Bulgarian Chemical Communications, Volume 42, Number 4 (pp. 343 348) 2010
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Bulgarian Chemical Communications, Volume 42, Number 4 (pp. 343 – 348) 2010 Evaluation of PCB’s chromatographic retention indices using multilinear regression method I. Stanculescu1,2*, G. Mindrila1, C. Mandravel1
Received August 6, 2010; Revised September 14, 2010 The multilinear regression method for polychlorinated biphenyls (PCBs) chromatographic retention indices evaluation was applied. Nine reference PCB's chromatographic retention indices (R) were evaluated using 8 calculated molecular properties (descriptors): molecular volume, molecular weight, partition coefficient (logP), van der Waals and solvent accessible surface, dipole moment, and frontier orbital energies. The best equations were selected via the highest value of the F quality index and the most efficient combinations of descriptors. As expected, the van der Waals surface descriptor appears frequently in the best quality equations. In the discussed equations, the logP descriptor, correlated with the lipophilicity and the reactivity indices of εHOMO and εLUMO, has the biggest weight. Keywords: PCBs; chromatographic retention indices; multilinear regression method; molecular descriptors INTRODUCTION Although the production of polychlorobiphenils (PCBs) is forbidden now, the problems of their recurrence in the environmental components are an issue due to the partitioning, biotransformation and bioaccumulation [1–11] of these hazardous chemicals. In these processes, the PCB adsorption in different phases [1–3] is very important. There are 209 PCB's congeners and their identification is a very difficult task. Such identification is possible trough determination of their retention times using the high resolution gas-chromotography [12–14]. The content of PCBs in transformers oil have been evaluated by GC–MS hyphenated method [15]. Now the chromatographic retention indices were evaluated using the multiple linear regression method (MLR).
(1)
MLR attempts to model the correlation between the chromatographic retention index R and the independent variables xi (descriptors), mediated by a0 - ai which are estimated regression parameters. Recently, B. Tiperciuc and C. Sarbu predicted the chromatographic retention indices (lipophilicity) of some new methyl thiazolil oxadiazoline derivatives using the MLR [16]. CALCULATION DETAILS Chromatographic retention index values of the PCBs are taken from two literature sources [17, 18]. The molecular weight is considered as a descriptor of a special type because the toxicity and the irreversible absorption increase with the complexity of its structure [12–14]. The molecular properties of the PCBs, the grid (solvent accessible) surface (Sg), the approximate (van der Waals) surface (Sa), the molecular volume (V), the dipole moment (μ), the partition coefficient (logP), the and frontier orbital energies (εHOMO, εLUMO) were calculated for structures, optimized with the AM1 method in the Restricted Hartree Fock (RHF) approximation in vacuo, using the HYPERCHEM software [19]. Minimum energy structures were obtained using the Root Mean Square (RMS) gradient of 0.01 kcal/mol·Å. Multilinear regression equations were derived trough the MATHCAD 7 software [20]. RESULTS and DISCUSSION In our study, we considered as descriptors the properties on molecular level such as the molecular volume and weight. We also took into consideration the properties significant for the energy of the molecular interaction: the partition coefficient, van der Waals and solvent accessible surface, and some properties, related to the nuclear-electronic level such as the dipole moment and frontier orbital energies. These descriptors can serve as a basis for the development of predictive models with improved accuracy and precision [21]. A set of 9 PCBs are included in this study: 1(1), 8(2), 31(3), 44(4), 101(5), 138(6), 180(7), 203(8) and 206(9). The bold characters indicate the compound in accordance with IUPAC Convention and the number of the chlorine atoms is given in the brackets [13, 14, 17, 22]. In this series, the PCB1 elutes first, and the PCB206 elutes last on almost every stationary phase, tested as showed in a 2008 research report of the LECO Corporation [18]. We assumed that these nine PCBs are representative for the multilinear regression study for two reasons: (i) it is considered one PCB of each of the nine classes and (ii) these nine PCB’s were proposed as reference compounds because they exhibit linear retention behavior on stationary phases [18]. For example, the regression of the PCB reference series (the retention time versus the chlorine atom number) demonstrates that the behavior is linear for the DB-XLB phase [12–14]. The CAS registry numbers, the retention indices (RT1 and RT2), and the descriptor values, calculated as described in the calculation detail paragraph, are listed in Table 1. This table shows an increase in the property values and the number of the chlorine atoms in the PCB molecules. Table 1. PCB CAS numbers, calculated molecular properties and chromatographic retention indices.
Taking into account only the combinations with Sa or Sg, 183 equations were derived for each of the retention index series: 27 equations with 2 descriptors, 50 with 3 descriptors, 55 with 4 descriptors, 36 with 5 descriptors, 13 with 6 descriptors, and 2 with 7 descriptors. In tables 2 and 3, according to then F values, the best 10 equations with 2-6 descriptors were selected for each of the index series, and the best 2 equations with 7 descriptors were selected for each of the retention index series. In practical terms, the MLR equations of Tables 2 and 3, were evaluated by values of correlation coefficient r2, F factor, and p value(the equation significance level. The correlation coefficient r2 is 0.999 for all equations. The F factor which is the measure of the regression relationship, was calculated with the formula: Surely, the weight of a descriptor is determined by the value of the ai coefficients. Thus, in Table 2, in the equations with 5, 6 and 7 descriptors, logP has the biggest weight almost always and the εHOMO descriptor has the second biggest weight. LogP has the biggest weight 4 times and εLUMO 5 times in the case of 4 descriptor equations. The biggest weight for the equations with 3 descriptors corresponds to εLUMO for half of the equations, and for 3 equations to μ, logP, and εHOMO. The biggest weight varies for the equations with 2 descriptors. We have similar comments about Table 3, and one may see that the M descriptor is never of the biggest weight. Table 2. Multilinear regression equations, obtained using RT1 (r2=0.999).
Table 3. Multilinear regression equations, obtained using RT2 (r2=0.999).
CONCLUSIONS Good correlations of chromatographic retention indices for the 9 PCBs with molecular properties using multilinear regression were obtained. The best 10 combinations of 2, 3, 4, 5 and 6 descriptors from the group of 8 considered were determined for each retention index series according the values of the regression quality indices [23, 24]. In the majority of best equations with the biggest F value, the presence of Sa descriptor shows the importance of the molecular surface and stationary phase interaction. The descriptors with the biggest weight are the logP, correlated with the lipophilicity, and the reactivity indices, εHOMO and εLUMO. Acknowledgements: The authors would like to thank to Prof. G. Surpateanu from the University of Dunkerque, France for the generous computational resources made available for us. This work was funded by the ANCS, DELCROM and ARCON projects, contract no. 92-086/2008 and 92-083/2008, respectively. REFERENCES
Определяне на индексите на задържане при хроматографския анализ на поли-хлорирани бифенили (PCB) с помощта на множествена линейна регресия Й. Станкулеску1,2, Г. Миндрила1, К. Мандравел1 Департамент по физикохимия, Химически факултет, Университет на Букурещ, бул. Кралица Елизабет,4-12 район 3, Букурещ 030018, Румъния 2 – Технологичен център IRASM, Национален институт по физика и чдрено инженерство “Хория Холубеи”, ул. Атомистилор, 407, Магуреле, Илфов 077125, Румъния Постъпила на 6 август, 2010 г.; преработена на 14 септември, 2010 г. (Резюме) Приложен е методът на множествената линейна регресия за определяне на времената на задържане при хроматографията на поли-хлорирани бифенили (PCB). Определени са девет референтни хроматографски индекса (R) използвайки 8 изчислени молекулни свойства (дескриптори): моларен обем, молекулна маса, коефициент на разпределение (logP), ван-дер-Ваалс’ова и достъпна повърхност по разтворител, диполен момент, and гранични орбитални енергии. Подбрани са най-подходящите уравнения според най-високия качетсвен индекс F и най-ефективната комбинация от дескриптори. Както се очаква, дескрипторът “ван-дер-Ваалс’ова повърхност” се явява често в най-добрите уравнения. В обсъжданите уравнения дескрипторът logP, корелиран с липофилността и индекса на реактовпспособност (εHOMO and εLUMO) има най-голямо тегло. 343 Каталог: bcc volumes bcc volumes -> Bulgarian Chemical Communications, Volume 41, Number 2 (pp. 104-109) 2009 bcc volumes -> Bulgarian Chemical Communications, Volume 41, Number 1 (pp. 23-30) 2009 bcc volumes -> Bulgarian Chemical Communications, Volume 41, Number 2 (pp. 127-132) 2009 bcc volumes -> Bulgarian Chemical Communications, Volume 40, Number 4 (pp. 464-468) 2008 bcc volumes -> Bulgarian Chemical Communications, Volume 41, Number 2 (pp. 133-137) 2009 bcc volumes -> Bulgarian Chemical Communications, Volume 40, Number 4 (pp. 397-400) 2008 bcc volumes -> Bulgarian Chemical Communications, Volume 46, Number 2 (pp. 330 333) 2014 bcc volumes -> Bulgarian Chemical Communications, Volume 44, Number 4 (pp. 307 309) 2012 bcc volumes -> Bulgarian Chemical Communications, Volume 47, Number 2, 2015 bcc volumes -> Bulgarian Chemical Communications, Volume 44, Number 4 (pp. 283 288) 2012 Изтегляне 220.34 Kb. Сподели с приятели:
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, where MSR is mean square regression, and MSE is mean square error [24]. An examination of Tables 2 and 3 shows that the same combinations of 6 descriptors (M, logP, ELUMO, Sa, V, μ), 5 descriptors (M, logP, ELUMO, Sa, μ) and 3 descriptors (ELUMO, Sa, μ ) give the biggest F value (see lines 12, 22 and 42 in the tables 2 and 3). The quality of the obtained equations was good, taking into consideration the r2 and F values. Additionally, the calculated p values (data not shown) are very small for the high quality obtained equations. As expected, M, , Sa, and logP descriptors are the most frequently used descriptors in the best equations, with highest F factor. Even equations with 2 descriptors have highest F values when Sa and are used as descriptors.