Explain the encapsulated anonymous function syntax

Summary

Can you explain the reasoning behind the syntax for encapsulated anonymous functions in JavaScript? Why does this work: (function(){})(); but this doesn’t: function(){}();?

What I know

In JavaScript, one creates a named function like this:

function twoPlusTwo(){
    alert(2 + 2);
}
twoPlusTwo();

You can also create an anonymous function and assign it to a variable:

var twoPlusTwo = function(){
    alert(2 + 2);
};
twoPlusTwo();

You can encapsulate a block of code by creating an anonymous function, then wrapping it in brackets and executing it immediately:

(function(){
    alert(2 + 2);
})();

This is useful when creating modularised scripts, to avoid cluttering up the current scope, or global scope, with potentially conflicting variables – as in the case of Greasemonkey scripts, jQuery plugins, etc.

Now, I understand why this works. The brackets enclose the contents and expose only the outcome (I’m sure there’s a better way to describe that), such as with (2 + 2) === 4.

What I don’t understand

But I don’t understand why this does not work equally as well:

function(){
    alert(2 + 2);
}();

Can you explain that to me?