193:, this corresponds to a complete, non-overlapping partitioning of a molecule into three-dimensional basins (atoms) that are linked together by shared two-dimensional separatrices (interatomic surfaces). Within each interatomic surface, the electron density is a maximum at the corresponding internuclear saddle point, which also lies at the minimum of the ridge between corresponding pair of nuclei, the ridge being defined by the pair of gradient trajectories (bond path) originating at the saddle point and terminating at the nuclei. Because QTAIM atoms are always bounded by surfaces having zero
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325:. QTAIM shows that a calculated stabilization for phenanthrene by 8 kcal/mol (33 kJ/mol) 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.
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The 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. Another critic argues that the stability of phenanthrene can be attributed to more effective pi-pi overlap
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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
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over the course of decades, beginning with analyses of theoretically calculated electron densities of simple molecules in the early 1960s and culminating with analyses of both theoretically and experimentally measured electron densities of crystals in the 90s. The development of QTAIM was driven by
344:(encountered in 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 rotation barrier are steric repulsion between the ortho-hydrogen atoms (planar) and breaking of
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in the gradient vector field of the electron density, they have some unique quantum mechanical properties compared to other subsystem definitions. These include unique electronic kinetic energy, the satisfaction of an electronic virial theorem analogous to the molecular electronic
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of atoms with an additive and characteristic set of properties, together with a definition of the bonds that link the atoms and impart the structure. QTAIM defines chemical bonding and structure of a chemical system based on the
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the assumption that, since the concepts of atoms and bonds have been and continue to be so ubiquitously useful in interpreting, classifying, predicting and communicating chemistry, they should have a well-defined physical basis.
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of the electron density. In addition to bonding, QTAIM allows the calculation of certain physical properties on a per-atom basis, by dividing space up into atomic volumes containing exactly one nucleus, which acts as a local
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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
202:, and some interesting variational properties. QTAIM has gradually become a method for addressing possible questions regarding chemical systems, in a variety of situations hardly handled before by any other
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QTAIM has also been applied to study the electron topology of solvated post-translational modifications to protein. For example, covalently bonded force constants in a set of lysine-arginine derived
521:
Matta, Chérif F.; Hernández-Trujillo, Jesús; Tang, Ting-Hua; Bader, Richard F. W. (2003). "Hydrogen–Hydrogen
Bonding: A Stabilizing Interaction in Molecules and Crystals".
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that occur exclusively at the nuclei, certain pairs of which are linked together by ridges of electron density. In terms of an electron density distribution's
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and electron density which is localized in the 3D space. The mathematical study of these features is usually referred to in the literature as charge density
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but in QTAIM the observed hydrogen hydrogen interactions are in fact stabilizing. It is well known that both kinked phenanthrene and chrysene are around 6
556:
Nash, A., de Leeuw, N. H., Birch, H. L. (2018). "Bonded Force
Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products".
626:
Dunitz, Jack D.; Gavezzotti, Angelo (2005). "Molecular
Recognition in Organic Crystals: Directed Intermolecular Bonds or Nonlocalized Bonding?".
185:
QTAIM rests on the fact that the dominant topological property of the vast majority of electron density distributions is the presence of strong
661:
Poater, Jordi; Visser, Ruud; SolĂ , Miquel; Bickelhaupt, F. Matthias (2007). "Polycyclic
Benzenoids: Why Kinked is More Stable than Straight".
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that describes the average manner in which the electronic charge is distributed throughout real space in the attractive field exerted by the
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were derived using the electronic structure calculations and then bond paths were used to illustrate differences in each of the applied
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experiments based on this theory, a bond path is identified between them. Both hydrogen atoms have identical electron density and are
263:. In these compounds the distance between two ortho hydrogen atoms again is shorter than their van der Waals radii and according to
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in the central double bond; the existence of bond paths are not questioned but the stabilizing energy derived from it is.
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587:"Computational study of glucosepane-water hydrogen bond formation: an electron topology and orbital analysis"
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the experimental Cl...Cl distance between two molecules is 327 picometres which is less than the sum of the
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functionals. Furthermore, QTAIM had been used to identify a bond path network of hydrogen bonds between
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QTAIM recovers the central operational concepts of the molecular structure hypothesis, that of a
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Nash, Anthony; Saßmannshausen, Jörg; Bozec, Laurent; Birch, Helen L.; De Leeuw, Nora H. (2017).
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from 38° to 0° is a summation of several factors. Destabilizing factors are the increase in
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In mainstream chemistry close proximity of two nonbonding atoms leads to destabilizing
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Bader, R. (1991). "A quantum theory of molecular structure and its applications".
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Bader, R.F.W. (2005). "The
Quantum Mechanical Basis for Conceptual Chemistry".
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paths of the electron density that originate and terminate at these points.
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with unusually short distances between neighboring molecules as observed by
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distribution function. An electron density distribution of a molecule is a
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Quantum chemical model of molecular and condensed matter electronic systems
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provides insufficient context for those unfamiliar with the subject
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of the electron density. In QTAIM an atom is defined as a
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and therefore they are very different from the so-called
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121:- are natural expressions of a system's observable
355:In QTAIM the energy increase on decreasing the
218:QTAIM is applied to the description of certain
713:Atoms in Molecules page at McMaster University
591:Journal of Biomolecular Structure and Dynamics
275:which are postulated for compounds such as (CH
364:- hydrogen bond between the ortho hydrogens.
8:
570:: CS1 maint: multiple names: authors list (
502:Bader, R.F.W. (1998). "Atoms in Molecules".
144:QTAIM was primarily developed by Professor
321:. One traditional explanation is given by
137:of the electron density together with the
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352:density over both rings (perpendicular).
73:Learn how and when to remove this message
246:The theory is also applied to so-called
628:Angewandte Chemie International Edition
504:Encyclopedia of Computational Chemistry
404:
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336:Another molecule studied in QTAIM is
332:Biphenyl, phenanthrene and anthracene
55:providing more context for the reader
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417:Atoms in Molecules: A Quantum Theory
310:/mol) more stable than their linear
91:quantum theory of atoms in molecules
18:Quantum Theory of Atoms in Molecules
255:as they occur in molecules such as
287:and also different from so-called
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663:The Journal of Organic Chemistry
419:. USA: Oxford University Press.
379:and nearby water molecules.
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369:advanced glycation end-products
174:, i.e. a system that can share
105:), is a model of molecular and
523:Chemistry - A European Journal
1:
604:10.1080/07391102.2016.1172026
109:electronic systems (such as
97:), sometimes referred to as
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148:and his research group at
481:10.1007/s00706-005-0307-x
718:Popelier Group Home Page
127:probability distribution
373:computational chemistry
640:10.1002/anie.200460157
535:10.1002/chem.200204626
469:Monatshefte fĂĽr Chemie
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250:hydrogen–hydrogen bond
243:in much the same way.
226:. For example, in the
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191:gradient vector field
289:agostic interactions
708:atoms and molecules
675:2007JOCh...72.1134P
454:10.1021/cr00005a013
236:van der Waals radii
158:functional grouping
150:McMaster University
51:improve the article
723:Multiwfn Home Page
342:molecular geometry
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172:proper open system
99:atoms in molecules
753:Quantum chemistry
728:AIM2000 Home Page
683:10.1021/jo061637p
634:(12): 1766–1787.
426:978-0-19-855865-1
393:Quantum chemistry
241:metallic hydrogen
228:crystal structure
224:X-ray diffraction
135:stationary points
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49:Please help
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377:glucosepane
361:bond length
323:Clar's rule
747:Categories
399:References
315:anthracene
489:121874327
319:tetracene
265:in silico
208:chemistry
168:attractor
63:July 2017
691:17288368
648:15685679
613:27092586
558:ChemRxiv
543:12740840
510:: 64–86.
415:(1994).
387:See also
338:biphenyl
261:chrysene
232:chlorine
180:topology
163:topology
139:gradient
111:crystals
671:Bibcode
312:isomers
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187:maxima
176:energy
131:nuclei
89:, the
485:S2CID
204:model
119:bonds
115:atoms
95:QTAIM
687:PMID
644:PMID
609:PMID
572:link
539:PMID
421:ISBN
317:and
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300:kcal
283:NHBH
259:and
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117:and
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