View source for Physics:Intermolecular force

{{short description|Force of attraction or repulsion between molecules and neighboring particles}}
An '''intermolecular force''' ('''IMF''') (or '''secondary force''') is the force that mediates interaction between molecules, including the [[Electromagnetism|electromagnetic forces of attraction
or repulsion]] which act between atoms and other types of neighbouring particles, e.g. [[Physics:Atom|atom]]s or [[Physics:Ion|ion]]s. Intermolecular forces are weak relative to [[Chemistry:Intramolecular force|intramolecular force]]s – the forces which hold a molecule together. For example, the [[Chemistry:Covalent bond|covalent bond]], involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of [[Chemistry:Force field|force fields]] frequently used in [[Chemistry:Molecular mechanics|molecular mechanics]].

The first reference to the nature of microscopic forces is found in Alexis Clairaut's work ''Théorie de la figure de la Terre,'' published in Paris in 1743.<ref>{{cite book | vauthors = Margenau H, Kestner NR | title=Theory of Intermolecular Forces |date=1969 |publisher=Pergamon Press |location=Oxford |isbn=978-0-08-016502-8 |edition=1st | series = International Series of Monographs in Natural Philosophy | volume = 18 }}</ref> Other scientists who have contributed to the investigation of microscopic forces include: [[Biography:Pierre-Simon Laplace|Laplace]], [[Biography:Carl Friedrich Gauss|Gauss]], [[Biography:James Clerk Maxwell|Maxwell]], [[Biography:Ludwig Boltzmann|Boltzmann]] and [[Biography:Linus Pauling|Pauling]].

Attractive intermolecular forces are categorized into the following types:
*[[Chemistry:Hydrogen bond|Hydrogen bond]]ing 
*Ion–dipole forces and ion–induced dipole force
*[[Chemistry:Cation–π interaction|Cation–π]], σ–π and π–π bonding
*[[Physics:Van der Waals force|Van der Waals force]]s – Keesom force, Debye force, and [[Physics:London dispersion force|London dispersion force]]
*[[Physics:Cation–cation bond|cation–cation bond]]<nowiki/>ing
*[[Chemistry:Salt bridge (protein and supramolecular)|Salt bridge (protein and supramolecular)]]

Information on intermolecular forces is obtained by macroscopic measurements of properties like [[Physics:Viscosity|viscosity]], pressure, volume, temperature (PVT) data. The link to microscopic aspects is given by [[Physics:Virial coefficient|virial coefficient]]s and intermolecular [[Physics:Pair potential|pair potentials]], such as the [[Chemistry:Mie potential|Mie potential]], [[Chemistry:Buckingham potential|Buckingham potential]] or [[Physics:Lennard-Jones potential|Lennard-Jones potential]].

In the broadest sense, it can be understood as such interactions between any particles ([[Physics:Molecule|molecule]]s, [[Physics:Atom|atom]]s, [[Physics:Ion|ion]]s and molecular ions) in which the formation of chemical, that is, ionic, covalent or metallic bonds does not occur. In other words, these interactions are significantly weaker than [[Chemistry:Covalent bond|covalent]] ones and do not lead to a significant restructuring of the [[Engineering:Electronic structure|electronic structure]] of the interacting particles. (This is only partially true. For example, all [[Biology:Enzyme|enzymatic]] and [[Chemistry:Catalysis|catalytic reactions]] begin with a weak intermolecular interaction between a substrate and an [[Biology:Enzyme|enzyme]] or a molecule with a catalyst, but several such weak interactions with the required spatial configuration of the active center of the enzyme lead to significant restructuring changes the energy state of molecules or substrate, which ultimately leads to the breaking of some and the formation of other covalent chemical bonds. Strictly speaking, all [[Biology:Enzyme catalysis|enzymatic reactions]] begin with intermolecular interactions between the [[Chemistry:Substrate|substrate]] and the enzyme, therefore the importance of these interactions is especially great in [[Biology:Biochemistry|biochemistry]] and [[Biology:Molecular biology|molecular biology]],<ref>{{Cite web |title=Biochemistry and Molecular Biology - Paperback - Despo Papachristodoulou, Alison Snape, William H. Elliott, Daphne C. Elliott - Oxford University Press |url=https://global.oup.com/ukhe/product/biochemistry-and-molecular-biology-9780198768111 |access-date=2024-01-04 |website=global.oup.com |language=en}}</ref> and is the basis of [[Biology:Enzyme|enzymology]]).

== Hydrogen bonding ==
{{Main|Chemistry:Hydrogen bond}}

A ''hydrogen bond'' is an extreme form of dipole-dipole bonding, referring to the attraction between a [[Chemistry:Hydrogen|hydrogen]] atom that is bonded to an element with high [[Chemistry:Electronegativity|electronegativity]], usually [[Chemistry:Nitrogen|nitrogen]], [[Chemistry:Oxygen|oxygen]], or [[Chemistry:Fluorine|fluorine]].<ref name=GoldBook-H02899>{{GoldBookRef |file= H02899 |title= hydrogen bond}}</ref> The hydrogen bond is often described as a strong electrostatic dipole–dipole interaction. However, it also has some features of covalent bonding: it is directional, stronger than a [[Physics:Van der Waals force|van der Waals force]] interaction, produces interatomic distances shorter than the sum of their [[Chemistry:Van der Waals radius|van der Waals radii]], and usually involves a limited number of interaction partners, which can be interpreted as a kind of [[Chemistry:Valence|valence]]. The number of Hydrogen bonds formed between molecules is equal to the number of active pairs. The molecule which donates its hydrogen is termed the donor molecule, while the molecule containing lone pair participating in H bonding is termed the acceptor molecule. The number of active pairs is equal to the common number between number of hydrogens the donor has and the number of lone pairs the acceptor has.

[[Image:Hydrogen-bonding-in-water-2D.svg|thumb|Hydrogen bonding in water]]

Though both not depicted in the diagram, water molecules have four active bonds. The oxygen atom’s two lone pairs interact with a hydrogen each, forming two additional hydrogen bonds, and the second hydrogen atom also interacts with a neighbouring oxygen. Intermolecular hydrogen bonding is responsible for the high boiling point of [[Chemistry:Water|water]] (100&nbsp;°C) compared to the other [[Chemistry:Hydrogen chalcogenide|group 16 hydrides]], which have little capability to hydrogen bond. Intramolecular hydrogen bonding is partly responsible for the [[Biology:Secondary structure|secondary]], [[Biology:Tertiary structure|tertiary]], and quaternary structures of [[Biology:Protein|protein]]s and [[Biology:Nucleic acid|nucleic acid]]s. It also plays an important role in the structure of [[Chemistry:Polymers|polymers]], both synthetic and natural.<ref>{{Citation | vauthors = Lindh U | contribution = Biological functions of the elements | veditors = Selinus O | title = Essentials of Medical Geology | pages = 129–177 | publisher = Springer | place = Dordrecht | year = 2013 | edition = Revised | isbn = 978-94-007-4374-8 | doi = 10.1007/978-94-007-4375-5_7 }}</ref>

==Beta bonding==
{{Main|Chemistry:Ionic bonding}}

The attraction between cationic and anionic sites is a noncovalent, or intermolecular interaction which is usually referred to as ion pairing or salt bridge.<ref>{{cite book | veditors = Ciferri A, Perico A |title=Ionic Interactions in Natural and Synthetic Macromolecules |date=2012 |publisher=John Wiley & Sons, Inc. |location=Hoboken, NJ |isbn=978-0-470-52927-0}}</ref>
It is essentially due to electrostatic forces, although in aqueous medium the association is driven by entropy and often even endothermic.  Most salts form crystals with characteristic distances between the ions; in contrast to many other noncovalent interactions, salt bridges are not directional and show in the solid state usually contact determined only by the van der Waals radii of the ions.
Inorganic as well as organic ions display in water at moderate ionic strength I similar salt bridge as association ΔG values around 5 to 6 kJ/mol for a 1:1 combination of anion and cation, almost independent of the nature (size, polarizability, etc.) of the ions.<ref>{{cite journal | vauthors = Biedermann F, Schneider HJ | title = Experimental Binding Energies in Supramolecular Complexes | journal = Chemical Reviews | volume = 116 | issue = 9 | pages = 5216–5300 | date = May 2016 | pmid = 27136957 | doi = 10.1021/acs.chemrev.5b00583 }}</ref> The ΔG values are additive and approximately a linear function of the charges, the interaction of e.g. a doubly charged phosphate anion with a single charged ammonium cation accounts for about 2x5 = 10 kJ/mol. The ΔG  values depend on the ionic strength I of the solution, as described by the Debye-Hückel equation, at zero ionic strength one observes ΔG = 8 kJ/mol.

==Dipole–dipole and similar interactions {{anchor|Dipole-dipole interactions}}==

Dipole–dipole interactions (or Keesom interactions) are electrostatic interactions between molecules which have permanent dipoles. This interaction  is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved. These interactions tend to align the molecules to increase attraction (reducing [[Physics:Potential energy|potential energy]]). An example of a dipole–dipole interaction can be seen in [[Chemistry:Hydrogen chloride|hydrogen chloride]] (HCl): the positive end of a polar molecule will attract the negative end of the other molecule and influence its position. Polar molecules have a net attraction between them. Examples of polar molecules include [[Chemistry:Hydrogen chloride|hydrogen chloride]] (HCl) and [[Chemistry:Chloroform|chloroform]] (CHCl<sub>3</sub>).


Often molecules contain dipolar groups of atoms, but have no overall [[Physics:Electric dipole moment|dipole moment]] on the molecule as a whole. This occurs if there is symmetry within the molecule that causes the dipoles to cancel each other out. This occurs in molecules such as tetrachloromethane and [[Chemistry:Carbon dioxide|carbon dioxide]]. The dipole–dipole interaction between two individual atoms is usually zero, since atoms rarely carry a permanent dipole.

The Keesom interaction is a van der Waals force. It is discussed further in the section "Van der Waals forces".

===Ion–dipole and ion–induced dipole forces===

Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules. Ion–dipole and ion–induced dipole forces are stronger than dipole–dipole interactions because the charge of any ion is much greater than the charge of a dipole moment. Ion–dipole bonding is stronger than hydrogen bonding.<ref>{{Cite book|title=Chemistry: A Molecular Approach| vauthors = Tro N |publisher=Pearson Education Inc|year=2011|isbn=978-0-321-65178-5|location=United States|pages=466}}</ref>

An ion–dipole force consists of an ion and a polar molecule interacting. They align so that the positive and negative groups are next to one another, allowing maximum attraction. An important example of this interaction is hydration of ions in water which give rise to [[Physics:Hydration energy|hydration enthalpy]]. The polar water molecules surround themselves around ions in water and the energy released during the process is known as hydration enthalpy. The interaction has its immense importance in justifying the stability of various ions (like Cu<sup>2+</sup>) in water.

An ion–induced dipole force consists of an ion and a non-polar molecule interacting. Like a dipole–induced dipole force, the charge of the ion causes distortion of the electron cloud on the non-polar molecule.<ref name=Michael-Blaber-1996>{{cite web | vauthors = Blaber M | date = 1996 | url = http://www.mikeblaber.org/oldwine/chm1045/notes/Forces/Intermol/Forces02.htm | title = Intermolecular Forces | work = mikeblaber.org | access-date = 2011-11-17 | archive-date = 2020-08-01 | archive-url = https://web.archive.org/web/20200801205131/http://www.mikeblaber.org/oldwine/chm1045/notes/Forces/Intermol/Forces02.htm | url-status = dead }}</ref>

==Van der Waals forces==
{{Main|Physics:Van der Waals force}}

The van der Waals forces arise from interaction between uncharged atoms or molecules, leading not only to such phenomena as the cohesion of condensed phases and physical absorption of gases, but also to a universal force of attraction between macroscopic bodies.<ref name=j1>{{cite journal | vauthors = Leite FL, Bueno CC, Da Róz AL, Ziemath EC, Oliveira ON | title = Theoretical models for surface forces and adhesion and their measurement using atomic force microscopy | journal = International Journal of Molecular Sciences | volume = 13 | issue = 10 | pages = 12773–12856 | date = October 2012 | pmid = 23202925 | pmc = 3497299 | doi = 10.3390/ijms131012773 | doi-access = free }}</ref>

===Keesom force (permanent dipole – permanent dipole) {{Anchor|Keesom force}}===
The first contribution to van der Waals forces is due to electrostatic interactions between rotating permanent dipoles, quadrupoles (all molecules with symmetry lower than cubic), and  multipoles.  It is termed the ''Keesom interaction'', named after Willem Hendrik Keesom.<ref>{{cite journal| vauthors = Keesom WH |title=The second virial coefficient for rigid spherical molecules whose mutual attraction is equivalent to that of a quadruplet placed at its center |url=http://www.dwc.knaw.nl/DL/publications/PU00012540.pdf |journal= Proceedings of the Royal Netherlands Academy of Arts and Sciences |year=1915 |volume= 18 |pages= 636–646}}</ref> These forces originate from the attraction between permanent dipoles (dipolar molecules) and are temperature dependent.<ref name=j1/>

They consist of attractive interactions between dipoles that are [[Physics:Canonical ensemble|ensemble]] averaged over different rotational orientations of the dipoles. It is assumed that the molecules are constantly rotating and never get locked into place. This is a good assumption, but at some point molecules do get locked into place. The energy of a Keesom interaction depends on the inverse sixth power of the distance, unlike the interaction energy of two spatially fixed dipoles, which depends on the inverse third power of the distance. The Keesom interaction can only occur among molecules that possess permanent dipole moments, i.e., two polar molecules. Also Keesom interactions are very weak van der Waals interactions and do not occur in aqueous solutions that contain electrolytes. The angle averaged interaction is given by the following equation:

:<math>\frac{-d_1^2 d_2^2}{24\pi^2 \varepsilon_0^2 \varepsilon_r^2 k_\text{B} T r^6} = V,</math>

where ''d'' = electric dipole moment, <math>\varepsilon_0</math> = permitivity of free space, <math>\varepsilon_r</math> = dielectric constant of surrounding material, ''T'' = temperature, <math>k_\text{B}</math> = Boltzmann constant, and ''r'' = distance between molecules.

===Debye force (permanent dipoles–induced dipoles) {{Anchor|Debye force}}===
The second contribution is the induction (also termed polarization) or Debye force, arising from interactions between rotating permanent dipoles and from the polarizability of atoms and molecules (induced dipoles). These induced dipoles occur when one molecule with a permanent dipole repels another molecule's electrons. A molecule with permanent dipole can induce a dipole in a similar neighboring molecule and cause mutual attraction. Debye forces cannot occur between atoms. The forces between induced and permanent dipoles are not as temperature dependent as Keesom interactions because the induced dipole is free to shift and rotate around the polar molecule. The Debye induction effects and Keesom orientation effects are termed polar interactions.<ref name=j1/>

The induced dipole forces appear from the induction (also termed polarization), which is the attractive interaction between a permanent multipole on one molecule with an induced (by the former di/multi-pole) 31 on another.<ref name=Blustin-1978>{{Cite journal |doi= 10.1007/BF00577166 |title= A Floating Gaussian Orbital calculation on argon hydrochloride (Ar·HCl) |journal= Theoretica Chimica Acta |volume= 47 |issue= 3 |pages= 249–257 |year= 1978 | vauthors = Blustin PH |s2cid= 93104668 }}</ref><ref name=Roberts-Orr-1938>{{Cite journal |doi= 10.1039/TF9383401346 |title= Induced dipoles and the heat of adsorption of argon on ionic crystals |journal= Transactions of the Faraday Society |volume= 34 |pages= 1346 |year= 1938 | vauthors = Roberts JK, Orr WJ }}</ref><ref name=Sapse-et-al-1979>{{Cite journal |doi= 10.1038/278332a0 |title= Ion-induced dipole H−n clusters |journal= Nature |volume= 278 |issue= 5702 |pages= 332–333 |year= 1979 | vauthors = Sapse AM, Rayez-Meaume MT, Rayez JC, Massa LJ |bibcode= 1979Natur.278..332S|s2cid= 4304250 }}</ref> This interaction is called the ''Debye force'', named after Peter J. W. Debye.

One example of an induction interaction between permanent dipole and induced dipole is the interaction between HCl and Ar. In this system, Ar experiences a dipole as its electrons are attracted (to the H side of HCl) or repelled (from the Cl side) by HCl.<ref name=Blustin-1978/><ref name=Roberts-Orr-1938/> The angle averaged interaction is given by the following equation:

:<math>\frac{-d_1^2 \alpha_2}{16\pi^2 \varepsilon_0^2 \varepsilon_r^2 r^6} = V,</math>

where <math>\alpha_2</math> = polarizability.

This kind of interaction can be expected between any polar molecule and non-polar/symmetrical molecule. The induction-interaction force is far weaker than dipole–dipole interaction, but stronger than the [[Physics:London dispersion force|London dispersion force]].

===London dispersion force (fluctuating dipole–induced dipole interaction)===
{{Main|Physics:London dispersion force}}

The third and dominant contribution is the dispersion or London force (fluctuating dipole–induced dipole), which arises due to the non-zero instantaneous dipole moments of all atoms and molecules. Such polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in non-polar molecules. Thus, London interactions are caused by random fluctuations of electron density in an electron cloud.  An atom with a large number of electrons will have a greater associated London force than an atom with fewer electrons. The dispersion (London) force is the most important component because all materials are polarizable, whereas Keesom and Debye forces require permanent dipoles. The London interaction is universal and is present in atom-atom interactions as well. For various reasons, London interactions (dispersion) have been considered relevant for interactions between macroscopic bodies in condensed systems. [[Physics:Hamaker theory|Hamaker]] developed the theory of van der Waals between macroscopic bodies in 1937 and showed that the additivity of these interactions renders them considerably more long-range.<ref name=j1/>

==Relative strength of forces==

{|class="wikitable"
!Bond type
!Dissociation energy<br />(kcal/mol)<ref name=Seyhan-Organic-Chemistry>{{cite book | vauthors = Eğe SN |title=Organic Chemistry: Structure and Reactivity |date=2004 |publisher=Houghton Mifflin Company |location=Boston |isbn=978-0-618-31809-4 |edition=5th | pages = 30–33, 67}}</ref>
!Dissociation energy
(kJ/mol)
!Note
|-
|Ionic lattice
|250–4000<ref name=Purdue-Lattice>{{cite web |title=Lattice Energies |url=http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch7/lattice.html |access-date=2014-01-21 | work = Division of Chemical Education | publisher = Purdue University }}</ref>
|1100–20000
|
|-
|Covalent bond
|30–260
|130–1100
|
|-
|[[Chemistry:Hydrogen bond|Hydrogen bond]]
|1–12
|4–50
|About 5&nbsp;kcal/mol (21&nbsp;kJ/mol) in water
|-
|Dipole–dipole
|0.5–2
|2–8
|
|-
|London dispersion forces
|<1 to 15
|<4 to 63
|Estimated from the enthalpies of vaporization of hydrocarbons<ref name=Majer-Svoboda-enthalpy-vap>{{cite book | vauthors = Majer V, Svoboda V |title=Enthalpies of Vaporization of Organic Compounds |date=1985 |publisher=Blackwell Scientific |location=Oxford |isbn=978-0-632-01529-0}}</ref>
|}

This comparison is approximate. The actual relative strengths will vary depending on the molecules involved. For instance, the presence of water creates competing interactions that greatly weaken the strength of both ionic and hydrogen bonds.<ref>{{Cite book | vauthors = Alberts B |url=https://www.worldcat.org/oclc/887605755 |title=Molecular biology of the cell |date=2015 |isbn=978-0-8153-4432-2 |edition=6th |location=New York, NY |oclc=887605755}}</ref> We may consider that for static systems, [[Chemistry:Ionic bonding|Ionic bonding]] and [[Chemistry:Covalent bond|covalent bond]]ing will always be stronger than intermolecular forces in any given substance. But it is not so for big moving systems like [[Biology:Enzyme|enzyme]] molecules interacting with [[Chemistry:Substrate|substrate]] molecules.<ref>{{cite journal | vauthors = Savir Y, Tlusty T | title = Conformational proofreading: the impact of conformational changes on the specificity of molecular recognition | journal = PLOS ONE | volume = 2 | issue = 5 | pages = e468 | date = May 2007 | pmid = 17520027 | pmc = 1868595 | doi = 10.1371/journal.pone.0000468 | bibcode = 2007PLoSO...2..468S | doi-access = free }}</ref> Here the numerous intramolecular (most often - [[Chemistry:Hydrogen bond|hydrogen bond]]s) bonds form an active intermediate state where the intermolecular bonds cause some of the [[Chemistry:Covalent bond|covalent bond]] to be broken, while the others are formed, in this way procceding the thousands of [[Biology:Enzyme catalysis|enzymatic reactions]], so important for living organisms.

==Effect on the behavior of gases==

Intermolecular forces are repulsive at short distances and attractive at long distances (see the [[Physics:Lennard-Jones potential|Lennard-Jones potential]]). In a gas, the repulsive force chiefly has the effect of keeping two molecules from occupying the same volume. This gives a [[Physics:Real gas|real gas]] a tendency to occupy a larger volume than an [[Physics:Ideal gas|ideal gas]] at the same temperature and pressure. The attractive force draws molecules closer together and gives a real gas a tendency to occupy a smaller volume than an ideal gas. Which interaction is more important depends on temperature and pressure (see [[Physics:Compressibility factor|compressibility factor]]).

In a gas, the distances between molecules are generally large, so intermolecular forces have only a small effect. The attractive force is not overcome by the repulsive force, but by the [[Physics:Thermal energy|thermal energy]] of the molecules. [[Physics:Thermodynamic temperature|Temperature]] is the measure of thermal energy, so increasing temperature reduces the influence of the attractive force. In contrast, the influence of the repulsive force is essentially unaffected by temperature.

When a gas is compressed to increase its density, the influence of the attractive force increases. If the gas is made sufficiently dense, the attractions can become large enough to overcome the tendency of thermal motion to cause the molecules to disperse. Then the gas can condense to form a solid or liquid, i.e., a condensed phase. Lower temperature favors the formation of a condensed phase. In a condensed phase, there is very nearly a balance between the attractive and repulsive forces.

==Quantum mechanical theories==


Intermolecular forces observed between atoms and molecules can be described phenomenologically as occurring between permanent and instantaneous dipoles, as outlined above. Alternatively, one may seek a fundamental, unifying theory that is able to explain the various types of interactions such as hydrogen bonding,<ref name=":0">{{Cite journal| vauthors = Arunan E, Desiraju GR, Klein RA, Sadlej J, Scheiner S, Alkorta I, Clary DC, Crabtree RH, Dannenberg JJ, Hobza P, Kjaergaard HG | display-authors = 6 |date=2011-07-08|title=Definition of the hydrogen bond (IUPAC Recommendations 2011)|journal=Pure and Applied Chemistry|volume=83|issue=8|pages=1637–1641|doi=10.1351/PAC-REC-10-01-02|s2cid=97688573|issn=1365-3075|doi-access=free}}</ref> [[Physics:Van der Waals force|van der Waals force]]<ref name=LD>{{cite book | vauthors = Landau LD, Lifshitz EM | title = Electrodynamics of Continuous Media | url = https://archive.org/details/electrodynamicso00land | url-access = registration | publisher = Pergamon | location = Oxford | date = 1960 | pages = [https://archive.org/details/electrodynamicso00land/page/368 368–376] }}</ref> and dipole–dipole interactions. Typically, this is done by applying the ideas of [[Physics:Quantum mechanics|quantum mechanics]] to molecules, and Rayleigh–Schrödinger [[Physics:Perturbation theory|perturbation theory]] has been especially effective in this regard. When applied to existing [[Chemistry:Quantum chemistry|quantum chemistry]] methods, such a quantum mechanical explanation of intermolecular interactions provides an array of approximate methods that can be used to analyze intermolecular interactions.<ref>{{cite journal | doi = 10.1021/ja00428a004 | title = Theory of the Chemical Bond | year = 1976 | vauthors = King M | journal = Journal of the American Chemical Society | volume = 98 | issue = 12 | pages = 3415–3420 }}</ref>  One of the most helpful methods to visualize this kind of intermolecular interactions, that we can find in quantum chemistry, is the [[Chemistry:Non-covalent interactions index|non-covalent interaction index]], which is based on the electron density of the system. London dispersion forces play a big role with this.

Concerning electron density topology, recent methods based on electron density gradient methods have emerged recently, notably with the development of IBSI (Intrinsic Bond Strength Index),<ref>{{cite journal | vauthors = Klein J, Khartabil H, Boisson JC, Contreras-García J, Piquemal JP, Hénon E | title = New Way for Probing Bond Strength | journal = The Journal of Physical Chemistry A | volume = 124 | issue = 9 | pages = 1850–1860 | date = March 2020 | pmid = 32039597 | doi = 10.1021/acs.jpca.9b09845 | s2cid = 211070812 | bibcode = 2020JPCA..124.1850K | url = https://hal.archives-ouvertes.fr/hal-02377737/file/4_IGM_bond13012020_11h49%20%281%29.pdf }}</ref> relying on the IGM (Independent Gradient Model) methodology.<ref>{{cite journal | vauthors = Lefebvre C, Rubez G, Khartabil H, Boisson JC, Contreras-García J, Hénon E | title = Accurately extracting the signature of intermolecular interactions present in the NCI plot of the reduced density gradient versus electron density | journal = Physical Chemistry Chemical Physics | volume = 19 | issue = 27 | pages = 17928–17936 | date = July 2017 | pmid = 28664951 | doi = 10.1039/C7CP02110K | bibcode = 2017PCCP...1917928L | url = https://hal.univ-reims.fr/hal-02505160/file/2017_IGM_PROMOL%20%281%29.pdf }}</ref><ref>{{cite journal | vauthors = Lefebvre C, Khartabil H, Boisson JC, Contreras-García J, Piquemal JP, Hénon E | title = The Independent Gradient Model: A New Approach for Probing Strong and Weak Interactions in Molecules from Wave Function Calculations | journal = ChemPhysChem | volume = 19 | issue = 6 | pages = 724–735 | date = March 2018 | pmid = 29250908 | doi = 10.1002/cphc.201701325 | url = https://hal.univ-reims.fr/hal-03377532/file/37_version.pdf }}</ref><ref>{{cite journal | vauthors = Ponce-Vargas M, Lefebvre C, Boisson JC, Hénon E | title = Atomic Decomposition Scheme of Noncovalent Interactions Applied to Host-Guest Assemblies | journal = Journal of Chemical Information and Modeling | volume = 60 | issue = 1 | pages = 268–278 | date = January 2020 | pmid = 31877034 | doi = 10.1021/acs.jcim.9b01016 | s2cid = 209488458 }}</ref>

== See also ==
{{div col|colwidth=18em}}
* [[Chemistry:Ionic bonding|Ionic bonding]]
* [[Chemistry:Salt bridge (protein and supramolecular)|Salt bridges]]
* [[Physics:Coomber's relationship|Coomber's relationship]]
* [[Chemistry:Force field|Force field]]
* [[Chemistry:Hydrophobic effect|Hydrophobic effect]]
* [[Chemistry:Intramolecular force|Intramolecular force]]
* [[Chemistry:Molecular solid|Molecular solid]]
* [[Chemistry:Polymer|Polymer]]
* Quantum chemistry computer programs
* [[Physics:Van der Waals force|van der Waals force]]
* [[Physics:Comparison of software for molecular mechanics modeling|Comparison of software for molecular mechanics modeling]]
* [[Chemistry:Non-covalent interactions|Non-covalent interactions]]
* [[Chemistry:Solvation|Solvation]]
{{div col end}}

== References ==
{{Reflist|30em}}


{{DEFAULTSORT:Intermolecular Force}}
[[Category:Intermolecular forces]]
[[Category:Chemical bonding]]

{{Sourceattribution|Intermolecular force}}