Sampling general distributions with quasi-regular grids: Application to the vibrational spectra calculations

Flynn, Shane W.; Mandelshtam, Vladimir A.

doi:10.1063/1.5134677

Cited by 6 publications

(19 citation statements)

References 28 publications

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“…We also refer the reader to our recent paper ( 24) where some of these grids were used to solve the Schrödinger equation with the 2D and 3D Morse potential, and the superiority of QRG was demonstrated.…”

Section: Uniform Quasi-randommentioning

confidence: 99%

“…To this end, in our recent paper 24 we introduced a new type of grid, a Quasi-Regular Grid (QRG), which seems to address all the concerns that exist in the quasi-random+rejection scheme. A QRG is obtained by treating the grid points as particles interacting via a shortrange pairwise energy functional.…”

Section: Introductionmentioning

confidence: 99%

“…Here, for the construction of a QRG we propose both an improved and simplified (compared to that in Ref. 24) solution based on the minimization of the energy functional, U(r (1)…”

Section: Introductionmentioning

confidence: 99%

“…not quite perfect) closed packed structure. Moreover, the lack of attractive terms in the energy functional (these terms were included in the original formulation 24 ) enormously simplifies the energy landscape that now has a small number of local minima which are all structurally equivalent. At the same time, the functional form of u ij is the key to maintaining the scaling law (2), i.e., defining the distance between the nearest neighbors in accordance with the local density of points P(r).…”

Section: Introductionmentioning

confidence: 99%

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Molecular spectra calculations using an optimized quasi-regular Gaussian basis and the collocation method

Flynn¹,

Mandelshtam²

2021

Preprint

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We revisit the collocation method of Manzhos and Carrington (J. Chem. Phys. 145, 224110, 2016) in which a distributed localized (e.g., Gaussian) basis is used to set up a generalized eigenvalue problem to compute the eigenenergies and eigenfunctions of a molecular vibrational Hamiltonian. Although the resulting linear algebra problem involves full matrices, the method provides a number of important advantages. Namely: (i) it is very simple both conceptually and numerically, (ii) it can be formulated using any set of internal molecular coordinates, (iii) it is flexible with respect to the choice of the basis, and (iv) it has the potential to significantly reduce the basis size through optimizing the placement and the shapes of the basis functions.In the present paper we explore the latter aspect of the method using the recently introduced, and here further improved, quasi-regular grids (QRGs). By computing the eigenenergies of the four-atom molecule of formaldehyde, we demonstrate that a QRG-based distributed Gaussian basis is superior to the previously used choices.

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Section: Uniform Quasi-randommentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Here, for the construction of a QRG we propose both an improved and simplified (compared to that in Ref. 24) solution based on the minimization of the energy functional, U(r (1)…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Molecular spectra calculations using an optimized quasi-regular Gaussian basis and the collocation method

Flynn¹,

Mandelshtam²

2021

Preprint

Self Cite

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show abstract

“…In all cases, the TDDS as well as its Shannon-entropy based modified form, were shown to provide accurate surfaces at much reduced computational cost 4, 5,10 . Similar approaches to obtain sample points have been developed by other investigators 11,12 .…”

Section: Si-2 Sampling Measures That Simplify the Computation Of E R{g β } (R) In Eq (8) Of The Papermentioning

confidence: 94%

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

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Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

Kumar

DeGregorio

Iyengar

2021

J. Chem. Theory Comput.

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We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree− Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graphtheoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree−Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

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Sampling general distributions with quasi-regular grids: Application to the vibrational spectra calculations

Cited by 6 publications

References 28 publications

Molecular spectra calculations using an optimized quasi-regular Gaussian basis and the collocation method

Molecular spectra calculations using an optimized quasi-regular Gaussian basis and the collocation method

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

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