Chemistry, Department of
http://hdl.handle.net/1974/767
2017-07-20T20:14:00ZSystematically Expanding Nondirect Product Bases Within the Pruned Multi-Configuration ime-dependent Hartree (MCTDH) Method: A Comparison With Multi-Layer MCTDH
http://hdl.handle.net/1974/15966
Systematically Expanding Nondirect Product Bases Within the Pruned Multi-Configuration ime-dependent Hartree (MCTDH) Method: A Comparison With Multi-Layer MCTDH
Wodraszka, Robert; Carrington, Tucker
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, CH3CN, 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.
2017-05-21T00:00:00ZAn Intertwined Method for Making Low-Rank, Sum-Of-Product Basis Functions that makes it Possible to Compute Vibrational Spectra of Molecules with more than 10 Atoms
http://hdl.handle.net/1974/15965
An Intertwined Method for Making Low-Rank, Sum-Of-Product Basis Functions that makes it Possible to Compute Vibrational Spectra of Molecules with more than 10 Atoms
Thomas, Phillip S.; Carrington, Tucker
We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (𝖢 𝟤 𝖧 𝟦 𝖮)
(C2H4O)
and cyclopentadiene (𝖢 𝟧 𝖧 𝟨 )
(C5H6)
, with 7 and 11 atoms, respectively.
2017-05-31T00:00:00ZPerspective: Computing (ro-)Vibrational Spectra of Molecules With More Than Four Atoms
http://hdl.handle.net/1974/15964
Perspective: Computing (ro-)Vibrational Spectra of Molecules With More Than Four Atoms
Carrington, Tucker
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
2017-03-31T00:00:00ZUsing Monomer Vibrational Wavefunctions as Contracted Basis Functions to Compute Rovibrational Levels of an H2O-Atom Complex in Full Dimensionality
http://hdl.handle.net/1974/15963
Using Monomer Vibrational Wavefunctions as Contracted Basis Functions to Compute Rovibrational Levels of an H2O-Atom Complex in Full Dimensionality
Wang, Xiao-Gang; Carrington, Tucker
In this paper, we present new ideas for computing rovibrational energy levels of molecules composed of two components and apply them to H2O–Cl−. When both components are themselves molecules, Euler angles that specify their orientation with respect to an axis system attached to the inter-monomer vector are used as vibrational coordinates. For H2O–Cl−, there is only one set of Euler angles. Using Euler angles as intermolecular vibrational coordinates is advantageous because in many cases coupling between them and coordinates that describe the shape of the monomers is unimportant. The monomers are not assumed to be rigid. In the most efficient calculation, vibrational wavefunctions of the monomers are used as contracted basis functions. Energy levels are calculated using the Lanczos algorithm.
2017-03-31T00:00:00Z