PK_a Calculations Of The Amines, Carboxylic Acids, Alcolhols And Phenols With The Density Functional Theory

The pKa values of the carboxylic acids, alcohols, phenols and amines in aqueous solution and nonaqueoussolvent DMSO are calculated with the density functional theory method at two level of the B3LYP/6-31+G(d,p) and B3LYP/6-311+G(d,p), and the polarizable continuum model (PCM) is used to describe the solvent in this paper. In the calculations of pKa values, the dissociation Gibbs free energies is directly calculated using the dissociation reactions of acids, i.e., no thermodynamic cycle is employed, which is different from the previous literatures. However, there is greater error when Gibbs free energy calculated by density functional is directly used to calculate pKa of acids. In this paper two correction methods are proposed to obtain the accurate pKa values of the common acids.The first kind is a method using the calibration Gibbs free energy. In this calculation, we choose reasonable H9O4+as hydrated proton, i,e., the following reaction is selected to calculate the Gibbs free energy of the dissociation of acids: HA(aq)+4H2O(aq)(?)A-(aq)+H9O4+(aq) AG=[G(A-(aq))+G(H9O4+(aq))-G(HA(aq))-4G(H2O(aq))]＝-RTln(Ka/[H2O]4) pKa=ΔG/(2.303RT)-41g([H2O])Taking [H2O]=55.56(mol·L-1), we can get the calculation formula of pKa values: pKa=ΔG/(2.303RT)-AThe plot of the experimental pKa(exp.) vs. ΔG/(2.303RT) is really a straight line for carboxylic acids, alcohols, phenols and amines. The intercept is not anastomotic with one in the equation above, and the slope is less than1, which shows the Gibbs free energy of acid dissociations from the calculation is greater than the actual value. By introducing a correction factors both B for the slope and A for the intercept, we can calculate pKawith the correction Gibbs free energy (BΔG), instead of ΔG and the correction the intercept A, i.e., pKa=BΔG/(2.303RT)-ADistinctly the higher accuracy pKa values can be obtain by means of the correction Gibbs free energy (BΔG) for carboxylic acids, alcohols, phenols and amines.The second kind is a method using the relative Gibbs free energy. In this calculation method the Gibbs free energys are calculated using the ionic equation, on which both sides the charge has been balanced. i.e., HA(aq)+A(s1)-(aq)(?)HA(S1)(aq)+A-(aq) HA(s2)(aq)+A(S1)-(aq)(?)HA(S1)(aq)+A-(s2)(aq) where HA(s1) and HA(S2) are two reference acids whose pKa value is known, expressed by pKa(s1) and pKa(s2), respectively. Then pKa can be calculated by the equation below: pKa=[PKa(s2)-pKa(s1)]ΔGr＋pKa(s1)Here, ΔGr (=ΔG(s1)/ΔG(s2)), is the relative change of Gibbs free energy. This is to say, when two reference acids, HA(s1) and HA(s2), are appropriately selected, accurate pKa values can be obtained by means of the calculation ΔGr.The results, which is calculated by the our methods for common acids, amines and alcohols and phenols, show that:(1) No thermodynamic cycle is employed in the calculations of pKa values by our methods, which is simple and economic in workload.(2)When pKa values are calculated with correction Gibbs free energy method A values are88.15,112.9and85.17, and B values are0.4427,0.5981and0.4425for the carboxylic acids, amines and alcohols(and phenols) in aqueous solution, respectively. A values are72.65,91.49and77.03, and B values are0.3712,0.5007and0.4055for the carboxylic acids, amines and alcohols(and phenols) in nonaqueoussolvent DMSO, respectively.(3)When the pKa values are calculated with the relatively Gibbs free energy method, the data analysis for carboxylic acids, alcohols, phenols, and amines indicates that accurate computational values of pKa can be obtained when trifluoroacetic acid (F3CCOOH) and heptanoic acid (CH3(CH2)5COOH) are chosen as the two reference molecules, HA(s1) and HA(s2), for carboxylic acids, and2,4,6-trinitrophenol (2,4,6-(NO2)3C6H2OH) and ethanol (CH3CH2OH) for both alcohols and phenols, and N-allylmethylamine (CH3NHCH2CHCH2) and o-fluoroaniline (o-FC6H4NH2) for amines.(4)High precision. We calculated the total amines, alcohols and phenols and carboxylic acids more than two hundreds of moleculars and more than four hundreds of pKa values, the calculation results show that, the maximum deviations and the standard deviations are0.88and0.35pKa units for the carboxylic acids,0.76and0.40for both the alcohols and phenols, and1.13and0.52pKaunits for the amines in aqueous solution, and are0.93and0.39pKa units for the carboxylic acids,0.92and0.42pKa units for the both phenols and alcohols, and0.97and0.49pKa units for the amines in nonaqueoussolvent DMSO, respectively.(5)Due to the influence of carboxyl groups, the calculation errors of the second ionization constants pKa(2) are greater than the first pKa(1) for the diacid.Through the calculation of the more than four hundreds of pKa values shows that both the calibration Gibbs free energy method and the relative Gibbs free energy method are simple, effective and high precision to the calculation of pKa values for the carboxylic acids, alcohols, phenols and amines.