Molecular geometry and dipole moments: polarity and intermolecular forces

Intuition Beginner

A dipole moment measures how unequally electrons are shared in a molecule. When two atoms with different electronegativities form a bond, the bonding electrons shift toward the more electronegative atom. This creates partial charges: a $\delta +$ on the less electronegative atom and a $\delta -$ on the more electronegative one. This charge separation is a bond dipole.

A bond dipole is a vector. It has magnitude (how strong the charge separation is) and direction (which way the electrons are pulled). The dipole points from $\delta +$ to $\delta -$, conventionally drawn as an arrow with a plus sign at the tail.

A molecular dipole moment is the vector sum of all bond dipoles in the molecule. Whether a molecule is polar depends on both the polarity of its individual bonds and its 3D geometry. Two identical bond dipoles pointing in opposite directions cancel, giving zero net dipole. Two bond dipoles at an angle add to give a nonzero resultant.

${\text{CO}}_2$ is linear with two equal C=O dipoles pointing in opposite directions. They cancel, so ${\text{CO}}_2$ is nonpolar. ${\text{H}}_2\text{O}$ is bent, so its two O-H dipoles do not cancel. Water is polar, with a dipole moment of 1.85 D (debye units). This is why water dissolves ionic compounds but ${\text{CO}}_2$ does not.

Molecular polarity controls intermolecular forces -- the attractions between molecules. Polar molecules attract each other through dipole-dipole interactions. Nonpolar molecules interact only through weaker London dispersion forces. When a hydrogen atom is bonded to N, O, or F, the resulting hydrogen bond is an especially strong dipole-dipole interaction that dramatically raises boiling points.

Visual Beginner

Symmetry and molecular polarity:

Molecule	Geometry	Bond dipoles	Molecular dipole	Polar?
${\text{CO}}_2$	Linear	C$\to$O each side	0 D (cancel)	No
${\text{H}}_2\text{O}$	Bent ($104.5^{\circ }$)	H$\to$O each side	1.85 D	Yes
${\text{BF}}_3$	Trigonal planar	B$\to$F each side	0 D (cancel)	No
${\text{NH}}_3$	Trigonal pyramidal	H$\to$N each side	1.47 D	Yes
${\text{CCl}}_4$	Tetrahedral	C$\to$Cl each side	0 D (cancel)	No
${\text{CHCl}}_3$	Tetrahedral (distorted)	3 C$\to$Cl + 1 C$\to$H	1.01 D	Yes
${\text{SF}}_6$	Octahedral	S$\to$F each side	0 D (cancel)	No

Intermolecular force hierarchy (increasing strength):

Force type	Present in	Relative strength	Example
London dispersion	All molecules	Weakest	${\text{CH}}_4$ (bp $-162^{\circ }$C)
Dipole-dipole	Polar molecules	Moderate	${\text{CH}}_3\text{Cl}$ (bp $-24^{\circ }$C)
Hydrogen bonding	N-H, O-H, F-H bonds	Strongest	${\text{H}}_2\text{O}$ (bp $100^{\circ }$C)

Worked example Beginner

Determine whether ${\text{NH}}_3$ (ammonia) is polar.

Step 1. Identify the geometry. Nitrogen has 5 valence electrons. Three form N-H bonds, leaving one lone pair. Steric number = 4, so the electron-domain geometry is tetrahedral. The molecular geometry is trigonal pyramidal (one lone pair).

Step 2. Evaluate bond dipoles. Each N-H bond has a dipole pointing from H ($\delta +$) toward N ($\delta -$), because nitrogen (3.04) is more electronegative than hydrogen (2.20).

Step 3. Add the bond-dipole vectors. Three N-H bond dipoles point upward toward the nitrogen. The lone pair also contributes a dipole in the same direction. Because the molecule is not planar (the nitrogen sits above the plane of the three hydrogens), the horizontal components of the three bond dipoles cancel by symmetry, but the vertical components add.

Step 4. Conclusion. ${\text{NH}}_3$ has a net dipole moment of 1.47 D directed along the $C_3$ axis from the H-plane toward the nitrogen. Ammonia is polar.

Compare with ${\text{BF}}_3$: trigonal planar, three identical B-F bond dipoles at $120^{\circ }$. The horizontal components cancel completely. ${\text{BF}}_3$ is nonpolar despite having polar bonds. The geometry makes the difference.

Check your understanding Beginner

Formal definition Intermediate+

Bond polarity and electronegativity

A bond dipole moment ${\vec{\mu }}_{\text{bond}}$ arises when two bonded atoms differ in electronegativity. The magnitude is

$${\mu }_{\text{bond}}=q\cdot d,$$

where $q$ is the effective charge separation (in units of $e$) and $d$ is the bond length. The SI unit is coulomb-metres (C$\cdot$m), but the practical unit is the debye (D), defined as $1\text{D}=3.336\times 10^{-30}\text{C}\cdot \text{m}$. A single elementary charge separated by 1 Angstrom gives $4.80\text{D}$.

Bond polarity correlates with the electronegativity difference $\Delta \chi$ between the bonded atoms:

$\Delta \chi$	Bond character	Dipole magnitude
0.0 - 0.4	Nonpolar covalent	$\approx 0$
0.4 - 1.7	Polar covalent	Moderate
> 1.7	Mostly ionic	Large

These boundaries are approximate. The Pauling electronegativity scale assigns $\chi =2.20$ for H and $\chi =3.98$ for F, giving $\Delta \chi =1.78$ for H-F -- a highly polar bond with $\mu =1.82\text{D}$.

Molecular dipole moments: vector addition

The molecular dipole moment is the vector sum of all bond dipoles and lone-pair contributions:

$${\vec{\mu }}_{\text{total}}=\sum _i{\vec{\mu }}_i.$$

For a molecule with two identical bond dipoles of magnitude ${\mu }_{\text{bond}}$ at angle $\theta$ to each other, the resultant is

$${\mu }_{\text{total}}=2{\mu }_{\text{bond}}\cos \left(\frac{\theta }{2}\right).$$

For ${\text{H}}_2\text{O}$: ${\mu }_{\text{bond}}(\text{O-H})\approx 1.51\text{D}$, $\theta =104.5^{\circ }$, giving ${\mu }_{\text{total}}=2(1.51)\cos (52.25^{\circ })=2(1.51)(0.612)=1.85\text{D}$, matching the experimental value.

For ${\text{CO}}_2$: ${\mu }_{\text{bond}}(\text{C=O})\approx 2.40\text{D}$, $\theta =180^{\circ }$, giving ${\mu }_{\text{total}}=2(2.40)\cos (90^{\circ })=0$. The bond dipoles cancel.

Symmetry and polarity: point-group criteria

A molecule is nonpolar if and only if its point group contains either:

1. A centre of inversion ($i$), or
2. A rotation axis $C_n$ with perpendicular mirror planes ${\sigma }_h$ (i.e., the point group is one of $D_{nh}$ or $D_{nd}$ for $n\ge 2$).

More practically: if a molecule has symmetry such that all bond dipoles cancel by vector addition, it is nonpolar. The common cases:

• Linear, symmetric ($D_{\infty h}$): ${\text{CO}}_2$, ${\text{BeCl}}_2$, ${\text{XeF}}_2$ -- nonpolar.
• Trigonal planar ($D_{3h}$): ${\text{BF}}_3$, ${\text{SO}}_3$ -- nonpolar.
• Tetrahedral ($T_d$): ${\text{CCl}}_4$, ${\text{CH}}_4$, ${\text{SF}}_4$ is seesaw ($C_{2v}$) -- polar.
• Octahedral ($O_h$): ${\text{SF}}_6$, ${\text{PF}}_6^{-}$ -- nonpolar.

Any molecule belonging to $C_n$ or $C_{nv}$ (lacking a horizontal mirror plane or inversion centre) is polar, provided it has polar bonds.

Intermolecular forces

London dispersion forces exist between all molecules. They arise from instantaneous dipole-induced dipole interactions. The magnitude depends on molecular polarizability (larger, more electron-rich molecules are more polarizable) and shape (more surface contact increases dispersion). The interaction energy between two polarizable molecules scales as

$$V_{\text{disp}}\propto -\frac{{\alpha }_1{\alpha }_2}{r^6},$$

where ${\alpha }_1,{\alpha }_2$ are the polarizabilities and $r$ is the intermolecular distance.

Dipole-dipole interactions occur between permanent molecular dipoles. The interaction energy between two aligned permanent dipoles scales as

$$V_{\text{dip-dip}}\propto -\frac{{\mu }_1^2{\mu }_2^2}{r^6{k}_{B}T}.$$

The temperature dependence arises because thermal motion disrupts dipole alignment.

Hydrogen bonding is a special case of dipole-dipole interaction requiring:

1. A hydrogen atom bonded to N, O, or F (the donor).
2. A lone pair on N, O, or F of another molecule (the acceptor).

Hydrogen bond energies range from 5-40 kJ/mol (conventional hydrogen bonds) up to $\sim$160 kJ/mol for the strongest short, symmetric hydrogen bonds in ions like ${\text{HF}}_2^{-}$.

The ion-dipole interaction is the strongest of the electrostatic intermolecular forces and is critical for solvation. The energy scales as $V\propto -\mu q/r^2$, where $q$ is the ionic charge and $\mu$ the solvent dipole moment. This is why polar solvents dissolve ionic compounds.

Counterexamples to common slips

• "Symmetric molecules are always nonpolar." Only geometric symmetry with identical substituents guarantees cancellation. ${\text{CHCl}}_3$ is tetrahedral but polar because the three Cl atoms and one H atom are chemically different, breaking the $T_d$ symmetry.

• "Lone pairs do not contribute to the dipole moment." Lone pairs carry electron density and contribute to the molecular dipole. In ${\text{NH}}_3$, the lone pair on nitrogen enhances the dipole moment along the $C_3$ axis. In ${\text{NF}}_3$, the lone pair dipole partially opposes the N-F bond dipoles, giving a surprisingly small molecular dipole of 0.24 D.

• "Larger molecules always have larger dipole moments." Dipole moment depends on the vector arrangement of bond dipoles, not on molecular size. ${\text{CCl}}_4$ (MW 154) has zero dipole; $\text{HCl}$ (MW 36.5) has a dipole of 1.08 D.

• "Hydrogen bonds only form between different molecules." Intramolecular hydrogen bonds occur within a single molecule when the donor and acceptor are in the right geometric arrangement. The enol form of acetylacetone is stabilised by an intramolecular O-H$\cdots$O hydrogen bond.

Key theorem with proof Intermediate+

Theorem (Dipole cancellation by symmetry). A molecule belonging to any point group that contains either an inversion centre $i$ or a $C_n$ axis with ${\sigma }_h$ mirror planes ($D_{nh}$, $D_{nd}$, $D_{\infty h}$) has zero permanent electric dipole moment. Conversely, molecules belonging to $C_n$ or $C_{nv}$ point groups ($n\ge 1$) generally possess a nonzero dipole moment along the $C_n$ axis, provided the individual bonds are polar.

Argument. An electric dipole moment $\vec{\mu }$ transforms as a vector under the symmetry operations of the molecular point group. For $\vec{\mu }$ to be nonzero, it must transform as the totally symmetric irreducible representation of the point group.

If the point group contains an inversion centre $i$, then the dipole vector transforms as $\vec{\mu }\to -\vec{\mu }$ under inversion (dipole is an odd-parity, or $u$, quantity). For $\vec{\mu }$ to be invariant, it must be zero. All centrosymmetric molecules (${\text{CO}}_2$, ${\text{SF}}_6$, ${\text{XeF}}_4$, benzene) are therefore nonpolar.

If the point group contains a $C_n$ axis with a perpendicular ${\sigma }_h$ mirror plane (i.e., $D_{nh}$ or $D_{nd}$), then the component of $\vec{\mu }$ parallel to $C_n$ is reversed by ${\sigma }_h$ and must vanish. The components perpendicular to $C_n$ vanish by the $C_n$ rotational symmetry (they must be invariant under $C_n$ rotation, which is impossible for a vector perpendicular to the axis unless it is zero, since a rotation by $2\pi /n$ maps it to a different direction). All components are zero, so $\vec{\mu }=0$.

For $C_{nv}$ groups: the $C_n$ axis does not reverse the parallel component of $\vec{\mu }$. The ${\sigma }_v$ mirror planes leave the component along $C_n$ unchanged. The perpendicular components vanish by $C_n$ symmetry. Therefore $\vec{\mu }$ is nonzero along $C_n$. Molecules like ${\text{H}}_2\text{O}$ ($C_{2v}$), ${\text{NH}}_3$ ($C_{3v}$), and ${\text{BrF}}_5$ ($C_{4v}$) are polar. $\square$

Bridge. This symmetry argument connects to 14.05.01 molecular orbital theory, where the same point-group symmetry determines whether a molecule can have a nonzero transition dipole moment and hence whether an electronic transition is allowed. The dipole moment is a ground-state property; the transition dipole is a transition property; but both are governed by the same group-theoretic selection rules. The classification also connects to 14.12.01 spectroscopy, where IR activity requires a change in dipole moment during a vibration, and Raman activity requires a change in polarizability.

Exercises Intermediate+

Multipole expansion and beyond-dipole interactions Master

The dipole moment is the first nonvanishing term in the multipole expansion of a charge distribution. For a general charge distribution $\rho (\mathbf{r})$, the electrostatic potential at a distant point $\mathbf{R}$ is

$$\Phi (\mathbf{R})=\frac{1}{4\pi {ϵ}_0}\left[\frac{Q}{R}+\frac{\vec{\mu }\cdot \hat{R}}{R^2}+\frac{1}{2}\sum _{\alpha ,\beta }\frac{Q_{\alpha \beta }{\hat{R}}_{\alpha }{\hat{R}}_{\beta }}{R^3}+\cdots \right],$$

where $Q$ is the total charge (zero for neutral molecules), $\vec{\mu }$ is the dipole moment, and $Q_{\alpha \beta }$ is the quadrupole moment tensor. The expansion converges for $R$ much larger than the molecular dimensions.

Quadrupole moments. Molecules with zero dipole moment may still have substantial quadrupole moments that affect physical behaviour. The quadrupole moment tensor is

$$Q_{\alpha \beta }=\int \rho (\mathbf{r})(3r_{\alpha }{r}_{\beta }-r^2{\delta }_{\alpha \beta })d\mathbf{r}.$$

${\text{CO}}_2$ has zero dipole but a large negative quadrupole moment ($Q_{zz}\approx -4.3\times 10^{-40}\text{C}\cdot {\text{m}}^2$). This arises from the charge distribution $(-\delta )(+2\delta )(-\delta )$ along the molecular axis. The quadrupole drives ${\text{CO}}_2$'s solubility in water (quadrupole-dipole interaction with water's permanent dipole) and the quadrupole-quadrupole interactions between ${\text{CO}}_2$ molecules in the solid and liquid phases.

Benzene has zero dipole but a large positive quadrupole moment from the $\pi$-electron cloud distributed above and below the ring plane. The ring carbons are partially positive; the $\pi$ cloud is negative. This quadrupole drives the characteristic face-to-face and parallel-displaced stacking geometries of aromatic rings and the cation-$\pi$ interactions important in protein-ligand binding.

Polarizability and induced dipoles. When a molecule is placed in an external electric field $\mathbf{E}$, its electron cloud distorts, creating an induced dipole:

$${\vec{\mu }}_{\text{ind}}=\alpha \mathbf{E},$$

where $\alpha$ is the (scalar, for isotropic molecules) polarizability. For anisotropic molecules, $\alpha$ is a tensor. The polarizability determines the London dispersion interaction energy between two molecules:

$$V_{\text{disp}}=-\frac{3}{2}\frac{{\alpha }_1{\alpha }_2}{r^6}\frac{I_1{I}_2}{I_1+I_2},$$

where $I_1,I_2$ are the ionisation energies. This is the London formula, showing that larger, more polarizable molecules have stronger dispersion forces.

The Lennard-Jones potential. The combined repulsion (Pauli exclusion at short range) and dispersion attraction gives the Lennard-Jones 12-6 potential:

$$V(r)=4ϵ\left[{\left(\frac{\sigma }{r}\right)}^{12}-{\left(\frac{\sigma }{r}\right)}^6\right],$$

where $ϵ$ is the well depth and $\sigma$ is the distance at which $V=0$. The $r^{-6}$ attractive term encompasses both dispersion and dipole-dipole (orientation-averaged) contributions. The $r^{-12}$ repulsive term is empirical. This potential is the workhorse of molecular dynamics simulations and captures the essential physics of intermolecular interactions for simple fluids.

Dipole moment measurement: experimental methods Master

Debye's method (solution measurement). The dipole moment of a molecule dissolved in a nonpolar solvent is determined from the Debye equation, which relates the molar polarisation $P_m$ to the dielectric constant ${ϵ}_r$ of the solution:

$$P_m=\frac{{ϵ}_r-1}{{ϵ}_r+2}\frac{M}{\rho }=\frac{N_A}{3{ϵ}_0}\left(\alpha +\frac{{\mu }^2}{3k_{B}T}\right),$$

where $M$ is the molar mass, $\rho$ is the density, $N_A$ is Avogadro's number, and $\alpha$ is the polarizability. By measuring $P_m$ at several temperatures and plotting $P_m$ vs $1/T$, the slope gives ${\mu }^2$ and the intercept gives $\alpha$. This is the classic method, developed by Debye in the 1910s and refined by Sutton and others ^{[Sutton 1958]}.

Microwave spectroscopy. The rotational spectrum of a polar molecule provides a direct measurement of the dipole moment. The Stark effect (splitting of rotational lines in an applied electric field) depends on ${\mu }^2$. The magnitude of the splitting gives the dipole moment to high precision ($\pm 0.01\text{D}$). This method works for gas-phase molecules and gives the dipole moment along each principal axis of the inertia tensor separately.

Molecular beam electric resonance. Developed by Ramsey and colleagues in the 1950s, this technique measures the dipole moment of isolated molecules in a molecular beam, free from solvent effects. It achieves the highest precision ($\pm 0.001\text{D}$) and can resolve the dipole moment in different vibrational states.

Computational prediction. Modern quantum-chemical methods (DFT, coupled-cluster) compute dipole moments from the electron density: $\vec{\mu }=\int \rho (\mathbf{r})\mathbf{r}d\mathbf{r}$. The accuracy depends on the basis set and electron correlation treatment. At the CCSD(T)/aug-cc-pVTZ level, computed dipole moments agree with experiment to within 0.05 D for small molecules.

Boiling point trends: a quantitative analysis Master

The boiling point of a liquid is the temperature at which the vapour pressure equals the external pressure. The enthalpy of vaporisation, $\Delta H_{\text{vap}}$, reflects the total intermolecular energy that must be overcome. For non-hydrogen-bonded liquids, $\Delta H_{\text{vap}}$ is dominated by dispersion and dipole-dipole contributions.

Group contributions and polarity. Within a homologous series, boiling points increase with molecular weight due to increasing dispersion forces. The polarity effect appears as a constant offset: for molecules of similar molecular weight, the more polar one has the higher boiling point. This offset is typically 30-80${}^{\circ }$C for molecules with $\mu \approx 1-2\text{D}$ compared to nonpolar analogues.

The boiling points of the first-row hydrides illustrate the hydrogen-bonding anomaly:

Compound	MW	$\mu$ (D)	bp (${}^{\circ }$C)
${\text{CH}}_4$	16	0	$-162$
${\text{NH}}_3$	17	1.47	$-33$
${\text{H}}_2\text{O}$	18	1.85	$+100$
HF	20	1.82	$+20$

${\text{H}}_2\text{O}$ has the highest boiling point despite being the lightest among the heavier three, because each water molecule can donate two hydrogen bonds (two O-H groups) and accept two (two lone pairs), forming an extensive 3D hydrogen-bond network. HF can donate one and accept three but forms linear chains rather than a 3D network. ${\text{NH}}_3$ can donate one and accept one, giving a less extensive network.

Trouton's rule and its exceptions. For many nonpolar liquids, $\Delta S_{\text{vap}}=\Delta H_{\text{vap}}/T_{\text{bp}}\approx 88\text{J/(mol}\cdot \text{K)}$ (Trouton's rule). Hydrogen-bonded liquids deviate significantly: water has $\Delta S_{\text{vap}}=109\text{J/(mol}\cdot \text{K)}$ at its normal boiling point, reflecting the large enthalpy cost of breaking the hydrogen-bond network. The deviation from Trouton's rule is a diagnostic for hydrogen bonding.

Connections Master

• Lewis structures and VSEPR 14.02.01. The molecular geometry determined by VSEPR is the primary input for predicting polarity. Symmetric geometries ($D_{nh}$, $T_d$, $O_h$) cancel bond dipoles; asymmetric geometries ($C_{nv}$) generally produce nonzero molecular dipoles. The steric number and lone-pair count determine the geometry, which determines the polarity.

• Hybridization 14.02.02. The hybridization at each atom determines the bond angles, which in turn determine the vector sum of bond dipoles. $s{p}^3$ centres with different substituents produce asymmetric charge distributions; $s{p}^2$ centres in double bonds constrain the substituents to a plane, enabling cis/trans polarity differences (as in cis- vs trans-dichloroethene).

• Atomic structure and electronegativity 14.01.02. Electronegativity differences between bonded atoms determine bond polarity. The periodic trends in electronegativity (increasing across a period, decreasing down a group) predict which bonds are polar and the direction of the bond dipole. These are the building blocks from which molecular dipoles are constructed.

• Solutions and phase equilibria 14.09.01. Molecular polarity determines solubility ("like dissolves like"), miscibility, and phase behaviour. The intermolecular forces discussed here (dispersion, dipole-dipole, hydrogen bonding) are the microscopic origin of macroscopic properties like vapour pressure, boiling point, and surface tension.

• Acid-base chemistry 14.10.01. Solvent polarity affects acid-base equilibria. Water's high dielectric constant (${ϵ}_r=80.1$ at $20^{\circ }$C) and hydrogen-bonding ability stabilise ions, making it an excellent solvent for ionic reactions. The leveling effect in water (no acid stronger than ${\text{H}}_3{\text{O}}^{+}$ can exist in aqueous solution) is a direct consequence of water's polarity.

• Molecular orbital theory 14.05.01. MO theory provides the quantitative framework for computing dipole moments from the electron density distribution. The vector-addition model of bond dipoles is an approximation; the MO approach computes $\vec{\mu }=\int \rho (\mathbf{r})\mathbf{r}d\mathbf{r}$ directly from the molecular wave function, capturing lone-pair contributions and electron delocalisation that the simple bond-dipole model misses.

• Spectroscopy 14.12.01. IR activity requires a change in dipole moment during a vibration. ${\text{CO}}_2$ has symmetric and antisymmetric C=O stretches: the symmetric stretch does not change the dipole (it remains zero) and is IR-inactive; the antisymmetric stretch creates a transient dipole and is IR-active. Raman activity requires a change in polarizability. The mutual exclusion rule for centrosymmetric molecules (IR-active modes are Raman-inactive and vice versa) follows directly from the symmetry analysis of the dipole moment.

Historical notes Master

Peter Debye (1884-1966) introduced the concept of the permanent electric dipole moment of molecules in 1912 and developed the theory of polar molecules in his 1929 monograph Polar Molecules ^{[Debye 1929]}. Debye showed that the temperature dependence of the dielectric constant of a gas or dilute solution reveals the molecular dipole moment, providing the first experimental method for measuring molecular polarity. He received the Nobel Prize in Chemistry in 1936 for this work.

Johannes van der Waals (1837-1923) formulated the equation of state that bears his name in 1873, incorporating intermolecular attractive forces (the $a/V^2$ term) and molecular volume (the $b$ term). The attractive forces between neutral molecules are now called van der Waals forces, encompassing London dispersion, dipole-dipole, and dipole-induced dipole interactions. Van der Waals received the Nobel Prize in Physics in 1910.

Fritz London (1900-1954) provided the quantum-mechanical explanation of dispersion forces in 1930, showing that fluctuations in the electron distribution of one molecule induce a dipole in a neighbouring molecule, producing an attractive interaction that varies as $r^{-6}$. This resolved the puzzle of why noble gases (with no permanent dipole) still condense to liquids at low temperatures.

Walter Kossel (1888-1956) and G.N. Lewis independently developed the concept that chemical bonding involves electron sharing (1916). Kossel extended this to ionic bonding and recognised that electronegativity differences produce charge separation in bonds, the physical origin of bond dipoles.

Linus Pauling formalised the electronegativity scale in 1932, providing the quantitative basis for predicting bond polarity from atomic properties. His scale, based on bond-energy differences, assigns $\chi$ values to every element and enables prediction of bond-dipole magnitudes from atomic data alone.

The hydrogen bond was first recognised by Wendell Latimer and Worth Rodebush in 1920, who noted that the anomalous properties of water and HF could only be explained by an attractive interaction between the hydrogen on one molecule and the lone pair on another. The term "hydrogen bond" was coined by Maurice Huggins in 1921.

A.D. Buckingham extended the multipole-moment framework to quadrupole and octupole moments in the 1950s and 1960s ^{[Buckingham 1959]}, providing the theoretical tools for understanding the intermolecular forces of nonpolar but quadrupolar molecules like ${\text{CO}}_2$ and benzene. Buckingham's work connected the experimentally measurable dielectric and refractive properties to the underlying multipole-moment tensor components.

Bibliography Master

• Debye, P., Polar Molecules (Chemical Catalog Company, 1929). The founding monograph on molecular dipole moments.
• London, F., "Zur Theorie und Systematik der Molekularkrafte", Z. Physik 63 (1930), 245-279. Quantum-mechanical theory of dispersion forces.
• Pauling, L., "The Nature of the Chemical Bond. IV", J. Am. Chem. Soc. 54 (1932), 3570-3582. Electronegativity scale.
• Sutton, L. E. et al., Tables of Interatomic Distances and Configuration in Molecules and Ions, Chem. Soc. Special Publication 11 (1958). Reference data for bond lengths and dipole moments.
• Buckingham, A. D., "Molecular Quadrupole Moments", Q. Rev. Chem. Soc. 13 (1959), 183-214. Multipole-moment theory and measurement.
• Latimer, W. M. & Rodebush, W. H., "Polarity and Ionization from the Standpoint of the Lewis Theory of Valence", J. Am. Chem. Soc. 42 (1920), 1419-1433. First recognition of the hydrogen bond.
• Barron, L. D., Molecular Light Scattering and Optical Activity (Cambridge University Press, 2004). Dipole moments, polarizability, and optical activity.
• Huheey, J. E., Keiter, E. A. & Keiter, R. L., Inorganic Chemistry, 4e (HarperCollins, 1993), Ch. 2. Bond polarity and electronegativity in inorganic systems.
• Zumdahl, S. S. & DeCoste, D. J., Chemical Principles, 8e (Cengage, 2017), Ch. 8.3-8.4, Ch. 10. Introductory treatment of molecular geometry and intermolecular forces.
• Atkins, P. & de Paula, J., Physical Chemistry, 12e (Oxford, 2023), Ch. 14. Intermolecular forces from a physical-chemistry perspective.