Singly excited bound states in continuum: a time-dependent perturbation approach

Summary Time-dependent coupled Hartree-Fock (TDCHF) scheme has been applied to study the behaviour of bound excited states embedded in the continuum for the negative ions Li^–, F^–, Na^– and Cl^–. The excited states have been obtained from the position of the poles of the dynamic polarizability values which are evaluated for all the ions within and beyond the normal dispersion region. Transition energies and dipole allowed oscillator strengths have been obtained for several transitions which lie in the continuum. Although the excited state functions are extremely diffuse, they show proper asymptotic behaviour and furnish correct number of nodes. Oscillator strengths are found to follow a different trend than observed in normal bound state calculations.     

A new perturbation approach to coupling between adiabatic states

A new perturbation expansion, formally related to Tanaka-Fukuda perturbation theory, is derived and applied to the general problem of nonadiabatic coupling. The coupling between adiabatic Born-Oppenheimer states in poly-atomic molecules is treated in detail in both the one- and multi-phonon limits, for which previous methods are often unreliable, even for order-of-magnitude estimates.     

Time-dependent photoionization of azulene: competition between ionization and relaxation in highly excited states

Pump-probe photoionization has been used to map the relaxation processes taking place from highly vibrationally excited levels of the S(2) state of azulene, populated directly or via internal conversion from the S(4) state. Photoelectron spectra obtained by 1+2(') two-color time-resolved photoelectron imaging are invariant (apart from in intensity) to the pump-probe time delay and to the pump wavelength. This reveals a photoionization process which is driven by an unstable electronic state (e.g., doubly excited state) lying below the ionization potential. This state is postulated to be populated by a probe transition from S(2) and to rapidly relax via an Auger-like process onto highly vibrationally excited Rydberg states. This accounts for the time invariance of the photoelectron spectrum. The intensity of the photoelectron spectrum is proportional to the population in S(2). An exponential energy gap law is used to describe the internal conversion rate from S(2) to S(0). The vibronic coupling strength is found to be larger than 60+/-5 microeV.     

On the relation between Peierls' perturbation theory for projected states and exchange perturbation theory

The derivations of a rather general class of exchange perturbation theories (or symmetry-adapted perturbation theories) and Peierls' perturbation theory for projected states are discussed. While the approaches are different, the equivalence of the resulting formalisms is established.     

Rotational perturbation between two electronically excited states of 4HeD

The rotational structure of the D ²Σ⁺ →A²Σ⁺ transition of ⁴HeD is highly perturbed, and this is caused by the near degeneracy of the D, ν=0 and C, ν=3 vibrational levels. A perturbation analysis is presented which yields the spectroscopic constants for both of the perturbing levels, yielding the first experimental information on a vibrationally excited state of HeH.     

Reactive cross-talk between adjacent tension-trapped transition states

Tension along a polymer chain traps neighboring s-trans/s-trans-1,3-diradicals from the mechanically induced ring opening of gem-difluorocyclopropanes (gDFCs). The diradicals correspond to the transition states of the force-free thermal isomerization reactions of gDFCs, and the tension trapping allows a new disproportionation reaction between two simultaneously trapped diradicals to take place.     

Adiabatic perturbation theory for the degenerate case. II. Perturbation of degenerate bound states embedded in the continuum

An adiabatic formula for the contracted Hamiltonian in a reference space containing bound-state eigenfunctions of degenerate energy levels embedded in the continuum is derived. A general factorization theorem for the dynamic operatorS_α(0, – ∞/λ) is proved, and the cancellation of the pole singularities in the perturbation series of the contracted Hamiltonian in adiabatic form is discussed.     

Time-dependent heat capacity in the glass transition region

Time-dependent, apparent heat capacities of glucose, poly(vinyl chloride), polystyrene, selenium, poly(methyl methacrylate), and poly(2,6-dimethyl-1,4-phenylene ether) in the glass transition region were determined by differential thermal analysis. The thermal history was set by linear cooling at rates between 0.007 and 160°C/min. Linear heating for analysis was carried out at rates between 0.3 and 600°C/min. Average activation energies of 52, 81, 90, 54, 77, and 108 kcal/mole, respectively, were evaluated by using the hole theory of glasses previously developed. Within experimental limitations all data could be described quantitatively by the theoretical expressions using only one parameter, the number of frozen-in holes, to described the thermal history. Experimental and theoretical limitations are discussed.     

Fine structure and transition probabilities of the 2p 5 nl bound excited states of Ne atom

We present a semi-empirical calculational procedure for thep ⁵ nl bound excited states of rare gas atoms based on the use of an LS-dependent orbital for an excitednl electron outside a frozen Hartree-Fockp ⁵ core. The spin-orbit interaction is accounted for approximately using a localized Hartree potential. The contribution from the long-range core polarization is estimated by using a parametrized potential. A model potential is also introduced to represent partially the short-range multi-electron interactions for thep ⁵ np levels. The energy levels are calculated by diagonalizing the Hamiltonian matrix following anLS →jl transformation. The calculated fine structure of the Nep ⁵ ns,p ⁵ np,p ⁵ nd, andp ⁵ nf ¦ (jl)KJ〉 levels are in close agreement with the observed level splittings. The transition probabilities are also in agreement with earlier theoretical and experimental results.     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Doubly excited states of highly stripped ions: a time dependent perturbation approach

Doubly excited singlet states have been calculated for the astrophysically important highly stripped He like ions Al^{11 +}, Si^{12 +}, P^{13 +}, S^{14 +} and Cl^{15 +} for the transitions 2s ²: ¹ S ^e, 2p ²: ¹ D ^e, 2snp: ¹ P ⁰, 2snd: ¹ D ^e and 2pnd: ¹F⁰ for n45. The transition energies are obtained from the position of resonances in the oscillations of the two electron charge cloud under an external harmonic perturbation. Linearised version of a suitably constructed variational functional is used for obtaining the response properties of the system. Most of the results are new. Agreement with the only few existing experimental data along this line is very reasonable. Analytic representations of the doubly excited states are obtained and the Coulomb repulsion integral in these states are estimated for checking the consistency of the wavefunctions. The doubly excited state wavefunctions so obtained may be used for evaluating other physical properties connected with transitions.     

Loosely bound states of three particles

Loosely bound states of three particles for particles interacting via short range forces were predicted by Efimov. They are shown to arise naturally in the adiabatic hyperspherical approximation presently used to compute reactions along hyperspherical coordinates. Because of the loosely bound nature of such states, the asymptotic form of the effective hyper-radial potential is critical. A variational wave function is suggested and is shown to reproduce the asymptotic potenial obtained by Efimov. Implications and extensions of the theory are suggested.     

On the calculation of transition states

An algorithm has been developed to calculate transition state geometries directly in the framework of ab initio single-determinant molecular orbital theory. As an example, the procedure is applied to the rearrangement of ethenylidene to acetylene.     

Time-dependent electrical properties of liquid crystal cells: unravelling the origin of ion generation

An understanding of possible sources of ion generation in liquid crystal materials is of utmost importance to ensure uncompromised performance of modern liquid crystal devices. In this paper, time-dependent electrical properties of filled liquid crystal cells are used to reveal important information about often overlooked source of ion generation in liquid crystals. This source of ions originates from the ionic contamination of substrates of the liquid crystal cell. Ionic contaminants can be inherently present in the alignment layers or can be induced by external factors such as mechanical rubbing or irradiation with light. The model of this ion generation process is presented and tested using existing experimental data.     

On the calculation of transition moments between states described in different orbital basis

The organization of a computer code to compute transition moments between states described in different orbital basis sets (a nonorthogonal transition moment) is described. The code is organized to minimize redundant work and allow efficient threshold checking. Three sample calculations are presented.     

Intruder states in multireference perturbation theory: the ground state of manganese dimer

A detailed analysis of a severe intruder state problem in the multistate multireference perturbation theory (MS-MRPT) calculations on the ground state of manganese dimer is presented. An enormous number of detected intruder states (> 5000) do not permit finding even an approximate shape of the X(1)Sigma(g) (+) potential energy curve. The intruder states are explicitly demonstrated to originate from quasidegeneracies in the zeroth-order Hamiltonian spectrum. The electronic configurations responsible for appearance of the quasidegeneracies are identified as single and double excitations from the active orbitals to the external orbitals. It is shown that the quasidegeneracy problem can be completely eliminated using shift techniques despite of its severity. The resultant curves are smooth and continuous. Unfortunately, strong dependence of the spectroscopic parameters of the X(1)Sigma(g) (+) state on the shift parameter is observed. This finding rises serious controversies regarding validity of employing shift techniques for solving the intruder state problem in MS-MRPT. Various alternative approaches of removing intruder states (e.g., modification of the basis set or changing the active space) are tested. None of these conventional techniques is able to fully avoid the quasidegeneracies. We believe that the MS-MRPT calculations on the three lowest A(g) states of manganese dimer constitute a perfect benchmark case for studying the behavior of MRPT in extreme situations.     

Accurate calculation of the bound states of Hellmann potential

Bound states of the Hellmann potential, which is a superposition of the attractive Coulomb (?A/r) and the Yukawa (Be ^?Cr /r) potential, are calculated by using a generalized pseudospectral method. Energy eigenvalues accurate up to 13–14 significant figures, and densities are obtained through a nonuniform, optimal spatial discretization of the radial Schrödinger equation. Both ground and excited states are reported for arbitrary values of the potential parameters covering a wide range of interaction. Calculations have been made for higher states as well as for stronger couplings. Some new states are reported here for the first time, which could be useful for future works. The present results are significantly improved in accuracy over all other existing literature values and offers a simple, accurate and efficient scheme for these and other singular potentials in quantum mechanics.     

Foundations of the relativistic theory of many-electron bound states

Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac–Coulomb Hamiltonian H_DC. However, because the electron–electron interaction mixes positive- and negative-energy states, the operator H_DC has no normalizable eigenfunctions. This fact undermines the quantum-theoretic rationale for the Dirac–Hartree–Fock (DHF ) equations and therefore that of the relativistic configuration-interaction (RCI ) and multiconfiguration Dirac–Fock (MCDF ) methods. An approach to this problem based on quantum electrodynamics is reviewed. It leads to a configuration-space Hamilton H which involves positive-energy projection operators dependent on an external potential U; identification of U with the nuclear potential V_ext corresponds to use of the Furry bound-state interaction picture. It is shown that the RCI method can be reinterpreted as an approximation scheme for finding eigenvalues of a Hamiltonian H, with U identified as the DHF potential; the theoretical interpretation of the MCDF method needs further clarification. It is emphasized that if U differs from V_ext one must consider the effects of virtual-pair creation by the difference potential δU = V_ext ? U; an approximate formula for the level-shift arising from δU is derived. Some ideas for dealing with the technical problems introduced by the projection operators are discussed and relativistic virial theorems are given. Finally, a possible scheme for adapting current MCDF methods to Hamiltonians involving projection operators is described.