Intermolecular force

In physics, chemistry, and biology, intermolecular forces are forces that act between stable molecules or between functional groups of macromolecules. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Foundations of modern biology There are five unifying principles In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by The term macromolecule by definition implies "large Molecule " Intermolecular forces (the weakest of which are van der Waal's forces) include momentary attractions between molecules, diatomic free elements, and individual atoms. The Van der Waals equation is an Equation of state that can be derived from a special form of the potential between a pair of molecules (hard-sphere repulsion They differ from covalent and ionic bonding in that they are not stable, but are caused by momentary polarization of particles. Because electrons have no fixed position in the structure of an atom or molecule, but rather are distributed in a probabilistic fashion based on quantum probability, there is a positive chance that the electrons are not evenly distributed and thus their electrical charges are not evenly distributed. See Schrödinger equation for the theories on wave functions and descriptions of position and velocity of quantum particles. In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system

In general one distinguishes short and long range van der Waal's forces. The former are due to intermolecular exchange and charge penetration. They fall off exponentially as a function of intermolecular distance R and are repulsive for interacting closed-shell systems. An electron shell may be crudely thought of as an Orbit followed by Electrons around an Atom nucleus. In chemistry they are well known, because they give rise to steric hindrance, also known as Born or Pauli repulsion. See also Intramolecular forces ' Steric effects arise from the fact that each Atom within a Molecule occupies a certain Long range forces fall off with inverse powers of the distance, R^-n, typically 3 ≤ n ≤ 10, and are mostly attractive.

The sum of long and short range forces gives rise to a minimum, referred to as Van der Waal minimum. The position and depth of the Van der Waal's minimum depends on distance and mutual orientation of the molecules. "General theory" This is because before the advent of quantum mechanics the origin of intermolecular forces was not well understood. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Especially the causes of hard sphere repulsion, postulated by Van der Waals, and the possibility of the liquefaction of noble gases were difficult to understand. Johannes Diderik van der Waals ( November 23, 1837 &ndash March 8, 1923) was a Dutch Scientist and Thermodynamicist Liquefaction of gases includes a number of phases used to convert a Gas into a Liquid state History Noble gas is translated from the German noun de ''Edelgas'' first used in 1898 by Hugo Erdmann to indicate their extremely low level of reactivity Soon after the formulation of quantum mechanics, however, all open questions regarding intermolecular forces were answered, first by S. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons C. Wang and then more completely and thoroughly by Fritz London. Fritz Wolfgang London ( March 7, 1900 &ndash March 30, 1954) was a German -born American theoretical Physicist.

The quantum mechanical basis for the majority of intermolecular effects is contained in a nonrelativistic energy operator, the molecular Hamiltonian. In Atomic molecular and optical physics as well as in Quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the This operator consists only of kinetic energies and Coulomb interactions. Usually one applies the Born-Oppenheimer approximation and considers the electronic (clamped nuclei) Hamilton operator only. In Quantum chemistry, the computation of the energy and Wavefunction of an average-size Molecule is a formidable task that is alleviated by the Born-Oppenheimer For very long intermolecular distances the retardation of the Coulomb force (first considered in 1948 for intermolecular forces by Hendrik Casimir and Dirk Polder) may have to be included. Hendrik Brugt Gerhard Casimir ( July 15, 1909 in 's-Gravenhage, Netherlands &ndash May 4, 2000 in Heeze Dirk Polder ( August 23, 1919, The Hague &mdash March 18, 2001, Iran) was a Dutch Physicist who together with Sometimes, e. g. , for interacting paramagnetic or electronically excited molecules, electronic spin and other magnetic effects may play a role. Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field Excitation is an elevation in energy level above an arbitrary baseline energy state In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In this article, however, retardation and magnetic effects will not be considered.

We will distinguish four fundamental interactions:

exchange
electrostatic
induction
dispersion.

1 Perturbation theory
2 Supermolecular approach
3 Exchange
4 Electrostatic interactions
5 London dispersion forces
6 Quantum mechanical theory of dispersion forces
7 Anisotropy and non-additivity of intermolecular forces
8 See also
9 References
10 External links
- 10.1 Software for calculation of intermolecular forces

Perturbation theory

The last three of the fundamental interactions are most naturally accounted for by Rayleigh-Schrödinger perturbation theory (RS-PT). In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system In this theory—applied to two monomers A and B—one uses as unperturbed Hamiltonian the sum of two monomer Hamiltonians,

$H^{(0)} \equiv H^{A}+ H^{B}.\,$

In the present case the unperturbed states are products

$\Phi_n^A \Phi_m^B\quad \hbox{with}\quad H^A \Phi_n^A = E_n^A\Phi_n^A\quad\hbox{and}\quad H^B \Phi_m^B = E_m^B\Phi_m^B$

Supermolecular approach

The early theoretical work on intermolecular forces was invariably based on RS-PT and its antisymmetrized variants. However, since the beginning of the 1990s it has become possible to apply standard quantum chemical methods to pairs of molecules. Computational chemistry is a branch of Chemistry that uses computers to assist in solving chemical problems This approach is referred to as the supermolecule method. In order to obtain reliable results one must include electronic correlation in the supermolecule method (without it dispersion is not accounted for at all), and take care of the basis set superposition error. Electronic correlation refers to the interaction between Electrons in a quantum system whose Electronic structure is being considered This is the effect that the atomic orbital basis of one molecule improves the basis of the other. Since this improvement is distance dependent, it gives easily rise to artifacts.

Exchange

The monomer functions Φ_n^A and Φ_m^B are antisymmetric under permutation of electron coordinates (i. e. , they satisfy the Pauli principle), but the product states are not antisymmetric under intermolecular exchange of the electrons. The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925 An obvious way to proceed would be to introduce the intermolecular antisymmetrizer $\tilde{\mathcal{A}}^{AB}$ . In Quantum mechanics, an antisymmetrizer \mathcal{A} (also known as antisymmetrizing operator) is a linear operator that makes a wave function of N identical But, as already noticed in 1930 by Eisenschitz and London,^[1] this causes two major problems. In the first place the antisymmetrized unperturbed states are no longer eigenfunctions of H⁽⁰⁾, which follows from the non-commutation

$\big[ \tilde{\mathcal{A}}^{AB}, H^{(0)}\big] \ne 0 .$

In the second place the projected excited states

$\tilde{\mathcal{A}}^{AB} \Phi^A_n \Phi^B_m$

become linearly dependent and the choice of a linearly independent subset is not apparent. In Linear algebra, a family of vectors is linearly independent if none of them can be written as a Linear combination of finitely many other vectors In the late 1960s the Eisenschitz-London approach was revived and different rigorous variants of symmetry adapted perturbation theory were developed. (The word symmetry refers here to permutational symmetry of electrons). The different approaches shared a major drawback: they were very difficult to apply in practice. Hence a somewhat less rigorous approach (weak symmetry forcing) was introduced: apply ordinary RS-PT and introduce the intermolecular antisymmetrizer at appropriate places in the RS-PT equations. This approach leads to feasible equations, and, when electronically correlated monomer functions are used, weak symmetry forcing is known to give reliable results. ^[2]^[3]

The first-order (most important) energy including exchange is in almost all symmetry-adapted perturbation theories given by the following expression

$E^{(1)}_\mathrm{antisymmetric} = \frac{ \langle \Phi_0^A \Phi_0^B| V^{AB}\tilde{\mathcal{A}}^{AB}| \Phi_0^A \Phi_0^B \rangle} { \langle \Phi_0^A \Phi_0^B| \tilde{\mathcal{A}}^{AB}| \Phi_0^A \Phi_0^B \rangle} .$

The main difference between covalent and non-covalent forces is the sign of this expression. In the case of chemical bonding this interaction is attractive (for certain electron-spin state, usually spin-singlet) and responsible for large bonding energies—on the order of a hundred kcal/mol. In the case of intermolecular forces between closed shell systems, the interaction is strongly repulsive and responsible for the "volume" of the molecule (see Van der Waals radius). Van der Waals Volume The van der Waals volume, V, also called the atomic volume or molecular volume, is the atomic property most directly Roughly speaking, the exchange interaction is proportional to the differential overlap between Φ₀^A and Φ₀^B. Since the wavefunctions decay exponentially as a function of distance, the exchange interaction does too. Hence the range of action is relatively short, which is why exchange interactions are referred to as short range interactions.

Electrostatic interactions

By definition the electrostatic interaction is given by the first-order Rayleigh-Schrödinger perturbation (RS-PT) energy (without exchange):

$E^{(1)}_\mathrm{electrostatic} = \langle \Phi_0^A \Phi_0^B| V^{AB}| \Phi_0^A \Phi_0^B \rangle .$

Let the clamped nucleus α on A have position vector R_α, then its charge times the Dirac delta function, Z_α δ(r-R_α), is the charge density of this nucleus. The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. The total charge density of monomer A is given by

$\rho^A_\mathrm{tot}(\mathbf{r}) = \sum_{\alpha} Z_\alpha \delta(\mathbf{r}-\mathbf{R}_\alpha) - \rho^A_\mathrm{el}(\mathbf{r})$

with the electronic charge density given by an integral over n_A - 1 primed electron coordinates:

$\rho^A_\mathrm{el}(\mathbf{r}) = n_A \int |\Phi^A_0(\mathbf{r}, \mathbf{r}'_2, \ldots, \mathbf{r}'_{n_A})|^2 d\mathbf{r}'_2 \cdots d\mathbf{r}'_{n_A}.$

An analogous definition holds for the charge density of monomer B. It can be shown that the first-order quantum mechanical expression can be written as

$E^{(1)}_\mathrm{electrostatic} = \int\int \rho^A_\mathrm{tot}(\mathbf{r}_1)\frac{1}{r_{12}} \rho^B_\mathrm{tot}(\mathbf{r}_2) d\mathbf{r}_1 d\mathbf{r}_2,$

which is nothing but the classical expression for the electrostatic interaction between two charge distributions. This shows that the first-order RS-PT energy is indeed equal to the electrostatic interaction between A and B.

Multipole expansion

At present it is feasible to compute the electrostatic energy without any further approximations other than those applied in the computation of the monomer wavefunctions. In the past this was different and a further approximation was commonly introduced: V^AB was expanded in a (truncated) series in inverse powers of the intermolecular distance R. This yields the multipole EXPANSION of the electrostatic energy. Since its concepts still pervade the theory of intermolecular forces, we will present it here. In this article the following expansion is proved

$V^{AB} = \sum_{\ell_A=0}^\infty \sum_{\ell_B=0}^\infty (-1)^{\ell_B} \binom{2\ell_A+2\ell_B}{2\ell_A}^{1/2} \sum_{M=-\ell_A-\ell_B}^{\ell_A+\ell_B} (-1)^{M} I_{\ell_A+\ell_B,-M}(\mathbf{R}_{AB})\; \left[\mathbf{Q}^{\ell_A} \otimes \mathbf{Q}^{\ell_B} \right]^{\ell_A+\ell_B}_M$

with the Clebsch-Gordan series defined by

$\left[\mathbf{Q}^{\ell_A} \otimes \mathbf{Q}^{\ell_B} \right]^{\ell_A+\ell_B}_M \equiv \sum_{m_A=-\ell_A}^{\ell_A} \sum_{m_B=-\ell_B}^{\ell_B}\; Q_{m_A}^{\ell_A} Q_{m_B}^{\ell_B}\;\langle \ell_A, m_A; \ell_B, m_B| \ell_A+\ell_B, M \rangle.$

and the irregular solid harmonic is defined by

$I_{L,M}(\mathbf{R}_{AB}) \equiv \left[\frac{4\pi}{2L+1}\right]^{1/2}\; \frac{Y_{L,M}(\widehat{\mathbf{R}}_{AB})}{R_{AB}^{L+1}}.$

The function Y_L,M is a normalized spherical harmonic, while

$Q^{\ell_A}_{m_A}$ and $Q^{\ell_B}_{m_B}$ are spherical multipole moment operators. A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. In Physics, the Clebsch-Gordan coefficients are sets of numbers that arise in Angular momentum coupling under the laws of Quantum mechanics. In Physics and Mathematics, the solid harmonics are solutions of the Laplace equation in Spherical polar coordinates. In Mathematics, the spherical harmonics are the angular portion of an Orthogonal set of solutions to Laplace's equation represented in a system of Spherical multipole moments are the coefficients in a Series expansion of a Potential that varies inversely with the distance R to a source i This expansion is manifestly in powers of 1/R_AB.

Insertion of this expansion into the first-order (without exchange) expression gives a very similar expansion for the electrostatic energy, because the matrix element factorizes,

$\begin{align} E^{(1)}_\mathrm{electrostatic} = & \sum_{\ell_A=0}^\infty \sum_{\ell_B=0}^\infty (-1)^{\ell_B} \binom{2\ell_A+2\ell_B}{2\ell_A}^{1/2} \\ &\sum_{M=-\ell_A-\ell_B}^{\ell_A+\ell_B} (-1)^{M} I_{\ell_A+\ell_B,-M}(\mathbf{R}_{AB})\; \left[\mathbf{M}^{\ell_A} \otimes \mathbf{M}^{\ell_B} \right]^{\ell_A+\ell_B}_M, \end{align}$

with the permanent multipole moments defined by

$M^{\ell_A}_{m_A} \equiv \langle \Phi_0^A | Q^{\ell_A}_{m_A}| \Phi_0^A\rangle \quad\hbox{and}\quad M^{\ell_B}_{m_B} \equiv \langle \Phi_0^B | Q^{\ell_B}_{m_B}| \Phi_0^B\rangle .$

We see that the series is of infinite length, and, indeed, most molecules have an infinite number of non-vanishing multipoles. In the past, when computer calculations for the permanent moments were not yet feasible, it was common to truncate this series after the first non-vanishing term.

Which term is non-vanishing, depends very much on the symmetry of the molecules constituting the dimer. For instance, molecules with an inversion center such as a homonuclear diatomic (e. g. , molecular nitrogen N₂), or an organic molecule like ethene (C₂H₄) do not possess a permanent dipole moment (l=1), but do carry a quadrupole moment (l=2). Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Structure This Hydrocarbon has four Hydrogen Atoms bound to a pair of Carbon atoms that are connected by a Double bond. Molecules such a hydrogen chloride (HCl) and water (H₂O) lack an inversion center and hence do have a permanent dipole. Water is a common Chemical substance that is essential for the survival of all known forms of Life. So, the first non-vanishing electrostatic term in, e. g. , the N₂—H₂O dimer, is the l_A=2, l_B=1 term. From the formula above follows that this term contains the irregular solid harmonic of order L = l_A + l_B = 3, which has an R^-4 dependence. But in this dimer the quadrupole-quadrupole interaction (R^-5) is not unimportant either, because the water molecule carries a non-vanishing quadrupole as well.

When computer calculations of permanent multipole moments of any order became possible, the matter of the convergence of the multipole series became urgent. It can be shown that, if the charge distributions of the two monomers overlap, the multipole expansion is formally divergent.

Ionic interactions

It is debatable whether ionic interactions are to be seen as intermolecular forces, some workers consider them rather as special kind of chemical bonding. The forces occur between charged atoms or molecules (ions). An ion is an Atom or Molecule which has lost or gained one or more Valence electrons giving it a positive or negative electrical charge Ionic bonds are formed when the difference between the electron affinity of one monomer and the ionization potential of the other is so large that electron transfer from the one monomer to the other is energetically favorable. The electron affinity, E ea of an Atom or Molecule is the energy required to detach an electron from a singly charged negative The ionization potential, ionization energy or EI of an Atom or Molecule is the Energy required to remove an Electron Since a transfer of an electron is never complete there is always a degree of covalent bonding.

Once the ions (of opposite sign) are formed, the interaction between them can be seen as a special case of multipolar attraction, with a 1/R_AB distance dependence. Indeed, the ionic interaction is the electrostatic term with l_A = 0 and l_B = 0. Using that the irregular harmonics for L = 0 is simply

$I_{0,0}(\mathbf{R}_{AB}) = \frac{1}{R_{AB}},$

and that the monopole moments and their Clebsch-Gordan coupling are

$M^{0_A}_0 = q_A,\quad M^{0_B}_0 = q_B \quad\hbox{and}\quad [\mathbf{M}^{0_A}\otimes \mathbf{M}^{0_A}]^0_0 = q_A q_B ,$

(where q_A and q_B are the charges of the molecular ions) we recover—as to be expected—Coulomb's law

$E^{(1)}_\mathrm{electrostatic} = \frac{q_A q_B}{R_{AB}} + \hbox{higher terms}.$

For shorter distances, where the charge distributions of the monomers overlap, the ions will repel each other because of inter-monomer exchange of the electrons. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form

Ionic compounds have high melting and boiling points due to the large amount of energy required to break the forces between the charged ions. When molten they are also good conductors of heat and electricity, due to the free or delocalized ions.

Dipole-dipole interactions

Dipole-dipole interactions, also called Keesom interactions or Keesom forces after Willem Hendrik Keesom, who produced the first mathematical description in 1921, are the forces that occur between two molecules with permanent dipoles. Willem Hendrik Keesom ( June 21, 1876, Texel &ndash March 24 1956, Leiden) was a Dutch Physicist They result from the dipole-dipole interaction between two molecules. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by An example of this can be seen in hydrochloric acid:

The molecules are depicted here as two point dipoles. Hydrochloric acid is the Solution of Hydrogen chloride ( H[[Chlorine Cl]] in water A point dipole is an idealization similar to a point charge (a finite charge in an infinitely small volume). A point dipole consists of two equal charges of opposite sign δ⁺ and δ^-, which are a distance d apart. This distance d is so small that at any distance R from the point dipole it can be assumed that d/R >> (d/R)². In this idealization the electrostatic field outside the charge distribution consists of one (R^-3) term only, see this article. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a The electrostatic interaction between two point dipoles is given by the single term l_A = 1 and l_B = 1 in the expansion above.

Obviously, no molecule is an ideal point dipole, and in the case of the HCl dimer, for instance, dipole-quadrupole, quadrupole-quadrupole, etc. interactions are by no means negligible (and neither are induction or dispersion interactions).

Note that almost always the dipole-dipole interaction between two atoms is zero, because atoms rarely carry a permanent dipole, see atomic dipoles. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a

Writing

$\boldsymbol{\mu}^A = (\mu_x^A, \mu_y^A, \mu_z^A) \quad\hbox{and}\quad \mu_z^A = \boldsymbol{\mu}^A\cdot \hat{\mathbf{R}}_{AB} \equiv \boldsymbol{\mu}^A\cdot \frac{\mathbf{R}_{AB}}{R_{AB}}$

and similarly for B, we get the well-known expression

$E_{\mathrm{dip-dip}} = \frac{1}{R^{3}_{AB}}\left[ \boldsymbol{\mu}^A\cdot\boldsymbol{\mu}^B - 3 (\boldsymbol{\mu}^A\cdot \hat{\mathbf{R}}_{AB}) (\hat{\mathbf{R}}_{AB}\cdot \boldsymbol{\mu}^B) \right].$

As a numerical example we consider the HCl dimer depicted above. We assume that the left molecule is A and the right B, so that the z-axis is along the molecules and points to the right. Our (physical) convention of the dipole moment is such that it points from negative to positive charge. Note parenthetically that in organic chemistry the opposite convention is used. Since organic chemists hardly ever perform vector computations with dipoles, confusion hardly ever arises. In organic chemistry dipoles are mainly used as a measure of charge separation in a molecule. So,

$\boldsymbol{\mu}^A = \boldsymbol{\mu}^B = \mu_\mathrm{HCl} \begin{pmatrix} 0 \\ 0 \\ -1 \end{pmatrix} \quad\hbox{and}\quad E_{\mathrm{dip-dip}} = \frac{-2\mu^2_\mathrm{HCl}}{R^{3}_{AB}}.$

The value of μ_HCl is 0. 43 (atomic units), so that at a distance of 10 bohr the dipole-dipole attraction is -3. Atomic units ( au) form a System of units convenient for Atomic physics, Electromagnetism, and Quantum electrodynamics, especially In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus. 698 10^-4 hartree (-0. A hartree (symbol E h is the atomic unit of Energy and is named after Physicist Douglas Hartree. 97 kJ/mol).

If one of the molecules is neutral and freely rotating, the total electrostatic interaction energy becomes zero. (For the dipole-dipole interaction this is most easily proved by integrating over the spherical polar angles of the dipole vector, while using the volume element sinθ dθdφ). In gases and liquids molecules are not rotating completely freely—the rotation is weighted by the Boltzmann factor exp(-E_dip-dip/kT), where k is the Boltzmann constant and T the absolute temperature. In Physics, the Boltzmann factor is a weighting factor that determines the relative probability of a state i in a multi-state system in Thermodynamic equilibrium Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics It was first shown by Lennard-Jones^[4] that the temperature-averaged dipole-dipole interaction is

$\overline{E}_\mathrm{dip-dip} = -\frac{2 |\mu^A|^2|\mu^B|^2}{3R_{AB}^6 kT}.$

Since the averaged energy has an R^-6 dependence, it is evidently much weaker than the unaveraged one, but it is not completely zero. Sir John Edward Lennard-Jones KBE FRS (born October 27, 1894; died November 1, 1954) was a Mathematician who held a chair of theoretical It is attractive, because the Boltzmann weighting favors somewhat the attractive regions of space. In HCl-HCl we find for T = 300 K and R_AB = 10 bohr the averaged attraction -62 J/mol, which shows a weakening of the interaction by a factor of about 16 due to thermal rotational motion.

Hydrogen bonding

Main article: Hydrogen bond

Hydrogen bonding is an intermolecular interaction with a hydrogen atom being present in the intermolecular bond. A hydrogen bond results from a Dipole-dipole force between an Electronegative atom and a Hydrogen atom bonded to Nitrogen, Oxygen A hydrogen bond results from a Dipole-dipole force between an Electronegative atom and a Hydrogen atom bonded to Nitrogen, Oxygen A hydrogen atom is an atom of the chemical element Hydrogen. The electrically neutral This hydrogen is covalently (chemically) bound in one molecule, which acts as the proton donor. The other molecule acts as the proton acceptor. In the following important example of the water dimer, the water molecule on the right is the proton donor, while the one on the left is the proton acceptor:

The hydrogen atom participating in the hydrogen bond is often covalently bound in the donor to an electronegative atom. Water ( H2[[oxygen O]] H OH) is the most abundant Molecule on Earth 's surface composing of about 70% of the Earth's surface as " Electronegativity " is the opposite of " Electropositivity," which describes an element's ability to donate electrons Examples of such atoms are nitrogen, oxygen, or fluorine. Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Fluorine, fluorum meaning "to flow" is the Chemical element with the symbol F and Atomic number 9 The electronegative atom is negatively charged (carries a charge δ^-) and the hydrogen atom bound to it is positively charged. Consequently the proton donor is a polar molecule with a relatively large dipole moment. Often the positively charged hydrogen atom points towards an electron rich region in the acceptor molecule. The fact that an electron rich region exists in the acceptor molecule, implies already that the acceptor has a relatively large dipole moment as well. The result is a dimer that to a large extent is bound by the dipole-dipole force.

For quite some time it was believed that hydrogen bonding required an explanation that was different from the other intermolecular interactions. However, reliable computer calculations that became possible during the 1980s have shown that only the four effects listed above play a role, with the dipole-dipole interaction being particularly important. Since the four effects account completely for the bonding in small dimers like the water dimer, for which highly accurate calculations are feasible, it is now generally believed that no other bonding effects are operative.

Hydrogen bonds are found throughout nature. In water the dynamics of these bonds produce unique properties essential to all known lifeforms. Hydrogen bonds, between hydrogen atoms and nitrogen atoms, of adjacent DNA base pairs generate intermolecular forces that improve binding between the strands of the molecule. Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known Hydrophobic effects between the double-stranded DNA and the solute nucleoplasm prevail in sustaining the double-helix structure of DNA.

London dispersion forces

Also called London forces, instantaneous dipole (or multipole) effects (spatially variable δ⁺) or Van der Waals forces, these involve the attraction between temporarily induced dipoles in nonpolar molecules (often disappear within an instant). The Van der Waals equation is an Equation of state that can be derived from a special form of the potential between a pair of molecules (hard-sphere repulsion This polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in nonpolar molecules. An example of the former is chlorine dissolving in water:

                 (+)(-)(+)  (-) (+)
[Permanent Dipole] H-O-H-----Cl-Cl [Induced Dipole]

Note added by other author: Sketched is an interaction between the permanent dipole on water and an induced dipole on chlorine. The latter dipole is induced by the electric field offered by the permanent dipole of water (see field from an electric dipole). In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a

This permanent dipole-induced dipole interaction is referred to as induction (or polarization) interaction and is to be distinguished from the London dispersion interaction. The latter is sometimes described as an interaction between two instantaneous dipoles, see molecular dipole. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a The Cl₂—Cl₂ interaction that now follows is an example of a proper London dispersion interaction.

                      (+) (-)    (+) (-)
[instantaneous dipole] Cl-Cl------Cl-Cl [instantaneous dipole]

Note added by other author: It must be pointed out that the London interaction is not the only interaction between two chlorine molecules in the region where the overlap between the respective charge distributions may be neglected. Each chlorine molecule carries permanent multipole moments of even order, the first one being a permanent quadrupole moment (order 2). Multipole moments are the Coefficients of a Series expansion of a Potential due to continuous or discrete sources (e A quadrupole or quadrapole is one of a sequence of configurations of — for example — electric charge or current or gravitational mass that can exist in ideal form but it The interaction between two permanent multipole moments also contributes to the intermolecular force and the first term (quadrupole-quadrupole) is as important as the London dispersion force.

London dispersion forces exist between all atoms. London forces are the only reason for rare-gas atoms to condense at low temperature.

Quantum mechanical theory of dispersion forces

The first explanation of the attraction between noble gas atoms was given by Fritz London in 1930. Fritz Wolfgang London ( March 7, 1900 &ndash March 30, 1954) was a German -born American theoretical Physicist. ^[5] He used a quantum mechanical theory based on second-order perturbation theory. In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system The perturbation is the Coulomb interaction V between the electrons and nuclei of the two monomers (atoms or molecules) that constitute the dimer. The second-order perturbation expression of the interaction energy contains a sum over states. The states appearing in this sum are simple products of the excited electronic states of the monomers. Thus, no intermolecular antisymmetrization of the electronic states is included and the Pauli exclusion principle is only partially satisfied. The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925

London developed the perturbation V in a Taylor series in $\frac{1}{R}$ , where $R$ is the distance between the nuclear centers of mass of the monomers. In Mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its Derivatives

This Taylor expansion is known as the multipole expansion of V because the terms in this series can be regarded as energies of two interacting multipoles, one on each monomer. A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. Substitution of the multipole-expanded form of V into the second-order energy yields an expression that resembles somewhat an expression describing the interaction between instantaneous multipoles (see the qualitative description above). Additionally an approximation, named after Albrecht Unsöld, must be introduced in order to obtain a description of London dispersion in terms of dipole polarizabilities and ionization potentials. Albrecht Otto Johannes Unsöld ( April 20, 1905 &ndash September 23, 1995) was a German Astrophysicist known for his contributions Polarizability is the relative tendency of a charge distribution like the Electron cloud of an Atom or Molecule, to be distorted from its normal shape The ionization potential, ionization energy or EI of an Atom or Molecule is the Energy required to remove an Electron

In this manner the following approximation is obtained for the dispersion interaction $E_{AB}^{\rm disp}$ between two atoms $A$ and $B$ . Here $α A$ and $α B$ are the dipole polarizabilities of the respective atoms. The quantities $I A$ and $I B$ are the first ionization potentials of the atoms and $R$ is the intermolecular distance.

Note that this final London equation does not contain instantaneous dipoles (see molecular dipoles). In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a The "explanation" of the dispersion force as the interaction between two such dipoles was invented after London gave the proper quantum mechanical theory. See the authoritative work^[6] for a criticism of the instantaneous dipole model and^[7] for a modern and thorough exposition of the theory of intermolecular forces.

The London theory has much similarity to the quantum mechanical theory of light dispersion, which is why London coined the phrase "dispersion effect" for the interaction that we described in this lemma. In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency

Anisotropy and non-additivity of intermolecular forces

Consider the interaction between two electric point charges at position $\vec{r}_1$ and $\vec{r}_2$ . By Coulomb's law the interaction potential depends only on the distance $|\vec{r}_1-\vec{r}_2|$ between the particles. The Coulomb barrier, named after physicist Charles-Augustin de Coulomb (1736&ndash1806 is the energy barrier due to Electrostatic interaction that two nuclei need For molecules this is different. If we see a molecule as a rigid 3-D body, it has 6 degrees of freedom (3 degrees for its orientation and 3 degrees for its position in R³). The interaction energy of two molecules (a dimer) in isotropic and homogeneous space is in general a function of 2×6−6=6 degrees of freedom (by the homogeneity of space the interaction does not depend on the position of the center of mass of the dimer, and by the isotropy of space the interaction does not depend on the orientation of the dimer). The analytic description of the interaction of two arbitrarily shaped rigid molecules requires therefore 6 parameters. (One often uses two Euler angles per molecule, plus a dihedral angle, plus the distance. The Euler angles were developed by Leonhard Euler to describe the orientation of a Rigid body (a body in which the relative position of all its points is constant ) The fact that the intermolecular interaction depends on the orientation of the molecules is expressed by stating that the potential is anisotropic. Since point charges are by definition spherical symmetric, their interaction is isotropic. Especially in the older literature, intermolecular interactions are regularly assumed to be isotropic (e. g. , the potential is described in Lennard-Jones form, which depends only on distance). A pair of neutral atoms or molecules is subject to two distinct forces in the limit of large separation and small separation an attractive force at long ranges ( van der Waals force, or

Consider three arbitrary point charges at distances r₁₂, r₁₃, and r₂₃ apart. The total interaction U is additive; i. e. , it is the sum

U = u (r 12) + u (r 13) + u (r 23).

Again for molecules this can be different. Pretending that the interaction depends on distances only—but see above—the interaction of three molecules takes in general the form

U = u (r 12) + u (r 13) + u (r 23) + u (r 12, r 13, r 23),

where $u (r 12, r 13, r 23)$ is a non-additive three-body interaction. Such an interaction can be caused by exchange interactions, by induction, and by dispersion (the Axilrod-Teller triple dipole effect). In Physics, the exchange interaction is a Quantum mechanical effect which increases or decreases the expectation value of the Energy or Distance The Axilrod-Teller potential is a three-body Potential that results from a third-order perturbation correction to the attractive London dispersion interactions

References

^ R. The hydrophobic effect is the property that non-polar molecules tend to form intermolecular aggregates in an aqueous medium and analogous intramolecular interactions An intramolecular force is any force that holds together the atoms making up a molecule or compound A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds Eisenschitz and F. London, Zeitschrift für Physik, vol. 60, p. 491 (1930). English translations in H. Hettema, Quantum Chemistry, Classic Scientific Papers, World Scientific, Singapore (2000), p. 336.
^ B. Jeziorski, R. Moszynski, and K. Szalewicz, Chemical Reviews, vol. 94, pp. 1887-1930 (1994).
^ K. Szalewicz and B. Jeziorski, in: Molecular Interactions, editor S. Scheiner, Wiley, Chichester (1995). ISBN 0471 959219.
^ J. E. Lennard-Jones, Proc. Physical Society (London), vol. 43, p. 461 (1931).
^ F. London, Zeitschrift für Physik, vol. 60, p. 245 (1930) and Z. Physik. Chemie, vol. B11, p. 222 (1930). English translations in H. Hettema, Quantum Chemistry, Classic Scientific Papers, World Scientific, Singapore (2000).
^ J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954
^ A. J. Stone, The Theory of Intermolecular Forces, 1996, (Clarendon Press, Oxford)

External links

Software for calculation of intermolecular forces

Quantum 3.2
SAPT: An ab initio quantumchemical package.

Dictionary