package Chemistry::PointGroup::T;
use 5.008001;
use strict;
use warnings;
our $VERSION = '0.01';
my $h = 12; # number of group elements
my @R = qw( E C3 C3_2 C2 ); # symmetry elements of T
my @hi = qw( 1 4 4 3 ); # number of elements in the i-th class
my @I = qw( A E T ); # irreducible representations
my %R;
@R{@R}=@hi;
# characters of the irreducible representations of T
my @A = qw( 1 1 1 1 );
my @E = qw( 2 -1 -1 2 );
my @T = qw( 3 0 0 -1 );
# my (%A, %E, %T);
# @A{@R} = @A; # A
# @E{@R} = @E; # E
# @T{@R} = @T; # T
sub new {
my $type = shift;
$type = ref($type) || $type;
my %Ur = @_;
return bless \%Ur, $type;
}
sub character_tables {
return <<'TABLE';
+----+------------------------+-------+
| T | E 4C3 4C3_2 3C2 | |
+----+------------------------+-------+
| A | 1 1 1 1 | |
| E | 2 -1 -1 2 | |
| T | 3 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))
# in the same order of @hi
my @rr = ($X_E, $X_C3, $X_C3_2, $X_C2);
# Irreducible representation
my $s = 0;
my $n_A = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A[$_] , $s] } (0..$#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 $n_T = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T[$_] , $s] } (0..$#hi))[-1]->[1];
my @ri = ($n_A, $n_E, $n_T);
my %ri = ();
@ri{@I} = @ri;
return %ri;
}
1;
__END__
=head1 NAME
Chemistry::PointGroup::T - Point group T
=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