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Poul Jorgensen - One of the best experts on this subject based on the ideXlab platform.

  • molecular response properties from a hermitian Eigenvalue Equation for a time periodic hamiltonian
    Journal of Chemical Physics, 2015
    Co-Authors: Filip Pawlowski, Jeppe Olsen, Poul Jorgensen
    Abstract:

    The time-dependent Schrodinger Equation for a time-periodic perturbation is recasted into a Hermitian Eigenvalue Equation, where the quasi-energy is an Eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian Eigenvalue Equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed sta...

  • molecular response properties from a hermitian Eigenvalue Equation for a time periodic hamiltonian
    Journal of Chemical Physics, 2015
    Co-Authors: Filip Pawlowski, Jeppe Olsen, Poul Jorgensen
    Abstract:

    The time-dependent Schrodinger Equation for a time-periodic perturbation is recasted into a Hermitian Eigenvalue Equation, where the quasi-energy is an Eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian Eigenvalue Equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model—the coupled cluster configuration interaction (CC-CI) model—where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field Equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.

Filip Pawlowski - One of the best experts on this subject based on the ideXlab platform.

  • molecular response properties from a hermitian Eigenvalue Equation for a time periodic hamiltonian
    Journal of Chemical Physics, 2015
    Co-Authors: Filip Pawlowski, Jeppe Olsen, Poul Jorgensen
    Abstract:

    The time-dependent Schrodinger Equation for a time-periodic perturbation is recasted into a Hermitian Eigenvalue Equation, where the quasi-energy is an Eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian Eigenvalue Equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed sta...

  • molecular response properties from a hermitian Eigenvalue Equation for a time periodic hamiltonian
    Journal of Chemical Physics, 2015
    Co-Authors: Filip Pawlowski, Jeppe Olsen, Poul Jorgensen
    Abstract:

    The time-dependent Schrodinger Equation for a time-periodic perturbation is recasted into a Hermitian Eigenvalue Equation, where the quasi-energy is an Eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian Eigenvalue Equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model—the coupled cluster configuration interaction (CC-CI) model—where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field Equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.

Jeppe Olsen - One of the best experts on this subject based on the ideXlab platform.

  • molecular response properties from a hermitian Eigenvalue Equation for a time periodic hamiltonian
    Journal of Chemical Physics, 2015
    Co-Authors: Filip Pawlowski, Jeppe Olsen, Poul Jorgensen
    Abstract:

    The time-dependent Schrodinger Equation for a time-periodic perturbation is recasted into a Hermitian Eigenvalue Equation, where the quasi-energy is an Eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian Eigenvalue Equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed sta...

  • molecular response properties from a hermitian Eigenvalue Equation for a time periodic hamiltonian
    Journal of Chemical Physics, 2015
    Co-Authors: Filip Pawlowski, Jeppe Olsen, Poul Jorgensen
    Abstract:

    The time-dependent Schrodinger Equation for a time-periodic perturbation is recasted into a Hermitian Eigenvalue Equation, where the quasi-energy is an Eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian Eigenvalue Equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model—the coupled cluster configuration interaction (CC-CI) model—where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field Equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.

Andreas Gorling - One of the best experts on this subject based on the ideXlab platform.

  • efficient exact exchange time dependent density functional theory methods and their relation to time dependent hartree fock
    Journal of Chemical Physics, 2011
    Co-Authors: Andreas Heselmann, Andreas Gorling
    Abstract:

    A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized Eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest Eigenvalues of the new TDEXX Eigenvalue Equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized Eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX Eigenvalue Equation, standard eigensolvers for large regular Eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the se...

Schoberl F. F. - One of the best experts on this subject based on the ideXlab platform.