Using an expanding nondirect product harmonic basis with an iterative eigensolver to compute vibrational energy levels with as many as seven atoms

The Journal of Chemical Physics

2017

Self Cite

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

“…48,70,71 Our implementation is close to that of Ref. 48. However, in our case, when the basis size is increased, the definition of all of the functions in the basis changes.…”

Section: Using An Expanding Nondirect Product Basis With Mctdhsupporting

confidence: 50%

“…A similar expanding basis idea has been used with phase-space localized and harmonic oscillator basis functions. 48,70,71 Our implementation is close to that of Ref. 48.…”

Section: Using An Expanding Nondirect Product Basis With Mctdhmentioning

confidence: 58%

See 1 more Smart Citation

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

Wodraszka

The Journal of Chemical Physics

2017

Self Cite

“…77 and with harmonic oscillator basis functions in Ref. 108. These ideas make it possible to evaluate MVPs without computing or storing Hamiltonian matrix elements.…”

Section: B Special-form/iterative-eigensolver/pruned-basis (Sf/i/p) mentioning

confidence: 99%

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

The Journal of Chemical Physics

2017

Self Cite

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

“…Many authors have implemented basis pruning strategies [16,18,19,53,62,63,[70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86]. Although pruning has the obvious advantage that it decreases the size of the vectors one must store and the spectral range of the Hamiltonian matrix, if one uses an iterative method, it complicates the evaluation of MVPs.…”

Section: Using Pruning To Reduce Both Basis and Grid Sizementioning

confidence: 99%

Iterative Methods for Computing Vibrational Spectra

2018

Mathematics

Self Cite

I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate (F) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.