XTB

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

Module

The XTB class is used to calculate electronic properties, such as, among others, bond orders, atomic charges, total, HOMO and LUMO energies, dipole moments, ionization potential, electron affinity.

Example

>>> from morfeus import XTB, read_xyz
>>> elements, coordinates = read_xyz("ammonia.xyz")
>>> xtb = XTB(elements, coordinates)
>>> xtb.get_bond_order(1, 2)
0.978270297857
>>> xtb.get_charges()
{1: -0.4344091, 2: 0.14479795, 3: 0.14480895, 4: 0.1448022}
>>> xtb.get_energy()
-4.42584832
>>> xtb.get_homo()
-0.3847857
>>> xtb.get_dipole()
array([ 0.38617738,  0.48077917, -0.31171428])
>>> xtb.get_ip()
11.6047
>>> xtb.get_ip(corrected=False)
16.4502
>>> xtb.get_ea()
-11.121

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

Example

>>> xtb.get_global_descriptor("electrophilicity")
0.0012869003485041107
>>> xtb.get_global_descriptor("nucleophilicity")
-11.6047
>>> xtb.get_fukui("electrophilicity")
{1: 0.205, 2: 0.265, 3: 0.265, 4: 0.265}
>>> xtb.get_fukui("nucleophilicity")
{1: 0.428, 2: 0.191, 3: 0.191, 4: 0.191}

Properties related to the solvation are also available with the XTB class.

Example

>>> xtb = XTB(elements, coordinates, solvent="water")
>>> xtb.get_solvation_energy(unit="kcal/mol")
-4.644374184273
>>> xtb.get_solvation_h_bond_correction(unit="kcal/mol")
-2.808641396951

The version of GFNn-xTB or the PTB method can be set using method=<int>|<str> with versions 1 and 2 and the additional method “ptb” currently supported. The molecular charge, number of unpaired electrons and solvent are also set while initializing the class, with charge=<int>, n_unpaired=<int> and solvent=<str> respectively.

A empirical correction term, given by Grimme and co-workers [1], is applied for the calculation of the ionization potential and electron affinity, which also affects some of the global and local descriptors. It can be disabled with corrected=False.

For more information and a list of all available electronic properties, 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 ammonia.xyz - - get_charges - 1
-0.4344091

Change version

$ morfeus xtb ammonia.xyz - --method='"1"' - get_charges - 1
-0.57697413

Background

Descriptors from conceptual DFT

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 [2]. The following global descriptors are available:

• Electrophilicity: \(\omega\)

• Nucleophilicity: \(N\)

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

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

They are calculated according to the following definitions [2][3]:

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

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 via the finite differences approach using the atomic charges from xtb. These include:

• Electron removal (nucleophilicity): \(f^-\)

• Electron addition (electrophilicity): \(f^+\)

• 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 [4]:

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

Solvation properties

The solvation free energy \(\Delta G_{solv}\) is calculated with xtb using the ALPB model [5]. Because the solvent is described implicitly as a dielectric medium, the hydrogen bonding (HB) between solute and solvent needs to be accounted for separately. The HB correction is calculated with:

\[\Delta G^{HB} = \sum_{A}^{N} \Delta G_{A}^{HB}\]

where \(\Delta G_{A}^{HB}\) is the atomic contribution to the HB correction and approximated in the ALPB model as [5]:

\[\Delta G_{A}^{HB} ≈ - g_{A}^{HB} q_{A}^{2} \frac{\sigma_{A}}{4\pi(R_{A}^{surf})^{2}}\]

where \(g_{A}^{HB}\) is the HB strength of the atom, \(q_{A}\) its charge, \(\sigma_{A}\) its SASA, and \(R_{A}^{surf}\) the atom vdW radius combined with the solvent probe radius.

References

[1]

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.

[2] (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.

[3]

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.

[4]

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.

[5] (1,2)

Sebastian Ehlert, Marcel Stahn, Sebastian Spicher, and Stefan Grimme. Robust and efficient implicit solvation model for fast semiempirical methods. Journal of Chemical Theory and Computation, 17(7):4250–4261, June 2021. doi:10.1021/acs.jctc.1c00471.