van der Waals radii taken from Bondi's compilation (1964).[2] Values from other sources may differ significantly (see text)
"Molecular volume" redirects here. The term may also refer to Amount of substance.
The van der Waals surface of a molecule is an abstract representation or model of that molecule, illustrating where, in very rough terms, a surface might reside for the molecule based on the hard cutoffs of van der Waals radii for individual atoms, and it represents a surface through which the molecule might be conceived as interacting with other molecules.[citation needed] Also referred to as a van der Waals envelope, the van der Waals surface is named for Johannes Diderik van der Waals, a Dutch theoretical physicist and thermodynamicist who developed theory to provide a liquid-gas equation of state that accounted for the non-zero volume of atoms and molecules, and on their exhibiting an attractive force when they interacted (theoretical constructions that also bear his name). van der Waals surfaces are therefore a tool used in the abstract representations of molecules, whether accessed, as they were originally, via hand calculation, or via physical wood/plastic models, or now digitally, via computational chemistry software. Practically speaking, CPK models, developed by and named for Robert Corey, Linus Pauling, and Walter Koltun,[3] were the first widely used physical molecular models based on van der Waals radii, and allowed broad pedagogical and research use of a model showing the van der Waals surfaces of molecules.
van der Waals volume and van der Waals surface area
Methane, CH4, space-filling, van der Waals-based representation, carbon (C ) in black, hydrogen (H) in white. In chemistry, a space-filling model is a type of three-dimensional (3D) molecular model where the atoms are represented by spheres whose radii are, either as van der Waals radii or otherwise, proportional to the radii of the atoms. Center-to-center distances of the atoms are proportional to the distances between the atomic nuclei, all in the same scale. Atoms of different chemical elements are usually represented by spheres of different colors, see below.
Related to the title concept are the ideas of a van der Waals volume, Vw, and a van der Waals surface area, abbreviated variously as Aw, vdWSA, VSA, and WSA.[citation needed] A van der Waals surface area is an abstract conception of the surface area of atoms or molecules from a mathematical estimation, either computing it from first principles or by integrating over a corresponding van der Waals volume. In simplest case, for a spherical monatomic gas, it is simply the computed surface area of a sphere of radius equal to the van der Waals radius of the gaseous atom:
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The van der Waals volume, a type of atomic or molecular volume, is a property directly related to the van der Waals radius, and is defined as the volume occupied by an individual atom, or in a combined sense, by all atoms of a molecule. It may be calculated for atoms if the van der Waals radius is known, and for molecules if its atoms radii and the inter-atomic distances and angles are known. As above, in simplest case, for a spherical monatomic gas, Vw is simply the computed volume of a sphere of radius equal to the van der Waals radius of the gaseous atom:
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For a molecule, Vw is the volume enclosed by the van der Waals surface; hence, computation of Vw presumes ability to describe and compute a van der Waals surface. van der Waals volumes of molecules are always smaller than the sum of the van der Waals volumes of their constituent atoms, due to the fact that the interatomic distances resulting from chemical bond are less than the sum of the atomic van der Waals radii. In this sense, a van der Waals surface of a homonuclear diatomic molecule can be viewed as an pictorial overlap of the two spherical van der Waals surfaces of the individual atoms, likewise for larger molecules like methane, ammonia, etc. (see images).
van der Waals radii and volumes may be determined from the mechanical properties of gases (the original method, determining the van der Waals constant), from the critical point (e.g., of a fluid), from crystallographic measurements of the spacing between pairs of unbonded atoms in crystals, or from measurements of electrical or optical properties (i.e., polarizability or molar refractivity). In all cases, measurements are made on macroscopic samples and results are expressed as molar quantities. van der Waals volumes of a single atom or molecules are arrived at by dividing the macroscopically determined volumes by the Avogadro constant. The various methods give radius values which are similar, but not identical—generally within 1–2Å (100–200pm). Useful tabulated values of van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will be seen to present different values for the van der Waals radius of the same atom. As well, it has been argued that the van der Waals radius is not a fixed property of an atom in all circumstances, rather, that it will vary with the chemical environment of the atom.[2]
Gallery
Ammonia, NH3, space-filling, van der Waals-based representation, nitrogen (N) in blue, hydrogen (H) in white.
Phosphine, PH3, space-filling, van der Waals-based representation, ball-and-stick model superimposed, phosphorus (P) in orange, hydrogen (H) in white.
A space-filling model of n-octane, the straight chain (normal) hydrocarbon composed of 8 carbons and 18 hydrogens, formulae: CH3CH2(CH2)4CH2CH3orC 8H 18. Note, the representative shown is of a single conformational "pose" of a population of molecules, which, because of low Gibbs energy barriers to rotation about its carbon-carbon bonds (giving the carbon "chain" great flexibility). normally is composed of a very large number of different such conformations (e.g., in solution).
An example of a three-dimensional, space-filling, van der Waals-based model of a complex molecule, THC, the active agent in medical marijuana. You may have to click on the image to see rotation.
Hydrogen sulfide, H2S, space-filling, van der Waals-based representation, ball-and-stick model superimposed, sulfur (S) in yellow, hydrogen (H) in white over-shaded with blue. It also shows on its surface the electrostatic potential surface, (computed for the molecule in unknown fashion), using computational chemistry tools. It is shaded from blue for electropositive areas to red for electronegative areas.
↑ Rowland RS, Taylor R (1996). "Intermolecular nonbonded contact distances in organic crystal structures: comparison with distances expected from Van der Waals radii". J. Phys. Chem. 100 (18): 7384–7391. doi:10.1021/jp953141+.
↑ Robert B. Corey & Linus Pauling, 1953, "Molecular models of amino acids, peptides, and proteins," Rev. Sci. Instrum.,24(8), pp. 621–627, DOI 10.1063/1.1770803, see , accessed 23 June 2015.
An intermolecular force is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. atoms or ions. Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics.
The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Four widely used definitions of atomic radius are: Van der Waals radius, ionic radius, metallic radius and covalent radius. Typically, because of the difficulty to isolate atoms in order to measure their radii separately, atomic radius is measured in a chemically bonded state; however theoretical calculations are simpler when considering atoms in isolation. The dependencies on environment, probe, and state lead to a multiplicity of definitions.
The van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state.
In molecular physics and chemistry, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanishes at longer distances between interacting molecules.
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. The method is applied mostly in chemical physics, materials science, and biophysics.
GROningen MOlecular Simulation (GROMOS) is the name of a force field for molecular dynamics simulation, and a related computer software package. Both are developed at the University of Groningen, and at the Computer-Aided Chemistry Group at the Laboratory for Physical Chemistry at the Swiss Federal Institute of Technology (ETH Zurich). At Groningen, Herman Berendsen was involved in its development.
Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms.
Molecular modelling encompasses all methods, theoretical and computational, used to model or mimic the behaviour of molecules. The methods are used in the fields of computational chemistry, drug design, computational biology and materials science to study molecular systems ranging from small chemical systems to large biological molecules and material assemblies. The simplest calculations can be performed by hand, but inevitably computers are required to perform molecular modelling of any reasonably sized system. The common feature of molecular modelling methods is the atomistic level description of the molecular systems. This may include treating atoms as the smallest individual unit, or explicitly modelling protons and neutrons with its quarks, anti-quarks and gluons and electrons with its photons.
The atomic radius of a chemical element is the distance from the center of the nucleus to the outermost shell of an electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bound in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. Under some definitions, the value of the radius may depend on the atom's state and context.
Van der Waals strain is strain resulting from Van der Waals repulsion when two substituents in a molecule approach each other with a distance less than the sum of their Van der Waals radii. Van der Waals strain is also called Van der Waals repulsion and is related to steric hindrance. One of the most common forms of this strain is eclipsing hydrogen, in alkanes.
In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol. Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.
In quantum chemistry, the quantum theory of atoms in molecules (QTAIM), sometimes referred to as atoms in molecules (AIM), is a model of molecular and condensed matter electronic systems in which the principal objects of molecular structure - atoms and bonds - are natural expressions of a system's observable electron density distribution function. An electron density distribution of a molecule is a probability distribution that describes the average manner in which the electronic charge is distributed throughout real space in the attractive field exerted by the nuclei. According to QTAIM, molecular structure is revealed by the stationary points of the electron density together with the gradient paths of the electron density that originate and terminate at these points.
In the context of chemistry, molecular physics, physical chemistry, and molecular modelling, a force field is a computational model that is used to describe the forces between atoms within molecules or between molecules as well as in crystals. Force fields are a variety of interatomic potentials. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system on the atomistic level. Force fields are usually used in molecular dynamics or Monte Carlo simulations. The parameters for a chosen energy function may be derived from classical laboratory experiment data, calculations in quantum mechanics, or both. Force fields utilize the same concept as force fields in classical physics, with the main difference being that the force field parameters in chemistry describe the energy landscape on the atomistic level. From a force field, the acting forces on every particle are derived as a gradient of the potential energy with respect to the particle coordinates.
A molecular model is a physical model of an atomistic system that represents molecules and their processes. They play an important role in understanding chemistry and generating and testing hypotheses. The creation of mathematical models of molecular properties and behavior is referred to as molecular modeling, and their graphical depiction is referred to as molecular graphics.
The accessible surface area (ASA) or solvent-accessible surface area (SASA) is the surface area of a biomolecule that is accessible to a solvent. Measurement of ASA is usually described in units of square angstroms. ASA was first described by Lee & Richards in 1971 and is sometimes called the Lee-Richards molecular surface. ASA is typically calculated using the 'rolling ball' algorithm developed by Shrake & Rupley in 1973. This algorithm uses a sphere of a particular radius to 'probe' the surface of the molecule.
In chemistry, a space-filling model, also known as a calotte model, is a type of three-dimensional (3D) molecular model where the atoms are represented by spheres whose radii are proportional to the radii of the atoms and whose center-to-center distances are proportional to the distances between the atomic nuclei, all in the same scale. Atoms of different chemical elements are usually represented by spheres of different colors.
Implicit solvation is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of molecular mechanics. The method is often applied to estimate free energy of solute-solvent interactions in structural and chemical processes, such as folding or conformational transitions of proteins, DNA, RNA, and polysaccharides, association of biological macromolecules with ligands, or transport of drugs across biological membranes.
COSMO is a calculation method for determining the electrostatic interaction of a molecule with a solvent. COSMO is a dielectric continuum model. These models can be used in computational chemistry to model solvation effects. COSMO has become a popular method of these solvation models in recent years. The COSMO formalism is similar to the method proposed earlier by Hoshi et al. The COSMO approach is based – as many other dielectric continuum models – on the surface segmentation of a molecule surface.
A Van der Waals molecule is a weakly bound complex of atoms or molecules held together by intermolecular attractions such as Van der Waals forces or by hydrogen bonds. The name originated in the beginning of the 1970s when stable molecular clusters were regularly observed in molecular beam microwave spectroscopy.
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.
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