MP-CITDSE

Modern Portable - Configuration Interaction Time Dependent Schrödinger Equation: is set of programs for the ab-initio solution of the Time-Dependent Schrödinger Equation (TDSE) in the case of 1- and/or 2-electron atom-laser interactions written in C++ 17. In many ways this package is a spiritual successor to [1].

Initially the 1-electron Time-Independent Schrödinger Equation (TISE) is solved on a basis of B-splines, as described in [2]. The 1-electron dipole transition elements are then obtained, using the 1-electron eigenstates of the TISE. From here, solution of the 1-electron TDSE is possible.
Moving onto the 2-electron problem, the inter-electronic interactions and 2-electron dipole transition elements, are calculated before forming the Configuration Interaction (CI) basis. Once the 2-electron time dependent Hamiltonian is obtained in the CI basis the 2-electron TDSE ma be solved.
As a form of result analysis this suite provides two programs for the calculation of photoelectron spectra from time dependent coefficients, one for the 1-electron, and another for the 2-electron problem. These programs also provide the ground state populations and ionisation yields.

The included programs are, in order of operation:

h1e - Solves the 1-electron TISE on a B-splines basis
w1e - Returns the wave function values and integration parameters for subsequent programs
d1e - Computes the 1-electron dipole matrices
id2ec - Indexes the configurations provided for each total (2-electron) angular momentum
r12 - Calculates the inter-electronic interactions for the 2-electron states
d2e - Computes the 2-electron dipole matrices using the 1-electron dipoles
w2e - Forms the CI 2-electron basis
tdse - Solves either the '-e 1' (1-electron) or '-e 2' (2-electron) TDSE for a given laser pulse
pes - Computes the photoelectron energy distribution from the provided '-e 1' or '-e 2' time dependent coefficients

Requirements

A C++17 or greater compatible compiler: g++ >= 10, clang++ >= 7; Intel's 2023 version of the icpx compiler and AMD's equivalent version of aocc-clang++ have both been tested and work as intended.

tbb - library for C++17 multithreading
hdf5 - data storage library
yaml-cpp - library for human readable (yaml) format configuration files
boost - specifically ::odeint for the tdse program
any parallel BLAS library - OpenBLAS and Intel MKL have both been tested and work as intended.
wigxjpf - library for wigner symbols [3]; (requires a fortran compiler) the cmake compilation downloads the latest version from github and links it automatically, for compilation with make a static version of the library (along with its licence) is provided in lib/wigxjpf.

Installing from repositories

RHEL linux

First make sure that you have the crb and epel repositories enabled then run:

sudo yum install yaml-cpp gsl gsl-devel boost boost-devel hdf5 hdf5-devel tbb-devel openblas openblas-devel lapack-devel

Debian/Ubuntu

sudo apt-get install libyaml-cpp-dev libhdf5-dev libboost-dev libgsl-dev libtbb-dev libopenblas-dev liblapacke-dev

Arch linux

sudo pacman -S yaml-cpp gsl boost hdf5 tbb openblas lapacke

Compilation

Cmake

This method doesn't work on Debian/Ubuntu because the linking of hdf5 via cmake is broken on those systems

Requires Cmake version 3.20 or greater.
To compile the code, including the wigxjpf library:

mkdir build && cd build
cmake -DBLA_VENDOR=<chosen blas library (default=OpenBLAS)> ..
make

If your BLAS library is installed in a non-standard location do:

cmake -DBLA_VENDOR=<blas library> -DBLA_HINT=<path to blas library> -DBLA_INC=<path to blas/lapack headers> ..

instead of the above cmake call.

If you are installing on Debian you may need to add the location of libhdf5.so to your PATH, you can then include the headers by using the:

-DH5_INC=<path/to/hdf5/include>

Make

Works out of the box for all RHEL Debian/Ubuntu or Arch based linux versions that ship with g++ >= 10

First set the variables BLAS_LIB, BLAS_INC, WIG_LIB, WIG_INC to the correct paths in src/Makefile. If you're using some non-standard install locations, you may also need to set: HDF5_LIB, HDF5_INC, YAML_LIB, YAML_INC, LAPACK_LIB and LAPACK_INC.
Then simpy run:

cd src
make

Running a 1-electron example

Structure

To run the electronic structure programs you can use the provided bin/run-structure.sh script.
For the 1-electron case do:

bin/run-structure.sh -e 1 -f inp/H_test.yaml

Alternatively you can run the programs individually

bin/h1e -f inp/H_test.yaml
bin/w1e -f inp/H_test.yaml
bin/d1e -f inp/H_test.yaml

TDSE Solution

bin/tdse -e 1 -f inp/H_test.yaml -o dat/H_tdat

If you wish to track the population of a specific state at each time step then use the optional parameters -n <primary quantum number> -l <angular quantum number>:

bin/tdse -e 1 -f inp/H_test.yaml -o dat/H_tdat -n 1 -l 1

In order to restart a previous run, or to start from custom initial conditions the program can be called with the -s <path to coefficient file> command line option, it will start at the time provided in the filename (eg: h_ct_0.0.dat will start at the beggining of the pulse but h_ct_50.1.dat will resume from 50.1 a.u. of time within the pulse)

bin/tdse -e 2 -f inp/H_test.yaml -o dat/H_tdat -s dat/H_tdat/h_ct_50.100000.dat

The default pulse envelope shape is sin^2, a gaussian shape is also provided, to change the envelope you need to modify the Field_Parameters:shape: "" parameter in your .yaml file. If you would like to add your own pulse shapes add them to src/tdse/pulse.cpp and src/tdse/include/pulse.hpp, modify src/tdse/tdse_main.cpp.

Text files contatining the time dependent coefficients will then be available in dat/H_tdat, a new file is created every 1/10th of the total pulse duration. The folder "dat/H_tdat" will be created at runtime, any UNIX-valid folder name can be used.
To obtain the photoelectron energy distribution run:

bin/pes -e 1 -f inp/H_test.yaml -i dat/H_tdat/h_ct_<time>.dat

By default this creates separate energy spectra for each 'l' in "dat/H_tdat/h_pes.dat" files. A a total spectrum can also be obtained by using the -s option.

bin/pes -e 1 -f inp/H_test.yaml -i dat/H_tdat/h_ct_<time>.dat -s

which creates a "h_pes.dat" file.

Running a 2-electron example

Structure

To run the electronic structure programs you can use the provided bin/run-structure.sh script.
For the 2-electron case do:

bin/run-structure.sh -e 2 -f inp/He_test.yaml -i inp/

Alternatively you can run the programs individually

bin/h1e -f inp/He_test.yaml
bin/w1e -f inp/He_test.yaml
bin/d1e -f inp/He_test.yaml
bin/id2ec -f inp/He_test.yaml -i inp/
bin/r12 -f inp/He_test.yaml -i inp/
bin/d2e -f inp/He_test.yaml -i inp/
bin/w2e -f inp/He_test.yaml

TDSE Solution

Works similarly to the 1-electron case, with the -e option is set to 2.

bin/tdse -e 2 -f inp/He_test.yaml -o dat/He_tdat
bin/tdse -e 2 -f inp/He_test.yaml -o dat/He_tdat -n 1 -l 1
bin/pes -e 2 -f inp/He_test.yaml -i dat/He_tdat/he_ct_<time>.dat
bin/pes -e 2 -f inp/He_test.yaml -i dat/He_tdat/he_ct_<time>.dat -s

I/O

All input parameters can be found in the supplied inp/H_test.yaml and inp/He_test.yaml files.
The 2e configurations are located in the inp/cfg-<L>.inp files.
To provide custom inputs youcan just copy the inp/ folder and rename/modify as needed

All structure calculation files can be found in the dat directory.
Most of the data is stored in the HDF5 format.

References

[1] Nikolopoulos L. A., A package for the ab-initio calculation of one-and two-photon cross sections of two-electron atoms, using a CI B-splines method. Computer physics communications. 2003 Feb 1;150(2):140-65.

[2] Bachau H, Cormier E, Decleva P, Hansen JE, Martín F. Applications of B-splines in atomic and molecular physics. Reports on progress in physics. 2001 Nov 19;64(12):1815.

[3] Johansson H. T. and Forssén C., Fast and Accurate Evaluation of Wigner 3j, 6j, and 9j Symbols Using Prime Factorization and Multiword Integer Arithmetic, SIAM J. Sci. Comput., 38(1) (2016), A376-A384.

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