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We explain the concept of superadiabatic representations and show how in the context of electronically non-adiabatic transitions they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic potential energy surfaces near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic electronic energies can be computed on the fly, and they only need to be computed to higher accuracy when an avoided crossing is detected. We test the quality of our method on the paradigmatic example of photo-dissociation of NaI, finding very good agreement with results of exact wave packet calculations. [ABSTRACT FROM AUTHOR]

The multiconfigurational time-dependent Hartree (MCTDH) approach is applied to an example showing very complex dynamics: the wave-packet dynamics on the three-dimensional B2 potential-energy surface of NO2. The ability of the MCTDH scheme to describe accurately the severe splitting of the wave packet on a saddle-shaped surface is demonstrated. Internal checks of the MCTDH calculation enable us to assess the degree of convergence without the need to resort to a numerically exact wave-packet calculation. As a representative observable the photodissociation spectrum is calculated and discussed. The A1/B2 vibronic coupling is neglected in our study, but the dynamics on the diabatic B2 surface is treated in its full three dimensionality. [ABSTRACT FROM AUTHOR]

The multiconfigurational time-dependent Hartree (MCTDH) approximation to the time-dependent Schrödinger 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’’ that are computed along with the MCTDH wave packet serve as a check of the degree of convergence without the need to resort to an exact (or more accurate) calculation. [ABSTRACT FROM AUTHOR]

The dissociation process of a triatomic molecule with strongly coupled electronic states is investigated by wave packet dynamics. Rotational and vibronic motion are separated for vanishing total angular momentum (J=0) in a linear molecule with conically intersecting Σ and Π electronic potential energy surfaces. All three remaining nuclear degrees of freedom are treated exactly. The time evolution of a wave packet prepared initially by photoionization of the neutral molecule is studied for different values of the nonadiabatic couplings and for different values of other relevant parameters. The potential surfaces studied include those modeling important aspects of the HCN+ system. Time dependent populations of diabatic and adiabatic electronic states are presented. The results can be interpreted by adapting ideas developed for vibronic coupling in bound systems to the dissociative situation. [ABSTRACT FROM AUTHOR]

The nuclear dynamics on potential energy surfaces which are strongly vibronically coupled through a conical intersection is investigated by exact (numerical) integration of the time-dependent Schrödinger equation. Results for realistic model systems including three nuclear degrees of freedom are presented: C2H+4, pyrazine and NO2. It was found previously for C2H+4 that the wave packet moves after an initial decay mainly on the lower adiabatic surface. This observation could be confirmed also for pyrazine and NO2. By varying the coupling strength λ also other types of behavior could be identified. A transition from adiabatic via intermediate to a diabatic nature of the system dynamics is found upon decreasing λ. Population of diabatic and adiabatic states in the long time limit are calculated by classical phase-space statistics. Analytic relations between the population of the diabatic states and the dynamical observables, coordinates and momenta, are derived. They allow for a deeper understanding of their long time limits. [ABSTRACT FROM AUTHOR]

The nuclear dynamics on potential energy surfaces with a conical intersection is investigated on the basis of exact (numerical) integration of the time-dependent Schrödinger equation. The ethylene cation is chosen as a typical realistic model system. Complementing earlier work we study the dynamics also in the adiabatic basis, which will be seen to allow for a more profound understanding of the decay and dephasing processes occurring in the system. The computational effort exceeds considerably that of propagation in the diabatic basis, to which previous related studies have been confined. To solve the resulting computational problems we develop and present a special multidimensional adaptation of the finite basis set method utilizing the product structure of the basis. It allows us to calculate propagation in a general potential including three vibrational modes. For the time integration a fourth order differencing scheme is introduced which is faster than the second order differencing-scheme and predictor–corrector approaches. [ABSTRACT FROM AUTHOR]

The dynamics of the vibrational predissociation of the I[sub 2]Ne[sub 2](B,ν=21) cluster is studied using a full-dimensional time-dependent wave packet approach. The 6-D propagation is performed with the multiconfiguration time-dependent Hartree (MCTDH) method. The time dependence of the I[sub 2] vibrational state populations is monitored during the dissociation process. The final vibrational populations are compared to experimental findings of Levy et al. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The full dimensional rate constant reported by Huarte-Larran˜aga and Manthe for the H+CH[sub 4]→H[sub 2]+CH[sub 3] reaction [Huarte-Larran˜aga and Manthe, J. Chem. Phys. 113, 5115 (2000)] is corrected by using an accurate vibrational partition function for CH[sub 4] instead of the harmonic normal-mode one used by them. The correction is shown to be substantial over the temperature range considered by Huarte-Larran˜aga and Manthe. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The correlation discrete variable representation (CDVR) enables multi-layer multi-configurational time-dependent Hartree (MCTDH) quantum dynamics simulations on general potential energy surfaces. In a recent study [R. Ellerbrock and U. Manthe, J. Chem. Phys. 156, 134107 (2022)], an improved CDVR that can account for the symmetry properties of a tree-shaped wavefunction representation has been introduced. This non-hierarchical CDVR drastically reduces the number of grid points required in the time-dependent quadrature used to evaluate all potential energy matrix elements. While the first studies on the non-hierarchical CDVR approach have been restricted to single-layer calculations, here the complete theory required for the implementation of the non-hierarchical CDVR approach in the multi-layer MCTDH context will be presented. Detailed equations facilitating the efficient recursive computation of all matrix elements are derived, and a new notation adapted to the symmetry properties of the tree-shaped representation is introduced. Calculations studying the non-adiabatic quantum dynamics of photoexcited pyrazine in 24 dimensions illustrate the properties of the non-hierarchical multi-layer CDVR., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Full-dimensional quantum dynamics simulations of the reaction of Cl with methane and its isotopomers are reported. Thermal rate constants are computed for the Cl + CH 4 → HCl + CH 3 , Cl + CHD 3 → HCl + CD 3 , and Cl + CD 4 → DCl + CD 3 reactions. Temperatures between 200 and 500 K are considered. In this temperature range, excellent agreement with the experiment is obtained. A detailed analysis of the kinetic isotope effect reveals the crucial importance of the CH 3 /CD 3 umbrella motion. Comparison with approximate ring-polymer molecular dynamics simulations shows significant differences depending on the isotope studied.

We present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

A new approach for the calculation of eigenstates with the state-averaged (multi-layer) multi-configurational time-dependent Hartree (MCTDH) approach is presented. The approach is inspired by the recent work of Larsson [J. Chem. Phys. 151, 204102 (2019)]. It employs local optimization of the basis sets at each node of the multi-layer MCTDH tree and successive downward and upward sweeps to obtain a globally converged result. At the top node, the Hamiltonian represented in the basis of the single-particle functions (SPFs) of the first layer is diagonalized. Here p wavefunctions corresponding to the p lowest eigenvalues are computed by a block Lanczos approach. At all other nodes, a non-linear operator consisting of the respective mean-field Hamiltonian matrix and a projector onto the space spanned by the respective SPFs is considered. Here, the eigenstate corresponding to the lowest eigenvalue is computed using a short iterative Lanczos scheme. Two different examples are studied to illustrate the new approach: the calculation of the vibrational states of methyl and acetonitrile. The calculations for methyl employ the single-layer MCTDH approach, a general potential energy surface, and the correlation discrete variable representation. A five-layer MCTDH representation and a sum of product-type Hamiltonian are used in the acetonitrile calculations. Very fast convergence and order of magnitude reductions in the numerical effort compared to the previously used block relaxation scheme are found. Furthermore, a detailed comparison with the results of Avila and Carrington [J. Chem. Phys. 134, 054126 (2011)] for acetonitrile highlights the potential problems of convergence tests for high-dimensional systems., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

A novel two-step method for formylation of fluoropyridines with silylformamidine Me 3 SiC(=NMe)NMe 2 (1) under catalyst-free conditions was developed. A series of all possible 18 fluoropyridines featuring one to four fluorine atoms were subjected to the reaction with 1 existing in equilibrium with its carbenic form Me 2 NC(:)N(Me)SiMe 3 (1'). Among them, 12 fluoropyridines were shown to react via C-H insertion. The reaction proceeded either at β- or γ-positions affording the corresponding aminals. The more fluorine atoms in pyridines, the easier the reaction proceeded. We also hypothesized that the pyridines in which the fluorine was substituted by other halogens would react in a similar manner. To test the hypothesis, a set of 3,5-disubstituted pyridines with various combination of halogen atoms was prepared. 3,5-Difluoropyridine was taken as a compound for comparison. All the pyridines in the series also reacted likewise. In most cases, hydrolysis of the aminals afforded the corresponding aldehydes. As DFT calculations indicate, the reaction mechanism includes deprotonation of pyridine by 1' as a strong base and the following rearrangement of the formed tight ionic pair to the final product. An alternative reaction pathway involving addition of 1' to the pyridine carbon with the following hydrogen transfer via a three-membered transition state structure required much higher activation energy., (© 2023 Wiley-VCH GmbH.)

The correlation discrete variable representation (CDVR) enables (multilayer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. The CDVR employs a set of grids corresponding to single-particle functions to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. In standard CDVR approaches, the number of grid points employed is tied to the number of corresponding single-particle functions. This limits the accuracy of the quadrature, which can be achieved for a given single-particle function basis. In this work, an extended CDVR approach that facilitates a numerically exact quadrature of all potential matrix elements is introduced. The number of grid points employed can be increased independent of the number of corresponding single-particle function to achieve any desired quadrature accuracy. The properties of the new scheme are illustrated by numerical calculations studying the photodissociation of NOCl and the vibrational states of CH3. Fast convergence with respect to the number of additional quadrature points is observed: Employing a single additional point in each physical or logical coordinate already ensures negligible quadrature errors., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Silylformamidine 1 exists in equilibrium with its carbenic form 1' due to an easy migration of the silyl group. The reaction of 1 with variously substituted fluorobenzenes proceeds as an insertion of the nucleophilic carbene 1' into the most acidic C-H bond upon mixing the reagents and does not require any catalyst. According to DFT calculations, the classical interpretation of the insertion reaction proceeding via a three-membered transition state structure requires high activation energy. Instead, low activation barriers are predicted for a transfer of the most acidic proton in the aromatic substrate to the carbene carbon. As the next step, a barrierless rearrangement of the formed ion pair toward the product completes the process. The reactivity of substituted benzenes in the reaction with silylformamidine can be roughly assessed by calculated p K a (DMSO) values for the C-H hydrogens. Benzene derivatives having p K a approx. less than 31 can undergo C-H insertion. The reaction provides aminals as the first products, which can easily be transformed into the corresponding aldehydes via acidic hydrolysis. As silylformamidine 1 is tolerant to many functional groups, the reaction can be applied to numerous benzene derivatives, making it a reliable strategy for application in organic synthesis.