Calculating vibrational spectra of molecules using tensor train decomposition

100

In this perspective, I review methods for computing (ro-)vibrational energy levels and wavefunctions of molecules with more than four atoms. I identify three problems one confronts (1) reducing the size of the basis; (2) computing hundreds of eigenvalues and eigenvectors of a large matrix; (3) calculating matrix elements of the potential, and present ideas that mitigate them. Most modern methods use a combination of these ideas. I divide popular methods into groups based on the strategies used to deal with the three problems. Published by AIP Publishing. [http://dx

Section: Discussionmentioning

confidence: 99%

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

Carrington

2017

100

“…In the variable n k case, we end up with a maximum error of 0.014 cm −1 and, according to the figure, it could be further decreased by increasing the size of the basis. The corresponding 69 energy levels and recently obtained highly accurate reference results 73 are reported in Table V. FIG. 3.…”

Section: Ml-mctdh Energies Computed With the B (Ml) Finalmentioning

confidence: 92%

“…73 When using ML-MCTDH, we select three sets of node basis sets, denoted, in order of increasing size, initial, inter, and final. To increase the size of the basis of a particular node, we decrease the cut-off threshold of the occupation numbers for the retained NOs of its children.…”

Section: Vibrational Energy Levels Of Ch 3 Cnmentioning

confidence: 99%

Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH

Wodraszka

Carrington

2017

We propose a pruned multi-configuration time-dependent Hartree (MCTDH) method with systematically expanding nondirect product bases and use it to solve the time-independent Schrödinger equation. No pre-determined pruning condition is required to select the basis functions. Using about 65 000 basis functions, we calculate the first 69 vibrational eigenpairs of acetonitrile, CH 3 CN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions. In addition, we compare the new pruned MCTDH method with the established multi-layer MCTDH (ML-MCTDH) scheme and determine that although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required. In our largest calculation, the vast majority of the energies have errors smaller than 0.01 cm −1 . Published by AIP Publishing. [http://dx

“…Only recently, developments for MPS and for the DMRG have been transferred to molecular quantum dynamics. [32][33][34][35][36][37][38][39][40] However, much remains to be done in order to systematically compare and apply the different approaches to molecular quantum dynamics. In particular, we are not aware of any direct comparisons between MPS and ML-MCTDH/TTNS for molecular systems.…”

Section: Introductionmentioning

confidence: 99%

Computing vibrational eigenstates with tree tensor network states (TTNS)

Larsson

2019

We present how to compute vibrational eigenstates with tree tensor network states (TTNS), the underlying ansatz behind the multilayer multi-configuration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group (DMRG). We apply this to compute the vibrational spectrum of acetonitrile (CH 3 CN) to high accuracy and compare TTNS with matrix product states (MPS), the ansatz behind the DMRG. The presented optimization scheme converges much faster than ML-MCTDH-based optimization. For this particular system, we found no major advantage of the more general TTNS over MPS. We highlight that for both TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of required parameters. We furthermore propose a procedure to find good trees.