raghurama123 / lcsto

LCSTO

A code to perform Roothan-Hartree-Fock calculation of 2-electron atoms using Linear Combination of Slater-Type Orbitals. The code was used in the work

  Exact separation of radial and angular correlation energies in two-electron atoms
  Anjana R.Kammath, Raghunathan Ramakrishnan
  Chem. Phys. Lett. 720, 93 (2019);
  https://doi.org/10.1016/j.cplett.2019.02.004

The atomic orbitals are selected as even-tempered basis functions which enables one to reproduce Raffenetti's results from

  Even‐tempered atomic orbitals. II. Atomic SCF wavefunctions in terms of even‐tempered exponential bases
  Richard C. Raffenetti
  J. Chem. Phys. 59, 5936 (1973); 
  https://doi.org/10.1063/1.1679962

The purpose of sharing the code and the following results is to demonstrate, how with a simple 'toy' program, historical results in quantum chemistry may be reproduced.

Results

=======================================================================
No. of basis functions                 SCF energy (hartree)
-----------------------------------------------------------------------
                               This code               Rafenetti's work
 1                         -2.847 656 250 000 
 2                         -2.861 672 626 180
 3                         -2.861 676 069 769        -2.861 679 036 686 
 4                         -2.861 679 875 445        -2.861 679 875 316 
 5                         -2.861 679 987 459        -2.861 679 986 833 
 6                         -2.861 679 993 337        -2.861 679 987 495 
 7                         -2.861 679 995 580        -2.861 679 994 968 
 8                         -2.861 679 995 606        -2.861 679 995 610 
12                                                   -2.861 679 995 615
=======================================================================

Sample run

> python3 lcsto.py 

No. of Slater-type basis functions: 1
Optimal Exponents generated using alpha = 1.0567284642370978  and beta= 1.5969097269003423
1.687499963232682
Total SCF energy in hartree: -2.8476562499999982 


No. of Slater-type basis functions: 2
Optimal Exponents generated using alpha = 0.7264028021946469  and beta= 2.0002189508643307
1.4529646509106866
2.906247429687532
Total SCF energy in hartree: -2.8616726261795105 


No. of Slater-type basis functions: 3
Optimal Exponents generated using alpha = 0.7499408016830662  and beta= 1.9223281763174245
1.441632333645436
2.7712904548568638
5.3273297261308805
Total SCF energy in hartree: -2.861676069768634 


No. of Slater-type basis functions: 4
Optimal Exponents generated using alpha = 0.8539368519660311  and beta= 1.6608849915181203
1.4182909011346119
2.3556180713011874
3.912410700373003
6.498064212904418
Total SCF energy in hartree: -2.8616798754451778