correspondence principle

Examples of correspondence principle in the following topics:

• Introduction

  • The portion of the infrared region most useful for analysis of organic compounds is not immediately adjacent to the visible spectrum, but is that having a wavelength range from 2,500 to 16,000 nm, with a corresponding frequency range from 1.9*1013 to 1.2*1014 Hz.
  • Consequently, virtually all organic compounds will absorb infrared radiation that corresponds in energy to these vibrations.
  • Infrared spectrometers, similar in principle to the UV-Visible spectrometer described elsewhere, permit chemists to obtain absorption spectra of compounds that are a unique reflection of their molecular structure.

• Indeterminacy and Probability Distribution Maps

  • This quantum uncertainty principle can also be expressed in terms of other variables.
  • Recall from the uncertainty principle that we cannot simultaneously know an electron's position and velocity—therefore we are unable to determine its trajectory.
  • The clouds of probability do not look like nor do they correspond to classical orbits.
  • The uncertainty principle prevents us from knowing how the electron gets from one place to another, and so an orbit really does not exist as such.

• The Building-Up (Aufbau) Principle

  • The Aufbau principle determines an atom's electron configuration by adding electrons to atomic orbitals following a defined set of rules.
  • The values ℓ = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively.
  • According to the Pauli Exclusion Principle, two electrons in an orbital will not spin the same way.
  • This assumption is approximately true—enough for the principle to be useful—but not physically reasonable.
  • Each diagonal read arrow corresponds to a different value of n + l.

• Free Energy Changes for Nonstandard States

  • Note that the origin corresponds to the composition at which half of the reactants have been converted into products.
  • In contrast, there is only a single value (point 2) of $\Delta G^{\circ}$, corresponding to the composition at which $\Delta G$ = 0 (point 1).
  • The equilibrium point of such a reaction would be at the origin, corresponding to half the reactants being converted to products.
  • The important principle to understand is that a negative $\Delta G^{\circ}$ does not mean that the reactants will be completely transformed into products.

• Changes in Concentration

  • The effect of changes in the concentration of products and reactants in a reversible reaction can be predicted by Le Chatelier's Principle.
  • This principle has a variety of names; in chemistry it is known as Le Chatelier's principle.
  • In turn, the rate of reaction, extent, and yield of products will be altered in correspondence with the impact on the system.
  • Using Le Chatelier's principle, we can predict that the amount of methanol will increase, decreasing the total change in CO.

• Electron Configurations and Magnetic Properties of Ions

  • The Aufbau principle (from the German Aufbau, meaning "building up, construction;" also called the Aufbau rule or building-up principle) is used to determine the electron configuration of an atom, molecule, or ion.
  • The principle postulates a hypothetical process in which an atom is "built up" by the progressive addition of electrons.
  • The number of electrons that can occupy each orbital is limited by the Pauli exclusion principle.
  • Each diagonal red arrow corresponds to a different value of n + l.
  • The periodic table can be broken into blocks, corresponding to the highest energy electrons.

• Periods 1 through 3

  • The principle of valence emerged, attributable to the presence or absence of electrons and the energy of those electrons in the volume around an atom's nucleus.
  • Electron are organized in energy levels or electron shells, which correspond to the periods on the periodic table.
  • The Aufbau principle describes the incremental filling of orbitals and building atoms with known electronic configurations.

• Crystal Structure: Packing Spheres

  • In principle, one can reconstruct the structure of an entire crystal by repeating the unit cell so as to create a three-dimensional lattice.
  • Each sphere that participates in a crystal structure has a coordination number, which corresponds to the number of spheres within the crystalline structure that touch the sphere that is being evaluated.

• Bonding and Antibonding Molecular Orbitals

  • For a corresponding σ-bonding orbital, such an orbital would be symmetrical, but are differentiated from it by an asterisk, as in σ*.
  • For a π-bond, corresponding bonding and antibonding orbitals would not have such symmetry around the bond axis, and are designated π and π* respectively.
  • The Aufbau principle states that orbitals are filled starting with the lowest energy
  • The Pauli exclusion principle states that the maximum number of electrons. occupying an orbital is two, with opposite spins.

• Pericyclic Reactions

  • The four principle classes of pericyclic reactions are termed: Cycloaddition, Electrocyclic, Sigmatropic, and Ene Reactions.
  • Corresponding intramolecular reactions, which create an additional ring, are well known.