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

Ziegler, Benjamin; Rauhut, Guntram

doi:10.1063/1.4943985

Cited by 70 publications

(44 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…67 Many other methods require SoP Hamiltonians or are much more efficient if SoP Hamiltonians are utilized, 22,68,69 and there are many algorithms available to fit the Hamiltonian in a SoP form efficiently, notably potfit and variants thereof, 70-72 neural networks, 73,74 or some interpolation techniques. 75,76 Note, however, that pruned DVR bases do not require SoP Hamiltonians (to be precise: A SoP form of the potential) and we show that these bases can be very successfully pruned.…”

Section: Introductionmentioning

confidence: 81%

Efficient molecular quantum dynamics in coordinate and phase space using pruned bases

Larsson

Hartke

Tannor

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned time-dependent dynamics using phase-spacelocalized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. For the examples studied, coordinate-space localization is the most important factor for efficient pruning and the pruned dynamics is much faster than the unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.

show abstract

Section: Introductionmentioning

confidence: 81%

Efficient molecular quantum dynamics in coordinate and phase space using pruned bases

Larsson

Hartke

Tannor

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Those surfaces are normally fitted using an advanced interpolation technology such as the Shepard interpolation, 67 neural network approach, 68 high-order polynomial expansion scheme, 69 and high-dimensional model representation (HDMR) methods. [70][71][72] Generally speaking, those methods usually…”

Section: Hamiltonian In Orthogonal Polyspherical Coordinatesmentioning

confidence: 99%

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

show abstract

“…Numerous developments in quantum chemistry promise an economical and flexible, yet, accurate access to ab initio local PESs of polyatomic molecules [40][41][42][43][44][45][46][47][48], for which the design of global PESs would be too cumbersome and expensive. The MOLPRO software package [49] comprises a versatile and flexible computational environment for VSCF/VCI calculations.…”

Section: Introductionmentioning

confidence: 99%

On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations

et al. 2020

View full text Add to dashboard Cite

The key feature of matrix-isolation infrared (MI-IR) spectroscopy is the isolation of single guest molecules in a host system at cryogenic conditions. The matrix mostly hinders rotation of the guest molecule, providing access to pure vibrational features. Vibrational self-consistent field (VSCF) and configuration interaction computations (VCI) on ab initio multimode potential energy surfaces (PES) give rise to anharmonic vibrational spectra. In a single-sourced combination of these experimental and computational approaches, we have established an iterative spectroscopic characterization procedure. The present article reviews the scope of this procedure by highlighting the strengths and limitations based on the examples of water, carbon dioxide, methane, methanol, and fluoroethane. An assessment of setups for the construction of the multimode PES on the example of methanol demonstrates that CCSD(T)-F12 level of theory is preferable to compute (a) accurate vibrational frequencies and (b) equilibrium or vibrationally averaged structural parameters. Our procedure has allowed us to uniquely assign unknown or disputed bands and enabled us to clarify problematic spectral regions that are crowded with combination bands and overtones. Besides spectroscopic assignment, the excellent agreement between theory and experiment paves the way to tackle questions of rather fundamental nature as to whether or not matrix effects are systematic, and it shows the limits of conventional notations used by spectroscopists.

show abstract

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

Cited by 70 publications

References 52 publications

Efficient molecular quantum dynamics in coordinate and phase space using pruned bases

Efficient molecular quantum dynamics in coordinate and phase space using pruned bases

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations

Contact Info

Product

Resources

About