Walsh diagram

Last updated
Walsh Diagram of an HAH molecule. Walsh diagram intro.svg
Walsh Diagram of an HAH molecule.

Walsh diagrams, often called angular coordinate diagrams or correlation diagrams, are representations of calculated orbital binding energies of a molecule versus a distortion coordinate (bond angles), used for making quick predictions about the geometries of small molecules. [1] [2] By plotting the change in molecular orbital levels of a molecule as a function of geometrical change, Walsh diagrams explain why molecules are more stable in certain spatial configurations (e.g. why water adopts a bent conformation). [3]

Contents

A major application of Walsh diagrams is to explain the regularity in structure observed for related molecules having identical numbers of valence electrons (e.g. why H2O and H2S look similar), and to account for how molecules alter their geometries as their number of electrons or spin state changes. Additionally, Walsh diagrams can be used to predict distortions of molecular geometry from knowledge of how the LUMO (Lowest Unoccupied Molecular Orbital) affects the HOMO (Highest Occupied Molecular Orbital) when the molecule experiences geometrical perturbation.

Walsh's rule for predicting shapes of molecules states that a molecule will adopt a structure that best provides the most stability for its HOMO. If a particular structural change does not perturb the HOMO, the closest occupied molecular orbital governs the preference for geometrical orientation. [4]

History

Walsh diagrams were first introduced by A.D. Walsh, a British chemistry professor at the University of Dundee, in a series of ten papers in one issue of the Journal of the Chemical Society . [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken. Specifically, Walsh calculated and explained the effect of changes in the shape of a molecule on the energy of molecular orbitals. Walsh diagrams are an illustration of such dependency, and his conclusions are what are referred to as the "rules of Walsh." [15]

In his publications, Walsh showed through multiple examples that the geometry adopted by a molecule in its ground state primarily depends on the number of its valence electrons. [16] He himself acknowledged that this general concept was not novel, but explained that the new data available to him allowed the previous generalizations to be expanded upon and honed. He also noted that Mulliken had previously attempted to construct a correlation diagram for the possible orbitals of a polyatomic molecule in two different nuclear configurations, and had even tried to use this diagram to explain shapes and spectra of molecules in their ground and excited states. [17] [18] However, Mulliken was unable to explain the reasons for the rises and falls of certain curves with increases in angle, thus Walsh claimed "his diagram was either empirical or based upon unpublished computations." [5]

Overview

Walsh originally constructed his diagrams by plotting what he described as "orbital binding energies" versus bond angles. What Walsh was actually describing by this term is unclear; some believe he was in fact referring to ionization potentials, however this remains a topic of debate. [19] At any rate, the general concept he put forth was that the total energy of a molecule is equal to the sum of all of the "orbital binding energies" in that molecule. Hence, from knowledge of the stabilization or destabilization of each of the orbitals by an alteration of the molecular bond angle, the equilibrium bond angle for a particular state of the molecule can be predicted. Orbitals which interact to stabilize one configuration (ex. Linear) may or may not overlap in another configuration (ex. Bent), thus one geometry will be calculably more stable than the other.

Typically, core orbitals (1s for B, C, N, O, F, and Ne) are excluded from Walsh diagrams because they are so low in energy that they do not experience a significant change by variations in bond angle. Only valence orbitals are considered. However, one should keep in mind that some of the valence orbitals are often unoccupied.

Generating Walsh diagrams

In preparing a Walsh diagram, the geometry of a molecule must first be optimized for example using the Hartree–Fock (HF) method [2] for approximating the ground-state wave function and ground-state energy of a quantum many-body system. [20] Next, single-point energies are performed for a series of geometries displaced from the above-determined equilibrium geometry. Single-point energies (SPEs) are calculations of potential energy surfaces of a molecule for a specific arrangement of the atoms in that molecule. In conducting these calculations, bond lengths remain constant (at equilibrium values) and only the bond angle should be altered from its equilibrium value. The single-point computation for each geometry can then be plotted versus bond angle to produce the representative Walsh diagram.

Structure of a Walsh diagram

A Walsh diagram for an AH2 molecule (e.g. H2O) Walshdiagram.gif
A Walsh diagram for an AH2 molecule (e.g. H2O)

AH2 Molecules

For the simplest AH2 molecular system, Walsh produced the first angular correlation diagram by plotting the ab initio orbital energy curves for the canonical molecular orbitals while changing the bond angle from 90° to 180°. As the bond angle is distorted, the energy for each of the orbitals can be followed along the lines, allowing a quick approximation of molecular energy as a function of conformation. It is still unclear whether or not the Walsh ordinate considers nuclear repulsion, and this remains a topic of debate. [21] A typical prediction result for water is a bond angle of 90°, which is not even close to the experimental derived value of 104°. At best the method is able to differentiate between a bent and linear molecule. [2]

This same concept can be applied to other species including non-hydride AB2 and BAC molecules, HAB and HAAH molecules, tetraatomic hydride molecules (AH3), tetraatomic nonhydride molecules (AB), H2AB molecules, acetaldehyde, pentaatomic molecules (CH3I), hexatomic molecules (ethylene), and benzene.

Reactivity

Walsh diagrams in conjunction with molecular orbital theory can also be used as a tool to predict reactivity. By generating a Walsh Diagram and then determining the HOMO/LUMO of that molecule, it can be determined how the molecule is likely to react. In the following example, the Lewis acidity of AH3 molecules such as BH3 and CH3+ is predicted.

Six electron AH3 molecules should have a planar conformation. It can be seen that the HOMO, 1e’, of planar AH3 is destabilized upon bending of the A-H bonds to form a pyramid shape, due to disruption of bonding. The LUMO, which is concentrated on one atomic center, is a good electron acceptor and explains the Lewis acid character of BH3 and CH3+. [22]

Walsh correlation diagrams can also be used to predict relative molecular orbital energy levels. The distortion of the hydrogen atoms from the planar CH3+ to the tetrahedral CH3-Nu causes a stabilization of the C-Nu bonding orbital, σ. [22]

A Walsh diagram for a planar AH3 molecule AH3walsh3.png
A Walsh diagram for a planar AH3 molecule
Orbital interaction diagram for nucleophilic addition to CH3 Nucleophilic2.gif
Orbital interaction diagram for nucleophilic addition to CH3

Other correlation diagrams

Other correlation diagrams are Tanabe-Sugano diagrams and Orgel diagrams.

See also

Related Research Articles

Molecular orbital Wave-like behavior of an electron in a molecule

In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

Robert S. Mulliken American physicist and chemist

Robert Sanderson Mulliken was an American physicist and chemist, primarily responsible for the early development of molecular orbital theory, i.e. the elaboration of the molecular orbital method of computing the structure of molecules. Mulliken received the Nobel Prize in Chemistry in 1966 and the Priestley Medal in 1983.

Lone pair Pair of valence electrons which are not shared with another atom in a covalent bond

In chemistry, 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.

In chemistry, molecular orbital theory is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century.

Molecular geometry Study of the 3D shapes of molecules

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.

In chemistry, a hypervalent molecule is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pentachloride, sulfur hexafluoride, chlorine trifluoride, the chlorite ion, and the triiodide ion are examples of hypervalent molecules.

VSEPR theory 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.

The Jahn–Teller effect is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science. The effect is named for Hermann Arthur Jahn and Edward Teller, who first reported studies about it in 1937. The Jahn–Teller effect, and the related Renner–Teller effect, are discussed in Section 13.4 of the spectroscopy textbook by Bunker and Jensen.

Bent bond Type of covalent bond in organic chemistry

In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a similar "bent" structure within small ring molecules, such as cyclopropane (C3H6) or as a representation of double or triple bonds within a compound that is an alternative to the sigma and pi bond model.

SIESTA (computer program)

SIESTA is an original method and its computer program implementation, to perform efficient electronic structure calculations and ab initio molecular dynamics simulations of molecules and solids. SIESTA's efficiency stems from the use of strictly localized basis sets and from the implementation of linear-scaling algorithms which can be applied to suitable systems. A very important feature of the code is that its accuracy and cost can be tuned in a wide range, from quick exploratory calculations to highly accurate simulations matching the quality of other approaches, such as plane-wave and all-electron methods.

Woodward–Hoffmann rules

The Woodward–Hoffmann rules, devised by Robert Burns Woodward and Roald Hoffmann, are a set of rules used to rationalize or predict certain aspects of the stereochemistry and activation energy of pericyclic reactions, an important class of reactions in organic chemistry. The rules are best understood in terms of the concept of the conservation of orbital symmetry using orbital correlation diagrams. The Woodward–Hoffmann rules are a consequence of the changes in electronic structure that occur during a pericyclic reaction and are predicated on the phasing of the interacting molecular orbitals. They are applicable to all classes of pericyclic reactions, including (1) electrocyclizations, (2) cycloadditions, (3) sigmatropic reactions, (4) group transfer reactions, (5) ene reactions, (6) cheletropic reactions, and (7) dyotropic reactions. Due to their elegance, simplicity, and generality, the Woodward–Hoffmann rules are credited with first exemplifying the power of molecular orbital theory to experimental chemists.

Bents rule

In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules 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.

Uranocene, U(C8H8)2, is an organouranium compound composed of a uranium atom sandwiched between two cyclooctatetraenide rings. It was one of the first organoactinide compounds to be synthesized. It is a green air-sensitive solid that dissolves in organic solvents. Uranocene, a member of the "actinocenes," a group of metallocenes incorporating elements from the actinide series. It is the most studied bis[8]annulene-metal system, although it has no known practical applications.

A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.

A halogen bond (XB) occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity. This type of interaction can be decomposed in terms of electrostatic, orbital mixing charge-transfer (CT) and dispersion terms. Halogen bonding occurs in various biological systems and processes, so it can be utilized in drug design.

Sextuple bond Covalent bond involving 12 bonding electrons

A sextuple bond is a type of covalent bond involving 12 bonding electrons and in which the bond order is 6. The only known molecules with true sextuple bonds are the diatomic dimolybdenum (Mo2) and ditungsten (W2), which exist in the gaseous phase and have boiling points of 4,639 °C (8,382 °F) and 5,930 °C (10,710 °F). There is strong evidence to believe that there is no element with atomic number below about 100 that can form a bond with a greater order than 6 between its atoms, but the question of possibility of such a bond between two atoms of different elements remains open. Bonds between heteronuclear systems with two atoms of different elements may not necessarily have the same limit.

Pople diagram

A Pople diagram or Pople's Diagram is a diagram which describes the relationship between various calculation methods in computational chemistry. It was initially introduced in January 1965 by Sir John Pople,, during the Symposium of Atomic and Molecular Quantum Theory in Florida. The Pople Diagram can be either 2-dimensional or 3-dimensional, with the axes representing ab inito methods, basis sets and treatment of relativity. The diagram attempts to balance calculations by giving all aspects of a computation equal weight.

Chemical bonding of water

Water is a simple triatomic bent molecule with C2v molecular symmetry and bond angle of 104.5° between the central oxygen atom and the hydrogen atoms. Despite being one of the simplest triatomic molecules, its chemical bonding scheme is nonetheless complex as many of its bonding properties such as bond angle, ionization energy, and electronic state energy cannot be explained by one unified bonding model. Instead, several traditional and advanced bonding models such as simple Lewis and VSEPR structure, valence bond theory, molecular orbital theory, isovalent hybridization, and Bent's rule are discussed below to provide a comprehensive bonding model for H
2O, explaining and rationalizing the various electronic and physical properties and features manifested by its peculiar bonding arrangements.

The bonding orbital is used in molecular orbital (MO) theory to describe the attractive interactions between the atomic orbitals of two or more atoms in a molecule. In MO theory, electrons are portrayed to move in waves. When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ constructive interference causes the density of the electrons to be found within the binding region, creating a stable bond between the two species.

References

  1. ↑ IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " correlation diagram ". doi : 10.1351/goldbook.C01348
  2. 1 2 3 Miller Carrie S (2015). "Walsh Diagrams: Molecular Orbital and Structure Computational Chemistry Exercise for Physical Chemistry". Journal of Chemical Education. 92: 1040–1043. doi:10.1021/ed500813d.
  3. ↑ Chen, E.; Chang, T. (1998). "Walsh Diagram and the Linear Combination of Bond Orbital Method". Journal of Molecular Structure: THEOCHEM . 431 (1–2): 127–136. doi:10.1016/S0166-1280(97)00432-6.
  4. ↑ Mulliken, R.S. (1955). "Structures of the Halogen Molecules and the Strength of Single Bonds". J. Am. Chem. Soc. 77 (4): 884–887. doi:10.1021/ja01609a020.
  5. 1 2 Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part I. AH2 Molecules". J. Chem. Soc. : 2260–2266. doi:10.1039/JR9530002260.
  6. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part II. AB2 and BAC Molecules". J. Chem. Soc. : 2266–2288. doi:10.1039/JR9530002266.
  7. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part III. HAB and HAAH Molecules". J. Chem. Soc. : 2288–2296. doi:10.1039/JR9530002288.
  8. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part IV. Tetratomic hydride molecules, AH3". J. Chem. Soc. : 2296–2301. doi:10.1039/JR9530002296.
  9. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part V. Tetratomic, non-hydride molecules, AB3". J. Chem. Soc. : 2301–2306. doi:10.1039/JR9530002301.
  10. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part VI. H2AB Molecules". J. Chem. Soc. : 2306–2317. doi:10.1039/JR9530002306.
  11. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part VII. A note on the near-ultra-violet spectrum of acetaldehyde". J. Chem. Soc. : 2318–2320. doi:10.1039/JR9530002318.
  12. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part VIII. Pentatomic molecules: CH3I Molecules". J. Chem. Soc. : 2321–2324. doi:10.1039/JR9530002321.
  13. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part IX. Hexatomic molecules: ethylene". J. Chem. Soc. : 2325–2329. doi:10.1039/JR9530002325.
  14. ↑ Walsh, A.D. (1953). "The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules. Part X. A note on the spectrum of benzene". J. Chem. Soc. : 2330–2331. doi:10.1039/JR9530002330.
  15. ↑ Mulliken, R.S. (1955). "Bond Angles in Water-Type and Ammonia-Type Molecules and Their Derivatives". J. Am. Chem. Soc. 77 (4): 887–891. doi:10.1021/ja01609a021.
  16. ↑ Walsh, A.D. (1976). "Some Notes on the Electronic Spectra of Small Polyatomic Molecules". Int. Rev. Sci.: Phys. Chem. Series 2. 3: 301–316.
  17. ↑ O'Leary, B.; Mallion, R.B. (1987). "Walsh Diagrams and the Hellman-Feynman Theorem: A Tribute to the Late Professor Charles A. Coulson, F.R.S. (1910-1974)". Journal of Mathematical Chemistry . 1 (4): 335–344. doi:10.1007/BF01205066.
  18. ↑ Atkins, P.W. (1970). Molecular Quantum Mechanics. Oxford, Massachusetts: Clarendon Press. ISBN   978-0-19-855129-4.
  19. ↑ Peters, D. (1966). "Nature of the One-Electron Energies of the Independent Electron Molecular Orbital Theoryand the Walsh Diagrams". Transactions of the Faraday Society . 6: 1353–1361.
  20. ↑ Chen, E.; Chang, T. (1997). "Orbital Interaction and the Mulliken-Walsh Diagram for AH2 Systems". Journal of the Chinese Chemical Society (Taipei) . 44: 559–565. doi:10.1002/jccs.199700086.
  21. ↑ Takahata, Y.; Parr, R.G. (1974). "Three Methods to Look at Walsh-type Diagrams Including Nuclear Repulsions". Bulletin of the Chemical Society of Japan . 47 (6): 1380–1386. doi: 10.1246/bcsj.47.1380 .
  22. 1 2 Atkins, P.W..; et al. (1970). Inorganic Chemistry: Shriver and Atkins. Oxford, U.K.: Oxford University Press. ISBN   978-0-19-926463-6.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.