Related Experiment Video
Updated: Jun 27, 2026
14:14
Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models
Published on: August 12, 2018
Using neural networks, optimized coordinates, and high-dimensional model representations to obtain a vinyl bromide
Sergei Manzhos1, Tucker Carrington
1Département de chimie, Université de Montréal, Case postale 6128, succursale Centre-ville Montréal, (Québec) H3C 3J7 Canada. sergei.manzhos@gmail.com
The Journal of Chemical Physics
|December 17, 2008
Summary
High-dimensional model representations (HDMRs) combined with neural networks (NNs) efficiently generate accurate molecular potentials. Optimized redundant coordinates simplify complex potentials into a sum-of-products form, crucial for quantum dynamics calculations.
Area of Science:
- Computational Chemistry
- Quantum Mechanics
- Machine Learning
Background:
- Accurate potential energy surfaces are essential for simulating molecular dynamics.
- High-dimensional model representations (HDMRs) offer a way to approximate these surfaces.
- Traditional HDMR methods face challenges with the combinatorial explosion of terms in high dimensions.
Purpose of the Study:
- To develop an efficient method for constructing high-dimensional potential energy surfaces.
- To leverage neural networks (NNs) within the HDMR framework.
- To enable the representation of complex potentials in a form suitable for quantum dynamics.
Main Methods:
- Utilizing neural networks (NNs) to fit high-dimensional model representations (HDMRs).
- Employing optimized redundant coordinates to reduce the number of terms in the HDMR.
- Using exponential neurons to achieve a sum-of-products form for the potential.
- Fitting 12- and 15-dimensional potential surfaces for vinyl bromide.
Main Results:
- Demonstrated successful fitting of 12- and 15-dimensional potentials using NN-based HDMRs.
- Showed that redundant coordinates effectively bypass the combinatorial complexity of traditional methods.
- Achieved a sum-of-products potential representation comparable in quality to full-dimensional fits.
- Reduced computational cost by building the full surface from lower-dimensional (e.g., 6D) NN fits.
Conclusions:
- NN-based HDMRs provide an effective approach for generating accurate potential energy surfaces.
- The sum-of-products form obtained is highly beneficial for quantum dynamics simulations.
- Optimized redundant coordinates are key to managing the complexity of high-dimensional problems.
Related Concept Videos
02:06Newman Projections
Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.
02:18Fischer Projections
Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...
02:27Predicting Molecular Geometry
VSEPR Theory for Determination of Electron Pair Geometries
03:24Hybridization of Atomic Orbitals I
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
02:00Molecular Models
Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models makes it easier to visualize the structures and shapes of atoms and molecules.
02:42Valence Bond Theory
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...