Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials

Self Cite

An efficient algorithm for compressing a given many-body potential energy surface (PES) of molecular systems into a grid-based matrix product operator (MPO) is proposed. The PES is once represented by a full-dimensional or truncated manybody expansion form, which is obtained by ab initio calculations at each grid mesh point, and then all terms in the expansion are compressed and merged into a single MPO while maintaining the bond dimension of the MPO as small as possible. It was shown that the ab initio PES of the H 2 CO was compressed by more than 2 orders of magnitude in the size of the site operators without loss of accuracy. By the use of grid basis, the tensor rank of the site operators of the MPO is reduced from four to three due to the diagonal nature of the position-dependent operators on grid basis, which significantly reduces the computational cost of the tensor contractions required in the real and imaginary time evolution of the matrix product state (MPS) wave functions with the grid-based MPO (Grid-MPO) Hamiltonian. Similar to other grid-based methods, Grid-MPO is easily applicable to any kinds of potentials of molecular systems, such as analytical empirical model potentials expressed by position operators and ab initio potentials, if the values at the grid points are available. Using the Grid-MPO combined with the MPS, we calculated the time correlation function of the Eigen cation H O (H O) 3 2 3+ to predict the infrared spectrum and compared with the experimental and the previous theoretical studies. The actual scaling with the size of systems was examined for the multidimensional Henon−Heiles Hamiltonian. It was shown that the method is considerably accelerated by the graphic processing unit (GPU) because the sizes of site operators were kept small and all tensors were able to be stored on the VRAM of a GPU.

Section: W Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Encoding a Many-Body Potential Energy Surface into a Grid-Based Matrix Product Operator

Hino,

Kurashige

2024

Self Cite

“…However, numerically exact full-quantum methods such as numerically exact wavepacket propagation approaches , are usually only feasible to a small number of degrees of freedom (DoFs) due to the curse of dimensionality. Through decomposing the wave function of a large high-rank tensor into the product of many small low-rank tensors, the time-dependent density matrix renormalization group (TD-DMRG) − and multiconfigurational time-dependent Hartree (MCTDH) − as well as its multilayer variant (ML-MCTDH) , increased the computational efficiency remarkably and made it feasible to simulate the dynamics of excitonic systems with up to a few hundred vibrational or phonon DoFs. This promotes the full QD simulations of nonadiabatic processes in realistic molecules with up to a few tens of atoms, ranging from charge transfer − or energy transfer to singlet fission …”

Section: Introductionmentioning

confidence: 99%

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Liu

Ma³

2023

Quantum dynamics (QD) simulation is a powerful tool for interpreting ultrafast spectroscopy experiments and unraveling their microscopic mechanism in out-of-equilibrium excited state behaviors in various chemical, biological, and material systems. Although state-of-the-art numerical QD approaches such as the time-dependent density matrix renormalization group (TD-DMRG) already greatly extended the solvable system size of general linearly coupled exciton–phonon models with up to a few hundred phonon modes, the accurate simulation of larger system sizes or strong system-environment interactions is still computationally highly challenging. Based on quantum information theory (QIT), in this work, we realize that only a small number of effective phonon modes couple to the excitonic system directly regardless of a large or even infinite number of modes in the condensed phase environment. On top of the identified small number of direct effective modes, we propose a hierarchical mapping (HM) approach through performing block Lanczos transformations on the remaining indirect modes, which transforms the Hamiltonian matrix to a nearly block-tridiagonal form and eliminates the long-range interactions. Numerical tests on model spin-boson systems and realistic singlet fission models in a rubrene crystal environment with up to 7000 modes and strong system-environment interactions indicate HM can reduce the system size by 1–2 orders of magnitude and accelerate the calculation by ∼80% without losing accuracy.

“…The correlated/coupled motion of the nuclei in a molecular system is an ultrafast phenomenon, and, as such, it must be studied using either experimental ultrafast techniques, which include pulse probe methods, or computer simulation methods aimed at the interpretation and simulation of two-dimensional spectra. ,− In theoretical chemistry, the identification of the uncoupled degrees of freedom is useful for computational methodologies that calculate the vibrational spectrum in reduced dimensionality, such as, for instance, semiclassical approaches, − QM/MM calculations, tensor-trains and sum of products of basis functions methods − and also the Multi-Configuration Time-Dependent Hartree method (MCTDH) − and methods based on MCTDH-like ansatz . Applications of all the aforementioned methods imply either that part of a system is partially independent of another or that the two parts have an artificial interaction.…”

Section: Introductionmentioning

confidence: 99%

Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings

Gandolfi,

Ceotto

2023

We propose a numerical technique to accurately simulate the vibrations of organic molecules in the gas phase, when pairs of atoms (or, in general, groups of degrees of freedom) are artificially decoupled, so that their motion is instantaneously decorrelated. The numerical technique we have developed is a symplectic integration algorithm that never requires computation of the force but requires estimates of the Hessian matrix. The theory we present to support our technique postulates a pair-decoupling Hamiltonian function, which parametrically depends on a decoupling coefficient α ∈ [0, 1]. The closer α is to 0, the more decoupled the selected atoms. We test the correctness of our numerical method on small molecular systems, and we apply it to study the vibrational spectroscopic features of salicylic acid at the Density Functional Theory ab initio level on a fitted potential. Our pair-decoupled simulations of salicylic acid show that decoupling hydrogen-bonded atoms do not significantly influence the frequencies of stretching modes, but enhance enormously the out-of-plane wagging and twisting motions of the hydroxyl and carboxyl groups to the point that the carboxyl and hydroxyl groups may overcome high potential energy barriers and change the salicylic acid conformation after a short simulation time. In addition, we found that the acidity of salicylic acid is more influenced by the dynamical couplings of the proton of the carboxylic group with the carbon ring than with the hydroxyl group.