package Chemistry::PointGroup::Td;
use 5.008001;
use strict;
use warnings;
our $VERSION = '0.01';
my $h = 24; # number of group elements
my @R = qw( E C3 C2 S4 sd ); # symmetry elements of Td
my @hi = qw( 1 8 3 6 6 ); # number of elements in the i-th class
my @I = qw( A1 A2 E T1 T2 ); # irreducible representations
my %R;
@R{@R}=@hi;
# characters of the irreducible representations of Td
my @A1 = qw( 1 1 1 1 1 );
my @A2 = qw( 1 1 1 -1 -1 );
my @E = qw( 2 -1 2 0 0 );
my @T1 = qw( 3 0 -1 1 -1 );
my @T2 = qw( 3 0 -1 -1 1 );
# my (%A1, %A2, %E, %T1, %T2);
# @A1{@R} = @A1; # A1
# @A2{@R} = @A2; # A2
# @E{@R} = @E; # E
# @T1{@R} = @T1; # T1
# @T2{@R} = @T2; # T2
sub new {
my $type = shift;
$type = ref($type) || $type;
my %Ur = @_;
return bless \%Ur, $type;
}
sub character_tables {
return <<'TABLE';
+-----+---------------------------+-------+
| Td | E 8C3 3C2 6S4 6sd | |
+-----+---------------------------+-------+
| A1 | 1 1 1 1 1 | |
| A2 | 1 1 1 -1 -1 | |
| E | 2 -1 2 0 0 | |
| T1 | 3 0 -1 1 -1 | |
| T2 | 3 0 -1 -1 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 $X_C2 = sprintf "%0.f", ($self->{C2} - 2) * (1 + 2 * (-1));
# improper operations Ur (-1 + 2 cos(r))
my $X_S4 = sprintf "%0.f", $self->{S4} * (-1 + 2 * (0));
my $X_sd = sprintf "%0.f", $self->{sd} * (-1 + 2 * 1);
# in the same order of @hi
my @rr = ($X_E, $X_C3, $X_C2, $X_S4, $X_sd);
# Irreducible representation
my $s = 0;
my $n_A1 = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A1[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_A2 = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A2[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_E = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $E[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_T1 = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T1[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_T2 = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T2[$_] , $s] } (0..$#hi))[-1]->[1];
my @ri = ($n_A1, $n_A2, $n_E, $n_T1, $n_T2);
my %ri = ();
@ri{@I} = @ri;
return %ri;
}
1;
__END__
=head1 NAME
Chemistry::PointGroup::Td - Point group Td
=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