Physics Colloquium: Michael Berry

August 19, 2019

Geometric phases and the separation of the world

The waves that describe systems in quantum physics can carry information about how their environment has been altered, for example by forces acting on them. This effect is the geometric phase. It also occurs in the optics of polarised light, where it goes back to the 1830s. The underlying mathematics is geometric: the phenomenon of parallel transport, which also explains how falling cats land on their feet, and why parking a car in a narrow space is difficult. Incorporating the back-reaction of the geometric phase on the dynamics of the changing environment exposes the unsolved problem of how strictly a system can be separated from a slowly-varying environment, and involves different mathematics: divergent infinite series.

Accurate Local Coupled Cluster Studies of the Chemistry and Physics of Molecules with 50 - 200 Atoms

June 25, 2018

The explicitly correlated coupled cluster with singles doubles, and perturbative triples [CCSD(T)-F12] method is often called the "silver standard" of electronic structure methods for non-metallic molecular systems when used with a atomic orbital basis set of good quality. It can yield "chemical accuracy" (defined as an accuracy within1 kcal/mol) of the potential energy surface of a large class of molecular systems within the Born-Oppenheimer approximation. Unfortunately, the computational effort of conventional CCSD(T)-F12 scales with the seventh power of the molecule's size and therefore its usage is usually limited to rather small systems with 5-20 atoms. The localization of molecular orbitals in non-metallic systems offers one route to apply accuracy-controlled approximations to electron-electron interactions while lowering the asymptotic scaling of the method to linear. However, improving on the accuracy of these "local approximations" to be on a par with or even better than the intrinsic accuracy of the CCSD(T)-F12 silver standard for molecules with 40 - 200 atoms has only been achieved very recently [Refs. 1-4].

After an introduction into the method, application examples on how it can be used as a tool for gaining new insight and high-quality data on physical and chemical behavior of molecules with 40 -200 atoms will be presented. Examples include reaction barriers and energies of organic and organometallic compounds of great interest in chemistry as well as physical properties of small dipolar molecules confined in carbon nanotubes [CNT(n,n), n=3,4,5]. Some of the results include benchmarking of a variety of widely used density functional theory (DFT) methods.

References: 

[1] M. Schwilk, D. Usvyat, H.- J. Werner, J. Chem. Phys., 142, 121102 (2015)

[2] M. Schwilk, Q. Ma, C. Köppl, H.- J. Werner, J. Chem. Theor. and Comp., 13, 3650 (2017)

[3] Q. Ma, M. Schwilk, C. Köppl, H.-J. Werner, J. Chem. Theor. and Comp., 13, 4871 (2017) 

[4] Q. Ma, H.-J. Werner, J. Chem. Theory Comp., 14, 198–215 (2018)

 

About the Speaker:

Since March 2018 Postdoc with Prof. O. A. v. Lilienfeld, University of Basel

2017 PhD in Theoretical Chemistry with Prof. H.-J. Werner, University of Stuttgart, Germany; Topic: Scalable electronic structure methods.

2012 Chemistry Diploma, University of Stuttgart, Germany.

2011 Diplôme d'Ingénieur Ecole Européenne de Chimie, Polymères et Matériaux de Strasbourg (ECPM Strasbourg), France.

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The work of Prof. Alexandre Tkatchenko is supported in part by the European Research Council under the European Union's Horizon 2020 research and innovation programme (grant agreement n. 725291)  and by FNR.