McMurchie-Davidson

This contains some simple routines to compute one and two electron integrals necessary for Hartree Fock calculations using the McMurchie-Davidson algorithm. The Hartree-Fock code can only handle closed shell molecules at the moment. It's not fast (though getting faster with Cython interface), but should be somewhat readable.

I'm slowly porting the integrals over to Cython and reoptimizing. I'm also thinking about reorganizing so as to make it easy to add functionality in the future.

Installation

Installation should be simple. For a local install, just

python setup.py build_ext --inplace install --user

Dependencies

You'll need numpy, scipy, and cython (for the integrals). Some post-SCF functionality requires bitstring, in order to handle the bitstring/integer representations for Slater determinants and to allow for the evaluation of Slater-Condon rules between arbitrary determinants. The install script should yell at you if you don't have the requisite dependencies. You can install them all at once if you have pip:

pip install numpy scipy cython bitstring

Testing

You can test the install with nosetests. In the head directory, just do

nosetests tests

it should take a few seconds, but everything should pass.

Running

Once you've installed, you can try running the input script sample-input.py:

python sample-input.py

which should do an SCF on water with an STO-3G basis and dump out to your terminal:

E(SCF)    =  -74.942079928060 in 10 iterations
  Convergence:
    FPS-SPF  =  3.377372360032819e-13
    RMS(P)   =  2.35e-12
    dE(SCF)  =  -9.95e-10
  Dipole X =  0.00000000
  Dipole Y =  1.53400931
  Dipole Z =  -0.00000000
E(MP2) =  -74.99122956422062

Input file specification

The input is fairly straightforward. Here is a minimal example using water.

from mmd.molecule import *
from mmd.scf import *

water = """
0 1
O    0.000000      -0.075791844    0.000000
H    0.866811829    0.601435779    0.000000
H   -0.866811829    0.601435779    0.000000
"""

# init molecule and build integrals
mol = Molecule(geometry=water,basis='sto-3g')

# do the SCF
mol.RHF()

The first lines import the molecule and scf modules, which we need to specify our molecule and the SCF routines. The molecular geometry follows afterward and is specified by the stuff in triple quotes. The first line is charge and multiplicity, followed by each atom and its Cartesian coordinates (in Angstrom).

water = """
0 1
O    0.000000      -0.075791844    0.000000
H    0.866811829    0.601435779    0.000000
H   -0.866811829    0.601435779    0.000000
"""

Then we generate create the molecule (Molecule object) and build the integrals, and finish by running the SCF.

At any point you can inspect the molecule. For example, you can dump out the (full) integral arrays:

print(mol.S)

which dumps out the overlap matrix:

[[ 1.     0.237  0.     0.     0.     0.038  0.038]
 [ 0.237  1.     0.     0.     0.     0.386  0.386]
 [ 0.     0.     1.     0.     0.     0.268 -0.268]
 [ 0.     0.     0.     1.     0.     0.21   0.21 ]
 [ 0.     0.     0.     0.     1.     0.     0.   ]
 [ 0.038  0.386  0.268  0.21   0.     1.     0.182]
 [ 0.038  0.386 -0.268  0.21   0.     0.182  1.   ]]

There is also some limited post-SCF functionality, hopefully more useful as a template for adding later post-SCF methods.

# do MP2
mp2 = PostSCF(mol)
mp2.MP2()

Examples

In the examples folder you can find some different scripts for setting up more complex jobs. For example, there is a simple script that does Born-Oppenheimer molecular dynamics on minimal basis hydrogen, aptly titled bomd.py. There are some real-time electronic dynamics in real-time.py. It's a good idea to check out the tests folder. In particular, tests/README.md contains an index to the different tests used, which gives some insight into the current functionality.