Wordpress Facebook Login Without a Plugin

Question

I found some scripts on how to create login from http://w4dev.com/wp/integrade-facebook-on-wp I have it laid down with no errors but every time i click the button the window just closes again can you have a check what i did wrong on functions or on the footer.

Footer

<?php
function fb_footer(){
if( is_user_logged_in()):
    echo "<script type='text/javascript'> jQuery('#facebook_connect').hide(); </script>";
return;
endif;
?>
<script type="text/javascript">
jQuery('#facebook_connect').click(function(){
FB.login(function(FB_response){
if( FB_response.status === 'connected' ){
    fb_intialize(FB_response);
}
},
{scope: 'email'});
});

function fb_intialize(FB_response){
    FB.api( '/me', 'GET', 
        {'fields':'id,email,username,verified,name'},
        function(FB_userdata){
            jQuery.ajax({
                type: 'POST',
                url: 'AJAXURL',
                data: {"action": "fb_intialize", "FB_userdata": FB_userdata, "FB_response": FB_response},
                success: function(user){
                    if( user.error ){
                        alert( user.error );
                    }
                    else if( user.loggedin ){
                        window.location.reload();
                    }
                }
            });
        }
    );
};
</script>
<?php
}
add_action( 'wp_footer', 'fb_footer' );
?>`

This is my functions

function fb_head(){
if( is_user_logged_in()) return;
?>
<script type="text/javascript">
window.fbAsyncInit = function(){
FB.init({appId:'APP_ID', status:true, cookie:true, xfbml:true, oauth:true});
};
</script>
<div id="fb-root"></div>
<script type="text/javascript">
(function() {
var e = document.createElement('script');
e.type = 'text/javascript';
e.src = document.location.protocol + '//connect.facebook.net/en_US/all.js';
e.async = true;
document.getElementById('fb-root').appendChild(e);
}());
</script>
<?php
}
add_action( 'wp_head', 'fb_head' );
function mytheme_enqueue_scripts(){
    wp_enqueue_script( 'jquery' );
}
add_action( 'wp_enqueue_scripts', 'mytheme_enqueue_scripts');
function wp_ajax_fb_intialize(){
@error_reporting( 0 ); // Don't break the JSON result
header( 'Content-type: application/json' );

if( !isset( $_REQUEST['FB_response'] ) || !isset( $_REQUEST['FB_userdata'] ))
die( json_encode( array( 'error' => 'Authonication required.' )));

$FB_response = $_REQUEST['FB_response'];
$FB_userdata = $_REQUEST['FB_userdata'];
$FB_userid = (int) $FB_userdata['id'];

if( !$FB_userid )
die( json_encode( array( 'error' => 'Please connect your facebook account.' )));

global $wpdb;
$user_ID = $wpdb->get_var( "SELECT user_id FROM $wpdb->usermeta WHERE meta_key = '_fbid' AND meta_value = '$FB_userid'" );

if( !$user_ID ){
$user_email = $FB_userdata['email'];
$user_ID = $wpdb->get_var( "SELECT ID FROM $wpdb->users WHERE user_email = '$user_email'" );

if( !$user_ID ){
if ( !get_option( 'users_can_register' ))
die( json_encode( array( 'error' => 'Registration is not open at this time. Please come back later..' )));

extract( $FB_userdata );

$display_name = $name;
$user_login = $username;

if( empty( $verified ) || !$verified )
die( json_encode( array( 'error' => 'Your facebook account is not verified. You hae to verify your account before proceed login or registering on this site.' )));

$user_email = $email;
if ( empty( $user_email ))
die( json_encode( array( 'error' => 'Please re-connect your facebook account as we couldnt find your email address..' )));

if( empty( $name ))
die( json_encode( array( 'error' => 'empty_name', 'We didnt find your name. Please complete your facebook account before proceeding..' )));

if( empty( $user_login ))
$user_login = sanitize_title_with_dashes( sanitize_user( $display_name, true ));

if ( username_exists( $user_login ))
$user_login = $user_login. time();

$user_pass = wp_generate_password( 12, false );
$userdata = compact( 'user_login', 'user_email', 'user_pass', 'display_name' );

$user_ID = wp_insert_user( $userdata );
if ( is_wp_error( $user_ID ))
die( json_encode( array( 'error' => $user_ID->get_error_message())));

update_user_meta( $user_ID, '_fbid', (int) $id );
}
else{
update_user_meta( $user_ID, '_fbid', (int) $FB_userdata['id'] );
}
}

wp_set_auth_cookie( $user_ID, false, false );
die( json_encode( array( 'loggedin' => true )));
}
add_action( 'wp_ajax_nopriv_fb_intialize', 'wp_ajax_fb_intialize' );

I dont really like using plugins which has extra queries that slows the site so id like to create one without plugins.