h2p-ricpad

An implementation of the Riccati-Padé method to solve the Schrödinger Equation for the hydrogen molecule ion.

Installation

This program is designed to run on GNU/Linux systems. For building it requires cmake, a working C++ compiler, and, additionally, the following libraries:

• Boost
• Eigen
• Ginac
• GMP
• MPFR

Instructions for installation in Ubuntu and derivates

First, install the dependencies with

sudo apt install build-essential cmake libeigen3-dev libboost-all-dev libgmp-dev libmpfr-dev libginac-dev

Then download this program with:

git clone https://github.com/javierelpianista/h2p-ricpad

(this step can be avoided if downloaded from a repository).

A folder called h2p-ricpad will be created in the current directory. CD to that folder, then follow the typical procedure to build with cmake

mkdir build
cd build
cmake ..
cmake --build .

If succesful, an executable named h2p-ricpad will be created in this folder.

Usage

Usage: h2p-ricpad MODE OPTIONS

MODE can be either 'minimum' for computing U, A, and  R simultaneously for 
the equilibrium internuclear distance,  'fixed', for computing U and A for 
a given R,  'coupling', for computing the coupling constant A, given U and R,  
'fixed-U', for computing U given A and R.
Required options for two- and three-parameters methods:
  --Dmin arg            Minimum D value
  --U0 arg              Initial value of the electronic+nuclear energy
  --A0 arg              Initial value of the coupling constant
  --R0 arg              Initial value of the internuclear distance

Non-mandatory options:
  --help                    Print this message
  --Dmax arg (=-1)          Maximum D value. If Dmax == -1, Dmax is assumed to 
                            be infinite
  --d arg (=0)              Value of d
  --double-D-lambda         Double the value of D for the lambda equation. 
                            Useful at small R.
  --double-D-mu             Double the value of D for the mu equation. Useful 
                            at large R.
  --m arg (=0)              Value of the quantum number associated with the 
                            angular part of the spheroidal equations
  --s arg (=0)              Value stating if the second spheroidal equation's 
                            eigenfuncions are even (s=0) or odd (s=1)
  --ndigits arg (=1000)     Number of digits for the numerical calculations
  --tol arg (=1E-100)       Tolerance for the Newton-Raphson method
  --h arg (=1E-200)         Step size for the Newton-Raphson method
  --hd arg (=1E-400)        Step size for the Newton-Raphson for the 
                            computation of numerical differentiation outside 
                            the Newton-Raphson iterations (Set this to at least
                            sqrt(h))
  --use-E                   Set this option if the provided value of U0 is the 
                            electronic energy, instead of the electronic + 
                            nuclear one
  --no-log                  Set this option if you don't want h2p to output to 
                            any files
  --log-nr                  Set this option to print out each Newton-Raphson 
                            iteration
  -o [ --output-file ] arg  Output file
  --nr-max-iter arg (=100)  Maximum number of Newton-Raphson iterations
  --target-digits arg (=-1) Target number of digits. If this number is reached,
                            the program stops.

Examples

The folder examples contains simple scripts that show how to use h2p-ricpad. Before using them, the h2p-ricpad executable should be either copied to or linked to it. If the instructions for installation were followed, then this should suffice.

cd examples
ln -s ../build/h2p-ricpad .
sh req.sh

The following files are provided:

• req.sh: computation of the equilibrium internuclear distance, electronic+nuclear energy, and separation constant for the ground state
• UA.sh: computation of the electronic+nuclear energy and separation constant for the ground state at a fixed internuclear distance.

Computation of potential energy curves

The Python3 script sweep.py that allows to use the h2p-ricpad program to compute the potential energy curve for several states. In order to use it, the user should open it and modify it according to their setup and preferences. It requires the libraries numpy and mpmath.

It can be used by writing python sweep.py

Where filename is a .csv file with a list of sets of l, m, I numbers. File examples/sweep_example.csv is provided as an example input file.