# Symmetry Adapted Linear Combination (SALC)

SALC is a method to combine TWO OR MORE orbitals into one group and to see how they behave as a group. The behavior is influenced by each other and by the orbital from the central atom. The treatment of SALC is somehow similar to that of central orbital.

The rule is as followed: If the symmetry operation does not change the orbital position = +1 If the symmetry operation changes the orbital position = 0 If the symmetry operation does not change the orbital position but changes the sign = -1 (It is very important to remember that changing position has the priority over changing sign)

Symmetry Adapted Linear Combinations are helpful in getting a three dimensional picture of how all aspects of binding works. This means it shows how the s, p and d bindings occur with respect to electron densities and their respective spin states. Different models are matched to see how a molecule will bond in an energetically favorable path and an equally unfavorable path. These are called binding and anti-bonding pairs. When there are lone pairs, there is not really a SALC because no combination of electron densities occur. [1]

Symmetry adapted linear combination models are done with knowledge of a molecular orbital. With both the use of a molecular orbital and symmetry adapted linear combination models, there can be a great deal of knowledge about how a molecule bonds with each ligand. The molecular orbital diagram helps to show all the states in which the molecule fills electrons, and their respective energy levels with respect to each other. In essence, using molecular orbital diagrams and symmetry adapted linear combination models, we can predict where electrons are most likely to be found and why. SALCs allow us to get a better understanding of how molecules exist in terms of how binding and spin states relate. [1]

1. ā a b symmetry adapted linear combinations, November 14th, 2012.

# Example

The example showing here is hydrogen atoms on water molecule.

The reducible and irreducible representation of the hydrogen atoms on water molecule

E = A stays at A, B stays at B = 1 + 1 = 2 C2 = A changes position to B, B changes position to A = 0 + 0 = 0 Sigma v (xz) = A statys at A, and B stays at B = 1 + 1 = 2 Sigma vā (yz) = A changes position to B, and B changes position to A = 0 + 0 = 0 So the reducible representations are 2 0 2 0 With simple reduction, one can tell that this can be reduced to A1 ( 1 1 1 1) and B1 ( 1 -1 1 -1)

Below is the outcome of the SALCs

File:The salcs.png
The SALCs made up of water s orbitals

# Reference

"Fourier Transform Infrared Spectroscopy (FTIR)." UC Davis Chem Wiki. N.p., n.d. Web. 8 Nov. 2012. <Fourier Transform Infrared Spectroscopy (FTIR)>.

"Symmetry Elements." N.p., n.d. Web. 09 Nov. 2012. <http://myphayao.com/symmetry-elements-examples/>.

Figueroa, Joshua. "Intro to Symmetry and Symmetry Element." Inorganic Chemistry. University of California, San Diego, La Jolla. Oct. 2012. Lecture.

Figueroa, Joshua. "Symmetry operation and character table." Inorganic Chemistry. University of California, San Diego, La Jolla. Oct. 2012. Lecture.

Figueroa, Joshua. "Character tables, irreducible representations of central atom." Inorganic Chemistry. University of California, San Diego, La Jolla. Oct. 2012. Lecture.

Figueroa, Joshua. "Symmetry elements and point groups." Inorganic Chemistry. University of California, San Diego, La Jolla. Oct. 2012. Lecture.

Figueroa, Joshua. "SALCS, molecular orbital diagrams and high symmetry point groups." Inorganic Chemistry. University of California, San Diego, La Jolla. Oct. 2012. Lecture.

"Symmetry Resources." Otterbein University. N.p., n.d. Web. 20 Nov. 2012. <http://symmetry.otterbein.edu/>.

"Point Group Symmetry Character Tables - Chemistry Online Education." Point Group Symmetry Character Tables - Chemistry Online Education. N.p., n.d. Web. 20 Nov. 2012. <http://www.webqc.org/symmetry.php>.

Miessler, Gary L., and Donald A. Tarr. Inorganic Chemistry. Upper Saddle River, NJ: Pearson Prentice Hall, 2011. Print.