods

2010 ◽  
Vol 108 (21-23) ◽  
pp. 2987-3015 ◽  
Author(s):  
Piotr Piecuch
Keyword(s):  
Coupled Cluster ◽  
Active Space ◽  
Coupled Cluster Methods ◽  
Cluster Methods
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