https://spindynamics.org/wiki/index.php?action=history&feed=atom&title=Cart2mode.m 2026-10-02T18:12:41Z Revision history for this page on the wiki MediaWiki 1.31.15 https://spindynamics.org/wiki/index.php?title=Cart2mode.m&diff=9873&oldid=prev 2026-08-06T04:38:02Z

<p>Document new Spinach 2.12 spin-boson functionality (PR 195)</p> <p><b>New page</b></p><div>{{DISPLAYTITLE:cart2mode.m}} __NOTOC__<br /> Converts Cartesian derivatives of spin Hamiltonian parameters, as produced by electronic structure theory packages, into the derivatives with respect to dimensionless mode coordinates that the bosonic mode specification interface of [[create.m]] expects in the inter.modes.coupling_mod and inter.modes.zeeman_mod fields. The dimensionless coordinate of each mode is (a+a')/sqrt(2), and the Cartesian displacement that it produces on a degree of freedom with mass m is scaled by sqrt(hbar/(m*omega)), where omega is the angular frequency of the mode. The function therefore contracts the Cartesian derivative array with the mass-weighted normal mode eigenvector and applies the zero-point displacement scaling.<br /> <br /> Both first and second derivatives are supported: the first order case describes a linear modulation of a spin interaction by a single mode, and the second order case describes the bilinear Raman-type modulation by a pair of modes, or the quadratic modulation by one mode when the same eigenvector is supplied twice.<br /> <br /> ==Syntax==<br /> <br /> mode_derivs=cart2mode(cart_derivs,eigvecs,masses,frqs)<br /> <br /> ==Parameters==<br /> <br /> cart_derivs - first derivatives of an interaction with<br /> respect to Cartesian displacements, in Hz<br /> per Angstrom, an array of dimension<br /> [d1 d2 3N] where N is the number of atoms<br /> and the Cartesian degrees of freedom are<br /> ordered [x1 y1 z1 x2 y2 z2 ...]; or second<br /> derivatives in Hz per Angstrom squared, an<br /> array of dimension [d1 d2 3N 3N]<br /> <br /> eigvecs - orthonormal mass-weighted normal mode<br /> eigenvector, a [3N 1] column vector for<br /> the first order case; two such vectors<br /> as a [3N 2] array for the second order<br /> case<br /> <br /> masses - atomic masses in unified atomic mass<br /> units, an [N 1] column vector<br /> <br /> frqs - mode frequency in Hz, a positive scalar<br /> for the first order case; a [1 2] vector<br /> for the second order case<br /> <br /> ==Outputs==<br /> <br /> mode_derivs - derivatives with respect to dimensionless<br /> mode coordinates, in Hz, a [d1 d2] array<br /> to be placed into the corresponding cell<br /> of inter.modes.coupling_mod (d1=3, d2=3)<br /> or inter.modes.zeeman_mod (d1=1, d2=3)<br /> <br /> ==Notes==<br /> <br /> # Raw Taylor derivatives are returned; the 1/2 factors of the Taylor expansion are applied by ''Spinach'' internally.<br /> # Derivative data in wavenumbers or meV should be converted into Hz with [[icm2hz.m]] or [[mev2hz.m]] beforehand.<br /> # Zero and negative frequency modes are rejected because their zero-point scaling is undefined.<br /> <br /> ==See also==<br /> [[create.m]], [[mev2hz.m]], [[icm2hz.m]], [[kelvin2hz.m]], [[hamiltonian.m]], [[Spin system specification]], [[Kernel utilities]]<br /> <br /> ''Version 2.12, authors: [[Ilya Kuprov]]''</div>

Kuprov