SalazarRodriguezCOOH

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Dec 6, 2023

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Determination of the pK a of Carboxylic Acids Allison M. Salazar Rodriguez DateString [] Wed 28 Aug 2013 19:30:32 Research Question The guiding question for this designated lab is: What single quantum descriptor provides the most accurate predictor for the pKa of carboxylic acids and what is the pK a value of the unknown carboxylic acid? To further this approach these questions with a solution, knowledge acquired regarding quantita- tive structure property relationships was utilized as well as an analysis and calculation of linear regres- sion lines for all six of the observed carboxylic acids. Scientific Background In this lab, because computational chemistry is being used to determine the prediction of an unknown pK a value it is important to first understand what computational chemistry helps us achieve and why we utilize this resource for predictions. So why do we use computational chemistry versus traditional chemistry? The reason why computational chemistry is so important to achieve solutions to questions like predictions is that this form of chemistry has the specific ability to predict characteristics and properties of molecules without having to perform traditional calculations in a laboratory setting or experiment! Imagine trying to work in a laboratory and finding the prediction to a theoretical prob- lem … you wouldn’t be able to observe anything tangible! This is why in order for the properties of molecules to be predicted, computational chemists develop procedures and equations for consequen- tial calculations. Just like in this lab, the prediction that is trying to be made is a very common molecular property, pK a . pK a is a measure of the strength of an acid, basically how strong or weak it is! Even though there is another tool to observe the strength of an acid, the pH scale, pK a is a more reflective measure which has similar properties: the lower the pK a , the more acidic. Printed by Wolfram Mathematica Student Edition

So now that we’ve discussed why we use computational chemistry and what is the variable property we are trying to predict today let us discuss the special type of technique that is going to be used as part of a computational chemist. The specific procedure we are going to be using is called QSPR: quantitative structure property relationship. But what does this mean?! Well, QSPR essentially just means using an equation to find a property of a molecule the quantitative statement being the equa- tion and the computational calculation being the structure. So how will this be done? What special type of equation will we use for correlation? Well, we are going to be using none other than a linear regression equation (y = mx + b)! It is between this equation where two variables will be used to be able to determine the pK a of our unknown carboxylic acid. The y in this instance will be the pK a and the x is one of six quantum descriptors, which are other factors and proper- ties of molecules that we can determine computationally. These quantum descriptors include energy, dipole moment, positive electrostatic potentials, HOMO energy, LUMO energy, and HOMO/LUMO gap energy. It is through the determination of the most accurate single quantum descriptor that will pro- vide the most accurate predictor for pKa, which is determined through the correlation coefficient closest to 1. Procedure Foremost, because this lab contains two portions it is crucial to first determine which of the acquired single quantum descriptors provides the most accurate predictor for the pK a of carboxylic acids. In order to do so each of these six carboxyl acids given has to be built and optimized via the North Car- olina High School Computational Chemistry Server via the computer program MOPAC PM3. The lab required that the acids be built separately in order for them to be properly optimized and symmetrized. To begin building the molecules, the first approach was to build the carbon backbone with the car- bonyl group of carbon and oxygen double bond (C=O) attached to then a hydroxide -OH group. Follow- ing this, a comprehensive cleanup was run with mechanic optimization as the initial form of optimiza- tion along with the symmetrization of the molecule. Proceeding with this molecular cleanup, a geome- try optimization under MOPAC PM3 was run congruent with standard procedure for any meaningful calculation to ensure that the atomic arrangement is stable enough for calculations to be conducted and has a potential energy surface minimum. Using a “New Job using this geometry” a molecular orbital calculation was run under the program MOPAC utilizing the same theory of PM3. After this was accomplished, the necessary single quantum descriptors were recorded which included the energy, dipole moment, HOMO energy, LUMO energy, and positive electrostatic potential energy for each of the six molecules. The majority of these descriptors are readily available after viewing the job for a respective molecule under “Calculated Qualities” but to find the positive electrostatic potential energy the color scheme for occupied orbitals had to be analyzed. To calculate the HOMO/LUMO gap the magnitude of the difference between HOMO and LUMO energies were taken. After all these values were inputted into a chart, three values had to be calculated: the slope, correlation, and intercept for each descriptor. The most accurate was determined by calculating the correlation between the quantum 2 SalazarRodriguezCOOH.nb Printed by Wolfram Mathematica Student Edition

descriptor and provided pK a value and the “R” value of the linear regression line closest to a value of 1 represents the best descriptor. Lastly, to roughly identify an estimate for the pKa of the unknown carboxylic acid, a slope intercept equation had to be generated using the generated slope and inter- cept from recorded values. Because y is the pKa this would predict the pK a value. Calculated Quantities In[725]:= data = "Cmpd" "pK a " "Energy" "Dipole" "ElPot" "HOMO" "LUMO" "HOMO / LUMO Gap" 1 1.23 - 154.87620 0.00 0.0138 - 11.594 - 0.979 10.615 2 4.19 - 36.4087 4.646 0.0482 - 10.62 - 0.7 10.894 3 3.51 - 107.25216 0.00 0.0373 - 11.081 - 1.659 8.961 4 3.1 - 121.67019 2.635 0.0428 - 11.483 - 1.746 9.395 5 4.7 - 70.27334 4.538 0.0556 - 10.677 - 0.423 11.06 ; In[727]:= Data = Delete [ data, 1 ] ; In[728]:= { cmpd, pka, energy, dipole, elpot, HOMO, LUMO, HLgap } = Transpose [ Alldata ] ; Computational Results: Linear Regression Comparison of Descriptors vs. pK a In[734]:= EnergyData = Transpose [{ energy, pka }] ; In[735]:= EnergyFunction = LinearModelFit [ EnergyData, { x1energy } , { x1energy }] Out[735]= FittedModel  5.83449 + 0.0253678 x1energy  In[732]:= energyfit = EnergyFunction [ "RSquared" ] ; In[744]:= Print [ "The correlation coefficient for the energies of the carboxylic acids in relation to their pK a is: ", energyfit ] The correlation coefficient for the energies of the carboxylic acids in relation to their pK a is: 0.764121 In[737]:= DipoleData = Transpose [{ dipole, pka }] ; SalazarRodriguezCOOH.nb 3 Printed by Wolfram Mathematica Student Edition

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In[738]:= DipoleFunction = LinearModelFit [ DipoleData, { x1dipole } , { x1dipole }] Out[738]= FittedModel  2.29517 + 0.444551 x1dipole  In[740]:= dipolefit = DipoleFunction [ "RSquared" ] ; In[745]:= Print [ "The correlation coefficient for the dipole moments of the carboxylic acids in relation to their pK a is: ", dipolefit ] The correlation coefficient for the dipole moments of the carboxylic acids in relation to their pK a is: 0.588781 In[746]:= ElPotData = Transpose [{ elpot, pka }] ; In[747]:= ElPotFunction = LinearModelFit [ ElPotData, { x1elpot } , { x1elpot }] Out[747]= FittedModel  0.125634 + 81.4458 x1elpot  In[748]:= elpotfit = ElPotFunction [ "RSquared" ] ; In[749]:= Print [ "The correlation coefficient for the positive electrostatic potentials of the carboxylic acids in relation to their pK a is: ", elpotfit ] The correlation coefficient for the positive electrostatic potentials of the carboxylic acids in relation to their pK a is: 0.943268 In[750]:= HOMOdata = Transpose [{ HOMO, pka }] ; In[751]:= HOMOfunction = LinearModelFit [ HOMOdata, { x1HOMO } , { x1HOMO }] Out[751]= FittedModel  32.7437 + 2.65059 x1HOMO  In[753]:= HOMOfit = HOMOfunction [ "RSquared" ] ; 4 SalazarRodriguezCOOH.nb Printed by Wolfram Mathematica Student Edition

In[755]:= Print [ "The correlation coefficient for the highest occupied molecular orbital of the carboxylic acids in relation to their pK a is: ", HOMOfit ] The correlation coefficient for the highest occupied molecular orbital of the carboxylic acids in relation to their pK a is: 0.79046 In[756]:= LUMOdata = Transpose [{ LUMO, pka }] ; In[757]:= LUMOfunction = LinearModelFit [ LUMOdata, { x1LUMO } , { x1LUMO }] Out[757]= FittedModel  4.20712 + 0.781843 x1LUMO  In[761]:= LUMOfit = LUMOfunction [ "RSquared" ] ; In[762]:= Print [ "The correlation coefficient for the lowest unoccupied molecular orbital of the carboxylic acids in relation to their pK a is: ", LUMOfit ] The correlation coefficient for the lowest unoccupied molecular orbital of the carboxylic acids in relation to their pK a is: 0.117154 In[764]:= HLgapData = Transpose [{ HLgap, pka }] ; In[765]:= HLgapFunction = LinearModelFit [ HLgapData, { x1HLgap } , { x1HLgap }] Out[765]= FittedModel  0.876663 + 0.242448 x1HLgap  In[767]:= HLgapFit = HLgapFunction [ "RSquared" ] ; In[770]:= Print [ "The correlation coefficient for the HOMO and LUMO gap energies of the carboxylic acids in relation to their pK a is: ", HLgapFit ] The correlation coefficient for the HOMO and LUMO gap energies of the carboxylic acids in relation to their pK a is: 0.0295578 Data Analysis and Calculations: Predicting pK a Value for Unknown Carboxylic Acid In[774]:= unknownpKa = ElPotFunction [ 0.0352 ] ; SalazarRodriguezCOOH.nb 5 Printed by Wolfram Mathematica Student Edition

In[775]:= Print [ "The predicted pK a value of the sixth unknown carboxylic acid is ", unknownpKa ] The predicted pK a value of the sixth unknown carboxylic acid is 2.99253 In[778]:= Alldata = 1 1.23 - 154.87620 0.00 0.0138 - 11.594 - 0.979 10.615 2 4.19 - 36.4087 4.646 0.0482 - 10.62 - 0.7 10.894 3 3.51 - 107.25216 0.00 0.0373 - 11.081 - 1.659 8.961 4 3.1 - 121.67019 2.635 0.0428 - 11.483 - 1.746 9.395 5 4.7 - 70.27334 4.538 0.0556 - 10.677 - 0.423 11.06 6 2.99 - 99.33978 1.654 0.0352 - 11.485 0.962 11.639 ; In[782]:= Grid [ Prepend [ Alldata, { "Carboxylic\nAcid", "pK a ", "Energy\n ( kcal / mol ) ", "Dipole\nMoment", "Positive\nElectrostatic\nPotentials", "HOMO\n ( eV ) ", "LUMO\n ( eV ) ", "HOMO / LUMO\nEnergy Gaps" }] , Alignment → Center, Frame → All ] Out[782]= Carboxylic Acid pK a Energy ( kcal / mol ) Dipole Moment Positive Electrostatic Potentials HOMO ( eV ) LUMO ( eV ) HOMO / LUMO Energy Gaps 1 1.23 - 154.876 0. 0.0138 - 11.594 - 0.979 10.615 2 4.19 - 36.4087 4.646 0.0482 - 10.62 - 0.7 10.894 3 3.51 - 107.252 0. 0.0373 - 11.081 - 1.659 8.961 4 3.1 - 121.67 2.635 0.0428 - 11.483 - 1.746 9.395 5 4.7 - 70.2733 4.538 0.0556 - 10.677 - 0.423 11.06 6 2.99 - 99.3398 1.654 0.0352 - 11.485 0.962 11.639 Figure 1. Completed data table of all six carboxylic acids, including predicted pK a value Lab Abstract In this lab, the question regarding the most accurate single quantum descriptor that provided the most accurate predictor for the pKa of carboxylic acids as well as the predicted value for the sixth unknown carboxylic acid was evaluated. The effect of the molecular orbital calculations on the six carboxylic acids and the determination of slopes for all six of the quantum descriptors in correlation to pKa was that the most accurate was positive electrostatic potential. The linear regression equation for this calculation was 32.7437 + 2.65059 x1HOMO which resulted in a then substitution of the sixth carboxylic acid positive electrostatic potential of 0.0352 that generated a predicted pKa value of 2.99. This lab primarily focused on the method of PM3 utilizing the computer program MOPAC for optimization as well as for the calculated theory of molecular orbital in the North Carolina High School Computational Chemistry Server. The data acquired were analyzed via data tables and the visualization of molecular orbitals through multiple linear regressions demonstrated mathematically. 6 SalazarRodriguezCOOH.nb Printed by Wolfram Mathematica Student Edition

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Keywords: multiple linear regression, carboxylic acid, pK a , quantum descriptors, correlation coefficient SalazarRodriguezCOOH.nb 7 Printed by Wolfram Mathematica Student Edition