# Calculation methods¶

The following methods in cclib allow further analysis of calculation output.

## C squared population analysis (CSPA)¶

CSPA can be used to determine and interpret the electron density of a molecule. The contribution of the a-th atomic orbital to the i-th molecular orbital can be written in terms of the molecular orbital coefficients:

$\Phi_{ai} = \frac{c^2_{ai}}{\sum_k c^2_{ki}}$

The CSPA class available from cclib.method performs C-squared population analysis and can be used as follows:

from cclib.io import ccread
from cclib.method import CSPA

data = ccread("mycalc.out")

m = CSPA(data)
m.calculate()


After the calculate() method is called, the following attributes are available:

• aoresults is a NumPy array[3] with spin, molecular orbital, and atomic/fragment orbitals as the axes (aoresults[0][45][0] gives the contribution of the 1st atomic/fragment orbital to the 46th alpha/restricted molecular orbital)

• fragresults is a NumPy array[3] with spin, molecular orbital, and atoms as the axes (atomresults[1][23][4] gives the contribution of the 5th atomic/fragment orbital to the 24th beta molecular orbital)

• fragcharges is a NumPy array[1] with the number of (partial) electrons in each atom (atomcharges[2] gives the number of electrons on the 3rd atom)

### Custom fragments¶

Calling the calculate method without an argument treats each atom as a fragment in the population analysis. An optional argument can be passed - a list of lists - containing the atomic orbital numbers to be included in each fragment. Calling with this additional argument is useful if one is more interested in the contributions of certain orbitals, such as metal d, to the molecular orbitals. For example:

from cclib.io import ccread
from cclib.method import CSPA

data = ccread("mycalc.out")

m = CSPA(data)
m.calculate([[0, 1, 2, 3, 4], [5, 6], [7, 8, 9]]) # fragment one is made from basis functions 0 - 4
# fragment two is made from basis functions 5 & 6
# fragment three is made from basis functions 7 - 9


### Custom progress¶

The CSPA class also can take a progress class as an argument so that the progress of the calculation can be monitored:

from cclib.method import CSPA
from cclib.parser import Gaussian
from cclib.progress import TextProgress

import logging

progress = TextProgress()
p = Gaussian("mycalc.out", logging.ERROR)
d = p.parse(progress)

m = CSPA(d, progress, logging.ERROR)
m.calculate()


## Mulliken population analysis (MPA)¶

MPA can be used to determine and interpret the electron density of a molecule. The contribution of the a-th atomic orbital to the i-th molecular orbital in this method is written in terms of the molecular orbital coefficients, c, and the overlap matrix, S:

$\Phi_{ai} = \sum_b c_{ai} c_{bi} S_{ab}$

The MPA class available from cclib.method performs Mulliken population analysis and can be used as follows:

import sys

from cclib.method import MPA
from cclib.parser import ccopen

d = ccopen(sys.argv[1]).parse()
m = MPA(d)
m.calculate()


After the calculate() method is called, the following attributes are available:

• aoresults: a three dimensional array with spin, molecular orbital, and atomic orbitals as the axes, so that aoresults[0][45][0] gives the contribution of the 1st atomic orbital to the 46th alpha/restricted molecular orbital,

• fragresults: a three dimensional array with spin, molecular orbital, and atoms as the axes, so that fragresults[1][23][4] gives the contribution of the 5th fragment orbitals to the 24th beta molecular orbital)

• fragcharges: a vector with the number of (partial) electrons in each fragment, so that fragcharges[2] gives the number of electrons in the 3rd fragment.

### Custom fragments¶

The calculate method chooses atoms as the fragments by default, and optionally accepts a list of lists containing the atomic orbital numbers (e.g. [[0, 1, 2], [3, 4, 5, 6], ...]) of arbitrary fragments. Calling it in this way is useful if one is more interested in the contributions of groups of atoms or even certain orbitals or orbital groups, such as metal d, to the molecular orbitals. In this case, fragresults and fragcharges reflect the chosen groups of atomic orbitals instead of atoms.

### Custom progress¶

The Mulliken class also can take a progress class as an argument so that the progress of the calculation can be monitored:

from cclib.method import MPA
from cclib.parser import ccopen
from cclib.progress import TextProgress
import logging

progress = TextProgress()
d = ccopen("mycalc.out", logging.ERROR).parse(progress)

m = MPA(d, progress, logging.ERROR)
m.calculate()


## Löwdin Population Analysis¶

The LPA class available from cclib.method performs Löwdin population analysis and can be used as follows:

import sys

from cclib.method import LPA
from cclib.parser import ccopen

d = ccopen(sys.argv[1]).parse()
m = LPA(d)
m.calculate()


## Density Matrix calculation¶

The Density class from cclib.method can be used to calculate the density matrix:

from cclib.parser import ccopen
from cclib.method import Density

parser = ccopen("myfile.out")
data = parser.parse()

d = Density(data)
d.calculate()


After calculate() is called, the density attribute is available. It is simply a NumPy array with three axes. The first axis is for the spin contributions, and the second and third axes are for the density matrix, which follows the standard definition.

## Mayer’s Bond Orders¶

This method calculates the Mayer’s bond orders for a given molecule:

import sys

from cclib.parser import ccopen
from cclib.method import MBO

parser = ccopen(sys.argv[1])
data = parser.parse()

d = MBO(data)
d.calculate()


After calculate() is called, the fragresults attribute is available, which is a NumPy array of rank 3. The first axis is for contributions of each spin to the MBO, while the second and third correspond to the indices of the atoms.

## Charge Decomposition Analysis¶

The Charge Decomposition Analysis (CDA) as developed by Gernot Frenking et al. is used to study the donor-acceptor interactions of a molecule in terms of two user-specified fragments.

The CDA class available from cclib.method performs this analysis:

from cclib.io import ccopen
from cclib.method import CDA

molecule = ccopen("molecule.log")
frag1 = ccopen("fragment1.log")
frag2 = ccopen("fragment2.log")

# if using CDA from an interactive session, it's best
# to parse the files at the same time in case they aren't
# parsed immediately---go get a drink!

m = molecule.parse()
f1 = frag1.parse()
f2 = frag2.parse()

cda = CDA(m)
cda.calculate([f1, f2])


After calculate() finishes, there should be the donations, bdonations (back donation), and repulsions attributes to the cda instance. These attributes are simply lists of 1-dimensional NumPy arrays corresponding to the restricted or alpha/beta molecular orbitals of the entire molecule. Additionally, the CDA method involves transforming the atomic basis functions of the molecule into a basis using the molecular orbitals of the fragments so the attributes mocoeffs and fooverlaps are created and can be used in population analyses such as Mulliken or C-squared (see Fragment Analysis for more details).

There is also a script provided by cclib that performs the CDA from a command-line:

\$ cda molecule.log fragment1.log fragment2.log
Charge decomposition analysis of molecule.log

MO#      d       b       r
-----------------------------
1:  -0.000  -0.000  -0.000
2:  -0.000   0.002   0.000
3:  -0.001  -0.000   0.000
4:  -0.001  -0.026  -0.006
5:  -0.006   0.082   0.230
6:  -0.040   0.075   0.214
7:   0.001  -0.001   0.022
8:   0.001  -0.001   0.022
9:   0.054   0.342  -0.740
10:   0.087  -0.001  -0.039
11:   0.087  -0.001  -0.039
------ HOMO - LUMO gap ------
12:   0.000   0.000   0.000
13:   0.000   0.000   0.000
......


### Notes¶

• Only molecular orbitals with non-zero occupancy will have a non-zero value.

• The absolute values of the calculated terms have no physical meaning and only the relative magnitudes, especially for the donation and back donation terms, are of any real value (Frenking, et al.)

• The atom coordinates in molecules and fragments must be the same, which is usually accomplished with an argument in the QM program (the NoSymm keyword in Gaussian, for instance).

• The current implementation has some subtle differences than the code from the Frenking group. The CDA class in cclib follows the formula outlined in one of Frenking’s CDA papers, but contains an extra factor of 2 to give results that agree with those from the original CDA program. It also doesn’t include negligible terms (on the order of 10^-6) that result from overlap between MOs on the same fragment that appears to be included in the Frenking code. Contact atenderholt (at) gmail (dot) com for discussion and more information.