ENDyne

ENDyne is defined as an extension of Python, which means that you can start the python interpreter and load ENDyne to make the ENDyne commands and data available in the interactive session or Python script. A session looks like:

edsparc% python
Python 2.0 (#3, Sep  3 2001, 11:50:37) [C] on sunos5
Type "copyright", "credits" or "license" for more information.
>>> import endyne
>>> endyne.version()
(5, 'A', 3, 1, 6, 'generic', 'Tue Jul 30 12:52:28 EDT 2002')
>>> 
		

edsparc% endyne test.inp
ENDyne version 5.A.3.1 test.inp

                             *****************
                             *  E N D y n e  *
                             *****************

                   Executable version  5 alpha development phase  3
                           Restart file format  6

		

edsparc% endyne test.rsl
ENDyne version 5.A.3.1 test.rsl
RSL file test.rsl opened with the command:
    rslfile = RSLopen('test.rsl','r')
Recorded state log (RSL) file
 name:    test.rsl
 mode:    r
 format:   6
 version:      5.0603
 begin:    0.0E+0 1
 end:      0.1 29
 current:  0.0E+0 -1
 records:  11
 flags:   ownself       T
          seekdone      T
          readonly      T
          flushbuf      F
          isopen        T
          rstisopen     F

endyne>>> 
		

endyne>>> print thing.__doc__
		

To allow application to negative ions, the algorithm allows putting too many elecrons on a center, after all centers are chemically neutral.

Version 5 uses an internal mechanism to store the last known good state in RAM. This method is more flexible and requires little or no user intervention. It works effectively with the Hindmarsh-Gear LUSEHG=T and Shampine-Gordon LUSESG=T methods. Because the Bulirsch-Stoer LUSEBS=T method does not step forward uniformly, the RAM backstep method is really equivalent to the old RSL method.

The use of the parameter RCNDLM is much more sensitive in the new algorithm. Therefore users who have set this parameter, should remove it from their input files to ensure the use of the default. A new parameter RCNDAC has been introduced, giving the relative accuracy of the condition number returned by LAPACK routines. The version 2 algorithm considered a new state bad if

When both target and projectile are atoms, there are three relative coordinates:
1) b: the impact parameter along the b axis,
2) z: the initial projectile distance along the beam axis,
3) phi: the angle defining the b-axis beam-axis plane around the beam axis.
For the most general case of two molecules, there are nine relative coordinates: b, z, phi as in the atom-atom case, plus:
4) alpha: azimuth for the projectile axis,
5) beta: azimuth for the target axis,
6) gamma: dihedral angle between the projectile axis and target axis,
7) chi: dihedral angle between the b-axis and beam-axis plane, and the projectile axis,
8) delta: projectile spin angle around the projectile axis,
9) epsilon: target spin angle around the target axis.

There are 6 distinct types with increasing number of relative coordinates.
39 The case of an atom and an atom has just three: b, z, phi.
59 The case of an atom and a diatomic molecule has five: b, z, phi, beta, chi.
69 The case of an atom and a polyatomic has six: b, z, phi, beta, chi, epsilon.
79 The case of two diatomic molecules has seven: b, z, phi, alpha, beta, gamma, chi.
89 The case of a diatomic molecule and a polyatomic has eight: b, z, phi, alpha, beta, gamma, chi, epsilon.
99 The case of two polyatomics has all nine: b, z, phi, alpha, beta, gamma, chi, delta, epsilon.

The program does not care whether the first cluster is the projectile or the target, hence to scatter a polyatomic on an atom, designate the atom as fragment 1 and target and the polyatomic as fragment 2 and projectile and use type 69.

Wave function with free electrons can be used to describe such processes as electron scattering on atoms and molecules;ionization of atoms and molecules during colissions and reactive processes; and recombination of ions with free electrons.

The use of the much more stringent backstep algorithm implemented in version 5 is essential for wave functions with free electrons, as the numerical integrator can produce nonsense much more easily than for wave functions with only atomic centers.

The use of coordinates for the center of free moving centers of basis functions introduces a duplication with the basis functions exapansion coefficients. To obtain a singularity free coordinate system for the phase space it is essential to perform a transformation. A new way to solve the dynamical equations has been implemented which constructs the complete symplectic form. The TDVP equations were solved by substitution in version 2, to save the space for the full symplectic form. However, the transformation is only meaningful on the entire symplectic form. The solution method with the full symplectic form is used when LUSPFM=T, and the singularity removing transformation is applied when LUSPTR=T. The Hamiltonian equation is solved with a general linear eqaution solver by default; with LUSPVD=T the equation is solved by singular value decomposition.

By turning on tracing LTRACE=T and LTRSPD=T detailed information about the solution of the equations is printed to the log file and, with LUSPVD=T, the singular values and right singular vectors are written to the RSL file in TRVEC1 and TRMAT1, respectively. The components of the singular vectors are in the order of the internal representation of the symplectic equation: real part of the Thouless coefficients, center positions, imaginary part of the Thouless coefficients, center momenta. TRVEC2 and TRVEC3 contain the velocities as computed by the substitution method (version 2) and by solving the symplectic form (version 5, LUSPFM=T). TRVEC4 holds the solution with the symplectic transformation LUSPTR=T. The velocity components are in the following order: Thouless coefficients, center positions, center momenta. TRVEC5 contains the force of the TDVP equation. The force components are in the same order as the velocities.

There is an extra singularity that can develop: the free center can get zero coefficients for all its basis functions. The algorithm to avoid this singularity in the nuclear metric uses an expanded state phase space. This feature can be turned on by setting LUSEXS=T.

Rules for choosing and constructing the basis set for free centers are still being developed. So far the only guideline is that there should be only basis functions of even angular momentum: s,d,g,j,... and not p,f,h,....

The optimization capability has now been completely disentangled from the propagation capability, thus increasing the stability and maintainability of the software system. The optimization functionality appears to be much improved.

Reordering can produce different looking Thouless coefficientcs. Now the Thouless coefficients printed in the output at the end of a run are normalized so that the largest component is equal to 1. The speed vectors are similarly normalized, which makes no sense!