Review of the Doctoral Thesis

Transcription

1 Prof. dr hab. Artur Michalak Zakład Chemii Teoretycznej Wydział Chemii Uniwersytet Jagielloński R. Ingardena 3, Kraków Tel Fax Review of the Doctoral Thesis Density Functional Theory and Information Theory Based Indices as Tools to Investigate the Reactivity of Chemical Systems and Their Applications by Mr. Meressa Abrha Welearegay, MSc The evaluated doctoral thesis submitted by Mr. Meressa Abrha Welearegay is based on his research in the field of theoretical chemistry, carried out in the Institute of Physical Chemistry of the Polish Academy of Science, within the International PhD Studies programme, under the guidance of Prof. Andrzej Holas (Supervisor) and Dr. Robert Balawender (Subsidiary Supervisor). During his PhD studies Mr. Welearegay spent also half a year at Mc Master University, Hamilton, Canada in the research group of Prof. Paul Ayers, and half a year at Vrije Universiteit Brussels, working under supervision of Prof. Paul Geerlings and Prof. Frank DeProft; his PhD thesis is therefore undoubtedly influenced by his foreign supervisors. The main goal of the PhD thesis by Mr. Welearegay has been formulated in a quite general way as to verify the usefulness of the density functional theory (DFT) and the information theory (IT) based indices as tools to investigate the properties of chemical systems. The thesis is focused on three different, very actual, main research topics: (i) applications of so called alchemical derivatives (alchemical potential and alchemical hardness i.e. first- and second-order derivatives of energy with respect to the nuclear charges) in analysis of the stability of possible, alternative transmutation products obtained from a given molecular system by the change in the nuclear charge(s) for a constant number of electrons; (ii) analysis of selected information theory (IT) -based quantities in the context of molecular group transferability / additivity of atoms and/or functional groups; (iii) development of the support-vector-machine (SVM) models for carcinogenic effects of polycyclic aromatic hydrocarbons. Results of Mr. Welearegay s PhD thesis have been presented so far in two scientific papers already published/accepted (in J. Chem. Theory Comp., and Phys. Chem. Chem. Phys.); two other articles are being prepared for publication. Thus, part of the outcomes of his research has already been positively verified in the review process of international scientific journals. The results have also been presented by the PhD student at scientific conferences (2 posters and oral communication). 1

2 The text of the thesis (in English, 146 pages in total) is divided into 7 main chapters; the first three (Introduction, Theoretical background, Chemical Space and Reactivity Indices, 48 pages in total) are of introductory character; the Author s results are presented in chapters 4-6 (Examples and Applications of Alchemical Derivatives, Information and Complexity Measures in the Molecular Reactivity Studies, Analysis of Carcinogenic Activity of Polycyclic Aromatic Hydrocarbons; 80 pages in total). The final conclusions are presented in the last chapter (Conclusions and Summary, 2 pages). In addition, in three appendices some theoretical concepts/relations used in the thesis are presented, including the compatibility, accuracy, and deficiency numbers, density and shape representation of information theory quantities, and the support vector machine algorithms. At the end of the thesis, the list of Author s publications, and the list of his conference presentations are presented, followed by the bibliographic list that includes 220 literature positions cited in the thesis. The thesis is supplemented by the Supporting Information Disk that contains very well organized, more detailed results, concerning Chapters 5-7. These files demonstrate and highlight the impressive amount of work that Mr. Welearegay did for his PhD research projects. For example, the file supporting chapter 4 includes 60 tables presented in 99 pages. In general, concerning language and presentation, the thesis is written in a good English, the text is clear, well structured, precise and logical; the Author avoids jargon. Examples of typos/spelling errors are rare and are not worth mentioning. In Chapter I, Introduction, the Author briefly presents the goals and the outline of the thesis, chapter by chapter. In Chapter II, Theoretical background, the overview of quantum chemistry and electronic structure methods is presented. Its major part (II.A, II.B, II.C) is very well written, with quite typical structure, starting from Schrodinger equation and variational principle, Born-Oppenheimer approximation, linear combination method, summarizing the basis sets, Hartree-Fock and post-hf methods, and finishing with Density Functional Theory and the Kohn-Sham method. The last part (II.D) is very original, focusing on density matrices, pure states and ensemble states. The theory presented in this section is very well illustrated by the examples presented in the last subsection. Chapter III, Chemical space and reactivity indices, is intended to give theoretical background for the Author s results presented in Chapter IV. Thus, the concept of chemical space is precisely introduced in section IIIA, based of consideration of conformational space, spatial configuration space, and charge configuration space. In section IIIB, the traditional DFT-based reactivity indices are discussed, resulting from derivatives with respect to the number of electrons and the external potential (chemical potential/electronegativity, hardness/softness, Fukui functions, etc.). Finally, in section IIIC, the alchemical derivatives are introduced, i.e. the energy derivatives with respect to nuclear charges, the alchemical potential, alchemical hardness, alchemical stiffness. In section IIID these derivatives are used to consider, the alchemical transmutation energy, i.e. the energy of transforming one molecule, let say AB, into another one CD, by changes in the nuclear charges the transformation of atom A into C, and atom B into D. At this point it should be clearly emphasized that the reaction equation (3-33),, does not correspond to the usual chemical reaction, in which the numbers of atoms (or moles) of given element are preserved on the two sides of equation, but it corresponds to alchemical reaction in which the atoms are transmutated. The Author could have used here different notation/arrows in eq. 3-33, to avoid misunderstanding. The text, however, is clear anyway, and the transmutation idea 2

3 is very nicely illustrated in Figure III-3, showing the isoelectronic transmutation tour from methane molecule (not methyl as stated in the figure caption, by the way) to neon atom. It is clearly explained in the text that the transmutation energy expressed by eq based on alchemical derivatives will be discussed as the approximation to the vertical transmutation energy, given by the energy difference for the species CD and AB at the same geometry. I would like to emphasize that reading both theoretical chapters (II and III) was a real pleasure, thanks to clarity of the presentation, and quite precise language and notation. Before discussing the results, let me first express some critical comments concerning the presented theory: 1) the transmutation energy for AB CD change, can be easily obtained as the exact energy difference from the results of quantum chemical calculations for species AB and CD at their (different) equilibrium geometries; such calculations nowadays can be performed for relatively huge molecular systems, and by using advanced computational methods of quantum chemistry they can lead to quite a high accuracy. The vertical transmutation energy is already approximation, neglecting the geometry relaxation. Moreover, the vertical transmutation energy is arbitrary, due to obvious asymmetry/shift in the two potential energy surfaces. 2) The emphasis in the evaluated thesis is placed on predicting the transmutation energies based on the results of calculations for AB, without doing the calculations for CD. This is a very attractive idea, indeed. Here however, the word predicting is a little misleading, as the alchemical derivatives are not among the standard results of calculations for AB. These derivatives must be computed in addition, although without considering explicitly the system CD. In other words, what is presented here is not a prediction, but rather the alternative way of calculating the (approximate) vertical transmutation energy. 3) Such an alternative way of calculating the approximated transmutation energy via alchemical derivatives can be indeed attractive, if the computational cost is significantly lower, and if the applied approximations allow for error estimation or the accuracy can be systematically improved in a computational protocols applied. 4) If one considers the simplest examples of transmutations H He + Li 2+ etc., for which we know the exact results, then the basis set problems become obvious. Calculation of the ground state energy of He + using the hydrogen 1s orbital without changing the exponent would lead to a disaster in accuracy. In other words, the exponents in the basis sets are crucial. The basis sets used in the typical quantum chemical calculations are Z-dependent, since in every case both, the exponents, and the coefficients have been optimized for specific atom (specific Z). In the above context, unfortunately, the crucial theoretical and computational details are not presented in thesis. The definitions of alchemical derivatives are quite simple and easy to understand. But the difficult part is the methodology for evaluation of the second derivatives. In eq (p. 44), the linear-response function is introduced. In p. 47 the Author points to ref. 87, saying only that the component resulting from the wavefunction modification, D al.,el., is calculated using the coupled perturbed self consistent field 3

4 theory( ). In my opinion, this is not sufficient: the methodology applied here should be carefully described, all the approximations used should be explained, together with their possible results on accuracy of the procedure, with special emphasis on the basis set problems. These details are crucial for understanding the results presented in the thesis. It would be really beneficial to the reader, to demonstrate in details how this methodology works for simple examples (e.g. the simplest transmutations, like H He +, or H 2 He 2 2+ ), before discussing the results of the calculations for more complicated molecules. In particular, after reading the reference 87, I am confused about basis sets applied in the calculations of the thesis. Were the standard basis sets used? Or modified, as described in Ref. 87? Again: this should be clearly explained. Here also comes the issue of computational cost (as crucial for competitiveness of the presented approach): what is the scaling with the system size of the procedure applied for evaluation the electronic part of alchemical derivatives? Can it be really competitive to the standard calculations of exact transmutation energy? The Author discusses the computation time just for one example of azaborapyrenes (p. 79), but based on timing for one example, it is not possible for the reader to draw any clear general conclusions. Let me now briefly review the results of the thesis. In Chapter IV (Examples and Applications of Alchemical Derivatives) the alchemical derivatives are used in the estimation of the transmutation energies for a very interesting set of considered transformations. The large set of the molecular systems included, combined with use of different XC functionals, and a wide selection of the basis sets, gives in total the remarkable set of computational results analyzed in this chapter. The amount of work is impressive. To the best of my knowledge, this is the widest study of alchemical derivatives done so far in literature. In the first section of this chapter (section IV.A), the alchemical derivatives are applied in the estimation of the deprotonation energies for the series of 20 different molecules. Here, two XC functionals, B3LYP and BP are tested in calculations involving different basis functions: cc-pvdz, cc-pvtz, aug-cc-pvdz, and aug-cc-vtz. The Author finds improvement in the correlation coefficient for the correlation of the vertical deprotonation energy with the alchemical-derivative-based estimation. In section IV.B the transmutation of the N 2 molecule into the corresponding isoelectronic species (CO, CN -,C 2 2-,NO +,O 2 2+ ) are considered. Again, a series of different basis sets is considered. The best result is observed in the case of the cc-pcvtz basis for the N 2 CO transmutation. In section IV.C two types of benzene transmutations are discussed, leading to azines and azaborines, and in section IV.D a set of transmutation starting from pyrene are discussed. Results presented in sections IV.C and IV.D show that alchemical derivatives lead to qualitatively correct prediction of the stability order of the alternative transmutation products. Finally in the last section of Chapter IV (IV.E) a very interesting discussion of the substituent effects on alchemical derivatives is presented, based on the results of calculations for 29 molecules. Results presented in Chapter V (Information and Complexity Measures in the Molecular Reactivity Studies) are not directly connected to alchemical derivatives and the theory presented earlier. Therefore, this chapter starts with a separate introductory section. 4

5 The analysis of the Information Theory (IT)-based quantities (Shannon entropy, Fisher information, Oniescu information) in the context of the transferability/additivity concepts is presented. Large molecular set including the total number of 399 molecules divided into three subsets was used in this study. The relationship between the discussed IT-based quantities and the DFT reactivity indices. The results lead to the main conclusion that the analyzed IT measures should be used in analysis concerning the pattern, organization, similarity of molecules, rather than in a direct reactivity studies. In the last Chapter VI (Analysis of Carcinogenic Activity of Polycyclic Aromatic Hydrocarbons), three Support Vector Machine based classification models are proposed and developed for carcinogenic effect of polycyclic aromatic hydrocarbons; they are based on different so called molecular descriptors. The results show that one of the proposed models leads to the accuracy of 93% of correct prediction. Unfortunately, the research in this part of Chapter VI goes beyond the research expertise of the reviewer, and therefore cannot be fully judged. Finally, in the last part of this chapter, the deprotonation energies estimated from alchemical derivatives for a set of 12 polycyclic aromatic hydrocarbons are analyzed in the context of their carcinogenic activity. The predicted preferences of radical attack seems to be in agreement with experimental data. I have the following comments/questions concerning the results presented in the thesis: 1) In the case of the deprotonation study: When comparing different basis sets, one can see systematic improvement in the calculated deprotonation energy with geometry relaxation, as well as in the vertical deprotonation energy: in Table IV-1 for B3LYP the average error in D 0 XH goes down from 77 to 13 kj/mol, the error in D ver XH from 138 kj/mol downto 44 kj/mol. However, for alchemical calculations no systematic improvement is seen, and in fact the mean errors increase: for D al XH from 181 to 279 kj/mol. This is confirmed by the detailed data in Supporting Information: in Table S1A for cc-pvdz the error changes between -81 and -300 kj/mol, and in Table S1G for aug-cc-vtz between -192 kj/mol and -388 kj/mol. Further, in the case of deprotonation energies, the correlation line in Figure IV-1 is shifted by 543 kj/mol. What is the reason for such large errors, and their increase when the basis set is improved? 2) In the case of N 2 transmutations: a) Tables S2A-S2E in the supporting information list the results obtained for 14 basis sets, while Table IV-3 in the main body of the thesis lists only 8 basis sets for one transmutation (N 2 CO). Different labeling of the basis is used in the supporting information (CCD, CCT, ACCD, etc.); it is possible, however, to guess that ACCTC corresponds to aug-cc-pcvtz by comparison of the tables. Then, it appears that for N 2 CN - and N 2 C 2 2- this basis set does not lead to the best accuracy, for the latter case the error is a.u. (that corresponds to ca. 250 kj/mol). 5

6 b) Tables S2A-S2E also show that in all considered cases, the agreement for the reverse transmutations (leading to N 2 ) is much worse. Can this be explained? 3) Table IV-3 shows that in the case of benzene transmutations the mean absolute error is the lowest in the cc-pvtz set for (C-H) n N n (0.039 a.u), while for (C) n N n and (C,C) n (B,N) n in the same basis set is by the order of magnitude larger ( a.u., i.e. ca kj/mol). 4) In the case of pyrene transmutation, in Figure IV-6 the correlation line is shifted by 3.3 a.u. (i.e. over 8000 kj/mol). One point (marked in red) was not included in the correlation. Which transmutation does it correspond to? And why the error for this point is so large? 5) Taking into account large errors discussed above, in my opinion, the enthusiastic final conclusion about the quantitative accuracy in the benzene case is not justified (p. 78: The obtained results are very good from the qualitative point of view and the quantitative point of view ) 6) It is not clear to me what are the final recommendations of the Author concerning the basis sets. 7) The results show that the alchemical derivatives can be indeed useful in scanning of chemical space when the transmutations starting from the same system are considered. But taking into account the computational cost, cannot the results of the same quality be obtained from the standard calculations of energy of the transmutation products based on much cheaper methodology (e.g. DFT calculations with small basis sets, or semiempirical calculations)? Despite some critical comments expressed in this review, my overall opinion on the thesis is positive. Mr. Meressa Abrha Welearegay has shown that he is able to formulate scientific problems and solve them using advanced theoretical methods of quantum chemistry. It is remarkable that three main topics studied in the PhD thesis are located in quite distant areas of theoretical chemistry. The amount of work presented in the thesis is impressive. Results of his PhD-research have already been published in two articles and presented in scientific conferences. The level of his doctoral dissertation, especially its theoretical part, has demonstrated his ability to communicate complex ideas and problems as well as the results of his own research. Therefore, I am convinced that the thesis of Mr. Meressa Abrha Welearegay fulfills the requirements of the Act of 14 March 2003 on Academic Degrees and Academic Title and Academic Degrees in Art and Academic Title in Art, and thus, can be allowed to the public defence. Kraków, June 3 rd, 2014 Prof. dr hab. Artur Michalak 6