Invoke browser X button with JavaScript

window.close()

This method is only allowed to be called for windows that were opened by a script using the window.open() method. If the window was not opened by a script, the following error appears in the JavaScript Console: Scripts may not close windows that were not opened by script. Mozilla Developer Network: window.close()

So, there is not a way to close browser via javascript, but if you wan't to tigger some code that is supposed to be executed when window closes try this:

//plain js
window.onunload();

//plain js
window.onbeforeunload();

//jQuery
$(window).unload();

Or if you want to execute code when user tries to close window, try this:

window.onbeforeunload = function(){
   // Do something
}
// OR
window.addEventListener("beforeunload", function(e){
   // Do something
}, false);

window.onunload = function(){
   // Do something
}
// OR
window.addEventListener("unload", function(e){
   // Do something
}, false);

// jQuery
$(window).unload(function(){
   // Do whatever you need
});

Since 25 May 2011, the HTML5 specification states that calls to window.alert(), window.confirm(), and window.prompt() methods may be ignored during this event. See the HTML5 specification for more details. MDN | window.onbeforeunload

These events are fired in this order:

1. window.beforeunload (cancellable event)
2. window.pagehide
3. window.unload