Chemistry::PointGroup::O - Point group O

package Chemistry::PointGroup::O;

use 5.008001;
use strict;
use warnings;

our $VERSION = '0.01';

my $h  = 24; # number of group elements
my @R  = qw( E C4 C2 C3 C2f ); # symmetry elements of O
my @hi = qw( 1  6  3  8  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 O
my @A1 = qw( 1  1  1  1  1 );
my @A2 = qw( 1 -1  1  1 -1 );
my @E  = qw( 2  0  2 -1  0 );
my @T1 = qw( 3  1 -1  0 -1 );
my @T2 = qw( 3 -1 -1  0  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';
+----+---------------------------+-------+
|  O |  E   6C4  3C2  8C23  6C2' |       |
+----+---------------------------+-------+
| A1 |  1    1    1    1     1   |       |
| A2 |  1   -1    1    1    -1   |       |
|  E |  2    0    2   -1     0   |       |
| T1 |  3    1   -1    0    -1   | x,y,x |
| T2 |  3   -1   -1    0     1   |       |
+----+---------------------------+-------+  
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 $X_C4  = sprintf "%0.f",  ($self->{C4}  - 2) * (1  + 2 * 0);
	my $X_C2  = sprintf "%0.f",  ($self->{C2}  - 2) * (1  + 2 * (-1));
	my $X_C3  = sprintf "%0.f",  ($self->{C3}  - 2) * (1  + 2 * (-0.5));
	my $X_C2f = sprintf "%0.f",  ($self->{C2f} - 2) * (1  + 2 * (-1));
	
	# improper operations  Ur (-1 + 2 cos(r))
	
	# in the same order of @hi
	my @rr = ($X_E, $X_C4, $X_C2, $X_C3, $X_C2f);
	
	# 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__