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Related Concept Videos

Electron Configurations02:46

Electron Configurations

Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p, 4s,...
The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...
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...
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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.
The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Extrapolating to the one-electron basis-set limit in electronic structure calculations.

A J C Varandas1

  • 1Departamento de Química, Universidade de Coimbra, 3004-535 Coimbra, Portugal. varandas@qtvs1.qui.uc.pt

The Journal of Chemical Physics
|July 7, 2007
PubMed
Summary

A new dual-level method accurately extrapolates atomic and molecular electron correlation energies to the complete basis set limit. This approach improves upon existing methods for calculating energies in quantum chemistry.

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Physics

Background:

  • Accurate calculation of electron correlation energies is crucial for predicting molecular properties.
  • Extrapolation to the infinite basis set limit is necessary to remove basis set incompleteness errors.
  • Existing extrapolation schemes can be computationally expensive or less accurate.

Purpose of the Study:

  • To develop and validate a simple, reliable dual-level extrapolation scheme for electron correlation energies.
  • To apply the method to both single-reference and multireference electronic structure calculations.
  • To compare the new method's performance against established extrapolation techniques.

Main Methods:

  • A novel dual-level extrapolation method treating singlet-pair and triplet-pair interactions uniformly.
  • Application to coupled-cluster singles and doubles (CCSD) energies using correlation-consistent basis sets (cc-pVXZ).
  • Extension to multireference configuration interaction (MRCI) calculations using augmented correlation-consistent basis sets (aug-cc-pVXZ).

Main Results:

  • The proposed dual-level method shows comparable or superior accuracy to existing methods for CCSD energies.
  • The method effectively extrapolates dynamical correlation in MRCI calculations, even without benchmark data.
  • A pragmatic extrapolation rule for Hartree-Fock and complete-active space self-consistent field (CASSCF) energies also performs well.

Conclusions:

  • The new dual-level extrapolation scheme offers a reliable and efficient way to obtain basis set limit energies.
  • This method is applicable to a wide range of quantum chemical calculations, including single- and multireference methods.
  • The findings provide a valuable tool for improving the accuracy of theoretical predictions in atomic and molecular science.