acidity.md

Acidity calculation

(This page is still under construction) We refer to paper for detailed description.{cite}Cheng.2009.10.1063/1.3250438,Mangold.2011.10.1021/ct100715x

The pKa of a species $\ce{AH}$ in aqueous solution is defined as

$$\ce{AH(aq) -> A^- (aq) + H^+ (aq)}$$

$$\mathrm{p}K_a = -\log{K_a}$$

The full expression for $\mathrm{p}K_a$ is

$$2.3 k_{\mathrm{B}} T\mathrm{p}K_a = (\Delta_{\mathrm{dp}} A_{\ce{AH}} - \Delta_{\mathrm{dp}} A_{\ce{H3O+}} - \Delta A_{\ce{Ad}} + \Delta A_{\ce{H2Od}} - \Delta A_{\mathrm{qc}} (\ce{AH}) + \Delta A_{\mathrm{qc}}(\ce{H3O+}) + \Delta A_{\ce{H3O+}})$$

Calculate Dummy Insertion Free Energy

$\Delta A_{\ce{Ad}}$ is dummy inerstion free energy corresponding to

$$\ce{A^-(aq) + H+(g)->Ad^-(aq) }$$

To calculate $\Delta A_{\ce{Ad}}$, you need calculate $\ce{Ad-}$ the vibrational frequency of mode i for dummy in gas phase. And save the frequncies as numpy array. Note that the unit of frequencies must be $cm^{-1}$. This function is straightforward implementation using eq.26 in reference.{cite}Mangold.2011.10.1021/ct100715x

from ectoolkits.analysis.acidity import get_dummy_insert_fe
import numpy as np

# the frequencies you calculated from gas phase molecules
frequencies_list = np.array([440, 1182, 2290])

get_dummy_insert_fe(frequencies_list, T=298)

these frequencies are taken from reference {cite}Mangold.2011.10.1021/ct100715x for the arginine molecule

The following output is

> 0.315428

We also implemented function for obtaining $\Delta A_{\ce{H2Od}}$, since $\Delta A_{\ce{H2Od}}$ has a special formula for correction, as described in reference.{cite}Cheng.2009.10.1063/1.3250438 To obtain the $\Delta A_{\ce{H2Od}}$, use the following code,

from ectoolkits.analysis.acidity import get_dummy_insert_fe_hydronium

get_dummy_insert_fe_hydronium()

You will obtain 0.334 eV as the result, which is actually a constant.

Calculate Quantum Correction Free Energy

$\Delta A_{\mathrm{qc}} (\ce{AH})$ is Nuclear Quantum Effects which are expected to be significant for proton. To calculate it, one need calculate vibrational frequencies for a gas phase molecule $\ce{AH}$. The units of frequencies must be $cm^{-1}$

from ectoolkits.analysis.acidity import get_quantum_correction
import numpy as np
# the frequencies you calculated from gas phase molecules
# these frequencies are taken from reference [2] for the arginine molecule.
frequencies_list = np.array([263, 1204, 3340])
get_quantum_correction(frequencies_list, T=298)

The following output is

> 0.175

We also implemented function for obtaining $\Delta A_{\mathrm{qc}}(\ce{H3O+})$, since $\Delta A_{\mathrm{qc}}(\ce{H3O+})$ has a special formula for correction, as described in reference.{cite}Mangold.2011.10.1021/ct100715x To obtain the $\Delta A_{\mathrm{qc}}(\ce{H3O+})$, use the following code,

from ectoolkits.analysis.acidity import get_quantum_correction_hydronium

get_quantum_correction_hydronium()

You will obtain 0.192 eV as the result, which is actually a constant.