Différences entre les versions de « Abstracts of the Kathmandu Workshop 2012 »
| Ligne 8 : | Ligne 8 : | ||
The abstracts are in the alphabetical order of the author names. | The abstracts are in the alphabetical order of the author names. | ||
| + | |||
| + | == Frank E. Harris == | ||
| + | |||
| + | ''University of Florida'' | ||
| + | |||
| + | '''Fully Correlated Wavefunctions for Small Atoms''' | ||
| + | |||
| + | While this work includes a lot that is new, I would expect to give a talk that is general enough to place the new developments in the context of the line of work that was started by Robert Hill and was advanced significantly by Rebane (St. Petersburg), with some further contributions from our laboratory and from others. | ||
| + | |||
== Helen van Aggelen == | == Helen van Aggelen == | ||
| Ligne 15 : | Ligne 24 : | ||
'''Variational optimization of second order density matrices for chemistry''' | '''Variational optimization of second order density matrices for chemistry''' | ||
| − | A myriad of ab initio methods uses simple mathematical objects to | + | 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. |
| − | 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 | + | 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. |
| − | 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 | + | Its major computational challenges originate from the method’s formulation as a vast semidefinite optimization problem. We have |
| − | 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 |
| − | implemented and compared several algorithms that exploit the specific | + | prohibitive. Both the second order methods and the zeroth order boundary point method that we tried performed quite similar, which |
| − | structure of the problem. Even so, their slow speed remains | + | suggests that the underlying problem responsible for their slow convergence, ill-conditioning due to the singularity of the optimal |
| − | prohibitive. Both the second order methods and the zeroth order | + | matrix, manifests itself in all these algorithms even though it is most explicit in the barrier method. |
| − | 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 | + | Significant progress in these two areas is needed to make the variational second order density matrix method competitive to comparable wavefunction based methods. |
| − | variational second order density matrix method competitive to | ||
| − | comparable wavefunction based methods. | ||
| Ligne 62 : | Ligne 52 : | ||
'''All you always wanted to know about many-electron harmonium atoms''' | '''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 | + | 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 |
| − | 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. | transformed coupling strength. | ||
Version du 17 janvier 2012 à 11:09
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The abstracts are in the alphabetical order of the author names.
Frank E. Harris
University of Florida
Fully Correlated Wavefunctions for Small Atoms
While this work includes a lot that is new, I would expect to give a talk that is general enough to place the new developments in the context of the line of work that was started by Robert Hill and was advanced significantly by Rebane (St. Petersburg), with some further contributions from our laboratory and from others.
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.
Henry Chermette
Université Lyon1
The Gradient-Regulated Connection of Generalized Gradient Exchange Functionals: Interest and Limitations
The Gradient-Regulated Connection (GRAC) has been introduced a few years ago by Baerends et al. in order to build a density functional potential model satisfying theoretical conditions and providing Kohn-Sham orbitals. Recently the GRAC has been used to build an exchange functional able to mix performances of a modified PBE for the bulk region, to those of the PW91 for the asymptotic one. This exchange functional, coupled with the TCA correlation functional, was able to significantly improve the modeling of weak interacting systems, while keeping a good accuracy for the atomization energies. The interest and the limitations of this approach is discussed.
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.
Khumbu Icefall seen from the Everest Base Camp