Centre for Modelling, Simulation and Design

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  • Item
    Correlation function approach to transition state resonances in collinear (He,H2+) collisions
    ( 1995-01-01) Mahapatra, Susanta ; Sathyamurthy, N.
    Dynamical resonances in collinear He+H2+ → HeH+ +H reaction on the McLaughlin-Thompson-Joseph-Sathyamurthy potential energy surface are identified in terms of the transition state spectrum I(E), computed by Fourier transforming the autocorrelation function C(t) for the system. Eigenenergies of quasibound states corresponding to the resonances, starting from the nonreactive regime up to the dissociation threshold are reported. The nature of some of the resonance states is investigated by calculating the eigenfunctions for the corresponding eigenenergies and also their lifetimes. The relation to the corresponding resonant periodic orbits in classical mechanics at those energies is also established. In addition we predict several resonances at higher energies not reported in earlier calculations. © 1995 American Institute of Physics.
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    Anomalous vibrational excitation in the small angle scattering of He+ from HCl at Εlab = 20-60 eV
    ( 1995-01-01) Ruhaltinger, T. ; Toennies, J. P. ; Wang, R. G. ; Mahapatra, S. ; NoorBatcha, I. ; Sathyamurthy, N.
    Energy loss spectra of forward scattered He+ ions in collisions with HCl are reported for collision energies (Εlab) in the range 20-60 eV. The spectra extend up to total energy transfers of about 2.5 eV, where the intensity is 6 orders of magnitude less than the elastic forward peak. At large energy transfers a number of broad maxima indicating a propensity for large Δν transitions are observed. Three-dimensional quasiclassical trajectory calculations treating HCl as a rigid rotor for the long range ion-dipole/quadrupole He+-HCl interaction and a short range repulsion corresponding to the isoelectronic He+-Ar account for much of the energy transfer at low ΔΕ. At higher ΔΕ, the rigid rotor model is clearly inadequate and a better description of the experiment requires consideration of high lying repulsive states of HCl+ which appear to be temporarily accessed by charge transfer. © 1995 American Chemical Society.
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    Transition state resonances in collinear (H-, H2) collisions
    ( 1995-07-21) Mahapatra, Susanta ; Sathyamurthy, N. ; Kumar, Sanjay ; Gianturco, F. A.
    The possibility of reactive scattering resonances in collinear (H-, H2) collisions is examined by computing the transition state spectra obtained by Fourier transforming temporal autocorrelation functions for wavepackets placed initially in the transition state region of the ab initio potential energy surface for the system. The nature of the resonances is investigated by computing the corresponding eigenfunctions and their lifetimes. © 1995.
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    Resonances in collinear H- + H2 → H2 + H- reaction: Energy-resolved reaction probabilities by the time-dependent wave packet approach
    ( 1996-01-01) Mahapatra, Susanta ; Sathyamurthy, N.
    We report here the results of a time-dependent quantal calculation for the collinear reaction H- + H2(υ=0) → H2 + H-, which reveals a large number of resonances, in contrast to a relatively smaller number for the neutral analogue, despite the similarities in their potential energy surfaces. © 1996 American Chemical Society.
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    Quantum chaos in collinear (He, H2+) collisions
    ( 1996-01-01) Mahapatra, Susanta ; Ramaswamy, Ramakrishna ; Sathyamurthy, N.
    The quasibound spectrum of the transition state in collinear (He, H2+) collisions is obtained from time-dependent wave packet calculations. Examination of short- and long-range correlations in the eigenvalue spectra through a study of the nearest neighbor spacing distribution, P(s), and the spectral rigidity, Δ3(L), reveals signatures of quantum chaotic behavior. Analysis in the time domain is carried out by computing the survival probability «P(t)» averaged over initial states and Hamiltonian. All these indicators show intermediate behavior between regular and chaotic. A quantitative comparison of «P(t)» with the results of random matrix theory provides an estimate of the fraction of phase space exhibiting chaotic behavior, in reasonable agreement with the classical dynamics. We also analyse the dynamical evolution of coherent Gaussian wave packets located initially in different regions of phase space and compute the survival probability, power spectrum and the volume of phase space over which the wave packet spreads and illustrate the different behaviors. © 1996 American Institute of Physics.
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    Collinear (He,HD+) and (He,DH+) collisions: Transition state resonances and dynamics by time-dependent quantal wave packet approach
    ( 1996-01-01) Mahapatra, S. ; Sathyamurthy, N.
    We examine the possibility of existence of dynamical resonances in collinear (He,HD+) and (He,DH+) collisions by analyzing their respective transition state spectra on the McLaughlin-Thompson-Joseph-Sathyamurthy potential energy surface (PES). The spectra are computed by Fourier transforming the temporal autocorrelation function, C(t), of the initial wave packet. Some of the well resolved resonances are analyzed by computing their eigenfunctions and lifetimes. The vibrational state (v) - selected energy resolved reaction probabilities (PvR(E)) for collinear (He,HD+) and (He,DH+) collisions are also calculated on the same PES by computing the reactive flux in the product channel. The PvR(E) values for HeHD+ show a characteristic staircase-like structure that can be related to threshold resonances. The PvR(E) values for HeDH+ on the other hand, are highly oscillatory, in keeping with the densely packed transition state spectrum. © 1996 American Institute of Physics.
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    Possibility of proton oscillations through the benzene ring
    ( 1996-12-01) Shresth, R. S. ; Manickavasagam, R. ; Mahapatra, S. ; Sathyamurthy, N.
    The possibility of proton oscillations above and below the plane of the benzene ring, through its centroid, in protonated benzene is pointed out, in this communication.
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    Resonances and chaos in the collinear collision system (He,H2+) and its isotopic variants
    ( 1997-01-01) Mahapatra, Susanta ; Sathyamurthy, N. ; Ramaswamy, Ramakrishna
    The collinear atom-diatom collision system provides one of the simplest instances of chaotic or irregular scattering, Classically, irregular scattering is manifest in the sensitive dependence of post-collision variables on initial conditions, and quantally, in the appearance of a dense spectrum of dynamical resonances. We examine the influence of kinematic factors on such dynamical resonances in collinear (He,H2+) collisions by computing the transition state spectra for collinear (He,HD+) and (He,DH+) collisions using the time-dependent quantum mechanical approach. The nearest neighbor spacing distribution P(s) and the spectral rigidity Δ3(L) for these resonances suggest that the dynamics is predominantly irregular for collinear (He,HD+) and predominantly regular for collinear (He,DH+). These findings are reinforced by a significantly larger "correlation hole" in ensemble averaged survival probability 〈〈P(t)〉〉 value for collinear (He,HD+) than for collinear (He,DH+). In addition we have also examined masurement of classical chaos through the dependence of the final vibrational action, nf, on the initial vibrational phase φi of the diatom, and Poincaré surfaces-of-section. They show that (He,HD+) collisions are partly chaotic over the entire energy range (0-2.78eV) while (He,DH+) collisions, in contrast, are highly regular at collision energies below the classical threshold for reaction. Above the threshold, the scattering remians regular for initial vibrational states v = 0 and 1 of DH+.
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    Negative imaginary potentials in time-dependent quantum molecular scattering
    ( 1997-03-07) Mahapatra, Susanta ; Sathyamurthy, Narayanasami
    Reflection or wrap around of the wavefunction from the grid edges is often avoided in time-dependent quantum mechanical calculations by using a negative imaginary potential (NIP) near the grid edges. The stability of the various (second-order differencing, split operator, Chebyshev polynomial and short iterative Lanczos) schemes used, in conjunction with the NIP, for time evolution is discussed using collinear (He, H2+) collisions as a test case. It is shown that the difficulties encountered in obtaining converged reaction probability [PR(E)] values at high energies for the system when NIPs are used, are avoided by using a properly chosen damping function externally.
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    Bound states and time-dependent dynamics of the N2H+ molecular ion in its ground electronic state. I. 2D treatment
    ( 1997-08-22) Mahapatra, S. ; Vetter, R. ; Zuhrt, Ch ; Nguyen, H. T. ; Ritschel, T. ; Zülicke, L.
    The ground-state potential energy surface (PES) for linear arrangements of the N2H+ molecular ion is numerically computed by the multireference single- and double-excitation configuration interaction (MRD-CI) technique. An analytical representation of the potential energy function is obtained by fitting a power series in the Simons-Parr-Finlan coordinates to the numerical data. For investigating the intramolecular dynamics we describe the nuclear motion by a Gaussian wave packet located initially in the strong interaction region of the PES. The vibrational eigenvalue spectrum is calculated by Fourier transforming the time autocorrelation function. The spectrum is then analyzed statistically in the light of random matrix theory (RMT) to understand the nature of the intramolecular dynamics. We examine the short-range correlation in the spectrum through the nearest neighbor level spacing distribution P(s) and the long-range correlation through Δ3 and Σ2 statistics. The spectrum in the time domain is analyzed by computing the ensemble averaged survival probability «P(t)«. The above four quantities obtained from the spectrum are compared with the distribution predicted for regular, irregular, and mixed (intermediate) spectra by the RMT. We find the system is of mixed type and the fractional irregularity is 0.7±0.05. In order to reveal a possible correspondence to the classical dynamics, we have carried out the spectral analysis of the dynamical variables for classical trajectories over a wide range of internal energies. In addition the classical dynamics of proton collisions with N2 molecules has also been preliminarily studied on the same PES, in particular the dependence of the final vibrational action nf on the initial vibrational phase φi of N2 and, furthermore, the Poincaré surface-of-section superimposed with the zero-order separatrix; we find a large number of trapped trajectories. © 1997 American Institute of Physics.
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    Resonances in He + H2+→HeH+ + H reaction in three-dimensions: Energy resolved total reaction probabilities by the time-dependent wave packet method
    ( 1997-11-01) Mahapatra, S. ; Sathyamurthy, N.
    Vib-rotational state-selected and energy resolved total reaction probabilities for the title reaction in three dimensions are calculated on the McLaughlin-Thompson-Joseph-Sathyamurthy potential energy surface, by the time-dependent wave packet (WP) method for the total angular momentum J = 0. The probabilities as obtained by the time-energy mapping of the reactive flux of the WP across a dividing surface in the asymptotic product channel reveal a large number of narrow resonances, in agreement with the time-independent quantum mechanical results available in the literature. While initial vibrational excitation of H2+ is shown, in general, to enhance the reaction probability considerably, in agreement with the experimental observations, rotational excitation has only a marginal influence. © 1997 American Institute of Physics.
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    Quantum mechanical study of optical emission spectra of rydberg-excited H3 and its isotopomers
    ( 1998-01-01) Mahapatra, Susanta ; Horst, Köppel
    Optical emission spectra of Rydberg-excited H3, D3, H2D, and D2H, in the range 200–400 nm, are investigated theoretically and compared with the experimental findings of Bruckmeier et al. [Phys. Rev. Lett. 72, 2550 (1994)]. The time-dependent wave packet method combined with the vibronic coupling theory for (E × ε) Jahn-Teller systems is utilized in order to calculate the corresponding Franck-Condon emission profiles from the upper n = 3 electronic state to the degenerate (2p)1E′ ground electronic manifold of those species. We obtain bimodal spectra with two maxima 9600cm−1 apart in good agreement with the experimental result. © 1998 American Physical Society.
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    Ground state potential energy surface, 3D time-dependent intramolecular dynamics and vibrational states of the N 2 H + molecular ion
    ( 1998-03-13) Mahapatra, S. ; Vetter, R. ; Zuhrt, Ch ; Nguyen, H. T. ; Ritschel, Th ; Zülicke, L.
    The 3D intramolecular dynamics of the N2H+ molecular ion in its electronic ground state is reported. A potential energy surface (PES) is numerically calculated by a multireference configuration interaction method. Employing this PES we calculated the bound-state eigenvalue spectrum of the N2H+ ion by applying the three-dimensional time-dependent wavepacket (WP) method for the total angular momentum J=0. The spectrum is obtained by Fourier transforming the time autocorrelation function of single Gaussian wavepackets initially located in the strong interaction region of the PES. We have carried out time-independent variational calculations to confirm the energy eigenvalues resulting from the WP calculations.
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    Spectra and time-dependent dynamics of H3 near the conical intersection in the (2p)1E′ ground electronic manifold
    ( 1998-12-01) Mahapatra, Susanta ; Köppel, Horst
    We report on the spectra and dynamics of H3 near the conical intersection in its (2p)1E′ ground electronic manifold. The time-dependent wave packet approach and the double many-body expansion (DMBE) potential energy surface (PES) are employed for this purpose. We use Jacobi coordinates (R,r,γ) and employ the fast Fourier transform method for R and r, and the discrete variable representation method for γ, in conjunction with the split-operator formalism to describe the evolution of the wave packet (WP) in space and time, respectively. While the main focus of the present work is to explicitly reveal the effects of nonadiabatic coupling between the two sheets of the DMBE PES, companion calculations are also carried out to investigate the dynamics on the uncoupled upper and lower adiabatic sheets, both in two and three dimensions (for total angular momentum J=0). A set of pseudospectra is calculated by Fourier transforming the time autocorrelation function of suitably chosen Gaussian wave packets located initially at the minimum energy point of the seam of conical intersections. The eigenstates thus obtained are assigned by computing their eigenfunctions by spectral quantization. In the coupled states treatment the WP is propagated in the diabatic representation. The time dependence of the adiabatic populations is calculated by using suitable adiabatic projection operators. We find strong effects of nonadiabatic coupling on the discrete vibrational energy levels of the upper adiabatic sheet, which all change to quasibound states in the coupled manifold. The comparison of the decay dynamics of various levels of the upper adiabatic sheet indicates considerable mode specificity (their lifetimes typically vary between 3 and 6 fs). On the other hand, resonances are seen to be less pronounced near the conical intersection on the lower adiabatic sheet (when compared to those in the literature, obtained near the collinear saddle point region). The effect of nonadiabatic coupling on them is only minor. We also report preliminary results on the optical emission spectrum of H3 and compare them with the experimental findings. © 1998 American Institute of Physics.
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    Impact of nonadiabatic coupling between the conically intersecting X̃2A1 and Ã2B2 states of NO2 on the negative ion photoelectron spectra of NO-2
    ( 1999-03-22) Mahapatra, S. ; Köppel, H. ; Cederbaum, L. S.
    Negative ion photoelectron spectra of NO-2 at 266 nm (4.660 eV) and 351 nm (3.532 eV) are theoretically calculated and compared with earlier experimental findings. A diabatic model Hamiltonian with linear vibronic coupling between the conically intersecting X̃2A1 and Ã2B2 states of NO2 is employed for this purpose. While the linear vibronic coupling model successfully reproduces the low resolution experimental photoelectron spectrum at 266 nm, second order coupling terms are necessary for the high resolution spectrum at 351 nm. The vibronic structure of the X̃2A1 state of NO2 in the photoelectron spectrum is found to be almost unaffected by the nonadiabatic coupling, whereas, the latter has a strong impact on the vibronic structure of the Ã2B2 state. The magnitude of the vibronic coupling constant, which has otherwise been overestimated by earlier theoretical studies, is calculated ab initio and its limits of validity are confirmed by the results from different ab initio calculations. © 1999 American Institute of Physics.
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    Semiclassical approach to the Rydberg emission spectra of H3 and its isotopomers
    ( 1999-06-18) Mahapatra, S. ; Köppel, H.
    We investigate the optical emission spectra of Rydberg-excited H3 and its isotopomers semiclassically in the framework of the reflection principle. The semiclassical spectra are also obtained with the approximation of a locally linear potential energy surface where the contribution from the breathing and the Jahn-Teller (JT) active modes are separable. While the JT mode brings out the energy splitting in the bimodal emission profiles, the breathing mode smears out their overall structure. Despite some severe limitations of the semiclassical results, the energy splitting is reproduced well. This enables us to establish a simple kinematic scaling of this quantity for different isotopomers. © 1999 Elsevier Science B.V. All rights reserved.
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    Theoretical investigation of Jahn-Teller and pseudo-Jahn-Teller coupling effects on the photoelectron spectrum of allene
    ( 1999-12-15) Mahapatra, S. ; Cederbaum, L. S. ; Köppel, H.
    The valence photoelectron spectrum of allene (C3H4) pertinent to the Ã2E/B̃2B2 interacting electronic manifold of the corresponding cation (C3H+4) is theoretically calculated and compared with the most recent high resolution He I excited experimental recording of Baltzer et al.[Chem. Phys. 196, 551 (1995)]. A model diabatic Hamiltonian within the linear vibronic coupling scheme and ab initio calculated coupling parameters are employed in our investigations. While the resolved vibrational progressions in the photoelectron band at low energies can be attributed to the E⊗B Jahn-Teller activity within the Ã2E electronic manifold, the diffuse structure in the photoelectron band at high energies is found to emerge from the mixing of the Ã2E electronic manifold with the B̃2B2 electronic state via degenerate vibrational modes. The latter demonstrates the importance of the pseudo-Jahn-Teller type of interactions in the photoelectron spectrum of allene. © 1999 American Institute of Physics.
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    Femtosecond wavepacket dynamics on strongly coupled potential energy surfaces
    ( 2000-01-01) Köppel, H. ; Döscher, M. ; Mahapatra, S.
    An overview is given of various results of ab initio quantum dynamical simulations on conically intersecting potential energy surfaces. Here, the nonadiabatic coupling effects are typically very strong, leading to a femtosecond (fs) population decay of the upper electronic state and to a diffuse appearance of the corresponding band in the electronic spectrum. For the lower electronic state we demonstrate the possibility of a bifurcation of the wavepacket that can lead to a manifestation of the geometric phase. The examples chosen to illustrate these phenomena are triatomic hydrogen, sulfur dioxide, and the radical cation of benzene. The latter systems features a complex `web' of different multidimensional, partly coalescing, conical intersections between up to eight potential energy surfaces. The resulting stepwise femtosecond decay processes give rise to a highly complex vibronic dynamics that is currently being modeled to an increasing degree of sophistication.
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    State specific dynamics of the H- + H2 → H2 + H- reaction: Energy resolved total reaction probabilities by the time-dependent wave packet method
    ( 2000-02-15) Mahapatra, Susanta
    Reagent ro-vibrational state-selected and energy resolved total reaction probabilities of the title reaction are calculated on the diatomics-in- molecules potential energy surface of Belyaev et al. (Chem. Phys., 1997, 220, 43). A three dimensional time-dependent wave packet (WP) method for the total angular momentum J = 0 is employed for the purpose. The reaction probabilities are obtained by the time-energy mapping of the reactive flux of the WP across a dividing surface in the asymptotic product channel. While the initial vibrational excitation of reagent H2 is shown, in general, to decrease the reaction probability at low and moderate energies, the initial rotational excitation does not lead to any such general trend. Existence of resonances is indicated in the reaction with ro-vibrationally hot H2 molecules. The energetic threshold and other dynamical features of the reaction are in accord with the experimental findings.
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    Time-dependent quantum mechanical investigation of dynamical resonances in three-dimensional HeH2+ and HeHD+ systems
    ( 2000-07-01) Maiti, B. ; Mahapatra, S. ; Sathyamurthy, N.
    An account is given on the bound and quasibound states of three dimensional HeH2+ and HeHD+ systems computed using a time-dependent quantum mechanical wave packet approach for J = O. It is shown that there is only one bound state for HeH2+, but two sets of bound states for HeHD+.