4448 PCHEM TERMS - Symmetry and Computational Chemistry

Even Function

Function is symmetric with respect to the origin; f(x) = f(-x)

from class notes, entered by Dr. Williams

Odd Function

Function is asymmetric with respect to the origin; f(-x)=-f(x)

from class notes, entered by Dr. Williams

Identity Symmetry Element, "E"

Mathematically, this symmetry element is the same as multiplying every coordinate by 1. Nothing changes. Every object possesses this symmetry element.

Atkins', Physical Chemistry 11th edition, pg 390, entered by Ryan Phillips. edited by DW

Horizontal Reflection Symmetry Element, "sigma-h"

This mirror plane is perpendicular to the principal axis.

Atkins', Physical Chemistry 11th edition, pg 389, entered by Ryan Phillips. edited by DW

Inversion Symmetry Element, "i"

Each point in a molecule is imagined as being moved in a straight line to the center of the molecule (the centre of symmetry) and out the same distance on the other side.

Atkins', Physical Chemistry 11th edition, pg 389, entered by Ryan Phillips.

Dashed bond (in a molecular structure)

lines represent bonds away from the viewer (behind the plane)

By Megan Mann

Wedge bond (in a molecular structure)

bonds towards the viewer (in front of the plane)

By Megan Mann

character table

Tables showing all the characters of the operations of a group. The symmetries of every motion and wave function are contained in this table.

Atkins', Physical Chemistry 11th edition, pg 401, By Megan Mann edited by DW

vertical reflection plane of symmetry sigma-v

This plane contains the principal axis in a vertical direction and contains more bonds than the other vertical plane. Atkins', Physical Chemistry 11th edition, pg389, By Megan Mann edited by DW

dihedral reflection plane of symmetry sigma-d

This plane contains the principal axis in a vertical direction, and contains fewer bonds than the other vertical plane. Atkins', Physical Chemistry 11th edition, pg 389, By Megan Mann edited by DW

reflection symmetry element (sigma)

The operation corresponding to a mirror plane that leaves the molecule unchanged.

Atkins', Physical Chemistry 11th edition, pg 389, By Megan Mann edited by DW

Schoenflies notation

Notation commonly used to classify molecules by their symmetry elements. This method uses a letter and subscripts to show the point group. ex C4v, D2h, C∞v, etc

Atkins', Physical Chemistry 11th edition, pg 390, entered by Patricia Hernandez edited by DW

symmetry operation

an action that leaves a molecule looking the same afterward, such as rotations, reflections, and inversions.

Atkins', Physical Chemistry 11th edition, pg 388, entered by Patricia Hernandez

symmetry element

a geometric item like a point, line, or plane that is used to reveal the symmetry of a molecule

Atkins', Physical Chemistry 11th edition, pg 388, entered by Patricia Hernandez edited by DW

Symmetry

A molecule possesses _________ when there are geometric operations that leave the molecule unchanged. From class notes, entered by Kyler Kelley edited by DW

Lewis Dot Theory

A simplified visual representation showing how pairs of electrons hold the atoms together in a molecule. This theory combines with VSEPR theory to produce 3D molecular geometries. From class notes, entered by Kyler Kelley edited by DW

Valence Shell Electron Pair Repulsion (VSEPR) Theory

This theory (a.k.a. Local Bond Theory) claims that each bond in a molecule consists of two local electrons. These electron pairs repel each other leading to various 3D shapes (tetrahedral, trigonal planar, etc) From class notes, entered by Kyler Kelley edited by DW

Mulliken Notation (of an irreducible representation)

This is the labeling of the rows of the character table. Each motion and electron orbital in a molecule will correspond to only one of these rows, entered by DW

Rotation Symmetry Element (C subscript n)

This geometric item is possessed by a molecule if rotation around the item by 360/n degrees leaves the molecule unchanged. Atkins', Physical Chemistry 11th edition, pg 389, entered by Ryan Phillips. edited by DW

Improper Rotation Symmetry Element (S subscript n)

This geometric item is possessed by a molecule if a rotation around the item by 360/n degrees and reflection through a perpendicular plane leaves the molecule unchanged. Atkins', Physical Chemistry 11th edition, pg 389, entered by Ryan Phillips. edited by DW

Direct Product Table

This table is used to track the symmetries in the integrand of the transition moment integral. This is a table that contains the results of all rows of a character table multiplied in all possible combinations. The product of any two rows of a character table will yield another row in the same character table (or a combination of rows). Atkins', Physical Chemistry 11th edition, pg 407, entered by Ryan Phillips. edited by DW

Asymmetric

A word meaning "not symmetric" or describing a condition where symmetry has been broken. By Megan Mann From lecture notes edited by DW

Point Group

A label (using Schoenflies Notation) that categorizes the symmetry of a molecule. Each _________ corresponds to a Character Table that reveals all the symmetry elements possessed by the molecule. Atkins', Physical Chemistry 11th edition, pg. 390, entered by Marrisa Martinez edited by DW

principal axis

The rotation axis (Cn) with the highest value of n. This is also used to define the z-axis used in the Character Table for that molecule. Atkins', Physical Chemistry 11th edition, pg. 389, entered by Marrisa Martinez edited by DW

polar molecule

molecule with a permanent electric dipole moment. examples are: HCl, O₃, NH₃

Atkins', Physical Chemistry 11th edition, pg. 394, entered by Marrisa Martinez

chiral molecule

a molecule that cannot be superimposed on its mirror image. these molecules are optically active.

Atkins', Physical Chemistry 11th edition, pg. 395, entered by Marrisa Martinez

achiral molecule

a molecule that can be superimposed on its mirror image.

Atkins', Physical Chemistry 11th edition, pg. 395, entered by Marrisa Martinez

Irreducible Representation

This is a row of the Character Table, labeled with Mulliken notation, and is a linearly independent vector representation of a motion, axis, or orbital of the molecule

By Kaylyn Keith from class notes, edited by DW

Reducible Representation

This is a combination of multiple rows of a Character Table, and is the sum of two or more irreducible representations

By Kaylyn Keith from class notes, edited by DW

gerade

German for even, used in Character Tables with inversion, used as a subscript g on the Mulliken notation if the character under inversion X(i) = +1. By Breanna Nelson from class notes, edited by DW

ungerade

German for uneven (odd), used in Character Tables with inversion, used as a subscript u on the Mulliken notation if the character under inversion X(i) = -1, By Breanna Nelson from class notes, edited by DW

Rayleigh scattering

Elastic scattering; the scattered photon has the same energy as the incident (incoming) photon. By Breanna Nelson from lecture 09 notes, edited by DW

Raman scattering

Inelastic scattering; the scattered photon has more or less energy than the incident (incoming) photon. By Breanna Nelson from lecture nine notes, edited by DW

Gaussian type orbital

an electron radial wave function in the form of e^(-r²). These can be computed much faster than the more accurate radial wave function e^(-r), which is why these are used in common computational chemistry software.

Atkins', Physical Chemistry 11th edition, pg 378, By Megan Mann edited by DW

ab initio method

Latin for "from initial", this calculation attempts to solve the electronic structure of molecules "from first principles" with minimal approximations. Atkins', Physical Chemistry 11th edition, pg 378, By Megan Mann, edited by DW

Semi-empirical method

a method for solving the electronic structure of molecules that treats valence electrons only and adjusts the nuclear charge (effective core potential) to reproduce experimental data such as ionization energies. Atkins', Physical Chemistry 11th edition, pg 378, By Megan Mann edited by DW

Density Functional Theory method

a method for solving the electronic structure of molecules using the electron density, ρ, rather than the wavefunction, ψ. Atkins', Physical Chemistry 11th edition, pg 379, By Megan Mann edited by DW

Isodensity surface

a surface of constant total electron density

Atkins', Physical Chemistry 11th edition, pg 379, By Megan Mann

Solvent accessible surface

The shape of a molecule generated by mapping the position of a sphere (representing a solvent molecule) rolling across the surface. Atkins', Physical Chemistry 11th edition, pg 379, By Megan Mann edited by DW

Electrostatic Potential (ESP) Map

The distribution of charge mapped over the electron density isosurface. Atkins', Physical Chemistry 11th edition, pg 379, By Megan Mann edited by DW

Red region on an ESP Map

An electron-rich region on an ESP Map, negative potential. Atkins', Physical Chemistry 11th edition, pg 379, By Megan Mann edited by DW

Blue region on an ESP Map

An electron-poor region on an ESP Map, positive potential, Atkins', Physical Chemistry 11th edition, pg 379, By Megan Mann edited by DW

Gaussian Line Shape

G = e^(-4Ln(2)(λ-λₙ→ₙ')²/∆λ²

The most common instrumental line shape, resulting from a normal distribution of random fluctuations. From lecture notes on Spectral Simulation, entered by Ryan Phillips. edited by DW

Lorentzian Line Shape

L = 1/(1+4(λ-λₙ→ₙ')²/∆λ²)

Also called the Natural Line Shape or the Uncertainty-limit Line Shape, and is only seen in very high resolution spectra. From lecture notes on Spectral Simulation, entered by Ryan Phillips. edited by DW

Voigt Line Shape

V = (aL(subscript ∆λ,n→n')(λ) + (1-a)G(subscript ∆λ,n→n')(λ))

This is a linear combination of the Gaussian and Lorentzian line shapes, and is only used when a high resolution spectrum is approaching the uncertainty limit. From lecture notes on Spectral Simulation, entered by Ryan Phillips. edited by DW

zero point energy

This is the energy of the lowest vibrational level (v = 0). The ______ is 1/2 the vibrational energy of that motion. Atkins', Physical Chemistry 11th edition, pg 274, By Phillip Paik edited by DW