Quantum-Chemical Descriptors in QSAR/QSPR Studies

1027 Quantum-Chemical Descriptors in QSAR/QSPR Studies Mati Karelson* and Victor S. Lobanov Department of Chemistry, University of Tartu, 2 Jakobi Str., Tartu, EE 2400, Estonia Alan R. Katritzky Center for Heterocyclic Compounds, Department of Chemistry, University of Florida, P.O. Box 117200, Gainesville, Florida 32611-7200 Received August 21, 1995 (Revised Manuscript Received February 26, 1996) Contents Recent progress in computational hardware and the development of efficient algorithms has assisted I. Introduction 1027 the routine development of molecular quantum- II. Quantum Chemical Methods 1027 mechanical calculations. New semiempirical meth- III. Quantum Chemical Descriptors 1029 ods supply realistic quantum-chemical molecular IV. QSAR/QSPR Results 1033 quantities in a relatively short computational time A. Biological Activities 1033 frame. Quantum chemical calculations are thus an B. Chemical Reactivities 1035 attractive source of new molecular descriptors, which C. Partition Coefficients 1036 can, in principle, express all of the electronic and D. Chromatographic Retention Indexes and 1036 geometric properties of molecules and their interac- Response Factors tions. Indeed, many recent QSAR/QSPR studies E. Other Physicochemical Properties 1037 have employed quantum chemical descriptors alone F. Substituent Constants 1038 or in combination with conventional descriptors. Quantum chemistry provides a more accurate and G. Solvational Characteristics 1038 detailed description of electronic effects than empiri- H. CoMFA 1040 cal methods.1 Quantum chemical methods can be V. Conclusions 1040 applied to quantitative structure-activity relation- VI. References 1041 ships by direct derivation of electronic descriptors from the molecular wave function. In many cases it has been established that errors due to the ap- I. Introduction proximate nature of quantum-chemical methods and the neglect of the solvation effects are largely trans- Quantitative structure-activity and structure- ferable within structurally related series; thus, rela- property relationship (QSAR/QSPR) studies are un- tive values of calculated descriptors can be meaning- questionably of great importance in modern chem- ful even though their absolute values are not directly istry and biochemistry. The concept of QSAR/QSPR applicable.2 Moreover, electronic descriptors derived is to transform searches for compounds with desired from the molecular wave function can be also parti- properties using chemical intuition and experience tioned on the basis of atoms or groups, allowing the into a mathematically quantified and computerized description of various molecular regions separately. form. Once a correlation between structure and Most work employing quantum chemical descrip- activity/property is found, any number of compounds, tors has been carried out in the field of QSAR rather including those not yet synthesized, can be readily than QSPR, i.e. the descriptors have been correlated screened on the computer in order to select structures with biological activities such as enzyme inhibition with the properties desired. It is then possible to activity, hallucinogenic activity, etc.3-6 In part this select the most promising compounds to synthesize has been because, historically, the search for quan- and test in the laboratory. Thus, the QSAR/QSPR titative relationships with chemical structure started approach conserves resources and accelerates the with the development of theoretical drug design process of development of new molecules for use as methods. Quantum-chemical descriptors have also drugs, materials, additives, or for any other purpose. been reported to correlate the reactivity of organic While it is not easy to find successful structure- compounds, octanol/water partition coefficients, chro- activity/property correlations, the recent exponential matographic retention indices, and various physical growth in the number of papers dealing with QSAR/ properties of molecules.7-11 QSPR studies clearly demonstrates the rapid progress The present article reviews applications of quan- in this area. To obtain a significant correlation, it is tum chemical descriptors in the development of crucial that appropriate descriptors be employed, QSAR/QSPR dealing with the chemical, physical, whether they are theoretical, empirical, or derived biochemical, and pharmacological properties of com- from readily available experimental characteristics pounds. of the structures. Many descriptors reflect simple molecular properties and thus can provide insight II. Quantum Chemical Methods into the physicochemical nature of the activity/ Methods based on classical molecular force fields property under consideration. and quantum-chemical methods are each capable of 1028 dynamic and dipole moment calculations but only quantum-chemical methods can estimate atomic σ charges, molecular orbital energies, and the many other electronic descriptors of potential value to QSAR studies.12 In principle, quantum-chemical theory should be able to provide precise quantitative descriptions of molecular structures and their chemical properties. However, due to mathematical and computational complexities this seems unlikely to be realized in the foreseeable future. Thus, researchers need to rely on methods which, although approximate, have now become routine and have been demonstrated to provide results of real utility. While the ab initio model Hamiltonian8 provides a Mati Karelson (born in 1948) is the Professor and Head of Theoretical complete representation of all nonrelativistic interac- Chemistry at the University of Tartu, Estonia. He received his Ph.D on tions between the nuclei and electrons in a molecule, physical organic chemistry in 1975. His research has dealt with the theory of solvent effects, the foundations of the QSAR/QSPR, and the available solutions of the respective Schro¨dinger development of the respective computer software. M. Karelson is a equations are necessarily approximate and the com- member of the International Socity of Quantum Biology and Pharmacology putational time is proportional to a high exponential and the New York Academy of Sciences. In 1994, he was nominated as (N4, N5) of the number of electrons in the molecule, a Courtesy Professor in Chemistry at the University of Florida. N; thus, practical ab initio calculations are severely limited by the types of atoms and size of molecules.13 However, even within these limitations molecules may be described by ab initio methods with some degree of reliability after an accurate search on the potential energy surface(s) has been carried out at a lower level of theory.8 Most ab initio calculations have been based on the orbital approximation (Har- tree-Fock method). In general, this method provides better results the larger the basis set (i.e. number of atomic orbitals) employed, although according to the variational principle this is strictly valid only for the total electron energy of the molecule.14 Other electronic properties, particularly those describing electron distribution in the molecule (dipole and higher moment, partial charges on atoms), are less directly related to the size of the basis set,15 and for such Victor S. Lobanov, born in 1966 in Yekaterinburg, Russia, received his properties more attention has to be paid to the M.S. in chemistry at the Moscow State University, Russia, in 1988. He balance of the basis set used.16 received his Ph.D. on QSAR/QSPR at the University of Tartu, Estonia, in A wide variety of ab intio methods beyond Har- 1995. tree-Fock have been developed and coded to account for electron correlations in the molecule. These include configuration interaction (CI),16-18 multicon- figurational self-consistent field (MC SCF),19-21 correlated pair many-electron theory (CPMET)22 and its various coupled-cluster approximations,23-27 and per- turbation theory (e.g. Møller-Plesset theory of various orders, MP2, MP3, MP4).17,28,29 Most of these methods are extremely time consuming and require large CPU memories and are therefore impractical for the calculation of extended sets of relatively large molecules (i.e., more than 10 atoms). As an alternative to ab initio methods, semiempirical quantum-chemical methods can be used for the calculation of molecular descriptors. These methods have been developed within the mathematical Alan R. Katritzky (born 1928, London, UK) is Kenan Professor of Chemistry framework of the molecular orbital theory (SCF MO), and Director of the Institute for Heterocyclic Compounds at the University but based on simplifications and approximations of Florida. A light-hearted account of his life appeared in the Journal of introduced into the computational procedure which − Heterocyclic Chemistry (1994, 31, 569 602) and an overview of his dramatically reduce the computational time.30,31 Ex- scientific work in Heterocycles (1994, 37,3−130). He is actively engaged in research and teaching, editing, industrial consulting, international travel, perimental data on atoms and prototype molecular and windsurfing. systems have often been used to estimate values of quantities used in the calculations as parameters. For minimizing the potential energy of a molecular this reason, these procedures are widely known as structure. Both approaches can be used for thermo- semiempirical methods.30,31 1029 In principle, any semiempirical method can be used It has already been mentioned that while the to calculate quantum chemical descriptors.1 A num- results produced by different semiempirical

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