Multiconfiguration time-dependent Hartree (MCTDH) study on rotational and diffractive inelastic molecule-surface scattering

Ehara, Masahiro; Meyer, Hans‐Dieter; Cederbaum, Lorenz S.

doi:10.1063/1.472616

Cited by 64 publications

(45 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The cost to determine the time-derivative (27) of the MCTDH-coefficients scales with sf n f +1 . Note, however, that the right hand side of (27) is evaluated in almost the same way as the mean-field matrix elements H (κ) rjl , (26), which allows the computation of iȦ as a by-product of the calculation of the mean-field matrices with only little additional cost.…”

Section: Computational Effortmentioning

confidence: 99%

“…III.B. An integration step in this simplified variant begins with the initial values A(t 0 ) and ϕ (κ) (t 0 ) being employed to determine the A-Hamiltonian matrix K(t 0 ) (27), the regularized density matrices ρ (κ) (t 0 ) (10) and (22), and the mean-field matrices H (κ) r (t 0 ) (26). With these matrices kept constant, the wave function is then propagated from t 0 to t 1 = t 0 + τ .…”

Section: A the Basic Ideasmentioning

confidence: 99%

“…Molecule surface scattering is another field of interest. 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].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

177

View full text Add to dashboard Cite

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...

show abstract

Section: Computational Effortmentioning

confidence: 99%

Section: A the Basic Ideasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

177

View full text Add to dashboard Cite

show abstract

“…The equations of motion which describe the expansion coefficients A j1..jf (t) and c jl (t) of both layers can be obtained from the Dirac-Frenkel variational principle. It should be noted that extensions which can further increase the efficiency of the original MCTDH approach utilize the combination of several physical coordinates in a single "logical" coordinate (mode combination MCTDH [91,92]) and employ more than two layers in the wavefunction representation (multi-layer MCTDH [93][94][95]). …”

Section: Efficient Numerical Techniquesmentioning

confidence: 99%

Accurate calculations of reaction rates: predictive theory based on a rigorous quantum transition state concept

Manthe

2011

Molecular Physics

View full text Add to dashboard Cite

“…[39,40] This method has been applied successfully to gas phase reactions and reactions at surfaces. [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] In this paper we report wavepacket simulations of CD 4 scattering including all internal vibrations for fixed orientations, performed on the same model PESs as in our previous paper. [38] Translational motion parallel to the surface and all rotational motion was neglected.…”

Section: Introductionmentioning

confidence: 99%

Energy distribution analysis of the wavepacket simulations of CH4 and CD4 scattering

Jansen

2000

Surface Science

View full text Add to dashboard Cite

The isotope effect in the scattering of methane is studied by wavepacket simulations of oriented CH 4 and CD 4 molecules from a flat surface including all nine internal vibrations. At a translational energy up to 96 kJ/mol we find that the scattering is still predominantly elastic, but less so for CD 4 . Energy distribution analysis of the kinetic energy per mode and the potential energy surface terms, when the molecule hits the surface, are used in combination with vibrational excitations and the corresponding deformation. They indicate that the orientation with three bonds pointing towards the surface is mostly responsible for the isotope effect in the methane dissociation.

show abstract

Multiconfiguration time-dependent Hartree (MCTDH) study on rotational and diffractive inelastic molecule-surface scattering

Abstract: A timedependent discrete variable representation for (multiconfiguration) Hartree methods

Cited by 64 publications

References 48 publications

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

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

Accurate calculations of reaction rates: predictive theory based on a rigorous quantum transition state concept

Energy distribution analysis of the wavepacket simulations of CH4 and CD4 scattering

Contact Info

Product

Resources

About