In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula.[1][2][3][4] Currently, it is best seen as an empirical relationship.[5]: 188  It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.

Sometimes we all need a little more energy than we thought to get going. This is the mental model of activation energy and it can help you solve problems.

What do the quantum eigenstates of 3D wells look like? In this video, we visualize the solutions of the 3D Schrödinger Equation computed for more than a total of 500 eigenstates of 2, 4, 8, and 12 wells, illustrating what the molecular orbitals for a molecule with that number of atoms look like. These simulations are made with qmsolve, an open-source python package that we are developing for solving and visualizing quantum physics. You can find the source code here: https://github.com/quantum-visualizations/qmsolve The way this simulator works is by discretizing the Hamiltonian of an arbitrary potential and diagonalizing it for getting the energies and the eigenstates of the system. The eigenstates of this video are computed with high accuracy (less than 1% of relative error) by diagonalizing a Hamiltonian matrix with a shape of 1,000,000 x 1,000,000. For a molecule that contains only a single electron, an orbital is exactly the same that its eigenstate. Therefore in these examples, the eigenstates are equivalent to the orbitals. In the video, it can be noticed that the first molecular orbitals can be visualized as a first-order approximation as a simple linear combination of the orbitals of a single well. However, as the energy of the eigenstates raises, their wave function starts to take much more complex shapes. Between each eigenstate is plotted a transition between two eigenstates. This is made by preparing a quantum superposition of the two eigenstates involved. #QuantumPhysics #MolecularOrbitals #QuantumChemistry