Molecular geometry

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Geometry of the water molecule with values for O-H bond length and for H-O-H bond angle between two bonds Water molecule dimensions.svg
Geometry of the water molecule with values for O-H bond length and for H-O-H bond angle between two bonds

Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom.

Contents

Molecular geometry influences several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism and biological activity. [1] [2] [3] The angles between bonds that an atom forms depend only weakly on the rest of molecule, i.e. they can be understood as approximately local and hence transferable properties.

Determination

The molecular geometry can be determined by various spectroscopic methods and diffraction methods. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques. X-ray crystallography, neutron diffraction and electron diffraction can give molecular structure for crystalline solids based on the distance between nuclei and concentration of electron density. Gas electron diffraction can be used for small molecules in the gas phase. NMR and FRET methods can be used to determine complementary information including relative distances, [4] [5] [6] dihedral angles, [7] [8] angles, and connectivity. Molecular geometries are best determined at low temperature because at higher temperatures the molecular structure is averaged over more accessible geometries (see next section). Larger molecules often exist in multiple stable geometries (conformational isomerism) that are close in energy on the potential energy surface. Geometries can also be computed by ab initio quantum chemistry methods to high accuracy. The molecular geometry can be different as a solid, in solution, and as a gas.

The position of each atom is determined by the nature of the chemical bonds by which it is connected to its neighboring atoms. The molecular geometry can be described by the positions of these atoms in space, evoking bond lengths of two joined atoms, bond angles of three connected atoms, and torsion angles (dihedral angles) of three consecutive bonds.

Influence of thermal excitation

Since the motions of the atoms in a molecule are determined by quantum mechanics, "motion" must be defined in a quantum mechanical way. The overall (external) quantum mechanical motions translation and rotation hardly change the geometry of the molecule. (To some extent rotation influences the geometry via Coriolis forces and centrifugal distortion, but this is negligible for the present discussion.) In addition to translation and rotation, a third type of motion is molecular vibration, which corresponds to internal motions of the atoms such as bond stretching and bond angle variation. The molecular vibrations are harmonic (at least to good approximation), and the atoms oscillate about their equilibrium positions, even at the absolute zero of temperature. At absolute zero all atoms are in their vibrational ground state and show zero point quantum mechanical motion, so that the wavefunction of a single vibrational mode is not a sharp peak, but approximately a Gaussian function (the wavefunction for n = 0 depicted in the article on the quantum harmonic oscillator). At higher temperatures the vibrational modes may be thermally excited (in a classical interpretation one expresses this by stating that "the molecules will vibrate faster"), but they oscillate still around the recognizable geometry of the molecule.

To get a feeling for the probability that the vibration of molecule may be thermally excited, we inspect the Boltzmann factor β ≡ exp(−ΔE/kT), where ΔE is the excitation energy of the vibrational mode, k the Boltzmann constant and T the absolute temperature. At 298 K (25 °C), typical values for the Boltzmann factor β are:

(The reciprocal centimeter is an energy unit that is commonly used in infrared spectroscopy; 1 cm−1 corresponds to 1.23984×10−4 eV). When an excitation energy is 500 cm−1, then about 8.9 percent of the molecules are thermally excited at room temperature. To put this in perspective: the lowest excitation vibrational energy in water is the bending mode (about 1600 cm−1). Thus, at room temperature less than 0.07 percent of all the molecules of a given amount of water will vibrate faster than at absolute zero.

As stated above, rotation hardly influences the molecular geometry. But, as a quantum mechanical motion, it is thermally excited at relatively (as compared to vibration) low temperatures. From a classical point of view it can be stated that at higher temperatures more molecules will rotate faster, which implies that they have higher angular velocity and angular momentum. In quantum mechanical language: more eigenstates of higher angular momentum become thermally populated with rising temperatures. Typical rotational excitation energies are on the order of a few cm−1. The results of many spectroscopic experiments are broadened because they involve an averaging over rotational states. It is often difficult to extract geometries from spectra at high temperatures, because the number of rotational states probed in the experimental averaging increases with increasing temperature. Thus, many spectroscopic observations can only be expected to yield reliable molecular geometries at temperatures close to absolute zero, because at higher temperatures too many higher rotational states are thermally populated.

Bonding

Molecules, by definition, are most often held together with covalent bonds involving single, double, and/or triple bonds, where a "bond" is a shared pair of electrons (the other method of bonding between atoms is called ionic bonding and involves a positive cation and a negative anion).

Molecular geometries can be specified in terms of 'bond lengths', 'bond angles' and 'torsional angles'. The bond length is defined to be the average distance between the nuclei of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds. For four atoms bonded together in a chain, the torsional angle is the angle between the plane formed by the first three atoms and the plane formed by the last three atoms.

There exists a mathematical relationship among the bond angles for one central atom and four peripheral atoms (labeled 1 through 4) expressed by the following determinant. This constraint removes one degree of freedom from the choices of (originally) six free bond angles to leave only five choices of bond angles. (The angles θ11, θ22, θ33, and θ44 are always zero and that this relationship can be modified for a different number of peripheral atoms by expanding/contracting the square matrix.)

Molecular geometry is determined by the quantum mechanical behavior of the electrons. Using the valence bond approximation this can be understood by the type of bonds between the atoms that make up the molecule. When atoms interact to form a chemical bond, the atomic orbitals of each atom are said to combine in a process called orbital hybridisation. The two most common types of bonds are sigma bonds (usually formed by hybrid orbitals) and pi bonds (formed by unhybridized p orbitals for atoms of main group elements). The geometry can also be understood by molecular orbital theory where the electrons are delocalised.

An understanding of the wavelike behavior of electrons in atoms and molecules is the subject of quantum chemistry.

Isomers

Isomers are types of molecules that share a chemical formula but have difference geometries, resulting in different properties:

Types of molecular structure

A bond angle is the geometric angle between two adjacent bonds. Some common shapes of simple molecules include:

VSEPR table

The bond angles in the table below are ideal angles from the simple VSEPR theory (pronounced "Vesper Theory")[ citation needed ], followed by the actual angle for the example given in the following column where this differs. For many cases, such as trigonal pyramidal and bent, the actual angle for the example differs from the ideal angle, and examples differ by different amounts. For example, the angle in H2S (92°) differs from the tetrahedral angle by much more than the angle for H2O (104.48°) does.

Atoms bonded to
central atom
Lone pairsElectron domains
(Steric number)
ShapeIdeal bond angle
(example's bond angle)
ExampleImage
202 linear 180° CO2 Linear-3D-balls.png
303 trigonal planar 120° BF3 Trigonal-3D-balls.png
213 bent 120° (119°) SO2 Bent-3D-balls.png
404 tetrahedral 109.5° CH4 AX4E0-3D-balls.png
314 trigonal pyramidal 109.5° (106.8°) [10] NH3 Pyramidal-3D-balls.png
224 bent 109.5° (104.48°) [11] [12] H2O Bent-3D-balls.png
505 trigonal bipyramidal 90°, 120° PCl5 Trigonal-bipyramidal-3D-balls.png
415 seesaw ax–ax 180° (173.1°),
eq–eq 120° (101.6°),
ax–eq 90°
SF4 Seesaw-3D-balls.png
325 T-shaped 90° (87.5°), 180° (175°) ClF3 T-shaped-3D-balls.png
235 linear 180° XeF2 Linear-3D-balls.png
606 octahedral 90°, 180° SF6 AX6E0-3D-balls.png
516 square pyramidal 90° (84.8°) BrF5 Square-pyramidal-3D-balls.png
426 square planar 90°, 180° XeF4 Square-planar-3D-balls.png
707 pentagonal bipyramidal 90°, 72°, 180° IF7 Pentagonal-bipyramidal-3D-balls.png
617 pentagonal pyramidal 72°, 90°, 144°XeOF5 Pentagonal-pyramidal-3D-balls.png
527 pentagonal planar 72°, 144° XeF5 Pentagonal-planar-3D-balls.png
808 square antiprismatic XeF2−8 Square-antiprismatic-3D-balls.png
909 tricapped trigonal prismatic ReH2−9 AX9E0-3D-balls.png

In art

Molecule Art is a relatively obscure form of abstract art in which Molecular Geometry, most often a skeletal formation.

3D representations

Formic-acid-3D-stick.png
L-aspartic-acid-3D-sticks.png
ATP-xtal-3D-sticks.png
Endohedral fullerene.png
NorbornylCation ElectronDensity.jpg
WinsteinYellow.jpg
Methanol-3D-balls.png
Methanol struktur.png
PropyleneGlycol-stickAndBall.png
3LRI SolutionStructureAndBackboneDynamicsOfHumanLong arg3 insulin-Like Growth Factor 1 02.png
Methanol.pdb.png
Ubiquitin spheres.png
P-cresol-spaceFilling.png
3GF1 Insulin-Like Growth Factor Nmr 10 01.png
Beta-meander1.png
MreB.png
Anthrax toxin protein key motif.svg
8tim TIM barrel.png

The greater the amount of lone pairs contained in a molecule, the smaller the angles between the atoms of that molecule. The VSEPR theory predicts that lone pairs repel each other, thus pushing the different atoms away from them.

See also

Related Research Articles

<span class="mw-page-title-main">Coordination complex</span> Molecule or ion containing ligands datively bonded to a central metallic atom

A coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds, especially those that include transition metals, are coordination complexes.

<span class="mw-page-title-main">Molecule</span> Electrically neutral group of two or more atoms

A molecule is a group of two or more atoms that are held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions.

<span class="mw-page-title-main">Energy level</span> Different states of quantum systems

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.

<span class="mw-page-title-main">Structural formula</span> Graphic representation of a molecular structure

The structural formula of a chemical compound is a graphic representation of the molecular structure, showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bonding within the molecule is also shown, either explicitly or implicitly. Unlike other chemical formula types, which have a limited number of symbols and are capable of only limited descriptive power, structural formulas provide a more complete geometric representation of the molecular structure. For example, many chemical compounds exist in different isomeric forms, which have different enantiomeric structures but the same molecular formula. There are multiple types of ways to draw these structural formulas such as: Lewis structures, condensed formulas, skeletal formulas, Newman projections, Cyclohexane conformations, Haworth projections, and Fischer projections.

<span class="mw-page-title-main">Lone pair</span> Pair of valence electrons which are not shared with another atom in a covalent bond

In science, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bond and is sometimes called an unshared pair or non-bonding pair. Lone pairs are found in the outermost electron shell of atoms. They can be identified by using a Lewis structure. Electron pairs are therefore considered lone pairs if two electrons are paired but are not used in chemical bonding. Thus, the number of electrons in lone pairs plus the number of electrons in bonds equals the number of valence electrons around an atom.

Gas electron diffraction (GED) is one of the applications of electron diffraction techniques. The target of this method is the determination of the structure of gaseous molecules, i.e., the geometrical arrangement of the atoms from which a molecule is built up. GED is one of two experimental methods to determine the structure of free molecules, undistorted by intermolecular forces, which are omnipresent in the solid and liquid state. The determination of accurate molecular structures by GED studies is fundamental for an understanding of structural chemistry.

<span class="mw-page-title-main">VSEPR theory</span> Model for predicting molecular geometry

Valence shell electron pair repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds, the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp3 mixtures in a tetrahedral arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.

<span class="mw-page-title-main">Trigonal pyramidal molecular geometry</span> Molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base

In chemistry, a trigonal pyramid is a molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base, resembling a tetrahedron (not to be confused with the tetrahedral geometry). When all three atoms at the corners are identical, the molecule belongs to point group C3v. Some molecules and ions with trigonal pyramidal geometry are the pnictogen hydrides (XH3), xenon trioxide (XeO3), the chlorate ion, ClO
3
, and the sulfite ion, SO2−
3
. In organic chemistry, molecules which have a trigonal pyramidal geometry are sometimes described as sp3 hybridized. The AXE method for VSEPR theory states that the classification is AX3E1.

<span class="mw-page-title-main">Trigonal bipyramidal molecular geometry</span> Molecular structure with atoms at the center and vertices of a triangular bipyramid

In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid. This is one geometry for which the bond angles surrounding the central atom are not identical, because there is no geometrical arrangement with five terminal atoms in equivalent positions. Examples of this molecular geometry are phosphorus pentafluoride, and phosphorus pentachloride in the gas phase.

<span class="mw-page-title-main">Octahedral molecular geometry</span> Molecular geometry

In chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa. The octahedron is one of the Platonic solids, although octahedral molecules typically have an atom in their centre and no bonds between the ligand atoms. A perfect octahedron belongs to the point group Oh. Examples of octahedral compounds are sulfur hexafluoride SF6 and molybdenum hexacarbonyl Mo(CO)6. The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves. For example, [Co(NH3)6]3+, which is not octahedral in the mathematical sense due to the orientation of the N−H bonds, is referred to as octahedral.

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.

<span class="mw-page-title-main">Tetrahedral molecular geometry</span> Central atom with four substituents located at the corners of a tetrahedron

In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The bond angles are cos−1(−13) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as in methane as well as its heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong to point group Td, but most tetrahedral molecules have lower symmetry. Tetrahedral molecules can be chiral.

<span class="mw-page-title-main">Bent's rule</span> Rule in geometry of individual molecules

In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:

Atomic s character concentrates in orbitals directed toward electropositive substituents.

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.

<span class="mw-page-title-main">Seesaw molecular geometry</span> Structural molecular geometry

Disphenoidal or seesaw is a type of molecular geometry where there are four bonds to a central atom with overall C2v molecular symmetry. The name "seesaw" comes from the observation that it looks like a playground seesaw. Most commonly, four bonds to a central atom result in tetrahedral or, less commonly, square planar geometry.

<span class="mw-page-title-main">Linear molecular geometry</span> 3D shape of molecules in which all bond angles are 180°

The linear molecular geometry describes the geometry around a central atom bonded to two other atoms placed at a bond angle of 180°. Linear organic molecules, such as acetylene, are often described by invoking sp orbital hybridization for their carbon centers.

<span class="mw-page-title-main">Bent molecular geometry</span>

In chemistry, molecules with a non-collinear arrangement of two adjacent bonds have bent molecular geometry, also known as angular or V-shaped. Certain atoms, such as oxygen, will almost always set their two (or more) covalent bonds in non-collinear directions due to their electron configuration. Water (H2O) is an example of a bent molecule, as well as its analogues. The bond angle between the two hydrogen atoms is approximately 104.45°. Nonlinear geometry is commonly observed for other triatomic molecules and ions containing only main group elements, prominent examples being nitrogen dioxide (NO2), sulfur dichloride (SCl2), and methylene (CH2).

<span class="mw-page-title-main">T-shaped molecular geometry</span> Type of molecular geometry

In chemistry, T-shaped molecular geometry describes the structures of some molecules where a central atom has three ligands. Ordinarily, three-coordinated compounds adopt trigonal planar or pyramidal geometries. Examples of T-shaped molecules are the halogen trifluorides, such as ClF3.

<span class="mw-page-title-main">Isomer</span> Chemical compounds with the same molecular formula but different atomic arrangements

In chemistry, isomers are molecules or polyatomic ions with identical molecular formula – that is, the same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism refers to the existence or possibility of isomers.

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