Shannon Entropy Based Time-Dependent Deterministic Sampling for Efficient “On-the-Fly” Quantum Dynamics and Electronic Structure

Hocker, David; Li, Xiaohu; Iyengar, Srinivasan S.

doi:10.1021/ct1005856

Cited by 17 publications

(57 citation statements)

References 117 publications

(241 reference statements)

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“…The independence of ͕P 1 ͖ on R QM is further facilitated by the introduction of grid-based electronic structure bases introduced in Ref. 46 and discussed in Sec. IV C. As a result, at each instant during the dynamics, only the one-electron portion is recomputed.…”

Section: B Discussion Of Algorithmic Issues and Computational Advantmentioning

confidence: 99%

“…In Ref. 46, we have introduced further modifications to the TDDS function, using the concept for Shannon's information entropy. 47,48 The associated TDDS functions are also utilized here for ͑a͒ placement of grid-based electronic structure basis functions, as discussed in Sec.…”

Section: Main Features Of Qwaimd and Associated Limitationsmentioning

confidence: 99%

“…In Ref. 46, these basis functions were benchmarked with respect to regular atom-centered basis functions. To arrive at a system independent choice for the grid-based basis parameters a i , d i , v ជ i , the TDDS formalism was employed.…”

Section: Generalized Grid-based Electronic Basis Functions That Dmentioning

confidence: 99%

“…͑25͔͒, a flexible and accurate scheme for distributing the grid-based Gaussian basis functions was devised in Ref. 46. It was found 46 that the Shannon entropy based TDDS functions provide a very accurate description of the potential surface while eliminating the basis set dependence on the quantum nuclear degrees of freedom.…”

Section: Generalized Grid-based Electronic Basis Functions That Dmentioning

confidence: 99%

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Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

Iyengar

2010

The Journal of Chemical Physics

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We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics ͑QWAIMD͒ method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD ͑xLag-QWAIMD͒ and diabatic extended Lagrangian-QWAIMD ͑DxLag-QWAIMD͒. In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.

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Section: B Discussion Of Algorithmic Issues and Computational Advantmentioning

confidence: 99%

Section: Main Features Of Qwaimd and Associated Limitationsmentioning

confidence: 99%

Section: Generalized Grid-based Electronic Basis Functions That Dmentioning

confidence: 99%

Section: Generalized Grid-based Electronic Basis Functions That Dmentioning

confidence: 99%

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Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

Iyengar

2010

The Journal of Chemical Physics

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“…Dans cet article, nous utilisons l'entropie de Shannon sur des chaînes de Markov cachées d'ordre 1 pour les données issues du modèle de synthèse (données simulées sous contraintes) ainsi que pour des données issues d'une GMAO (sous-ensemble d'un processus continu). L'entropie de Shannon est définie [7] comme suit :…”

Section: Mesures De Pertinence Des Modèles 231 Entropie De Shannonunclassified

Modélisation du niveau de dégradation d’un système industriel à l’aide de modèles de Markov cachés

Robles¹,

Avila²,

Duculty³

et al. 2015

Congrès Lambda Mu 19 De Maîtrise Des Risques Et Sûreté De Fonctionnement

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RésuméLes modèles de Markov cachés ou HMM 1 sont largement utilisés dans les domaines de la reconnaissance des formes, de la parole ainsi que dans la modélisation de processus complexes. Nous proposons dans cette étude d'évaluer la pertinence des paramètres de modèles de Markov cachés de façon objective sans connaissance a priori. Nous présentons des critères permettant d'évaluer la pertinence d'événements stochastiques issus de modèles de Markov cachés. Nous étayons notre étude en nous appuyant sur l'exemple concret d'un processus industriel. Nous évaluons alors les paramètres de sortie des différents modèles testés sur ce processus, pour finalement s'orienter vers le modèle le plus pertinent. Nous validons nos méthodes de mesures de pertinence en retrouvant la topologie ayant servi à construire le modèle. Nous confrontons nos résultats provenant d'un modèle de synthèse avec des données provenant du processus industriel maintenu. Nous concluons alors sur la topologie qui traduit le mieux la dégradation d'un système réel. SummaryHidden Markov Models are widely used in the fields of pattern recognition, speech and the modeling of complex processes. We propose in this study to assess the relevance of the parameters of hidden Markov models without a priori knowledge. First, we present different criteria usually used in model selection. We study a concrete example of an industrial process. We then evaluate the output parameters of the different models tested in this process, to finally find the most appropriate model. We validate our methods by finding the topology used to build the model. We compare our results with synthetic data. We conclude that the topology 2 best reflects the degradation of a real system.

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Shape entropy’s response to molecular ionization

et al. 2013

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In this work we define a shape entropy by calculating the Shannon's entropy of the shape function. This shape entropy and its linear response to the change in the total number of electrons of the molecule are explored as descriptors of bonding properties. Calculations on selected molecular systems were performed. According to these, shape entropy properly describes electron delocalization while its linear response to ionization predicts changes in bonding patterns. The derivative of the shape entropy proposed turned out to be fully determined by the shape function and the Fukui function.

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Shannon Entropy Based Time-Dependent Deterministic Sampling for Efficient “On-the-Fly” Quantum Dynamics and Electronic Structure

Cited by 17 publications

References 117 publications

Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

Modélisation du niveau de dégradation d’un système industriel à l’aide de modèles de Markov cachés

Shape entropy’s response to molecular ionization

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