[Dolphinsiu]

For trans-M(CO)3(PR3)2, D3h point group,

D3h              E    2 C3   3 C2     sigma h    2 S3    3 sigma v
Red.(CO)       3      0       1            3         0           1

Red.(CO) = A1' + E' (That's what my professor writes)

Actually I don't know why Red.(CO) = A1' + E', which is read from the character table?

Also the same problem, for D5h point group,

D5h              E   2 C5   2 C5^2  5 C2  sigma h  2 S5  2 S5^3   5 sigma v
Red.             7     2          2        1       5          0       0              3

Also, my professor writes Red. = 2A' + E' + E2' + A2''

How this reducible representation comes from??? Thank you!

[Alpha-Omega]

Please see the two attached Word Documents:  D_3h Point Group and D_5h Point Group.

[Dolphinsiu]

Thank you very much! Do you have all character table for all point group symmetry (except D3h,D5h as you have given) for the downloading? Or a website that can check character table? Thank you!

[Alpha-Omega]

Here you go:

This site gives you all the Point Group Symmetry Tables (i.e., click on a point group symmetry symbol to get irreducible representations, character and product tables):

http://www.webqc.org/symmetry.php


Point Group Symmetry:

http://www.phys.ncl.ac.uk/staff/njpg/symmetry/


Molecular Symmetry On-Line:

http://telem.openu.ac.il/symmetry/


Point Group Flow Chart:

http://www.science.siu.edu/chemistry/tyrrell/group_theory/sym1.html


This website offers a reduction operator calculator:
This calculator allows you to reduce a reducible representation for a wide range of chemically relevant point groups using the reduction operator. Note there is a link below the calculator that allows you to change the point group.

http://www.hull.ac.uk/chemistry/reductionOperator.php?group=d5h


This site explains the conventions for symmetry notation.  It explains that Conventions of the symmetry notations are given in the paper: R. S. Mulliken,. J. Chem. Phys., 23, (1955) 1997.

http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/40_conventions_for_symmetry_notations.html


The following are web pages are also extremely useful:


Introduction To Symmetry and Poit Groups (includes examples of construction):

http://chemistry.umeche.maine.edu/Modeling/symmetry.html


This is one of my favorites:

http://www.reciprocalnet.org/edumodules/symmetry/


This offers exercises in Point Group Symmetry-great practice for modeling the operations:

http://www.ch.ic.ac.uk/vchemlab/symmetry/

P.S. I fixed the TYPOS in thos attachments 

[Dolphinsiu]

Thank you very much!

[Alpha-Omega]

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