Doing computational chemistry requires (1) the technical know-how to use special software and computers and (2) the knowledge to understand what the software is telling you.
On that second point, there’s a lot of math and physics behind the theories of chemistry—and its great stuff! But before you dive into studying a lot of formal math and physics, its good to know what you’re working towards. Chris Cramer (a professor at U. Minnesota) is a computational chemist who has written a computational chemistry textbook and put a bunch of free video lectures up on Youtube that explain the concepts behind computational chemistry at a level that most students can understand. If you’ve taken general chemistry, an organic chemistry course, and a couple semester of calculus (multivariable calculus is great, but not absolutely necessary), these videos are great background and inspiration. As you move through the video series (49 total — a full course!) the material gets rich, but if you follow along you should understand the spirit of it.
Lecture 1: Basic potential energy surface of a bond stretching; 3N-6 dimensional PES to analyze; we typically use 2D or 1D slices of that
(can skip Lectures 2 and 3)
Lecture 4: PES approximated by a parabola for bond stretch and bond angles; Parabolas differ based on atom type; torsional angles have periodic PES; all the various force constants, equilibrium bond lengths/angles, etc. define the strain energy model
Lecture 5: More terms for the strain energy/force-field model, focusing on non-bonded interactions (Lennard-Jones, Coulomb, hydrogen-bonding, dipole-dipole). Non-bonded interactions can be attractive (unlike strain energy which is only repulsive). Discussion of force field energy extrema, particular example of sucrose PES for two torsion angles.
Lecture 6: More discussion of PES and how to search them for the minima. Phase space (in terms of the harmonic oscillator). Numerical computation of trajectories.
(you can watch Lectures 7 and 8 if you want to focus on molecular dynamics simulations)