Publication: INFLUENCIA DE LA LONGITUD DE TOLMAN EN EL CÁLCULO DE LA ENERGÍA NECESARIA PARA DISOLVER UN SOLUTO, USANDO UN MODELO DE MEDIO CONTINUO
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Date
2020-01
Authors
OYARZÚN MUÑOZ, VALENTINA CONSTANZA
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Abstract
Para calcular la energía de solvatación no-polar para una pequeña molécula orgánica neutral
en un medio acuoso, se debe entender la naturaleza de la tensión superficial en una interfase
entre agua líquida y vapor. La energía no-polar es la suma de la energía necesaria para generar
una cavidad en el medio acuoso, y el costo energético debido a la interacción no electroes-
tática entre la especie y el medio por fuerzas débiles de Van der Waals. Es aceptado en la
comunidad científica que la tensión superficial depende de el radio de curvatura por medio
de la longitud de Tolman, sin embargo la forma de la variable de Tolman es desconocida y el
valor numérico (hasta su signo) sigue siendo debatido.
Utilizamos aproximaciones de la energía no-polar para 502 moléculas orgánicas pequeñas
y neutrales obtenidas por Mobley et al. (2009) [1] por dinámica molecular de solvente ex-
plícito, y datos de Cooper et al. (2019) de la energía de Van der Waals [2]. Mediante un
procedimiento general de mínimos cuadrados lineales, encontramos un valor para la función
de corrección de la tensión superficial que se ajusta a los datos de Mobley. Evalúamos cuatro
simplificaciones de la ecuación Gibbs-Tolman-Koenig-Buff (GTKB) para encontrar patrones
en la variable de Tolman, graficando los resultados contra el radio de curvatura. Con estos
resultados diseñamos distintos modelos para calcular la energía de formación de cavidad,
generando el modelo con una pequeña muestra de las especies, y prediciendo la energía de
formación de cavidad para el resto de las 502 especies totales. Además, empleamos modelos
para predecir la energía de formación de cavidad considerando un valor de la longitud de
Tolman constante para las simplificaciones de GTKB.
Para un total de 16 modelos, la correlación con los datos de Mobley et al. (2009) es superior a
0,90 para 6, 13, y 16 modelos al usar 20, 50 y 100 especies para generarlos, respectivamente.
La mayoría de los modelos empleados, 14 de 16, aumentan en exactitud al generar el modelo
con más especies y predecir la energía de formación de cavidad para las especies restantes,
lo que es esperado. El mejor modelo siempre presenta una correlación superior a 0,99. Los
resultados obtenidos presentan poca correlación con los resultados de Mobley et al. (2009)
para especies cuyo costo energético es muy bajo (< 9 kcal/mol) o alto (> 15 kcal/mol).
Los modelos que entregan resultados con mayor correlación (> 0,97) consideran Tolman
constante, y los gráficos que muestran el comportamiento de Tolman en función con el radio
de curvatura no demuestran una clara dependencia entre estas.
To estimate the non-polar solvation energy for an organic molecule functional group in water in bulk, we must first understand the nature of surface tension in a liquid-vapor interface. Non-polar solvation free energy is the sum of the energy necessary to create a cavity in bulk water, and the cost of the non electrostatic interaction between the functional group and medium through weak Van der Waal forces. The dependancy of surface tension on the Tolman’s length is widely accepted in the scientific community, however the form of the Tolman variable is unknown and the numeric value (even its sign) is still debated. Our theoretical values are approximations of the non-polar energy for 502 functional groups published by Mobley et al. (2009) [1], obtined through the method of molecular dynamics, and aproximations of the Van der Waals energy by Cooper (2019) [2]. Through least squares lineal regression, a fitted value for the correctional factor of the surface tension may be found. Additionally, four simplifications of the Gibbs-Tolman-Koenig-Buff (GTKB) equation are evaluated to find patterns in the Tolman variable, later graphing the results for theTolman length against the radius of curvature. With these results, various models can be designed and used to predict the energy of cavity formation for other functional groups. Furthermore, constant Tolman length values are also tested, obtained through the four simplifications of the GTKB equation. For a total of 16 models, the pearson correlation coeficient of prediction results and theo- retical values is over 0,90 for 6, 13, and 16 models using 20, 50 and 100 functional groups to design them, respectively. 14 models improved in their linear relationship stregnth as the amount of functional groups used in their design increased as expected. The best perfor- ming model has a pearson correlation over 0,99 regardless of how many functional groups are used in its design. For species whose energetic cost of cavity formation is either too low (< 9 kcal/mol) or too high (> 15 kcal/mol), prediction results overestime and subestimate energy costs, respectively. The best performing models (> 0,97) all consider a constant Tol- man value, and graphing fitted Tolman values against the radius of curvature does not show a clear relationship between the two.
To estimate the non-polar solvation energy for an organic molecule functional group in water in bulk, we must first understand the nature of surface tension in a liquid-vapor interface. Non-polar solvation free energy is the sum of the energy necessary to create a cavity in bulk water, and the cost of the non electrostatic interaction between the functional group and medium through weak Van der Waal forces. The dependancy of surface tension on the Tolman’s length is widely accepted in the scientific community, however the form of the Tolman variable is unknown and the numeric value (even its sign) is still debated. Our theoretical values are approximations of the non-polar energy for 502 functional groups published by Mobley et al. (2009) [1], obtined through the method of molecular dynamics, and aproximations of the Van der Waals energy by Cooper (2019) [2]. Through least squares lineal regression, a fitted value for the correctional factor of the surface tension may be found. Additionally, four simplifications of the Gibbs-Tolman-Koenig-Buff (GTKB) equation are evaluated to find patterns in the Tolman variable, later graphing the results for theTolman length against the radius of curvature. With these results, various models can be designed and used to predict the energy of cavity formation for other functional groups. Furthermore, constant Tolman length values are also tested, obtained through the four simplifications of the GTKB equation. For a total of 16 models, the pearson correlation coeficient of prediction results and theo- retical values is over 0,90 for 6, 13, and 16 models using 20, 50 and 100 functional groups to design them, respectively. 14 models improved in their linear relationship stregnth as the amount of functional groups used in their design increased as expected. The best perfor- ming model has a pearson correlation over 0,99 regardless of how many functional groups are used in its design. For species whose energetic cost of cavity formation is either too low (< 9 kcal/mol) or too high (> 15 kcal/mol), prediction results overestime and subestimate energy costs, respectively. The best performing models (> 0,97) all consider a constant Tol- man value, and graphing fitted Tolman values against the radius of curvature does not show a clear relationship between the two.
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Keywords
TOLMAN , TENSIÓN SUPERFICIAL , ENERGÍA LIBRE DE SOLVATACIÓN