Intermolecular force
Intermolecular forces are the attractive electrostatic interactions that occur between molecules, atoms, or ions, typically ranging in strength from 1 to 12 kJ/mol, which is significantly weaker than intramolecular covalent bonds (50–200 kJ/mol).[1] These forces are responsible for holding particles together in liquids and solids, thereby determining key physical properties such as melting and boiling points, viscosity, surface tension, and solubility.[1][2] Unlike intramolecular forces, which maintain the structure within a single molecule, intermolecular forces act between separate particles and are essential for understanding phase transitions and the behavior of substances in various states.[2] The primary types of intermolecular forces include London dispersion forces, dipole-dipole interactions, hydrogen bonding, and ion-dipole interactions.[1] London dispersion forces arise from temporary fluctuations in electron distribution, creating instantaneous dipoles that induce attractions in neighboring molecules; these are present in all molecules and increase with molecular size and polarizability.[1] Dipole-dipole interactions occur between molecules with permanent dipoles, where the positive end of one molecule attracts the negative end of another, becoming stronger with greater polarity.[1] Hydrogen bonding is a particularly strong form of dipole-dipole interaction involving a hydrogen atom bonded to highly electronegative atoms like nitrogen, oxygen, or fluorine, leading to elevated boiling points in compounds such as water.[1] Ion-dipole forces, relevant in solutions, involve attractions between ions and polar molecules, facilitating processes like the dissolution of salts in water.[1] These forces collectively influence a wide range of phenomena in chemistry and related fields, from the cohesion of liquids to the structure of biological macromolecules, underscoring their fundamental role in molecular recognition and material properties.[2][1]Overview
Definition and Scope
Intermolecular forces are the attractive or repulsive forces that operate between molecules as distinct wholes, in contrast to the stronger covalent or ionic bonds that form within individual molecules by linking atoms. These forces arise primarily from electrostatic interactions between charged or polar regions of molecules and are responsible for determining key physical properties such as boiling points, viscosities, and solubilities.[3] The scope of intermolecular forces extends across all phases of matter—gases, liquids, and solids—where they influence molecular arrangement and behavior, as well as in complex biological assemblies like protein folding, enzyme-substrate binding, and nucleic acid structures. For instance, cohesive forces between water molecules contribute to its high surface tension, enabling phenomena like capillary action, while adhesive forces allow geckos to scale vertical surfaces through van der Waals interactions between their setae and substrates. In biomolecules, these forces stabilize secondary and tertiary structures, facilitating essential cellular processes.[4][5][6] Modern comprehension of intermolecular forces traces back to Fritz London’s seminal 1930 paper, which provided the quantum mechanical foundation for understanding dispersion forces between nonpolar molecules, marking a pivotal advancement in the field. Typically, these forces operate at energy scales of 1–50 kJ/mol, orders of magnitude weaker than the 100–1000 kJ/mol required to break intramolecular bonds, underscoring their role in reversible associations rather than permanent linkages. Hydrogen bonding exemplifies a relatively strong intermolecular interaction within this range, while van der Waals forces represent weaker components.[3][7]Distinction from Intramolecular Forces
Intramolecular forces encompass the strong interactions that hold atoms together within a single molecule or ion, primarily including covalent bonds, ionic bonds within polyatomic ions, and metallic bonds in metals. These forces are responsible for defining the molecular geometry and ensuring the overall stability of the chemical entity. For instance, the arrangement of atoms in a molecule like methane (CH₄) is determined by the tetrahedral geometry arising from sp³ hybridization and valence shell electron pair repulsion (VSEPR) theory, which minimizes repulsion among bonding and lone electron pairs./03:_Compounds/3.09:_Intramolecular_forces_and_intermolecular_forces) In contrast, intermolecular forces operate between separate molecules or ions, facilitating the assembly of these units into liquids, solids, or gases, and are generally much weaker than their intramolecular counterparts. This distinction is crucial: intramolecular forces establish the identity and structural integrity of individual molecules, while intermolecular forces influence collective behavior, such as transitions between phases like melting or boiling. The energy required to disrupt intramolecular bonds far exceeds that needed to overcome intermolecular attractions; for example, breaking a C–H covalent bond in methane demands approximately 413 kJ/mol, whereas the molar enthalpy of vaporization of water, which involves overcoming intermolecular hydrogen bonds, is about 41 kJ/mol at its boiling point./03:_Compounds/3.09:_Intramolecular_forces_and_intermolecular_forces)[8][9] The implications of this divide are profound in chemistry. Intramolecular forces primarily dictate a molecule's reactivity, as chemical reactions typically involve the formation or cleavage of these bonds to create new substances. Conversely, intermolecular forces govern key physical properties, including solubility in solvents (via compatibility of attractions), boiling and melting points (reflecting the energy to separate molecules), and viscosity (measuring resistance to flow due to molecular interactions).[10]Types of Intermolecular Forces
Hydrogen Bonding
Hydrogen bonding is a type of intermolecular force characterized by the attraction between a hydrogen atom covalently bonded to a highly electronegative atom—typically nitrogen (N), oxygen (O), or fluorine (F)—and a lone pair of electrons on another electronegative atom, often also N, O, or F.[11] This interaction arises due to the significant electronegativity difference, which creates a partial positive charge (δ+) on the hydrogen and a partial negative charge (δ-) on the electronegative atom, enabling strong electrostatic attraction.[12] The geometry of hydrogen bonds is highly directional, favoring a linear arrangement denoted as X–H···Y, where X and Y are electronegative atoms and the bond angle ∠X–H···Y approaches 180°.[13] This linearity maximizes the overlap of orbitals and the electrostatic interaction, with the strength deriving from both electrostatic contributions and a partial covalent character due to charge transfer between the donor and acceptor.[14] The energy of hydrogen bonds typically ranges from 10 to 40 kJ/mol, considerably stronger than ordinary dipole-dipole interactions, and can be approximated using an electrostatic model based on partial charges: E_{HB} \approx \frac{q_H \cdot q_Y}{4\pi\epsilon_0 r^2} where q_H and q_Y are the partial charges on the hydrogen and acceptor atom, respectively, \epsilon_0 is the vacuum permittivity, and r is the distance between them.[12][15] Prominent examples of hydrogen bonding include the water dimer, where O–H···O interactions contribute to the liquid's cohesive properties; DNA base pairing, such as between adenine and thymine (two hydrogen bonds) or guanine and cytosine (three); and protein secondary structures like alpha helices and beta sheets, stabilized by backbone N–H···O=C bonds.[11][12] Hydrogen bonds can be intramolecular, occurring within a single molecule to stabilize conformations, or intermolecular, linking separate molecules into networks.[16] In extended networks, such as those in water or biological polymers, cooperativity enhances bond strength, where the formation of one hydrogen bond polarizes adjacent groups, facilitating stronger subsequent bonds.[17] This cooperative effect is crucial for the stability of supramolecular assemblies.Ionic and Charge-Based Interactions
Ionic and charge-based interactions encompass electrostatic attractions between ions or charged species and molecules possessing partial or induced charges, playing a crucial role in stabilizing structures in biological and material systems. These forces arise from the Coulombic attraction between opposite charges, modulated by distance and environmental factors, and are distinct from covalent bonding due to their non-directional nature and relative weakness in solvated environments.[18] Salt bridges represent a key example of ionic interactions, involving electrostatic attractions between oppositely charged amino acid residues, such as aspartate (Asp) and arginine (Arg), where the carboxylate group of Asp interacts with the guanidinium group of Arg. In proteins, these bridges form when at least two heavy atoms from the oppositely charged groups are within hydrogen-bonding distance, providing structural stability despite their modest energetic contribution in aqueous media, typically around 12 kJ/mol for surface-exposed bridges.[19][20] Ion-dipole interactions occur between a fully charged ion and a polar molecule with a permanent dipole moment, such as the attraction between a sodium ion (Na⁺) and water, where the negative oxygen end of the water dipole aligns toward the cation. The force governing this interaction is given by F = \frac{q \mu \cos \theta}{4 \pi \epsilon_0 r^2} where q is the ion charge, \mu is the dipole moment, \theta is the angle between the dipole axis and the line connecting the ion to the dipole center, \epsilon_0 is the permittivity of free space, and r is the distance between the ion and the dipole center. This force decreases with the square of the distance, making it significant at short ranges, as seen in the solvation of ions by polar solvents.[21] Ion-induced dipole interactions arise when a charged ion polarizes a nearby nonpolar or weakly polar molecule, creating a temporary dipole that leads to attraction, exemplified in the hydration shells around ions where the ion's electric field induces dipoles in surrounding water molecules, enhancing solvation stability. These interactions contribute to the hierarchical ordering of water dipoles in the ion's first hydration shell, influencing ion mobility and specificity in aqueous environments.[22][23] In biological contexts, such as protein folding, salt bridges and ion-dipole forces stabilize secondary and tertiary structures by counterbalancing hydrophobic effects and guiding residue positioning. In solid-state applications, these interactions dominate crystal lattices like sodium chloride (NaCl), where Coulombic forces between Na⁺ and Cl⁻ ions hold the ionic array together, though weaker than in vacuum due to lattice vibrations. Solvent effects significantly screen these Coulomb interactions through the Debye length, a characteristic distance over which the electric potential decays exponentially in electrolyte solutions, typically on the order of nanometers in physiological conditions, reducing interaction strength via mobile ion redistribution.[24][25] Unlike covalent ionic bonds, which involve complete electron transfer and form strong, directional intramolecular links with energies exceeding 300 kJ/mol, ionic intermolecular forces are weaker, non-directional attractions between pre-existing ions or charged groups, readily disrupted in solution and contributing only modestly to overall stability. These forces are generally stronger than hydrogen bonds in non-aqueous environments but comparable or weaker in polar solvents.[18]Dipole-Dipole Interactions
Dipole-dipole interactions arise from the electrostatic attraction between the partial positive charge on one polar molecule and the partial negative charge on another, specifically in neutral molecules possessing permanent dipole moments. These forces are inherently orientation-dependent, favoring alignments where opposite poles are closest, but in fluids, thermal motion causes rapid reorientations, necessitating a statistical average known as the Keesom interaction to describe the net effect. The average potential energy of the Keesom interaction between two identical dipoles separated by a distance r is expressed as E_\text{Keesom} = -\frac{\mu^4}{3 (4\pi \epsilon_0)^2 k_B T r^6}, where \mu is the magnitude of each dipole moment, \epsilon_0 is the vacuum permittivity, k_B is the Boltzmann constant, and T is the absolute temperature. This formulation accounts for the thermal averaging over all possible orientations, resulting in a net attractive force that scales inversely with the sixth power of the separation distance, similar to other van der Waals components.[26] In practical examples, dipole-dipole interactions are evident in the liquid phase of hydrogen chloride (HCl), where the polar HCl molecules align to stabilize the condensed state through these attractions. Likewise, in liquid acetone, the permanent dipoles of the carbonyl groups facilitate orientational ordering, enhancing cohesion among the molecules. These interactions are distinct from those involving ions inducing temporary dipoles in neutral molecules, which fall under Debye forces rather than permanent dipole alignments.[11] The strength of dipole-dipole interactions exhibits a pronounced temperature dependence, becoming more significant at lower temperatures where thermal agitation is reduced, allowing better dipole alignment and thus deeper energy minima. Conversely, at higher temperatures, the $1/T term in the Keesom energy expression diminishes the interaction's magnitude, as random orientations dominate. This temperature sensitivity contributes to phenomena such as elevated boiling points for polar substances relative to non-polar analogs of comparable molecular weight.[26]Van der Waals Forces
Keesom Forces
Keesom forces, also known as orientation forces, describe the electrostatic interactions between two molecules possessing permanent electric dipole moments, arising from the mutual alignment of these dipoles under thermal motion.[27] These interactions form one component of the van der Waals forces and are particularly relevant in polar substances where dipole moments are fixed and significant. The theory was first developed by W. H. Keesom in 1921, providing the foundational mathematical framework for averaging dipole orientations in gases.[28] The interaction energy between two fixed dipoles separated by distance r depends on their relative orientations, characterized by angles \theta_1, \theta_2, and \phi, where \theta_1 and \theta_2 are the angles between each dipole and the intermolecular axis, and \phi is the azimuthal angle between their planes. The potential energy U(\theta_1, \theta_2, \phi) is given by U(\theta_1, \theta_2, \phi) = \frac{\mu_1 \mu_2}{4\pi \epsilon_0 r^3} \left( \cos\theta_1 \cos\theta_2 - 2 \sin\theta_1 \sin\theta_2 \cos\phi \right), where \mu_1 and \mu_2 are the dipole moments, and \epsilon_0 is the vacuum permittivity.[27] This expression derives from the classical electrostatic interaction of point dipoles, assuming no higher multipoles, and can be positive (repulsive) or negative (attractive) depending on the configuration; for instance, head-to-tail alignment yields attraction. To account for molecular rotation in fluids, Keesom introduced thermal averaging over all possible orientations, weighted by the Boltzmann factor \exp(-U / kT), where k is the Boltzmann constant and T is temperature. The average interaction energy \langle U \rangle is thus \langle U \rangle = \frac{\int U \exp(-U / kT) \, d\Omega_1 d\Omega_2}{\int \exp(-U / kT) \, d\Omega_1 d\Omega_2}, with integrals over the solid angles d\Omega = \sin\theta \, d\theta \, d\phi. In the high-temperature limit where kT \gg |U| (valid for dilute gases), higher-order terms vanish, and the average simplifies via perturbation theory to \langle U \rangle \approx -\frac{\langle U^2 \rangle}{3kT}, where the angular average \langle U^2 \rangle evaluates to \frac{2 \mu_1^2 \mu_2^2}{(4\pi \epsilon_0)^2 r^6}. This yields the orientation-averaged Keesom energy U_\text{Keesom} = -\frac{2\mu_1^2 \mu_2^2}{(4\pi \epsilon_0)^2 3 kT r^6}. The factor of $1/r^6 emerges from the $1/r^3 dependence of U combined with the averaging.[27] This form highlights the inverse temperature dependence, as thermal agitation disrupts favorable alignments at higher T.[29] In applications, Keesom forces contribute significantly to the non-ideal behavior of polar gases, such as sulfur dioxide (SO₂), which has a dipole moment of approximately 1.62 D. For SO₂, these interactions influence the second virial coefficient B(T) in the virial expansion of the equation of state, PV = RT (1 + B(T)/V + \cdots), where the Keesom term provides a temperature-dependent attractive correction proportional to -\mu^4 / (kT)^2. Experimental measurements of B(T) for SO₂ confirm this contribution, aiding in the determination of intermolecular potentials.[30] The Keesom model assumes rigid, non-deformable dipoles and neglects inductive effects where one dipole polarizes the other, limiting its accuracy in highly polarizable systems or at short distances.[27]Debye Forces
Debye forces, also known as induction or dipole-induced dipole interactions, occur when a molecule possessing a permanent electric dipole moment exerts an electric field that distorts the electron distribution in a neighboring nonpolar molecule, thereby inducing a temporary dipole moment in the latter. This induced dipole then experiences an attractive force from the original permanent dipole, resulting in a net attractive interaction between the two molecules. The mechanism is purely electrostatic, with the strength depending on the magnitude of the permanent dipole and the ease with which the nonpolar molecule can be polarized.[31] The potential energy of the Debye interaction is described by the formula E_\text{Debye} = -\frac{\alpha \mu^2}{2 (4\pi \epsilon_0)^2 r^6}, where \alpha is the static electric polarizability of the inducible molecule, \mu is the magnitude of the permanent dipole moment, \epsilon_0 is the permittivity of free space, and r is the intermolecular separation distance. This r^{-6} dependence arises from the r^{-3} fall-off of the electric field from the dipole combined with the r^{-3} scaling of the induced dipole energy. The factor of $1/2 accounts for the self-energy of the induced dipole in the field. This expression was derived in the context of early theories of molecular polarization by Peter J. W. Debye in his seminal work on polar media.[32] A representative example is the interaction between hydrogen chloride (HCl), which has a permanent dipole moment of approximately 1.08 D, and argon (Ar), a nonpolar atom with high polarizability (\alpha \approx 1.64 \times 10^{-24} cm³). The dipole of HCl induces a transient dipole in Ar, leading to an attractive force that contributes to the binding in the HCl–Ar van der Waals complex, with a well depth of approximately 2.2 kJ/mol (185 cm^{-1}).[33] Debye forces also play a key role in the dielectric properties of mixtures, such as polar gases with nonpolar components, where the induction term enhances the overall polarizability beyond that of permanent dipoles alone, as incorporated in Debye's theory of dielectrics. Unlike orientation-dependent interactions, Debye forces are independent of temperature because the induction process does not require thermal averaging of molecular orientations; the permanent dipole's field acts directly regardless of rotational motion. These forces are additive to other van der Waals components, such as Keesom and London dispersion forces, forming part of the total attraction in systems with both polar and nonpolar species; for instance, the ion-induced dipole interaction is a close analog but involves a full charge rather than a dipole.[34]London Dispersion Forces
London dispersion forces, also known as dispersion forces or induced dipole-induced dipole interactions, originate from quantum mechanical correlations in the electron densities of atoms and molecules. These correlations cause temporary fluctuations in electron distribution, creating instantaneous dipoles that induce complementary dipoles in neighboring particles, resulting in an attractive force. This phenomenon is universal, occurring between all atoms and molecules regardless of polarity, and was first theoretically derived by Fritz London in 1930 using second-order perturbation theory to explain attractions between noble gas atoms. The effect stems from the dynamic correlation of electron motions, where the non-static nature of electron clouds leads to correlated polarization without requiring permanent dipoles. Theoretically, the interaction energy for London dispersion between two identical atoms or molecules is approximated by the London formula: E_{\text{London}} = -\frac{3}{4} \frac{\alpha^2 I}{(4\pi \epsilon_0)^2 r^6 (I + E_{\text{ion}})} where \alpha is the polarizability, I is the ionization energy, E_{\text{ion}} is an average excitation energy (often approximated as I), \epsilon_0 is the vacuum permittivity, and r is the intermolecular distance. This simplifies to E = -C_6 / r^6, with the dispersion coefficient C_6 = \frac{3}{4} \frac{\alpha^2 I}{ (4\pi \epsilon_0)^2 (I + E_{\text{ion}})}, highlighting the inverse sixth-power dependence that makes the force short-ranged. The derivation relies on quantum mechanical treatment of dipole fluctuations, confirming the force's attractive nature and its dominance at longer ranges compared to repulsive Pauli forces. In nonpolar molecules, London dispersion forces are the primary intermolecular interaction. For example, in noble gases like helium (He-He), these forces are the sole attractive mechanism, explaining their low but measurable boiling points despite lacking permanent dipoles. Similarly, in hydrocarbons such as methane (CH₄), dispersion forces govern molecular cohesion, as evidenced by the increasing boiling points across the alkane series due to enhanced electron cloud interactions. These forces dominate in apolar systems, contributing significantly to properties like solubility and phase behavior in nonpolar solvents.[35] The strength of London dispersion forces increases with molecular size and the number of electrons, as larger polarizability \alpha enhances the magnitude of induced dipoles; for instance, dispersion interactions grow stronger from methane to larger alkanes due to expanded electron clouds farther from the nucleus. This scaling is quantified at macroscopic levels through Hamaker constants, which integrate pairwise dispersion interactions over bulk volumes and depend on material density and dielectric properties, enabling predictions of colloidal stability and adhesion in ceramics and nanomaterials.[35]Relative Strengths and Influences
Hierarchy of Force Strengths
Intermolecular forces exhibit a clear hierarchy based on their typical interaction energies, which dictate their relative influence on molecular associations. Ionic interactions, including salt bridges between charged groups, represent the strongest category, with energies ranging from 50 to 800 kJ/mol in vacuum, reflecting the Coulombic attraction between oppositely charged ions (or partial charges in salt bridges) at typical separation distances of 2–5 Å.[36][37] Hydrogen bonding follows as the next strongest, typically 10–40 kJ/mol, arising from electrostatic attraction between a hydrogen atom bonded to an electronegative atom (like N, O, or F) and another electronegative atom. Dipole–dipole interactions, involving permanent dipoles on polar molecules, have energies of 5–25 kJ/mol. Weakest overall are van der Waals forces, spanning 0.05–70 kJ/mol, with London dispersion forces—a subset driven by transient dipoles—contributing around 1–10 kJ/mol in nonpolar systems.[38] The following table summarizes these approximate strengths, including representative examples where the dominant force governs cohesion in a crystal lattice:| Force Type | Approximate Energy (kJ/mol) | Example |
|---|---|---|
| Ionic/Salt Bridges | 50–800 (vacuum) | NaCl ionic lattice: ~787 |
| Hydrogen Bonding | 10–40 | Water molecules in ice |
| Dipole–Dipole | 5–25 | Acetone molecules |
| Van der Waals (Dispersion) | 0.05–70 (~1–10 typical) | I₂ molecular crystal: ~62 (cohesion from sublimation) |