Hans-Dieter Meyer

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...

Variational quantum approaches for computing vibrational energies of polyatomic molecules

In this article, we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of those methods by presenting applications to molecules with more than four atoms. This demonstrates the great progress that has been made in this field in the last decade in dealing with the exponential scaling with the number of vibrational degrees of freedom. In this review we present three methods that effectively obviate this bottleneck. The first important idea is the n-mode representation of the Hamiltonian and notably the potential. The potential (and other functions) is represented as a sum of terms that depend on a subset of the coordinates. This makes it possible to compute matrix elements, form a Hamiltonian matrix, and compute its eigenvalues and eigenfunctions. Another approach takes advantage of this multimode representation and represents the terms as a sum of products. It then exploits the powerful multiconfiguration Hartree time-dependent method to solve the time-dependent Schrödinger equation and extract the eigenvalue spectrum. The third approach we present uses contracted basis functions in conjunction with a Lanczos eigensolver. Matrix vector products are done without transforming to a direct-product grid. The usefulness of these methods is demonstrated for several example molecules, e.g. methane, methanol and the Zundel cation.

Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6×10(7)time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5×10(5) coefficients and requiring a shorter computation time.

Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics

The infrared absorption spectrum of the protonated water dimer (H5O2+) is simulated in full dimensionality (15 dimensional) in the spectral range of 0-4000 cm(-1). The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method for propagation of wavepackets. All the fundamentals and several overtones of the vibrational motion are computed. The spectrum of H5O2+ is shaped to a large extent by couplings of the proton-transfer motion to large amplitude fluxional motions of the water molecules, water bending and water-water stretch motions. These couplings are identified and discussed, and the corresponding spectral lines are assigned. The large couplings featured by H5O2+ do not hinder, however, to describe the coupled vibrational motion by well defined simple types of vibration (stretching, bending; etc.) based on well defined modes of vibration, in terms of which the spectral lines are assigned. Comparison of our results to recent experiments and calculations on the system is given. The reported MCTDH IR spectrum is in very good agreement to the recently measured spectrum by Hammer et al. [J. Chem. Phys. 122, 244301 (2005)].

Studying molecular quantum dynamics with the multiconfiguration time‐dependent Hartree method

This review covers the multiconfiguration time‐dependent Hartree (MCTDH) method, which is a powerful and general algorithm for solving the time‐dependent Schrödinger equation. The formal derivation is discussed as well as applications of the method. Recent extensions of MCTDH are treated in brief, namely, MCTDHB and MCTDHF, for treating identical particles (bosons and fermions), and the very powerful multilayer (ML‐MCTDH) formalism. Compact representations of potential energy surfaces (PESs) are also discussed, as the representation of a PES becomes a major bottleneck when going to larger systems (nine or more dimensions) while employing a full‐dimensional, complicated, and nonseparable PES. As applications of MCTDH, we discuss the calculation of photoionization and photoexcitation spectra of the vibronically coupled systems butatriene and pyrazine, respectively, and the infra‐red spectrum of the Zundel cation (protonated water dimer) H5O+2.

Multistate vibronic interactions in the benzene radical cation. II. Quantum dynamical simulations

The multistate vibronic dynamics in the X 2E1g-Ẽ 2B2u electronic states of the benzene radical cation is investigated theoretically by an ab initio quantum-dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from the previous Paper I. Vibronic line spectra are obtained with the Lanczos procedure. Extensive calculations on wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Up to five coupled electronic potential energy surfaces and 13 vibrational degrees of freedom have been included in these calculations. As a result, the impact of a third electronic state (X or B) on a strongly coupled manifold (B-C or D-Ẽ states) is quantitatively assessed. It leads to a restructuring of the spectral envelope which is stronger for the B-D-Ẽ than for the X-B-C system. The internal conversion dynamics is characterized by a stepwise transfer of electronic population to the lowest electronic s...

Full-dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. I. Hamiltonian setup and analysis of the ground vibrational state.

Quantum-dynamical full-dimensional (15D) calculations are reported for the protonated water dimer (H5O2+) using the multiconfiguration time-dependent Hartree (MCTDH) method. The dynamics is described by curvilinear coordinates. The expression of the kinetic energy operator in this set of coordinates is given and its derivation, following the polyspherical method, is discussed. The potential-energy surface (PES) employed is that of Huang et al. [J. Chem. Phys. 122, 044308 (2005)]. A scheme for the representation of the PES is discussed which is based on a high-dimensional model representation scheme, but modified to take advantage of the mode-combination representation of the vibrational wave function used in MCTDH. The convergence of the PES expansion used is quantified and evidence is provided that it correctly reproduces the reference PES at least for the range of energies of interest. The reported zero point energy of the system is converged with respect to the MCTDH expansion and in excellent agreement (16.7 cm(-1) below) with the diffusion Monte Carlo result on the PES of Huang et al. The highly fluxional nature of the cation is accounted for through use of curvilinear coordinates. The system is found to interconvert between equivalent minima through wagging and internal rotation motions already when in the ground vibrational state, i.e., T=0. It is shown that a converged quantum-dynamical description of such a flexible, multiminima system is possible.

A study of the mode-selective trans-cis isomerization in HONO using ab initio methodology

Ab initio calculations on the six-dimensional cis--trans double minimum potential energy surface of the electronic ground state of the HONO molecule were performed using a coupled cluster approach. An analytic fit to the data points was established. The interconversion barrier was calculated to be 4105 cm(-1). The nuclear motion problem was solved variationally using a full six-dimensional Hamiltonian in internal coordinates. The eigenstates up to about 3650 cm(-1) were tentatively assigned by harmonic quantum numbers. The assignment was based on the mean values of the internal coordinates of the six-dimensional eigenfunctions and on a comparison of the eigenenergies with those calculated by second-order perturbation theory from a full quartic force field in dimensionless normal coordinates. In cold matrices the trans- and the cis-OH nu(1) stretching modes and the first trans- and cis-NO 2nu(2) stretching overtones lead to isomerization. In the isolated molecule these modes (J=0) were found to be entirely localized. However, several overtones of the nu(4) ONO bending and nu(5) N-O stretching, which are close in energy to the OH stretch and combined with the torsional mode, were found to be strongly cis-trans delocalized.

Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration time-dependent Hartree method

A theoretical study of the vibrational spectrum of the CHF(3) molecule is carried out with the aid of the multiconfiguration time-dependent Hartree (MCTDH) algorithm. In order to obtain the eigenvalues and the eigenstates, recent developments in the MCTDH improved relaxation method in a block form are exploited. Around 80 eigenvalues are reported, which are converged with a very high accuracy. The results obtained with our study are compared with those of a previous work using the wave operator sorting algorithm approach. The present investigation exemplifies the robustness and the accuracy of the improved relaxation method.