Uwe Manthe

The multi-configurational time-dependent Hartree approach

Abstract A new multi-configurational approach to the time-dependent Schrodinger equation is proposed. This approach leads to working equations which are particularly simple and transparent. It can be used for n degrees of freedom and for any choice of the number of configurations. The new approach is tested on a model of coupled oscillators showing fast convergence towards the exact results as the number of configurations is increased.

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

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...

A multilayer multiconfigurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces

The multiconfigurational time-dependent Hartree (MCTDH) approach facilitates multidimensional quantum dynamics calculations by representing the wavepacket in an optimal set of time-dependent basis functions, called single-particle functions. Choosing these single-particle functions to be themselves multidimensional wavefunctions which are represented using a MCTDH representation, a multilayer MCTDH scheme has been constructed and used for quantum dynamics calculations treating up to 1000 degrees of freedom rigorously [Wang and Thoss, J. Chem. Phys. 199, 1289 (2003)]. The present work gives a practical scheme which facilitates the application of the multilayer MCTDH approach, which previously has only been employed to study systems described by model-type Hamiltonians, to molecular systems described by more complicated Hamiltonians and general potential energy surfaces. A multilayer extension of the correlation discrete variable representation (CDVR) scheme employed in MCTDH calculations studying quantum dynamics on general potential energy surfaces is developed and tested in a simple numerical application. The resulting multilayer MCTDH/CDVR approach might offer a perspective to rigorously describe the quantum dynamics of larger polyatomic systems.

Full dimensional quantum calculations of the CH4+H→CH3+H2 reaction rate

Accurate full-dimensional quantum mechanical calculations are reported for the CH4+H→CH3+H2 reaction employing the Jordan–Gilbert potential energy surface. Benchmark results for the thermal rate constant and the cumulative reaction probability are presented and compared to classical transition state theory as well as reduced dimensionality quantum scattering calculations. The importance of quantum effects in this system is highlighted.

Full‐dimensional quantum mechanical calculation of the rate constant for the H2+OH→H2O+H reaction

The cumulative reaction probability (CRP) (the Boltzmann average of which is the thermal rate constant) has been calculated for the reaction H2+OH↔H2O+H in its full (six) dimensionality for total angular momentum J=0. The calculation, which should be the (numerically) exact result for the assumed potential energy surface, was carried out by a direct procedure that avoids having to solve the complete state‐to‐state reactive scattering problem. Higher angular momenta (J≳0) were taken into account approximately to obtain the thermal rate constant k(T) over the range 300<T<700 K; the result is significantly larger than the experimental values (a factor of ∼4 at 300 K), indicating that a more accurate potential energy surface is needed in order to provide a quantitative description of this reaction.

The cumulative reaction probability as eigenvalue problem

It is shown that the cumulative reaction probability for a chemical reaction can be expressed (absolutely rigorously) as N(E)=∑kpk(E), where {pk} are the eigenvalues of a certain Hermitian matrix (or operator). The eigenvalues {pk} all lie between 0 and 1 and thus have the interpretation as probabilities, eigenreaction probabilities which may be thought of as the rigorous generalization of the transmission coefficients for the various states of the activated complex in transition state theory. The eigenreaction probabilities {pk} can be determined by diagonalizing a matrix that is directly available from the Hamiltonian matrix itself. It is also shown how a very efficient iterative method can be used to determine the eigenreaction probabilities for problems that are too large for a direct diagonalization to be possible. The number of iterations required is much smaller than that of previous methods, approximately the number of eigenreaction probabilities that are significantly different from zero. All of ...

Multiconfigurational time‐dependent Hartree study of complex dynamics: Photodissociation of NO2

The multiconfigurational time‐dependent Hartree (MCTDH) approach is applied to an example showing very complex dynamics: the wave‐packet dynamics on the three‐dimensional B2 potential‐energy surface of NO2. The ability of the MCTDH scheme to describe accurately the severe splitting of the wave packet on a saddle‐shaped surface is demonstrated. Internal checks of the MCTDH calculation enable us to assess the degree of convergence without the need to resort to a numerically exact wave‐packet calculation. As a representative observable the photodissociation spectrum is calculated and discussed. The A1/B2 vibronic coupling is neglected in our study, but the dynamics on the diabatic B2 surface is treated in its full three dimensionality.

Time‐dependent photodissociation of methyl iodide with five active modes

Advances in the time propagation of multidimensional wave packets are exploited to present the A‐band photodissociation dynamics of methyl iodide for five active vibrational modes on the three relevant excited ab initio potential surfaces. The five modes considered represent all of the experimentally observed dynamical activity. The only modes neglected are the asymmetric C–H stretch and the asymmetric deformation of the methyl group. The kinetic energy operator corresponding to these five degrees of freedom is derived. The fully quantum mechanical calculation was implemented upon grids using 2880 distinct time‐dependent configurations, determined by the multiconfigurational time‐dependent Hartree algorithm, for each electronic state. All of the currently known experimental results regarding the umbrella vibration, symmetric C–H stretching vibration, perpendicular rotation, and parallel rotation of the photodissociated methyl radical fragment are well reproduced. The full wavelength dependence of all of t...

New method for calculating wave packet dynamics: Strongly coupled surfaces and the adiabatic basis

The nuclear dynamics on potential energy surfaces with a conical intersection is investigated on the basis of exact (numerical) integration of the time‐dependent Schrodinger equation. The ethylene cation is chosen as a typical realistic model system. Complementing earlier work we study the dynamics also in the adiabatic basis, which will be seen to allow for a more profound understanding of the decay and dephasing processes occurring in the system. The computational effort exceeds considerably that of propagation in the diabatic basis, to which previous related studies have been confined. To solve the resulting computational problems we develop and present a special multidimensional adaptation of the finite basis set method utilizing the product structure of the basis. It allows us to calculate propagation in a general potential including three vibrational modes. For the time integration a fourth order differencing scheme is introduced which is faster than the second order differencing‐scheme and predicto...

Quantum mechanical calculations of the rate constant for the H2+OH→H+H2O reaction: Full‐dimensional results and comparison to reduced dimensionality models

The cumulative reaction probability is calculated for the H2+OH→H+H2O reaction in its full (six) dimensionality for total angular momentum J=0. The calculation, which should give the (numerically) exact result for the assumed potential energy surface, yields the cumulative reaction probability directly, without having to solve the complete state‐to‐state reactive scattering problem. Higher angular momenta (J≳0) were taken into account approximately to obtain the thermal rate constant k(T) over the range 300°<T<700°. The result deviates significantly from the experimental rate constant, suggesting that the potential energy surface needs to be improved. A systematic series of reduced dimensionality calculations is carried out in order to characterize the behavior and reliability of these more approximate treatments; a comparison of the full dimensional results with previous reduced dimensionality calculations is also made.