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 |
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- | 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} & | + | |
- | \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. | + | |
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- | + | ||
- | 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 ===== | + | |
- | + | ||
- | ==== Excitation energies for acetone ==== | + | |
- | + | ||
- | <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 | + | |
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- | &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 | + | |
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- | | + | |
- | &END OT | + | |
- | & | + | |
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- | &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 ! identical | + | |
- | EXCH_CORRECTION_FUNC NONE | + | |
- | ADMM_PURIFICATION_METHOD NONE | + | |
- | &END AUXILIARY_DENSITY_MATRIX_METHOD | + | |
- | & | + | |
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- | &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 | + | |
- | + | ||
- | </ | + | |
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- | In the resulting output file, there is a '' | + | |
- | The initial guess is referring to the zeroth-order KS energy differences with the printout also listing the transition from the corresponding occupied to virtual orbital. | + | |
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- | <code cp2k> | + | |
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- | State | + | |
- | number | + | |
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- | 10 5 | + | |
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- | </ | + | |
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- | After convergence of the iterative Davidson algorithm, CP2K is printing for each of the calculated excited states the excitation energy in eV, the corresponding transition dipole as well as the oscillator strength. | + | |
- | The form of the dipole transition integrals can be chosen by modifying the keyword '' | + | |
- | When referring to the length form, the reference point to calculate electric dipole moments can be chosen in the subsection by specifying the coordinates of the reference point '' | + | |
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- | <code cp2k> | + | |
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- | </ | + | |
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- | A more detailed analysis of the excitations is given subsequently, | + | |
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- | <code cp2k> | + | |
- | + | ||
- | ------------------------------------------------------------------------------- | + | |
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- | State | + | |
- | number | + | |
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- | 12 | + | |
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- | 10 | + | |
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- | 11 | + | |
- | 12 | + | |
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- | 12 | + | |
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- | </ | + | |
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- | ==== Excited-state gradient for acetone ==== | + | |
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- | ===== FAQ ===== | + | |
- | + |
howto/tddft.1658179937.txt.gz · Last modified: 2022/07/18 21:32 by ahehn