HESSEMAT: Difference between revisions

Revision as of 11:38, 2 November 2023

HESSEMAT defines the Hesse matrix in Cartesian coordinates (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \underline{\mathbf{H}}^\mathbf{x}} ) for the use in Thermodynamic integration with harmonic reference. For a system containing Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): N atoms, HESSEMAT has Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle (3N+1)(N+1)} lines. The first line specifies potential energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle V_{0,\mathbf{x}}(\mathbf{x}_0)} (in eV) of the relaxed system for which Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \underline{\mathbf{H}}^\mathbf{x}} is computed. The following Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 3N 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 3N block of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle N+1} lines each. Each block contains information related to a single eigenmode of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \underline{\mathbf{H}}^\mathbf{x}} : the first line specified the eigenvalue (in eV/Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle {\AA}^2} ) and remaining and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): N lines the eigenvector (in Cartesian coordinates) in a 3-column format.

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 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/{\AA}<math>^2</math>) and remaining and <math>N</math> lines the eigenvector (in Cartesian coordinates) in a 3-column format.
+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 eigenvector (in Cartesian coordinates) in a 3-column format.