```{index} HFLD ``` (sec:spectroscopyproperties.hfld)= # The Hartree-Fock plus London Dispersion (HFLD) Method The efficient and accurate HFLD method{cite}`HFLD` can be used for the quantification and analysis of noncovalent interactions between a pair of user-defined fragments. Starting from ORCA 5.0, an open shell variant of the HFLD method is also available.{cite}`HFLDos` The leading idea here is to solve the DLPNO coupled cluster equations while neglecting intramonomer correlation. The LED scheme is then used to extract the London dispersion (LD) energy from the intermolecular part of the correlation. Finally, the resulting LD energy is used to correct interaction energies computed at the HF level. Hence, HFLD can be considered as a dispersion-corrected HF approach in which the dispersion interaction between the fragments is added at the DLPNO-CC level. As such, it is particularly accurate for the quantification of noncovalent interactions such as those found in H-bonded systems, pre-reactive intermediates (e.g., Frustrated Lewis Pairs), dispersion and electrostatically bound systems. Larger errors are in principle expected for transition metal complexes, as it is the case for any dispersion corrected Hartree-Fock scheme. The efficiency of the approach allows the study of noncovalent interactions in systems with several hundreds of atoms. Some of the most important aspects of the method are summarized below: - **Accuracy and Recommended Settings** \ For noncovalent interactions, HFLD typically provides an accuracy comparable to that of the DLPNO-CCSD(T) method if default PNO settings are used. For the HFLD scheme, these are defined as TCutPNO = 3.3e-7 and TCutPairs 1e-5. If used in conjuction with a def2-TZVP(-f) basis set, these settings are typically denoted as `HFLD*` and are recommended for standard applications on large systems {cite}`HFLDos`. For example, `HFLD*` settings were used in Ref. {cite}`altun2021unveiling` to elucidate the complex pattern of interactions responsible for the stability of the DNA duplex. If great accuracy is required, it is recommended to use TightPNO settings in conjuction with TCutPNO 1e-8 and two-point basis set extrapolation (aug-cc-pVTZ/aug-cc-pVQZ) to approach the CBS limit. These settings are typically denoted as the **gold** HFLD settings {cite}`HFLDos`. - **Reference determinant in the Open shell HFLD scheme** \ In the open shell case, HFLD relies on a restricted reference determinant for the calculation of the LD energy. If the QRO determinant is used as reference, the reference interaction energy can in principle be computed at the UHF or QRO levels. This leads to two different schemes, namely the QRO/HFLD and UHF/HFLD. Alternatively, the restricted open-shell HF (ROHF) determinant can be used as reference in HFLD calculations, which leads to the ROHF/HFLD approach. The energy value reported as `FINAL SINGLE POINT ENERGY` in the output corresponds to the UHF/HFLD scheme by default, which is typically slightly more accurate. See Ref. {cite}`HFLDos` for details. - **Efficency** \ The calculation of the dispersion correction typically requires the same time as an HF calculation. This is true for small as well as for large systems. - **Analysis of Intermolecular Interactions** \ The HFLD method can be combined with the Local Energy Decomposition (LED) to study intermolecular interactions in great detail. The LED dispersion energy obtained with HFLD is often very close to that obtained from a full DLPNO-CCSD(T) calculation. Hence, HFLD can be used as a cost-effective alternative to DLPNO-CCSD(T) to study, among other things, the importance of London dispersion in molecular chemistry. - **Additional considerations** \ (i) One can specify `NormalPNO` or `TightPNO` settings in the simple input line. The corresponding DLPNO thresholds would be in this case fully consistent with those used in the DLPNO-CCSD(T) method. (ii) The dispersion energy in the HFLD approach slightly depends on the choice of the localization scheme used for occupied orbitals and PNOs. Default settings are recommended for all intents and purposes. However, it is important to note that the localization iterations for occupied and virtual orbitals must be fully converged in order to obtain consistent results. To achieve this goal, it might be necessary to increase `LocMaxIter` or `LocMaxIterLed` (see below). However, this is typically necessary only if very large basis sets (e.g. aug-cc-pV5Z) are used. (iii) Importantly, the method benefits from the use of tightly converged SCF solutions. For closed-shell systems, a useful diagnostic in this context is the "Singles energy" term that is printed in the LED part of the output. This term must be smaller than 1e-6 for closed shell species. If this is not the case, one should change the settings used for the SCF iterations. Note also that all the features of the LED scheme (e.g. automatic fragmentation) are also available for the HFLD method. Note that, as HFLD relies on both the DLPNO-CCSD(T) and LED methods, the options of both schemes can be used in principle in conjunction with HFLD. Some examples are shown below: ```orca ! HFLD aug-cc-pVDZ aug-cc-pVDZ/C aug-cc-pVTZ/JK RIJK TightSCF %mdci LED 1 # localization method for the PNOs. Choices: # 1 = PipekMezey # 2 = FosterBoys (default, recommeded for the HFLD method) PrintLevel 3 # Selects large output for LED and prints the # detailed contribution # of each DLPNO-CCSD strong pair LocMaxIterLed 600 # Maximum number of localization iterations for PNOs LocMaxIter 300 # Maximum number of localization iterations for # occupied orbitals LocTolLed 1e-6 # Absolute threshold for the localization procedure for PNOs DoLEDHF true # Decomposes the reference energy in the LED part. # By default, it is set to false in HFLD for efficiency reasons. TCutPNO 3.33e-7 # cutoff for PNO occupation numbers. TCutPairs 1e-5 # cutoff for estimated pair correlation energies # to be included in the CC treatment end ``` (sec:spectroscopyproperties.hfld.basicusage)= ## Basic Usage The Hartree-Fock plus London Dispersion method is invoked using the `!HFLD` keyword in the simple input line. ```orca ! HFLD aug-cc-pvdz aug-cc-pvdz/C ``` (sec:spectroscopyproperties.hfld.example)= ## Example An input example is reported below. ```{literalinclude} ../../orca_working_input/C05S13_241.inp :language: orca ``` In the corresponding output, after the DLPNO-CC iterations and the LED output, the following information is printed: ``` ---------------------------- ---------------- Inter-fragment dispersion -0.001871763 ---------------------------- ---------------- ------------------------- -------------------- FINAL SINGLE POINT ENERGY -114.932878050741 ------------------------- -------------------- ``` The total HFLD energy of the adduct is thus -114.932878050741 a.u.. To compute interaction energies, we have to subtract from this value the Hartree-Fock energies of the monomers in the geometry they have in the complex, i.e., -38.884413525377 and -76.040412827089 a.u. for CH$_2$ and H$_2$O, respectively. The total interaction energy is thus -0.00805 a.u. or -5.1 kcal/mol (the corresponding DLPNO-CCSD(T)/TightPNO/CBS value is -5.3 kcal/mol {cite}`altun2018open`). Note that, to obtain binding energies, the geometric preparation should be added to this value. This can be computed using a standard computational method, e.g, DFT or DLPNO-CCSD(T). (sec:spectroscopyproperties.hfld.keywords)= ## Keywords ```{index} HFLD Keywords ``` :::{note} As HFLD relies on both the DLPNO-CCSD(T) and LED methods, the options of both schemes can be used in principle in conjunction with HFLD. ::: (tab:spectroscopyproperties.hfld.keywords.simple)= :::{table} Simple input keywords for the Hartree Fock plus London Dispersion. | Keyword | Description | |:--------------------------------|:--------------------------------------------------| | `HFLD` | Activates the Hartree Fock plus London Dispersion method | ::: (tab:spectroscopyproperties.hfld.keywords.block)= :::{table} `%mdci` block input keywords for the Hartree Fock plus London Dispersion. | Keyword | Options | Description | |:--------------------------------|:------------------|:-----------------------------------------------------| | `LED` | `1` | PipekMezey used as localization method for the PNOs | | | `2` | FosterBoys used as localization method for the PNOs (default starting from ORCA 4.2) | | `PrintLevel` | `3` | Selects large output for LED and prints the detailed contribution of each DLPNO-CCSD strong pair | | `LocMaxIterLed` | `` | Maximum number of localization iterations for PNOs (set to 600 by default) | | `LocMaxIter` | `` | Maximum number of localization iterations for occupied orbitals (set to 128 by default) | | `LocTocLed` | `` | Absolute threshold for the localization procedure for PNOs (set to 1e-6 by default) | | `DoLEDHF` | `true/false` | Decomposes the reference energy in the LED part (by default, it is set to false in HFLD for efficency reasons). | | `TCutPNO` | `` | Cutoff for PNO occupation numbers (set to 3.33e-7 by default). | | `TCutPairs` | `` | Cutoff for estimated pair correlation energies to be included in the CC treatment (set to 1e-5 by default). | :::