Abstracts of the Kathmandu Workshop 2012

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The abstracts are in the alphabetical order of the author names.

Helen van Aggelen

Ghent University

Variational optimization of second order density matrices for chemistry

A myriad of ab initio methods uses simple mathematical objects to describe a chemical system in order to avoid the ‘exponential wall’ inherent to the wavefunction. This talk evaluates the use of variational second order density matrix methods for chemistry and identifies the major theoretical and computational challenges that need to be overcome to make it successful for chemical applications.

Its major theoretical challenges originate from the need for the second order density matrix to be N-representable: it must be derivable from an ensemble of N-electron states. Our calculations have pointed out major drawbacks of commonly used necessary N-representability conditions, such as incorrect dissociation into fractionally charged products and size-inconsistency, as well as flaws in the description of spin properties. We have derived subspace energy constraints that fix these problems, albeit in an ad-hoc manner.

Its major computational challenges originate from the method’s formulation as a vast semidefinite optimization problem. We have implemented and compared several algorithms that exploit the specific structure of the problem. Even so, their slow speed remains prohibitive. Both the second order methods and the zeroth order boundary point method that we tried performed quite similar, which suggests that the underlying problem responsible for their slow convergence, ill-conditioning due to the singularity of the optimal matrix, manifests itself in all these algorithms even though it is most explicit in the barrier method.

Significant progress in these two areas is needed to make the variational second order density matrix method competitive to comparable wavefunction based methods.

Jerzy Cioslowski

University of Szczecin

All you always wanted to know about many-electron harmonium atoms

Recent theoretical and numerical developments on electronic structures of harmonium atoms with more than two electrons are reviewed, including FCI and Monte Carlo results, as well as a new accurate representations for the total anergy and its components in terms of a transformed coupling strength.