Reference.Variables.hamilt.pot

Variable "hamilt.pot" in the Matlab/Octave version of WavePacket

WavePacket comes with a small library of potential energy functions, many of which are for very special purposes; in case of doubt, you can look into their classdef files, where some easily accessible additional information should wait for the patient reader. You can find the complete list by looking into the corresponding package folder.

What we consider to be the more general classdef's are described below. Some of the potentials are restricted to special setups, these restrictions are also pointed out.

pot.chain	Chain of harmonic oscillators (model for phonons in 1D), for details see here. Also for coupled electrons and phonons with tuning (χ,ρ,σ) and coupling (τ) mechanisms, for details see here	default
oNN	harmonic frequency ω: nearest neighbors	0
oPR	harmonic frequency ν: position restraints	0
oCM	harmonic frequency Ω: center-of-mass restraint	0
r_e	equilibrium distance	0
pbc	toggle periodic boundary conditions	false
off	vertical energy offset	0
chi	electron-phonon-tuning χ: localized	0
rho	electron-phonon-tuning ρ: non-symmetric	0
sig	electron-phonon-tuning σ: symmetrized	0
tau	electron-phonon-coupling τ: pair distance	0

pot.con_int	Generic conical intersections in two dimensions, for details see here. Requires two coupled channels, and a two-dimensional grid.	default
omega	Quadratic force constant (ω)	1
kappa	Linear Jahn-Teller coupling parameter (κ)	1
gamma	Quadratic Jahn-Teller coupling parameter (γ)	0
delta	Energy gap parameter (δ); for 1D models only!	0
x_ci	x-shift of conical intersection	0
y_ci	y-shift of conical intersection	0

pot.henon	Henon-Heiles system in two dimensions. Requires a single channel, and a two-dimensional grid.
A	Quadratic force constant
L	Cubic parameter

pot.interp	Interpolates the potential from an input file. See here for details about file names and format	default
pos_conv	Conversion factor to apply to coordinates. The values in the file are given in units of pos_conv Bohr radii	1
pot_conv	Conversion factor for the potential. The values in the file are given in units of pot_conv Hartree	1
method	Method to use for interpolation. See the Matlab/Octave function interp1() for a list of valid methods	"spline"
n_pts	Array that gives the number of points in the file along each degree of freedom. Can be ignored for one-dimensional data

pot.leps	London-Eyring-Polanyi-Sato surface (essentially a superposition of diatomic Morse potentials) for a triatomic system ABC in bond length coordinates. Requires 2 degrees of freedom and a single channel. The potential assumes that the first degree of freedom is the AB distance and the second the BC distance. Most parameters are arrays that give the values (in this order) of the AB, BC, and AC bond.
ang	The fixed bending angle between AB and BC.
d_e	Array of the dissociation energies.
r_e	Array of the equilibrium distances.
alf	Array of the range parameters.
s_p	Array of the Sato parameters.

pot.morse	Superposition of Morse potentials. This potential supports any number of dimensions and (coupled) channels. Unless otherwise noted, each parameter must be given as a matrix, where the element (k,m) gives the parameter for the m-th channel and along the k-th degree of freedom.	default
d_e	Matrix of dissociation energies
r_e	Matrix of equilibrium distances	0
alf	Matrix of range parameters.
t_e	Array whose m-th element gives the constant energy offset for the minimum of the potential on the m-th channel	0

pot.pendulum	Orienting/aligning potential for generalized pendula which conditionally permits a certain number of exact energies and wavefunctions, for details see 2014 or 2015 or 2017 work by B. Schmidt and B. Friedrich	default
xi	csc² term (ξ)	0
chi	cot × csc term (χ)	0
eta	Orientation (−η)	0
zeta	Alignment (−ζ)	0
v_0	Energy shift (V0)	0
omg	Harmonic oscillators, scalar or row of length 2	n.a.

Note that one or two harmonic oscillator potentials are optionally added to the pendular potential when simulating in 2 or 3 dimensions, respectively.

pot.razavy	Razavy's symmetric double well potential (single Schrödinger equations, one-dimensional grid) which conditionally permits a certain number of exact energies and wavefunctions, for details see here or there.
modified	default is "false"
s	strength parameter (if modified=false)
n	magic number: if integer, then n analytic solutions exist (if modified=false)
eta	η parameter (if modified=true)
zeta	ζ parameter (if modified=true)

pot.single	Single crossing (two coupled Schrödinger equations and a one-dimensional grid): a hyperbolic potential and a harmonic potential with constant diabatic coupling, for details see here.	default
A	Prefactor of the hyperbolic potential	1
B	Force constant of the harmonic excited state	1
C	Strength of the diabatic coupling between the two states	0.1

pot.dual	Dual crossing (two coupled Schrödinger equations and a one-dimensional grid): a constant potential and a harmonic potential with constant diabatic coupling, for details see here.	default
A	Constant potential	1
B	Prefactor of parabola	1
C	Strength of the diabatic coupling between the two states	0.1

pot.taylor	Taylor series expansion of potential. Works for coupled channels and multidimensional grids	default
hshift	Horizontal shift: reference position for Taylor expansion A vector containing the values for each degree of freedom	empty
vshift	Vertical shift: constant energy offset	0
coeffs	Taylor series coefficients (i.e. derivatives) have to be given as a matrix. The number of rows gives the order after which the Taylor series is truncated. The number of columns must equal the number of dimensions of the grid.	empty

pot.tully1	Tully's single crossing example, for details see here and J. C. Tully's original work. Requires two coupled channels, and a one-dimensional grid.	default
A	Tully parameter A	0.01
B	Tully parameter B	1.6
C	Tully parameter C	0.005
D	Tully parameter D	1

pot.tully2	Tully's double crossing example, for details see here and J. C. Tully's original work. Requires two coupled channels, and a one-dimensional grid.	default
A	Tully parameter A	0.10
B	Tully parameter B	0.28
C	Tully parameter C	0.015
D	Tully parameter D	0.06
E	Tully parameter E	0.05

pot.tully3	Tully's extended crossing example, for details see here and J. C. Tully's original work. Requires two coupled channels, and a one-dimensional grid.	default
A	Tully parameter A	0.0006
B	Tully parameter B	0.10
C	Tully parameter C	0.90

pot.vibronic	Vibronic coupling for a one-dimensional crystal (i.e. a chain with periodic boundaries) or, equivalently, for a regular polygon-shaped molecule (C_n symmetry) , for details see here and there. For N coupled channels, and an N-dimensional grid. Restriction to lower dimensionality also possible	default
N	Number of electronic sites	3
U	Electronic site energy	0
W	Electronic coupling strength
O	Harmonic frequency (omega) of one particle
S	Selection of phonons	1:N
K	Linear electron-phonon coupling strength (Jahn-Teller)	0
L	Linear electron-phonon coupling strength (Pseudo-Jahn-Teller)	0