Related Experiment Video
Updated: May 18, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
High-activity perturbation expansion for the hard square lattice gas
1Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India.
Abstract:
We study a system of particles with nearest- and next-nearest-neighbor exclusion on the square lattice (hard squares). This system undergoes a transition from a fluid phase at low density to a columnar-ordered phase at high density. We develop a systematic high-activity perturbation expansion for the free energy per site about a state with perfect columnar order. We show that the different terms of the series can be regrouped to get a Mayer-like series for a polydisperse system of interacting vertical rods in which the nth term is of order z(-(n+1)/2), where z is the fugacity associated with each particle. We sum this series to get the exact expansion to order 1/z(3/2).
Related Concept Videos
Trends in Lattice Energy: Ion Size and Charge
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Heat and Free Expansion
The Van der Waals Equation
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
Van der Waals Equation
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
