A ground state potential energy surface for HONO based on a neural network with exponential fitting functions

2017 ◽  
Vol 19 (33) ◽  
pp. 22272-22281 ◽  
Author(s):  
Ekadashi Pradhan ◽  
Alex Brown
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Energy Surface ◽  
Exponential Fitting ◽  
Sum Of Products ◽  
State Potential ◽  
Vibrational Energies ◽  
Energy Surfaces

Using CCSD(T)-F12/cc-pVTZ-F12 and CCSD(T)/CBS ab initio energies, two different six-dimensional ground state potential energy surfaces for HONO have been fit in sum-of-products form using neural network exponential fitting functions and tested by computing vibrational energies with MCTDH.

scholarly journals Ground state potential energy surfaces around selected atoms from resonant inelastic x-ray scattering

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Simon Schreck ◽  
Annette Pietzsch ◽  
Brian Kennedy ◽  
Conny Såthe ◽  
Piter S. Miedema ◽  
...  
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Energy Surface ◽  
X Ray ◽  
X Ray Scattering ◽  
State Potential ◽  
Energy Surfaces ◽  
Ray Scattering

Abstract Thermally driven chemistry as well as materials’ functionality are determined by the potential energy surface of a systems electronic ground state. This makes the potential energy surface a central and powerful concept in physics, chemistry and materials science. However, direct experimental access to the potential energy surface locally around atomic centers and to its long-range structure are lacking. Here we demonstrate how sub-natural linewidth resonant inelastic soft x-ray scattering at vibrational resolution is utilized to determine ground state potential energy surfaces locally and detect long-range changes of the potentials that are driven by local modifications. We show how the general concept is applicable not only to small isolated molecules such as O2 but also to strongly interacting systems such as the hydrogen bond network in liquid water. The weak perturbation to the potential energy surface through hydrogen bonding is observed as a trend towards softening of the ground state potential around the coordinating atom. The instrumental developments in high resolution resonant inelastic soft x-ray scattering are currently accelerating and will enable broad application of the presented approach. With this multidimensional potential energy surfaces that characterize collective phenomena such as (bio)molecular function or high-temperature superconductivity will become accessible in near future.

scholarly journals Hybrid Quantum-Classical Neural Network for Calculating Ground State Energies of Molecules

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 828
Author(s):  
Rongxin Xia ◽  
Sabre Kais
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Potential Energy Curves ◽  
The Neural Network ◽  
State Potential ◽  
Molecular Potential Energy ◽  
Simple Molecules ◽  
Energy Surfaces

We present a hybrid quantum-classical neural network that can be trained to perform electronic structure calculation and generate potential energy curves of simple molecules. The method is based on the combination of parameterized quantum circuits and measurements. With unsupervised training, the neural network can generate electronic potential energy curves based on training at certain bond lengths. To demonstrate the power of the proposed new method, we present the results of using the quantum-classical hybrid neural network to calculate ground state potential energy curves of simple molecules such as H2, LiH, and BeH2. The results are very accurate and the approach could potentially be used to generate complex molecular potential energy surfaces.

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.

Triplet and ground state potential energy surfaces of 1,4-diphenyl-1,3-butadiene: theory and experiment

2008 ◽  
Vol 7 (5) ◽  
pp. 566 ◽  
Author(s):  
J. Saltiel ◽  
O. Dmitrenko ◽  
Z. S. Pillai ◽  
R. Klima ◽  
S. Wang ◽  
...  
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
State Potential ◽  
Energy Surfaces ◽  
Theory And Experiment

Fitting potential energy surfaces to sum-of-products form with neural networks using exponential neurons

2017 ◽  
Vol 16 (05) ◽  
pp. 1730001 ◽  
Author(s):  
Alex Brown ◽  
E. Pradhan
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Ab Initio ◽  
Potential Energy Surfaces ◽  
Quantum Dynamics ◽  
The Neural Network ◽  
Sum Of Products ◽  
High Level ◽  
Energy Surfaces ◽  
Dynamics Problems

In this paper, the use of the neural network (NN) method with exponential neurons for directly fitting ab initio data to generate potential energy surfaces (PESs) in sum-of-product form will be discussed. The utility of the approach will be highlighted using fits of CS2, HFCO, and HONO ground state PESs based upon high-level ab initio data. Using a generic interface between the neural network PES fitting, which is performed in MATLAB, and the Heidelberg multi-configuration time-dependent Hartree (MCTDH) software package, the PESs have been tested via comparison of vibrational energies to experimental measurements. The review demonstrates the potential of the PES fitting method, combined with MCTDH, to tackle high-dimensional quantum dynamics problems.

scholarly journals Erratum: Ground state potential energy surfaces around selected atoms from resonant inelastic x-ray scattering

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Simon Schreck ◽  
Annette Pietzsch ◽  
Brian Kennedy ◽  
Conny Såthe ◽  
Piter S. Miedema ◽  
...  
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
X Ray ◽  
X Ray Scattering ◽  
State Potential ◽  
Energy Surfaces ◽  
Ray Scattering

Theoretical insight into the C–H and C–C scission mechanism of ethane on a tetrahedral Pt4subnanocluster

RSC Advances ◽  
2015 ◽  
Vol 5 (51) ◽  
pp. 40978-40988 ◽  
Author(s):  
Hong-Quan Fu ◽  
Ben-Fang Su ◽  
Hua-Qing Yang ◽  
Chang-Wei Hu
Keyword(s):  
Excited State ◽  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Activation Mechanism ◽  
First Excited State ◽  
State Potential ◽  
Energy Surfaces ◽  
Theoretical Insight ◽  
Insight Into

The activation mechanism of C2H6on a Pt4cluster has been theoretically investigated in the ground state and the first excited state potential energy surfaces at the BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level.

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