Atoms in molecules

<h2 id="applications">Applications</h2>
QTAIM is applied to the description of certain <a href="/facts/Crystal/e2R2mk3E">organic crystals</a> with unusually short distances between neighboring molecules as observed by <a href="/facts/X-ray_diffraction/WtI0F5DN">X-ray diffraction</a>. For example in the <a href="/facts/Crystal_structure/bJ4bCeHd">crystal structure</a> of molecular <a href="/facts/Chlorine/y27UwYBM">chlorine</a>, the experimental Cl...Cl distance between two molecules is 327 picometres, which is less than the sum of the <a href="/facts/Van_der_Waals_radius/PNoSTW41">van der Waals radii</a> of 350 picometres. In one QTAIM result, 12 bond paths start from each chlorine atom to other chlorine atoms including the other chlorine atom in the molecule. The theory also aims to explain the metallic properties of <a href="/facts/Metallic_hydrogen/Wc4P3R6I">metallic hydrogen</a> in much the same way.
The theory is also applied to so-called hydrogen–hydrogen bonds<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> as they occur in molecules such as <a href="/facts/Phenanthrene/tE9YALIM">phenanthrene</a> and <a href="/facts/Chrysene/vnLxHKSE">chrysene</a>. In these compounds, the distance between two ortho hydrogen atoms again is shorter than their van der Waals radii, and according to <a href="/facts/In_silico/g2Cz0ejg">in silico</a> experiments based on this theory, a bond path is identified between them. Both hydrogen atoms have identical electron density and are <a href="/facts/Electron_shell/QxI30eh9">closed shell</a> and therefore they are very different from the so-called <a href="/facts/Dihydrogen_bond/JehDE0LI">dihydrogen bonds</a> that are postulated for compounds such as <a href="/facts/Ammonia_borane/MnkyINUI">H3NBH3</a>, and also different from so-called <a href="/facts/Agostic_interaction/4VDvImoz">agostic interactions</a>.

In mainstream chemistry descriptions, close proximity of two nonbonding atoms leads to destabilizing <a href="/facts/Steric_repulsion/TnX5c8HG">steric repulsion</a> but in QTAIM the observed hydrogen-hydrogen interactions are in fact stabilizing. It is well known that both kinked <a href="/facts/Phenanthrene/tE9YALIM">phenanthrene</a> and <a href="/facts/Chrysene/vnLxHKSE">chrysene</a> are around 6 <a href="/facts/Calorie/ntNMPx65">kcal</a>/<a href="/facts/Mole_(unit)/kCMFwCc0">mol</a> (25 <a href="/facts/Kilojoule/9ndq9jD2">kJ</a>/mol) more stable than their linear <a href="/facts/Isomer/PXlvDVdg">isomers</a> <a href="/facts/Anthracene/mV8Sblcq">anthracene</a> and <a href="/facts/Tetracene/sIrDNTRA">tetracene</a>. One traditional explanation is given by <a href="/facts/Clar%27s_rule/K52xSfNC">Clar's rule</a>. QTAIM shows that a calculated stabilization of 8 kcal/mol (33 kJ/mol) for phenanthrene is the result of destabilization of the compound by 8 kcal/mol (33 kJ/mol) originating from electron transfer from carbon to hydrogen, offset by 12.1 kcal (51 kJ/mol) of stabilization due to a H...H bond path. The electron density at the critical point between the two hydrogen atoms is low (0.012 e) for phenanthrene. Another property of the bond path is its curvature. 
Another molecule analyzed by QTAIM is <a href="/facts/Biphenyl/WWuTjvpd">biphenyl</a>. Its two phenyl ring planes are oriented at a 38° angle with respect to each other, with the planar <a href="/facts/Molecular_geometry/7USG5zDn">molecular geometry</a> (resulting from a rotation around the central C-C bond) destabilized by 2.1 kcal/mol (8.8 kJ/mol) and the perpendicular one destabilized by 2.5 kcal/mol (10.5 kJ/mol). The classic explanations for this rotational barrier are steric repulsion between the ortho-hydrogen atoms (planar) and breaking of <a href="/facts/Delocalization/jsquhECb">delocalization</a> of <a href="/facts/Pi_orbital/3Q6LAGYK">pi</a> density over both rings (perpendicular).
In QTAIM, the energy increase on decreasing the <a href="/facts/Dihedral_angle/C9WEJsuS">dihedral angle</a> from 38° to 0° is a summation of several factors. Destabilizing factors are the increase in <a href="/facts/Bond_length/rHHIBH6q">bond length</a> between the connecting carbon atoms (because they have to accommodate the approaching hydrogen atoms) and transfer of electronic charge from carbon to hydrogen. Stabilizing factors are increased delocalization of pi-electrons from one ring to the other and (the one that tips the balance) is a hydrogen–hydrogen bond between the ortho hydrogens.
QTAIM has also been applied to study the electron topology of solvated post-translational modifications to proteins. For example, covalent–bond force constants in a set of lysine-arginine <a href="/facts/Advanced_glycation_end-products/Xv9BaHTf">advanced glycation end-products</a> were derived using electronic structure calculations, and then bond paths were used to illustrate differences in each of the applied <a href="/facts/Computational_chemistry/KyuCgRV3">computational chemistry</a> functionals. <a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> Furthermore, QTAIM had been used to identify a bond-path network of hydrogen bonds between <a href="/facts/Glucosepane/xKCDLlSS">glucosepane</a> and nearby water molecules. <a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> 
The hydrogen-hydrogen bond is not without its critics. According to one, the relative stability of phenanthrene compared to its isomers can be adequately explained by comparing resonance stabilizations.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> Another critic argues that the stability of phenanthrene can be attributed to more effective pi-pi overlap in the central double bond; the existence of bond paths is not questioned but the stabilizing energy derived from them is.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Quantum_chemistry/H9AXV0lx">Quantum chemistry</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://www.updatedgkpro.online/2020/08/defination-of-atoms-and-moleculewhat-is.html">atoms and molecules</a></li>
<li><a href="http://www.chemistry.mcmaster.ca/aim/">Atoms in Molecules page at McMaster University</a></li>
<li><a href="https://www.qct.manchester.ac.uk/">Popelier Group Home Page</a></li>
<li><a href="http://sobereva.com/multiwfn/">Multiwfn Home Page</a></li>
<li><a href="http://www.aim2000.de/">AIM2000 Home Page</a></li>
<li><a href="http://aim.tkgristmill.com/">AIMAll Home Page</a></li>
<li><a href="http://xd.chem.buffalo.edu/">XD Home Page</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Bader, Richard (1994). Atoms in Molecules: A Quantum Theory. USA: Oxford University Press. ISBN 978-0-19-855865-1. <a href="978-0-19-855865-1" target="_blank">978-0-19-855865-1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Bader, R. (1991). "A quantum theory of molecular structure and its applications". Chemical Reviews. 91 (5): 893–928. doi:10.1021/cr00005a013. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Bader, R.F.W. (2005). "The Quantum Mechanical Basis for Conceptual Chemistry". Monatshefte für Chemie. 136 (6): 819–854. doi:10.1007/s00706-005-0307-x. S2CID 121874327. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Bader, R.F.W. (1998). "Atoms in Molecules". Encyclopedia of Computational Chemistry. 1: 64–86. <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Matta, Chérif F.; Hernández-Trujillo, Jesús; Tang, Ting-Hua; Bader, Richard F. W. (2003). "Hydrogen–Hydrogen Bonding: A Stabilizing Interaction in Molecules and Crystals". Chemistry - A European Journal. 9 (9): 1940–1951. doi:10.1002/chem.200204626. PMID 12740840. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Nash, A., de Leeuw, N. H., Birch, H. L. (2018). "Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products". ChemRxiv.{{cite journal}}: CS1 maint: multiple names: authors list (link) <a href="/wiki/Template:Cite_journal" target="_blank">/wiki/Template:Cite_journal</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Nash, Anthony; Saßmannshausen, Jörg; Bozec, Laurent; Birch, Helen L.; De Leeuw, Nora H. (2017). "Computational study of glucosepane-water hydrogen bond formation: an electron topology and orbital analysis". Journal of Biomolecular Structure and Dynamics. 35 (5): 1127–1137. doi:10.1080/07391102.2016.1172026. PMID 27092586. <a href="https://doi.org/10.1080%2F07391102.2016.1172026" target="_blank">https://doi.org/10.1080%2F07391102.2016.1172026</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Dunitz, Jack D.; Gavezzotti, Angelo (2005). "Molecular Recognition in Organic Crystals: Directed Intermolecular Bonds or Nonlocalized Bonding?". Angewandte Chemie International Edition. 44 (12): 1766–1787. doi:10.1002/anie.200460157. PMID 15685679. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Poater, Jordi; Visser, Ruud; Solà, Miquel; Bickelhaupt, F. Matthias (2007). "Polycyclic Benzenoids: Why Kinked is More Stable than Straight". The Journal of Organic Chemistry. 72 (4): 1134–1142. Bibcode:2007JOCh...72.1134P. doi:10.1021/jo061637p. PMID 17288368. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
</ol>

Atoms in molecules open-in-new

Atoms in molecules