TY - JOUR
T1 - Accurate quantum dynamics calculations using symmetrized Gaussians on a doubly dense von Neumann lattice
AU - Halverson, Thomas
AU - Poirier, Bill
N1 - Funding Information:
This work was largely supported by a grant from The Robert A. Welch Foundation (D-1523). In addition, a CRIF MU instrumentation grant (CHE-0840493) from the National Science Foundation is acknowledged. We also gratefully acknowledge the following entities for providing access and technical support for their respective computing clusters: the Texas Tech University High Performance Computing Center, for use of the Hrothgar facility; NSF CHE-0840493 and the Texas Tech University Department of Chemistry and Biochemistry, for use of the Robinson cluster; Carlos Rosales-Fernandez and the Texas Advanced Computing Center, for use of the Lonestar facility.
PY - 2012/12/14
Y1 - 2012/12/14
N2 - In a series of earlier articles [B. Poirier, J. Theor. Comput. Chem. 2, 65 (2003);10.1142/S0219633603000380 B. Poirier and A. Salam, J. Chem. Phys. 121, 1690 (2004);10.1063/1.1767511 B. Poirier and A. Salam, J. Chem. Phys. 121, 1704 (2004)10.1063/1.1767512], a new method was introduced for performing exact quantum dynamics calculations. The method uses a "weylet" basis set (orthogonalized Weyl-Heisenberg wavelets) combined with phase space truncation, to defeat the exponential scaling of CPU effort with system dimensionality-the first method ever able to achieve this long-standing goal. Here, we develop another such method, which uses a much more convenient basis of momentum-symmetrized Gaussians. Despite being non-orthogonal, symmetrized Gaussians are collectively local, allowing for effective phase space truncation. A dimension-independent code for computing energy eigenstates of both coupled and uncoupled systems has been created, exploiting massively parallel algorithms. Results are presented for model isotropic uncoupled harmonic oscillators and coupled anharmonic oscillators up to 27 dimensions. These are compared with the previous weylet calculations (uncoupled harmonic oscillators up to 15 dimensions), and found to be essentially just as efficient. Coupled system results are also compared to corresponding exact results obtained using a harmonic oscillator basis, and also to approximate results obtained using first-order perturbation theory up to the maximum dimensionality for which the latter may be feasibly obtained (four dimensions).
AB - In a series of earlier articles [B. Poirier, J. Theor. Comput. Chem. 2, 65 (2003);10.1142/S0219633603000380 B. Poirier and A. Salam, J. Chem. Phys. 121, 1690 (2004);10.1063/1.1767511 B. Poirier and A. Salam, J. Chem. Phys. 121, 1704 (2004)10.1063/1.1767512], a new method was introduced for performing exact quantum dynamics calculations. The method uses a "weylet" basis set (orthogonalized Weyl-Heisenberg wavelets) combined with phase space truncation, to defeat the exponential scaling of CPU effort with system dimensionality-the first method ever able to achieve this long-standing goal. Here, we develop another such method, which uses a much more convenient basis of momentum-symmetrized Gaussians. Despite being non-orthogonal, symmetrized Gaussians are collectively local, allowing for effective phase space truncation. A dimension-independent code for computing energy eigenstates of both coupled and uncoupled systems has been created, exploiting massively parallel algorithms. Results are presented for model isotropic uncoupled harmonic oscillators and coupled anharmonic oscillators up to 27 dimensions. These are compared with the previous weylet calculations (uncoupled harmonic oscillators up to 15 dimensions), and found to be essentially just as efficient. Coupled system results are also compared to corresponding exact results obtained using a harmonic oscillator basis, and also to approximate results obtained using first-order perturbation theory up to the maximum dimensionality for which the latter may be feasibly obtained (four dimensions).
UR - http://www.scopus.com/inward/record.url?scp=84871240486&partnerID=8YFLogxK
U2 - 10.1063/1.4769402
DO - 10.1063/1.4769402
M3 - Article
C2 - 23248981
AN - SCOPUS:84871240486
SN - 0021-9606
VL - 137
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 22
M1 - 224101
ER -