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Related Concept Videos

Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...
Atomic Orbitals02:44

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

Overview of Molecular Orbital Theory
Hybridization of Atomic Orbitals I03:24

Hybridization 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...
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Multi-Jastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo.

Thomas Bouabça1, Benoît Braïda, Michel Caffarel

  • 1Laboratoire de Chimie et Physique Quantiques, CNRS UMR5626-IRSAMC et Université de Toulouse, Toulouse Cedex 31000, France.

The Journal of Chemical Physics
|August 7, 2010
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Summary

Researchers developed a new electronic trial wavefunction for quantum Monte Carlo (QMC) calculations. This multi-Jastrow form improves accuracy in electronic correlation and nodal structure for QMC simulations.

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Area of Science:

  • Computational Chemistry
  • Quantum Monte Carlo Methods
  • Electronic Structure Theory

Background:

  • Standard Jastrow-Slater wavefunctions use a single global Jastrow term.
  • This global term limits the accurate description of diverse electronic correlations in molecular systems.
  • Improving nodal accuracy is crucial for reliable fixed-node diffusion Monte Carlo (FN-DMC) calculations.

Purpose of the Study:

  • To introduce a novel electronic trial wavefunction incorporating individual Jastrow factors for molecular orbitals.
  • To enhance the description of local electronic correlations in various molecular environments.
  • To improve the nodal structure for more accurate FN-DMC calculations and enable modular wavefunction construction.

Main Methods:

  • Development of a multi-Jastrow trial wavefunction with localized Jastrow factors attached to molecular orbitals.
  • Detailed presentation of computational methods for calculating derivatives of the multi-Jastrow function.
  • Application to atoms (O, S, Cu) and the FH molecule using Variational Monte Carlo (VMC) and FN-DMC.

Main Results:

  • Significant improvement in the ground-state energy of the copper atom using the multi-Jastrow form at the VMC level, capturing ~75% of the correlation energy.
  • The multi-Jastrow nodes for the FH molecule yielded a near-exact FN-DMC dissociation energy (D(0)=-140.7(4) kcal/mol), outperforming standard nodes (D(0)=-138.3(4) kcal/mol).
  • Demonstrated potential for defining and pre-optimizing local, transferable correlated units for complex wavefunction construction.

Conclusions:

  • The proposed multi-Jastrow wavefunction offers a more physically grounded and accurate approach for QMC calculations.
  • This method enhances the treatment of electronic correlations and nodal properties, leading to improved accuracy in molecular simulations.
  • The modular nature of local Jastrow terms facilitates the construction of sophisticated trial wavefunctions from simpler components.