10

Seeing that this question has gathered attention but no replies, I will give it a stab. Note that I am not an expert on DFT or functional calculus, so take this with a grain of salt. As usual, suggestions to the post will be welcome! Using an approach I saw here, we can use a chain rule and obtain the following: $$\frac{\delta F[\rho(\boldsymbol{r})]}{\delta ...


9

I think a good way to see this is to simplify the stage a little. Imagine we want to solve the Schrödinger equation for a Hamiltonian $H$. For this we take a very simple basis, namely just two real-valued functions $\{f_1, f_2\}$. If we variationally optimise the trial wavefunction from this basis, we are presented with an approximation to the ground state ...


9

Given that variational quantum Monte Carlo (VQMC) is specifically for calculating ground state properties, it shouldn't have any problem with finding the $T=0$ energy. It may be difficult to do a material as complicated as gold, but I'm not an expert in this field by any means. This article discusses structural optimization with VQMC: S. Tanaka J. Chem. ...


6

You can, in fact, do better as the answer to this Physics.SE question of yours indicates, assuming you're after an asymptotic expression. I haven't read the book you mention, but if you're familiar with the bra-ket notation, I recommend the discussion of variational methods in Sakurai's Modern Quantum Mechanics. The following will be based on Sakurai's ...


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