In molecular similarity there is a premise “similar molecules tend to behave similarly”; however in the actual quantum similarity field there is no clear methodology to describe the similarity in chemical reactivity, and with this end an analysis of charge-transfer (CT) processes in a series of Diels-Alder (DA) reactions between cyclopentadiene (Cp) and cyano substitutions on ethylene has been studied. The CT analysis is performed in the reagent assuming a grand canonical ensemble and the considerations for an electrophilic system using B3LYP/6-31 and M06-2X/6-311 + methods. An analysis for CT was performed in agreement with the experimental results with a good statistical correlation relating the polar character to the bond force constants in DA reactions. The quantum distortion analysis on the transition states (TS) was performed using molecular quantum similarity indexes of overlap and coulomb showing good correlation between the rate constants and quantum similarity indexes. In this sense, an electronic reorganization based on molecular polarization in terms of CT is proposed; therefore, new interpretations on the electronic systematization of the DA reactions are presented, taking into account that today such electronic systematization is an open problem in organic physical chemistry. Additionally, one way to quantify the similarity in chemical reactivity was shown, taking into account the dependence of the molecular alignment on properties when their position changes; in this sense a possible way to quantify the similarity of the CT in systematic form on these DA cycloadditions was shown. 1. Introduction Since its discovery, the Diels-Alder (DA) reactions have become one of the most relevant reactions in synthetic organic chemistry due to their ability to create cyclic unsaturated compounds with a predictable stereochemistry and regioselectivity [1–8]. For its amazing performance and utility especially in organic chemistry its discovery was recognized by the Nobel Prize in Chemistry. DA reactions have been mechanistically classified as pericyclic reactions [9, 10]. The viability of these chemical processes has been related to the well-known Woodward-Hoffmann rules [11, 12]. But some mechanistic aspects of DA reactions still remain which have not been explicated in appropriate way and therefore its electronic systematization is an open problem in organic chemistry until today and can be considered as a bottleneck in DA reactions. Analysis based on the orbital symmetry, regioselectivity, and stereoselectivity in DA reactions confirms that many
References
[1]
F. Fringuelli and A. Tatacchi, Diels-Alder Reactions: Selected Practical Methods, Wiley, New York, NY, USA, 2001.
[2]
P. B. Karadakov, D. L. Cooper, and J. Gerratt, “Modern valence-bond description of chemical reaction mechanisms: Diels-Alder reaction,” Journal of the American Chemical Society, vol. 120, no. 16, pp. 3975–3981, 1998.
[3]
H. Lischka, E. Ventura, and M. Dallows, “The Diels-Alder reaction of ethene and 1,3-butadiene: an extended multireference ab initio investigation,” ChemPhysChem, vol. 5, no. 9, pp. 1365–1371, 2004.
[4]
E. Kraka, A. Wu, and D. Cremer, “Mechanism of the diels-Alder reaction studied with the united raction valley approach: mechanistic differences between symmetry-allowed and symmetry-forbidden reactions,” Journal of Physical Chemistry A, vol. 107, no. 42, pp. 9008–9021, 2003.
[5]
H. Isobe, Y. Takano, Y. Kitagawa et al., “Systematic comparisons between broken symmetry and symmetry-adapted approaches to transition states by chemical indices: a case study of the Diels-Alder reactions,” Journal of Physical Chemistry A, vol. 107, no. 5, pp. 682–694, 2003.
[6]
O. Diels and K. Alder, “Synthesen in der hydroaromatischen Reihe,” Justus Liebigs Annalen Der Chemie, vol. 460, no. 1, pp. 98–122, 1928.
[7]
K. N. Houk, R. J. Loncharich, J. F. Blake, and W. L. Jorgensen, “Substituent effects and transition structures for Diels-Alder reactions of butadiene and cyclopentadiene with cyanoalkenes,” Journal of the American Chemical Society, vol. 111, no. 26, pp. 9172–9176, 1989.
[8]
K. C. Nicolaou, S. A. Snyder, T. Montagnon, and G. Vassilikogiannakis, “The Diels-Alder reaction in total synthesis,” Angewandte Chemie: International Edition, vol. 41, no. 10, pp. 1668–1698, 2002.
[9]
I. Fleming, Frontier Orbitals and Organic Chemical Reactions, John Wiley and Sons, New York, NY, USA, 1976.
[10]
I. Fleming, Pericyclic Reaction, Oxford University Press, Oxford, UK, 1999.
[11]
R. B. Woodward and R. Hoffmann, “The conservation of orbital symmetry,” Angewandte Chemie: International Edition, vol. 8, no. 11, pp. 781–853, 1969.
[12]
R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry, Academic Press, New York, NY, USA, 1970.
[13]
R. Walsh and J. M. Wells, “The kinetics of reversible Diels-Alder reactions in the gas phase—part II. Cyclopentadiene and ethylene,” Journal of the Chemical Society, Perkin Transactions, vol. 2, pp. 52–55, 1976.
[14]
J. Sauer, H. Wiest, and A. Mielert, “Eine studie der Diels-Alder-reaktion—I. Die reaktivit t von dienophilen gegenüber cyclopentadien und 9.10-dimethyl-anthracen,” Chemische Berichte, vol. 97, pp. 3183–3207, 1964.
[15]
L. Domingo, J. M. Aurell, P. Pérez, and R. Contreras, “Origin of the synchronicity on the transition structures of polar Diels-Alder reactions. Are these reactions [4 + 2] processes?” Journal of Organic Chemistry, vol. 68, pp. 3884–3890, 2003.
[16]
L. Domingo and J. Saéz, “Understanding the mechanism of polar Diels-Alder reactions,” Organic & Biomolecular Chemistry, vol. 7, pp. 3576–3583, 2009.
[17]
L. Domingo, J. M. Aurell, P. Pérez, and R. Contreras, “Quantitative characterization of the local electrophilicity of organic molecules. Understanding the regioselectivity on Diels-Alder reactions,” Journal of Physical Chemistry A, vol. 106, pp. 6871–6875, 2002.
[18]
W. Yang, R. G. Parr, and R. Pucci, “Electron density, Kohn-Sham frontier orbitals, and Fukui functions,” The Journal of Chemical Physics, vol. 81, no. 6, pp. 2862–2863, 1984.
[19]
P. W. Ayers, W. T. Yang, and L. J. Bartolotti, “Fukui function,” in Chemical Reactivity Theory: A Density Functional View, P. K. Chattaraj, Ed., pp. 255–267, CRC Press, Boca Raton, Fla, USA, 2009.
[20]
P. W. Ayers and M. Levy, “Perspective on: density functional approach to the frontier-electron theory of chemical reactivity,” Theoretical Chemistry Accounts, vol. 103, no. 3-4, pp. 353–360, 2000.
[21]
A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Dover Publishing, Mineola, NY, USA, 1996.
[22]
C. J. Cramer, Essentials of Computational Chemistry, John Wiley and Sons, Chichester, UK, 2002.
[23]
T. Sommerfeld, “Lorentz trial function for the hydrogen atom: a simple, elegant exercise,” Journal of Chemical Education, vol. 88, no. 11, pp. 1521–1524, 2011.
[24]
K. Fukui, “The role of frontier orbitals in chemical reactions (Nobel lecture),” Angewandte Chemie International, vol. 21, no. 11, pp. 801–809, 1982.
[25]
K. Fukui, T. Yonezawa, and H. Shingu, “A molecular orbital theory of reactivity in aromatic hydrocarbons,” The Journal of Chemical Physics, vol. 20, no. 4, pp. 722–725, 1952.
[26]
M. Bernard, Organic Chemistry: Reactions and Mechanisms, Pearsons, Upper Saddle River, NJ, USA, 2004.
[27]
H. Eyring, “The activated complex and the absolute rate of chemical reactions,” Chemical Reviews, vol. 17, no. 1, pp. 65–77, 1935.
[28]
K. J. Laidler and M. C. King, “The development of transition-state theory,” Journal of Physical Chemistry, vol. 87, no. 15, pp. 2657–2664, 1983.
[29]
P. Geerlings, P. W. Ayers, A. Toro-Labbé, P. K. Chattaraj, and F. De Proft, “The Woodward-Hoffmann rules reinterpreted by conceptual density functional theory,” Accounts of Chemical Research, vol. 45, no. 5, pp. 683–695, 2012.
[30]
P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Physical Review, vol. 136, no. 3B, pp. B864–B871, 1964.
[31]
D. H. Ess, G. O. Jones, and K. N. Houk, “Conceptual, qualitative, and quantitative theories of 1, 3-dipolar and Diels-Alder cycloadditions used in synthesis,” Advanced Synthesis and Catalysis, vol. 348, pp. 2337–2361, 2006.
[32]
E. Goldstein, B. Beno, and K. N. Houk, “Density functional theory prediction of the relative energies and isotope effects for the concerted and stepwise mechanisms of the Diels-Alder reaction of butadiene and ethylene,” Journal of the American Chemical Society, vol. 118, no. 25, pp. 6036–6043, 1996.
[33]
F. Bernardi, A. Bottini, M. A. Robb, M. J. Field, I. H. Hillier, and M. F. Guest, “Towards an accurate ab initio calculation of the transition state structures of the Diels-Alder reaction,” Journal of the Chemical Society, Chemical Communications, vol. 7, no. 15, pp. 1051–1052, 1985.
[34]
F. Bernardi, A. Bottoni, M. J. Field et al., “MC-SCF study of the Diels-Alder reaction between ethylene and butadiene,” Journal of the American Chemical Society, vol. 110, no. 10, pp. 3050–3055, 1988.
[35]
R. E. Townshend, G. Ramunni, G. Segal, W. J. Hehre, and L. Salem, “Organic transition states. V: the diels-alder reaction,” Journal of American Chemical Society, vol. 98, no. 8, pp. 2190–2198, 1976.
[36]
W. L. Jorgensen, D. Lim, and J. F. Blake, “Ab initio study of Diels-Alder reactions of cyclopentadiene with ethylene, isoprene, cyclopentadiene, acrylonitrile, and methyl vinyl ketone,” Journal of the American Chemical Society, vol. 115, no. 7, pp. 2936–2942, 1993.
[37]
S. Berski, J. Andrés, B. Silvi, and L. R. Domingo, “The joint use of catastrophe theory and electron localization function to characterize molecular mechanisms: a density functional study of the Diels-Alder reaction between ethylene and 1,3-butadiene,” Journal of Physical Chemistry A, vol. 107, no. 31, pp. 6014–6024, 2003.
[38]
L. A. Burke and G. Leroy, “Corrigendum,” Theoretica Chimica Acta, vol. 44, no. 2, pp. 219–221, 1977.
[39]
L. A. Burke, G. Leroy, and M. Sana, “Theoretical study of the Diels-Alder reaction,” Theoretica Chimica Acta, vol. 40, no. 4, pp. 313–321, 1975.
[40]
M. Ortega, A. Oliva, J. M. Lluch, and J. Bertran, “The effect of the correlation energy on the mechanism of the Diels-Alder reaction,” Chemical Physics Letters, vol. 102, no. 4, pp. 317–320, 1983.
[41]
K. N. Houk, Y. T. Lin, and F. K. Brown, “Evidence for the concerted mechanism of the Diels-Alder reaction of butadiene with ethylene,” Journal of the American Chemical Society, vol. 108, no. 3, pp. 554–556, 1986.
[42]
F. K. Brown and K. N. Houk, “The STO-3G transition structure of the Diels-Alder reaction,” Tetrahedron Letters, vol. 25, no. 41, pp. 4609–4612, 1984.
[43]
M. J. S. Dewar, S. Olivella, and J. J. P. Stewart, “Mechanism of the Diels-Alder reaction: reactions of butadiene with ethylene and cyanoethylenes,” Journal of the American Chemical Society, vol. 108, no. 19, pp. 5771–5779, 1986.
[44]
K. N. Houk and L. L. Munchausen, “Ionization potentials, electron affinities, and reactivities of cyanoalkenes and related electron-deficient alkenes: a frontier molecular orbital treatment of cyanoalkene reactivities in cycloaddition, electrophilic, nucleophilic, and radical reactions,” Journal of the American Chemical Society, vol. 98, no. 4, pp. 937–946, 1976.
[45]
Y. Cao, S. Osune, Y. Liang, R. C. Haddon, and K. N. Houk, “Diels-alder reactions of graphene: computational predictions of products and sites of reaction,” Journal of the American Chemical Society, vol. 135, no. 46, pp. 17643–17649, 2013.
[46]
T. Karcher, W. Sicking, J. Sauer, and R. Sustmann, “Solvent effects on endo-exo selectivities in (4+2) cycloadditions of cyanoethylenes,” Tetrahedron Letters, vol. 33, no. 52, pp. 8027–8030, 1992.
[47]
W. L. Jorgensen, D. Lim, and J. F. Blake, “Ab initio study of Diels-Alder reactions of cyclopentadiene with ethylene, isoprene, cyclopentadiene, acrylonitrile, and methyl vinyl ketone,” Journal of the American Chemical Society, vol. 115, no. 7, pp. 2936–2942, 1993.
[48]
B. S. Jursic, “Comparison of AM1 and density functional theory generated transition state structures and activation energies for cyanoalkenes addition to cyclopentadiene,” Journal of Molecular Structure: THEOCHEM, vol. 358, pp. 139–143, 1995.
[49]
V. Branchadell, “Density functional study of Diels-Alder reactions between cyclopentadiene and substituted derivatives of ethylene,” International Journal of Quantum Chemistry, vol. 61, no. 3, pp. 381–388, 1997.
[50]
G. O. Jones, V. A. Guner, and K. N. Houk, “Diels-Alder reactions of cyclopentadiene and 9,10-dimethylanthracene with cyanoalkenes: the performance of density functional theory and hartree-fock calculations for the prediction of substituent effects,” Journal of Physical Chemistry A, vol. 110, no. 4, pp. 1216–1224, 2006.
[51]
R. Ponec, Topics in Current Chemistry, Springer, Berlin, Germany, 1995.
[52]
R. Carbó-Dorca, “Mathematical aspects of the LCAO MO first order density function (5): centroid shifting of MO shape functions basis set, properties and applications,” Journal of Mathematical Chemistry, vol. 51, no. 1, pp. 289–296, 2013.
[53]
F. Fratev, O. E. Polansky, A. Mehlhorn, and V. Monev, “Application of distance and similarity measures. The comparison of molecular electronic structures in arbitrary electronic states,” Journal of Molecular Structure, vol. 56, pp. 245–253, 1979.
[54]
O. E. Polansky and G. Derflinger, “Zur Clar'schen Theorie Lokaler Benzoider Gebiete in Kondensierten Aromaten,” International Journal of Quantum Chemistry, vol. 1, no. 4, pp. 3379–3401, 1967.
[55]
P. E. Bowen-Jenkins, D. L. Cooper, and W. G. Richards, “Ab initio computation of molecular similarity,” Journal of Physical Chemistry, vol. 89, no. 11, pp. 2195–2197, 1985.
[56]
E. E. Hodgkin and W. G. Richards, “A semi-empirical method for calculating molecular similarity,” Journal of the Chemical Society, Chemical Communications, vol. 17, pp. 1342–1344, 1986.
[57]
R. Ponec and C. Czech, “Topological aspects of chemical reactivity. On the similarity of molecular structures,” Chemical Communications, vol. 52, pp. 555–562, 1987.
[58]
R. Ponec and M. Strnad, “Position invariant index for assessment of molecular similarity,” Croatica Chemica Acta, vol. 66, pp. 1123–1127, 1993.
[59]
D. L. Cooper and N. L. Allan, “A novel approach to molecular similarity,” Journal of Computer-Aided Molecular Design, vol. 3, no. 3, pp. 253–259, 1989.
[60]
D. L. Cooper and N. L. Allan, “Molecular dissimilarity: a momentum-space criterion,” Journal of the American Chemical Society, vol. 114, no. 12, pp. 4773–4776, 1992.
[61]
R. Carbó-Dorca and B. Calabuig, “Molecular quantum similarity measures and N-dimensional representation of quantum objects. I. Theoretical foundations,” International Journal of Quantum Chemistry, vol. 42, no. 6, pp. 1681–1693, 1992.
[62]
J. Cioslowski and E. D. Fleischmann, “Assessing molecular similarity from results of ab initio electronic structure calculations,” Journal of the American Chemical Society, vol. 113, no. 1, pp. 64–67, 1991.
[63]
Carbó-Dorca and R. Arnau M, “How similar is a molecule to another An electron density measure of similarity between two molecular structures,” International Journal of Quantum Chemistry, vol. 17, no. 6, pp. 1185–1189, 1980.
[64]
L. Amat and R. Carbó-Dorca, “Use of promolecular ASA density functions as a general algorithm to obtain starting MO in SCF calculations,” International Journal of Quantum Chemistry, vol. 87, no. 2, pp. 59–67, 2002.
[65]
X. Gironés and R. Carbó-Dorca, “Modelling toxicity using molecular quantum similarity measures,” QSAR and Combinatorial Science, vol. 25, pp. 579–589, 2006.
[66]
M. M. Deza and E. Deza, Encyclopedia of Distances, Springer, Berlin, Germany, 2009.
[67]
S. K. Berberian, Introduction To Hilbert Space, Oxford University Press, New York, NY, USA, 1961.
[68]
R. Carbó-Dorca and E. Besalú, “Centroid origin shift of quantum object sets and molecular point clouds description and element comparisons,” Journal of Mathematical Chemistry, vol. 50, pp. 1161–1178, 2012.
[69]
L. D. Mercado and R. Carbó-Dorca, “Quantum similarity and discrete representation of molecular sets,” Journal of Mathematical Chemistry, vol. 49, no. 8, pp. 1558–1572, 2011.
[70]
R. Carbó-Dorca and X. Gironés, “Foundation of quantum similarity measures and their relationship to QSPR: density function structure, approximations, and application examples,” International Journal of Quantum Chemistry, vol. 101, no. 1, pp. 8–20, 2005.
[71]
R. Carbó-Dorca, “Scaled Euclidian distances: a general dissimilarity index with a suitably defined geometrical foundation,” Journal of Mathematical Chemistry, vol. 50, no. 4, pp. 734–740, 2012.
[72]
P. Bultinck, X. Gironés, and R. Carbó-Dorca, “Molecular quantum similarity: theory and applications,” in Reviews in Computational Chemistry, vol. 21, chapter 2, p. 127, 2005.
[73]
R. Carbó-Dorca and E. Besalú, “Communications on quantum similarity (2): a geometric discussion on holographic electron density theorem and confined quantum similarity measures,” Journal of Computational Chemistry, vol. 31, no. 13, pp. 2452–2462, 2010.
[74]
R. Carbó-Dorca and L. D. Mercado, “Commentaries on quantum similarity (1): density gradient quantum similarity,” Journal of Computational Chemistry, vol. 31, no. 11, pp. 2195–2212, 2010.
[75]
R. Carbó-Dorca, E. Besalú, and L. D. Mercado, “Communications on quantum similarity—part 3: a geometric-quantum similarity molecular superposition algorithm,” Journal of Computational Chemistry, vol. 324, pp. 582–599, 2011.
[76]
M. Randi？, “On characterization of molecular branching,” Journal of the American Chemical Society, vol. 97, no. 23, pp. 6609–6615, 1975.
[77]
R. Carbó-Dorca, “Scaled Euclidian distances: a general dissimilarity index with a suitably defined geometrical foundation,” Journal of Mathematical Chemistry, vol. 50, no. 4, pp. 734–740, 2012.
[78]
R. Carbó-Dorca, “Collective Euclidian distances and quantum similarity,” Journal of Mathematical Chemistry, vol. 51, no. 1, pp. 338–353, 2013.
[79]
P. W. Ayers, J. S. M. Anderson, and L. J. Bartolotti, “Perturbative perspectives on the chemical reaction prediction problem,” International Journal of Quantum Chemistry, vol. 101, no. 5, pp. 520–534, 2005.
[80]
J. L. Gázquez, “Perspectives on the density functional theory of chemical reactivity,” Journal of the Mexican Chemical Society, vol. 52, pp. 3–10, 2008.
[81]
R. G. Parr, L. V. Szentpály, and S. Liu, “Electrophilicity index,” Journal of the American Chemical Society, vol. 121, no. 9, pp. 1922–1924, 1999.
[82]
A. T. Maynard, M. Huang, W. G. Rice, and D. G. Covell, “Reactivity of the HIV-1 nucleocapsid protein p7 zinc finger domains from the perspective of density-functional theory,” Proceedings of the National Academy of Sciences of the United States of America, vol. 95, no. 20, pp. 11578–11583, 1998.
[83]
H. Chermette, “Chemical reactivity indexes in density functional theory,” Journal of Computational Chemistry, vol. 20, no. 1, pp. 129–154, 1999.
[84]
S. Liu, “Conceptual density functional theory and some recent developments,” Acta Physico-Chimica Sinica, vol. 25, pp. 590–600, 2009.
[85]
S. Berski, J. Andrés, B. Silvi, and L. R. Domingo, “The joint use of catastrophe theory and electron localization function to characterize molecular mechanisms. A density functional study of the Diels-Alder reaction between ethylene and 1,3-butadiene,” Journal of Physical Chemistry A, vol. 107, no. 31, pp. 6014–6024, 2003.
[86]
A. Morales-Bayuelo, “Understanding the electronic reorganization in the thermal isomerization reaction of trans-3,4-dimethylcyclobutene. Origins of outward Pseudodiradical {2n + 2π} torquoselectivity,” International Journal of Quantum Chemistry, vol. 113, no. 10, pp. 1534–1543, 2013.
[87]
A. Morales-Bayuelo and R. Vivas-Reyes, “Theoretical model for the polarization molecular and Hückel treatment of PhosphoCyclopentadiene in an external electric field: Hirschfeld study,” Journal of Mathematical Chemistry, vol. 51, no. 7, pp. 1835–1852, 2013.
[88]
A. Morales-Bayuelo and R. Vivas-Reyes, “Topological model to quantify the global reactivity indexes as local in Diels-Alder reactions, using density function theory (DFT) and local quantum similarity (LQS),” Journal of Mathematical Chemistry, vol. 51, no. 1, pp. 125–143, 2013.
[89]
A. Morales-Bayuelo, V. Valdiris, and R. Vivas-Reyes, “Mathematical analysis of a series of 4-acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6-pyridylpyrimidines: a simple way to relate quantum similarity to local chemical reactivity using the Gaussian orbitals localized theory,” Journal of Theoretical Chemistry, vol. 2014, Article ID 624891, 13 pages, 2014.
[90]
A. Morales-Bayuelo and R. Vivas-Reyes, “Topological model to quantify the global reactivity indexes as local in Diels-Alder reactions, using density function theory (DFT) and local quantum similarity (LQS),” Journal of Mathematical Chemistry, vol. 51, no. 1, pp. 125–143, 2013.
[91]
A. Morales-Bayuelo, R. Baldiris, J. Torres, J. E. Torres, and R. Vivas-Reyes, “Theoretical study of the chemical reactivity and molecular quantum similarity in a series of derivatives of 2-adamantyl-thiazolidine-4-one using density functional theory and the topo-geometrical superposition approach,” International Journal of Quantum Chemistry, vol. 112, no. 14, pp. 2681–2687, 2012.
[92]
P. Geerlings, F. De Proft, and W. Langenaeker, “Conceptual density functional theory,” Chemical Reviews, vol. 103, no. 5, pp. 1793–1873, 2003.
[93]
H. Chermette, “Chemical reactivity indexes in density functional theory,” Journal of Computational Chemistry, vol. 20, no. 1, pp. 129–154, 1999.
[94]
P. W. Ayers and R. G. Parr, “Variational principles for describing chemical reactions: the Fukui function and chemical hardness revisited,” Journal of the American Chemical Society, vol. 122, no. 9, pp. 2010–2018, 2000.
[95]
P. Geerlings and F. De Proft, “Conceptual and computational dft as a chemist's tool,” in Recent Advances in Computational Chemistry, vol. 1, pp. 137–167, 2002.
[96]
P. W. Ayers, S. B. Liu, and T. L. Li, “Stability conditions for density functional reactivity theory: an interpretation of the total local hardness,” Physical Chemistry Chemical Physics, vol. 13, pp. 4427–4433, 2011.
[97]
P. Geerlings and F. de Proft, “Chemical reactivity as described by quantum chemical methods,” International Journal of Molecular Sciences, vol. 3, pp. 276–309, 2002.
[98]
R. F. Nalewajski and R. G. Parr, “Information theory, atoms in molecules, and molecular similarity,” Proceedings of the National Academy of Sciences, vol. 97, pp. 8879–8882, 2000.
[99]
P. Bultinck and R. Carbó-Dorca, “Molecular quantum similarity using conceptual DFT descriptors,” Journal of Chemical Sciences, vol. 117, pp. 425–435, 2005.
[100]
R. Vivas-Reyes, A. Arias, J. Vandenbussche, C. V. Alsenoy, and P. Bultinck, “Quantum similarity of isosteres coordinate versus momentum space and influence of alignment,” Journal of Molecular Structure: THEOCHEM, vol. 943, no. 1-3, pp. 183–188, 2010.
[101]
R. Carbó-Dorca, Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, Kluwer Academic Publishers, 1995.
[102]
P. Bultinck, S. V. Damme, and R. Carbó-Dorca, Chemical Reactivity Theory: A Density Functional View, CRC Press, 2009.
[103]
J. Mestres, M. Solà, M. Besalú, M. Duran, and R. Carbó-Dorca, “Electron density approximations for the fast evaluation of quantum molecular similarity measures,” in A Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, pp. 77–85, Kluwer Academic Publishers, 1995.
[104]
R. G. Pearson, Chemical Hardness, Wiley-VCH, Weinheim, Germany, 1997.
[105]
W. T. Yang and R. G. Parr, “Hardness, softness, and the fukui function in the electronic theory of metals and catalysis,” Proceedings of the National Academy of Sciences of the United States of America, vol. 82, no. 20, pp. 6723–6726, 1985.
[106]
M. T. Chandra and A. K. Nguyen, “Fukui function and local softness as reactivity descriptors,” in Chemical Reactivity Theory: A Density-Functional View, P. K. Chattaraj, Ed., p. 163, Taylor and Francis, New York, NY, USA, 2008.
[107]
R. G. Parr, L. V. Szentpály, and S. Liu, “Electrophilicity index,” Journal of the American Chemical Society, vol. 121, no. 9, pp. 1922–1924, 1999.
[108]
R. G. Parr and W. Yang, “Density functional approach to the frontier-electron theory of chemical reactivity,” Journal of the American Chemical Society, vol. 106, no. 14, pp. 4049–4050, 1984.
[109]
K. Fukui, “Role of frontier orbitals in chemical reactions,” Science, vol. 218, no. 4574, pp. 747–754, 1982.
[110]
J. Tomasi and M. Persico, “Molecular interactions in solution: an overview of methods based on continuous distributions of the solvent,” Chemical Reviews, vol. 94, no. 7, pp. 2027–2094, 1994.
[111]
E. Cances, B. Mennucci, and J. Tomasi, “A new integral equation formalism for the polarizable continuum model: theoretical background and applications to isotropic and anisotropic dielectrics,” Journal of Chemical Physics, vol. 107, article 3032, 1997.
[112]
A. D. McLean and G. S. Chandler, “Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11-18,” The Journal of Chemical Physics, vol. 72, no. 10, pp. 5639–5648, 1980.
[113]
R. Carbó-Dorca and E. Besalú, “EMP as a similarity measure: a geometric point of view,” Journal of Mathematical Chemistry, vol. 51, no. 1, pp. 382–389, 2013.
[114]
E. E. Hodgkin and W. G. Richards, “Molecular Similarity,” Chemische Berichte, vol. 24, p. 1141, 1988.
[115]
R. Carbó-Dorca, “Scaled Euclidian distances: a general dissimilarity index with a suitably defined geometrical foundation,” Journal of Mathematical Chemistry, vol. 50, no. 4, pp. 734–740, 2012.
[116]
A. Morales-Bayuelo, H. Ayazo, and R. Vivas-Reyes, “Three-dimensional quantitative structure-activity relationship CoMSIA/CoMFA and LeapFrog studies on novel series of bicyclo [4.1.0] heptanes derivatives as melanin-concentrating hormone receptor R1 antagonists,” European Journal of Medicinal Chemistry, vol. 45, no. 10, pp. 4509–4522, 2010.
[117]
X. Gironés and R. Carbó-Dorca, “TGSA-Flex: extending the capabilities of the Topo-Geometrical superposition algorithm to handle flexible molecules,” Journal of Computational Chemistry, vol. 25, no. 2, pp. 153–159, 2004.
[118]
L. Chen, “Substructure and maximal common substructure searching,” in Computational Medicinal Chemistry For Drug Discovery, P. Bultinck, H. De Winter, W. Langenaeker, and J. P. Tollenaere, Eds., p. 483, Marcel Dekker, New York, NY, USA, 2003.
[119]
X. Girones, D. Robert, and R. Carbó-Dorca, “TGSA: a molecular superposition program based on topo-geometrical considerations,” Journal of Computational Chemistry, vol. 22, no. 2, pp. 255–263, 2001.
[120]
H. B. Schlegel, “Optimization of equilibrium geometries and transition structures,” Journal of Computational Chemistry, vol. 3, pp. 214–218, 1982.
[121]
H. B. Schlegel, “Geometry optimization on potential energy surface,” in Modern Electronic Structure Theory, D. R. Yarkony, Ed., World Scientific Publishing, Singapore, 1994.
[122]
M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., GAUSSIAN 09, Revision C. 01, Gaussian, Wallingford, Conn, USA, 2010.
[123]
A. D. Becke, “Density-functional thermochemistry. III. The role of exact exchange,” The Journal of Chemical Physics, vol. 98, no. 7, pp. 5648–5652, 1993.
[124]
C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Physical Review B: Condensed Matter, vol. 37, pp. 785–789, 1998.
[125]
P. J. Stephens, F. J. Delvin, C. F. Chablowski, and M. J. J. Firsch, “Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields,” Physical Chemistry, vol. 98, no. 45, pp. 11623–11627, 1994.
[126]
J. A. Pople, P. V. Schleyer, W. J. Hehre, and L. Radom, AB INITIO molecular orbital theory, 1986.
[127]
S. C. Pellegrinet, M. A. Silva, and J. M. Goodman, “Theoretical evaluation of the origin of the regio- and stereoselectivity in the Diels-Alder reactions of dialkylvinylboranes: studies on the reactions of vinylborane, dimethylvinylborane, and vinyl-9-BBN with trans-piperylene and isoprene,” Journal of the American Chemical Society, vol. 123, no. 36, pp. 8832–8837, 2001.
[128]
T. C. Dinadayalane, R. Vijaya, A. Smitha, and G. N. Sastry, “Diels-Alder reactivity of butadiene and cyclic five-membered dienes ((CH)4X, X = CH2, SiH2, O, NH, PH, and S) with ethylene: a benchmark study,” Journal of Physical Chemistry A, vol. 106, no. 8, pp. 1627–1633, 2002.
[129]
R. Jasiński, Koifman, and A. Barański, “A B3LYP/6-31G(d) study of Diels-Alder reactions between cyclopentadiene and (E)-2-arylnitroethenes,” Central European Journal of Chemistry, vol. 9, no. 6, pp. 1008–1018, 2011.
[130]
B. M. El Ali, “AJSE Relaunched in cooperation with Springer,” Arabian Journal for Science and Engineering, vol. 36, no. 1, p. 1, 2011.
[131]
M. Kwiatkowska, R. Jasinski, M. Mikulska, and A. Baranski, “Secondary alpha-deuterium kinetic isotope effects in [2+4] cycloaddition of (E)-2-phenylnitroethene to cyclopentadiene,” Monatshefte Für Chemie, vol. 141, no. 5, pp. 545–548, 2010.
[132]
R. Jasinski and A. Baranski, “Molecular mechanism of Diels-Alder reaction between (E)-3, 3, 3-trichloro-1-nitropropene and cyclopentadiene: B3LYP/6-31G(d) computational study,” Turkish Journal of Chemistry, vol. 37, pp. 848–852, 2013.
[133]
Y. Zhao and D. G. Truhlar, “The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals,” Theoretical Chemistry Accounts, vol. 120, no. 1–3, pp. 215–241, 2008.
[134]
C. González and H. B. Schlegel, “Reaction path following in mass-weighted internal coordinates,” Journal of Physical Chemistry, vol. 94, no. 14, pp. 5523–5527, 1990.
[135]
C. González and H. B. Schlegel, “Improved algorithms for reaction path following: higher-order implicit algorithms,” Journal of Chemical Physics, vol. 95, pp. 5853–5860, 1991.
[136]
P. Geerlings, R. Vivas-Reyes, F. De Proft, M. Biesemans, and R. Willem, “DFT based reactivity descriptors and their application to the study of organotin compounds,” in Metal-Ligand Interactions,, vol. 116 of NATO Science Series, pp. 461–495, 2003.
[137]
P. Geerlings, R. Vivas-Reyes, F. de Proft, M. Biesemans, and R. Willem, “DFT-based reactivity descriptors and their application to the study of organotin compounds,” Cheminform, vol. 35, no. 49, 2004.
[138]
P. W. Ayers and R. G. Parr, “Variational principles for describing chemical reactions: the Fukui function and chemical hardness revisited,” Journal of the American Chemical Society, vol. 122, no. 9, pp. 2010–2018, 2000.
[139]
P. Bultinck, C. Van Alsenoy, P. W. Ayers, and R. Carbó-Dorca, “Critical analysis and extension of the Hirshfeld atoms in molecules,” Journal of Chemical Physics, vol. 126, no. 14, Article ID 144111, 2007.
[140]
P. K. Chattaraj and D. R. Roy, “Update 1 of: electrophilicity index,” Chemical Reviews, vol. 107, no. 9, pp. PR46–PR74, 2007.
[141]
M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., GAUSSIAN 09, Revision C. 01, Gaussian, Wallingford, Conn, USA, 2010.
[142]
D. H. Ess and K. N. Houk, “Distortion/interaction energy control of 1,3-dipolar cycloaddition reactivity,” Journal of the American Chemical Society, vol. 129, no. 35, pp. 10646–10647, 2007.
[143]
D. H. Ess and K. N. Houk, “Theory of 1,3-dipolar cycloadditions: distortion/interaction and frontier molecular orbital models,” Journal of the American Chemical Society, vol. 130, no. 31, pp. 10187–10198, 2008.
[144]
A. M. Sarotti, “Unraveling polar Diels-Alder reactions with conceptual DFT analysis and the distortion/interaction model,” Organic and Biomolecular Chemistry, vol. 12, pp. 187–199, 2014.
[145]
H. Jiao and P. von Ragué Schleyer, “Aromaticity of pericyclic reaction transition structures: magnetic evidence,” Journal of Physical Organic Chemistry, vol. 11, no. 8-9, pp. 655–662, 1998.
[146]
F. Feixas, E. Matito, J. Poater, and M. Solà, “On the performance of some aromaticity indices: a critical assessment using a test set,” Journal of Computational Chemistry, vol. 29, no. 10, pp. 1543–1554, 2008.
[147]
E. Matito, J. Poater, M. Duran, and M. Solà, “An analysis of the changes in aromaticity and planarity along the reaction path of the simplest Diels-Alder reaction. Exploring the validity of different indicators of aromaticity,” Journal of Molecular Structure: THEOCHEM, vol. 727, no. 1-3, pp. 165–171, 2005.
[148]
G. Boon, W. Langenaeker, F. De Proft, H. De Winter, J. P. Tollenaere, and P. Geerlings, “Systematic study of the quality of various quantum similarity descriptors. Use of the autocorrelation function and principal component analysis,” Journal of Physical Chemistry A, vol. 105, no. 38, pp. 8805–8814, 2001.
[149]
P. Seneta and F. Aparicio, “Density functional theory fragment descriptors to quantify the reactivity of a molecular family: application to amino acids,” Journal of Chemical Physics, vol. 126, Article ID 145105, 2007.
[150]
E. M. Burgess and C. L. Liotta, “Principle of orbital distortion,” Journal of Organic Chemistry, vol. 46, no. 8, pp. 1703–1708, 1981.
[151]
K. N. Houk, M. N. Paddon-Row, N. G. Rondan et al., “Theory and modeling of stereoselective organic reactions,” Science, vol. 231, no. 4742, pp. 1108–1117, 1986.
[152]
D. H. Rouvray, “Definition and role of similarity concepts in the chemical and physical sciences,” Journal of chemical information and computer science, vol. 32, pp. 580–586, 1992.
[153]
D. H. Rouvray, “Similarity studies. 1. The necessity for analogies in the development of science,” Journal of Chemical Information and Computer Sciences, vol. 34, no. 2, pp. 446–452, 1994.
[154]
E. C. Kirby and D. H. Rouvray, “Sixth international conference on mathematical chemistry,” Journal of Chemical Information and Computer Sciences, vol. 36, no. 3, pp. 345–346, 19961996.
[155]
S. R. Heller, “Similarity in organic chemistry: a summary of the Beilstein Institute Conference,” Journal of Chemical Information and Computer Sciences, vol. 32, pp. 578–579, 1992.
