The complexation of metal ions with various organic ligands in water: prediction of stability constants by QSPR ensemble modelling

  • Vitaly Solov’ev
  • Natalia Kireeva
  • Svetlana Ovchinnikova
  • Aslan Tsivadze
Original Article


Quantitative structure–property relationship modelling of the stability constants (log K) for the 1:1 (M:L) complexes of metal ions (M = Li+, Na+, K+, Be2+, Al3+, Ga3+, In3+, VO2+, Fe3+, Th4+, NpO2 +, Am3+) with structurally diverse organic ligands in aqueous solution was performed using ensemble multiple linear regression (eMLR) analysis, support vector machines, associative neural networks and substructural molecular fragments’ descriptors. The models were validated with cross-validation procedures and with complementary external test set. For eMLR in the 5-fold cross-validation, root-mean squared error of log K varies from 0.49 (Li+) to 2.30 (In3+), and it is comparable with the systematic errors in experimental data. Designed predictor for end users implements consensus models together with the estimation of their applicability domain.


QSPR modelling of stability constants Complexes of Li+, Na+, K+, Be2+, Al3+, Ga3+, In3+, VO2+, Fe3+, Th4+, NpO2+ and Am3+ with organic ligands in water Ensemble multiple linear regression analysis Support vector machines Associative neural networks Substructural molecular fragments’ descriptors 



Applicability domain


Associative neural networks


Consensus model


5-Fold cross-validation


Ensemble multiple linear regression


Forecast by molecular fragments


Forward variable selection


In SIlico design and data analysis


Organic ligand




Metal ion


Mean absolute error


Leave-one-out cross–validation correlation coefficient


Quantitative structure–property relationships


Squared coefficient of determination


Root-mean squared error


Structure data file


Substructural molecular fragments


Support vector machines



We gratefully acknowledge Prof. L. Pettit for the English language improvement of the paper. V.S. thanks Dr. G. Pettit and Prof. L. Pettit from Academic Software for providing new version of the IUPAC Stability Constants Database.

Supporting Information

1). Structure data file Li_Na_K_Be_Al_Ga_In_V_Fe_Th_Np_Am.SDF contains the 2D structures of the organic ligands (L) and the experimental stability constant values (log K) for the equilibrium M + L = ML (M = Li+, Na+, K+, Be2+, Al3+, Ga3+, In3+, VO2+, Fe3+, Th4+, NpO2 + and Am3+) in water at 298 K and an ionic strength 0.1 M. 2). Predictive performances of the eMLR consensus models in 5CV (Table SI 1). 3). Predictive performances of the SVM models in 5CV (Table SI 2). 4). Predictive performances of the ASNN models in 5CV (Table SI 3). 5). The statistical parameters of the best individual eMLR models and optimal descriptor types according to the training subsets of the 5CV procedure (Table SI 4).

Supplementary material

10847_2015_543_MOESM1_ESM.docx (46 kb)
Supplementary material 1 (DOCX 46 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Vitaly Solov’ev
    • 1
  • Natalia Kireeva
    • 1
    • 2
  • Svetlana Ovchinnikova
    • 1
    • 2
  • Aslan Tsivadze
    • 1
  1. 1.Institute of Physical Chemistry and ElectrochemistryRussian Academy of SciencesMoscowRussian
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia

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