Invalid initializer member declaration error reading out XML

I have 2 classes:

 public class Person
    {
        public PersonDetail personDetails { get; set; }        
    }

    public class PersonDetail
    {
        public int Id { get; set; }
        public string Name { get; set; }
        public string Function { get; set; }
    }

When I want to read out the persons from the xml file I get this error "Invalid initializer member declaration":

 foreach (var item in xmlFile.Descendants("person"))
            {
                if (item.Element("id") != null)
                {
                    testList.Add(new Person()
                    {
                        **personDetails.Id** = item.Element("id").Value,
                        **personDetails.Name** = item.Element("name").Value,
                        **personDetails.Function** = item.Element("function").Value
                    });
                }
            }

I can't reach "id", "name" and "function" via "personDetails". Any ideas?