Abstract
The Source Function, a chemical descriptor introduced by Bader and Gatti in 1998, represents a challenging tool to see the electron density from an unusual perspective. Namely, as caused, at any point in the space, by source contributions operating at all other points of space. Summing up the local sources over the atomic basins of a system, enable us to regard the electron density at any system’s location as determined by smaller or larger contributions from all the atoms or group of atoms of the system. Such decomposition of sources provides valuable chemical insight and it may be applied, on the same grounds, to theoretically or experimentally derived electron densities. Two recent Source Function developments, specifically its application to detect subtle electron delocalization effects and its extension to the electron spin density sources are reviewed through this chapter. An original application, as viewed through the eyes of the Source Function, then follows each illustrated development. Precisely: (a) the electron delocalization mechanisms in complex and non planar aromatic systems, like the homotropylium cation and the 1,6-methano[10]annulene, and (b) the spin density transferability properties in a series of n-alkyl radicals.
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Notes
- 1.
Actually, the pseudo-7MR system is not rigorously planar. Here we intend the mean least-squares plane passing through the sp2 atoms.
Abbreviations
- bcp:
-
Bond critical point
- BP:
-
Bond path
- CP:
-
Critical point
- DI:
-
Delocalization index
- ED:
-
Electron density
- FHDD:
-
Fermi Hole Delocalization Density index
- HOMA:
-
Harmonic Oscillator Model of Aromaticity
- LS:
-
Local Source Function
- MO:
-
Molecular Orbital
- NBCC:
-
Non Bonded Charge Concentration
- NICS:
-
Nucleus-Independent Chemical Shift
- QTAIM:
-
Quantum Theory of Atoms in Molecules
- PAH:
-
Polycyclic Aromatic Hydrocarbons
- PDI:
-
Para-Delocalization Index
- rp :
-
Reference point
- SDD:
-
Electron Spin Density Distribution
- SF:
-
Source Function (for the electron density)
- SFS :
-
Source Function (for the electron spin density)
- SF%:
-
Percentage Source Function (for the electron density)
- SFS%:
-
Percentage Source Function (for the electron spin density)
- SFLAI:
-
Source Function Local Aromaticity Index
- 3MR:
-
Three-Membered Ring
- 6MR:
-
Six-Membered Ring
- 7MR:
-
Seven-Membered Ring
- 10MR:
-
Ten-Membered Ring
References
Bader RFW, Gatti C (1998) A Green’s function for the density. Chem Phys Lett 287:233–238
Gatti C (2012) The source function descriptor as a tool to extract chemical information from theoretical and experimental electron densities. Struct Bond 147:193–286
Gatti C (2013) Challenging chemical concepts through charge density of molecules and crystals. Phys Scripta 87:048102 (38 pp)
Arfken G (1985) Mathematical methods for physicists. Academic Press, Orlando
Bader RFW (1990) Atoms in molecules: a quantum theory. In: International series of monographs on chemistry, vol 22. Oxford Science Publications, Oxford UK
Gatti C, Cargnoni F, Bertini L (2003) Chemical information from the source function. J Comput Chem 24:422–436
Hansen NK, Coppens P (1978) Electron population analysis of accurate diffraction data. 6. testing aspherical atom refinements on small-molecule data sets. Acta Cryst A 34:909–921
Stewart RF, Bentley J, Goodman B (1975) Generalized X-ray scattering factors in diatomic molecules. J Chem Phys 63:3786–3793
Gatti C, Macchi P (eds) (2012) Modern charge density analysis. Springer, Dordrecht
Lo Presti L, Gatti C (2009) Using the source function descriptor to dampen the multipole model bias in charge density studies from X-ray structure factor refinements. Chem Phys Lett 476:308–316
Farrugia LJ, Cameron E, Tegel M (2006) Chemical bonds without “chemical bonding”? a combined experimental and theoretical charge density study on an iron trimethylenemethane complex. J Phys Chem A 110:7952–7961
Farrugia LJ, Cameron E, Lenz D et al (2009) The QTAIM approach to chemical bonding between transition metals and carbocyclic rings: a combined experimental and theoretical study of (η 5-C5H5)Mn(CO)3, (η 6-C6H6)Cr(CO)3, and (E)-{(η 5-C5H4)CF-CF(η 5-C5H4)}(η 5-C5H5)2Fe2. J Am Chem Soc 131:1251–1268
McGrady GS, Sirsch P, Chatterton NP et al (2009) Nature of the bonding in metal-silane σ-complexes. Inorg Chem 48:1588–1598
Gatti C, Lasi D (2007) Source function description of metal–metal bonding in d-block organometallic compounds. Faraday Discuss 135:55–78
Monza E, Gatti C, Lo Presti L et al (2011) Revealing electron delocalization through the source function. J Phys Chem A 115:12864–12878
Lo Presti L, Ellern A, Destro R et al (2011) Rationalizing the effect of halogenation on the molecular structure of simple cyclobutene derivatives by topological real-space analysis of their electron density. J Phys Chem A 115:12695–12707
Schmökel M, Cenedese S, Overgaard J et al (2012) Testing the concept of hypervalency: charge density analysis of K2SO4. Inorg Chem 51:8607–8616
Engels B, Schmidt TC, Gatti C et al (2012) Challenging problems in charge density determination. Struct Bond 147:47–98
Cocq K, Lepetit C, Maraval V et al (2015) “Carbo-aromaticity” and novel carbo-aromatic compounds. Chem Soc Rev 44:6535–6559. doi:10.1039/c5cs00244c
Bader RFW, Slee S, Cremer D et al (1983) Description of conjugation and hyperconjugation in terms of electron distributions. J Am Chem Soc 105:5061–5068
Cremer D, Kraka E, Slee S et al (1983) Description of homoaromaticity in terms of electron distributions. J Am Chem Soc 105:5069–5075
Barzaghi M, Gatti C (1987) Homoaromaticity versus Mobius aromaticity. J Chimie Physique 84:783–789
Gatti C, Barzaghi M, Simonetta M (1985) Charge density topological approach to the Dinorcaradiene↔[10]Annulene equilibrium in some 11, 11-Disubstituted 1,6-Methane[10]annulenes. J Am Chem Soc 107:878–887
Simonetta M, Barzaghi M, Gatti C (1986) Cyclopropane ring closure in 11,11-Disubstituted 1,6-methano[10]annuelens. J Mol Struct (THEOCHEM) 138:39–50
Mc Weeney R (1960) Some recent advances in density matrix theory. Rev Mod Phys 32:335–369
Bader RFW, Stephens ME (1975) Spatial localization of the electronic pair and number distributions in molecules. J Am Chem Soc 97:7391–7399
Fradera X, Austen MA, Bader RFW (1999) The Lewis model and beyond. J Phys Chem A 103:304–314
Poater J, Fradera X, Duran M et al (2003) The delocalization index as an electronic aromaticity criterion: application to a series of planar polycyclic aromatic hydrocarbons. Chem Eur J 9:400–406
Matta CF, Hernàndez-Trujillo J (2003) Bonding in polycyclic aromatic hydrocarbons in terms of the electron density and of electron delocalization. J Phys Chem A 107:7496–7504
Kruszewski J, Krygowski TM (1972) Definition of aromaticity basing on the harmonic oscillator model. Tetrahedron Lett 13:3839–3842
Krygowski TM (1993) Crystallographic studies of inter- and intramolecular interactions reflected in aromatic character of π-electron systems. J Chem Inf Comput Sci 33:70–79
Elser V, Haddon RC (1987) Icosahedral C60: an aromatic molecule with a vanishingly small ring current magnetic susceptibility. Nature 325:792–794
Schleyer PVR, Maerker C, Dransfeld A et al (1996) Nucleus-independent chemical shifts: a simple and efficient aromaticity probe. J Am Chem Soc 118:6317–6318
Bultinck P (2007) Critical analysis of the local aromaticity concept in poly-aromatic hydrocarbons. Faraday Discuss 135:347–365 and references therein
Katritzky AR, Barczynski Musumarra G et al (1989) Aromaticity as a quantitative concept. 1. A statistical demonstration of the orthogonality of classical and magnetic aromaticity in five- and six-membered heterocycles. J Am Chem Soc 111:7–15
Gatti C, Saleh G, Lo Presti L et al (2012) Making experiment and theory talking together: electron delocalization effects and non covalent interactions detection via the Source Function and the Reduced Density Gradient. In: Abstracts (page 42) of the Sagamore meeting XVII on Charge Spin and Momentum Densities, Daini Meisui Tei, Sapporo, Hokkaido, Japan, 15–20 July 2012
Gatti C (2013) New descriptors for an “unbiased” and chemically insightful comparison of ab-initio and X-ray derived charge densities. In: Abstracts of Natta’s Seeds Grow, From the crystallography and modelling of stereoregular polymers to the challenges of complex systems, International symposium on occasion of the 50th anniversary of the award of the Nobel Prize for Chemistry to Giulio Natta and Ziegler, Politecnico di Milano, 21–22 Nov 2013
Saleh G (2014) Chemical paradigms seen through charge density descriptor lenses, Ph.D. thesis, Università degli Studi, Milano, Italy
Gatti C, Saleh G, Lo Presti L (2015) Source Function applied to experimental densities reveals subtle electron delocalization effects and appraises their transferability properties in crystals. Acta Cryst B, invited feature article under review
Hendrickson JB, Cram DJ, Hammond GS (1970) Organic chemistry, 3rd edn. McGraw-Hill, New York
Cysewski P (2011) Influence of thermal vibrations on aromaticity of benzene. Phys Chem Chem Phys 13:12998–13008
Breslow R (1973) Antiaromaticity. Acc Chem Res 6:393–398
Pal R, Mukherjee S, Chandrasekhar S et al (2014) Exploring cyclopentadienone antiaromaticity: charge density studies of various tetracyclones. J Phys Chem A 118:3479–3489
Anslyn EV, Dougherty DA (2006) Modern physical organic chemistry. University Science Books
Yao T, Yu H, Vermeij RJ et al (2008) Nonplanar aromatic compounds. Part 10: a strategy for the synthesis of aromatic belts-all wrapped up or down the tubes? Pure Appl Chem 80:533–546
Bodwell GJ, Bridson JN, Cyrañski MK et al (2003) Nonplanar aromatic compounds. 8. Synthesis, crystal structures, and aromaticity investigations of the 1, n-Dioxa[n](2,7)pyrenophanes. How does bending affect the cyclic π-electron delocalization of the pyrene system? J Org Chem 68:2089–2098
Dobrowolski MA, Cyrañski MK, Merner BL et al (2008) Interplay of π-electron delocalization and strain in [n](2,7)Pyrenophanes. J Org Chem 73:8001–8009
Claessens CG, González-Rodríguez D, Rodríguez-Morgade MS et al (2014) Subphthalocyanines, subporphyrazines, and subporphyrins: singular nonplanar aromatic systems. Chem Rev 114:2192–2277
Winstein S, Sonnenberg J, deVries L (1959) The Tris-homocyclopropenyl cation. J Am Chem Soc 81:6523–6524
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the “Gold Book”). McNaught AD, Wilkinson A (eds) Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006) created by Nic M, Jirat J, Kosata B; updates compiled by Jenkins A. ISBN 0–9678550-9-8. doi:10.1351/goldbook
Freeman PK (2005) Neutral homoaromaticity in some heterocyclic systems. J Org Chem 70:1998–2001
Williams RV, Kurtz HA (1994) Homoaromaticity. Adv Phys Org Chem 29:273–331
Jorgensen WL (1975) Chemical consequences of orbital interactions. II. Ethylene and butadiene bridged polycyclic hydrocarbons containing three- and four-membered rings. J Am Chem Soc 97:3082–3090
Jorgensen WL (1976) The energetic impact of monohomoaromaticity. J Am Chem Soc 98:6784–6789
Haddon RC (1974) Homoaromatic, nonhomoaromatic, antihomoaromatic, and dihomoaromatic character. Tetrahedron Lett 2797–2800
Haddon RC (1974) The involvement of the cyclobutane ring in homoaromatic conjugation. Tetrahedron Lett 15:4303–4304
Haddon RC (1975) Perturbational molecular orbital (PMO) theory of homoaromaticity. J Am Chem Soc 97:3608–3615
Hehre WJ (1973) Homoaromatic stability. J Am Chem Soc 95:5807–5809
Childs RF, Cremer D, Elia G (1995) Cyclopropyl homoconjugation-experimental facts and interpretations. In: Rappoport Z (ed) The chemistry of functional groups: the chemistry of the cyclopropyl group, vol 2. Wiley, Chichester, pp 411–468 and references therein
Cremer D, Reichel F, Kraka E (1991) Homotropenylium cation: structure, stability, and magnetic properties. J Am Chem Soc 113:9459–9466
Childs RF (1984) The homotropylium ion and homoaromaticity. Acc Chem Res 17:347–352
Williams RV (2001) Homoaromaticity. Chem Rev 101:1185–1204
Minkin VI, Glukhovtsev MN, Simkin BY (1994). Homoaromaticity. Aromaticity and antiaromaticity. Electronic and structural aspects, Chapter 6. Wiley, New York, pp 230–251
Reindl B, Clark T, Schleyer PVR (1998) Modern molecular mechanics and ab initio calculations on benzylic and cyclic delocalized cations. J Phys Chem A 102:8953–8963
Alkorta I, Elguero J, Eckert-Maksič M et al (2004) Influence of the H/F replacement on the homoaromaticity of homotropylium ion: a GIAO/DFT theoretical study. Tetrahedron 60:2259–2265
Cremer D, Olsson L, Reichel F et al (1993) Calculation of NMR chemical shifts—the third dimension of quantum chemistry. Isr J Chem 33:369–385
Brown EC, Bader RFW, Werstiuk NH (2009) QTAIM study on the degenerate Cope rearrangements of 1,5-Hexadiene and Semibullvalene. J Phys Chem A 113:3254–3265
Genaev AM, Sal’nikov GE, Shubin VG (2007) Energy barriers to carousel rearrangements of carbocations: quantum-chemical calculations vs. experiment. Russ J Org Chem 43:1134–1138
Barzaghi M, Gatti C (1988) Substituent effect on the planarization energy and the relative stability of Winstein and Möbius structures of the homotropylium cation. J Mol Struct (THEOCHEM) 167:275–300
Godbout N, Salahub DR, Andzelm J et al (1992) Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation. Can J Chem 70:560–571
Frisch MJ, Trucks GW, Schlegel HB et al (2009) Gaussian 09, Revision A.1. Gaussian, Inc., Wallingford
Gatti C Unpublished result (available upon request)
Available from Prof. Bader’s RFW Laboratory. McMaster University, Hamilton, Canada L8S 4M1. http://www.chemistry.mcmaster.ca/aimpac/
Cordero B, Gómez V, Platero-Plats AE et al (2008) Covalent radii revisited. Dalton Trans 2832–2838
Hill RK, Giberson CB, Silverton JV (1988) Forfeiture of the aromaticity of a Bridged[10]Annulene by benzannelation. J Am Chem Soc 110:497–500
Mitchell RH (2001) Measuring aromaticity by NMR. Chem Rev 101:1301–1316
Creary X, Miller KJ (2003) Stabilized and destabilized carbocations in the 1,6-methano[10]annulene series. J Org Chem 68:8683–8692
Creary X, Miller KJ (2002) 1,6-Methano[10]annulene-stabilized radicals. Org Lett 3493–3496
Vogel E, Roth HD (1964) Synthese eines cyclodecapentaens. Angew Chem 76:145
Bianchi R, Pilati T, Simonetta M (1972) A very long carbon–carbon bond in a cyclopropane derivative. J Chem Soc Chem Commun 1073–1074
Bianchi R, Morosi G, Mugnoli A et al (1973) The influence of substituents on the equilibrium bisnorcaradiene-[10]annulene. The crystal and molecular structure of 11,11-dimethyltricyclo[4,4,1,01,6]undeca-2,4,7,9-tetraene. Acta Crystallogr Sect B 29:1196–1208
Bianchi R, Pilati T, Simonetta M (1981) On the equilibrium [10]Annulene↔Bisnorcaradiene. X-ray study of the β-Form of 11-Methyltricyclo[4.4.1.01,6]undeca-2,4,7,9-tetraene-11-carbonitrile at two temperatures. J Am Chem Soc 103:6426–6431
Vogel E, Scholl T, Lex J et al (1982) Norcaradiene valence tautomer of a 1,6-Methanol[10]annulene:Tricyclo[4.4.1.01,6]undeca-2,4,7,9-tetraene-11,11-dicarbonitrile. Angew Chem Int Ed Engl 21:869–870
Caramori GF, Kleber T, Galembeck SE et al (2007) Aromaticity and homoaromaticity in Methano[10]annulenes. J Org Chem 72:76–85
Bianchi R, Destro R, Merati F (1991) Electrostatic properties and topological analysis of the charge density of syn-1,6:8,13-Biscarbonyl[14]Annulene derived from X-ray diffraction data at 16 K. In: Jeffrey GA, Piniella JF (eds) The application of charge density research to chemistry and drug design, vol 250. NATO ASI Series, pp 340–340
Ohno H, Chiba D, Matsukura F et al (2000) Electric-field control of ferrromagnetism. Nature 408:944–946
Issadore D, Park YI, Shao H et al (2014) Magnetic sensing technologies for molecular analyses. Lab Chip 14:2385–2397
Zhang Q, Li B, Chen L (2013) First-principle study of microporous magnets M-MOF-74 (M = Ni Co, Fe, Mn): the role of metal centers. Inorg Chem 52:9356–9362
Eisenträger A, Vella D, Griffiths IM (2014) Particle capture efficiency in a multi-wire model for high gradient magnetic separation. Appl Phys Lett 105:033508
Coey JMD (2010) Magnetism and magnetic materials. Cambridge University Press, Cambridge
Nandi S (2003) Magnetic X-ray scattering. In: Characterization of materials. Wiley
Shirane G, Shapiro SM, Tranquada JM (2002) Neutron scattering with a triple-axis spectrometer—basic techniques. Cambridge University Press, Cambridge
Gillon B, Sangregorio C, Caneschi A et al (2007) Experimental spin density in the high spin ground state of the Fe8pcl cluster. Inorg Chim Acta 360:3802–3806
Gatti C, Orlando AM, Lo Presti L (2015) Insights on spin poplarization through the spin density source function. Chem. Sci. 6:3845–3852
Pacansky J, Waltman RJ, Barnes RA (1993) Studies on the structure and β-bond scission reactions of primary Alkyl radicals, CH3(CH2)nCH2O, for n = 1–6. J Phys Chem 97:10694–10701
Deutsch M, Gillon B, Claiser N et al (2014) First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments. IUCrJ 1:194–199
Acknowledgments
We thank the Danish National Research Foundation for partial funding of this work through the Center for Materials Crystallography (DNRF93).
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Gatti, C., Orlando, A.M., Monza, E., Lo Presti, L. (2016). Exploring Chemistry Through the Source Function for the Electron and the Electron Spin Densities. In: Chauvin, R., Lepetit, C., Silvi, B., Alikhani, E. (eds) Applications of Topological Methods in Molecular Chemistry. Challenges and Advances in Computational Chemistry and Physics, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-29022-5_5
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