The multiconfigurational time‐dependent Hartree (MCTDH) approximation to the time‐dependent Schrodinger equation is tested for a realistic three‐dimensional example, the photodissociation of NOCl. The working equations of the MCTDH scheme introduced earlier are discussed in some detail. A computational scheme is presented which allows for efficient numerical MCTDH calculations. This scheme is applied to the photodissociation of NOCl after excitation to the S1 surface. The results are compared to the results of an exact wave‐packet dynamics calculation. Fast convergence of the MCTDH results toward the exact one is found as the number of configurations is increased. The computation times of the MCTDH calculations are found to be much shorter than those of the exact calculation. Even MCTDH calculations including sufficiently many configurations for a fully converged (quasiexact) description require over two orders of magnitude less CPU time than an exact calculation. The so‐called ‘‘natural populations’’ tha...

Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl

The time-dependent quantum wave packet approach has been improved and formulated to treat the multiple surface problems and thus provided a new simple, yet a clear quantum picture for interpreting the reaction mechanism underlying the nonadiabatic dynamical processes. The method keeps the salient feature of the original quantum wave packet theory developed for single surface problems, i.e. the introduction of the absorbing potential and the grid basis including the discrete variable representation and the fast Fourier transformation, which makes the present methodology a very efficient implement for the nonadiabatic quantum scattering calculations. Here, we review the theoretical basis of this approach and its applications to the fundamental triatomic chemical reactions, the latter include the nonadiabatic dynamics calculations on the F + H2, F + HD, F + D2, O(1D) + N2, O(3P, 1D) + H2, D+ + H2, and H+ + D2 reactions. We also present a thorough historical overview of the theoretically nonadiabatic dynamica...

The time-dependent quantum wave packet approach to the electronically nonadiabatic processes in chemical reactions

We show how to extract S matrix elements for reactive scattering from just the real part of an evolving wave packet. A three-term recursion scheme allows the real part of a wave packet to be propagated without reference to its imaginary part, so S matrix elements can be calculated efficiently. Our approach can be applied not only to the usual time-dependent Schrodinger equation, but to a modified form with the Hamiltonian operator Ĥ replaced by f(Ĥ), where f is chosen for convenience. One particular choice for f, a cos−1 mapping, yields the Chebyshev iteration that has proved to be useful in several other recent studies. We show how reactive scattering can be studied by following time-dependent wave packets generated by this mapping. These ideas are illustrated through calculation of collinear H+H2→H2+H and three-dimensional (J=0)D+H2→HD+D reactive scattering probabilities on the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential energy surface.

Quantum dynamics with real wave packets, including application to three-dimensional (J=0) D + H2 → HD + H reactive scattering

The gas temperature in non-equilibrium plasmas is often obtained from the plasma-induced emission by measuring the rotational temperature of a diatomic molecule in its excited state. This is motivated by both tradition and the availability of low budget spectrometers. However, non-thermal plasmas do not automatically guarantee that the rotational distribution in the monitored vibrational level of the diatomic molecule is in equilibrium with the translational (gas) temperature. Often non-Boltzmann rotational molecular spectra are found in non-equilibrium plasmas. The deduction of a gas temperature from these non-thermal distributions must be done with care as clearly the equilibrium between translational and rotational degrees of freedom cannot be achieved. In this contribution different methods and approaches to determine the gas temperature are evaluated and discussed. A detailed analysis of the gas temperature determination from rotational spectra is performed. The physical and chemical background of non-equilibrium rotational population distributions in molecular spectra is discussed and a large range of conditions for which non-equilibrium occurs are identified. Fitting procedures which are used to fit (non-equilibrium) rotational distributions are analyzed in detail. Lastly, recommendations concerning the conditions for which the gas temperatures can be obtained from diatomic spectra are formulated.

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Gas temperature determination from rotational lines in non-equilibrium plasmas: a review

Controlling chemical reactions with light rests on the idea of exciting a vibration that becomes the reaction coordinate in subsequent chemistry. Vibrational excitation techniques such as infrared or stimulated Raman excitation of fundamental vibrations or vibrational overtone excitation of higher levels permit the preferential cleavage of a bond in a photodissociation or bimolecular reaction. The key to bond-selected chemistry is the initial preparation of a suitable vibrational state followed, in the case of bond-selected photodissociation, by electronic excitation or, in the case of bond-selected bimolecular reaction, by collision with a reactive atom. Such experiments demonstrate bond-selected chemistry, permit detailed comparison to theory, and reveal general principles of vibrational state control of chemical reactions.

Bond-Selected Chemistry: Vibrational State Control of Photodissociation and Bimolecular Reaction

The photodissociation of water in the first absorption band, H{sub 2}O(X) + {Dirac_h}{omega} {yields} H{sub 2}O(A{sup 1}B{sub 1}) {yields} H({sup 2}S) + OH({sup 2}II), is a prototype of fast and direct bond rupture in an excited electronic state. It has been investigated from several perspectives-absorption spectrum, final state distributions of the products, dissociation of vibrationally excited states, isotope effects, and emission spectroscopy. The availability of a calculated potential energy surface for the A state, including all three internal degrees of freedom, allows comparison of all experimental data with the results of rigorous quantum mechanical calculations without any fitting parameters or simplifying model assumptions. As the result of the confluence of ab initio electronic structure theory, dynamical theory, and experiment, water is probably the best studied and best understood polyatomic photodissociation system. In this article we review the joint experimental and theoretical advances which make water a unique system for studying molecular dynamics in excited electronic states. We focus our attention especially on the interrelation between the various perspectives and the correlation with the characteristic features of the upper-state potential energy surface. 80 refs., 14 figs.

Photodissociation of water in the first absorption band: A prototype for dissociation on a repulsive potential energy surface

Experimental and theoretical studies of the photodissociation of single vibrational states in HOD provide a qualitative and quantitative understanding of the dissociation dynamics and bond selectivity of this process. Vibrationally mediated photodissociation, in which one photon prepares a vibrational state that a second photon dissociates, can selectively cleave the O–H bond in HOD molecules containing four quanta of O–H stretching excitation. Dissociation of HOD(4νOH) with 266 or 239.5‐nm photons produces OD fragments in at least a 15 fold excess over OH, but photolysis of the same state with 218.5‐nm photons produces comparable amounts of OH and OD. Wave packet propagation calculations on an ab initio potential energy surface reproduce these observations quantitatively. They show that the origin of the selectivity and its energy dependence is the communication of the initial vibrational state with different portions of the outgoing continuum wave function for different photolysis energies.Experimental and theoretical studies of the photodissociation of single vibrational states in HOD provide a qualitative and quantitative understanding of the dissociation dynamics and bond selectivity of this process. Vibrationally mediated photodissociation, in which one photon prepares a vibrational state that a second photon dissociates, can selectively cleave the O–H bond in HOD molecules containing four quanta of O–H stretching excitation. Dissociation of HOD(4νOH) with 266 or 239.5‐nm photons produces OD fragments in at least a 15 fold excess over OH, but photolysis of the same state with 218.5‐nm photons produces comparable amounts of OH and OD. Wave packet propagation calculations on an ab initio potential energy surface reproduce these observations quantitatively. They show that the origin of the selectivity and its energy dependence is the communication of the initial vibrational state with different portions of the outgoing continuum wave function for different photolysis energies.

An experimental and theoretical study of the bond selected photodissociation of HOD

The photodissociation of H2S through excitation in the first absorption band (λ≊195 nm) is investigated by means of extensive ab initio calculations. Employing the MRD‐CI method we calculate the potential energy surfaces for the lowest two electronic states of 1A‘ symmetry varying both HS bond distances as well as the HSH bending angle. (In the C2v point group these states have electronic symmetry 1B1 and 1A2, respectively.) The lower adiabatic potential energy surface is dissociative when one H atom is pulled away whereas the upper one is binding. For the equilibrium angle of 92° in the electronic ground state they have two conical intersections, one occurring near the Franck–Condon point. Because of the very small energy separation between these two states nonadiabatic coupling induced by the kinetic energy operator in the nuclear degrees of freedom are substantial and must be incorporated in order to describe the absorption and subsequent dissociation process in a realistic way. In the present work we ...

Nonadiabatic effects in the photodissociation of H2S in the first absorption band: An ab initio study

We calculated the absorption spectra of H2O and D2O in the second absorption band around 128 nm using a two‐dimensional ab initio potential energy surface for the B(1A1) electronic state. Nonadiabatic coupling to the lower states A and X and the vibrational degree of freedom of the OH fragment are completely neglected. Despite these limitations the agreement with the measured spectra is very satisfactory. The overall shape, the width, and the energetical position of the maximum are well described. Most important, however, is the reproduction of the diffuse vibrational structures superimposed on the broad background. It is demonstrated that this structure is not caused by pure bending‐excitation in the B state with associated bending quantum numbers ν’2=1,2,3,... as originally assumed. Because the equilibrium HOH bending angle and the equilibrium H–OH distance are very different in the ground and in the excited state, the main part of the spectrum and especially the diffuse structures occur at high ene...

Photodissociation dynamics of water in the second absorption band. II. Ab initio calculation of the absorption spectra for H2O and D2O and dynamical interpretation of ‘‘diffuse vibrational’’ structures

We present the results of a three‐dimensional wave packet study on the photodissociation of ClNO through excitation of the first singlet state S1. The calculations employ an ab initio potential energy surface depending on the Cl–N and N–O bond coordinates and the ClNO bending angle. By expanding the wave packet in terms of the eigenfunctions of the NO rotor, the time‐dependent Schrodinger equation is transformed into a coupled set of 60 two‐dimensional partial differential equations which are solved by discretization on a grid. The wave packet yields the absorption spectrum and all partial dissociation cross sections for producing the NO fragment in a particular vibrational–rotational state (nj). The photodissociation of ClNO via the S1 state is a relatively fast process and the necessary propagation time is on the order of 50 fs. The calculated data agree well with recent experimental results. For the first time, we can directly compare the wavelength dependence of partial photodissociation cross section...

Klaus Weide

Papers

Photodissociation of water in the first absorption band: A prototype for dissociation on a repulsive potential energy surface

An experimental and theoretical study of the bond selected photodissociation of HOD

Nonadiabatic effects in the photodissociation of H2S in the first absorption band: An ab initio study

Photodissociation dynamics of water in the second absorption band. II. Ab initio calculation of the absorption spectra for H2O and D2O and dynamical interpretation of ‘‘diffuse vibrational’’ structures

The direct photodissociation of ClNO(S1): An exact three‐dimensional wave packet analysis