Complex basis functions revisited: Implementation with applications to carbon tetrafluoride and aromatic N-containing heterocycles within the static-exchange approximation

White, Alec F.; Head‐Gordon, Martin; McCurdy, C. W.

doi:10.1063/1.4906940

Cited by 61 publications

(72 citation statements)

References 71 publications

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“…Several approaches have been proposed for the computation of resonances. The list comprises artificial stabilizing potentials, [28][29][30][31] stabilization methods, 32,33 complex scaling, [34][35][36][37][38] exterior complex scaling, 39,40 complex basis functions, 41,42 and complex absorbing potentials (CAPs). [43][44][45][46][47][48] Here, we employ the CAP approach, where an imaginary potential is added to the Hamiltonian in order to describe the resonance as an L 2 -integrable discrete state.…”

Section: Introductionmentioning

confidence: 99%

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Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments

Jagau

Krylov

2016

The Journal of Chemical Physics

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The theoretical description of electronic resonances is extended beyond calculations of energies and lifetimes. We present the formalism for calculating Dyson orbitals and transition dipole moments within the equation-of-motion coupled-cluster singles and doubles method for electron-attached states augmented by a complex absorbing potential (CAP-EOM-EA-CCSD). The capabilities of the new methodology are illustrated by calculations of Dyson orbitals of various transient anions. We also present calculations of transition dipole moments between transient and stable anionic states as well as between different transient states. Dyson orbitals characterize the differences between the initial neutral and final electron-attached states without invoking the mean-field approximation. By extending the molecular-orbital description to correlated many-electron wave functions, they deliver qualitative insights into the character of resonance states. Dyson orbitals and transition moments are also needed for calculating experimental observables such as spectra and cross sections. Physically meaningful results for those quantities are obtained only in the framework of non-Hermitian quantum mechanics, e.g., in the presence of a complex absorbing potential (CAP), when studying resonances. We investigate the dependence of Dyson orbitals and transition moments on the CAP strength and illustrate how Dyson orbitals help understand the properties of metastable species and how they are affected by replacing the usual scalar product by the so-called c-product.

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Section: Introductionmentioning

confidence: 99%

“…We note that electronic resonances rarely have been characterized beyond energy and lifetime. For some species, contour plots of HF orbitals 42,64,65,67 and attachment densities 68 have been reported. Our article presents the first implementation and calculation of transition moments and Dyson orbitals for metastable states.…”

Section: Introductionmentioning

confidence: 99%

Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments

Jagau

Krylov

2016

The Journal of Chemical Physics

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“…Stabilization methods 11,12 and associated analytic continuation methods, [13][14][15] use continuum eigenvalues from bound state calculations to extract resonance a) Electronic mail: mhg@cchem.berkeley.edu b) Electronic mail: cwmccurdy@ucdavis.edu parameters. Complex coordinate methods 4,[16][17][18][19][20][21] compute the Siegert energy as an eigenvalue of a transformed, non-Hermitian, Hamiltonian operator. Bound state extrapolation 22,23 or analytic continuation 24,25 methods rely on the analytic continuation of bound-state energies to find resonance parameters.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

White

Head‐Gordon

McCurdy

2017

The Journal of Chemical Physics

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The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. We critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2 Π g shape resonance of N − 2 which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

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“…In this subsection, we explain the CBF method can be used to solve variationally a driven‐type Schrödinger equation with the outgoing boundary condition in eqs. and using only

L^{2}

basis functions.…”

Section: Theorymentioning

confidence: 99%

“…The complex basis function (CBF) method, an extension of the complex scaling method, can be recognized as one of the L 2 methods to solve driven‐type Schrödinger equation in the application to photoionization cross sections. The method has been applied to general molecules by combining with various excited state calculation methods .…”

Section: Introductionmentioning

confidence: 99%

Optimization of complex slater‐type functions with analytic derivative methods for describing photoionization differential cross sections

Matsuzaki

Yabushita

2017

J Comput Chem

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The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc.

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Complex basis functions revisited: Implementation with applications to carbon tetrafluoride and aromatic N-containing heterocycles within the static-exchange approximation

Cited by 61 publications

References 71 publications

Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments

Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

Optimization of complex slater‐type functions with analytic derivative methods for describing photoionization differential cross sections

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