Time-Dependent Density Functional Theory Assessment of UV

Nov 7, 2012 - The CAM-B3LYP functional showed the best overall performance and ... James Xiao , Vijila Chellappan , Timothy E. Rosser , Erwin Reisner ...
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Time-Dependent Density Functional Theory Assessment of UV Absorption of Benzoic Acid Derivatives Hao-Bo Guo,†,‡ Feng He,§ Baohua Gu,§ Liyuan Liang,§ and Jeremy C. Smith*,†,‡ †

UT/ORNL Center for Molecular Biophysics and §Environmental Sciences Division, , Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡ Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee, 37996, USA S Supporting Information *

ABSTRACT: Benzoic acid (BA) derivatives of environmental relevance exhibit various photophysical and photochemical characteristics. Here, time-dependent density functional theory (TDDFT) is used to calculate photoexcitations of eight selected BAs and the results are compared with UV spectra determined experimentally. High-level gas-phase EOM-CCSD calculations and experimental aqueous-phase spectra were used as the references for the gas-phase and aqueousphase TDDFT results, respectively. A cluster-continuum model was used in the aqueous-phase calculations. Among the 15 exchange−correlation (XC) functionals assessed, five functionals, including the meta-GGA hybrid M06-2X, double hybrid B2PLYPD, and range-separated functionals CAM-B3LYP, ωB97XD, and LC-ωPBE, were found to be in excellent agreement with the EOM-CCSD gas-phase calculations. These functionals furnished excitation energies consistent with the pH dependence of the experimental spectra with a standard deviation (STDEV) of ∼0.20 eV. A molecular orbital analysis revealed a πσ* feature of the low-lying transitions of the BAs. The CAM-B3LYP functional showed the best overall performance and therefore shows promise for TDDFT calculations of processes involving photoexcitations of benzoic acid derivatives. (DFT).8,9 In early attempts to calculate low-lying excitation energies of a set of small to medium sized molecules, the popular hybrid functional B3LYP10 was found to correctly order excited states with errors of ∼0.4 eV.11 The past decade has seen fast and furious development of both DFT and TDDFT,8,12 and the consequent feasibility of reaching so-called “chemical accuracy”13 (e.g., 0.10 eV) in excitation energies with TDDFT calculations. However, as with its DFT counterpart, because any given functional employs density functional assumptions that are different from the others, the TDDFT performance of any given XC functional with different target molecules and computational tasks varies considerably. Therefore, prior to studies of their excited states with the TDDFT method it is always a necessity to benchmark the XC functionals to find out the best one(s) for any given set of molecules. Recent TDDFT assessments (see ref 13 for a perspective) have been performed by aiming to correctly interpret excitation energies and were compared with either in vacuo calculations at a high level of theory (e.g., CASPT236 or EOM-CCSD37) or with experimental spectra measured in the gas phase or in solution.13−26 These studies highlighted several TDDFT approaches in calculations of the excited singlet states, including the double hybrid functional B2PLYPD,20 the meta-GGA Minnesota functionals,24c,f and range-separated functionals such as ωB97XD24d and CAM-B3LYP.19 Some studies13,14,23,24a

1. INTRODUCTION Benzoic acid (BA) derivatives represent a simple but important class of natural humic substances, which are degradation products from dead plants, animals or other organisms in the ecosystem.1,2 Under solar irradiation in the ultraviolet (UV) region, BAs frequently undergo excited state configurational changes involving substances with which they directly or indirectly interact, and this may subsequently bring about electron and/or proton transfers,3 isomerizations,4 photolysis5 or other reactions including metal reduction.6 For example, a recent study revealed that UV irradiation of several benzoic acid derivatives at wavelengths of their low-lying electronic states significantly promotes the photoreduction of Hg(II) in aqueous solution.6 Therefore, systematic investigation of the photoexcitation of BAs is of considerable importance for furthering our understanding of the mechanism of Hg(II) photoreduction and other photophysical or photochemical processes via BA photoactivation. However, even for a single BA molecule such as salicylic acid (SA), the photophysical and photochemical properties are complex.7 To complement experiment, theoretical approaches such as time-dependent density functional theory (TDDFT)8 are promising for examining the excited states of BAs. TDDFT has been widely used to calculate electronically excited states of molecules with both reasonable accuracy and moderate computational expense.8 According to the Runge−Gross theorem,9 TDDFT uses exchange−correlation (XC) functionals developed in ground states and thereby inherits the advantages and disadvantages of ground state density functional theory © 2012 American Chemical Society

Received: August 24, 2012 Revised: November 6, 2012 Published: November 7, 2012 11870

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in combination with a continuum representation for the extended solvent environment, i.e., in a “cluster-continuum” approach.30 Here, the solvent effect was addressed by this approach with the SMD33 dielectric continuum and a single water molecule added for each negatively charged carboxyl group. The geometries optimized using the cluster-continuum approach are denoted as the MP2A set. Frequency calculations were performed to ensure that the optimized configurations are minima on the potential energy surfaces. In the TDDFT assessment, vertical excitation energies are compared with the absorption maxima of the experimental UV spectra. There are two reasons for this. First, although the 0−0 transition energy is physically correct and detectable, its calculation demands much more extensive computational effort than calculating the vertical transition energies;13,25 and second, the 0−0 transition is expected only when the ground state vibrational energy levels are widely spaced compared to the thermal energy,27 which may not be the case for solvent spectra. Therefore, the Franck−Condon vertical transitions often give good matches with the experimental spectra in solution. All TDDFT calculations were performed using the Gaussian 09 program.34 The XC functionals assessed include the pure density functionals BLYP,35a B97D,35b HCTH,35c M06-L,35d hybrid functionals B3LYP,10 B3PW91,35e X3LYP,35f O3LYP,35g BMK,35h and TPSSh,35i the meta-GGA hybrid functional M062X,35j the double hybrid functional B2PLYPD,35k and the rangeseparate functionals CAM-B3LYP,35l ωB97XD,35m and LCωPBE.35n The comparison was carried out in two stages. First, EOMCCSD37 calculations with the basis set 6-31+G(d) using the MP2G model in the gas phase were used as the references to assess all fifteen XC functionals listed above. In this stage, only the low-lying excitation energies (S0 → S1) for 16 molecules were compared with the EOM-CCSD benchmarks. In the second stage, selected XC functionals that appropriately reproduced the EOM-CCSD results for both the transition energies and oscillator strengths were further assessed using the MP2A set of configurations and the experimental spectra in aqueous solution. In this step, the SMD continuum model and nonequilibrium solvation were applied with the optical dielectric constant (ε = 1.78) of water for the TDDFT calculations. The BA derivatives have three characteristic absorption peaks around 190 nm (6.5 eV, A band), 230 nm (5.5 eV, B band), and 280 nm (4.5 eV, C band), respectively.38 The absorption maxima and their corresponding extinction coefficients in the A, B and C bands were used as the references. Experimental transition energies and the extinctions of the absorption maxima were chosen for comparison with the calculated excitation energies and oscillators, respectively. Absorptions identified from the shoulder peaks were obtained using Gaussian deconvolutions, comprising the C-band peaks of BA and PA, the B-band peaks of AA, SA, TSA, and PA, and the high-pH spectrum of pABA and low-pH spectrum of pHBA. All Gaussian deconvolutions resulted in high fitting coefficients (>0.998) (Figure S2, Supporting Information). Altogether, this stage assessed excitations comprising 16 neutral and 21 negatively charged species, respectively, comprising 16 C-band, 12 B-band and 9 A-band peaks. Using the CAM-B3LYP functional, standard Pople basis sets comprising 3-21G, 6-31G, 6-31G(d), 6-31+G(d), 6-31+G(d,p), 6-31++G(d,p), and 6-311++G(d,p) were assessed. Only a moderate basis set effect was found, except that the diffuse functions on heavy atoms were found to be importance in the

also accentuated the importance of using a continuum model to describe solvent effects in comparison with the experimental spectra measured in aqueous or organic solutions. Using gas-phase spectra21b or high-level gas-phase calculations21a (e.g., at the EOM-CCSD15 level of theory) to assess XC functionals, it is common to calculate the 0−0 transitions using TDDFT adiabatic calculations. Experimental spectra measured in solution are generally broadened by solvent effects, with maxima corresponding to Franck−Condon vertical excitations.27 Hence, in the above assessments13,24−26 the vertical transition energies were compared with the experimental absorption maxima. Molecular spectra are characterized not only by their electronic transition energies but also by their absorbance, which in TDDFT calculations is determined by the oscillator strengths, and these have been examined in some of the previous TDDFT assessments.15,16 The oscillator strength of a particular excitation is proportional to the transition probability of this excitation.27 In experimental spectra, however, the absorbance of an absorption peak may arise from the overlapping of a series of different transitions because of the broadening effect, and this renders the assignment of TDDFT oscillator strengths to experimental extinctions challenging. In these cases, a compromise is to use high-level calculations (e.g., EOM-CCSD15) as the TDDFT benchmarks. In the present work, TDDFT calculations are combined with spectroscopic measurements to study the UV absorption in aqueous solution of benzoic acid (BA) and several ortho- and para-substituted BA molecules in their neutral (benzoic acid) and anionic (benzoate) forms. Fifteen exchange−correlation (XC) functionals, including pure DFT, GGA hybrid, meta-hybrid, and double-hybrid, as well as range-separated functionals, were used to calculate the excitation energies and oscillator strengths and compared to both the EOM-CCSD benchmarks calculated in the gas-phase and experimental spectra measured in aqueous solutions at both low and high pH, at which the compounds are in carboxylic acid and carboxylate forms, respectively.

2. METHODS The UV spectra of all BA derivatives (2 μM), including benzoic acid (BA), anthranilic acid (AA), salicylic acid (SA), thiosalicylic acid (TSA), phthalic acid (PA), p-aminobenzoic acid (pABA), phydroxybenzoic acid (pHBA), and p-mercaptobenzoic acid (pMBA), were measured at two different pH conditions (low and high) adjusted using dilute NaOH or HCl in deionized (DI) water. The low and high pH values were selected on the basis of pKa values of BAs, at which the BA is either fully protonated (low pH) or deprotonated (high pH). The UV spectra of AA, SA, PA, pABA and pHBA at pH = 4.2 were reported previously.6 The Møller−Plesset second-order perturbation (MP2) with the basis set 6-31+G(d) was used in ab initio energy minimizations. The MP2 optimization has produced both the correct geometry and electric dipole moments for pABA with improved performance relative to DFT.28 Two sets of geometries were used in the TDDFT assessment. The first set was calculated in the gas phase and is denoted the MP2G set. Because all experimental spectra were measured in aqueous solution, it is important to take solvent effects into account for calculations of the UV spectra. A number of dielectric continuum models29 have been developed that provide relatively accurate calculations of solvation free energies,30 pKa values,31 and molecular spectra.32 For ions and other charged species, however, it was found that additional explicit solvent molecule(s) may need to be included 11871

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Figure 1. Experimental UV spectra of benzoic acid derivatives: BA, benzoic acid; AA, anthranilic acid; SA, salicylic acid; TSA, thiosalicylic acid; PA, phthalic acid; pABA, p-aminobenzoic acid; pHBA, p-hydroxybenzoic acid; pMBA, p-mercaptobenzoic acid. The pKa values of the carboxylic acid groups are given, and the locations of the A, B, and C absorption bands are labeled.

TDDFT calculations. Therefore, only the 6-31+G(d) basis set was used for further calculations, including the molecular orbital analysis and UV spectra calculations. The basis set assessment is given in the Supporting Information (Figure S1). The

coordinates of the configurations of both the MP2G and MP2A sets and the Gaussian deconvolution of the experimental shoulder peaks are also given in the Supporting Information (Figure S2). 11872

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has also been observed in L-cysteine films.42c However, gas-phase IR spectroscopy and DFT calculations suggest the carboxylate configuration for L-cysteine.42d According to the experimental pKa's at high pH in aqueous solution, TSA should prefer the carboxylate state. When the cluster-continuum model was used and one explicit H2O molecule was added to interact with the carboxylate, the optimized configuration showed the correct high-pH configuration of TSA (Figure 2B). In contrast, simply adding the explicit H2O molecule in the gas phase without the aqueous continuum model led to the incorrect thiolate configuration (Figure 2B). Therefore, both the explicit (cluster) and implicit (continuum) solvent components are necessary to correctly optimize the negatively charged carboxylate of BAs. In subsequent calculations, for all BA molecules, the MP2A set of configurations was optimized with a single H2O molecule added to interact with each negatively charged carboxylate. The low-pH states of all BAs except phthalic acid (PA) are neutral and therefore no H2O molecule was added in these optimizations. If multiple configurations were obtained as the local minima on the potential energy surface, the lowest potential energy configuration was chosen for subsequent TDDFT assessment. For example, for the two carboxylates and two explicit H2O molecules in phthalate at high pH, the optimized configuration is the one with a hydrogen bond between the two water molecules, which has the lowest potential energy and thus was chosen in the MP2A set for the assessment (Figure 3).

3. RESULTS AND DISCUSSION 3.1. Experimental Aqueous Spectra. Figure 1 summarizes the experimental spectra of all BAs studied in the present work. For each compound, the experimental pHs were chosen according to the pKa values of the carboxylic acid and the substituting group so that the low- and high-pH spectra stand for benzoic acid and benzoate, respectively, with the substituent group unaffected. For example, in pMBA the pKa of the carboxylic acid group is 4.039 and that of the thiol group is 6.8,40 and therefore the spectra measured at pH = 2.0 and pH = 5.0 were used in the TDDFT assessment (Figure S3, Supporting Information). Figure 1 indicates a systematic blue-shift of the low-lying excitation energies of all BAs with increased pH (see below). 3.2. Configurations. Gas-phase optimizations led to configurations corresponding to pKa values opposite to what is found in aqueous solution. Significantly, in the MP2G set, the gas-phase high pH configuration of thiosalicylic acid (TSA) is a thiolate instead of a carboxylate (Figure 2), which is not the

Figure 3. Four optimized configurations (A, B, C, and D) of the phthalate ion with two H2O molecules interacting with the two carboxylate groups. The potential energies (kcal/mol) relative to that in the MP2A set (D) are listed.

Figure 2. Configurations of thiosalicylic acid (TSA) at high pH optimized (A) without and (B) with an explicit H2O molecule. The GAS structure in (A) belongs to the MP2G and the SMD structure in (B) to the MP2A set, respectively. Both explicit (cluster) and implicit (continuum) solvents are necessary to correctly optimize the negatively charged carboxylate of TSA.

3.3. Gas-Phase Calculations Compared with EOMCCSD References. In the first set of comparison calculations, the gas-phase data calculated at the EOM-CCSD37 level of theory were used as references, with the aim of finding out the TDDFT functionals best representing the excited states of BAs. Table 1 compares the performance of 15 XC functionals for the transition energies of all 16 low-lying excitation energies with the EOM-CCSD data. In some cases the pure DFT functionals (BLYP,35a B97D,35b HCTH,35c M06-L35d) and GGA hybrid functionals (B3LYP,10 B3PW91,35e X3LYP,35f O3LYP,35g TPSSh35i) resulted in qualitatively different pH effects than the EOM-CCSD calculations. For example, whereas EOM-CCSD yielded a 0.16 eV blue shift (increase in transition energy) of benzoate relative to benzoic acid (BA), TDDFT calculations with these functionals instead led to strong red shifts (decrease in transition energy) ranging from −0.39 eV (X3LYP35f) to −1.64 eV (HCTH35c) (Table S1, Supporting Information). Similar situations were found in the calculations of AA, PA, pABA, pHBA, and pMBA. Notably, the high-pH gaseous TSA showed a −0.61 eV red shift

aqueous-phase protonation state expected from the pKa's of the carboxylic acid (pKa = 3.5) and thiol (pKa = 8.8) in TSA. Using a continuum model of either SMD33 or IEF-PCM41 in the optimization also yielded a thiolate configuration of TSA at high pH (Figure 2). Also, the excitation energy of the gas-phase thiolate configurations of TSA showed significant discrepancy with the experimental absorptions measured in aqueous solution, with an underestimation of over 2 eV (Table S1, Supporting Information). The thiolate configurations of TSA at high pH may arise from the proton affinity of oxygen being higher than that of sulfur. These results resemble findings on the configurations of anionic L-cysteine.42 Indeed, both experimental and theoretical studies have found that in L-cysteine the thiol group has a lower acidity than the carboxylic acid group,42a and in the gas-phase Lcysteine assumes the thiolate configuration instead of carboxylate.42b Moreover, this type of unconventional zwitterionic state 11873

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different functionals, see Table S3 in the Supporting Information) is useful for clustering different XC functionals. Figure 4 shows a contour map of the R2 matrix. This matrix

Table 1. TDDFT Results Relative to EOM-CCSD Data Calculated Using the MP2G Seta XC functional 35a

BLYP B97D35b HCHT35c M06-L35d B3LYP10 B3PW9135e X3LYP35f O3LYP35g BMK35h TPSSh35i M06−2X35j B2PLYPD35k CAM-B3LYP35l ωB97XD35m LC-ωPBE35n

MAEb (eV)

STDEVc (eV)

R2 d

2.14 (1.59) 1.97 (1.56) 2.12 (1.57) 1.66 (1.26) 1.39 (1.13) 1.32 (1.11) 1.36 (1.10) 1.78 (1.28) 0.74 (0.79) 1.50 (1.23) 0.75 (0.78) 0.59 (0.63) 0.79 (0.81) 0.76 (0.78) 0.49 (0.59)

0.71 (0.21) 0.70 (0.18) 0.74 (0.17) 0.52 (0.20) 0.39 (0.19) 0.33 (0.19) 0.39 (0.19) 0.65 (0.19) 0.21 (0.17) 0.46 (0.18) 0.17 (0.15) 0.17 (0.12) 0.18 (0.15) 0.20 (0.17) 0.20 (0.14)

0.14 (0.88) 0.15 (0.87) 0.16 (0.89) 0.32 (0.86) 0.61 (0.94) 0.67 (0.94) 0.62 (0.95) 0.21 (0.92) 0.80 (0.94) 0.41 (0.93) 0.92 (0.93) 0.92 (0.97) 0.88 (0.95) 0.77 (0.84) 0.74 (0.91)

a

In parentheses are the results using the excitation energies for neutral molecules. bMean absolute error. cStandard deviation of errors. d Square of linear correlation coefficient. Figure 4. Contour plot the R2 matrix (R is the linearity coefficient between two arrays of data) of the transition energies calculated from the 15 functionals: 1, BLYP; 2, B97D; 3, HCTH; 4, M06-L; 5, O3LYP; 6, B3PW91; 7, X3LYP; 8, B3LYP; 9, TPSSh; 10, BMK; 11, M06-2X; 12, B2PLYPD; 13, CAM-B3LYP; 14, ωB97XD; 15, LC-ωPBE. The R2 plot indicates four groups with the functionals 1−5, 6−9, 10−13, and 14−15, respectively.

in the EOM-CCSD calculation compared to its low-pH counterpart. This red shift, which was reproduced by all TDDFT calculations, may arise from the thiolate configuration in the gas phase. The experimental aqueous spectrum of TSA, however, exhibits a blue shift at high-pH (Figure 1), indicating that the high-pH aqueous configuration of TSA may be a carboxylate with a thiol group, consistent with the pKa values and the cluster-continuum calculations. Furthermore, the high-pH configuration of pHBA showed several low-lying excitations in the EOM-CCSD calculation with a red shift of −0.44 eV compared to the low-pH configuration. The TDDFT calculations using the nine XC functionals mentioned above, however, resulted in a much larger red shift ranging from −1.14 (B3PW91) to −2.34 (HCTH) eV (Table S1, Supporting Information). In contrast to the above findings the EOM-CCSD data were appropriately reproduced by the other six functionals, among which the mega-GGA hybrid M06-2X35j and doubly hybrid B2PLYPD35k were in best agreement, with STDEVs of 0.167 and 0.174 eV, respectively (Table 1). The range-separated functionals (CAM-B3LYP,35l ωB97XD,35m and LC-ωPBE35n) also showed correct trends and relatively good agreement with EOMCCSD for the excitation energies. Further, the hybrid functional BMK35h also yielded relatively good results, comparable in quality to the range-separated functionals. These well-performing functionals (M06-2X,35j B2PLYPD,35k CAM-B3LYP,35l ωB97XD,35m LC-ωPBE,35n and BMK35h) also correctly represent the transition energy differences between all low and high-pH configurations of the MP2G set. However, if only the low-pH configurations are included, all functionals reasonably estimate the excitation energies (in parentheses in Table 1); e.g., the most popular B3LYP functional yields a STDEV of only 0.19 eV and R2 of 0.95. In contrast to the excitation energies, the oscillator strength of the functionals varies relatively little (Figure S4, Supporting Information). R2 values for oscillator strengths between the TDDFT and EOM-CCSD data vary from 0.70 (HCTH) to 0.83 (B2PLYPD). However, R2 values between calculations using any two TDDFT functionals are generally higher than 0.95 (not shown). The R2 matrix (with linearity coefficients between any two arrays of low-lying excitation energies calculated with two

clearly indicates that the 15 functionals can be clustered into four groups. Group 1 comprises BLYP, B97D, HCTH, M06-L, and O3LYP, group 2 comprises B3PW91, X3LYP, B3LYP and TPSSh, group 3 BMK, M06-2X, CAM-B3LYP, B2PLYPD, and ωB97XD, and group 4 ωB97XD and LC-ωPBE. ωB97XD is included in two groups because calculations using this functional exhibit a large R2 value with other functionals in both group 3 and 4. The R2 value between two functionals of the same group are larger than 0.85 (red in the contour plot), whereas the R2 value between functionals from different groups are much smaller. Groups 1 and 2 are composed of functionals that incorrectly interpret the trends reflected in EOM-CCSD calculations, whereas groups 3 and 4 give results in good agreement with the EOM-CCSD data. This classification is consistent with the STDEV data presented in Table 1. Hence, further assessments were performed using only the best functionals, i.e., those in groups 3 and 4. 3.4. Aqueous-Phase Calculations Compared with Experimental Reference. The best five functionals selected from the first stage (groups 3 or 4), i.e., M06-2X,35j B2PLYPD,35k CAM-B3LYP,35l ωB97XD,35m and LC-ωPBE,35n were employed using the MP2A set and compared with the experimental spectra. A feature of the aqueous experimental spectra that is significantly different from the gas-phase calculations presented above is that all these spectra exhibit a blue shift at elevated pH. This pH effect is given in Table 2 for the low-lying C-band absorption peaks (see Table S2, Supporting Information, for full data). The SMD33 solvent model was used in all TDDFT calculations. The calculated absorption peaks corresponding to the A, B, and C bands can be compared with those peaks that are clearly separated in the experimental aqueous spectra. Those absorption peaks that cannot be clearly distinguished were excluded at this stage. 11874

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effects. Here, the TDDFT calculations using the MP2A set of coordinates, compared with the experimental spectra in aqueous solution, are used to examine the pH and substitution effects. 3.5.1. pH Effect. The pH of natural waters in the United States varies from 4.1 to 5.9.43 In this pH range, BAs may exist as either benzoic acid or benzoate, or in an equilibrium between the two states, depending on the pKa values of the carboxylic acid groups. The experimental UV spectra presented here were measured at both low and high pHs, at which the compounds in aqueous solution are in the benzoic acid and benzoate states, respectively. Therefore, these spectra provide a good platform for studying the electronic absorptions of BAs in both protonated and deprotonated states. At high pH, i.e., for the benzoates of the selected BA derivatives, the low-lying (C-band) excitations are blue-shifted relative to the low pH benzoic acids (Table 2). The magnitude of this blue shift ranges from 0.06 eV (PA) to 0.31 eV (pABA). All functionals assessed here exhibit trends consistent with both this experimental pH effect and that given by EOM-CCSD calculations (Table S4, Supporting Information). 3.5.2. Substitution Effect. Both the substituting groups and their positions determine the substitution effect. As shown in the experimental spectra (Figure 1), compared to unsubstituted BA, in benzoic acids ortho substitution leads to a red shift of the lowlying excitation in the order of −NH2 (−0.75 eV) > −SH (−0.56 eV) > −OH (−0.45 eV) > −COO− (−0.11 eV), and for benzoates, the red shifts are in the same order, i.e., −NH2 (−0.76 eV) > −SH (−0.60 eV) > −OH (−0.58 eV) > −COO− (−0.31 eV). The para-substituted benzoic acids, however, possess lowlying excitations that are less red-shifted for −NH2 (−0.21 eV) and −SH (0.0 eV) and even reversed to blue shift for −OH (0.33 eV). For the para-substituted benzoates, both −NH2 and −SH groups lead to a red shift of −011 eV and the −OH group to a blue shift of 0.28 eV. The red-shift by ortho-substitution of the −XH groups (X = N, O, S) may originate from the hydrogen bonding between the substituting group and the carboxylic acid (or carboxylate) group, which are missing in the parasubstitutions. The TDDFT calculations using the five functionals also correctly represent the blue shift for pHBA. However, there is disagreement between TDDFT calculations and experimental spectra in that, whereas in the experimental spectra parasubstitution (pABA or pHBA) further enhances the blue-shift amplitude compared with corresponding ortho-substitution (AA or SA), the TDDFT calculations lead to a reversed trend. However, these TDDFT results are all in agreement with the EOM-CCSD calculations (Table 2 and S4, Supporting Information). The substitution effects on electronic transition energies do not correlate directly with the Hammett coefficients of the substituting groups partly because the latter are derived from ground state equilibrium constants, such as pKa's or bond dissociation energies,44 whereas the low-lying transition energies measured by UV spectroscopy are the lowest dipole-allowed optical energy gaps between the ground and excited states.45 3.5.3. Frontier Orbitals of BAs. All the low-lying excitations of BAs involve transitions from HOMO (highest occupied molecular orbital) to LUMO (lowest unoccupied molecular orbital). These frontier orbitals indicate that the low-lying excitations may be either ππ* or πσ* transitions (Figure 5). Whereas the acids of the BA derivatives (BA, AA, SA, TSA, PA, and pMBA) undergo ππ* excitations at the low-lying absorption peak, pABA and pHBA and all the deprotonated benzoates exhibit πσ* excitations. Although the added H2O molecules that

Table 2. Experimental pH Effect on Low-Lying Excitations (C Band) of BA Derivativesa compoundb λl (nm) BA AA SA TSA PA pABA pHBA pMBA

272 326 302 310 281 284 254 272

Eex l (eV)

λh (nm)

Eex h (eV)

Δλ (nm)

ΔEex (eV)

4.56 3.81 4.11 4.00 4.42 4.37 4.89 4.56

259 308 295 298 277 265 245 265

4.79 4.03 4.21 4.16 4.48 4.68 5.07 4.68

4 18 7 14 7 19 9 7

0.23 0.22 0.10 0.16 0.06 0.31 0.18 0.12

a

The absorption wavelengths/excitation energies of the low-lying absorption peaks at low and high pHs (Figure 1) are denoted λl/Eex l b and λh/Eex Abbreviations: BA, benzoic acid; AA, h , respectively. anthranilic acid; SA, salicylic acid; TSA, thiosalicylic acid; PA, phthalic acid; pABA, p-aminobenzoic acid; pHBA, p-hydroxybenzoic acid; pMBA, p-mercaptobenzoic acid.

For all 37 excitations, the five functionals examined yielded a STDEV of ∼0.20 eV with R2 larger than 0.9 (Table 3). The TDTable 3. TDDFT Results Using the MP2A Set Relative to Experimental Aqueous Spectraa XC functional 35j

M06-2X B2PLYPD35k CAM-B3LYP35l ωB97XD35m LC-ωPBE35n

MAEb (eV)

STDEVc (eV)

R2,d

0.29 (0.28) 0.41 (0.42) 0.24 (0.24) 0.27 (0.27) 0.47 (0.48)

0.21 (0.13) 0.22 (0.12) 0.20 (0.12) 0.20 (0.14) 0.20 (0.13)

0.93 (0.98) 0.93 (0.98) 0.94 (0.98) 0.93 (0.96) 0.94 (0.97)

a

In parentheses are the results using the excitation energies for neutral molecules. bMean absolute error. cStandard deviation of errors. d Square of linear correlation coefficient.

CAM-B3LYP calculation yielded the best results on average for the 37 excitations, with STDEV of 0.20 eV, R2 of 0.94 and MAE of 0.24 eV. For excitations of the neutral molecules (16 energies), CAM-B3LYP still produces the best fit with STDEV of 0.12 eV (close to the chemical accuracy of 0.10 eV13), R2 of 0.98 and MAE of 0.24 eV, indicating that the errors may be mainly associated with the negatively charged species and, similar to the solvation free energy and pKa calculations,30,31 a better description for the solvation of ions may likely improve the TDDFT performance. The above two stages of the comparison collectively indicate that the best XC functionals are those with the meta-GGA hybrid functional (M06-2X), the doubly hybrid functional with correlation corrections equivalent to MP2 (B2PLYPD), and the range-separated functionals with dispersion corrections (CAM-B3LYP, ωB97XD, and LC-ωPBE). This trend has also been reported in other TDDFT assessments.19,20,24 The traditional hybrid functional BMK also exhibited relatively better performance than other hybrid functionals or pure DFT functionals, even though it was originally developed for ground state calculations.35h 3.5. Low-Lying Excitations of BAs. A previous study of Hg(II) photoreduction under UV radiation showed that the lowlying excitations of several BAs significantly enhance the reduction rate of Hg(II).6 Hence, to understand the mechanism of Hg(II) photoreduction in the presence of BAs, it is important to understand the low-lying electronic excitations of BAs. The low-lying absorptions are strongly influenced by various factors, two of particular importance being the pH and substitution 11875

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Figure 5. Frontier orbitals of the BA derivatives: BA (1), benzoic acid; AA (2), anthranilic acid; SA (3), salicylic acid; TSA (4), thiosalicylic acid; PA (5), phthalic acid; pABA (6), p-aminobenzoic acid; pHBA (7), p-hydroxybenzoic acid; pMBA (8), p-mercaptobenzoic acid. One H2O molecule is added to donate a hydrogen bond to each carboxylate; these H2O molecules, however, are involved neither in the HOMO nor in the LUMO. The πσ* transitions are found for all high pH configurations; for the low pH configurations, all the other functionals experience ππ* excitations except pABA and pHBA, which exhibit πσ* in the low pH, benzoic acid state.

TDDFT method and the XC functionals.24a The calculated excitation energies are sometimes blue-shifted relative to experiment, sometimes red-shifted, and sometimes a good match. The blue shifts relative to experiments for the calculated C-band of AA, SA, and TSA may originate from the πσ* feature shown above. Without sufficient perturbation by the aqueous solvent the intermolecular hydrogen bond of the ortho-groups −NH2, −OH or −SH to the carboxyl, may be overestimated, leading to a blue shift in the spectrum. The B and A-bands for these ortho-substituted BAs, however, were less affected. The calculated spectra of BA and PA have red-shifted C-bands. The calculated spectra of pABA, pHBA, and pMBA are consistent with the corresponding experimental spectra. The spectra calculated using TDB2PLYPD, TDM06-2X, TDωB97XD, and TDLC-ωPBE exhibit trends similar to those of the TDCAMB3LYP spectra and are provided in the Supporting Information (Figure S5).

interact with the carboxylate significantly alter the configurations of the BAs, they do not participate in the frontier orbitals, indicating that the excitations are dominated by the BAs. However, hydrogen bonding to the solvent H2O molecule switches the ππ* state to πσ*. For p-OH and p-NH2-substituted BAs, this πσ* feature is also observed for the low-pH configurations. This type of excitation and the corresponding πσ* state has been previously reported in high-level calculations on phenol, indole and pyrrole (ref 46). A conical intersection (CI) between the ground state (S0) and excited state (S1) potential energy surfaces have been suggested as a hydrogen-atom detachment mechanism for OH or NH2 groups attached to an aromatic ring.47a Further studies of phenol and thiophenol derivatives proposed a scenario of excited state H-atom detachment either via a CI between the ππ* (S1) and πσ* (S2) states47a,b or through H-atom tunneling from ππ* to πσ*.47c The present calculations and the low-lying orbital analysis indicate a possible πσ* (S1) excitation of phenol, thiophenol and aniline on −COO− substitution. Moreover, potential H-detachment upon UV irradiation supports a radical mechanism of Hg(II) reduction upon UV radiation in the presence of BA substituents.6 3.6. Calculated vs Experimental Spectra. The first 50 singlet excitations based on the MP2A set of configurations and the cluster-continuum solvent model, and calculated using TDCAM-B3LYP, that gave the lowest STDEV and largest R2 to the experimental results (Table 3) were transformed into band spectra using a Gaussian expansion with a full-width-at-halfmaximum (fwhm) of 0.25 eV for all excitations. Comparisons of the calculated spectra and the experimental spectra are shown in Figure 6. In the calculated spectra a linear regression was used to account for the systematic errors from

4. CONCLUSIONS The present work examines TDDFT calculations of UV spectra of eight benzoic acid derivatives using a set of fifteen XC functionals. The corresponding UV spectra were also measured in aqueous solution at different pHs, such that the compounds are protonated at low pH and deprotonated at high pH, respectively. There were two stages in the assessment. In the first stage, gasphase calculations were performed and compared with the highlevel EOM-CCSD gas-phase benchmarks. The best five functionals, i.e., ωB97XD, LC-ωPBE, M06-2X, B2PLYPD, and CAM-B3LYP were selected and used in the second stage, in which the experimental spectra measured in aqueous solution were used as the reference data. In this step, a cluster-continuum 11876

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Figure 6. Calculated spectra (dashed lines) using TDCAM-B3LYP and cluster-continuum solvent model based on the MP2A set of configurations. The experimental spectra (solid lines) are shown for comparison. Key: BA, benzoic acid; AA, anthranilic acid; SA, salicylic acid; TSA, thiosalicylic acid; PA, phthalic acid; pABA, p-aminobenzoic acid; pHBA, p-hydroxybenzoic acid; pMBA, p-mercaptobenzoic acid.

set effects were found and diffuse functions for non-hydrogen atoms appear to be necessary. The low-lying excitations of BAs with −NH2, −OH, or −SH group exhibit a πσ* characteristic, and therefore photoirradiation at the low-lying absorption

model was used to describe the aqueous solvent. This procedure reproduced the configurations of BAs consistent with their experimental pKa values and yielded the same pH and substitution effects as the experimental spectra. Moderate basis 11877

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regions of these BA substituents may result in subsequent Hatom detachment and radical formation. The present analysis is useful in defining XC functionals that are suitable for describing the photoexcitation of BAs, and thus for the study of environmentally relevant photochemical and photophysical processes, including Hg(II) photoreduction in the presence of BAs.

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ASSOCIATED CONTENT

* Supporting Information S

Full citation of ref 34. Figures S1−S5: excitation energies, Gaussian deconvolutions, pH effect on pMBA UV absorption, comparison of oscillator strengths, calculated spectra. Tables S1−S4: excitation energies, R2 matrix, pH effect on low-lying excitations. Coordinates of the MP2G and MP2A configurations used in the present study. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was conducted as a part of the Mercury Science Focus Area research program at Oak Ridge National Laboratory (ORNL), which is sponsored by the Office of Biological and Environmental Research of the U.S. Department of Energy (DOE). ORNL is managed by UT-Battelle LLC for US DOE under contract DE-AC05-00OR22725. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231.

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