package Chemistry::PointGroup::Oh;
use 5.008001;
use strict;
use warnings;
our $VERSION = '0.01';
my $h = 48; # number of group elements
my @R = qw( E C3 C2 C4 C2f i S4 S6 sh sd ); # symmetry elements of Oh
my @hi = qw( 1 8 6 6 3 1 6 8 3 6 ); # number of elements in the i-th class
my @I = qw( A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u ); # irreducible representations
my %R;
@R{@R}=@hi;
# characters of the irreducible representations of Oh
my @A1g = qw( 1 1 1 1 1 1 1 1 1 1 );
my @A2g = qw( 1 1 -1 -1 1 1 -1 1 1 -1 );
my @Eg = qw( 2 -1 0 0 2 2 0 -1 2 0 );
my @T1g = qw( 3 0 -1 1 -1 3 1 0 -1 -1 );
my @T2g = qw( 3 0 1 -1 -1 3 -1 0 -1 1 );
my @A1u = qw( 1 1 1 1 1 -1 -1 -1 -1 -1 );
my @A2u = qw( 1 1 -1 -1 1 -1 1 -1 -1 1 );
my @Eu = qw( 2 -1 0 0 2 -2 0 1 -2 0 );
my @T1u = qw( 3 0 -1 1 -1 -3 -1 0 1 1 );
my @T2u = qw( 3 0 1 -1 -1 -3 1 0 1 -1 );
# my (%A1g, %A2g, %Eg, %T1g, %T2g, %A1u, %A2u, %Eu, %T1u, %T2u);
# @A1g{@R} = @A1g; # A1g
# @A2g{@R} = @A2g; # A2g
# @Eg{@R} = @Eg; # Eg
# @T1g{@R} = @T1g; # T1g
# @T2g{@R} = @T2g; # T2g
# @A1u{@R} = @A1u; # A1u
# @A2u{@R} = @A2u; #A2u
# @Eu{@R} = @Eu; # Eu
# @T1u{@R} = @T1u; # T1u
# @T2u{@R} = @T2u; # T2u
sub new {
my $type = shift;
$type = ref($type) || $type;
my %Ur = @_;
return bless \%Ur, $type;
}
sub character_tables {
return <<'TABLE';
+-----+---------------------------------------------------+-------+
| Oh | E 8C3 6C2 6C4 3C2f i 6S4 8S6 3sh 6sd | |
+-----+---------------------------------------------------+-------+
| A1g | 1 1 1 1 1 1 1 1 1 1 | |
| A2g | 1 1 -1 -1 1 1 -1 1 1 -1 | |
| Eg | 2 -1 0 0 2 2 0 -1 2 0 | |
| T1g | 3 0 -1 1 -1 3 1 0 -1 -1 | |
| T2g | 3 0 1 -1 -1 3 -1 0 -1 1 | |
| A1u | 1 1 1 1 1 -1 -1 -1 -1 -1 | |
| A2u | 1 1 -1 -1 1 -1 1 -1 -1 1 | |
| Eu | 2 -1 0 0 2 -2 0 1 -2 0 | |
| T1u | 3 0 -1 1 -1 -3 -1 0 1 1 | x,y,z |
| T2u | 3 0 1 -1 -1 -3 1 0 1 -1 | |
+-----+---------------------------------------------------+-------+
TABLE
}
sub symmetry_elements {
return @R;
}
sub normal_modes {
my $self = shift;
return (3 * $self->{E} - 6);
}
sub irr {
my $self = shift;
# E C3 C2 C4 C2f i S4 S6 sh sd
# 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));
my $X_C4 = sprintf "%0.f", ($self->{C4} - 2) * (1 + 2 * 0);
my $X_C2f = sprintf "%0.f", ($self->{C2f} - 2) * (1 + 2 * (-1));
# improper operations Ur (-1 + 2 cos(r))
my $X_i = sprintf "%0.f", $self->{i} * (-1 + 2 * (-1));
my $X_S4 = sprintf "%0.f", $self->{S4} * (-1 + 2 * 0);
my $X_S6 = sprintf "%0.f", $self->{S6} * (-1 + 2 * (0.5));
my $X_sh = sprintf "%0.f", $self->{sh} * (-1 + 2 * 1);
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_C4, $X_C2f,
$X_i, $X_S4, $X_S6, $X_sh, $X_sd);
# Irreducible representation
my $s = 0;
my $n_A1g = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A1g[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_A2g = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A2g[$_] , $s] } (0..$#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 $n_T1g = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T1g[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_T2g = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T2g[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_A1u = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A1u[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_A2u = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $A2u[$_] , $s] } (0..$#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 $n_T1u = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T1u[$_] , $s] } (0..$#hi))[-1]->[1];
$s = 0;
my $n_T2u = sprintf"%0.f",
(1/$h)*(map { [ $s += $hi[$_] * $rr[$_] * $T2u[$_] , $s] } (0..$#hi))[-1]->[1];
my @ri = ($n_A1g, $n_A2g, $n_Eg, $n_T1g, $n_T2g,
$n_A1u, $n_A2u, $n_Eu, $n_T1u, $n_T2u);
my %ri = ();
@ri{@I} = @ri;
return %ri;
}
1;
__END__
=head1 NAME
Chemistry::PointGroup::Oh - Point group Oh
=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