Why do 2d,1d, and 3f orbitals not exist?

The notation you're using, such as "2d," "1d," and "3f," doesn't correspond to the usual orbital notation used in chemistry and physics. In the context of atomic and molecular orbitals, the notation typically consists of three components: a principal quantum number (n), an angular momentum quantum number (l), and a magnetic quantum number (m). Here's how the notation works:

Principal Quantum Number (n): This represents the energy level or shell of the orbital and can take on positive integer values (1, 2, 3, ...). It determines the overall size of the orbital and the average distance of the electron from the nucleus.

Angular Momentum Quantum Number (l): This determines the shape of the orbital and can take on values from 0 to (n - 1). The values of l correspond to different subshells:

l = 0 corresponds to an s orbital (e.g., 1s, 2s, 3s, ...)
l = 1 corresponds to a p orbital (e.g., 2p, 3p, 4p, ...)
l = 2 corresponds to a d orbital (e.g., 3d, 4d, 5d, ...)
l = 3 corresponds to an f orbital (e.g., 4f, 5f, 6f, ...)
Magnetic Quantum Number (m): This specifies the orientation of the orbital within a subshell and can take on values from -l to +l, including 0.

So, for example, you may have orbitals like 1s, 2s, 2p, 3d, 4f, etc., where the numbers represent the principal quantum number, the letter represents the angular momentum quantum number, and the combination of these numbers and letters uniquely identifies different orbitals.

The notations you mentioned, "2d," "1d," and "3f," are not valid according to this standard notation. If you have any further questions or need clarification on specific orbitals, please provide more context or details, and I'd be happy to assist you further.