The statement that is not correct for the periodic classification of elements is Option D.

Let's analyze each option for clarity:

Option A: The properties of elements are the periodic functions of their atomic numbers.

This statement is correct. The modern periodic table is arranged in order of increasing atomic number, and the properties of elements repeat periodically. This periodicity in properties arises due to the similar electronic configurations that occur periodically as the atomic number increases.

Option B: Non-metallic elements are lesser in number than metallic elements.

This statement is also correct. In the periodic table, the majority of elements are metals. Non-metals make up a smaller fraction of the elements, predominantly located in the upper right corner of the periodic table plus hydrogen.

Option C: The first ionization energies of elements along a period do not vary in a regular manner with increase in atomic number.

This statement is correct. As you move from left to right within a period, the first ionization energy generally increases. However, there are exceptions (such as between Groups II and III where the first ionization energy drops slightly), which means the variation isn't strictly regular or linear but shows a general trend with minor irregularities due to electronic structure differences.

Option D: For transition elements, the d-subshells are filled with electrons monotonically with increase in atomic number.

This statement is incorrect, which makes it the answer. In the series of transition elements, the filling of d-subshells with electrons doesn't always happen monotonically (i.e., in a strictly increasing order). The electron configuration of transition metals can appear complex due to the involvement of both 4s and 3d subshells, where electrons may not fill sequentially. A notable exception can be seen in elements like chromium and copper, where electron configurations show anomalies (e.g., $$\text{Cr: [Ar]} 3d^5 4s^1$$ instead of the expected $$3d^4 4s^2$$). This statement falsely suggests a regular, uninterrupted filling pattern.