• Corpus ID: 202578095

Scalable approximation of Green's function for estimation of anharmonic energy corrections

  title={Scalable approximation of Green's function for estimation of anharmonic energy corrections},
  author={Prashant Rai and Khachik Sargsyan and Habib N. Najm and So Hirata},
  journal={arXiv: Chemical Physics},
A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck in extending this approach to bigger molecules is that the storage of the Green's function scales exponentially with the number of atoms in the molecule. In this article, we present a method that overcomes this limitation by approximating the Green's function… 



Stochastic many-body perturbation theory for anharmonic molecular vibrations.

A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation

Variational quantum approaches for computing vibrational energies of polyatomic molecules

In this article, we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of

Multiresolution potential energy surfaces for vibrational state calculations

A compact and robust many-mode expansion of potential energy surfaces (PES) is presented for anharmonic vibrations of polyatomic molecules, where the individual many-mode terms are approximated with

Permutationally invariant potential energy surfaces in high dimensionality

We review recent progress in developing potential energy and dipole moment surfaces for polyatomic systems with up to 10 atoms. The emphasis is on global linear least squares fitting of tens of

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

ABSTRACT A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions.

A simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products to show the same scalings in computational cost and memory requirements as the potfit approach.

Second-order many-body perturbation expansions of vibrational Dyson self-energies.

Second-order many-body perturbation theories for anharmonic vibrational frequencies and zero-point energies of molecules are formulated, implemented, and tested and the rules for enumerating and algebraically interpreting energy and self-energy diagrams are elucidated in detail.

Multi-layer Potfit: an accurate potential representation for efficient high-dimensional quantum dynamics.

  • F. Otto
  • Computer Science
    The Journal of chemical physics
  • 2014
Multi-layer Potfit (MLPF), a novel fitting scheme that results in a PES representation in the hierarchical tensor (HT) format, based on the hierarchical singular value decomposition, which can yield a near-optimal fit and give strict bounds for the obtained accuracy.

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

A method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing to suggest a more efficient scaling of computational cost with molecular size as compared to other methods.