Energy and lifetime of temporary anion states of uracil by stabilization method

To investigate the temporary anion states of uracil, density functional theory with asymptotically corrected potentials is adopted. The stabilized Koopmans' theorem and stabilized Koopmans-based approximation are used in conjunction with an analytic continuation procedure to calculate its resonance energies and lifetimes. Results indicate the presence of several low-lying π* and σ* temporary anion states of uracil. The characteristics of these resonance orbitals are also analyzed. By comparing them with the experimental values and theoretical calculations, it is believed that the stabilization approach can provide more information on the resonance states.     

Implementation of the complex coordinate method for resonances and photoionization cross sections by means of matrix element extrapolation

A new implementation of the complex coordinate method for calculation of molecular resonances and photoionization cross sections is presented. The method originates from the idea of analytic continuation of stabilization graphs, but instead all matrix elements are numerically continued. Exterior scaling is invoked in conjunction with the use of dilationally adapted basis sets. It is operationally equivalent to the bivariational method in the Feshbach-partitioned manifold of complex basis functions, but no complex integrals are calculated. Instead, the complex eigenvalue problem arises from the analytical continuation of the realvalued matrix elements pertinent to any atomic or molecular structure code in its standard (real) form. That includes the possibility of using numerical basis sets. Since the method does not require modification of existing numerical codes, it can serve as a complement to any large scale CI or MCSCF molecular structure calculation.     

Correlated complex independent particle potential for calculating electronic resonances

We have formulated and applied an analytic continuation method for the recently formulated correlated independent particle potential [A. Beste and R. J. Bartlett J. Chem. Phys. 120, 8395 (2004)] derived from Fock space multireference coupled cluster theory. The technique developed is an advanced ab initio tool for calculating the properties of resonances in the low-energy electron-molecule collision problem. The proposed method quantitatively describes elastic electron-molecule scattering below the first electronically inelastic threshold. A complex absorbing potential is utilized to define the analytic continuation for the potential. A separate treatment of electron correlation and relaxation effects for the projectile-target system and the analytic continuation using the complex absorbing potential is possible, when an approximated form of the correlated complex independent particle potential is used. The method, which is referred to as complex absorbing potential-based correlated independent particle (CAP-CIP), is tested by application to the well-known (2)Pi(g) shape resonance of e-N(2) and the (2)B(2g) shape resonance of e-C(2)H(4) (ethylene) with highly satisfactory results.     

Failure of strong asymptotic conditions in four-dimensional field theories

It is shown that the renormalization group imposes severe restrictions on analytic continuation in coupling constant in the case of field theories in four dimensions.     

Single-root,real-basis-function method with correct branch-point structure for complex resonances energies

We present a new method for analytic continuation of real variational eigenvalues to calculate the complex energy of a collisional or photofragmentation resonance. The method is tested successfully against accurate quantum-mechanical results for model problems.     

Mode specificity of unimolecular rate constants in the Hénon-Heiles system

The tunneling widths of high-energy metastable states lying in the classical irregular region of the Hénon-Heiles potential energy surface were calculated via complex analytical continuation of stabilization graphs. Mode specificity is demonstrated in that the lifetimes of normal-mode, local-bond-mode, and mode-mixed states at nearby energies differ by an order of magnitude.     

The application of exterior complex scaling in calculations on resonances in nuclear motion in molecular systems

The application of the method of exterior complex scaling to find complex resonance energies by direct numerical integration is presented. Details of the numerical procedures required are discussed and results are presented for rotational predissociation resonances in H₂. The advantage of the exterior-scaling approach is that it requires analytic continuation of the potential to complex values of the coordinates only in the asymptotic or near-asymptotic region. Therefore any representation of the potential is adequate, including piecewise-continuous representations such as cubic splines. In contrast, application of the usual complex-scaling (rotated coordinates) procedure generally requires that the potential be represented by a single analytic function.     

Semiclassical study of collision-induced predissociation: Comparison of the Landau-Zener model with the method of analytic continuation

Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I₂. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.     

Application of Analytic Continuations to Avoided Crossings

The two-root (i,j,k) generalized Padé approximation (GPA) and three-root (i,j,k,l) GPA as well as the two-root continued fraction approximation (CFA) and the three-root CFA are applied to the model of a three-state avoided crossing. These two procedures for analytic continuation are compared. The results indicate that both methods provide good continuation into the complex plane and can be applied to locate the complex branch point. When the same input data are chosen, the GPA works slightly better than the CFA. According to our analysis, the two-root procedure can be applied to locate the branch point around each region of avoided crossing in the problem of a multi-state avoided crossing. The accuracy of the result is found to be associated the location of complex branch point.     

Resonant branch cuts in a generalized Friedrichs model

We study an example of a generalized Friedrichs model, in which a continuous-continuous coupling produces a pair of resonances as branch cuts of the analytic continuation of the reduced resolvent of the perturbed Hamiltonian to the second sheet of the Riemann surface associated to a transformation of the type w = z + α √z. To define the perturbation, we use the theory of self-adjoint extensions of symmetric operators proposed by the group of St. Petersburg. © 1996 John Wiley & Sons, Inc.     

Effective potential analytic continuation calculations of real time quantum correlation functions: asymmetric systems

We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact results, we find that for an asymmetric anharmonic oscillator the EPAC results are in very good agreement with the exact ones at low temperature, while this agreement becomes worse as the temperature increases. We also show that the EPAC calculation for a certain type of asymmetric potentials can be reduced to that for the corresponding symmetric potentials.     

Transport properties of normal liquid helium: comparison of various methodologies

We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.     

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium

Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids.     

Vibrational contributions to cubic response functions from vibrational configuration interaction response theory

In continuation of our recent paper on vibrational quadratic response functions for vibrational configuration interaction wave functions, we present in this paper a derivation and implementation of the pure vibrational cubic response function for vibrational configuration interaction wave functions. In addition, we present combined electronic and vibrational cubic response functions derived from sum-over-states expressions in the Born-Oppenheimer framework and a discussion of complicating issues. The implementation enables analytic calculation of the pure vibrational cubic response function via response theory, which constitutes a part of the vibronic cubic response function.     

Ionization probability of the hydrogen atom suddenly released from confinement

The problem of the stability of a confined atom when it is extracted from the confining cavity has been investigated, modeled by a spherical hard wall potential. The ionization probability when the atom is released from confinement has been obtained. The dependence of the ionization probability on the confinement radius and on the quantum numbers of the initial confined state has been studied. The probability density function of the ionization energy of the ejected electron has been obtained for the different cases considered. The oscillatory structure of this distribution function, with a principal maximum located in the neighborhood of the energy of the initial state and minima very close to zero has been elucidated. The sudden approximation has been applied and the analytic continuation method has been used to calculate the different stationary states.     

Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators

We apply the effective potential analytic continuation (EPAC) method to the calculation of real time quantum correlation functions involving operators nonlinear in the position operator q. For a harmonic system the EPAC method provides the exact correlation function at all temperature ranges, while the other quantum dynamics methods, the centroid molecular dynamics and the ring polymer molecular dynamics, become worse at lower temperature. For an asymmetric anharmonic system, the EPAC correlation function is in very good agreement with the exact one at t = 0. When the time increases from zero, the EPAC method gives good coincidence with the exact result at lower temperature. Finally, we propose a simplified version of the EPAC method to reduce the computational cost required for the calculation of the standard effective potential.     

Density functional theory of complex transition densities

We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.     

Proof of the Fukui conjecture via resolution of singularities and related methods. IV

The present article is a direct continuation of the previous part III of this series of articles, which have been devoted to cultivating a new interdisciplinary region between chemistry and mathematics. In the present part IV, we develop two sets of fundamental theoretical tools, using methods from the field of resolution of singularities and analytic curves. These two sets of tools are essential in structurally elucidating the assertion of the Fukui conjecture (concerning the additivity problems) and the crux of the functional asymptotic linearity theorem (functional ALT) that proves the conjecture in a broad context. This conjecture is a vital guideline for a future development of the repeat theory (RST)—the central unifying theory in the First and the Second Generation Fukui Project.     

Role of resonances in building cross sections: Comparison between the Mittag–Leffler and the T‐matrix Green function expansion approaches

Peaks in collision cross sections are often interpreted as resonances. The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S‐matrix and the associated Green function. The performance of the Mittag–Leffler expansion and T‐matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s‐wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag–Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S‐matrix residue. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007