Multi-configurational Time-dependent Hartree Approach Research Articles

A transition state view on reactive scattering: Initial state-selected reaction probabilities for the H+CH4→H2+CH3 reaction studied in full dimensionality

Initial state-selected reaction probabilities for the H+CH(4)→H(2)+CH(3) reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A(1), 1F(2), and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A(1) and 1F(2) vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.

Multiconfiguration time-dependent Hartree approach for electron-nuclear correlation in strong laser fields

The multiconfiguration time-dependent Hartree approach is applied to study the electron-nuclear correlation in the dynamics of molecules subject to strong external laser fields, using the example of a model hydrogen molecular ion. The ground state of the system is well described by as few as two single-particle functions per degree of freedom. A significantly larger but moderate number of configurations is required to predict laser-induced fragmentation probabilities and high-order harmonic generation spectra accurately, showing that the correlation between electronic and nuclear degree of freedom is strongly increased by the presence of the laser field.

Full-Dimensional Quantum Reaction Rate Calculations for H + CH4 → H2 + CH3 on a Recent Potential Energy Surface

The thermal rate constant of the H + CH(4) → H(2) + CH(3) reaction on the recent potential energy surface (PES) of Corchado et al (CBE) (Corchado, J. C.; Bravo, J. L.; Espinosa-Garcia, J. J. Chem. Phys. 2009, 130, 184314) is computed employing the state-averaged multiconfigurational time-dependent Hartree approach in the temperature range 250-500 K. The CBE PES is global and is based on an analytic functional form that is fast to evaluate. This surface is therefore potentially useful for testing new quantum dynamics methods, and reference rate constants for this purpose are presented here. The thermal rate constants obtained are compared to results previously obtained on an accurate PES particularly designed for thermal rate constant calculations (Wu, T.; Werner, H.; Manthe, U. Science 2004, 306, 2227). The two sets of rate constants are found to agree almost perfectly.

Multiconfiguration time-dependent Hartree approach to study the OH+H2 reaction

Full dimensional quantum scattering calculations have been carried out for the OH + H(2) --> H(2)O + H reaction on the Walch-Dunning-Schatz-Elgersma and Yang-Zhang-Collins-Lee surfaces employing an exact form of the kinetic energy operator. The multiconfiguration time-dependent Hartree (MCTDH) method has been used to perform the wave packet propagations. The MCTDH method uses relatively little memory and its numerical effort scales much more slowly with the dimensionality of the system compared to conventional propagation methods. The reaction probabilities and cross sections obtained on both the surfaces using the MCTDH method are in good agreement with the previous theoretical results. However, the cross sections on the two surfaces differ significantly as a function of the translational energy of the reagents. The difference in barrier heights for the two surfaces along with the transition state structures account for the different reaction probabilities obtained over the entire energy range considered.

Quantum dynamics of the H+CH4→H2+CH3 reaction in curvilinear coordinates: Full-dimensional and reduced dimensional calculations of reaction rates

Full-dimensional quantum dynamics calculations for the H+CH(4)-->H(2)+CH(3) reaction using curvilinear coordinates are presented. A curvilinear coordinate system to describe reactions of the type X+YCH(3)-->XY+CH(3) is developed which facilitates efficient calculations using the multiconfigurational time-dependent Hartree (MCTDH) approach. To describe the bending motion of the X and Y atoms relative to the axis defined by the CH(3) fragment, coordinates based on stereographic projection are introduced. These coordinates yield a kinetic energy operator free of singularities within the dynamically relevant region. Employing this curvilinear coordinate system, full-dimensional and reduced dimensional MCTDH calculations study the cumulative reaction probability (for J=0) and the thermal rate constant for the H+CH(4) reaction on the Jordan-Gilbert potential energy surface [J. Chem. Phys. 102, 5669 (1995)]. The full-dimensional results agree very well with previous full-dimensional MCTDH results which used transition state based normal coordinates. The results of our eight-dimensional (8D) calculations are in reasonable agreement with the full-dimensional ones. They deviate significantly from older 8D results of Zhang et al. [J. Chem. Phys. 127, 234213 (2007)] but agree well with more recent results from the same group.

Multiconfiguration time-dependent Hartree and classical dynamics studies of the photodissociation of HF and HCl molecules adsorbed on ice: Extension to three dimensions

The 3D photodissociation dynamics of HCl and HF molecules adsorbed on ice is studied by quantum and classical simulations. The quantum calculations are carried out with the multiconfiguration time-dependent Hartree (MCTDH) approach. Dynamical observables like angular distributions in the momentum space of the H fragments, absorption cross sections are computed. The results are compared with our previous 2D studies. As expected, less encapsulation of the H atom between the ice surface and the halogen atom is obtained in the 3D study, resulting in less pronounced interference structures in the photoabsorption cross sections and in a decrease of the classical rainbow peaks observed in the 2D scheme. Although the amplitudes of the oscillations corresponding to quantum interferences in the asymptotic angular distribution of the H fragment are different between the 2D and 3D results, the qualitative pattern of the oscillations is similar in the 2D and 3D approaches. In addition, a good agreement is observed for the angular distribution between the classical and the quantum calculations.

Dissociative electron attachment to HCN and HNC

Previous experimental and theoretical studies on HCN and HNC have indicated the presence of both $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ low-lying shape resonances. The energy and autoionization width of these resonant states depend on the stretching and bending of the molecule and lead primarily to a $({\text{CN}}^{\ensuremath{-}}+\text{H})$ product. In this work, we present a comparative study of the dissociation mechanism of these isomers. We carried out electron scattering calculations using the complex-Kohn variational method as a function of the three internal degrees of freedom to obtain the resonance energy surfaces and autoionization widths. We then use these data as input to form the Hamiltonian relevant to the nuclear dynamics. The multidimensional wave equation is solved using the multiconfiguration time-dependent Hartree approach. We compute the relative dissociative electron attachment cross sections and examine the isotope effect relative to each isomer.

Layered discrete variable representations and their application within the multiconfigurational time-dependent Hartree approach

The multiconfigurational time-dependent Hartree (MCTDH) approach facilitates multidimensional quantum dynamics calculations by employing a layered representation: in the upper layer of the representation the multidimensional wave function is expanded in a basis of time-dependent single-particle functions, in the lower layer then these single-particle functions are represented in a larger time-independent basis. This two layer approach can be generalized to a multilayer MCTDH representation to further increase the numerical efficiency. In recent work [U. Manthe, J. Chem. Phys. 128, 164116 (2008)], a quadrature scheme has been introduced which facilitates multilayer MCTDH calculations for Hamiltonians with general potential energy functions. Based on time-dependent discrete variable representation (DVR) grids corresponding to the single-particle function bases the scheme employs the correlation DVR (CDVR) approach. The present work shows that serious problems arise when this original multilayer CDVR approach is applied for accurate calculations of vibrational states. A solution to these problems is presented which uses a revised scheme to define the time-dependent DVR grids entering into the CDVR scheme. Applications studying the vibrational states of CH(3) demonstrate that the resulting revised multilayer MCTDH/CDVR approach yields smoothly convergent and accurate results.

Heat transport through model molecular junctions: A multilayer multiconfiguration time-dependent Hartree approach

A numerically exact approach is proposed to study heat transport through a molecular junction that is coupled to two phonon reservoirs at different temperatures. Within a spin-boson type model, the junction is represented by a two level subsystem and the phonon reservoirs are described by two independent harmonic baths. Quantum simulations of the thermal flux (heat current) are performed employing the multilayer multiconfiguration time-dependent Hartree theory. Results for the transient and stationary heat current are discussed for different physical regimes. Furthermore, the validity of Redfield theory, as an example of an approximate approach applicable for weak system–bath coupling, is examined using the proposed numerically exact approach.

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.

The state averaged multiconfigurational time-dependent Hartree approach: Vibrational state and reaction rate calculations

The multiconfigurational time-dependent Hartree (MCTDH) approach uses optimized sets of time-dependent basis functions, called single-particle functions, to represent multidimensional wavefunctions and thereby facilitates efficient multidimensional quantum dynamics studies. The single-particle function bases are usually optimized for a single wavefunction. Here, an approach is studied which utilizes a common single-particle function basis to represent several wavefunctions simultaneously, i.e., the single-particle function basis is constructed to result in an optimized averaged description of a number of wavefunctions. The approach can favorably be used to obtain eigenstates of Hamiltonians or to represent thermal ensembles. Test calculations studying the vibrational states of CH(3) and the thermal rate constant of the H+CH(4)-->H(2)+CH(3) reaction are presented. It is found that the required size of the single-particle functions basis does not increase when the number of wavefunctions described simultaneously is increased. As a consequence, the new approach offers an increased efficiency, e.g., for MCTDH rate constant calculations.

Quantum dynamics of the CH3 fragment: A curvilinear coordinate system and kinetic energy operators

A curvilinear coordinate system for AB(3) fragments is given. The corresponding exact kinetic energy operator is derived and a series of simpler, progressively more approximate kinetic energy operators are suggested. The operators are tailored for quantum dynamics simulations using the multiconfigurational time-dependent Hartree approach. It is outlined how these fragment coordinates can be utilized to set up coordinate systems for larger systems such as AB(3)C or AB(3)CD. Calculations of the vibrational levels of CH(3) and quantum dynamics studies investigate the accuracy of the different kinetic energy operators suggested.

Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach

The recently proposed multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) approach to evaluating reactive quantum dynamics is applied to two model condensed-phase proton transfer reactions. The models consist of a one-dimensional double-well "system" that is bilinearly coupled to a "bath" of harmonic oscillators parameterized to represent a condensed-phase environment. Numerically exact quantum-mechanical flux correlation functions and thermal rate constants are obtained for a broad range of temperatures and system-bath coupling strengths, thus demonstrating the efficacy of the ML-MCTDH approach. Particular attention is focused on the regime where low temperatures are combined with weak system-bath coupling. Under such conditions it is found that long propagation times are often required and that quantum coherence effects may prevent a rigorous determination of the rate constant.

Accurate and approximate thermal rate constants for polyatomic chemical reactions

In favourable cases it is possible to calculate thermal rate constants for polyatomic reactions to high accuracy from first principles. Here, we discuss the use of flux correlation functions combined with the multi-configurational time-dependent Hartree (MCTDH) approach to efficiently calculate cumulative reaction probabilities and thermal rate constants for polyatomic chemical reactions. Three isotopic variants of the H2 + CH3 → CH4 + H reaction are used to illustrate the theory. There is good agreement with experimental results although the experimental rates generally are larger than the calculated ones, which are believed to be at least as accurate as the experimental rates. Approximations allowing evaluation of the thermal rate constant above 400 K are treated. It is also noted that for the treated reactions, transition state theory (TST) gives accurate rate constants above 500 K. TST theory also gives accurate results for kinetic isotope effects in cases where the mass of the transfered atom is unchanged. Due to neglect of tunnelling, TST however fails below 400 K if the mass of the transferred atom changes between the isotopic reactions.

First ultraviolet absorption band of methane: An ab initio study

Quantum mechanical calculations of the cross sections for photodissociation of CH4 and CD4 in the 1t2-->3s band are presented. The potential energy surfaces for the three states correlating with the 1 1T2 state at tetrahedral geometries are calculated. The elements of the (3x3) matrix representing the electronic Hamiltonian in the diabatic basis are expanded in powers of nuclear coordinates, up to the second order. The expansion coefficients are based on accurate multireference configuration interaction calculations. The electronically nonadiabatic dynamics is treated with the multiconfiguration time-dependent Hartree approach. All nine internal degrees of methane are included in the quantum dynamics simulations. The calculated cross section agrees well with experiment. Semiclassical calculations using the reflection principle suggest that the peaks in the spectrum correspond to the three adiabatic electronic states correlating with the 1 1T2 state at Td geometries. However, the non-Born-Oppenheimer terms in the Hamiltonian have a strong effect on the positions of the peaks in the absorption spectrum. The results of semiclassical calculations, which neglect these terms, are therefore quite different from the accurate quantum results and experiment.

Identifying adenine–thymine base pairing by anharmonic analysis of the hydrogen-bonded NH stretching vibrations

Infrared spectra in the frequency range of hydrogen-bonded NH stretching vibrations of three different adenine–thymine gas-phase isomers are studied. This includes the adenine symmetric and antisymmetric NH 2 vibrations as well as the thymine NH vibration. The ab initio Hamiltonian combines single mode potentials on a grid with up to fourth order force constants to account for mode coupling. Infrared absorption spectra are obtained from dipole autocorrelation functions using the multiconfiguration time-dependent Hartree-approach. In the range of the thymine NH vibration the spectra are sufficiently different to allow for a clear assignment of the experimentally observed isomer.

Calculation of reactive flux correlation functions for systems in a condensed phase environment: A multilayer multiconfiguration time-dependent Hartree approach

A numerically exact quantum mechanical approach is proposed to evaluate thermal rate constants for systems in a model condensed phase environment. Employing the reactive flux correlation function formalism, the approach efficiently combines the multilayer multiconfiguration time-dependent Hartree theory with an importance sampling scheme for thermal distribution of the initial states. The performance of the method is illustrated by applications to two models of condensed phase dynamics: the donor-acceptor electron transfer model also known as the spin-boson model and a model for proton transfer reactions in the condensed phase.

On the integration of the multi-configurational time-dependent Hartree (MCTDH) equations of motion

The multi-configurational time-dependent Hartree approach facilitates multi-dimensional wave packet calculations studying polyatomic reaction processes. The efficiency of the approach results from the use of an optimally adapted time-dependent basis of single-particle functions employed in the wavefunction representation. As a consequence, the equations of motion are non-linear. An efficient integration scheme for these equations has been developed by Beck and Meyer [Z. Phys. D 42 (1997) 113]. The scheme is optimally suited for studies of systems where the Hamiltonian can be represented as a sum of products of single-particle operators. Employing the same basic ideas, the present work now introduces and discusses revised integration schemes which are more efficient for systems, where the Hamiltonian includes a general potential energy function. The H + CH 4 → H 2 + CH 3 reaction is employed as an example to test the efficiency of the different schemes.

Quantum-mechanical evaluation of the Boltzmann operator in correlation functions for large molecular systems: A multilayer multiconfiguration time-dependent Hartree approach

It is shown that the Boltzmann operator in time correlation functions for complex molecular systems can be evaluated in a numerically exact way employing the multilayer formulation of the multiconfiguration time-dependent Hartree theory in combination with Monte Carlo importance sampling techniques. The performance of the method is illustrated by selected applications to photoinduced intervalence electron transfer reactions in the condensed phase. Furthermore, the validity of approximate schemes to evaluate the Boltzmann is discussed.

Calculating initial-state-selected reaction probabilities from thermal flux eigenstates: A transition-state-based approach

An approach for the calculation of initial-state-selected reaction probabilities utilizing a transition-state view and the multiconfigurational time-dependent Hartree approach is presented. Using flux correlation functions, wave packets located in the transition-state region are constructed and propagated into the asymptotic region to obtain initial-state-selected reaction probabilities. A complete set of reaction probabilities is obtained from a single set of thermal flux eigenstates. Concepts previously applied with success to the calculation of k(T) or N(E) are transferred to the calculation of state-selected probabilities. The benchmark H+H(2) (J=0) reaction on the LSTH potential-energy surface is used to test the reliability of this approach.