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Ionization Energy03:12

Ionization Energy

44.9K
The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy (IE1). The first ionization energy for an element, X, is the energy required to form a cation with 1+ charge:
44.9K
Ionic Radii03:10

Ionic Radii

35.0K
Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it is smaller than the atom from which it is derived. For example, the covalent radius of an aluminum atom (1s22s22p63s23p1) is 118 pm, whereas the ionic radius of an Al3+ (1s22s22p6) is 68 pm. As electrons are removed from the outer valence shell, the remaining core electrons occupying smaller shells experience a greater effective nuclear...
35.0K
Factors Affecting Activity Coefficient01:17

Factors Affecting Activity Coefficient

1.8K
The extended Debye-Hückel equation indicates that the activity coefficient of an ion in an aqueous solution at 25°C depends on three partially interdependent properties: the ionic strength of the solution, the charge of the ion, and the ion size. 
The activity coefficient value for an ion is close to one when the solution has almost zero ionic strength, i.e., when the solution shows close to ideal behavior. As the ionic strength of the solution increases from 0 to 0.1 mol/L, a...
1.8K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

27.6K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
27.6K
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

31.3K
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.
31.3K
Atomic Radii and Effective Nuclear Charge03:08

Atomic Radii and Effective Nuclear Charge

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The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.
64.0K

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Related Experiment Video

Updated: Apr 12, 2026

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
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Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

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Density-functional errors in ionization potential with increasing system size.

Sarah R Whittleton1, Xochitl A Sosa Vazquez1, Christine M Isborn1

  • 1Chemistry and Chemical Biology, School of Natural Sciences, University of California, Merced, 5200 North Lake Road, Merced, California 95343, USA.

The Journal of Chemical Physics
|May 17, 2015
PubMed
Summary

Density-functional approximations often underestimate ionization potentials for larger hydrocarbons due to delocalization error. Accuracy does not reliably transfer from small to large molecules, even with functional tuning.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Density-functional theory (DFT) is widely used for electronic structure calculations.
  • Accurate prediction of ionization potentials (IPs) is crucial for understanding molecular behavior.
  • Systematic errors in DFT can arise from approximations, particularly with increasing molecular size.

Purpose of the Study:

  • To investigate the impact of molecular size on the accuracy of DFT-calculated ionization potentials.
  • To analyze the role of delocalization error in IP underestimation for hydrocarbons.
  • To evaluate the effectiveness of computational strategies in mitigating these errors.

Main Methods:

  • Calculated ionization potentials for 28 hydrocarbons (alkanes, alkenes, oligoacenes) using various DFT approximations.
  • Analyzed the relationship between molecular size and IP accuracy.
  • Investigated the influence of delocalization error and fractional-charge behavior.
  • Assessed the impact of including exact exchange and tuning long-range corrected functionals.

Main Results:

  • A systematic underestimation of ionization potentials was observed as molecular size increased.
  • Delocalization error was identified as the primary cause for IP underestimation in larger systems.
  • Many DFT approximations exhibited non-size-extensive behavior for IP computation.
  • Inclusion of exact exchange reduced errors, but functional tuning did not consistently improve accuracy.

Conclusions:

  • The accuracy of DFT functionals for ionization potentials is highly dependent on molecular size.
  • Delocalization error poses a significant challenge for accurate IP prediction in larger molecular systems.
  • Performance of a DFT functional on small molecules does not guarantee its reliability for larger systems.