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Leo Manfredi > Chemistry-PointGroup-0.01 > Chemistry::PointGroup



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Chemistry::PointGroup - Group theory for normal modes of vibration


        # the benzene molecule 
        use Chemistry::PointGroup::D6h;
        my @R = Chemistry::PointGroup::D6h->symmetry_elements;
        my @Ur = qw(12 0 0 0 4 0 0 0 0 12 0 4);
        my %Ur;
        my $mol = new Chemistry::PointGroup::D6h( %Ur );
        my %ri_mol = $mol->irr;
        print "Irreducible Representations:\n";
        print map {$ri_mol{$_}," ",$_,"\t"} sort keys %ri_mol;

        print "\n\n";
        my $benzene = 
               E => 12, C6 => 0, C3 => 0, C2 => 0, C2f => 4, C2s => 0,
                         i => 0,  S3 => 0, S6 => 0, sh => 12, sd => 0, sv => 4);
        my %ri_benzene = $benzene->irr;
        print "Irreducible Representations:\n";
        print map{$ri_benzene{$_}," ", $_,"\t"} sort keys %ri_benzene;
        print "\n";
        print "Normal Modes: ", $benzene->normal_modes,"\n";
        print "Table of Characters\n", 
                        Chemistry::PointGroup::D6h->character_tables, "\n\n";

        # methane
        use Chemistry::PointGroup::Td;
        my @sy = Chemistry::PointGroup::Td->symmetry_elements;
        print "Symmetry elements: @sy\n";
        print "CH4\n";
        my $met = Chemistry::PointGroup::Td->new( 
                        E => 5, C3 => 2, C2 => 1, S4 => 1, sd => 3);
        my %ri_met = $met->irr;
        print "Irreducible Representations:\n";
        print map{$ri_met{$_}," ", $_, "\t"} sort keys %ri_met;
        print "\n";
        print "Normal Modes: ", $met->normal_modes,"\n";
        print "Table of Characters\n", $met->character_tables, "\n\n";
        # ammonia
        use Chemistry::PointGroup::C3v;
        print "NH3\n";
        my $am = Chemistry::PointGroup::C3v->new(E => 4, C3 => 1, sv => 2);
        my %ri_am = $am->irr;
        print "Irreducible Representations:\n";
        print map{$ri_am{$_}," ",$_,"\t"} sort keys %ri_am;
        print "\n";
        print "Normal Modes: ", $am->normal_modes,"\n";
        print "Table of Characters\n", $am->character_tables, "\n\n";
        # CHCl3
        use Chemistry::PointGroup::C3v;
        print "CHCl3\n";
        my $cl = Chemistry::PointGroup::C3v->new(E => 5, C3 => 2, sv => 3);
        my %ri_cl = $cl->irr;
        print "Irreducible Representations:\n";
        print map{$ri_cl{$_}," ", $_,"\t"} sort keys %ri_cl;
        print "\n";
        print "Normal Modes: ", $cl->normal_modes,"\n";
        print "Table of Characters\n", $cl->character_tables, "\n\n";

        # Trans N2F2
        use Chemistry::PointGroup::C2h;
        my @sy = Chemistry::PointGroup::C2h->symmetry_elements;
        print "Symmetry elements: @sy\n";
        print "Trans N2F2\n";
        my $nf = Chemistry::PointGroup::C2h->new( E => 4, C2 => 0, i => 0, sh=> 4);
        my %ri_nf = $nf->irr;
        print "Irreducible Representations:\n";
        print map{$ri_nf{$_}," ", $_, "\t"} sort keys %ri_nf;
        print "\n";
        print "Normal Modes: ", $nf->normal_modes,"\n";
        print "Table of Characters\n", $nf->character_tables, "\n\n";


Many common molecules, for example, water, ammonia, methane,etc., possess some symmetry. In calculating the normal modes and frequencies of vibration, symmetry considerations can reduce enormously the labor of the calculations. The symmetry and geometry of a molecular model can be used to determine the number and symmetry of fundamental frequencies, their degeneracies, the selection rules for the infrared and Raman spectra.


$mol = Chemistry::PointGroup::XX->new( %U )

Create a new Chemistry::PointGroup::XX object, where XX is a point group. The value of %U is the number of atoms which are not shifted when the symmetry operation R acts on the atoms of the molecule. The key of %U is the symmetry operation.

$table = $mol->character_tables

Return the table of characters

@R = $mol->symmetry_elements

Return the symmetry operations

$modes = $mol->normal_modes

Return the number of normal modes of vibration

%ri = $mol->irr

Return the Irreducible Representations for the vibrations. The key of %ri is the irreducible representations and the value is the number of this representation

See Molecular vibrations The Theory of Infrared and Raman Vibrational Spectra, E.B. Wilson, J.C. Decius and P.C. Cross, Dover - ISBN 0-486-63941-X




Chemistry::PointGroup::C1, Chemistry::PointGroup::Ci,
Chemistry::PointGroup::Cs, Chemistry::PointGroup::C2,
Chemistry::PointGroup::C2h, Chemistry::PointGroup::C2v,
Chemistry::PointGroup::D2, Chemistry::PointGroup::D2h,
Chemistry::PointGroup::C4, Chemistry::PointGroup::S4,
Chemistry::PointGroup::C4h, Chemistry::PointGroup::C4v,
Chemistry::PointGroup::D2d, Chemistry::PointGroup::D4,
Chemistry::PointGroup::D4h, Chemistry::PointGroup::C3,
Chemistry::PointGroup::S6, Chemistry::PointGroup::C3v,
Chemistry::PointGroup::D3, Chemistry::PointGroup::D3d,
Chemistry::PointGroup::C3h, Chemistry::PointGroup::C6,
Chemistry::PointGroup::C6h, Chemistry::PointGroup::D3h,
Chemistry::PointGroup::C6v, Chemistry::PointGroup::D6,
Chemistry::PointGroup::D6h, Chemistry::PointGroup::T,
Chemistry::PointGroup::Th, Chemistry::PointGroup::Td,
Chemistry::PointGroup::O, Chemistry::PointGroup::Oh,


Leo Manfredi, <>


Copyright 2006 by Leo Manfredi

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

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