I am studying statistical mechanics and force-fields, and I see a lot of this formula being thrown around with no explanation: $$U_{\mathrm{dihedral}} = \begin{cases} k(1+\cos (n\psi + \phi)),& n>0 \\ k(\psi - \phi)^2, & n=0 \\ \end{cases} $$ The only explanation I read is: this...

If all the excited molecules at higher S1 vibrational states rapidly relax to the lowest S1 vibrational state, why do the fluorescence transitions from v' = 1, v' = 2, v' = 3, and other states to v" = 0 have different wavelengths? Why don't they all relax to v' = 0 first and then all transition t...

I am quite a beginner in DFT and I am studying the theory behind the computational tools. I have some doubts about the Columb approximate functional term: $U[n] = \frac{1}{2} \int d^3 r \int d^3 r^\prime \frac {n(\mathbf{r}) n(\mathbf{r}^\prime)}{|\mathbf{r} -\mathbf{r}^\prime|}$ If I use the de...

I know that the standard reduction potential of $\ce{Zn^{2+}}$ to $\ce{Zn} $ is $\pu{-0.76 V}$ and the one of $\ce{Ca^{2+}}$ to $\ce{Ca}$ is $\pu{-2.87 V}.$ But on the atomic level, why does this potential depend on the chemical element?

Mass of nucleon means mass of one proton or neutron. $$\text{No of nucleons} = \frac{\text{mass of one atom} }{\text{Mass of one nucleon}}$$ Now, I have confusion in this formula that why is it division. Mass of an atom = mass of electron + mass of proton + neutron. Now, I am not exactly sure if ...

Currently I am doing TD-DFT calculations in Gaussian and want to calculate transition dipole moment for $S_1$ transition manually. However, I do not manage to retrieve molecular orbital coefficients for the excited states in Gaussian, just the ground state with population keyword and a few hours ...

When trying to solve the Schrodinger equation for the electronic hamiltonian: $$H_{el} = \sum_{i=1}^{N} \bigg( - \frac{1}{2}\nabla_i^2 - \sum_A \frac{Z}{r_{i_A}} \bigg) + \sum_{i>j=1}^{N}\frac{1}{r_{ij}}$$ we note that two prominent integrals arise: These are the exchange integral: $$ K_b(1)\ch...