package Chemistry::PointGroup::Th;
use 5.008001;
use strict;
use warnings;
our $VERSION = '0.01';
my $h = 24; # number of group elements
my @R = qw( E C3 C3_2 C2 i S6 S6_5 sh ); # symmetry elements of Th
my @hi = qw( 1 4 4 3 1 4 4 4 3 ); # number of elements in the i-th class
my @I = qw( Ag Au Eg Eu Tg Tu ); # irreducible representations
my %R;
@R{@R}=@hi;
# characters of the irreducible representations of Th
my @Ag = qw( 1 1 1 1 1 1 1 1 );
my @Au = qw( 1 1 1 1 -1 -1 -1 -1 );
my @Eg = qw( 2 -1 -1 2 2 -1 -1 2 );
my @Eu = qw( 2 -1 -1 2 -2 1 1 -2 );
my @Tg = qw( 3 0 0 -1 1 0 0 -1 );
my @Tu = qw( 3 0 0 -1 -1 0 0 1 );
# my (%Ag, %Au, %Eg, %Eu, %Tg, %Tu);
# @Ag{@R} = @Ag; # Ag
# @Au{@R} = @Au; # Au
# @Eg{@R} = @Eg; # Eg
# @Eu{@R} = @Eu; # Eu
# @Tg{@R} = @Tg; # Tg
# @Tu{@R} = @Tu; # Tu
sub new {
my $type = shift;
$type = ref($type) || $type;
my %Ur = @_;
return bless \%Ur, $type;
}
sub character_tables {
return <<'TABLE';
+-----+---------------------------------------------+-------+
| Th | E 4C3 4C3_2 3C2 i 4S6 4S6_5 3sh | |
+-----+---------------------------------------------+-------+
| Ag | 1 1 1 1 1 1 1 1 | |
| Au | 1 1 1 1 -1 -1 -1 -1 | |
| Eg | 2 -1 -1 2 2 -1 -1 2 | |
| Eu | 2 -1 -1 2 -2 1 1 -2 | |
| Tg | 3 0 0 -1 1 0 0 -1 | |
| Tu | 3 0 0 -1 -1 0 0 1 | x,y,x |
+-----+---------------------------------------------+-------+
TABLE
}
sub symmetry_elements {
return @R;
}
sub normal_modes {
my $self = shift;
return (3 * $self->{E} - 6);
}
sub irr {
my $self = shift;
# proper operations ( Ur - 2 ) (1 + 2 cos(r))
my $X_E = sprintf "%0.f", ($self->{E} - 2) * (1 + 2 * 1);
my $X_C3 = sprintf "%0.f", ($self->{C3} - 2) * (1 + 2 * (-0.5));
my $X_C3_2 = sprintf "%0.f", ($self->{C3_2} - 2) * (1 + 2 * (-0.5));
my $X_C2 = sprintf "%0.f", ($self->{C2} - 2) * (1 + 2 * (-1));
# improper operations Ur (-1 + 2 cos(r))
my $X_i = sprintf "%0.f", $self->{i} * (-1 + 2 * (-1));
my $X_S6 = sprintf "%0.f", $self->{S6} * (-1 + 2 * (0.5));
my $X_S6_5 = sprintf "%0.f", $self->{S6_5} * (-1 + 2 * (0.5));
my $X_sh = sprintf "%0.f", $self->{sh} * (-1 + 2 * 1);
# in the same order of @hi
my @rr = ($X_E, $X_C3, $X_C3_2, $X_C2, $X_i, $X_S6, $X_S6_5, $X_sh);
# Irreducible representation
my $s = 0;
my $n_Ag = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $Ag[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_Au = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $Au[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_Eg = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $Eg[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_Eu = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $Eu[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_Tg = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $Tg[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_Tu = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $Tu[$_] , $s] } (0..$#hi))[-1]->[1];
my @ri = ($n_Ag, $n_Au, $n_Eg, $n_Eu, $n_Tg, $n_Tu);
my %ri = ();
@ri{@I} = @ri;
return %ri;
}
1;
__END__
=head1 NAME
Chemistry::PointGroup::Th - Point group Th
=head1 SYNOPSIS
see L<Chemistry::PointGroup>
=head1 DESCRIPTION
see L<Chemistry::PointGroup>
=head1 SEE ALSO
L<Chemistry::PointGroup>
=head1 AUTHOR
Leo Manfredi, E<lt>manfredi@cpan.orgE<gt>
=head1 COPYRIGHT AND LICENSE
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.
=cut