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 Title: A VARIATIONAL METHOD FOR COMPUTING VIBRATIONAL SPECTRA OF MOLECULES WITH UP TO 18 ATOMS Author(s): Carrington, Tucker Contributor(s): Thomas, Phillip Subject(s): Mini-symposium: New Ways of Understanding Molecular Spectra Abstract: I shall present an improvement and applications of the Hierarchical Intertwined Reduced-Rank Block Power Method (J. Chem. Phys, 146, 204110 (2017)) for solving the vibrational Schroedinger equation. The improvement decreases the memory required to compute a spectrum. Variational calculations for molecules with a dozen atoms are now possible on a desktop computer. The memory cost scales linearly with the number of atoms in the molecule. We apply the HI-RRBPM to compute vibrational spectra of uracil and naphthalene, with 12 and 18 atoms, respectively. The HI-RRBPM uses a direct product basis but: 1) it is not necessary to store a direct-product-basis matrix representation of the Hamiltonian matrix (for naphthalene the size of the matrix would be $\sim 10^{48}$); 2) it is not necessary to store vectors whose length is equal to the size of the direct-product basis. This is accomplished by using sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. The number of terms in the SOP basis functions is minimized by optimising the factors. Representing vibrational wavefunctions as optimised SOPs reveals the essential entangledness and provides new understanding. The method only works if the Hamiltonian is itself a SOP. Issue Date: 06/18/18 Publisher: International Symposium on Molecular Spectroscopy Citation Info: APS Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/100803 DOI: 10.15278/isms.2018.MH03 Other Identifier(s): MH03 Date Available in IDEALS: 2018-08-172018-12-12
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