A hierarchy of potential energy surfaces constructed from energies and energy derivatives calculated on grids

Matito, Eduard
Toffolı, Danıele
Christiansen, Ove
In this work we develop and test a methodology for the generation of Born-Oppenheimer potential energy surfaces (PES) for use in vibrational structure calculations. The method relies on the widely used restricted-mode-coupling expansion of the fully coupled potential surface where only up to n or less vibrational coordinates are coupled in the potential. Low-order derivatives of the energy are then used to extrapolate the higher mode-coupling potential terms; derivative information is thus used in a convenient way for the evaluation of higher mode couplings avoiding their explicit calculation on multidimensional grids. The formulation, which is a variant of the popular modified Shepard interpolation, is general for any extrapolation of (n+p)-mode-coupling terms from n-mode couplings and can be applied to the energy or any other molecular property surface for which derivative information is available. The method depends only on analytical parameter-free weight functions that satisfy important limiting conditions and control the contribution from each direction of extrapolation. The procedure has been applied on a representative set of 13 molecules, and its accuracy has been tested using only gradients and using both gradients and Hessians. The results provide evidence for the importance of higher mode couplings and illustrate the cost efficiency of the proposed approach.


YURTSEVER, E (Walter de Gruyter GmbH, 1988-08-01)
Different variational schemes for solving the Schrodinger equation are tested for the model potential of Kratzer-Fues. Wavefunctions are analyzed in terms of their global (expectation values) and local properties which are expressed as functions of coordinates. The Rayleigh-Ritz variation almost uniformly produces the most accurate expectation values. However the point properties show qualitatively different behaviour for different regions of the coordinate space. To define the local quality, a set of crite...
Vibrational spectroscopy of hydrogen-bonded systems: Six-dimensional simulation of the IR spectrum of F-(H2O) complex
Toffolı, Danıele; Sparta, Manuel; Christiansen, Ove (Elsevier BV, 2011-06-24)
The vibrational dynamics of the F-(H2O) complex is studied using highly accurate six-dimensional molecular potential energy and dipole moment surfaces calculated at the CCSD (T)/cc-pVQZ and CCSD (T)/augcc-pVTZ levels with a multiresolution approach. The extent of mode-coupling is investigated with full vibrational configuration-interaction (FVCI) calculations. Coriolis coupling effects are also included with the aim to obtain quantitative agreement with the experimental data available. The vibrational absor...
Structural and electronic properties of ZnmCdn microclusters: density functional theory calculations
Erkoç, Şakir (Elsevier BV, 2003-02-28)
The structural and electronic properties of isolated neutral ZnmCdn clusters for m + n less than or equal to 3 have been investigated by performing density functional theory calculations at B3LYP level. The optimum geometries, vibrational frequencies, electronic structures, and the possible dissociation channels of the clusters considered have been obtained.
Potential Energy Surfaces for Vibrational Structure Calculations from a Multiresolution Adaptive Density-Guided Approach: Implementation and Test Calculations
Sparta, Manuel; Hoyvik, Ida-Marie; Toffolı, Danıele; Christiansen, Ove (American Chemical Society (ACS), 2009-07-30)
A multiresolution procedure to construct potential energy surfaces (PESs) for use in vibrational structure calculations is developed in the framework of the adaptive density-guided approach. The implementation of the method allows the construction of hybrid PESs with different mode-coupling terms calculated with a variety of combinations of electronic structure methods and basis sets. Furthermore, the procedure allows the construction of hybrid PESs that incorporate a variety of contributions and correction...
A Numerical Study of a Modular Sparse Grad-Div Stabilization Method for Boussinesq Equations
Demir, Medine; Kaya Merdan, Songül (2019-10-10)
This study presents a modular sparse grad-div stabilization method for solving the Boussinesq equations. Unlike the usual grad-div stabilization which produces fully coupled block matrices, the proposed stabilization method produces block upper triangular matrices. Thus, the proposed method is more attractive in terms of both its computational cost and solution accuracy. We provide unconditional stability results for velocity and temperature. Two numerical experiments are performed to demonstrate the effici...
Citation Formats
E. Matito, D. Toffolı, and O. Christiansen, “A hierarchy of potential energy surfaces constructed from energies and energy derivatives calculated on grids,” JOURNAL OF CHEMICAL PHYSICS, pp. 0–0, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56534.