From f1c8d858cc40458db72530664c8c8a6eb0c36de8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Ole=20Sch=C3=BCtt?= Date: Sun, 10 Dec 2023 22:18:44 +0100 Subject: [PATCH] Manual: Migrate howto:tddft from wiki (Orig. Author: Anna Hehn) --- docs/methods/properties/index.md | 2 +- docs/methods/properties/tddft.md | 512 +++++++++++++++++++++++++++++++ 2 files changed, 513 insertions(+), 1 deletion(-) create mode 100644 docs/methods/properties/tddft.md diff --git a/docs/methods/properties/index.md b/docs/methods/properties/index.md index b83dbf925c..b40b9d3283 100644 --- a/docs/methods/properties/index.md +++ b/docs/methods/properties/index.md @@ -6,7 +6,7 @@ titlesonly: maxdepth: 1 --- X-Ray -Optical +tddft Infrared raman nmr diff --git a/docs/methods/properties/tddft.md b/docs/methods/properties/tddft.md new file mode 100644 index 0000000000..82f8d2e152 --- /dev/null +++ b/docs/methods/properties/tddft.md @@ -0,0 +1,512 @@ +# Optical Spectroscopy + +This is a short tutorial on how to run linear-response time-dependent density functional theory +(LR-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 [Strand2019] and in [Hehn2022] for +corresponding excited-state gradients. Note that the current module is based on an earlier TDDFT +implementation [](#Iannuzzi2005). Please cite these papers if you were to use the TDDFT module for +the computation of excitation energies ([Strand2019], [](#Iannuzzi2005)) or excited-state gradients +([Hehn2022]). + +## 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 + +$$ +\mathbf{A} \mathbf{X}^p &= \Omega^p \mathbf{S} \mathbf{X}^p \, , \\ +\sum_{\kappa k} [ F_{\mu \kappa \sigma} \delta_{ik} - F_{ik \sigma} S_{\mu \kappa} ] X^p_{\kappa k \sigma} + \sum_{\lambda} K_{\mu \lambda \sigma} [\mathbf{D}^{{\rm{\tiny{X}}}p}] C_{\lambda i \sigma} &= \sum_{\kappa} \Omega^p S_{\mu \kappa} X^p_{\kappa i \sigma} \, . +$$ + +The Hermitian matrix $\mathbf{A}$ contains as zeroth-order contributions the difference in the +Kohn-Sham (KS) orbital energies $\mathbf{F}$, and to first order kernel contributions $\mathbf{K}$ +which comprise --depending on the chosen density functional approximation -- Coulomb $\mathbf{J}$ +and exact exchange $\mathbf{K}^{\rm{\tiny{EX}}}$ contributions as well as contributions due to the +exchange-correlation (XC) potential $\mathbf{V}^{\rm{\tiny{XC}}}$ and kernel +$\mathbf{f}^{\rm{\tiny{XC}}}$, + +$$ +F_{\mu \nu \sigma} [\mathbf{D}] &= h_{\mu \nu} + J_{\mu \nu \sigma} [\mathbf{D}] - a_{\rm{\tiny{EX}}}K^{\rm{\tiny{EX}}}_{\mu \nu \sigma} [\mathbf{D}] + V_{\mu \nu \sigma}^{\rm{\tiny{XC}}} \, , \\ +K_{\mu \nu \sigma} [\mathbf{D}^{{\rm{\tiny{X}}}p}] &= J_{\mu \nu \sigma} [\mathbf{D}^{{\rm{\tiny{X}}}p}] - a_{\rm{\tiny{EX}}} K^{\rm{\tiny{EX}}}_{\mu \nu \sigma}[\mathbf{D}^{{\rm{\tiny{X}}}p}] + \sum_{\kappa \lambda \sigma'} f^{\rm{\tiny{XC}}}_{\mu \nu \sigma,\kappa \lambda \sigma'} D_{\kappa \lambda \sigma'}^{{\rm{\tiny{X}}}p} \, . +$$ + +$\mathbf{S}$ 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, + +$$ +D_{\mu \nu \sigma} &= \sum_k C_{\mu k \sigma} C_{\nu k \sigma}^{\rm{T}} \, , \\ +D_{\mu \nu \sigma}^{{\rm{\tiny{X}}}p} &= \frac{1}{2} \sum_{k} ( X^p_{\mu k \sigma} C_{\nu k \sigma}^{\rm{T}} + C_{\mu k \sigma} (X^p_{\nu k \sigma})^{\rm{T}} ) \, . +$$ + +Within the current implementation, symmetrization and orthogonalization of the response density +matrix is ensured at each step of the Davidson algorithm. The current implementation features to +approximate the exact exchange contribution of hybrid functionals using the auxiliary density matrix +method (ADMM). Furthermore, the standard kernel can be approximated using the semi-empirical +simplified Tamm-Dancoff approximation (sTDA), neglecting in this case XC contributions and +approximating both Coulomb and exchange contributions $\mathbf{J}$ and $\mathbf{K}$ using +semi-empirical operators $\boldsymbol{\gamma}^{\rm{\tiny{J}}}$ and +$\boldsymbol{\gamma}^{\rm{\tiny{K}}}$ depending on the interatomic distance $R_{AB}$ of atoms $A$ +and $B$, + +$$ +\gamma^{\rm{\tiny{J}}}(A,B) &= \left ( \frac{1}{(R_{AB})^{\alpha} + \eta^{-\alpha}} \right)^{1/\alpha} \, , \\ +\gamma^{\rm{\tiny{K}}}(A,B) &= \left ( \frac{1}{(R_{AB})^{\beta} +( a_{\rm{\tiny{EX}}}\eta)^{- \beta} } \right )^{1/\beta} \, , +$$ + +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, oscillator strengths can be calculated for molecular systems in +the length form and for periodic systems using the velocity form (see [Strand2019]). + +Based on the TDA eigenvalue problem, excited-state gradients can be formulated based on a +variational Lagrangian for each excited state $p$, + +$$ +L [\mathbf{X}, \mathbf{C}, \Omega, \bar{\mathbf{W}}^{\rm{\tiny{X}}}, \bar{\mathbf{Z}}, \bar{\mathbf{W}}^{\rm{\tiny{C}}} ] &= \Omega - \sum_{\kappa \lambda k l \sigma} \Omega ( X_{\kappa k \sigma }^{\rm{T}} S_{\kappa \lambda } X_{\lambda l \sigma} - \delta_{kl} ) \\ +&- \sum_{kl \sigma} ( \bar{W}_{kl \sigma}^{\rm{\tiny{X}}} )^{\rm{T}} \sum_{\kappa \lambda} \frac{1}{2} ( C_{\kappa k \sigma}^{\rm{T}} S_{\kappa \lambda} X_{\lambda l \sigma} + X_{\kappa k \sigma}^{\rm{T}}S_{\kappa \lambda} C_{\lambda l \sigma}) \\ +&+ \sum_{\kappa k \sigma}( \bar{Z}_{\kappa k \sigma})^{\rm{T}} \sum_{\lambda} ( F_{\kappa \lambda \sigma}C_{\lambda k \sigma} - S_{\kappa \lambda } C_{\lambda k \sigma} \varepsilon_{k \sigma}) \\ +&- \sum_{kl\sigma} (\bar{W}^{\rm{\tiny{C}}}_{kl \sigma})^{\rm{T}} ( S_{kl \sigma} - \delta_{kl})\, . +$$ + +introducing Lagrange multipliers $\bar{\mathbf{W}}^{\rm{\tiny{X}}}$, +$\bar{\mathbf{W}}^{\rm{\tiny{C}}}$, and $\bar{\mathbf{Z}}$ to ensure stationarity of the +corresponding ground-state (GS) equations and to account for the geometric dependence of the +Gaussian orbitals and thus requiring to solve the Z vector equation iteratively. + +## The LR-TDDFT input section + +To compute absorption spectra, parameters defining the LR-TDDFT computation have to be specified in +the [TDDFPT](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT) subsection. Furthermore, +[RUN_TYPE](#CP2K_INPUT.GLOBAL.RUN_TYPE) has to be set to `ENERGY` and the underlying KS ground-state +reference has to be specified in the [DFT](#CP2K_INPUT.FORCE_EVAL.DFT) section. + +The most important keywords and subsections of [TDDFPT](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT) +are: + +- [KERNEL](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.KERNEL): option for the kernel matrix + $\mathbf{K}$ to choose between the full kernel for GGA or hybrid functionals and the simplified + TDA kernel +- [NSTATES](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.NSTATES): number of excitation energies to be + computed +- [CONVERGENCE](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.CONVERGENCE): threshold for the convergence + of the Davidson algorithm +- [RKS_TRIPLETS](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.RKS_TRIPLETS): option to switch from the + default computation of singlet excitation energies to triplet excitation energies +- [RESTART](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.RESTART): the keyword enables the restart of + the TDDFPT computation if a corresponding restart file (.tdwfn) exists +- [WFN_RESTART_FILE_NAME](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.WFN_RESTART_FILE_NAME): for a + restart of the TDDFPT computation, the name of the restart file has to be specified using this + keyword + +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 `EXCITED_STATES` of the +section `DFT`. + +## Simple examples + +### Excitation energies for acetone + +The following input is a standard input for calculating excitation energies with the hybrid +functional PBE0. It should be noted that it is possible to compute the exact exchange integrals for +hybrid functionals analytically at however high computational costs. It is therefore recommended to +use the Auxiliary Density Matrix Method (ADMM) [](#Guidon2010) to approximate the exact exchange +contribution. For GGAs, the corresponding ADMM sections are not required and it is sufficient to +specify the chosen functional in the subsection `&XC_FUNCTIONAL` of the `&XC` section. + +```none +&GLOBAL + PROJECT S20Acetone + RUN_TYPE ENERGY + PREFERRED_DIAG_LIBRARY SL + PRINT_LEVEL medium +&END GLOBAL +&FORCE_EVAL + METHOD Quickstep + &PROPERTIES + &TDDFPT ! input section for TDDFPT + KERNEL FULL ! specification of the underlying kernel matrix K + ! FULL kernel is for GGA and hybrid functional computations + ! sTDA kernel is referring to a semi-empirical sTDA computation + NSTATES 10 ! specifies the number of excited states to be computed + MAX_ITER 100 ! number of iterations for the Davidson algorithm + CONVERGENCE [eV] 1.0e-7 ! convergence threshold in eV + RKS_TRIPLETS F ! Keyword to choose between singlet and triplet excitations + ! &XC ! If choosing kernel FULL, the underlying functional can be + ! &XC_FUNCTIONAL PBE0 ! specified by adding an XC section + ! &END XC_FUNCTIONAL ! The functional can be chosen independently from the chosen + ! &END XC ! GS functional except when choosing ADMM + ! &MGRID ! It is also possible to choose a separate grid for the real-space + ! CUTOFF 800 ! integration of the response density in the TDDFT part, + ! REL_CUTOFF 80 ! however, in general a consistent setup for GS and ES is recommended + ! &END MGRID + &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 + PRECONDITIONER FULL_ALL + MINIMIZER DIIS + &END OT + &OUTER_SCF + MAX_SCF 900 + EPS_SCF 1.0E-7 + &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 + &MGRID + CUTOFF 800 + REL_CUTOFF 80 + &END MGRID + &AUXILIARY_DENSITY_MATRIX_METHOD ! For hybrid functionals, it is recommended to choose ADMM + METHOD BASIS_PROJECTION ! the ADMM environment for ground and excited state has to be + EXCH_SCALING_MODEL NONE ! identical + EXCH_CORRECTION_FUNC NONE ! Triple-zeta auxiliary basis sets are recommended (see below) + ADMM_PURIFICATION_METHOD NONE ! For periodic systems (see below), only specific ADMM options + &END AUXILIARY_DENSITY_MATRIX_METHOD ! are available + &POISSON + PERIODIC NONE + POISSON_SOLVER WAVELET + &END + &XC + &XC_FUNCTIONAL PBE0 + &END XC_FUNCTIONAL + &END XC + &END DFT + &SUBSYS + &CELL + ABC [angstrom] 14.0 14.0 14.0 + PERIODIC NONE + &END CELL + &COORD + 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 + &TOPOLOGY + &CENTER_COORDINATES T + &END + &END + &KIND H + BASIS_SET ORB DZVP-MOLOPT-PBE0-GTH-q1 ! in general it is recommended to use larger basis sets + BASIS_SET AUX_FIT admm-dzp-q1 ! for the primary and auxiliary basis (TZVP/tzp) + 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 `TDDFPT` section reporting the steps of the calculations. +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. + +```none + ------------------------------------------------------------------------------- + - TDDFPT Initial Guess - + ------------------------------------------------------------------------------- + State Occupied -> Virtual Excitation + number orbital orbital energy (eV) + ------------------------------------------------------------------------------- + 1 12 13 6.63336 + 2 11 13 9.62185 + 3 10 13 10.34045 + 4 9 13 10.78846 + 5 8 13 11.05691 + 6 12 14 12.07194 + 7 7 13 12.42370 + 8 6 13 12.63557 + 9 12 15 12.65312 + 10 5 13 12.68633 +``` + +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 [DIPOLE_FORM](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.DIPOLE_MOMENTS.DIPOLE_FORM). Possible +options are `BERRY` (valid for fully periodic systems only), `LENGTH` (valid for molecular systems +only) and `VELOCITY` (both). 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 +[REFERENCE_POINT](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.DIPOLE_MOMENTS.REFERENCE_POINT) or by +choosing one of the options `COM` (center of mass), `COAC` (center of atomic charges), +`USER_DEFINED` (user-defined point) and `ZERO` (origin of the coordinate system) for the +[REFERENCE](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.DIPOLE_MOMENTS.REFERENCE) keyword. + +```none + ------------------------------------------------------------------------------- + - TDDFPT run converged in 10 iteration(s) + ------------------------------------------------------------------------------- + + R-TDDFPT states of multiplicity 1 + Transition dipoles calculated using velocity formulation + + State Excitation Transition dipole (a.u.) Oscillator + number energy (eV) x y z strength (a.u.) + ------------------------------------------------------------------------ + TDDFPT| 1 4.67815 2.4840E-08 -1.9187E-08 5.9673E-08 5.21038E-16 + TDDFPT| 2 8.73074 -8.1610E-09 1.0502E-08 9.1823E-08 1.84132E-15 + TDDFPT| 3 9.17033 1.6661E-02 2.4911E-08 -9.2612E-08 6.23670E-05 + TDDFPT| 4 9.70094 -2.3716E-09 7.2323E-07 7.0660E-01 1.18663E-01 + TDDFPT| 5 9.88658 -3.1922E-08 -4.1476E-01 1.0768E-06 4.16669E-02 + TDDFPT| 6 10.78269 3.5483E-08 4.2695E-01 -1.3123E-07 4.81550E-02 + TDDFPT| 7 10.82893 2.3885E-01 -3.0329E-08 4.5882E-09 1.51356E-02 + TDDFPT| 8 10.92800 -2.4034E-07 -2.4299E-08 5.8160E-08 1.65293E-14 + TDDFPT| 9 11.32208 8.3808E-08 -6.8844E-01 1.9166E-07 1.31469E-01 + TDDFPT| 10 11.97282 1.2605E-08 1.7029E-08 3.3026E-01 3.19930E-02 +``` + +A more detailed analysis of the excitations is given subsequently, listing orbital contributions for +each transition with the corresponding excitation amplitudes. The keyword +[MIN_AMPLITUDE](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.MIN_AMPLITUDE) regulates the threshold for +the smallest amplitude to print. + +```none +------------------------------------------------------------------------------- + - Excitation analysis - + ------------------------------------------------------------------------------- + State Occupied Virtual Excitation + number orbital orbital amplitude + ------------------------------------------------------------------------------- + 1 4.67815 eV + 12 13 0.998438 + 2 8.73074 eV + 10 13 0.995560 + 6 13 0.087643 + 3 9.17033 eV + 9 13 0.993356 + 7 13 0.075589 + 4 9.70094 eV + 11 13 -0.893130 + 12 16 0.297568 + 5 13 0.269023 + 12 28 -0.108047 + 9 15 0.066145 + 9 30 -0.050159 +``` + +### Excited-state gradient for acetone + +To perform an excited-state optimization for emission spectroscopy, the run type has to be set to +`GEO_OPT` and the state to be optimized has to be specified in the +[EXCITED_STATES](#CP2K_INPUT.FORCE_EVAL.DFT.EXCITED_STATES) section. Note that the number of excited +states chosen in the TDDFPT section should be larger or at least equal to the number of the chosen +excited state. + +```none + &GLOBAL + PROJECT S20Acetone + RUN_TYPE ENERGY_FORCE ! The run type has to be changed to ENERGY_FORCE of GEO_OPT + PREFERRED_DIAG_LIBRARY SL + PRINT_LEVEL medium + &END GLOBAL + &PROPERTIES + &TDDFPT + NSTATES 10 + MAX_ITER 100 + CONVERGENCE [eV] 1.0e-7 + RKS_TRIPLETS F + ADMM_KERNEL_CORRECTION_SYMMETRIC T ! required keyword when using hybrid functionals and ADMM for + &END TDDFPT ! the exact exchange contribution for ES gradients + &END PROPERTIES + ... + &DFT + &QS + METHOD GPW + EPS_DEFAULT 1.0E-17 + EPS_PGF_ORB 1.0E-20 + &END QS + &EXCITED_STATES T + STATE 1 ! the excited state to be optimized has to be specified in this section + &END EXCITED_STATES + &SCF + SCF_GUESS restart + &OT + PRECONDITIONER FULL_ALL + MINIMIZER DIIS + &END OT + &OUTER_SCF + MAX_SCF 900 + EPS_SCF 1.0E-7 + &END OUTER_SCF + MAX_SCF 10 + EPS_SCF 1.0E-7 + &END SCF + ... + &END DFT +``` + +The resulting output file contains for each step of the geometry optimization the already explained +output of the TDDFPT computation and additionally information on the excited state that is optimized +as well as the iterative solution of the Z vector equations. + +```none + !--------------------------- Excited State Energy ----------------------------! + Excitation Energy [Hartree] 0.1719188002 + Total Energy [Hartree] -36.3332484083 + !-----------------------------------------------------------------------------! + !--------------------------- Excited State Forces ----------------------------! + + Iteration Method Restart Stepsize Convergence Time + ------------------------------------------------------------------------------ + 1 PCG F 0.00E+00 0.0231470476 0.02 + 2 PCG F 0.30E+00 0.0003972862 1.56 + 3 PCG F 0.60E+00 0.0000361012 3.11 + 4 PCG F 0.62E+00 0.0000031865 4.65 + 5 PCG F 0.63E+00 0.0000002183 6.19 + 6 PCG F 0.73E+00 0.0000000147 7.73 + 7 PCG F 0.70E+00 0.0000000014 9.27 + 8 PCG F 0.72E+00 0.0000000001 10.82 + 9 PCG F 0.71E+00 0.0000000000 12.35 + !-----------------------------------------------------------------------------! + + ENERGY| Total FORCE_EVAL ( QS ) energy [a.u.]: -36.333248408276823 + + ------------------------------------------------------------------------------- +``` + +### Choosing a semi-empirical kernel + +To speed up computation times for broad-band absorption spectra, a semi-empirical simplified +Tamm-Dancoff (sTDA) kernel can be chosen by setting +[KERNEL](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.KERNEL) to `sTDA`. The semi-empirical electron +repulsion operators depend on several empirical parameters, which need to be adjusted depending on +the system under investigation. Most importantly, the amount of exact exchange, scaled by adjusting +the parameter $a_{\rm{\tiny{EX}}}$ needs to be chosen carefully and is really crucial to ensure a +well-balanced treatment of exact exchange in the GS and ES potential energy surfaces. Too large +fractions of exchange in the excited state can lead to negative excitation energies. In general, a +relatively small amount of exchange $a_{\rm{\tiny{EX}}}=0.2 / 0.1$ is therefore recommended. + +For details on the STDA method see also . + +The most important keywords of the subsection [sTDA](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.STDA) +are: + +- [FRACTION](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.STDA.FRACTION): fraction of exact exchange + $a_{\rm{\tiny{EX}}}$ +- [MATAGA_NISHIMOTO_CEXP](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.STDA.MATAGA_NISHIMOTO_CEXP): + keyword to modify the parameter $\alpha$ of $\gamma^{\rm{\tiny{J}}}$ +- [MATAGA_NISHIMOTO_XEXP](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.STDA.MATAGA_NISHIMOTO_XEXP): + keyword to modify the parameter $\beta$ of $\gamma^{\rm{\tiny{K}}}$ +- [DO_EWALD](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.STDA.DO_EWALD): keyword to switch on Ewald + summation for the Coulomb contributions, required when treating periodic systems. (Exact exchange + is treated within the minimum image convention and does not require any adjustment.) + +```none +&PROPERTIES + &TDDFPT + KERNEL sTDA ! switches on the semi-empirical kernel sTDA + &sTDA + FRACTION 0.2 ! it is crucial to adjust the fraction of exact exchange + &END sTDA + NSTATES 10 + MAX_ITER 100 + CONVERGENCE [eV] 1.0e-7 + RKS_TRIPLETS F + &END TDDFPT +&END PROPERTIES +``` + +In the output, it can be checked that the sTDA kernel was switched on and the correct parameters for +$\alpha$, $\beta$ and $a_{\rm{\tiny{EX}}}$ were chosen: + +```none + sTDA| HFX Fraction 0.2000 + sTDA| Mataga-Nishimoto exponent (C) 1.5160 + sTDA| Mataga-Nishimoto exponent (X) 0.5660 + sTDA| TD matrix filter 0.10000000E-09 + + ------------------------------------------------------------------------------- + - sTDA Kernel: Create Matrix SQRT(S) - + ------------------------------------------------------------------------------- +``` + +The subsequent printout is then identical to the printout for GGA and hybrid functional kernels: + +```none + R-TDDFPT states of multiplicity 1 + Transition dipoles calculated using velocity formulation + + State Excitation Transition dipole (a.u.) Oscillator + number energy (eV) x y z strength (a.u.) + ------------------------------------------------------------------------ + TDDFPT| 1 4.88982 8.2927E-09 8.6085E-09 -2.2495E-08 7.77366E-17 + TDDFPT| 2 9.05888 4.5649E-09 -4.9483E-09 -8.2739E-08 1.52940E-15 + TDDFPT| 3 9.23700 1.4100E-02 -1.2802E-08 3.2962E-08 4.49914E-05 + TDDFPT| 4 9.52129 1.1297E-08 -4.7865E-08 8.3174E-01 1.61372E-01 + TDDFPT| 5 10.01790 -9.4987E-09 -4.8324E-01 -5.0387E-08 5.73140E-02 + TDDFPT| 6 10.86728 -1.6175E-08 -3.6799E-01 -7.5353E-09 3.60529E-02 + TDDFPT| 7 10.97656 -3.7898E-01 -1.0287E-08 -3.3941E-09 3.86231E-02 + TDDFPT| 8 11.21831 4.5569E-08 -4.2529E-09 1.9115E-08 6.76117E-16 + TDDFPT| 9 11.40817 2.7777E-08 -6.8033E-01 -3.7411E-08 1.29362E-01 + TDDFPT| 10 11.82525 -1.2576E-09 1.3562E-08 3.8592E-01 4.31486E-02 +``` + +It should be noted that it is possible to combine sTDA with the semi-empirical ground-state +reference GFN1-xTB. However, it is then recommended to adjust all parameters [](#Grimme2016) and to +apply corrections to shift the virtual KS orbital eigenvalues. A shift can be applied by adding the +keyword [EV_SHIFT](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.EV_SHIFT) (for open-shell systems +[EOS_SHIFT](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.EOS_SHIFT)). + +### Periodic systems + +Adjustments are required when switching to periodic boundary conditions. As already mentioned above, +oscillator strengths should be calculated using the `BERRY` or `VELOCITY` formulation. When choosing +the `sTDA` kernel, [DO_EWALD](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.STDA.DO_EWALD) has to be +switched to true to activate Ewald summation for Coulomb contributions. When computing ES gradients +using [KERNEL](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.KERNEL) `FULL` in combination with hybrid +functionals and ADMM, only the ADMM2 method relying on basis projection is implemented in +combination with the default for the exchange functional for the first-order GGA correction term. + +```none +&AUXILIARY_DENSITY_MATRIX_METHOD + METHOD BASIS_PROJECTION + ADMM_PURIFICATION_METHOD NONE + EXCH_SCALING_MODEL NONE + EXCH_CORRECTION_FUNC PBEX +&END +``` + +### Natural transition orbitals + +Natural transition orbitals (NTOs) are printed when choosing `PRINT_LEVEL medium` in the `GLOBAL` +section or when enabling the +[NTO_ANALYSIS](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.PRINT.NTO_ANALYSIS) section. For this +purpose it is required to generate unoccupied orbitals and the keyword +[LUMO](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.NLUMO) enables to adjust the number of unoccupied +orbitals. It is possible to print the NTOs as `CUBE_FILES` or in Molden format, with the latter +being activated with the keyword +[MOS_MOLDEN](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.PRINT.MOS_MOLDEN). + +[hehn2022]: https://doi.org/10.1021/acs.jctc.2c00144 +[strand2019]: https://doi.org/10.1063/1.5078682