HESSEMAT: Difference between revisions

Latest revision as of 14:10, 17 October 2024

HESSEMAT defines the Hesse matrix in Cartesian coordinates ( ${\underline{𝐇}}^{𝐱}$ ) for the use in Thermodynamic integration with harmonic reference. For a system containing $N$ atoms, HESSEMAT has $(3 N + 1) (N + 1)$ lines. The first line specifies potential energy $V_{0, 𝐱} (𝐱_{0})$ (in eV) of the relaxed system for which ${\underline{𝐇}}^{𝐱}$ is computed. The following $3 N$ lines are reserved for positions in fractional coordinates of all atoms constituting the system, whereby each line should contain three components of position vector of a single atom. The remaining part of HESSEMAT consist of $3 N$ block of $N + 1$ lines each. Each block contains information related to a single eigenmode of ${\underline{𝐇}}^{𝐱}$ : the first line specified the eigenvalue (in eV/ $Å^{2}$ ) and remaining and $N$ lines the corresponding eigenvector (in Cartesian coordinates) in a 3-column format.

How to run thermodynamic integration calculations is given here.

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-{{FILE|HESSEMAT}}) defines the Hesse matrix in Cartesian coordinates for the use in  [[:Category:Thermodynamic integration with harmonic reference|Thermodynamic integration with harmonic reference]].
+{{FILE|HESSEMAT}} defines the Hesse matrix in Cartesian coordinates (<math>\underline{\mathbf{H}}^\mathbf{x}</math> ) for the use in  [[Thermodynamic integration#Thermodynamic integration with harmonic reference|Thermodynamic integration with harmonic reference]].
+For a system containing <math> N</math> atoms, {{FILE|HESSEMAT}} has <math>(3N+1)(N+1)</math> lines.
+The first line specifies potential energy <math>V_{0,\mathbf{x}}(\mathbf{x}_0)</math>  (in eV) of the relaxed system for which <math>\underline{\mathbf{H}}^\mathbf{x}</math> is computed.
+The following <math>3N</math> lines are reserved for positions in fractional coordinates of all atoms constituting the system, whereby each line should contain three components of position vector of a single atom. The remaining part of {{FILE|HESSEMAT}} consist of <math>3N</math> block of <math>N+1</math> lines each.
+Each block contains information related to a single eigenmode of <math>\underline{\mathbf{H}}^\mathbf{x}</math>: the first line specified the  eigenvalue (in eV/<math>{\AA}^2</math>) and remaining and <math>N</math> lines the corresponding eigenvector (in Cartesian coordinates) in a 3-column format.
+How to run thermodynamic integration calculations is given [[Thermodynamic integration calculations#Alternative way of thermodynamic integration for harmonic solid|here]].
+== Related tags and articles ==
+{{TAG|TILAMBDA}}, {{TAG|REPORT}}
+[[Category:Advanced molecular-dynamics sampling]][[Category:Files]]