Reactive scattering using the multiconfiguration time-dependent Hartree approximation: General aspects and application to the collinear H+H2→H2+H reaction

Jäckle, A.; Meyer, Hans‐Dieter

doi:10.1063/1.469292

Cited by 61 publications

(53 citation statements)

References 29 publications

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“…͑3͒ can be a problem. Elaborate schemes have been designed by Jäckle and Meyer 16,17 to construct optimal expansion series for given potentials. However, the large number of expansion terms required can considerably reduce the numerical efficiency of the MCTDH approach.…”

Section: An Analysis Of the Tddvrmentioning

confidence: 99%

A time-dependent discrete variable representation for (multiconfiguration) Hartree methods

Manthe

1996

The Journal of Chemical Physics

176

104

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A time-dependent discrete variable representation for evaluation of potential energy matrix elements in Hartree and multiconfiguration Hartree approaches is presented. In contrast to other time-dependent discrete variable representations, the scheme presented treats separable parts of the potential exactly and not by quadrature. Thus, accurate results can be obtained even for very small sizes of the time-dependent grid. Time-dependent Hartree and multiconfiguration Hartree calculations for the photodissociation of NOCl after S 0 →S 1 -excitation demonstrate the accuracy of this discrete variable representation.

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Section: An Analysis Of the Tddvrmentioning

confidence: 99%

A time-dependent discrete variable representation for (multiconfiguration) Hartree methods

Manthe

1996

The Journal of Chemical Physics

176

104

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“…Rotational excitation via molecule/surface scattering has been investigated for the systems H 2 /LiF [25] and N 2 /LiF [26], dissociation was studied for a H 2 /metal system [27] and for CH 4 /Ni [28], and photodissociation has been analyzed for CH 3 I/MgO [29,30]. MCTDH has also been used to study the hydrogen exchange reaction H + H 2 → H 2 + H [31] and to explore the absorption spectrum of pyrazine [32]. The latter work is particularly remarkable because there it was possible to accurately account for the motion of 14 vibrational modes on two coupled electronic potential energy surfaces.…”

Section: Introductionmentioning

confidence: 99%

An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method

Beck¹,

Meyer²

1997

Z Phys D - Atoms, Molecules and Clusters

175

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An efficient and robust integration scheme tailored to the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method is presented. An error estimation allows the automatical adjustment of the step size and hence controls the integration error. The integration scheme decouples the MCTDH equations of motion into several disjoined subsystems, of which one determines the time evolution of the MCTDH-coefficients. While the conventional MCTDH equations are non-linear, the working equation for the MCTDH-coefficients becomes linear in the present integration scheme. To investigate the integrator's performance it is applied to the photodissociation process of methyl iodide. The results of the novel integration scheme are in perfect agreement to those obtained by solving the MCTDH working equations conventionally. The computation time, however, is reduced by a factor of about ten when the new integration scheme is used to propagate large systems. PACS: 02.70.Ns, 31.70.Hq I IntroductionThe time-dependent quantum mechanical treatment of molecular dynamics, which numerically solves the time-dependent Schrödinger equation, has gained rapidly increasing interest and importance during the last fifteen years. Although for time-independent Hamiltonians this approach is formally equivalent to solving the time-independent Schrödinger equation, it offers a number of advantages. While in the timeindependent framework one has to solve an eigenvalue problem, one is faced in the time-dependent picture with an initial value problem, which is mathematically simpler. Moreover, time-dependent methods can handle systems that involve continuum states (e. g. chemical reactions or photodissociation processes) very easily. Employing a time-independent procedure in this case, the wave function becomes a continuum function subject to complicated scattering boundary conditions. In contrast, turning to a time-dependent treatment the wave function remains square integrable, and there is virtually no difference between propagating a wave-packet that is a superposition of bound or of continuum states. Besides these rather technical advantages, time-dependent schemes offer a deeper insight into the dynamics, and hence lead to a better understanding of the physical process under investigation. Finally, if the Hamiltonian is itself time-dependent, one must of course adopt the time-dependent framework.Apart from the development of the computational facilities there has been a considerable progress over the last fifteen years in improving the algorithms for solving the time-dependent Schrödinger equation numerically exactly. Powerful integrators [1,2] and representation schemes [3][4][5][6] are now available. Nevertheless, a numerically exact quantum mechanical treatment of the wave-packet dynamics is in general restricted to three-or four-dimensional systems due to the exponential increase of numerical effort and main memory with the number of degrees of freedom.To overcome these limitations it is essential to develop approximate s...

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“…In analogy to the product form of the wave function, we can choose to express the individual terms (H m H t ) of the Hamiltonian as a product of one-mode terms (h t m ) for mode m. This leads to a sum-over-product form of the Hamiltonian, 61,62 …”

Section: Theorymentioning

confidence: 99%

Automatic determination of important mode–mode correlations in many-mode vibrational wave functions

König

Christiansen

2015

The Journal of Chemical Physics

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We introduce new automatic procedures for parameterizing vibrational coupled cluster (VCC) and vibrational configuration interaction wave functions. Importance measures for individual mode combinations in the wave function are derived based on upper bounds to Hamiltonian matrix elements and/or the size of perturbative corrections derived in the framework of VCC. With a threshold, this enables an automatic, system-adapted way of choosing which mode-mode correlations are explicitly parameterized in the many-mode wave function. The effect of different importance measures and thresholds is investigated for zero-point energies and infrared spectra for formaldehyde and furan. Furthermore, the direct link between important mode-mode correlations and coordinates is illustrated employing water clusters as examples: Using optimized coordinates, a larger number of mode combinations can be neglected in the correlated many-mode vibrational wave function than with normal coordinates for the same accuracy. Moreover, the fraction of important mode-mode correlations compared to the total number of correlations decreases with system size. This underlines the potential gain in efficiency when using optimized coordinates in combination with a flexible scheme for choosing the mode-mode correlations included in the parameterization of the correlated many-mode vibrational wave function. All in all, it is found that the introduced schemes for parameterizing correlated many-mode vibrational wave functions lead to at least as systematic and accurate calculations as those using more standard and straightforward excitation level definitions. This new way of defining approximate calculations offers potential for future calculations on larger systems.

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Reactive scattering using the multiconfiguration time-dependent Hartree approximation: General aspects and application to the collinear H+H2→H2+H reaction

Cited by 61 publications

References 29 publications

A time-dependent discrete variable representation for (multiconfiguration) Hartree methods

A time-dependent discrete variable representation for (multiconfiguration) Hartree methods

An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method

Automatic determination of important mode–mode correlations in many-mode vibrational wave functions

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