Introduction on "Optical Spectroscopy"; clean comments in common/bibliography.F

docs/methods/properties/bandstructure_gw.md

@@ -25,7 +25,7 @@ electronic band structure of a solid. This approximation comes with limitations:
 
 - When using one of the common GGA exchange-correlation (xc) functionals, the band gap in the KS-DFT
   band structure $\varepsilon_{n\mathbf{k}}^\text{DFT}$ is much too small compared to experimental
-  band gaps (Fig. 26 in \[[](#Golze2019))\]. Even with the exact xc functional, the band gap in the
+  band gaps (Fig. 26 in \[[](#Golze2019)\]). Even with the exact xc functional, the band gap in the
   KS-DFT band structure $\varepsilon_{n\mathbf{k}}^\text{DFT}$ will be too small due to the
   derivative discontinuity.
 
@@ -127,7 +127,7 @@ In the upper *GW* section, the following keywords have been used:
 
 - [QUADRATURE_POINTS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.QUADRATURE_POINTS): Number
   of imaginary-frequency points used for computing the self-energy (Eq. (21) in
-  \[[](#Wilhelm2016))\]. 100 points are usually enough for converging quasiparticle energies within
+  \[[](#Wilhelm2016)\]). 100 points are usually enough for converging quasiparticle energies within
   10 meV.
 
 - [SELF_CONSISTENCY](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.GW.SELF_CONSISTENCY):
@@ -281,7 +281,7 @@ Running the input file requires access to a large computer (the calculation took
 nodes on Noctua2 cluster in Paderborn). The computational parameters from this input file reach
 numerical convergence of the band gap within ~ 50 meV (TZVP basis set, 10 time and frequency
 points). Detailed convergence tests are available in the SI, Table S1 of \[[](#Graml2024)\] We
-recommend the numerical parameters from the input file for large-scale GW calculations. The code
+recommend the numerical parameters from the input file for large-scale *GW* calculations. The code
 prints restart files with ending .matrix that can be used to restart a crashed calculation.
 
 In case anything does not work, please feel free to contact jan.wilhelm (at) ur.de.

docs/methods/properties/optical/index.md

@@ -9,4 +9,58 @@ tddft
 bethe-salpeter
 ```
 
-TODO: Add Introduction and comparison between TDDFT and BSE.
+Optical spectroscopy is a technique used to study the interaction between light and matter. It
+involves measuring the absorption, emission, or scattering of light by molecules, atoms, or
+materials. The resulting spectra provide valuable information about the electronic structure, energy
+levels, and dynamics of the system under investigation.
+
+In optical spectroscopy, one of the key quantities of interest is the excitation energy
+($\Omega_n$). This is the energy required to excite a molecule from its ground state to an excited
+state. These excitation energies are directly related to the positions and intensities of spectral
+lines observed in absorption and emission spectra.
+
+The excitation energies $\Omega_n$ can be computed using various theoretical approaches. Two
+commonly used methods are linear-response Time-Dependent Density Functional Theory (LR-TDDFT) and
+the linear-response *GW*/Bethe-Salpeter Equation (*GW*/BSE) approach. Both methods can be formulated
+using Casida's equation
+
+$$\left( \begin{array}{cc}A &  B\\B &  A\end{array} \right)\left( \begin{array}{cc}\mathbf{X}^{(n)}\\\mathbf{Y}^{(n)}\end{array} \right) = \Omega^{(n)}\left(\begin{array}{cc}1&0\\0&-1\end{array}\right)\left(\begin{array}{cc}\mathbf{X}^{(n)}\\\mathbf{Y}^{(n)}\end{array}\right) \quad .$$
+
+We abbreviate $A$ and $B$ as matrices with index $A_{ia,jb}$, i.e. they have
+$N_\mathrm{occ}N_\mathrm{empty}$ rows and $N_\mathrm{occ}N_\mathrm{empty}$ columns. The matrices $A$
+and $B$ are different in TDDFT and *GW*/BSE; for TDDFT they read (for singlet excitations, details
+on the TDDFT page)
+
+$$ \begin{align}
+    A_{ia,jb} &= (\varepsilon_a^\text{DFT}-\varepsilon_i^\text{DFT})\delta_{ij}\delta_{ab} + 
+    2v_{ia,jb} + \langle ia|f_\text{xc}(\Omega^{(n)})|jb\rangle \quad ,\\[0.5em]
+    B_{ia,jb} &= 2v_{ia,bj} +  \langle ia|f_\text{xc}(\Omega^{(n)})|jb\rangle \quad ,
+\end{align}$$
+
+and for *GW*/BSE (details on the *GW*/BSE page):
+
+$$ \begin{align}
+    A_{ia,jb} &= (\varepsilon_a^{GW}-\varepsilon_i^{GW})\delta_{ij}\delta_{ab} + 
+    2v_{ia,jb} - W_{ij,ab} \quad ,\\[0.5em]
+    B_{ia,jb} &= 2 v_{ia,bj} - W_{ib,aj} \quad .
+\end{align}$$
+
+TDDFT with the common Adiabatic Local Density Approximation (ALDA) or with a hybrid functional (i.e.
+PBE0) can be a good choice for calculating excitation energies of molecules. Exceptions include
+charge-transfer excitations where the excited electron is transferred over a significant distance
+within the molecule. In such cases, range-separated hybrid functionals might be needed.
+
+For solids, the applicability of TDDFT can depend on whether the solid is metallic or has a finite
+bandgap. For metals, ALDA often yields good excitation energies. However, for semiconductors and
+insulators, ALDA fails because the ALDA xc kernel does not adequately include the Coulomb
+interaction between the electron and the hole of the electron-hole pair (exciton) that forms upon
+excitation. In contrast, the *GW*/BSE approach is well-suited for computing the excitation energies
+of excitons in semiconductors and insulators. *GW*/BSE accounts for the attractive interaction
+between the electron and hole in the A-matrix via the screened Coulomb interaction $W_{ij,ab}$. This
+inclusion is crucial for accurately describing excitonic effects, which are significant in materials
+with a finite bandgap.
+
+Thus, TDDFT with ALDA/hybrid functionals is convenient and computationally less demanding than
+*GW*/BSE for molecular systems and metals, *GW*/BSE can describe excitonic effects in semiconductors
+and insulators. For a more detailed discussion on TDDFT and *GW*/BSE, we recommend for example C. A.
+Ullrich, *Time-Dependent Density-Functional Theory - Concepts and Applications*.

src/common/bibliography.F

@@ -12,17 +12,10 @@
 !>      (often ourselves, but this need not to be the case), and as a form
 !>      of documentation.
 !>
-!>      reference_manager.F provides an easy way to cite these references from the code
+!>      add references here as an easy way to cite these references from the code
 !>      (e.g., whenever the relevant part of the code is executed)
 !>      and to add citations to the input
 !>      at the end of the run a bibliography is printed that can be used, e.g., in papers
-!> \note
-!>      references need to be input using the ISI citation format, because it is
-!>      uniform, easy to parse, and can be exported for example from web of science.
-!>      (mark the reference, and click 'export to reference software', open the resulting file)
-!>      Furthermore, it can be easily converted to and from using the bibutils tools
-!>      a collection of easy to use conversion programs that can be found at
-!>      https://ctan.org/pkg/bibutils by Chris Putnam
 !> \author Joost VandeVondele
 ! **************************************************************************************************
 MODULE bibliography
@@ -104,10 +97,16 @@ CONTAINS
 !> \par History
 !>      08.2007 created [Joost VandeVondele]
 !> \note
-!>     - note that the ISI record is fixed format (line length limited and the
-!>       first 3 characters can indicate record type)
 !>     - please add DOI whenever available, this will result in a clickable
 !>       link in the input reference manual.
+!>     - please provide for journal articles:
+!>       - all author names, abbreviate the first names
+!>       - the title of the article
+!>       - the abbreviated journal name (please use the ISO4 standard)
+!>       - volume
+!>       - pages (in case there is starting and end page: please provide start page-end page;
+!>                in case there is article number, e.g. J. Chem. Phys, Phys. Rev., then provide
+!>                the article number)
 ! **************************************************************************************************
    SUBROUTINE add_all_references()
       CALL add_reference(key=Ceriotti2012, &