EF Core - Self referencing relationship with custom foreign/principal key not mapped properties

I am trying to implement a self-referencing relationship in EF Core. I am trying to use a custom foreign key and principal key that are not mapped to a real database columns.

With the below code, I get the error

'No backing field could be found for property 'HeadOfHouseholdForeignKey' of entity type 'Person' and the property does not have a setter

Is there a way to have these foreign/principal keys which aren't mapped to a column in the DB? Is there a way to do it nicely in EF Core?

Example:

PersonContext.cs

using Microsoft.EntityFrameworkCore;

namespace ConsoleApp1
{
    public class PersonContext : DbContext
    {
        DbSet<Person> People;
        protected override void OnModelCreating(ModelBuilder builder)
        {
            builder.Entity<Person>()
                .HasOne(p => p.HeadOfHouseHold)
                .WithMany()
                .HasForeignKey(p => p.HeadOfHouseholdForeignKey)
                .HasPrincipalKey(p => p.HeadOfHouseholdPrincipalKey);
        }
    }
}

Person.cs

namespace ConsoleApp1
{
    internal class Person
    {
        public int PersonId { get; set; }
        public string Name { get; set; }

        public string FamilyName { get; set; }

        public string PersonSequenceNumber { get; set; }

        public Person HeadOfHouseHold { get; set; }

        public string HeadOfHouseholdForeignKey
        {
            get
            {
                // Head of household always has '01' as PersonSequenceNumber in DB, other members increment from 01 to 02, 03, etc
                if (PersonSequenceNumber != "01")
                {
                    return FamilyName + "01";
                }
                else
                {
                    return null;
                }
            }
        }

        public string HeadOfHouseholdPrincipalKey
        {
            get
            {
                return FamilyName + PersonSequenceNumber;

            }
        }
    }
}