2016 Volume 15 Issue 1 Pages 13-21
Computational chemistry programs were evaluated as aids to teaching qualitative analytical chemistry. Computational chemical calculations can predict absorption spectra, thus enabling the modeling of indicator dissociation mechanisms by different computational chemical programs using a personal computer. An updated MNDO program among 51 programs was found to be the best predictor to explain the dissociation mechanisms of isobenzofuranones and sulfonephthaleins. Unknown dissociation constants were predicted from atomic partial charges instead of Hammett's constants.
How to quantitatively teach qualitative analytical chemistry is a very important subject for analytical chemists. Previously, a method to teach molecular interaction mechanisms in chromatography was quantitatively achieved using molecular mechanics and MOPAC programs [1]. Furthermore, the reaction mechanisms of highly sensitive detections were also quantitatively described [2,3]. Further study was carried out for simple detection, indicator's color changes by using updated computational chemical programs.
Color indicators have been the backbone of simple pH tests and titration analyses. The spectrophotometric determination of hydrogen ion concentrations by using color indicators was described [4]. The precision of indicator dissociation constants was evaluated and the dissociation mechanisms (pKa) were described in detail. The pKa values were found to vary according to salt, temperature, and the laboratories where the work was conducted [5,6]. The effects of salts and proteins on the spectra of some dyes and indicators were studied [7]. The dissociation processes were described in detail by Kolthoff [5]. However, the absorption wavelength and electron density changes were not well described. The dissociation mechanisms, maximum wavelengths, and electron density maps of isobenzofuranones and sulfonephthaleins were, therefore, evaluated by in silico analysis despite the anticipated poor precision. The experimentally measured dissociation of phenolphthalein is described using four dissociation structures, where the ionization of two phenolic hydroxyl groups converts the neutral molecular form into the red quinoid form. Further dissociation from the quinoid structure to the alcoholic form eliminates the color. The dissociation mechanisms can also be described using three structures without the need for a transition structure [8].
There are many color indicators having chemical structures similar to phenolphthalein; these indicators should have similar dissociation mechanisms. The differences in their dissociation constants depend on the inductive effects of the substituents. The associated four dissociation structures were constructed and their spectra and HOMO and LUMO electron density maps were calculated. The unreported dissociation constants were predicted from atomic partial charge calculated using an empirical program PM6. There still remains the limitation that computational chemistry programs can estimate the spectra only in the absence of solvents.
The computers used were PowerMac G3 and Dell Optiplex running on ChemIntosh® from SoftShell (SanDiego, CA) and CAChe® and SciGress® programs from Fujitsu (Tokyo, Japan). The spectra were measured in aqueous solutions using a Shimadzu UV1200 (Tokyo, Japan). Indicators used are listed below. The SciGress program provides different programs to calculate electronic spectra, including MNDO, AM1, PM3, PM5, PM6, RM1, PDDG/MNDO, PDDG/PM3, DFT, ZINDO/S, INDO/S, CNDO/S, CNDO/S2, CNDO/S3, CNDO/2, CI, RPA, ZINDO, and MO-S. The dissociation spectra of phenolphthalein structures were calculated using these programs and used to evaluate the accuracy of the programs. The properties of the indicators are summarized in Table 1. The abbreviations of computational chemical programs are summarized later.
o-Cresolphthalein:3,3-bis(4-hydroxy-3-methylphenyl)-isobenzofuran-1(3H)-one
α-Naphtholphthalein:3,3-bis(4-hydroxynaphthalene-1-yl)-2-benzofuran-1-one
Phenolphthalein:3,3-bis(4-hydroxyphenyl)isobenzofuran-1(3H)-one
Thymolphthalein:3,3-bis(4-hydroxy-2-methyl-5-propane-2-ylphenyl)-2-benzofuran-1-one
Bromocresolgreen;2,6-Dibromo-4-[7-(3,5-dibromo-4-hydroxy-2-methyl-phenyl)-9,9-dioxo-8-oxa-9λ6-thiabicyclo[4.3.0]nona-1,3,5-triene-7-yl]-3-methylphenol
Bromocresolpurple:4,4'-(1,1-dioxido-3H-2,1-benzoxathiole-3,3-diyl)bis(2-bromo-6-methylphenol)
Bromophenolblue:4,4'-(1,1-dioxido-3H-2,1-benzoxathiole-3,3-diyl)bis(2,6-dibromophenol)
Bromothymolblue:4,4'-(1,1-dioxido-3H-2,1-benzoxathiole-3,3-diyl)bis(2-bromo-6-isopropyl-3-methylphenol)
Chlorophenolred:2-chloro-4-[3-(3-chloro-4-hydroxyphenyl)-1,1-dioxobenzo(c)oxathiol-3-yl]phenol
Cresolred:4,4'-(1,1-dioxido-3H-2,1-benzoxathiole-3,3-diyl)bis(2-methylphenol)
Cresolpurple:4,4'-(1,1-dioxido-3H-2,1-benzoxathiol-3-yldine)bis(3-methylphenol)
Phenolred:4,4'-(3H-2,1-benzoxathiole-3-ylidene)bisphenol
Thymolblue:4-[9-(4-hydroxy-2-methyl-5-propane-2-yl-phenyl)-7,7-dioxo-8-oxa-7λ6-thiabicyclo[4.3.0]nona-1,3,5-trien-9-yl]-5-methyl-2-propane-2-yl-phenol
The basic structures of isobenzofuranones and the dissociated phenolphthalein molecules drawn using Chemintosh® are shown in Figures 1 and 2, respectively. There are many computational chemistry programs available to create electronic spectra. The programs used are summarized in Table 2. The spectra of phenolphthalein structure 3, shown in Figure 3, were calculated to compare MM2 and MM3 using programs 3, 4, and 25 (a, b). Structure 3 was initially optimized using MM2 for programs 3 and 25 (a), and MM3 for programs 4 and 25 (b). Programs 3 and 4 are ZINDO and program 25 is MO-S MNDO. The basic geometries can be optimized using molecular mechanics, either MM2 or MM3. MM3 was found to show weak absorption spectra, and did not provide definite information about the maximum absorption wavelengths. Structures optimized using MM3 exhibited weak molar absorptivities and red shift. The intensity was about half of that of calculated using MM2 as shown in Figure 3, and semi-empirical combinations did not work in many cases, with computer error messages being generated. Therefore, MM2 was chosen as the initial program, and the spectra of dissociated phenolphthaleins were calculated using SciGress programs. The results are summarized in Table 3, where some absorption wavelengths are given following their absorption strength. The three dimensional structures of phenolphthalein optimized using the MM2 program are shown in Figure 4 with HOMO and LUMO electron density maps optimized using semi-empirical programs (PM6).
Chemical structures of isobenzofurans.
Dissociation scheme of phenolphthalein.
Comparison of UV-Vis spectra of dissociated phenolphthalein structures using different programs
Comparison of ZINO and MO-W, MNDO using CI at MM2 and MM3 geometry of phenolphthalein structure 3.
HOMO and LUMO electron density maps of phenolphthalein dissociation. structures 1-4.
The estimated wavelength of structure 3 representing the red color varied from 310 to 813 nm. Absorption spectra are generally shifted to lower wavelength in polar solution. Therefore, the calculated wavelengths should be higher than the measured wavelength of 550 nm. Programs 2, 3, 14–16, 18–21, 25, 27, 28, 32–35, 37, 42, 49, and 50 were acceptable candidates for further study. Therefore, the spectra of structures 1 and 4 were calculated using these programs.
The evolution of computational chemistry programs should improve the precision of predicted spectra. However, these results indicate that no single program accurately predicts spectra for all types of compounds. By comparison of the configuration interaction (CI) and analogous random-phase approximation (RPA) using MM2 geometry, MO-S, RPA, MM2, and AM1, or PM3 or PM5 combinations predicted greater red shifts than MO-S, CI, MM2, and AM1, or PM3 or PM5 combinations. CNDO/2, CNDO/S2, CNDO/S3, and RPA combinations were not suitable for phenolphthalein structure 3, but CNDO/2, CNDO/S2, CNDO/S3, and CI combinations estimated the red shift wavelength quite well. CNDO/S and CI or RPA combinations worked well, but INDO/S and CI or RPA combinations gave overly strong red shift. However, ZINDO gave a relatively better wavelength prediction. A Zerner modification seemed to improve the original INDO performance for phenolphthalein structure 3. The combination of RPA and a semi-empirical geometry such as AM1, PM3, PM5, or RM1 gave higher wavelengths than that of a CI and semi-empirical combination, but the calculated wavelength were still relatively short. PDDD and MNDO combinations worked fine with CI; however, a combination of PDDG/MNDO and RPA showed increased red shifts. In general, CI was better than RPA that gave weak visible wavelengths, as well as than RM1. As described in reference 8, CI was much more accurate than RPA and even predicted the wavelength difference. The long calculation times for CI have been reduced by the development of fast personal computers.
These results differed from those of six carotenoids [17]. In calculations of the electronic wavelength spectra of carotenoids in conjugated molecules, INDO/S, provided the best agreement with the experiment. AM1 and PM3 values were very similar with a small shift of PM3 energies toward the blue light. Compared with INDO/S, AM1 and PM3 results were shifted either to the blue or red, depending on the molecules chosen. MNDO and MINDO/3 gave energies generally red-shifted compared to those of INDO/S [8]. Vertical excitation energies computed with INDO/S showed the best agreement with the experiment. However, this approximation was not adequate for ground-state molecules. On the other hand, the electronic spectra showed reasonable agreement with experiment and reproduced the basic trends [17], though MNDO was the best for phenolphthalein. The small wavelength difference cannot be justified because the solvent effect was not included in the calculation. Combinations of CNDO and RPA showed strong blue shift, except for CNDO/S. Despite these programs having been basically evolved from NDDO, the order of development is NDDO < CNDO < INDO < MINDO < MNDO < AM1 < DFT<PM3 < PM5<RM1 < PM6. As described, AM1 and PM3 have been developed from MNDO [18], but MNDO showed the best agreement with the experimental results for the phenolphthalein structure 3.
In ZINDO programs, INDO/S showed red shift, and AM1, PM3, PM5, PM6, and RM1 showed blue shift. MM3 geometries exhibited complicated spectra. ZINDO and CI with AM1, PM3, or PM5 geometries gave lower wavelengths than MO-S and CI at AM1, PM3, or PM5/MM2 geometries. ZINDO with semi-empirical geometries (AM1, PM3, PM5, PM6, or RM1) demonstrated lower absorption wavelengths than with either MM2 or MM3 geometries. MO-S with a semi-empirical program with MM2 or MM3 geometries showed higher absorption wavelengths. INDO gave higher red shift than MNDO.
MO-S, CI, and MNDO combinations at MNDO geometry showed the most reasonable wavelength, and PDDG/MNDO combination produced the best result. AM1, PM3, PM5, and RM1 geometries showed blue shift. However, this approximation was not adequate for the ground state compounds. On the other hand, AM1, PM3, and PM5 showed reasonable agreement with the experiment for the ground state spectra. The estimated spectra of phenolphthalein structure 1 indicated strong absorption at lower wavelengths; however some programs showed weak visible absorption. If the weak absorption cannot be neglected, programs 42, 43, 49, and 50 are not suitable for this study. The calculated spectra of phenolphthalein structure 4 also indicated visible absorption using programs 14, 15, 25, 26, 28, 35, 36, 37, 49, and 50. The RPA program does not seem to be suitable for the calculation of phenolphthalein spectra.
Color is not related to single wavelength as summarized in Table 2. If the absorption spectra of structure 2 are acceptable, programs 3 and 25 can be used to calculate the spectrum of the unstable, transition state structure 2. Program 9 only showed the visible spectra for the structure 3, with significant blue shift. Program 42 gave the best wavelength; however, structure 4 showed weak visible absorptions. In acidic condition (0.05 M phosphoric acid), structure 1 should absorb at 230 nm. Programs 53 and 75 demonstrated high absorption but programs 3 and 9 showed weak absorption, and the maximum absorption wavelength was lower than 200 nm. Other isobenzofuranones, o-cresolphthalein, thymolphthalein, and α−naphthylphthalein showed results similar to those obtained for phenolphthalein. Structure 2 optimized by MM2 showed strong visible absorption. The best visible absorption was obtained by program 42; however structures 1, 2, and 4 showed weak visible-light absorption. Structures optimized using PM6 (program 9) showed the best wavelength selectivity, but the structure 3 wavelength showed blue shift.
The ZINDO-DFT combination did not deliver reasonable wavelengths, even with calculation times of longer than 14 hours. Therefore, this was not used further. RM1 was also not suitable for phenolphthalein. The ADF program was listed but not included in this SciGress program.
Since phenolphthalein was discovered in 1871, many similar compounds have been synthesized and used as color indicators (Table 1). Because their dissociation mechanisms must be the same as that of phenolphthalein, their spectra and electron density maps have been calculated. Their structures are summarized in Figure 5, and the estimated dissociated structures are shown in Figure 6, with chlorophenol red as an example. The spectra of dissociated compounds are summarized in Table 3, where these spectra were calculated using programs 5, 9, 25, and 42. Structures 1 and 4 spectra should be non-color, therefore only their longest wavelengths are listed to indicate their color. Structures 2 and 3 spectra should be visible but several calculated wavelengths did not demonstrate their visible spectra.
Chemical structure of sulfonephthaleins.
Dissociation scheme of chlorophenol red.
These programs were selected based on the results of phenolphthalein. The MNDO element of PDDG/MNDO gave an error message for phenylsulfonephthalein because the original MNDO cannot handle sulfur. MNDO in programs 42 and 49 appears to have been updated. Alkyl-substituted sulfonephthaleins gave results similar to those of isobenzofuranones. The visible absorption of structures 1, 2, and 4, optimized with MNDO or PM6, was weak, and structure 2 optimized with MM2 showed strong visible absorption. Chloro-substituted isobenzofuranones showed results similar to isobenzosulfones and alkyl-substituted sulfonephthaleins. The most complicated results were obtained for bromo-substituted sulfonephthaleins. In particular, bromocresol purple and bromophenol blue showed very poor performance. Their structures optimized using PM6 or MNDO did not show reasonable visible absorption spectra, which may be because of poor properties of bromine that has a strongly negative inductive effect.
This in silico analysis quantitatively demonstrated the dissociation mechanisms together with their HOMO and LUMO electron distributions, as shown in Figure 4. In the ionization process, the LUMO indicated the resonance form that caused the red shift. The increased π-electron delocalization in the anion produces a smaller HOMO-LUMO gap and increased absorption wavelength [14]. The dissociation constants were affected by the inductive effects of substituents. Alkyl groups (+I effect) produce higher dissociation constant shift, and halogens (-I effect) provide lower dissociation constant shift, similar to the dissociation constants of phenolic compounds where their dissociation constants were predicted from their oxygen atomic partial charges [19]. The atomic partial charges (apc) of oxygen calculated using MOPAC-PM5 are summarized in Table 1. The dissociation of two hydroxyl groups is the main mechanism, and both have the same chance of dissociation. Therefore, the sum of these oxygen atomic partial charges of structure 3 was used to predict unknown pKa values. The reference pKa values from reference 18 were used as the standard values. The predicted pKa values were calculated from the following equation: pKa = −29.966 (pKa reference) − 37.079 giving r = 0.972 (n = 9). The predicted pKa values are listed in Table 1. MNDO was the best program to calculate these spectra, but the apc values calculated using MNDO were not suitable for pKa prediction. In addition, this method can be used to design better reagents those have improved wavelength selectivity and absorption intensity.
The comparison of calculated spectra indicates that a selection of program set was not easy for a variety of compounds. This is a tedious process to find the best program set to obtain an identical spectrum with the measured spectrum. However, we have to recognize the estimated spectra were calculated in vacua, but the experimental spectra were measured in pH controlled aqueous solution, This means that chemically estimated computational spectra should be used as the relative information to study the color indicator mechanisms.
Computational chemical analysis can help to teach qualitative analytical chemistry better. For spectral predictions and the visualization of the electron-transfer mechanisms of color indicators, combinations of MO-S or MNDO with CI seemed to give the best results for isobenzofuranones and sulfonephthaleins (structure 3). The MO-S and CI combination was suitable for the ground-state structure of isobenzofuranones and sulfonephthaleins (structures 1 and 4). The precision of computational chemical programs has been improved for protein analysis; however, the above results demand further improvement for small molecules. 51 programs are collected, some programs included water for the calculation; however, estimation of solvent effects remains as a challenge. Above results will help to improve the precision of up-dated programs to predict spectra of a variety of compounds with a program selection guide.
4.1 Abbreviations of computational chemical programsThe following programs are listed in SciGress programs, however, the selection guide is not available. First, constructed structures were mainly optimized by MM2; then their spectra were calculated using the following programs.
ADF: Amsterdam Density Functional (DFT-Density Functional Theory- for molecules, heavy elements, transition metals) [18]
AM1: Austin Model 1-semi-empirical method for the quantum calculation of molecular electronic structure in computational chemistry based on NDDO [20,21,22].
CEO: Collective Electronic Oscillators [17,22]
CI: Configuration Interaction [23,24]
CNDO: Complete Neglect of Differential Overlap [25,26,27,28,29]
CNDO/S: CNDO for Spectroscopy
DFT: Density Functional Theory [30,31]
DFT B88: DFT Becke88- pure GGA [32,33]
GGA: Generalized Gradient Approximation [32,34]
LYP: GGA correlation functional from Lee, Yang and Parr functional [32,33]
INDO: Intermediate Neglect of Differential Overlap [17,23,24,35]
INDO/S: INDO for Spectroscopy [17,36]
MNDO: Modified NDDO; does not take intra-account delocalization effect, uses only s and p orbital sets [18,21,37,38,39].
MNDO/d: MINDO with d-orbital [40]
MINDO/3: version up product of INDO; Modified Neglect of Diatomic Differential Overlap [24,35,40]
MO-S: Molecular Orbital package to calculate Spectroscopic properties of a molecule [SciGress, Fujitsu]
NDDO: Neglect of Diatomic Differential Overlap [21,24]
PDDG: Pairwise Distance Directed Gaussian modification of NDDO provides good description of the van der Waals attraction between atoms [38].
PM3: Parametric Model 3; Reparametrization of MNDO with core-core repulsion term similar to those of AM1 [20,21,38].
PM5: Parametric Model 5; Version-up program of PM3 [21]
PM6: Version-up program of PM5, however, PM6 can handle more elements compared to PM5 according to James Stewart [21,41].
PW91: Perdew-Wang 1991 functional [32,33,34,42,43]
RM1: Recife Model 1, Semi-empirical methods, Reparametrization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I [21,41,44].
RPA: reference 22
SAOP: Statistical Average of Orbital Potentials [42]
TZP: Triple-Zquality augmented by one set of Polarization functions [32]
ZINDO: reference 23
ZORA: Zero-Order Regular Approximation [42]
