Semiclassical wave packet study of ozone forming reaction

We have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to J=50 were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the time-independent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony's method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and 2 cm(-1) for under-the-barrier and over-the-barrier states, respectively. The SWP lifetimes in the range of 0.5相似文献   

Direct calculation of resonant states in reactive scattering. Application to linear triatomic systems

A direct method for calculating resonant states in reactive scattering is suggested, permitting us to obtain the characteristics of multichannel resonances (partial width amplitudes). The method is based on the construction of a Laurent expansion of the scattering matrix S(? ?iΓ/2) in the complex plane. The position of the poles of the S matrix are derived by solving the dynamical problem with complex energy values. The residue at the pole gives all the information concerning the partial widths. The method is applied to a linear triatomic reactive scattering problem. The properties of the resonant states in the H + H₂ system are calculated as an example. Two broad resonances are found which have not been reported in previous calculations. The interference of overlapping resonances is shown to have a profound effect on the energy dependence of the transition probabilities.     

On the role of scattering resonances in the F+HD reaction dynamics

We study scattering resonances in the F+HD-->HF+D reaction using a new method for direct evaluation of the lifetime Q-matrix [Aquilanti et al., J. Chem. Phys. 2005, 123, 054314]. We show that most of the resonances are due to van der Waals states in the entrance and exit reaction channels. The metastable states observed in the product reaction channel are assigned by calculating the energy levels and wave functions of the HF...D van der Waals complex. The behavior of resonance energies, widths, and decay branching ratios as functions of total angular momentum is analyzed. The effect of isotopic substitution on resonance energies and lifetimes is elucidated by comparison with previous results for the F+H2 reaction. It is demonstrated that HF(v'=3) products near threshold are formed by decay of the narrow resonances supported by van der Waals wells in the exit channel. State-to-state differential cross sections in the HF(v'=3) channel exhibit characteristic forward-backward peaks due to the formation of a long-lived metastable complex. The role of the exit-channel resonances in the interpretation of molecular beam experiments is discussed.     

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     

Vibrational predissociation dynamics of Cl2(B)-He2: a wave packet study

The vibrational predissociation of Cl(2)(B)-He(2) has been studied using a full dimensional wave packet method. The aim is to investigate the effect of increasing the grid size in the dissociative coordinates and the propagation time, on the convergence of observable magnitudes like predissociation lifetimes and Cl(2) product vibrational and rotational distributions. In particular, convergence of vibrational distributions is significantly affected by an artifact caused by the use of finite grids and absorbing conditions for the wave packet, combined with the presence of a sequential dissociation process. The results show that the lifetimes and the Cl(2)(B) rotational distributions are not greatly affected by increasing propagation time and grid size. However, convergence of the Cl(2) vibrational distribution is very slow, and the strategy of converging this property by increasing the grid size becomes impractical. An approximate model to estimate the Cl(2) vibrational populations is suggested, which is found to provide realistic distributions as compared with the available experimental ones. The main feature of the model is that its assumptions are closely based on the nature of the vibrational predissociation process occurring in the type of complexes. This feature of the model, in addition to its simplicity of implementation and negligible extra computational cost, contributes to the general applicability of the approach to BC(B)-Rg(2) complexes.     

Role of resonances in building collision cross-sections: Mittag-Leffler-based study

The method of complex dilation is used to define the partial wave S-matrix in the sector of the fourth quadrant of the complex energy plane. Two ways of obtaining the expansion coefficients—the partial wave S-matrix residues—are studied. The Mittag-Leffler decomposition of the partial wave S-matrix as a sum of residue terms and an integral contribution is used to define the contributions of a number of the partial wave S-matrix poles, related to a 1-D potential, to the corresponding S-wave cross-section. The obtained expansion demonstrates a way of describing the contribution from a single pole to the partial wave S-matrix and thereby to various types of cross-sections. Our model study shows how peaks in a cross-section not only can be attributed to so-called isolated resonances but also to a set of overlapping barrier-type resonances. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Indirect coupling to quadrupolar nuclei: observation of 1J(105Pd,31P) in one- and two-dimensional 31P CP/MAS spectra

High-resolution solid-state 31P cross-polarization magic angle spinning (CP/MAS) spectra of a series of Pd(II) complexes were obtained. All of these spectra exhibit low-intensity satellite peaks flanking the main resonances which are assigned to originate from a combination of direct (D) and indirect (J) spin-spin coupling between the 31P and the 105Pd spins. The parameter 1J(105Pd,31P) is found to be sensitive to the nature of the ligand in a trans position and thus of great value in assigning the configuration, i.e. cis or trans, in square-planar complexes of Pd(II). A linear relationship between 1J(105Pd,31P) and 1J(195Pt,31P) in analogous Pd(II) and Pt(II) complexes is suggested, the latter parameter being a factor of ca 14 larger. Two-dimensional exchange spectroscopy proved valuable in resolving overlapping resonances and relating pairs of inequivalent 31P spins within the same complex and spreading their satellite manifolds into two dimensions. These two spectral features are unrelated, being due to dipolar coupling among the phosphorus spins in the former and finite lifetimes of the spin states of the 105Pd isotope in the latter case.     

Roughness induced surface acoustic resonances

The vibrational and electronic spectra of a semi-infinite crystal with a planar surface is modified in presence of surface inhomogeneities or roughness such as ridges or grooves, quantum wires or tips… Using a Green's function formalism, we present an exact numerical method for obtaining the variation of the density of states associated with the adsorption of a ridge on a flat surface or with a groove cut into an otherwise planar surface. This general method is applied to the determination of the acoustic resonances of shear horizontal polarization associated with such deterministic surface protuberances or indentations. The positions and widths of the peaks in the total or local densities of states give the frequencies and lifetimes of the resonances, which may be more or less pronounced features depending on the relative parameters of the substrate and ridge materials. We also investigate the modifications of these acoustic surface shape resonances due to the interaction between two such defects. This calculation can also be transposed to the study of electronic structure of a wire near a flat surface, in the framework of an effective mass model.     

A full-dimensional quantum dynamical approach to the vibrational predissociation of Cl2-He2

A full-dimensional, fully coupled wave packet method is proposed and applied to investigate the vibrational predissociation dynamics of the Cl2(B,v')-He2 complex. Simulations are carried out for the resonance states associated with the v'=10-13 initial vibrational excitations of Cl2, and the results are compared with the available experimental data. A good agreement with experiment is achieved for the resonance lifetimes (typically within experimental error) and the Cl(2) fragment rotational distributions. The mechanism of dissociation of the two He atoms is found to be dominantly sequential, through the Deltav'= -2 channel. The probabilities obtained for the Deltav'= -1 dissociation channel are, however, overestimated due to the use of absorbing boundary conditions combined with finite grid effects. It is suggested that a mechanism of energy redistribution through the couplings between the van der Waals modes of the two weak bonds takes place in the Deltav'= -1 dissociation. This mechanism is consistent with the resonance lifetimes and Cl2 rotational distributions predicted. The favorable comparison with most of the experimental data supports the reliability of the potential used to model Cl2(B,v')-He2, at least in the present range of v' levels.     

Shape resonances as poles of the semiclassical Green's function obtained from path-integral theory: application to the autodissociation of the He2++ 1sigma(g)+ state

It is known that one-dimensional potentials, V(R), with a local minimum and a finite barrier towards tunneling to a free particle continuum, can support a finite number of shape resonance states. Recently, we reported a formal derivation of the semiclassical Green's function, G(SC)(E), for such V(R), with one and two local minima, which was carried out in the framework of the theory of path integrals [Th. G. Douvropoulos and C. A. Nicolaides, J. Phys. B 35, 4453 (2002); J. Chem. Phys. 119, 8235 (2003)]. The complex poles of G(SC)(E) represent the energies and the tunneling rates of the unstable states of V(R). By analyzing the structure of G(SC)(E), here it is shown how one can compute the energy, E(nu), and the radiation-less width, gamma(nu), of each resonance state beyond the Wentzel-Kramers-Brillouin approximation. In addition, the energy shift, delta(nu), due to the interaction with the continuum, is given explicitly and computed numerically. The dependence of the accuracy of the semiclassical calculation of E(nu) and of gamma(nu) on the distance from the top of the barrier is demonstrated explicitly. As an application to a real system, we computed the vibrational energies, E(nu), and the lifetimes, tau(nu), of the 4He2++, nu = 0, 1, 2, 3, 4, and 4He3He++ nu = 0, 1, 2, 3, 1sigma(g)+ states, which autodissociate to the He(+)+He+ continuum. We employed the V(R) that was computed by Wolniewicz [J. Phys. B 32, 2257 (1999)], which was reported as being accurate, over a large range of values of R, to a fraction of cm(-1). For example, for J = 0, the results for the lowest and highest vibrational levels for the 4He2+ 1sigma(g)+ state are nu = 0 level, E0 = 10,309 cm(-1) below the barrier top, tau0 = 6400 s; nu = 4 level, E4 = 96.6 cm(-1) below the barrier top, tau4 = 31 x 10(-11) s. A brief presentation is also given of the quantal methods (and their results) that were applied previously for these shape resonances, such as the amplitude, the exterior complex scaling, and the lifetime matrix methods.     

Excitation pulse deconvolution in luminescence lifetime analysis for oxygen measurements in vivo

Oxygen-dependent quenching of phosphorescence has been proven to be a valuable tool for the measurement of oxygen concentrations both in vitro and in vivo. For biological measurements the relatively long lifetimes of phosphorescence have promoted time-domain-based devices using xenon arc flashlamps as the most common excitation light source. The resulting complex form of the excitation pulse leads to complications in the analysis of phosphorescence lifetimes and ultimately to errors in the recovered pO2 values. Although the problem has been recognized, the consequences on in vivo phosphorescence lifetime measurements have been neglected so far. In this study, the consequences of finite excitation flash duration are analyzed using computer simulations, and a method for the recovery of phosphorescence decay times from complex photometric signals is presented. The analysis provides an explanation as to why different calibration constants are reported in the literature and presents a unified explanation whereby calibration constants are not solely a property of the dye but also of the measuring device. It is concluded that complex excitation pulse patterns without appropriate analysis methods lead to device-specific calibration constants and nonlinearity and can be a potent source of errors when applied in vivo. The method of analysis presented in this article allows reliable phosphorescence lifetime measurements to be made for oxygen pressure measurements and can easily be applied to existing phosphorimeters.     

Determination of the local structure and parameters of the one-electron potential from XANES data (inverse problem of XANES theory)

A method of obtaining complex information on the structure of polyatomic systems using experimental data for one-electron quasistationary state (shape resonance) is developed. The method involves the equation for S-matrix poles in the muffintin (MT) approximation. The parameters of the model (intemuclear distances, valence angles, and potential characteristics) are fitted in such a way that the S-matrix poles in a complex energy plane be maximally close to {E-iГ/2}, where E and Fare the energies and widths of the XANES maxima of one-electron origin. Testing the method on a number of objects shows that it determines internuclear distances with an accuracy of 1% and valence angles with an accuracy of 3%. Among the potentials of this type, the empirical potentials obtained are the best for describing shape resonances. The suggested scheme is applicable in determining the microstructure and in the cases where the diffraction methods of structural analysis do not work (unordered systems, molecular adsorption on the surface of solids, etc.). Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 6, pp. 1013–1017, November–December, 1998.     

Resonances in three-dimensional H + HLi scattering: a time-dependent wave packet dynamical study

This paper examines the resonances in H + HLi scattering. The signature of these resonances is obtained from the oscillations in its reaction probability versus energy curves. They are identified here from a set of pseudospectra calculated for different initial locations of a stationary Gaussian wave packet on the ab initio potential energy surface (PES) reported by Dunne, Murrel, and Jemmer. The nuclear motion on this PES is monitored with the aid of a time-dependent wave packet method and the pseudospectrum are calculated by Fourier transforming the time autocorrelation function of the initial wave packet. The resonances are further examined and assigned by computing their eigenfunctions through spectral quantization algorithm. Both the linewidth as well as decay lifetimes of the resonances are reported.     

Stark and field-born resonances of an open square well in a static external electric field

The resonance positions, widths (inverse lifetimes), and wave functions of a square-potential well in the presence of a static electric field are calculated by using the outgoing boundary conditions. Our study concentrates on the field-born states that, unlike the well-known Stark resonances, are not associated with the field-free bound states. The effect of a lower cutoff of the static field on the field-born resonance phenomena is studied. The feasibility of experiments, where the isolated long-lived and overlapping short-lived field-born resonances can be explored, is discussed.     

Interacting resonances in the F+H2 reaction revisited: complex terms, Riemann surfaces, and angular distributions

We study the effect of overlapping resonances on the angular distributions of the reaction F+H2(v=0,j=0)-->HF(v=2,j=0)+H in the collision energy range from 5 to 65 meV, i.e., under the reaction barrier. Reactive scattering calculations were performed using the hyperquantization algorithm on the potential energy surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. The positions of the Regge and complex energy poles are obtained by Pade reconstruction of the scattering matrix element. The Sturmian theory is invoked to relate the Regge and complex energy terms. For two interacting resonances, a two-sheet Riemann surface is contracted and inverted. The semiclassical complex angular momentum analysis is used to decompose the scattering amplitude into the direct and resonance contributions.     

Quantum dynamics of Ne-Br2 vibrational predissociation: the role of continuum resonances as doorway states

Wave-packet simulations of the Ne-Br2(B,upsilon') vibrational predissociation dynamics in the range upsilon' = 16-29 are reported. The aim is to interpret recent time-dependent pump-probe experiments [Cabrera et al., J. Chem. Phys. 123, 054311 (2005)]. Good agreement is found between the calculated and the experimental lifetimes corresponding to decay of the Ne-Br2(B,upsilon') initial state and to appearance of Br2(B,upsilon相似文献   

A quantum wave packet dynamical study of the electronic and spin-orbit coupling effects on the resonances in Cl(2P) + H2 scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.     

Efficient numerical method for locating Feshbach resonances of ultracold molecules in external fields

Collision properties of atoms and molecules in low temperature gases can be controlled by applying an external magnetic or electric field. The external field shifts the energy levels of the colliding particles, which gives rise to Feshbach resonances modifying the scattering cross sections. The resonances occur at particular magnitudes of the external field, where a bound state of the collision complex is degenerate with a scattering state. The positions of the resonances in the external field are usually identified by computing either the scattering cross sections or the bound states of the collision complex as functions of the external field magnitude. We propose a more efficient method for locating Feshbach resonances that requires neither of these computations. In particular, we show that the positions of Feshbach resonances can be identified by computing the log-derivative of the total wave function in a classically allowed region as a function of the external field strength. This procedure is particularly useful for locating narrow Feshbach resonances that may be hard to identify with the other methods.     

Concentrated solution viscosities of polymeric associates

Reasons have been advanced why in some cases concentrated-polymer-solution viscosity measurements are not a suitable method for determining the degree of association of groups attached to polymer chains. These are based on the finite lifetimes of associates compared with the finite lifetimes of the entanglements, which are the major contributors to concentrated-polymer-solution viscosities. The validity of these reasons has been checked in a system where the degree of association of polymer chains can be measured spectroscopically. It was found that the viscosity of these solutions was considerably less than that calculated by the concentrated-solution viscosity equation for solutions of polymers of the average molecular weight expected from the spectroscopically found degree of association.     

The general concept of signal–noise separation (SNS): mathematical aspects and implementation in magnetic resonance spectroscopy

Magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI) are increasingly recognized as potentially key modalities in cancer diagnostics. It is, therefore, urgent to overcome the shortcomings of current applications of MRS and MRSI. We explain and substantiate why more advanced signal processing methods are needed, and demonstrate that the fast Padé transform (FPT), as the quotient of two polynomials, is the signal processing method of choice to achieve this goal. In this paper, the focus is upon distinguishing genuine from spurious (noisy and noise-like) resonances; this has been one of the thorniest challenges to MRS. The number of spurious resonances is always several times larger than the true ones. Within the FPT convergence is achieved through stabilization or constancy of the reconstructed frequencies and amplitudes. This stabilization is a veritable signature of the exact number of resonances. With any further increase of the partial signal length N, towards the full signal length N, i.e., passing the stage at which full convergence has been reached, it is found that all the fundamental frequencies and amplitudes “stay put”, i.e., they still remain constant. Moreover, machine accuracy is achieved here, proving that when the FPT is nearing convergence, it approaches straight towards the exact result with an exponential convergence rate (the spectral convergence). This proves that the FPT is an exponentially accurate representation of functions customarily encountered in spectral analysis in MRS and beyond. The mechanism by which this is achieved, i.e., the mechanism which secures the maintenance of stability of all the spectral parameters and, by implication, constancy of the estimate for the true number of resonances is provided by the so-called pole-zero cancellation, or equivalently, the Froissart doublets. This signifies that all the additional poles and zeros of the Padé spectrum will cancel each other, a remarkable feature unique to the FPT. The FPT is safe-guarded against contamination of the final results by extraneous resonances, since each pole due to spurious resonances stemming from the denominator polynomial will automatically coincide with the corresponding zero of the numerator polynomial, thus leading to the pole-zero cancellation in the polynomial quotient of the FPT. Such pole-zero cancellations can be advantageously exploited to differentiate between spurious and genuine content of the signal. Since these unphysical poles and zeros always appear as pairs in the FPT, they are viewed as doublets. Therefore, the pole-zero cancellation can be used to disentangle noise as an unphysical burden from the physical content in the considered signal, and this is the most important usage of the Froissart doublets in MRS. The general concept of signal–noise separation (SNS) is thereby introduced as a reliable procedure for separating physical from non-physical information in MRS, MRSI and beyond.