Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions

2016

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We demonstrate that it is possible to use a variational method to compute 50 vibrational levels of ethylene oxide (a seven-atom molecule) with convergence errors less than 0.01 cm. This is done by beginning with a small basis and expanding it to include product basis functions that are deemed to be important. For ethylene oxide a basis with fewer than 3 × 10 functions is large enough. Because the resulting basis has no exploitable structure we use a mapping to evaluate the matrix-vector products required to use an iterative eigensolver. The expanded basis is compared to bases obtained from pre-determined pruning condition. Similar calculations are presented for molecules with 3, 4, 5, and 6 atoms. For the 6-atom molecule, CHCH, the required expanded basis has about 106 000 functions and is about an order of magnitude smaller than bases made with a pre-determined pruning condition.

Section: Introductionmentioning

confidence: 99%

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

Brown

2016

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“…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: 75%

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

Wodraszka

2017

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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

“…A pruned basis of products of PSL functions has also been used with an iterative eigensolver. 77,78 Because even the pruned PSL basis is large, it is essential to develop tools for efficiently evaluating MVPs. The cost of matrix-vector products depends on the size of the basis but also on the structure of the basis.…”

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

confidence: 99%

“…2,39,40,60,69-74 (2) has been used in some recent papers. [75][76][77][78][79][80][81] If the harmonic frequencies of all the coordinates are similar, then a product harmonic oscillator basis (HOB) can be effectively pruned by retaining only basis functions for which…”

Section: B Eigensolversmentioning

confidence: 99%

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

2017

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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