In our recent communication , we have employed atomic descriptors derived from density functional theory (DFT) based methods to predict the bioconcentration factor (BCF) of polychlorinated biphenyls (PCBs) in fish. PCBs belong to important group of environmental pollutants, which were industrially used as dielectric fluids in transformers and capacitors, as hydraulic and heat transfer fluids, and as plasticizers . These chemicals were either washed down into the soil or into the water bodies . From the soil, these are absorbed by the plants along with water and minerals, and from the water bodies, these are taken up by aquatic plants and animals . This is one of the ways in which they enter the food chain . As these chemicals are not degradable, these get accumulated progressively at each tropic level    . As human beings occupy the top level in any food chains, the maximum concentration of these chemicals gets accumulated in our bodies  - . Fish are the principal target organisms of BCF assessment due to their relevance as food for many species including humans and the availability of standardized testing protocols   . In general, however, experimental determination of BCFs is expensive and demanding if performed correctly. Hence, a number of QSAR based study of BCFs of the PCBs were made time to time   -  because QSAR technique  increases the probability of success and reduce the time and cost in exploring the toxicological and ecological characteristics of molecules. A number of quantum chemical descriptors    have been identified in the framework of QSAR. In the present work, we present the DFT based derived quantum chemical descriptor to correlate the BCF of PCBs.
In 1960s, Hohenberg and Khon put forward two basic theorems to which DFT is based on and its performance in the description of structure, energetic, and magnetic molecular properties has been quite substantially reviewed time to time  - . DFT methods are, in general, capable of generating a variety of isolated molecular properties, such as dipole moment, ionization energy, electron affinity, electronegativity, hardness, softness, electrophilicity index, etc., quite accurately    . Here, following seven quantum chemical descriptors based on DFT method  have been tested and the final QSAR model was constructed with the help of significant descriptors. A concise description of these descriptors is as below.
The dipole moment is used to describe the polarity of the molecule  The dipole moment, μ, of a molecule is the vector sum of the dipole moments of the bonds and is calculated according to the rule of vector addition. If two bonds with the dipole moments P and Q are at an angle θ the total dipole moment is given by
For instance, two identical bonds with the opposite directions (θ = 180˚) have μ = 0. For identical bonds (P = Q) Equation (1) yields
Ionization energy (IE), electron affinity (EA), electronegativity (χ), hardness (η) and softness (S) are defined as  
where μ is chemical potential, E is the total energy, N is number of electrons of the chemical species and v(r) the external potential. The operation definition of electronegativity, hardness and global softness are defined as:
Parr et al. introduced the global electrophilicity index , in terms of chemical potential and hardness. The electrophilicity index, ω, is a reliable property of a chemical system and its operation definition is
3. Materials and Methods
Fifty seven PCB congeners listed in Figure 1 are the study materials for the present study. These congeners were taken from the literature with their experimental logarithmic BCF values (LogBCFexp) for several fish species (guppies, fathead minnow, rainbow trout, and bluegill sunfish) . For BCF prediction, the 3D modeling  and geometry optimization of all the compounds have been performed on workspace program of CAChe pro software of Fujitsu  using the B88-PW91 GGA energy function with the DZVP basis set. The values of various descriptors, such as dipole moment (μ), ionization energy (IE) and electron affinity (EA) have been directly obtained from DFT calculation results and have been tabulated in Table 1. However, the values of electronegativity (χ), hardness (η), softness (S) and electrophilicity index (ω) have been calculated by solving equations given in theory and the necessary values taken from DFT calculation results and have also been tabulated in Table 1. The Project Leader program associated with CAChe has been used for multiple linear regression (MLR) analysis  using leave-out method and various regression equations have been developed for prediction of BCF (LogBCFpre).
4. Results and Discussion
The assessment of BCF of a hypothetical compound is of prime interest. The QSAR method saves time and cost in determining the BCF of a series of compounds with the help of BCF of previously known compounds. The biphenyl
Figure 1. Biphenyl, its chloro-derivatives and their congeners with their experimental logarithmic BCF .
and its fifty seven chloro-derivatives (mono-, di-, tri, tetra-, penta-, hexa-, hepta-, nona- and decachlorobiphenyl are one, eight, four, ten, nine, twelve, six, five and one in number, respectively) and their experimental logarithmic BCF values have been taken from the literature. A number of quantum chemical descriptors have been identified which are capable of successfully correlating the activity with the structure of a chemical system. The present study is based on seven
Table 1. Values of quantum chemical descriptors, experimental BCF and predicted BCF.
adata point not used in the model, µ is the dipole moment in debye, IP is the ionization energy in eV, EA is the electron affinity in eV, χ is the electronegativity in eV, η is the absolute hardness in eV, S is the global softness and ω is the electrophilicity of the molecule.
quantum chemical reactivity descriptors: dipole moment, ionization potential, electron affinity, electronegativity, hardness, softness and electrophilicity index. Dipole moment (μ) gives valuable information regarding the symmetry of molecule. It also helps in explaining the solubility of substances. The computational result of dipole moment of the compounds (Table 1) show that all the compounds have definite dipole moment, except compound no. 1 and 10. Thus, both of these compounds are symmetrical. The range of dipole moment is 0.002 - 0.011D (5), 0.156 - 0.933D (8), 1.073 - 1.997D (20), 2.005 - 2.875D (18) and 3.141 - 3.668D (5). Ionization potential (IP) of a molecule is the minimal energy needed for the detachment of an electron for a molecule. According to Koopman’s theorem the IE is simply the eigenvalue of HOMO with change in sign and characterizes the susceptibility of the molecule toward attack by electrophiles. IP value as included in Table 1 shows that fifteen compounds have their IP in the range of 5.557 - 5.971 eV and the rest forty five in the range of 6.028 - 6.535 eV. Electron affinity (EA) is the energy difference between an uncharged species and its negative ion. It is an important property of atoms and molecules. According to Koopman’s theorem  the EA is simply the eigenvalue of LUMO with change in sign and characterizes the susceptibility of the molecule toward attack by nucleophiles. The experimental and/or theoretical determination of this quantity is an important task. A close look at Table 1, shows all the compounds have definite value of electron affinity (1.812 to 1.998 eV (5) and 2.084 - 2.960 eV (53). Electronegativity (χ) measures the ability to attract electron itself. Large χ values characterize acids and small χ values are found for bases. If two molecules are brought together, electrons will flow from the one of lower χ to that of higher χ. All the compounds have definite value of χ ranging from 4.003 to 4.591 eV, except three compounds (1, 2 and 11) have χ value lower than 4.0 eV. The parameter hardness (η) is interpreted as the resistance of the chemical potential to change in the number of electrons or resistance to deformation or change. All the compounds have definite value of η in the range 1.609 - 1.998 eV (46) and 2.0 - 2.191 eV (12). The minimum value of hardness is zero and it corresponds to the maximum softness (S). The ranges of softness values are 0.228 - 0.299 (50) and 0.302 - 0.311 (8). Electrophilicity index (ω) measures the stabilization in energy when the system acquires an additional electronic charge from the environment. The electrophilicity index is positive, definite quantity and the direction of the charge is completely determined by the electronic chemical potential (μ = −χ) of the molecule because an electrophile is a chemical species capable of accepting electrons from the environment and its energy must decrease upon accepting electronic charge. All the compounds have definite value of ω included in Table 1. The range of ω is 3.657 - 3.999 (5), 4.179 - 4.991 (34), 5.014 - 5.8 (15) and 6.041 - 6.487 (4).
Multiple linear regression analyses were employed to developed reliable models for the prediction of BCF. For MLR analysis, above descriptors (Table 1) were used as independent variables and the experimental logarithmic BCF values as dependent variable. MLR analysis has been made by Project Leader software associated with CAChe, using the descriptors in various combinations. The best seven models (for k = 1, 2, 3, 4, 5, 6 and 7) are presented here.
When, k = 1, single descriptor has been used as independent variable, then with respect to each descriptor seven equations were made and the best-fitted equation of this class is Equation (8), where IP is the ionization potential of the molecule and, it has a positive descriptor coefficient magnitude that shows that its direct relationship with the BCF.
The predicted logarithmic BCF values from Equation (8) are also given in Table 1. The statistical quality of the equation is good as is evident from its correlation coefficient r2 value = 0.9118 and a cross-validated coefficient = 0.8953. The predicted BCF is reliable as is evident from its standard error (SE) value. The trend of the experimental and predicted BCFs is shown in Figure 2(a) which shows that there is little difference between experimental and predicted BCFs.
For k = 2, the best-fitted equation is Equation (9), where µ and IP is the dipole moment and ionization potential of the molecule, respectively. Both, µ and
Figure 2. Trend of experimental BCF and predicted BCF.
IP have positive descriptor coefficient magnitudes that show direct relationships with the BCF.
The predicted logarithmic BCF values from Equation (9) are also given in Table 1. The statistical quality of the equation is more reliable than Equation (8) as is evident from its correlation coefficient r2 value = 0.91389 and a cross-validated coefficient = 0.8986. The predicted BCF is reliable as is evident from its standard error (SE) value. The trend of the experimental and predicted BCFs is shown in Figure 2(b).
For k = 3, the best-fitted equation is Equation (10), where IP, EA and χ is the ionization potential, electron affinity and of the molecule, respectively.
Both, IP and EA have negative descriptor coefficient magnitudes that show indirect relationships with the BCF, while the third descriptor, χ, has a positive magnitude i.e., direct relationship. The statistical quality of the equation is r2 = 0.9102, = 0.8946 and SE = 0.2775. The predicted logarithmic BCF values as obtained from this model are also given in Table 1. The trend of the experimental and predicted BCFs is shown in Figure 2(c).
For k = 4, the best-fitted equation is Equation (11). The variables of this model are dipole moment, ionization potential, electron affinity and electronegativity, all with negative descriptor coefficient magnitudes except the electronegativity.
For k = 5, the best-fitted equation is the Equation (12). The variables of this model are dipole moment, ionization potential, electron affinity, electronegativity and softness all with negative descriptor coefficient magnitudes except the electronegativity.
For k = 6, the best-fitted equation is the Equation (13). The variables of this model are ionization potential, electron affinity, electronegativity, hardness, softness and electronegativity index.
For k = 7, seven descriptors have been used as independent variables and the resulted equation is Equation (14).
For comparative study and selection of the reliable model among the above seven models, the regression summary is presented as below.
Regression summary of the above models
From the above summary, the reliable model is the Equation (9) as it has higher value of r2 and , lower values of “k” and SE than other models. The current study accounts for previous findings in most easier and convenient way. Ivanciuc et al., for the first time made QSAR study on these compounds aggregated from various literature reports. Predictive ability of their models was “r” between 0.903 and 0.935 for splinoid QSSAR and “r” between 0.745 and 0.887 for cluster-expansion . In continuation to this Katritzky et al., reported QSAR results of the same data sets based on 486 constitutional, topological, geometrical, electrostatic, quantum chemical and thermodynamic descriptors derived solely from molecular structure using CODESSA Pro software and proposed that two-parameter model satisfactorily describes the relationship between observed and calculated values in terms of statistical parameters . E.B. de Melo reported QSAR results based on E-state and topological descriptors using SMILE software and the best model present five descriptors (one E-state index and four topological descriptors) . Liu et al. made QSAR studies of BCFs of PCBs using DFT, PCS and CoMFA, and their result show that the electrostatic descriptors (R2 = 0.926; Q2 = 0.821; RMSE = 0.235) play a more significant role in BCFs of PCBs . Using deep belief network QSPR models for predicting the physicochemical properties of PCBs were also made by Safder et al. .
On the basis of present study, it has been concluded that DFT-based quantum chemical descriptors have sufficient reliability to relate the bioconcentration factors of polychlorinated biphenyls with their electronic structures. The QSAR model, “LogBCFpre = 0.0319265 × µ +3.68314 × IP − 17.7294”, can be useful for predicting the BCF of compounds prior to their synthesis and dipole moment and ionization potential are reliable descriptors for predicting BCF, and Both dipole moment and ionization potential have direct relationship with log BCF.
The authors are thankful to Principal M.L.K. (P.G.) College; Balrampur, for providing the laboratory facilities to conduct the calculation.
 Soni, A.K., Sahu, V.K. and Sahu, S. (2017) DFT-Based Prediction of Bioconcentration Factors of Polychlorinated Biphenyls in Fish Species Using Atomic Descriptors. Asian Journal of Chemistry, 29, 2515-2521.
 Halsall, C.J., Lee, R.G.M., Coleman, P.J., Burnett, V., Hardingjones, P. and Jones, K.C. (1995) PCBs in UK Urban Air. Environmental Science & Technology, 29, 2368-2376.
 Senthilkumar, K., Kannan, K., Subramanian, A. and Tanabe, S. (2001) Accumulation of Organochlorine Pesticides and Polychlorinated Biphenyls in Sediments, Aquatic Organisms, Birds, Bird Eggs and Bat Collected from South India. Environmental Science and Pollution Research, 8, 35-47.
 (1996) The Role of Bioaccumulation in Environmental Risk Assessment: The Aquatic Environment and Related Food Webs. Technical Report 67, European Centre for Ecotoxicology and Toxicology of Chemicals (ECETOC), Brussels.
 Hope, B., Scatolini, S. and Titus, E. (1998) Bioconcentration of Chlorinated Biphenyls in Biota from the North Pacific Ocean. Chemosphere, 36, 1247-1261.
 Kunisue, T., Watanabe, M., Subramanian, A., Titenko, A.M. and Tanabe, S. (2003) Congener-Specific Patterns and Toxic Assessment of Polychlorinated Biphenyls in Resident and Migratory Birds from Southern India and Lake Baikal in Russia. Archives of Environmental Contamination and Toxicology, 45, 547-561.
 Swanson, G.M., Ratcliffe, H.E. and Fischer, L.J. (1995) Human Exposure to Policlorinated Biphenyls (PCBs): A Critical Assessment of the Evidence for Adverse Health Effects. Regulatory Toxicology and Pharmacology, 21, 136-150.
 Schade, G. and Heinzow, B. (1998) Organochlorine Pesticides and Polychlorinated Biphenyls in Human Milk of Mothers Living in Northern Germany: Current Extent of Contamination, Time Trend from 1986 to 1997 and Factors That Influence the Levels of Contamination. The Science of the Total Environment, 215, 31-39.
 Devanathan, G., Subramanian, A., Someya, M., Sudaryanto, A., Isobe, T., Takahashi, S., Chakraborty, P. and Tanabe, S. (2009) Persistent Organochlorines in Human Breast Milk from Major Metropolitan Cities in India. Environmental Pollution, 157, 148-154.
 Devanathan, G., Isobe, T., Subramanian, A., Asante, K.A., Natrajan, S., Palanlappan, P., Takahashi, S. and Tanabe, S. (2012) Contamination Status of Polychlorinated Biphenyls and Brominated Flame Retardants in Environmental and Biota Samples from India. In: Kawaguchi, M., Misaki, K., Sato, H., Yokokawa, T., Itai, T., Nguyen, T.M., Ono, J. and Tanabe, S., Eds., Interdisciplinary Studies on Environmental Chemistry—Environmental Pollution and Ecotoxicology, TERRAPUB, Tokyo, 269-277.
 Cok, I., Bilgili, A., Ozdemir, M., Ozbek, H., Bilgili, N. and Burgaz, S. (1997) Organo-Chlorine Pesticides Residues in Human Breast Milk from Agricultural Regions of Turkey, 1995-1996. Bulletin of Environmental Contamination and Toxicology, 59, 577-582.
 Bysshe, S.E. (1982) Bioconcentration Factor in Aquatic Organisms. In: Lyman, W.J., Reehl, W.F. and Rosenblatt, D.H., Eds., Handbook of Chemical Property Estimation Methods, McGraw Hill, New York, 5.
 Katritzky, A.R., Radzvilovits, M., Slavov, S., Kasemets, K., Tamm, K. and Karelson, M. (2010) Quantitative Structure-Activity Relationship Modeling of Bioconcentration Factors of Polychlorinated Biphenyls. Toxicological & Environmental Chemistry, 92, 1233-1247.
 Sahu, S.K., Ajmal, P.Y., Pandit, G.G. and Puranik, V.D. (2009) Vertical Distribution of Polychlorinated Biphenyl Congeners in Sediment Core from Thane Creek Area of Mumbai, India. Journal of Hazardous Materials, 164, 1573-1579.
 Mori, C., Fukata, H., Sakurai, K., Jotaki, T., Todaka, E. and Saito, Y. (2008) Strong Correlation between the Concentration of Dioxins and Total PCBs in Current Japanese People. Chemosphere, 73, 235-238.
 Wang, D.G., Yang, M., Jia, H.L., Zhou, L. and Li, Y.F. (2008) Levels, Distributions and Profiles of Polychlorinated Biphenyls in Surface Soils of Dalian, China. Chemosphere, 73, 38-42.
 Qin, L.T., Liu, S.S., Liu, H.L. and Ge, H.L. (2007) A New Predictive Model for the Bioconcentration Factors of Polychlorinated Biphenyls (PCBs) Based on the Molecular Electronegativity Distance Vector (MEDV). Chemosphere, 70, 1577-1587.
 Ivanciuc, T., Ivanciuc, O. and Klein, D.J. (2006) Modeling the Bioconcentration Factors and Bioaccumulation Factors of Polychlorinated Biphenyls with Posetic Quantitative Super-Structure/Activity Relationships (QSSAR). Molecular Diversity, 10, 133-145.
 Dearden, J.C. and Shinnawei, N.M. (2004) Improved Prediction of Fish Bioconcentration Factor of Hydrophobic Chemicals. SAR and QSAR in Environmental Research, 15, 449-455.
 Sacan, M.T., Erdem, S.S., Ozpinar, G.A. and Balcioglu, I.A. (2004) QSPR Study on the Bioconcentration Factors of Nonionic Organic Compounds in Fish by Characteristic Root Index and Semi-Empirical Molecular Descriptors. The Journal for Chemical Information and Computer Scientists, 44, 985-992.
 Khadikar, P.V., Singh, S., Mandloi, D., Joshi, S. and Bajaj, A.V. (2003) QSAR Study on Bioconcentration Factor (BCF) of Polyhalogented Biphenyls Using the PI Index. Bioorganic & Medicinal Chemistry, 11, 5045-5050.
 Tao, S., Hu, H., Lu, X., Dawson, R.W. and Xu, F. (2000) Fragment Constant Method for Prediction of Fish Bioconcentration Factors of Non-Polar Chemicals. Chemosphere, 41, 1563-1568.
 Bintein, S., Devillers, J. and Karcher, W. (1993) Nonlinear Dependence of Fish Bioconcentration on n-Octanol/Water Partition Coefficient. SAR and QSAR in Environmental Research, 1, 29-39.
 Sabljic, A., Gusten, H., Hermens, J. and Opperhuizen, A. (1993) Modeling Octanol/Water Partition Coefficients by Molecular Topology: Chlorinated Benzenes and Biphenyls. Environmental Science & Technology, 27, 1394-1402.
 Pasha, F.A., Srivastava, H.K. and Singh, P.P. (2005) Comparative QSAR Study of Phenol Derivatives with the Help of Density Functional Theory. Bioorganic & Medicinal Chemistry, 13, 6823-6829.
 Chandrakumar, K.R.S. and Pal, S. (2002) The Concept of Density Functional Theory Based Descriptors and Its Relation with the Reactivity of Molecular Systems: A Semi-Quantitative Study. International Journal of Molecular Sciences, 3, 324-337.
 Geerlings, P., Proft, F.D. and Martin, J.M.L. (1996) In Recent Developments. In: Seminario, S., Ed., Density Functional Theory (Theoretical and Computational Chemistry), Elsevier, Amsterdam, Vol. 5, 773-809.
 Siegbahn, P.E. and Blomberg, M.R.A. (1999) Density Functional Theory of Biologically Relevant Metal Centers. Annual Review of Physical Chemistry, 50, 221-249.
 Ordejon, P., Artacho, E. and Soler, J.M. (1996) Selfconsistent Order-N Density-Functional Calculations for Very Large System. Physical Review B, 53, R10441.
 Singhal, K., Sahu, V.K., Singh, P. and Raj, P. (2014) DFT-Based Prediction of Antifungal and Insecticidal Activities of Perfluorophenyl Antimony (III) and Antimony (V) Chlorides. Medicinal Chemistry Research, 23, 1758-1767.
 DeProft, F. and Geerlings, P. (1997) Calculation of Ionization Energies, Electron Affinities, Electronegativity and Hardness Using Density Functional Methods. Journal of Chemical Physics, 106, 3270-3279.
 Parthasarathi, R., Subramanian, V., Roy, D.R. and Chattaraj, P.K. (2004) Electrophilicity Index as a Possible Descriptor of Biological Activity. Bioorganic & Medicinal Chemistry, 12, 5533-5543.
 de Melo, E.B. (2012) A New Quantitative Structure-Activity Relationship Model to Predict Bioconcentration Factors of Polychlorinated Biphenyls (PCBs) in Fish Using E-State Index and Lopological Descriptors. Ecotoxicology and Environmental Safety, 75, 213.
 Liu, H., Liu, H., Sun, P. and Wanq, Z. (2014) QSAR Studies of Bioconcentration Factors of Polychlorinated Biphenyls (PCBs) Using DFT, PCS and CoMFA. Chemosphere, 114, 101-105.
 Safder, U., Nam, K., Kim, D., Shahlaei, M. and Yoo, C. (2018) Quantitative Structure-Property Relationship (QSPR) Models for Predicting the Physicochemical Properties of Polychlorinated Biphenyls (PCBs) Using Deep Belief Network. Ecotoxicology and Environmental Safety, 162, 17-28.