IntPak

Simple and slow integral package for Gaussian basis functions.¹² IntPak has the ability to compute various types of one-, two-, three-, and four-electron integrals using various operators.³⁴⁵ IntPak is extremely slow but the implementation is straightforward.

Contributors:

• Pierre-Francois Loos

Installation guide

The IntPak software can be downloaded on GitHub as a Git repository

git clone https://github.com/pfloos/IntPak.git

The repository should be self-contained as I have added the required subroutines from the library slatec. BLAS and LAPACK might be also required.

Compile the code

cd src; make

Run the code

./bin/IntPak

Set up the options

The options are gathered in input/int and it looks like this

# Debuggin mode?
  F
# Chemist notation for two-electron integral?
  F
# Exposant of the Slater geminal
  1.0
# One-electron integrals: Ov Kin Nuc
                          T  T   T
# Two-electron integrals: ERI F12 Yuk Erf
                          T   F   F   F
# Three-electron integrals: Type1 Type2 Type3
                            F     F     F
# Four-electron integrals: Type1 Type2 Type3
                           F     F     F

In this case, the usual one-electron integrals are going to be computed (overlap, kinetic and nuclear attraction) as well as the electron repulsion integrals (ERIs). Other two-electron integrals over the operator f12 (f12 being a Gaussian or Slater geminal), f12/r12, and erf(r12)/r12 can also be computed. For the three- and four-electron integrals, see the corresponding papers. ³⁴⁵

The basis set is given in input/basis while the molecular geometry is given in input/molecule. The molecule file looks like this for N2 (the coordinates are given in bohr):

# nAt nEla nElb nCore nRyd
    2    7    7     0    0
# Znuc   x            y           z
  N        0.0000000000         0.0000000000         1.0400863244
  N        0.0000000000         0.0000000000        -1.0400863244

A concrete example is given in the repository. Additional tuning can be done in the main source file src/IntPak.f90. In particular, one can tune the coefficients and exponents of the Gaussian geminals that are used to fit the Slater geminal.

Have fun!

Footnotes

1. P. M. W. Gill, Adv. Quantum Chem. 25, 141 (1994). ↩

2. R. Ahlrichs, Phys. Chem. Chem. Phys. 8, 3072 (2006). ↩

3. G. M. J. Barca, P. F. Loos and P. M. W. Gill, J. Chem. Theory Comput. 12, 1735 (2016). ↩ ↩²

4. G. M. J. Barca and P. F. Loos, Adv. Quantum Chem. 76, 147 (2018). ↩ ↩²

5. G. M. J. Barca and P. F. Loos, J. Chem. Phys. 147, 024103 (2017). ↩ ↩²