The reason why this particular wave function is so useful is because by taking its partial derivatives, one can gain information about Dipole moments, polarizability, molecular structures, and even spectra: electronic, photoelectron, vibrational, rotaional, NMR, etc. The is essentially the solution to to the electronic Schrodinger equation, producing the particular wave function that’s dependent on electrons only. The process is to solve each Schrodinger equation separately for the electrons and the nuclei. As a result, the Born-Oppenheimer approximation was created in order to solve this problem and it essentially splits the Schrodinger equation into two separate solves. These 162 variables describe the spatial coordinate of the electrons and the nuclei, essentially the location of these subatomic particles in a certain Hilbert Space. However, a huge problem with solving the Schrodinger equation as it has 162 variables that need to be solved in order to determine the necessary information. These atoms usually include smaller elements, specifically those from the 2nd transition row and above, since these are less massive and therefore have less electrons and interactions between the subatomic molecules. Note that for all non-relativistic atoms– meaning atoms that don’t need to be “corrected” using Einstein’s Special Relativity– the time independent Schrodinger equation, as mentioned in the previous blog post, is all that is needed to determine all knowable information about the system. This blog post will introduce some of the mathematics used in quantum chemistry and give an overview of the many methods that are used to approximate the behaviors of systems such as the hydrogen atom, and many other elements and molecules. Therefore, quantum mechanics must be used, and by a well-known postulate of quantum mechanics, quantum mechanical models provide all knowable information about a system.The concepts of orbitals and the probability of electrons discussed in the previous post are a direct result of quantum mechanics, and hence many people accept that quantum mechanics is the reason chemistry can exist today in its rigorous form. Molecules are small enough that classical mechanics doesn’t always provide a good description. Quantum chemistry, as the name implies, is the application of quantum mechanics to atoms and subatomic particles in order to provide extremely accurate models of what’s exactly happening. Before we can begin, we must discuss what exactly quantum chemistry is used for, and the many methods that it involves. As mentioned in our previous blog post, the goal of this post and later posts is to eventually get into the nitty gritty mathematics of quantum chemistry.
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