Resonances, Cross Sections, and Partial Widths by the Complex Coordinate Method

Moiseyev, Nimrod

doi:10.1002/ijch.199100036

Cited by 44 publications

(11 citation statements)

References 76 publications

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“…With the use of real basis functions, the Euclidean inner product is equal to the c-product defined by Moiseyev et al, 48 although it should be noted that the c-product has a more general definition allowing its use also with complex basis functions 49 ͑this is not relevant for the present application, in which we require the Hamiltonian matrix to be complex symmetric͒. It should be noted that, if real basis functions are used, a complex symmetric Hamiltonian can also be obtained with the use of a complex scaling approach; 50,51 this approach was used in the first application of the Lanczos method to the calculation of resonances. 29 Rather then reorthogonalizing the generated Lanczos vectors with respect to one another, the implementation by Cullum and Willoughby 47 uses an algorithm to identify spurious eigenvalues arising from the loss of orthogonality.…”

Section: ͑11͒mentioning

confidence: 99%

Dissociative chemisorption of H2 on Cu(100): A four-dimensional study of the effect of parallel translational motion on the reaction dynamics

Kroes

Wiesenekker

Baerends

et al. 1996

The Journal of Chemical Physics

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We investigate the usefulness of a hybrid method for scattering with resonances. Wave packet propagation is used to obtain the time-dependent wave function ⌿(t) up to some time T at which direct scattering is over. Next, ⌿(t) is extrapolated beyond T employing resonance eigenvalues and eigenfunctions obtained in a Lanczos procedure, using ⌿(T) as starting vector to achieve faster convergence. The method is tested on one two-dimensional ͑2D͒ and one four-dimensional ͑4D͒ reactive scattering problem, affected by resonances of widths 0.1-5 meV. Compared to long time wave packet propagation, the hybrid method allows large reductions in the number of Hamiltonian operations N H required for obtaining converged reaction probabilities: A reduction factor of 24 was achieved for the 2D problem, and a factor of 6 for the 4D problem.

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Section: ͑11͒mentioning

confidence: 99%

Dissociative chemisorption of H2 on Cu(100): A four-dimensional study of the effect of parallel translational motion on the reaction dynamics

Kroes

Wiesenekker

Baerends

et al. 1996

The Journal of Chemical Physics

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“…3 The introduction of the complex scaling method 4 brought in new rigorous mathematical formulations, together with further developments of basis-set expansion methods. 5 Being based on the rotation of the coordinates into the complex plane, the original version of this method required the analytic continuation of the potential, which sometimes could be difficult or even impossible to obtain.…”

Section: Introductionmentioning

confidence: 99%

Recursion polynomial expansion of the Green’s function with absorbing boundary conditions: Calculations of resonances of HCO by filter diagonalization

Grozdanov

Mandelshtam

Taylor

1995

The Journal of Chemical Physics

143

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A simple recursion polynomial expansion of the Green's function with absorbing boundary conditions. Application to the reactive scattering An iterative method for calculating resonance positions and widths is developed. The system Hamiltonian with an asymptotic complex absorbing potential is represented by a large and sparse matrix. A small set of ''good'' basis functions suitable for diagonalizing the Hamiltonian matrix in a given energy window is generated by acting with a polynomial expansion of the imaginary part of the system Green's function onto a generic initial wave packet. As an application to a realistic three-dimensional system, the calculation of 65 resonances of the nonrotating HCO molecule up to the energy 9000 cm Ϫ1 is presented. The method is shown to be rapidly convergent and accurate, especially for narrow resonances.

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“…One approach is to calculate the rates using an ab initio scattering method, as is done for the decay of inner-shell vacancies of atoms and small molecules [13][14][15]. Another approach relies on the Hamiltonian continued into the complex energy plane [16,17]. The decaying states become resonances with complex energies, where the imaginary part is related to the inverse lifetime.…”

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confidence: 99%

Giant Intermolecular Decay and Fragmentation of Clusters

1997

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In sharp contrast to molecules, electronic states of clusters with an excited intermediate-shell electron can efficiently decay via an intermolecular Coulombic mechanism. Explicit examples are presented using large scale ab initio propagator calculations. The mechanism is illustrated and its generality is stressed. [S0031-9007(97) PACS numbers: 36.40.Cg, 31.50. + w, 34.50.Gb Quantum states of electronic systems typically decay by photon and/or electron emission. Energetically low lying states decay radiatively while highly excited levels involving the excitation of inner-shell electrons decay more efficiently by emitting an electron (Auger decay). It is only for very deep inner-shell electrons of heavy elements that x-ray emission constitutes the prominent decay channel [1]. States which can decay only radiatively, i.e., states with excited outer-shell electrons, exhibit an exceedingly long lifetime (ഠ nanoseconds) compared to Auger-decaying states. For instance, a vacancy in the 1s shell of a fluorine atom has a lifetime of about 3.3 fs (0.20 eV linewidth) [2]. This lifetime depends only weakly on whether the fluorine atom is free or integrated in a molecular system. The total decay rate is essentially determined by the neighboring atomic electrons. Deeper electron vacancies typically decay faster. An excited or ionized state of the sulfur atom with a vacancy in the 1s shell, for example, lives for about 1.6 fs [3], and if the vacancy is in the 2p shell the lifetime extends to 66 fs [4].As mentioned above, the environment of the atom influences only moderately the lifetime of the deep vacancy (e.g., of a F1s vacancy). If at all, we can only expect interesting environmental effects on the total Auger decay rate to take place for vacancies in intermediate shells.However, a closer look at the energetics of the decay in typical molecules brings a problem to light. The ionization potential (IP) of a F2s electron in, say, the HF molecule, is about 40 eV [5], but the release of these 40 eV is insufficient to ionize a second electron: the lowest double ionization potential (DIP) of HF is about 45 eV [6]. Similarly, the IP of an O2s electron in H 2 O is approximately 35 eV [7], again too small an energy to allow a second electron to leave the system. The lowest DIP of water is about 38 eV [8]. The situation changes substantially as we move to clusters. While the IP of intermediate shells differs only slightly from that of the monomer unit, some DIPs are lowered considerably in the cluster and the autoionization channel opens. More importantly, we shall also show in this Letter that the accessible decay becomes dramatically efficient in clusters.Atomic and molecular clusters have been subject to continuous interest over many years [9][10][11]. Most of the interest has been devoted to the possible geometrical structures and properties of the clusters in their electronic ground state. Much less attention has been paid to excited electronic states and no attention to highly excited states involving intermediate shell ele...

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Resonances, Cross Sections, and Partial Widths by the Complex Coordinate Method

Cited by 44 publications

References 76 publications

Dissociative chemisorption of H2 on Cu(100): A four-dimensional study of the effect of parallel translational motion on the reaction dynamics

Dissociative chemisorption of H2 on Cu(100): A four-dimensional study of the effect of parallel translational motion on the reaction dynamics

Recursion polynomial expansion of the Green’s function with absorbing boundary conditions: Calculations of resonances of HCO by filter diagonalization

Giant Intermolecular Decay and Fragmentation of Clusters

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