Multilayer Multiconfiguration Time-dependent Hartree Calculations Research Articles

A multi-layer multi-configurational time-dependent Hartree approach to lattice models beyond one dimension.

The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is an efficient method to study quantum dynamics in real and imaginary time. The present work explores its potential to describe quantum fluids. The multi-layer MCTDH approach in second quantization representation is used to study lattice models beyond one dimension at finite temperatures. A scheme to map the lattice sites onto the MCTDH tree representation for multi-dimensional lattice models is proposed. A statistical sampling scheme previously used in MCTDH calculations is adapted to facilitate an efficient description of the thermal ensemble. As example, a two-dimensional hard-core Bose-Hubbard model is studied considering up to 64 × 64 lattice sites. The single particle function basis set size required to obtain converged results is found to not increase with the lattice size. The numerical results properly simulate the finite temperature Berezinskii-Kosterlitz-Thouless phase transition.

Multilayer Multiconfiguration Time-Dependent Hartree Study on the Mode-/Bond-Specific Quantum Dynamics of Water Dissociation on Cu(111).

In this work, full-dimensional (9D) quantum dynamics calculations on mode-/bond-specific surface scattering of a water molecule on a copper (111) rigid surface are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. To easily perform the ML-MCTDH calculations on such a triatomic molecule-surface system, we first choose specific Jacobi coordinates as a set of coordinates of water. Next, to efficiently perform the 9D ML-MCTDH wavepacket propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific dissociation probabilities of H2O on Cu(111) are computed, and mode-/bond-specific dynamics are demonstrated by comparison with a probability curve computed for a water molecule in the ground state. The dependence of the dissociation probability of the initial state of H2O is studied, and it is found that the excitation-specific dissociation probabilities can be divided into three groups. We find that the vibrationally excited states enhance the dissociation reactivity of H2O, while the rotationally excited states hardly influence it.

Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. II. Benchmarks and applications.

In Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], we presented the ring-polymer instanton with explicit friction (RPI-EF) method and showed how it can be connected to the ab initio electronic friction formalism. This framework allows for the calculation of tunneling reaction rates that incorporate the quantum nature of the nuclei and certain types of non-adiabatic effects (NAEs) present in metals. In this paper, we analyze the performance of RPI-EF on model potentials and apply it to realistic systems. For a 1D double-well model, we benchmark the method against numerically exact results obtained from multi-layer multi-configuration time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for medium and high friction strengths and less accurate for extremely low friction values. We also show quantitatively how the inclusion of NAEs lowers the crossover temperature into the deep tunneling regime, reduces the tunneling rates, and, in certain regimes, steers the quantum dynamics by modifying the tunneling pathways. As a showcase of the efficiency of this method, we present a study of hydrogen and deuterium hopping between neighboring interstitial sites in selected bulk metals. The results show that multidimensional vibrational coupling and nuclear quantum effects have a larger impact than NAEs on the tunneling rates of diffusion in metals. Together with Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], these results advance the calculations of dissipative tunneling rates from first principles.

First-Principles Quantum and Quantum-Classical Simulations of Exciton Diffusion in Semiconducting Polymer Chains at Finite Temperature.

We report on first-principles quantum-dynamical and quantum-classical simulations of photoinduced exciton dynamics in oligothiophene chain segments, representative of intrachain exciton migration in the poly(3-hexylthiophene) (P3HT) polymer. Following up on our recent study (Binder R.; Burghardt, I. Faraday Discuss. 2020, 221, 406), multilayer multiconfiguration time-dependent Hartree calculations for a short oligothiophene segment comprising 20 monomer units (OT-20) are carried out to obtain full quantum-dynamical simulations at finite temperature. These are employed to benchmark mean-field Ehrenfest calculations, which are shown to give qualitatively correct results for the present system. Periodic boundary conditions turn out to significantly improve earlier estimates of diffusion coefficients. Using the Ehrenfest approach, a series of calculations are subsequently carried out for larger lattices (OT-40 to OT-80), leading to estimates for temperature-dependent mean-squared displacements, which are found to exhibit a near-linear dependence as a function of time. The resulting diffusion coefficient estimates are an increasing function of temperature, whose detailed functional form depends on the degree of static disorder. With a realistic static disorder parameter (σs ≃ 0.06 eV), the diffusion coefficients decrease from D ∼ 1 × 10-2 cm2 s-1 to D ∼ 1 × 10-3 cm2 s-1, in qualitative agreement with experimental data for P3HT. The dynamical scenario obtained from our simulations shows that exciton migration in P3HT-type chains is a largely adiabatic process throughout the temperature regime we investigated (i.e., T = 50-300 K). The resulting picture of exciton migration is a coherent, but not bandlike, motion of an exciton-polaron driven by fluctuations induced by low-frequency modes. This process acquires partial hopping character if static disorder becomes prominent and Anderson localization sets in.

Quantum dynamics of multi-dimensional rhodopsin photoisomerization models: Approximate versus accurate treatment of the secondary modes

We numerically investigate the quantum dynamics of the high-dimensional rhodopsin photoisomerization models of Hahn and Stock using the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. The original two-state two-mode model is augmented with additional Raman-active modes observed experimentally and by a bath of low frequency modes that accounts in a generic fashion for the effect the protein and solvent environment. A previously used approximate method in which the two primary modes are treated using an accurate quantum dynamical method while the secondary modes are treated using the time-dependent Hartree (TDH) method is tested against ML-MCTDH calculations. It is shown that the former method does not capture the main effect of these modes on the electronic populations, on the coherent torsional dynamics and on the quantum yield of the photoisomerization reaction. Our ML-MCTDH calculations predict small photoisomerization quantum yields, in contradiction with the experiments, and call for a revision of the model.

A full-dimensional multilayer multiconfiguration time-dependent Hartree study on the ultraviolet absorption spectrum of formaldehyde oxide.

Employing the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method in conjunction with the multistate multimode vibronic coupling Hamiltonian (MMVCH) model, we perform a full dimensional (9D) quantum dynamical study on the simplest Criegee intermediate, formaldehyde oxide, in five lower-lying singlet electronic states. The ultraviolet (UV) spectrum is then simulated by a Fourier transform of the auto-correlation function. The MMVCH model is built based on extensive MRCI(8e,8o)/aug-cc-pVTZ calculations. To ensure a fast convergence of the final calculations, a large number of ML-MCTDH test calculations is performed to find an appropriate multilayer separations (ML-trees) of the ML-MCTDH nuclear wave functions, and the dynamical calculations are carefully checked to ensure that the calculations are well converged. To compare the computational efficiency, standard MCTDH simulations using the same Hamiltonian are also performed. A comparison of the MCTDH and ML-MCTDH calculations shows that even for the present not-too-large system (9D here) the ML-MCTDH calculations can save a considerable amount of computational resources while producing identical spectra as the MCTDH calculations. Furthermore, the present theoretical B̃(1)A'←X̃(1)A' UV spectral band and the corresponding experimental measurements [J. M. Beames, F. Liu, L. Lu, and M. I. Lester, J. Am. Chem. Soc. 134, 20045-20048 (2012); L. Sheps, J. Phys. Chem. Lett. 4, 4201-4205 (2013); W.-L. Ting, Y.-H. Chen, W. Chao, M. C. Smith, and J. J.-M. Lin, Phys. Chem. Chem. Phys. 16, 10438-10443 (2014)] are discussed. To the best of our knowledge, this is the first theoretical UV spectrum simulated for this molecule including nuclear motion beyond an adiabatic harmonic approximation.

A multilayer MCTDH study on the full dimensional vibronic dynamics of naphthalene and anthracene cations

Employing the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method in conjunction with the multistate multimode vibronic coupling Hamiltonian model, we perform a full dimensional quantum dynamical study on the naphthalene (48D) and anthracene (66D) radical cations in their six lowest-lying doublet electronic states. For easily comparing results of full and reduced dimensionalities, MCTDH simulations based on larger sizes of primitive basis functions and single-particle functions than the previous ones [S. Ghanta, V. S. Reddy, and S. Mahapatra, Phys. Chem. Chem. Phys. 13, 14531 (2011)], are also performed. Extensive ML-MCTDH test calculations are performed to find appropriate ML separations of the wave functions (so-called ML-trees), and the convergence of the dynamical calculations are carefully checked. The ML-MCTDH method was developed for efficiently simulating quantum dynamics of large systems, and in fact the full dimensional ML-MCTDH calculations save a considerable amount of CPU-time in comparison with corresponding reduced dimensional MCTDH simulations. On basis of the present full and reduced dimensional simulations, the photoelectron (PE) spectra of these two cations are simulated and compared with corresponding experimental spectra. The agreement between theoretical and experimental PE spectra is good. Both full and reduced dimensional simulations give all main bands in the PE spectra. The vibronic energy-level positions from both ML-MCTDH and MCTDH calculations agree with corresponding experimental results. These quantum dynamical studies also complement the observations on diffuse interstellar bands with the wavelength of ~7088, ~6707, ~6490, ~6120, and ~5959 Å measured by astronomers as well as laboratory experimentalists.

Full dimensional quantum-mechanical simulations for the vibronic dynamics of difluorobenzene radical cation isomers using the multilayer multiconfiguration time-dependent Hartree method

Full dimensional multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) calculations of the dynamics of the three difluorobenzene cationic isomers in five lowest-lying doublet electronic states using the ab initio multistate multimode vibronic coupling Hamiltonian (MMVCH) model are carried out using the Heidelberg MCTDH package. The same dynamical problems, but treated with the MCTDH scheme and using a reduced dimensional ab initio MMVCH model, have been previously reported [S. Faraji, H.-D. Meyer, and H. Köppel, "Multistate vibronic interactions in difluorobenzene radical cations. II Quantum dynamical simulations," J. Chem. Phys. 129, 074311 (2008)]. For easy comparison with the reduced dimensional results, 11D or 10D ML-MCTDH calculations are also performed. Extensive ML-MCTDH test calculations are performed to find appropriate ML-MCTDH wavefunction structures (ML-trees), and the convergence of the ML-MCTDH calculations are carefully checked to ensure accurate results. Based on the appropriate ML-trees, the photoelectron (PE) spectrum and the mass analyzed threshold ionization (MATI) spectrum are simulated, analyzed, and compared with corresponding experimental spectra. Because of its efficient simulation capability for large systems, ML-MCTDH calculations save a considerable amount of central processing unit (CPU)-time, even when a reduced dimensional MMVCH is used, i.e., the same reduced model as in the corresponding MCTDH calculations. Simulations of the experimental PE spectra by full dimensional ML-MCTDH calculations reproduced main peaks, which originate from different electronic states. The agreement is improved as compared to the reduced dimensionality calculations. Unfortunately, the experimental PE spectra are not very well resolved. Therefore, we compare our calculations additionally with highly resolved MATI spectra, which, however, are only available for the X̃ state. Based on a series of ML-MCTDH simulations with longer propagation time for X̃, a number of vibrational modes, including fundamentals, their combinations, and overtones are simulated and assigned by comparing with the experimental assignments and the ab initio frequencies. Excellent correlation between the experimental and full dimensional ML-MCTDH results show that ML-MCTDH is accurate and very efficient and that the ab initio MMVCH model is very suitable for ML-MCTDH calculations.

Intramolecular proton transfer in malonaldehyde: Accurate multilayer multi-configurational time-dependent Hartree calculations

Full-dimensional (multilayer) multi-configurational time-dependent Hartree calculations studying the intramolecular proton transfer in malonaldehyde based on a recent potential energy surface (PES) [Wang et al., J. Chem. Phys. 128, 224314 (2008)] are presented. The most accurate calculations yield a ground state tunneling splitting of 23.8 cm(-1) and a zero point energy of 14,678 cm(-1). Extensive convergence tests indicate an error margin of the quantum dynamics calculations for the tunneling splitting of about 0.2 cm(-1). These results are to be compared with the experimental value of the tunneling splitting of 21.58 cm(-1) and results of Monte Carlo calculations of Wang et al. on the same PES which yielded a zero point energy of 14,677.9 cm(-1) with statistical errors of 2-3 cm(-1) and a tunneling splitting of 21.6 cm(-1). The present data includes contributions resulting from the vibrational angular momenta to the tunneling splitting and the zero point energy of 0.2 cm(-1) and 2.4 cm(-1), respectively, which have been computed using a perturbative approach.

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.