Explicitly correlated potential energy surface of , including relativistic and adiabatic corrections

2006 ◽  
Vol 364 (1848) ◽  
pp. 2855-2876 ◽  
Author(s):  
Werner Kutzelnigg ◽  
Ralph Jaquet
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Relativistic Effects ◽  
Large Set ◽  
Excited Singlet ◽  
Correct Treatment ◽  
Nuclear Masses ◽  
Explicitly Correlated ◽  
State Potential

After a short historical account of the theory of the ion, two ab initio methods are reviewed that allow the computation of the ground-state potential energy surface (PES) of in the Born–Oppenheimer (BO) approximation, with microhartree or even sub-microhartree accuracy, namely the R12 method and the method of explicitly correlated Gaussians. The BO-PES is improved by the inclusion of relativistic effects and adiabatic corrections. It is discussed how non-adiabatic effects on rotation and vibration can be simulated by corrections to the moving nuclear masses. The importance of the appropriate analytic fit to the computed points of the PES for the subsequent computation of the rovibronic spectrum is addressed. Some recent extensions of the computed PES in the energy region above the barrier to linearity are reviewed. This involves a large set of input geometries and the correct treatment of the dissociation asymptotics, including the coupling with the first excited singlet state. Some comments on this state as well as on the lowest triplet state of are made. The paper ends with a few remarks on the ion .

Theoretical study of the Cl(2P) + SiH4 reaction: Global potential energy surface and product pair-correlated distributions. Comparison with experiment.

2021 ◽  
Author(s):  
J. Espinosa-Garcia ◽  
Jose Carlos Corchado
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Theoretical Study ◽  
Title Reaction ◽  
Comparison With Experiment ◽  
Explicitly Correlated ◽  
High Level ◽  
First Time ◽  
Product Pair

For the theoretical study of the title reaction, an analytical full-dimensional potential energy surface named PES-2021 was developed for the first time, by fitting high-level explicitly-correlated ab initio data. This...

scholarly journals Progress in calculating the potential energy surface of H 3 +

2012 ◽  
Vol 370 (1978) ◽  
pp. 5001-5013 ◽  
Author(s):  
Ludwik Adamowicz ◽  
Michele Pavanello
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Molecular Geometry ◽  
Computational Procedure ◽  
Energy Functional ◽  
Basis Functions ◽  
Vibrational States ◽  
Energy Gradient ◽  
Explicitly Correlated

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh–Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H rovibrational spectrum is reproduced at the 0.1 cm −1 accuracy level up to 16 600 cm −1 above the ground state.

Potential Energy Surfaces

1996 ◽  
Author(s):  
Tomas Baer ◽  
William L. Hase
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Potential Energy Surfaces ◽  
Energy Surface ◽  
Electronic States ◽  
Dissociation Energies ◽  
State Potential ◽  
Energy Surfaces

Properties of potential energy surfaces are integral to understanding the dynamics of unimolecular reactions. As discussed in chapter 2, the concept of a potential energy surface arises from the Born-Oppenheimer approximation, which separates electronic motion from vibrational/rotational motion. Potential energy surfaces are calculated by solving Eq. (2.3) in chapter 2 at fixed values for the nuclear coordinates R. Solving this equation gives electronic energies Eie(R) at the configuration R for the different electronic states of the molecule. Combining Eie(R) with the nuclear repulsive potential energy VNN(R) gives the potential energy surface Vi(R) for electronic state i (Hirst, 1985). Each state is identified by its spin angular momentum and orbital symmetry. Since the electronic density between nuclei is different for each electronic state, each state has its own equilibrium geometry, sets of vibrational frequencies, and bond dissociation energies. To illustrate this effect, vibrational frequencies for the ground singlet state (S0) and first excited singlet state (S1) of H2CO are compared in table 3.1. For a diatomic molecule, potential energy surfaces only depend on the internuclear separation, so that a potential energy curve results instead of a surface. Possible potential energy curves for a diatomic molecule are depicted in figure 3.1. Of particular interest in this figure are the different equilibrium bond lengths and dissociation energies for the different electronic states. The lowest potential curve is referred to as the ground electronic state potential. The primary focus of this chapter is the ground electronic state potential energy surface. In the last section potential energy surfaces are considered for excited electronic states. A unimolecular reactant molecule consisting of N atoms has a multidimensional potential energy surface which depends on 3N-6 independent coordinates. For the smallest nondiatomic reactant, a triatomic molecule, the potential energy surface is four-dimensional (three independent coordinates plus the energy). Since it is difficult, if not impossible, to visualize surfaces with more than three dimensions, methods are used to reduce the dimensionality of the problem in portraying surfaces. In a graphical representation of a surface the potential energy is depicted as a function of two coordinates with constraints placed on the remaining 3N-8 coordinates.

scholarly journals Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

RSC Advances ◽  
2018 ◽  
Vol 8 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Walter A. Rabanal-León ◽  
William Tiznado ◽  
Edison Osorio ◽  
Franklin Ferraro
Keyword(s):  
Genetic Algorithm ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Crucial Role ◽  
Energy Surface ◽  
Relativistic Effects ◽  
Spin Orbit ◽  
Adequate Treatment ◽  
Structural Assignment

Theoretical inclusion of relativistic effects (scalar and spin–orbit) play a crucial role to assure an adequate structural assignment on lead clusters.

Global analytical ab initio ground-state potential energy surface for the C(1D)+H2 reactive system

2014 ◽  
Vol 140 (23) ◽  
pp. 234301 ◽  
Author(s):  
Chunfang Zhang ◽  
Mingkai Fu ◽  
Zhitao Shen ◽  
Haitao Ma ◽  
Wensheng Bian
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Ground State ◽  
Energy Surface ◽  
Reactive System ◽  
State Potential

scholarly journals Ultrafast Evolution of the Excited-State Potential Energy Surface ofTiO2Single Crystals Induced by Carrier Cooling

2013 ◽  
Vol 110 (6) ◽  
Author(s):  
Elisabeth M. Bothschafter ◽  
Alexander Paarmann ◽  
Eeuwe S. Zijlstra ◽  
Nicholas Karpowicz ◽  
Martin E. Garcia ◽  
...  
Keyword(s):  
Excited State ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
State Potential
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