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2.4: Solubility in an aqueous world - noncovalent interactions in depth

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    Introduction

    In sections 2.1, we explored the role of water as a solvent.  Using the adage "like dissolves like" that you may have learned in introductory chemistry and biology courses, we can rationalize what substance might dissolve in water.  We related this to the types and strengths of attractive interactions that occur between solute and solvent.  If in sum they are stronger than self interactions (solute-solute and solvent-solvent), the solute would dissolve (to a reasonable extent) in the solvent.  We also discussed entropic contributions to the dissolution process.  For now we will refocus on the noncovalent interactions. 

    In introductory science courses, noncovalent interaction are often described as intermolecular forces. This term is ambiguous when applied to biochemistry. Take for example hydrogen bonds.  They occur between two water molecules, for example, but within larger molecules (like proteins) if hydrogen bond donors and acceptors within the molecule get close enough to each other in space.

    The table below summarizes the common noncovalent interactions/“intermolecular forces” that you studied in introductory science classes.    It is hard enough for students to recognize and identify these interactions between two small molecules let alone in large molecules like proteins.  We will explore these in more detail below, and give examples of noncovalent interactions between small molecules and within large ones such sproteins.  We'll also add a few more specific examples of interactions.

    Noncovalent Interactions - "Intermolecular Forces" 

    Interaction

    Type

    Example

    Distance
    Dependence

    Relative Strength

    (Kcal/mol)

    Direction Dependence

    Ion-Ion

     

    Table-IonIon-01.svg

    1/r

    60

    nondirectional

    H-Bonds

    Table-Hbond-01.svg

     

    3-15

    directional

    Ion-dipole

    Table-IonDipole-01.svg

    1/r2

    3-5

    directional

    Dipole-dipole

    Table-DipoleDipole.svg

    1/r3

    0.5-1

    directional

    Induced Dipole-

    Induced Dipole

    Table-IndDipIndDipole-01.svg

    1/r6

    0.5

    (depend on size)

    nondirectional

    Even though there are many different types of noncovalent interactions, there is one fundamental principle that applies to all of them:  they originate in the electrostatic force between two charged objects. There is one simple law, Coulomb’s Law, which you would have discussed in introductory science courses, and one simple equation, the describes the electrostatic force:

    \[F=\dfrac{k Q_{1} Q_{2}}{r^{2}}\]

    where F is the force (attractive or repulsive) between two particles of charge Q1 and Q2 with their centers separated by some distance r.   Replace the charges with masses of two objects and you have Newton's Law of Gravitation.  Both are inverse squared laws

    All of the interactions described in the table above arise from the electrostatic force. The magnitude of the attractions for the interactions depend on the way charge is distributed in the attracting species. Each has a different dependency on distance.

    Different words are used to describe  noncovalent interactions.  This can be distressing to learners who might hear different definitions used by chemists and biologist for the same noncovalent interactions.  Some use van der Waals forces to describe induced dipole -induced dipole interactions, while other use London dispersion forces or hydrophobic forces/interactions.  Others use van der Waals forces to describe all noncovalent interactions except for ion-ion.  To avoid ambiguity, let's looks at the IUPAC Gold Book Compendium of Chemical Terminology, which offers this definition of van der Waals forces: 

    Definition: van der Waals Forces

    "The attractive or repulsive forces between molecular entities (or between groups within the same molecular entity) other than those due to bond formation or to the electrostatic interaction of ions or of ionic groups with one another or with neutral molecules. The term includes: dipole–dipole, dipole-induced dipole, and London (instantaneous induced dipole-induced dipole) forces. The term is sometimes used loosely for the totality of nonspecific attractive or repulsive intermolecular forces".    IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.

    Figure \(\PageIndex{1}\) below summarizes covalent and noncovalent interactions, using that definition.

     

    IMFTable-01.svg

    Figure \(\PageIndex{1}\): Noncovalent Interactions

    Using this definition, hydrogen bonds are usually consider a type of dipole-dipole interaction. Historically, several of the noncovalent interactions have alternative names based on the person associated with them.  Only the names van der Waal and London are commonly used.  

    Even the word "force" is potentially ambiguous.  To a physicist, there are only four known forces, gravitational (between two objects with mass), electromagnetic (between charges - the electrostatic force, and moving charges - the magnetic force), the strong force (holding the nucleus together) and the weak force (also nuclear and involved in radioactive decay). We'll try to use the word interaction throughout this book.

    Interactions within small molecules, such as covalent bonds, and between molecules, such as induced dipole-induced dipole, vary as some function of r, the distance between the two interacting particle.  Only ion-ion interactions vary as 1/r2 however.  Attractions lower overall energy while repulsions raise it.  At some optimal distance, when the interactions are most attractive, the system is in its most energetically favored state.   The relationship between the potential energy for covalent bond formation and for the noncovalent attraction of two atoms as a function of distance is shown in general form in Figure \(\PageIndex{2}\): below. 

     EpotvsR_H2_He2.svg

    Figure \(\PageIndex{2}\): Potential Energy for Covalent and Noncovlanet interactions

    The curve in black shows the the shape of Epot vs r for the formation of a covalent bond between H atoms.  The Morse potential energy function is used to model energy as a function of r for simple diatomic molecules.  The red line shows the shape of Epot vs r for the noncovalent attraction of two He atoms through induced dipole-induced dipole interactions. It is modeled using the Lennard Jones (6-12) potential function (see below). Each has an optimal r0 (the bond length for H2 and two times the van der Waals radius, rW, of each He in 2He).  The energy required to break the induced dipole-induced dipole interactions between He atoms is very small, which accounts for the fact that liquid He, in which many He are interacting, only exists at very cold temperatures (boiling point = -269 Celsius).  Although the graph for H2 shows the relationship between the potential energy and r0 for the covalent bond, in reality the sources of stability of any covalent bond is complex and requires in addition a term for the kinetic energy of the electron.  Fundamentally, the strength of a covalent bond is best described through analysis of the quantum wave functions for the system.  The average single covalent bond strength depends on the atoms bonded and varies between 30-120 kcal/mol, a factor of 4.

    Another confusing feature when discussing noncovalent interactions is that while we talk about forces (like the electrostatic force), we often draw graphs of energy E vs r, the distance between two interacting particles.  Let briefly examine the relationship between potential energy (Epot) and force for the electrostatic force given by Coulomb's Law by using a more familiar example, the next gravitational force of a stationary ball place at various points on a hill, as illustrated in Figure \(\PageIndex{3}\) below. 

    EpotvsR_BallHill_Energy.svg

    Figure \(\PageIndex{3}\): Potential Energy vs r for a ball on a hill

    Assume the ball is motionless at each position in the diagram so only potential energy can be considered.  The red arrows (vectors) represent the relative net downward force on the ball at each position. At the top and bottom of the hill, the net downward forces are zero. As the slope of the hill increases, the net downward forces increases.  The force is directly proportional to the slope (dE/dr), or simply: 

    \[F=-\frac{\Delta \mathrm{E}}{\Delta \mathrm{r}}=-\frac{\mathrm{dE}}{\mathrm{dr}}\]

    Now let's apply this same relationship to Coulomb's Law for the force.  Rearranging gives

    \[dE=-\mathrm{Fdr}=-\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{\mathrm{r}^{2}} \mathrm{dr}\]

    Using calculus and integrating both sides of the equations gives this general relationship between E and r for the electrostatic forces:

    \[E=\mathrm{kq}_{1} \mathrm{q}_{2}\left(\frac{1}{\mathrm{r}}\right)\]

    A graph of Epot vs r for the electrostatic force is shown in Figure \(\PageIndex{4}\) below. Note that the curves are hyperbolic (1/r) functions of r.  There are attractive OR repulsive components.

    GraphElectrostaticPot.svg

    Figure \(\PageIndex{4}\): Electrostatic potential vs distance r

    An equation for Epot vs r for the induced dipole - induced dipole interactions can also be derived.  For this interaction, Epot has a different dependency on r and has both an attractive (Epot α -1/r6) AND repulsive term (Epot α +1/r12) which are added together (as each attracting species has both δ+ and δ- charges). This potential is called the Lennard-Jones or 6-12 potential.  The graph inf Figure \(\PageIndex{5}\) below shows the attractive and repulsive terms separated out as well as the net Epot vs r. Note how similar these curves are to the graphs for electrostatic energy.

    LennardJonesPot.svg

    Figure \(\PageIndex{5}\): Leonnard Jones Potential

    Now, let's look at the noncovalent interactions more carefully using examples of small and big molecules.  

    Ion-Ion.

    All introductory chemistry and biology textbooks differentiate ionic and covalent bonding.  Ionic bonding occurs between fully charged species.  Some ions are monatomic (like Na+ or Cl-), formed from gaining or loosing electrons.  Others are polyatomic (like ammonium - NH4+ or acetate - CH3COO+), generally formed from molecules gaining or losing protons in Brønsted acid/base reactions.  Polyatomic ions are also called molecular ions. An example of the monatomic salt NaCl and the molecular salt ammonium acetate are shown in 2D Lewis structure and molecular modeling representations (spheres and sticks) in Figure \(\PageIndex{6}\): below.     

    ion-ion_simplesalts.svg

    Figure \(\PageIndex{6}\): Representations of monatomic and polyatomic/molecular salts

    Now an intramolecular ionic bond can form within a larger molecule if a negatively charged group in the molecule comes close enough in 3D space to a positively charged group in the same molecule.  In contrast to the examples shown above, the ionic bonds within large molecules like proteins do not occur within a large lattice of ions held together by multitudes of similar ionic bonds.  Rather a single ionic bond could exist and persist in a larger molecule held together by a multitude of other noncovalent interaction.  An ionic bond between a single monatomic or polyatomic cation and anion would not exist in aqueous solution long as the species would dissociate into separate ions solvated by water.  Hence the ionic bond that exist between charged groups within a large molecule like a protein exists in such a different environment than a solid crystal lattice that we give it a different name.  It is called a salt bridge, as the ionic bond bridges distal parts of the larger molecule.  We also categorize it as an ion-ion noncovalent attraction. 

    Figure \(\PageIndex{7}\) below shows a salt bridge (represented as a yellow line) between the side chains of two amino acids, asparatic acid (Asp) 67 (-CH2COO-, similar to acetate) and lysine (Lys) 69 (-RCH2NH3+, similar to NH4+) in a protein, human lysozyme.   

    ion-ion_saltbrigeproteins.svg

    Figure \(\PageIndex{7}\): Salt bridge in human lysozyme

     

    Figure \(\PageIndex{8}\) below shows an interactive iCn3D model of salt bridge between the carboxylate side chain of Asp 67 and the amine side chain of Lys  69 in  human lysozyme (1REX).

    Asp67 -Lys 69_SaltBridge_ humanlysozyme (1REX).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{8}\): Salt bridge (represented as a yellow line) between Asp 67 and Lys  69 in  human lysozyme (1REX). (Copyright; author via source). 
    Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...1qpAtSs3CuvVs8

    Most of the protein's atoms have been removed to simplify the structure.  We haven't studied proteins yet, but to a first approximation they are polymers consisting of amino acid monomers.  The backbone of the polymer contains repeating amide group which contains and N-H hydrogen bond donor and a C=O hydrogen bond acceptor.  Each amino acid contains an R group side chain oriented away from the backbone.  The R groups can be fully charge, polar or nonpolar.

    This protein, containing 129 amino acids in a large polymer of over a 1000 atoms, has just 10 salt bridges within the most stable structure of the protein.  The structure files that contain the x,y, and z coordinates of the atoms in a large biomacromolecule like a protein usually don't give coordinates for hydrogen atoms in the structure since they are too small to detect by techniques such as x-ray crystallography or cryoelectron microscopy, which are used to determine the structure of large biomacromolecules .  Computer programs can be used to add them so they can be visualized in modeling programs.  The left molecule in the above figure shows a stick model of just a small part of the protein containing a single salt bridge. The blue represents a nitrogen with a +1 formal charge in the side chain of lysine. 

    Hydrogen atoms have been added in the right molecule to show a better ideal of actual distance between adjacent atoms.  Quantum calculations of actual electron density in molecular ions such as H3O+ and NH4+ (and charged amines) show that the electron density in these cations is actually shifted to the electronegative O and N atoms with electron deficiencies over the bonded H atoms (in contrast to the simpler ideal of formal charge), even though we state that the N in a charged amine has a positive formal charge.  

    Graphs of E vs r for the electrostatic and other interactions show that as r increases past the optimal interaction distance, the attractions decrease.  When modeling most noncovalent interactions in large molecules, programs generally use cutoff values of 5-6 Angstroms, beyond which the interactions do not contribute to stabilization. The ion-ion interaction is the strongest interaction of all, given a fixed distance for comparison.

    Hydrogen Bond (H-bond)

    The name hydrogen bond is a bit ambiguous, which leads to its misunderstanding by students.  It is not a covalent bond between two atom X and H, such as C-H and O-H.  For our purposes, it involves 3 atoms, X-H and :Y on two different molecules or those near each other in a large molecule.  X is an electronegative atom (such as F, O, N) and :Y is an electronegative atom with a lone pair (such as :O or :N). The H on X-H (for example O-H or N-H) is slightly positive (δ+) since the X-H bond is polar covalent and electron density in the bond is drawn toward the electronegative atom (for example O or N).  The slightly positive H, given its small size compared to all other atoms, can get very close to a lone pair on an slightly negative (δ-) electronegative atom (for example O or N) on another molecule.  Since r, the distance between the δ+ H and δ- N or O on two separate molecules is small, Coulomb's Law informs us that the attractive force is significant.  This interaction is highly directional and distance dependent, which accounts for the large range in relative strength (3-15 kcal/mol) for hydrogen bonds within large molecules.  The δH is called the H bond donor, while the δ- :N or :O, which interacts with it is the H bond acceptor.

    Figure \(\PageIndex{9}\) below shows multiple representations of a central water molecule hydrogen-bonded to four other water molecules.  The left image shows lone pairs as purple spheres.

    5Waters_HBond_multipleReps.svg

    Figure \(\PageIndex{9}\):  Multiple representation of hydrogen bonding among 5 water molecules

    A common difficulty for students is to identify which of the myriad of hydrogen atoms in any structure can engage in hydrogen bonds.  One way is to circle all δHs in structures (i.e. those covalently attached to N or O) and see if there are any nearby δ- :Ns or :O close enough to form a hydrogen bond. Figure \(\PageIndex{10}\) below shows a molecule of methanol forming two hydrogen bonds to two different water molecules. Only 1 of the 4 Hs on methanol is δ+ (circled in green).  The others are covalently bonded to a carbon and we consider that bond nonpolar covalent.

    HbondsMeOH.svg

    Figure \(\PageIndex{10}\): Hydrogen bond between methanol and waters

    Hydrogen bonds are abundant in large molecules like proteins.  They occur between backbone atoms, between backbone and side chains atoms, between side chain atoms and between protein atoms and water. Their strength depends on the magnitude of δand δ charges on the H bond donor and acceptor atoms, respectively, and the distance r between them.  Three types of H bonds have been categorized based on their relative strengths based in large part on the distance between the donor and acceptor: 

    • weak or conventional (2.4 to 12 kcal mol)
    • strong or low barrier (12 to 24 kcal mol), often called short hydrogen bonds (SHB)
    • very strong or no barrier >24 kcal/ ol) (Frey et al). 

    In very large proteins of known 3D structures, H bonds are calculated by locating all donors and acceptors with 3 +/- x angstroms from each other.  Most structural files do not include H atoms so the 3 Angstrom distance is from the centers of the electronegative atoms, typically N and O, involved in the hydrogen bond, as shown in Figure \(\PageIndex{11}\) below (purple bracket). 

    HbondDistance_vanderWaalsDistance.svg

    Figure \(\PageIndex{11}\): Hydrogen bonding distances between the center of a participating N with a H donor and an O with a H bond acceptor

    Conventional H bonds vary between 2.8-3.2 A, which gives a distance range from the actual δ+ hydrogen to the acceptor δ N or O (the red line below) of 1.8 to 2.2 A.  Short H bonds are < 2.7A which is smaller the the sums of the van der Waals radii of N and O (blue and red circle below), suggesting that the bond has covalent character (see below).  Those between 2.5 - 2.7 are characterized as strong, low barrier, or short hydrogen bonds.  Analysis of a large number of PDB structure of protein shows many short hydrogen bonds characterized by these properties:

    •  the donor and acceptor electronegative atoms A and B are N or O
    • r, the separation distance, is 2.3 A to 2.7 °A
    • the A–H–B angle is 1350.

    A detailed analysis of high quality proteins structures show that there is one short hydrogen bond for every 16 conventional.  They are found in proteins, protein-ligand complexes and in DNA and are involved in many aspects of molecular function.

    It would seem likely that the δH atom, which is covalently attached to a heteroatom like O or N (A), and which is attracted to another heteroatom B, could be exchanged between the two heteroatoms as shown in the chemical equation below, where ---- represents a H bond.

    A-H ----B ↔  A ----H-B

    A very strong/no barrier H bonds occurs if A and B are very close, have similar δcharges and with similar pKa so that the H atom could be equally shared between A and B.  It is represented by equation: 

    A ||| H ||| B

    An example is FHF- (F||| H |||F)-  in which there is no barrier for the H to move from one heteroatom to another. 

    It thus appears that for strong and very strong H bonds, what we call the hydrogen bond has some covalent bond character.  Quantum calculations show that there is overlap between the unoccupied antibonding σ*molecular orbital of X-H (the hydrogen donor) and the non-bonding lone electron pair molecular orbital of the hydrogen bond acceptor molecule.

    Even though water is such a simple and ubiquitous molecules, scientists are still struggling to fully understand its properties.  Lewis structures of water can explain so much of its physical and chemical properties.  However, look at Figure \(\PageIndex{12}\) below, which shows the electron density around water calculated using quantum theory. 

    waterelectrondensity.svg

    Figure \(\PageIndex{12}\): Electron density around a water molecule.  https://commons.wikimedia.org/wiki/F...balls.png#file

    Do you see any "rabbit ears" (i.e. lone pairs) emanating from the oxygen atom? Don't think so!  Nevertheless, everyone still uses Lewis structures with lone pairs to explain the chemistry of water.  We present this figure in preparation for a discussion at the end of this section of a recently discovered noncovalent interaction called the halogen bond, which requires an understanding of the "real" electron density around bonded atoms.

    Now let's look at some hydrogen bonds within a single protein molecule.  Figure \(\PageIndex{13}\) below hydrogen bonds (yellow dotted line) between serine (Ser) 24 (side chain -CH2OH) and asparagine (Asn) 27 (side chain -CH2(C=O)NH2 of hen egg white lysozome (1REX).  As in the figure above showing a salt bridge in the protein, two images are shown, one with polar H atoms added.  Find the H bonds between the side chains, between side chains and backbone, and between backbone hydrogen bond donors and acceptors.

    1rex_HbondsSess2_S24N27_with_withoutHs.svg

    Figure \(\PageIndex{13}\):  More hydrogen bonds in hen egg white lysozome (1REX)

    Proteopedia has an excellent review of hydrogen bonds.

    Dipole-Dipole

    This interaction involves the alignment of permanent dipoles in molecules such that the geometric center of the δ+ of one permanent dipole on one molecule is close to and aligned with the geometric center of δ- of the permanent dipole on another.  Figure \(\PageIndex{14}\) below shows two acetone molecules interacting through dipole-dipole interactions.  

     

    2acetones.svg

    Figure \(\PageIndex{14}\): Attractions of two acetones through dipole-dipole interactions

    The arrow represents the molecule dipole moment vector (as opposed to individual bond dipole moment for each polar covalent bond in the molecule). Note the difference in the Figure \(\PageIndex{15}\).  The molecular dipole is the vector sum of the bond dipoles.

     

    151611849161611773.jpg 

    Figure \(\PageIndex{15}\):  Difference between bond and molecular dipoles.  https://chem.libretexts.org/Bookshel...bond%20dipoles.

    None of the H atoms bonded to carbon in acetone are δ+ so the molecules contains no H bond donors.  Although they contain a δ- oxygen, a hydrogen bond acceptor, two molecules of acetone cannot hydrogen bond to themselves.  They can form hydrogen bonds to water. Pure liquid acetone evaporates readily (BP 560 C) due to this lack of strong hydrogen bonds.

    You can imagine two water molecules forming dipole-dipole interactions as well.  However tilting the molecule to align the lone pair on an O with the δ+H on another water molecule and presto, you have a hydrogen bond.  H bonds are often viewed as a special case of a dipole-dipole interaction.

    Modeling programs can determine the charge on each atom of a large molecule like a protein and determine the geometric center and magnitude of overall + and - charge. A line drawn between them would give the permanent "dipole" moment of the entire protein.  More simply, the molecular dipole is the vector sum of all of the individual bond dipole moments.  Entire proteins have a net dipole moment which probably facilitates the interaction of the protein with other proteins or ligands. Figure \(\PageIndex{16}\) below shows the net dipole moment for the protein carboxypeptidase A1 (2v77).  This was calculated using the Protein Dipole Moments Server.  Protein, however, do have net charges (not considering any bound counterions) so the molecular dipole for a protein is a bit different conceptually than for a small molecule. Nevertheless it is a good way to quantitate asymmetric charge distribution in large biomolecules.  Asymmetric charge distributions would influence molecular properties.

    2v77_wholeproteindipoleCarboxypeptidas.svg 

    Figure \(\PageIndex{16}\):  Net dipole moment of the protein carboxypeptidase A1  (2v77)

     

    Ion-Dipole

    Figure \(\PageIndex{17}\) below shows interactions between a Na+ ion and the dipoles of multiple water molecules.

     

    c11-ion-dipole.png

    Figure \(\PageIndex{17}\):  Ion-dipole interactions between Na+ and water.  https://chem.libretexts.org/Courses/...-Dipole_Forces

    Figure \(\PageIndex{18}\) below shows an interactive iCn3D model of the molecular ion sulfate SO42- bound to a protein through its hydrogen bonding and ion-dipole noncovalent interactions with protein side chain and backbone groups in the sulfate binding protein from Salmonella typhimurium.  

    sulfate bound to sulfate binding protein from Salmonella typhimurium (1sbp).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{18}\): Sulfate bound to sulfate binding protein from S. typhimurium (1sbp).  Hydrogen bonds are shown as green and yellow lines.  (Copyright; author via source).  Click the image for a popup or use this external link:  https://structure.ncbi.nlm.nih.gov/i...JvqQuZZnvf3AU8

    The SO42- is buried within the protein. The green and yellow dotted line shown hydrogen bonds between the sulfate and amide N-Hs on the protein chain surrounding it and the a side chain of the protein.  Modeling programs don't shows lines depicting dipole-x interactions.  The SO42- through its oxygens can form hydrogen bonds with nearby donors.

    Figure \(\PageIndex{19}\) below shows an interactive iCn3D model of another example of protein backbone and side chains ion-dipole interactions, this time with a Na+ ion, a simple non-transition state metal ion, which can not form hydrogen bond. The protein is tryptophan synthase from Salmonella typhimurium (6dz4).  The red spheres represent water oxygen atoms (no hydrogen atoms shown).  

    Sodium ion binding site in tryptophan synthase from Salmonella typhimurium (6dz4).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{19}\): Sodium ion binding site in tryptophan synthase from Salmonella typhimurium (6dz4).  Click the image for a popup or use this external link:  https://structure.ncbi.nlm.nih.gov/i...pDnU36vXXPeyX7

    The ions illustrated in these last two cases are not transition metal ions, whose interactions of ligands can best be considered using ligand field theory and the formation of covalent (dative) bonds between electron pair donors on nucleophilic side chain/main chain atoms and d orbitals on the transition metal.

     

    Induced Dipole - Induced Dipole

    These noncovalent interactions occur when a temporary dipole, created by random fluctuations in electron density in one molecule, induces a temporary dipole in another one nearby.  These interactions are weak and can easily be broken by raising the temperature.  Induced dipole-induced dipole interactions allow nonpolar gases like He, N2 and O2 and CH4 to be liquefied but it takes higher pressures and/or low temperatures to force molecule close enough and slow them down enough for the sufficient interactions to occur to liquefy the molecules.  Although individually weak,  the larger the molecules, the greater the extent of induced dipole-induced dipole interactions and the greater the forces of interactions among molecules.  This is reflected in the fact that methane, CH4, is a gas room temperature, octane, C8H18 is a liquid and C30H62 is a solid.

    Figure \(\PageIndex{20}\) below shown induced dipole interactions between two molecules.

    ldfs.svg

    Figure \(\PageIndex{20}\):  Induced dipole-induced dipole interactions.  https://boisestate.pressbooks.pub/ch...ecular-forces/

     

    Induced dipole-induced dipole interactions are important among large biomolecules as well.  Figure \(\PageIndex{21}\) below shows an interactive iCn3D model of a hydrophobic cluster around the side chain of a hydrophobic amino acid, valine 143 in human carbonic anhydrase II (4ca2). Val 143 is highlighted in yellow and shown with normal atom (CPK) colors. White to green indicate nonpolar amino acids while dark blue indicate polar ones.  

    Valine143HphoPocket in human carbonic anhydrase II (4ca2).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{21}\): Hydrophobic cluster around the side chain of a hydrophobic amino acid, valine 143 in human carbonic anhydrase II (4ca2).  Click the image for a popup or use this external link:https://structure.ncbi.nlm.nih.gov/i...6rgjajJsg3Xvg8

    You can see that the side chain of Val 143 (highlighted in yellow) is completely surrounded by nonpolar amino acids.  If the structure was rendered in spacefill instead of sticks, Val 143 would be closely packed to maximize induced dipole-induced dipole interactions.

    It is important to note that there is no "hydrophobic force".  The term hydrophobic interactions is often use to describe interactions mediated by induced dipole-induced dipole  interactions between and among molecules or parts of molecules.  Induced dipole-induced dipole interactions also occur between polar molecules, but they are weaker than the hydrogen bonding and dipole-dipole interactions between them.

     

    Pi stacking

    Aromatic rings that are stacked over each other can engage in induced-induced dipole and dipole-induced dipole interactions, depending on if heteroatoms are present in the aromatic ring.  Figure \(\PageIndex{22}\) below shows an example for benzene in which a staggered arrangement of the rings is more attractive.

    clipboard_eb483630e17251b599848f0574e2e2ab3.png

    Figure \(\PageIndex{22}\):  Pi stacking in benzene.  https://chem.libretexts.org/Bookshel...g_interactions

    For a biological example, everyone is familiar with the structure of B-DNA in which the bases A, G, C and T point inward perpendicular to the double helix axis  and are stacked over each other.

    Figure \(\PageIndex{23}\) below shows an interactive iCn3D model of a short stretch of DNA with a sugar-phosphate backbone and bases colored in magenta and cyan.  Fives bases on one strand are shown in stick and atomic color to clearly show the pi stacking interactions of the aromatic ring.

    Pi_stackingBNA (5t4w).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{23}\): Pi stacking in B-DNA (5t4w).  Click the image for a popup or use this external link:  https://structure.ncbi.nlm.nih.gov/i...euHaVfXwk18JJ8

    Pi stacking also occurs in proteins.  Figure \(\PageIndex{24}\) below shows an interactive iCn3D model of two sets of pi stacking interactions in the protein arginine kinase (1M15).  The aromatic side chains involved in pi stacking are shown in cyan.

    Pi_stackingArginineKinase (1m15).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{24}\): Pi stacking in Arginine Kinase (1M15).  Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...owSDJ2DUqtwk8A 

     

    Cation - Pi

    Figure \(\PageIndex{25}\) below shows an interactive iCn3D model  a specific example of an ion - induced dipole interaction (called a cation-pi interaction) between a sodium ion (blue sphere) and the aromatic ring of the side chain tryptophan (cyan) in hen egg white lysozyme (1lpi).   

    NaW_Cat_Pi_Interaction_1LPI.png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{25}\): Cation-Pi stacking (ion-induced dipole) in hen egg white lysozyme (1lpi).  Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...13gw1hmVYrBL8A

    Example \(\PageIndex{1}\)

    For another example of a cation-pi interaction, open up iCn3D with 1REX and view the interaction of lysine (K1) side chain with the nonpolar aromatic ring of phenylalanine (F3).

    Solution

    https://structure.ncbi.nlm.nih.gov/i...4d3wXXsSEYhgv7

     

    Here are some more examples.

    Exercise \(\PageIndex{1}\)

    Select the link below to answer the following questions.

    https://structure.ncbi.nlm.nih.gov/i...BN15qZbAL6SF39 

    1.  What type of noncovalent interaction best describes the red dotted line in the structure.

    2.  What type of noncovalent interaction best describes the red dotted line in the structure.

    Answer

    1.  cation-pi

    2.  pi stacking

    Halogen Bond

    Lastly we come to the halogen bond.  You might ask if there are halogens found in proteins.  The answer is no (until one is found!) but halogenated molecules (drugs, xenobiotics, toxins) bind proteins.  Consider the C-X bond where X is a halogen. The electronegativity of C is 2.56 while the halogens have these electronegativity values: F (3.98), Cl (3.16), Br (2.96), and I (2.66).  Compare these to oxygen (3.44) and N (3.04).  Covalent bond between two bonded atoms whose electronegativity differences are between 0.4 and 1.8 are considered polar covalent, so C-F, C-Cl and C-Br are considered polar covalent.  The C-I bond is the longest and iodine is the most polarizable of these halogens.  An alkyl halide with a C-I bond can undergo Sn2 nucleophilic substitution reactions with I- being an excellent leaving group.  Hence the C-I bond behaves somewhat as a polar covalent bond.

    Nevertheless, quantum calculations show that the electron density is not uniformly spread around the X halogen in a C-X bond, but rather is pulled more toward the C, leaving the distal end of the halogen depleted in electron density and slightly positive. This region of relatively depleted electron density is called the σ-hole. Color coded renderings of the electron density of the halogen involved in a C-X bond show the halogen atom to have band (like Jupiter) with the more negative electrostatic potential (represented in blue) closest to C and the more positive potential, the σ-hole (represented in red), at the end farthest from the C atom.  Calculations show that this effect is greatest for the heavier halogens (Br, I) which, because of their size, have longer C-X bonds.   The halogen's slightly positive σ-hole can act analogously to a H bond donor in its interactions with nearby  δ- :O and :N atoms/lone pairs.  This might take a while to fully grasp since you have always heard that in general the halogens are more electronegative than C and would hence would always be  δ- when bonded to it.   This case is similar to our chemical intuition about lone pair "rabbit ears" on oxygen, which quantum calculations show not to be an accurate representation of the electron density (see Fig xx).

    Figure \(\PageIndex{26}\) below show the electrostatic potential on a halogen X atom covalently attached to a carbon in two different molecules, CF3-I and :NC-Br.  The red distal end is the σ-hole relatively depleted in electron density and with a higher, more positive electrostatic potential.  (This is opposite the usual coloration that biochemist use in which oxygen (δ- or fully -) is colored red and nitrogen (in a protonated amine with a positive charge) is shown in blue.)

    halogenbondCNBRandCF3I_betacopy.svg

    Figure \(\PageIndex{26}\): Electrostatic potential on a halogen X atom on CF3-I and :NC-Br

    Figure \(\PageIndex{27}\) below shows a molecule with a carbonyl (a hydrogen bond acceptor with a δ- :O) interacting with another molecule through either a hydrogen bond or a halogen bond.  Again the red distal end of the halogen X is the σ-hole relatively depleted in electron density.  

     

    halogenbond.svg

    Figure \(\PageIndex{27}\):  Comparison of a hydrogen and halogen bond (noncovalent interaction)

    Medicinal chemist often use halogen substituents on drug molecules to alter binding specificity, membrane diffusion and t1/2 of the drug.  Increasing, they are using halogen bonds in rational drug design to increase drug affinity to target proteins.

    Figure \(\PageIndex{28}\) below shows an interactive iCn3D model below shows the interaction of a haloaminopyrimidine inhibitor bound to its binding site on the c-Jun N-Terminal Kinase (JNK) protein (2P33).

    haloaminopyrimidine inhibitor c-Jun N-Terminal Kinase (JNK) protein (2P33).png

    NIH_NCBI_iCn3D_Banner.svg Figure \(\PageIndex{28}\): Haloaminopyrimidine inhibitor bound to its binding site on the c-Jun N-Terminal Kinase (JNK) protein (2P33).  Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/icn3d/share.html?H4Wabj8my3VsYLSi6

    Note that the sulfur of methionine is forming a halogen bond with the Cl atom.  Although the electronegativity of sulfur is 2.58, close to that of cabon (2.55), nevertheless, sulfur is larger and more polarizable so it also develops a slightly positive σ-hole distal to the carbon atom.  Analysis of PDB files shows that S--O interactions are common in protein and most likely impacts protein stability. 

    Ultimately all ensembles of molecules/ions reach a low if not lowest energy state under a given set of condition.  Noncovalent attractions are maximized and repulsions minimized to achieve this state.  Consider for example solid sodium chloride held together by ionic bonds.  The ions are closest packed (face-centered cubic) and cannot get closer together (packing density of about 74%) as simple packing considerations and repulsive electrostatic forces and collective van der Waals interactions would prevent it.  Each Na+ is surrounded by 6 Cl- ions and vice versa. 

    When large molecules like proteins assume a low energy state, they maximize the attractive noncovalent interactions described in this section while minimizing repulsive ones within a molecule (in given solvent conditions).  Packing density reaches similar values as for closest packed spheres (NaCl for example).  Figure \(\PageIndex{29}\) below shows a slice through a protein and through the crystal lattice of NaCl.  The gray circles on the protein show the faces of the sliced atoms.  They are superimposed on the surface of the protein shown in colored spheres.  If you took a series of cross-sectional slices throughout the protein, you would get a better picture of packing density than a single slice alone. Collective van der Waals interactions are found among all atoms and ions in a protein, which accounts for the closest packing of most atoms, polar and nonpolar, with the packed protein structure. 

    crosssect42ptpackingdensity.svg

    Figure \(\PageIndex{29}\):  A slice through a protein and through the crystal lattice of NaCl

    Here is a link to an JSmol tutorial by David Marcy et al, An Introduction to Chemical Bonds and Protein Structure

    References

    IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.

    https://chem.libretexts.org/Bookshel...g_interactions

    https://boisestate.pressbooks.pub/ch...ecular-forces/

    A low-barrier hydrogen bond in the catalytic triad of serine proteases, PA Frey et al, Science 264, 1927-1930 (1994)
    DOI: 10.1126/science.7661899

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