howto:tddft
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- | ====== How to run a LR-TDDFT calculation for absorption and emission spectroscopy ====== | + | This page has been moved to: https://manual.cp2k.org/trunk/methods/properties/optical/tddft.html |
- | + | ||
- | This is a short tutorial on how to run linear-response TDDFT computations for absorption and emission spectroscopy. The TDDFT module enables a description of excitation energies and excited-state computations within the Tamm-Dancoff approximation (TDA) featuring GGA and hybrid functionals as well as semi-empirical simplified TDA kernels. The details of the implementation can be found in [[https:// | + | |
- | Note that the current module is based on an earlier TDDFT implementation [[https://chimia.ch/ | + | |
- | Please cite these papers if you were to use the TDDFT module for the computation of excitation energies or excited-state gradients. | + | |
- | + | ||
- | ===== Brief theory recap ===== | + | |
- | + | ||
- | The implementation in CP2K is based on the Tamm-Dancoff approximation (TDA), which describes each excited state $p$ with the excitation energy $\Omega^p$ and the corresponding excited-state eigenvectors $\mathbf{X}^p$ as an Hermitian eigenvalue problem | + | |
- | + | ||
- | \begin{equation} \label{tda_equation} | + | |
- | \begin{aligned} | + | |
- | \mathbf{A} \mathbf{X}^p = \Omega^p \mathbf{X}^p \, , \\ | + | |
- | \sum_{\kappa k} [ F_{\mu \kappa \sigma} \delta_{ik} - F_{ik \sigma} S_{\mu \kappa} ] X^p_{\kappa k \sigma} + \sum_{\lambda} K_{\mu \lambda \sigma} [\mathbf{X}^p] C_{\lambda i \sigma} = \sum_{\kappa} \Omega^p S_{\mu \kappa} X^p_{\kappa i \sigma} \, . | + | |
- | \end{aligned} | + | |
- | \end{equation} | + | |
- | + | ||
- | The Hermitian matrix $\mathbf{A}$ contains as zeroth-order contributions the difference in the Kohn-Sham (KS) orbital energies $\mathbf{F}$, | + | |
- | + | ||
- | \begin{equation} \label{f_and_k_matrix} | + | |
- | \begin{aligned} | + | |
- | F_{\mu \nu \sigma} [\mathbf{D}] &= h_{\mu \nu} + J_{\mu \nu \sigma} [\mathbf{D}] - a_{\rm{\tiny{EX}}}K^{\rm{\tiny{EX}}}_{\mu \nu \sigma} [\mathbf{D}] + V_{\mu \nu \sigma}^{\rm{\tiny{XC}}} \, , \\ | + | |
- | K_{\mu \nu \sigma} [\mathbf{D}^{\rm{\tiny{X}}}] & | + | |
- | \end{aligned} | + | |
- | \end{equation} | + | |
- | + | ||
- | $\mathbf{S}$ denotes the atomic-orbital overlap matrix, $\mathbf{C}$ the occupied ground-state KS orbitals and $\mathbf{D}$ and $\mathbf{D}^{\rm{\tiny{X}}}$ ground-state and response density matrices, | + | |
- | + | ||
- | \begin{equation}\label{density_matrices} | + | |
- | \begin{aligned} | + | |
- | D_{\mu \nu \sigma} = \sum_k C_{\mu k \sigma} C_{\nu k \sigma}^{\rm{T}} \, , \\ | + | |
- | D_{\mu \nu \sigma}^{\rm{\tiny{X}}} = \frac{1}{2} \sum_{k} ( X^p_{\mu k \sigma} C_{\nu k \sigma}^{\rm{T}} + C_{\mu k \sigma} (X^p_{\nu k \sigma})^{\rm{T}} ) \, . | + | |
- | \end{aligned} | + | |
- | \end{equation} | + | |
- | + | ||
- | Within the current implementation, | + | |
- | The current implementation features to approximate the exact exchange contribution of hybrid functionals using the auxiliary density matrix method (ADMM). Furthermore, | + | |
- | + | ||
- | \begin{equation} \label{stda_kernel} | + | |
- | \begin{aligned} | + | |
- | \gamma^{\rm{\tiny{J}}}(A, | + | |
- | \gamma^{\rm{\tiny{K}}}(A, | + | |
- | \end{aligned} | + | |
- | \end{equation} | + | |
- | + | ||
- | that depend on the chemical hardness $\eta$, the Fock-exchange mixing parameter $a_{\rm{\tiny{EX}}}$ and powers of $\alpha$ and $\beta$ for either Coulomb and exchange interactions. | + | |
- | + | ||
- | + | ||
- | Within the current implementation, | + | |
- | + | ||
- | Based on Eq.\ (\ref{tda_equation}), | + | |
- | + | ||
- | \begin{equation} | + | |
- | \begin{aligned} | + | |
- | L [\mathbf{X}, | + | |
- | & | + | |
- | &+ \sum_{\kappa k \sigma}( \bar{Z}_{\kappa k \sigma})^{\rm{T}} | + | |
- | &- \sum_{kl\sigma} (\bar{W}^{\rm{\tiny{C}}}_{kl \sigma})^{\rm{T}} | + | |
- | \end{aligned} | + | |
- | \end{equation} | + | |
- | + | ||
- | introducing Lagrange multipliers $\bar{\mathbf{W}}^{\rm{\tiny{X}}}$, | + | |
- | + | ||
- | + | ||
- | ===== The LR-TDDFT input section ===== | + | |
- | + | ||
- | To compute absorption spectra, parameters defining the LR-TDDFT computation have to be specified in the '' | + | |
- | + | ||
- | The most important keywords and subsections of '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | * '' | + | |
- | + | ||
- | To compute excited-state gradients and thus corresponding fluorescence spectra, the excited state to be optimized furthermore has to be specified by adding the subsection '' | + | |
- | + | ||
- | ===== Simple examples ===== | + | |
- | + | ||
- | ==== Acetone molecule==== | + | |
- | + | ||
- | <code - acetone_tddft.inp> | + | |
- | + | ||
- | & | + | |
- | PROJECT S20Acetone | + | |
- | RUN_TYPE ENERGY | + | |
- | PREFERRED_DIAG_LIBRARY SL | + | |
- | PRINT_LEVEL medium | + | |
- | &END GLOBAL | + | |
- | & | + | |
- | METHOD Quickstep | + | |
- | & | + | |
- | & | + | |
- | | + | |
- | ! FULL kernel is for GGA and hybrid functional computations | + | |
- | ! sTDA kernel is referring to a semi-empirical sTDA computation | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | &END TDDFPT | + | |
- | &END PROPERTIES | + | |
- | &DFT | + | |
- | &QS | + | |
- | METHOD GPW | + | |
- | EPS_DEFAULT 1.0E-17 | + | |
- | EPS_PGF_ORB 1.0E-20 | + | |
- | &END QS | + | |
- | &SCF | + | |
- | SCF_GUESS restart | + | |
- | &OT | + | |
- | | + | |
- | | + | |
- | &END OT | + | |
- | & | + | |
- | | + | |
- | | + | |
- | &END OUTER_SCF | + | |
- | MAX_SCF 10 | + | |
- | EPS_SCF 1.0E-7 | + | |
- | &END SCF | + | |
- | POTENTIAL_FILE_NAME POTENTIAL_UZH | + | |
- | BASIS_SET_FILE_NAME BASIS_MOLOPT_UZH | + | |
- | BASIS_SET_FILE_NAME BASIS_ADMM_UZH | + | |
- | & | + | |
- | CUTOFF 800 | + | |
- | REL_CUTOFF 80 | + | |
- | &END MGRID | + | |
- | & | + | |
- | METHOD BASIS_PROJECTION | + | |
- | EXCH_SCALING_MODEL NONE | + | |
- | EXCH_CORRECTION_FUNC NONE | + | |
- | ADMM_PURIFICATION_METHOD NONE | + | |
- | &END AUXILIARY_DENSITY_MATRIX_METHOD | + | |
- | & | + | |
- | | + | |
- | | + | |
- | &END | + | |
- | &XC | + | |
- | & | + | |
- | & | + | |
- | &END XC | + | |
- | &END DFT | + | |
- | & | + | |
- | &CELL | + | |
- | ABC [angstrom] 14.0 14.0 14.0 | + | |
- | PERIODIC NONE | + | |
- | &END CELL | + | |
- | & | + | |
- | C 0.000000 1.282877 -0.611721 | + | |
- | C 0.000000 -1.282877 -0.611721 | + | |
- | C 0.000000 0.000000 0.185210 | + | |
- | O 0.000000 0.000000 1.392088 | + | |
- | H 0.000000 2.133711 0.059851 | + | |
- | H -0.876575 1.319344 -1.256757 | + | |
- | H 0.876575 1.319344 -1.256757 | + | |
- | H 0.000000 -2.133711 0.059851 | + | |
- | H 0.876575 -1.319344 -1.256757 | + | |
- | H -0.876575 -1.319344 -1.256757 | + | |
- | &END COORD | + | |
- | & | + | |
- | & | + | |
- | & | + | |
- | &END | + | |
- | &KIND H | + | |
- | BASIS_SET ORB DZVP-MOLOPT-PBE0-GTH-q1 | + | |
- | BASIS_SET AUX_FIT admm-dzp-q1 | + | |
- | POTENTIAL GTH-PBE0-q1 | + | |
- | &END KIND | + | |
- | &KIND O | + | |
- | BASIS_SET ORB DZVP-MOLOPT-PBE0-GTH-q6 | + | |
- | BASIS_SET AUX_FIT admm-dzp-q6 | + | |
- | POTENTIAL GTH-PBE0-q6 | + | |
- | &END KIND | + | |
- | &KIND C | + | |
- | BASIS_SET ORB DZVP-MOLOPT-PBE0-GTH-q4 | + | |
- | BASIS_SET AUX_FIT admm-dzp-q4 | + | |
- | POTENTIAL GTH-PBE0-q4 | + | |
- | &END KIND | + | |
- | &END SUBSYS | + | |
- | &END FORCE_EVAL | + | |
- | + | ||
- | </ | + | |
- | + | ||
- | In the resulting output file, there is a '' | + | |
- | + | ||
- | ===== FAQ ===== | + |
howto/tddft.1658167266.txt.gz · Last modified: 2022/07/18 18:01 by ahehn