This page contains a list of undergraduate and graduate courses taught at NYU by Prof. Tuckerman for which extensive lecture notes and other course materials have been developed, links to these course pages, and a short description of each course.

# Undergraduate Courses

## CHEM-UA 127: Advanced General Chemistry I

This course is the first half of a broad survey of general chemistry topics covered at an advanced, calculus-based level. The primary focus of the course is an introduction to the quantum theory of chemical bonding, including discussions of the basic postulates of quantum mechanics, simple analytically solvable examples in one dimension, the hydrogen atom and general considerations of atomic structure and atomic orbitals, molecular orbitals, and molecular structure. Other topics covered in the course include introductions to organic chemistry, techniques of spectroscopy, solid-state chemistry, soft condensed matter chemistry, and nuclear chemistry.

## CHEM-UA 652: Thermodynamics, Kinetics, and Statistical Mechanics

This course is taught as part of a two-semester undergraduate course in physical chemistry. Topics covered include an introduction to classical statistical mechanics including a discussion of the fundamental equilibrium ensembles, derivations of virial coefficients, and the van der Waals equation. From there, the course proceeds to discuss the theory of diffusion, the laws of thermodynamics, solutions, phase equilibria, and chemical equilibria. The course finishes with a discussion of chemical kinetics, including basic rate laws, catalysis, transition-state theory, complex reaction mechanisms, and the theory of reactors with examples of continuously stirred tank reactors and plug-flow reactors.

# Graduate Courses

## CHEM-GA 2600: Statistical Mechanics

This is a rigorous course in the theory of statistical mechanics with a focus on topics of importance in theoretical and computational chemistry. The course begins with an introduction to Lagrangian and Hamiltonian mechanics, a discussion of phase spaces, and a derivation of the Liouville theorem, the Liouville equation, and its equilibrium solutions. The discussion then turns to the fundamental equilibrium ensembles, their basic thermodynamic relations, phase space distributions, and partition functions. Examples of the ideal gas and harmonic baths are used to illustrate how the ensembles work. After this basic introduction, computational methods used to perform statistical mechanics calculations on more realistic problems are discussed, including molecular dynamics, thermostats and barostats, and Monte Carlo methods. It should be emphasized that this part of the course is *not* meant to teach how to run packages but to present the actual algorithms used and where they come from. After this, enhanced sampling methods for computing free energies of rare events in complex systems are discussed. The second part of the course proceeds to a discussion of quantum statistical mechanics, density matrices, and a derivation of the Feynman path integral formulation. The course finishes with a discussion of both classical and quantum time-dependent statistical mechanics, including a derivation of linear response theory, time correlation functions, Green-Kubo theory, classical and approximate quantum (imaginary-time path integral) methods for computing time correlation functions, and finally stochastic dynamics in the form of the Langevin and generalized Langevin equations.

## CHEM-GA 2666: Quantum Chemistry

This is the first half of a course entitled Quantum Chemistry and Dynamics covering the “quantum chemistry” portion. Topics covered include a review of the basic postulates of quantum mechanics, an exact treatment of the hydrogen molecule ion, a discussion of the variational principle and its use to approximate the molecular orbitals of the hydrogen molecule ion. The course then turns to a discussion of many electron systems, starting with an introduction to the concept of spin, systems of identical fermions, the Born-Oppenheimer approximation, and basic methods of quantum chemistry, including Hartree-Fock theory and Møller-Plesset perturbation theories. The course finishes with a discussion of density functional theory, including the Hohenberg-Kohn theorem, Kohn-Sham theory, the adiabatic connection formula, and approximations to exchange and correlation.