Computational Chemistry 4.3 - Born-Oppenheimer Approximation

Short lecture on the Born-Oppenheimer approximation for molecular systems.
The molecular Hamiltonian is too complex to solve the exact solutions to the Schrodinger equation. This is because of the N-body problem, where we must simultaneously solve for the interactions of all pairs of particles (a very difficult NP-complete problem). This complexity is reduced by using the Born-Oppenheimer approximation, which treats the heavy, slow-moving nuclei as fixed and stationary relative to the light, fast-moving electrons. This simplifies the molecular Hamiltonian by making the nuclear kinetic energy zero and turning the nuclear-nuclear repulsion into a simple algebraic sum for a given spatial configuration of nuclei.
Notes Slide: i.imgur.com/7A...
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[@aminamouhamed456]

Thank you for all the content, it's absolutely great!! Could you please make a video on how to use a cluster such as Archer2 and then run some simple simulations and explain the meaning of the output file, what to expect in terms of time etc?

[@user-rr9or5dk4m]

3:31 electron mass is one electron or electrons?

[@panyakorntaweechat8586]

The internuclear distances can also effect to E(elec), right? Because overlap integrals depend on nuclear coordinates and the overlap integrals effect to E(elec). But they were assumed that they didn't effect to the format of electronic wave function, so the computatinal physicists and chemists used the format of H-atom wave functions to develop the basis sets.

[@TMPChem]

Welcome back, Panyakorn. The way in which the nuclear coordinates affects the electronic wavefunction and energy is referred to as a "parametric dependence". Nuclear coordinates are specified at the beginning of the problem as parameters, and after that are treated as fixed constants. This is in contrast to electronic coordinates, which are explicit variables of the problem, and form the variable space in which the answer is expressed. We can solve the wavefunction for any set of nuclear coordinates, but once we specify nuclear coordinates the answer is a 3N-dimensional electronic wavefunctions in terms of {x_i, y_i, z_i}. This is all independent from the development of atomic orbital basis sets. The hydrogen-like orbitals are a starting point, but the exponents and linear combinations of those functions are tuned to atom-specific values, such that for a given basis set each nucleus has a distinct set of optimal basis functions. These basis function parameters / coefficients are chosen in an ad hoc fashion, often to minimize error relative to a certain desired property, and anyone can define a new basis set for a new special purpose any time they like, but to be publishable research peer reviewers should request that the basis set is publicly available for other to reproduce the calculations.

[@rosittasantorini3917]

Could you give a good reference textbook which includes this information for further reading? Many thanks for the videos they are extremely informative and clear to follow.

[@TMPChem]

The recommended textbook for Physical Chemistry is McQuarrie and Simon, for which there is an excellent notes map compiled by UC Davis: chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Map%3A_Physical_Chemistry_(McQuarrie_and_Simon)

[@ibrahimnazemqader9153]

Thanks a lot ... دەست خۆش

[@TMPChem]

Thanks for watching, Ibrahim.

[@apburner1]

First.