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24

These are a few extra points to complement Andrew Rosen's comprehensive response: To be absolutely clear, typical DFT calculations are not performed at 0K, a better description of what happens is that they are performed "for a static crystal". Static crystal means that the atoms are fixed at their crystallographic positions (which is what a typical DFT ...


19

You are correct that KS-DFT, strictly speaking, involves calculations of a potential energy surface at 0 K. However, if you accept that the density functional approximation you are using is sufficiently accurate, it is not too difficult of a stretch to go from 0 K to finite temperature conditions for an application of interest. The key assumption is that the ...


16

CDFT: Current DFT Current DFT is defined via the generalized Hohenberg-Kohn theorem (HKT), which extends the traditional HKT to account for the effect of magnetic fields. The generalized HKT says that the scalar potential $\mathbf{V}$, the (nondegenerate) ground state wavefunction $\Psi$, and the vector potential $\mathbf{A}$ are uniquely determined by the ...


14

OF-DFT: Orbital-free density functional theory Hohenberg and Kohn established that the ground state energy, $E$, of interacting electrons in a potential, $v(\mathbf{r})$, is a functional of the electron density, $n(\mathbf{r})$: $$ \tag{1} E[n] = F[n] + \int \mathrm{d}\mathbf{r} \, v(\mathbf{r}) n(\mathbf{r}) . $$ While this statement is formally true, we do ...


11

$\Delta$SCF This method generates excited states by changing the occupancy of a ground state determinant and then carrying out a new SCF with that initial guess, with some restriction throughout to prevent variational collapse back to the ground state [1]. The most common approach to stay out of the ground state is the Maximum Overlap Method (MOM), which ...


11

Basis set name versus number of total orbitals I would like to first address a part of the question that appears to be a misconception about the use of a 6-31+G(d,p) basis set, since you wrote: "In my understanding of such basis sets, it is difficult to do this." 6-31+G(d,p) is not a "big" or "small" basis set, unless we're ...


11

Kohn-Sham DFT may only be rigorous at zero temperature, but at nonzero temperature, Kohn-Sham-Mermin DFT is an equally rigorous replacement. There are two major differences Rather than deriving the orbital equations from a minimization of the energy, $E$, one minimizes the free energy $F = E - TS$, where $S$ is the entropy. A practical consequence is ...


10

Time-evolution of conceptual DFT quantities has been considered starting, I think, with Chattaraj ~2000. (I imagine there is some earlier work by Ghosh and/or Harbola, but I do not know a reference.) Example references: IJQC v91 633 (2003); J. Phys. Chem. A (Feature article) v21, 4513 (2019); Chapter 13 in "Theoretical Aspects of Chemical Reactivity&...


9

GW+BSE: Excited states in the framework of many-body Green's function comprise charged excitations, where the number of electrons in the system changes from $N$ to $N-1$ or $N + 1$, and natural excitations, where the number of electrons remains constant. In the $|N\rangle \rightarrow |N-1\rangle$ case, an electron in the valence band (occupied orbital) is ...


8

This second dipole moment is almost surely the excited state. You can see the nuclear contributions are identical and the rotational constants are also the same. This means they are both calculations of the same geometry. You can also see the magnitude of the dipole moment increases in the second calculation. This is very common in excited states. The ...


8

I am not aware of any public codes that have a force implementation for excited state calculations using the Bethe-Salpeter equation (happy to be corrected on this front). However, the methodology to do this was published some time ago by Ismail-Beige and Louie in this paper, where they also have an in-house implementation that they use to validate the ...


8

The expression you are describing is equation (6) from your first link: $$R_j=\frac{3\hbar c\ln(10)1000}{16\pi^2N_A}\int_\text{band j}\frac{\Delta\epsilon}{\omega}d\omega\tag{1}$$ which defines the rotatory strength $R_j$ of a band $j$ as the differential absorption coefficient integrated over that band, with the units changed via a prefactor containing the ...


7

The time scale is related to time derivative of the kinetic energy of electrons defined as: $$T(t) = \sum_{i} \int |\nabla \phi_{i}(\mathbf{r},t)|^{2} d^{3} \mathbf{r}$$ You have this for time-derivative of the kinetic energy: $$\frac{d T(t)}{d t} \simeq \frac{T(t=0)}{\tau}$$ Where $\tau$ is the relaxation time for kinetic energy in the order of period ...


7

The question cites a 2008 paper about fairly large molecules (e.g. bithiophene N-succinimidyl esters), in which TD-DFT gave significantly wrong results, so the authors recommended RI-CC2. The question then asks if there's any example where TD-DFT was insufficient for a smaller system. After searching the literature, I have found an example of a small ...


6

Density functional perturbation theory (DFPT) This method refers to the calculation of the linear response of the system under some external perturbation. Consider some set of parameters $\{\lambda_i\}$. The first and second derivatives of the total energy with respect to these parameters in DFT read: $$ \frac{\partial E}{\partial\lambda_i}=\int\frac{\...


6

I think you should take care of all possible interactions to get close to the real picture. In periodic solids, there might be electron-hole interaction (solve BSE equation for it), el-phonon coupling, etc. Note that, QE epsilon.x is the lowest level of approximation for the solids (IPA) and it doesn't include any non-local part and local field effects. ...


4

TD-DFT works best for valence-valence excitation energies, but does not very well for charge-transfer excitation (unless xc potentials are constructed to lower delocalization error). Core-excitation energies are also not described will with TD-DFT.


4

KS-DFT: Kohn-Sham DFT The KS-DFT is proposed to deal with the problems of orbital-free DFT (OFDFT), which has been explained by @wcw. OFDFT attempts to compute the energy of interacting electrons, as the functional of the density. While this brute force approach is in principle correct, in practice it is not very accurate. This is due to the lack of accurate ...


4

Real-time TDDFT (RT-TDDFT) This is the straightforward non-perturbative solution of the TDDFT equations by means of direct propagation in time. Pioneered by Theilhaber and Yabana & Bertsch it has since found its way into several molecular or solid-state codes. The TDDFT equations in the Kohn–Sham (KS) framework are $$ i \frac{\partial}{\partial t} \phi_i ...


4

You should consider the states (roots) with non-zero oscillator strength. It means that the transition from the ground to excited state is allowed by the transition dipole moment rule. So, in your case root number 3 is the first excited state with oscillator strength of 0.16, whilst root number 5 is the second excited state with oscillator strength of 0.24. ...


4

The SIESTA code has a branch (rel-Max-2) developed by researchers from Max Plank institute that include the calculations of forces and real-time TDDFT. The TDDFT is merged into the main development branch and will be released in versions newer than 4.1 (i.e. 4.2 or 5.0). To download it, go to the Gitlab page: https://gitlab.com/siesta-project/siesta/-/tree/...


1

If I'm interpreting the manual correctly, it is not possible to define a complex external potential in CP2K. It specifies that the VALUES keyword to define the corresponding PARAMETERS of your potential has to be real. I don't know anything about the internal code of CP2K, so I don't know if this would be a simple modification of the code to accept complex ...


1

Someone else can probably answer this in more detail, but most software packages allow for simulated spectra to be calculated just as you have said (not just the excitations). You can probably take the spectra and treat it the same as your experimental spectra. At the very least, I was able to find a recent paper that appears to have done exactly just that. ...


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