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Springer eBooks

Time Dependent Antisymmetrized Geminal Power Theory using a Coherent State Formulation

Erik Deumens, Brian Weiner, Yngve Öhrn

Published Jan 1, 1987• 3 citations
Publisher
DOI
10.1007/978-94-009-3855-7_9

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Coherent state approach to electron nuclear dynamics with an antisymmetrized geminal power state

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A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.

Journal of Mathematical Physics•Mar 1, 1994•17 citations

The Jastrow antisymmetric geminal power in Hilbert space: Theory, benchmarking, and application to a novel transition state

Eric Neuscamman

The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert space successfully overcomes two key failings of other pairing theories, namely, a lack of inter-pair correlations and a lack of multiple resonance structures, while maintaining a polynomially scaling cost, variational energies, and size consistency. Here, we present efficient quantum Monte Carlo algorithms that evaluate and optimize the JAGP energy for a cost that scales as the fifth power of the system size. We demonstrate the JAGP's ability to describe both static and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as well as to a novel, multi-reference transition state of ethene. JAGP's accuracy in these systems outperforms even the most sophisticated single-reference methods and approaches that of exponentially scaling active space methods.

arXiv:1308.5297•The Journal of Chemical Physics•Nov 18, 2013•73 citations

Generalized Coherent States: A Novel Approach

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

Journal of Mathematical Sciences•Jun 8, 2005•7 citations
A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.
The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert space successfully overcomes two key failings of other pairing theories, namely, a lack of inter-pair correlations and a lack of multiple resonance structures, while maintaining a polynomially scaling cost, variational energies, and size consistency. Here, we present efficient quantum Monte Carlo algorithms that evaluate and optimize the JAGP energy for a cost that scales as the fifth power of the system size. We demonstrate the JAGP's ability to describe both static and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as well as to a novel, multi-reference transition state of ethene. JAGP's accuracy in these systems outperforms even the most sophisticated single-reference methods and approaches that of exponentially scaling active space methods.