How are trends in ionisation energy explained?

Horizontal trend: First ionisation energies increase going to the right in a period. This is due to an increase in the atomic mass (and number of protons) and hence in the electrostatic attraction between the nucleus and the electrons. As the attraction is higher, electrons are held more tightly to the nucleus and it is harder to remove them from an atom. However, 2 exceptions occur:when an electron is removed from a singly occupied p subshell (for example I.E. of B: 1s² 2s² 2p¹ is lower than I.E. of Be: 1s²2s²) -- this is due to the increased distance from the nucleus which causes a reduced attraction & screening by the s electrons (which reduces the amount of positive charge that the p electron experiences)repulsion between 2 electrons in the same orbital (for example I.E. of O: 1s²2s²2p_x²2p_y¹2p_z¹ is lower than I.E. of N: 1s²2s²2p_x¹2p_y¹2p_z¹)Vertical trend: First ionisation energies decrease down the group because n increases (distance from the nucleus increases).