I am currently a senior year chemistry undergraduate with a keen interest towards pursuing a PhD in the fields of Quantum Dynamics. I have a strong background in mathematics and undergraduate quantum physics, but I am getting quickly overwhelmed when trying to read journal articles in current quantum chemistry This for example . I have realized I need to go through some rigorous learning before I am able to grasp what modern day research in this field is about, but it is very difficult to find resources that would help me learn the things I want while being legible to an undergraduate. To give you an idea of what I want to learn :
- A rigorous treatment of the Born-Oppenheimer approximation. I have come to realize that it goes much deeper than just "Ignore Nuclear Kinetic Energy". I want to know about potential energy surfaces, when do they intersect (?) and how it is related to things like the "adiabatic approximation" and how we deal with phenomenon like "internal conversion".
- The basics of the Multi-configuration time dependent hartree (MCTDH) formalism that is used to simulate quantum dynamics.
- What is "Surface Hopping" formalism. How it provides a cheaper alternative to purely quantum treatments.
- What are conical intersections and how they represent a complete breakdown of the BO approximation.
So that the members of the group can help me more easily, here are things I am already comfortable with:
- Mathematics - Linear Algebra, Group Theory, Representation Theory for Finite Groups, A bit of Lie groups, Basics of ODEs, Multivariable Analysis.
- Physics - Classical Mechanics and Classical Field Theory, Relativity, Quantum Mechanics (at the level of Sakurai's Modern Quantum Mechancis), Introductory parts of QFT.
- Electronic Structure Theory - I have just started studying it (mostly refering Helgaker) but I have become comfortable with the standard and the second-quantized versions of HF Theory and I have been able to write my own HF code to simulate the Energy v/s bond length curve of $H_2$ molecule using an STO-3G basis set.
Most of the members on this forum are way more experienced than me so I look forward to listening what might your helpful suggestions be.