XTB

Electronic parameters can be calculated at the GFN1-xTB or GFN2-xTB levels using the xtb-python interface (which needs to be installed).

Module

The XTB class is used to calculate electronic properties. Simple quantities such as the ionization potential, electron affinity, HOMO, LUMO energies and dipole moment are available as well as the atomic charges and bond orders.

Example

>>> from morfeus import read_xyz
>>> from morfeus import XTB
>>> elements, coordinates = read_xyz("ammonia.xyz")
>>> xtb = XTB(elements, coordinates)
>>> xtb.get_ip()
16.49875404054677
>>> xtb.get_ip(corrected=True)
11.652754040546771
>>> xtb.get_ea()
-5.736519991532061
>>> xtb.get_homo()
-0.39012010481047976
>>> xtb.get_charges()
{1: -0.42539265,
 2: 0.14180091,
 3: 0.14179421,
 4: 0.14179754}
>>> xtb.get_bond_order(1, 2)
0.9786781554103448
>>> xtb.get_dipole()
array([0.48187417, 0.06877519, 0.55556546])

In addition, global and local descriptors from conceptual density functional theory can also be calculated.

Example

>>> from morfeus import read_xyz
>>> from morfeus import XTB
>>> elements, coordinates = read_xyz("ammonia.xyz")
>>> xtb = XTB(elements, coordinates)
>>> xtb.get_global_descriptor("electrophilicity", corrected=True)
0.00643909828825333
>>> xtb.get_global_descriptor("nucleophilicity", corrected=True)
-11.652754040546771
>>> xtb.get_fukui("electrophilicity")
{1: -0.20661935,
 2: -0.26445605,
 3: -0.26448747,
 4:-0.26443713}
>>> xtb.get_fukui("nucleophilicity")
{1: -0.42294271,
 2: -0.19234974,
 3: -0.19235729,
 4:-0.19235026}

The version of GFNX-xTB can be set using version=<int> with versions 1 and 2 currently supported. A correction term can be applied for the calculation of the ionization potential and electron affinity using corrected=True, which also affects some of the global and local descriptors. For a full list of descriptors and their definitions, see the Background.

For more information, use help(XTB) or consult the API: XTB.

Command line script

The command line script gives access to the basic functionality from the terminal.

Get charge

$ morfeus xtb Et.gjf - - get_charges - 1
0.03220302786615441

Change version

$ morfeus xtb Et.gjf - --version='"1"' - get_charges - 1
0.02564834649261168

Background

ᴍᴏʀғᴇᴜs can compute both simple electronic parameters such as charges, HOMO and LUMO energies and bond orders, as well as descriptors from conceptual density functional theory [1]. The following global descriptors are available:

• Electrophilicity: \(\omega\)

• Nucleophilicity: \(N\)

• Electrofugality: \(\nu_{electrofugality}\)

• Nucleofugality: \(\nu_{nucleofugality}\)

They are calculated according to the following definitions [1][2]:

\[ \begin{align}\begin{aligned}\omega &= \frac{(IP + EA)^2}{8(IP - EA)} = \frac{\mu^2}{2\eta}\\N &= -IP\\\nu_{electrofugality} &= \frac{(IP - 3EA)^2}{8(IP - EA)} = -EA + \omega\\\nu_{nucleofugality} &= \frac{(3IP - EA)^2}{8(IP - EA)} = IP + \omega\end{aligned}\end{align} \]

Where \(IP\) is the ionization potential, \(EA\) is the electron affinity, \(\mu\) is the chemical potential and \(\eta\) is the hardness given by

\[ \begin{align}\begin{aligned}\mu &= - \frac{IP + EA}{2}\\\eta &= IP - EA\end{aligned}\end{align} \]

The Fukui coefficients are calculated calculated via the finite differences approach using the atomic charges from xtb. These include:

• Electron removal: \(f^-\)

• Electron addition: \(f^+\)

• Radical attack: \(f\)

• Dual descriptor: \(f^{(2)}\)

Which are calculated as follows.

\[ \begin{align}\begin{aligned}f^- &= q_{N-1} - q_{N}\\f^+ &= q_{N} - q_{N+1}\\f &= (q_{N-1} - q_{N+1}) / 2\\f^{(2)} &= f^+ - f^- = 2 q_{N} - q_{N+1} - q_{N-1}\end{aligned}\end{align} \]

The Fukui coefficient for electron removal is also called the coefficient for electrophilic attack and is a measure of nucleophilicity. The coefficient for electron addition is also called the coefficient for nucleophilic attack and is a measure of electrophilicity. The somewhat unintuitive names is due to the notion that another molecule would attack as a nucleophile/electrophile. The coefficient for radical attack is often used for radical reactivity. In addition, the local electrophilicity (\(l_{\omega}\)) and nucleophilicity (\(l_N\)) are also available and calculated as [3].

\[ \begin{align}\begin{aligned}l_{\omega} &= - \frac{\mu}{\eta}f + \frac{1}{2}(\frac{\mu}{\eta})^2 f^{(2)}\\l_N &= f^-\end{aligned}\end{align} \]

The ionization potentials and electron affinities calculated with xtb can be corrected using the empirical terms given by Grimme and co-workers [4].

References

[1] (1,2)

R Luis Domingo, Mar Ríos-Gutiérrez, and Patricia Pérez. Applications of the conceptual density functional theory indices to organic chemistry reactivity. Molecules, 21(6):748, 2016. doi:10.3390/molecules21060748.

[2]

Paul W. Ayers, James S. M. Anderson, Juan I. Rodriguez, and Zobia Jawed. Indices for predicting the quality of leaving groups. Physical Chemistry Chemical Physics, 7(9):1918–1925, 2005. doi:10.1039/B500996K.

[3]

Javier Oller, Patricia Pérez, Paul W. Ayers, and Esteban Vöhringer-Martinez. Global and local reactivity descriptors based on quadratic and linear energy models for α,β-unsaturated organic compounds. International Journal of Quantum Chemistry, 118(20):e25706, 2018. doi:10.1002/qua.25706.

[4]

Hagen Neugebauer, Fabian Bohle, Markus Bursch, Andreas Hansen, and Stefan Grimme. Benchmark study of electrochemical redox potentials calculated with semiempirical and DFT methods. The Journal of Physical Chemistry A, 124(35):7166–7176, 2020. doi:10.1021/acs.jpca.0c05052.