.. tip:: All input files can be downloaded: :download:`Files `. eda ===== .. contents:: :local: This keyword defines how to perform an energy decomposition analysis (EDA) calculation. Options ------------ .. option:: type .. list-table:: :stub-columns: 1 * - Value - ``tso`` for block localized wavefunction energy decomposition analysis (TSO-EDA). * - - ``gks`` for generalized Kohn-Sham energy decomposition analysis (GKS-EDA). * - - ``mb_tso`` for many-body interaction TSO-EDA. * - - ``mb_gks`` for many-body interaction GKS-EDA. * - Default - None Both GKS-EDA and TSO-EDA is available for intermolecular interaction analysis. Furthermore, combined with the many-body expansion scheme, two new methods, i.e. many-body GKS-EDA and many-body TSO-EDA, are available for the analysis of many-body interactions. In Qbics, we **recommend to use TSO-EDA for EDA calculations.** .. option:: frag This option defines the fragments' partition of an system. The format is: ``frag num_electrons spin_multiplicity atom_range`` which is the same as the keyword ``frag`` in ``scfguess`` option. See :doc:`scfguess`. .. option:: nobsse Do not do the Boys and Bernardi's counterposise (CP) correction for basis set superposition error (BSSE). Qbics does BSSE correction by default. You can use this keword to avoid it when you don't need to consider BSSE. .. option:: tso_for_guess Do TSO calculation first for the initial guess of fragments' wavefunction, which is necessary for the case there are fragments with C∞ group symmetry such as an atom. For ``tso``` and ``mb_tso``, this is default. While for ``gks`` and ``mb_gks``, this is optional. .. option:: mb_level .. list-table:: :stub-columns: 1 :widths: 5 20 * - Value - An integer * - Default - ``2`` Truncation level for many-body interaction analysis, i.e. ``mb_gks`` and ``mb_tso`` calculations. The value should **NOT** be smaller than 2 and equal to or greater than the number of fragments. Usually, ``4`` is a good choice, if the number of fragments is larger than 4. Higher order terms are very small and can be ignored. .. warning:: For EDA tasks, you should add ``type U`` in the ``scf`` keyword to ensure the unrestricted calculation. Otherwish, the calculation will be failed. Theoretical Background ------------------------- .. hint:: If you use ``tso`` and ``mb_tso``, please cite the following reference: - `J. Chem. Theory Comput. 2023, 19, 1777 `_ - `Phys. Chem. Chem. Phys. 2024, 26, 17549 `_ If you use ``gks`` and ``mb_gks``, please cite the following reference: - `J. Phys. Chem. A 2014, 118, 2531 `_ - `WIREs Comput. Mol. Sci. 2020, 10, e1460 `_ - `Phys. Chem. Chem. Phys. 2024, 26, 17549 `_ TSO-EDA ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ TSO-EDA is based on target state optimization self-consistent field method (`J. Chem. Theory Comput. 2023, 19, 1777 `_) and decomposes the total interaction energy into five terms, i.e. electrostatic, exchange, polarization, charge transfer, and dispersion energies. The sum of electrostattic and exchange energy is the Heitler-London term (`Phys. Chem. Chem. Phys. 2024, 26, 17549 `_): .. figure:: figs/eda-2.jpg Here: - Ectrostatic term: Represents the semiclassical Coulombic interaction of charged particles from different monomers; - Exchange term: Represents quantum effect due to the antisymmetric character of the electronic wave function and the satisfaction of the Pauli exclusion principle; - Polarization term: Represents the polarization of the electron density of one monomer by the presence of other monomer; - Charge transfer term: Represents the charge transfer between monomers; - Dispersion term: Represents the dispersion interaction between monomers. The BSSE effect is included in charge transfer term. All above terms can be found in Qbics output. Many-Body TSO-EDA ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This method is developed in `Phys. Chem. Chem. Phys. 2024, 26, 17549 `_ and is used to analyze the many-body effects in a molecular cluster. The total interaction energy is decomposed into 2-body, 3-body, and higher-order terms, like this: .. math:: \Delta E^{\text{int}} = \frac{1}{2!} \sum_{I_1 \neq I_2}^{N} \Delta E_{I_1 I_2}^{(2)} +\frac{1}{3!} \sum_{I_1 \neq I_2 \neq I_3}^{N} \Delta E_{I_1 I_2 I_3}^{(3)} + \cdots + \frac{1}{n!} \sum_{I_1 \neq \cdots \neq I_n}^{N} \Delta E_{I_1 \cdots I_n}^{(n)} + \cdots + \Delta E_{I_1 \cdots I_N}^{(N)} \equiv \sum_{n=2}^{N} \Delta E^{(n)} The terms higher than :math:`\Delta E^{(2)}` is the many-body interaction term. Usually the most important one is the three-body effect :math:`\Delta E^{(3)}`, the effects of which can be decomposed into three ones: - :math:`\Delta E^{(3)} < 0`: Indicate a **cooperative effect** of the monomers in a cluster. The many-body interaction is stabilizing the cluster. This is often seen in hydrogen bonding clusters, like water clusters. - :math:`\Delta E^{(3)} > 0`: Indicate an **anti-cooperative effect** of the monomers in a cluster. The many-body interaction is destabilizing the cluster. This is often seen in a cluster of charged species, like ionic liquid clusters. Also see below. - :math:`\Delta E^{(3)} \approx 0`: Indicate a **non-cooperative effect** of the monomers in a cluster. There is little many-body interaction in the cluster. This is often seen in a cluster of molecules without charges or hydrogen bonds. Each order can be decomposed into electrostatic, exchange, polarization, charge transfer, and dispersion terms: .. math:: \Delta E_X^{(n)} = \Delta E_X^{(n)\text{-el}} + \Delta E_X^{(n)\text{-ex/xc}} + \Delta E_X^{(n)\text{-pl}} + \Delta E_X^{(n)\text{-ct}} + \Delta E_X^{(n)\text{-disp}} Usually, electrostatic and exchange terms are highly additive, while polarization and charge transfer terms are non-additive. The dispersion term is always additive. Input Examples -------------------- Example: EDA for GeH\ :sub:`3`\ F-NCH Complex by B3LYP-D3BJ/def2-SVP ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ For the complex GeH\ :sub:`3`\ F-NCH, we can do EDA calculation by the following input: .. code-block:: bash :linenos: :caption: eda-1.inp mol Ge 0.00000000 0.00221863 -0.79935317 H 0.00000000 1.48645043 -0.40384625 H 1.28514604 -0.74161126 -0.40477816 H -1.28514603 -0.74161126 -0.40477816 F 0.00000000 0.00108752 -2.56116087 C 0.00000000 -0.00225138 3.35662076 H 0.00000000 -0.00220444 4.43604901 N 0.00000000 -0.00207825 2.20326200 end basis def2-svp end scf charge 0 spin2p1 1 type U # For EDA calculations, this must be added explicitly. end grimmedisp type bj end eda type tso # You can also change it to: gks frag 0 1 1-5 # Define GeH3F. frag 0 1 6-8 # Define HCN. end task eda b3lyp end The atom indices are shown below: .. figure:: figs/basinfo-1.jpg The results are: .. tabs:: .. tab:: TSO-EDA Results .. code-block:: bash :linenos: :caption: eda-tso.out WITH BSSE correction: Electrostatic interaction energy: -4.98 kcal/mol Exchange-correlation interaction energy: 4.22 kcal/mol Polarization interaction energy: -0.62 kcal/mol Charge transfer interaction energy: -1.31 kcal/mol Grimme's dispersion interaction: -1.58 kcal/mol ---------------------------------------------------------------- Total interaction energy: -4.27 kcal/mol .. tab:: GKS-EDA Results .. code-block:: bash :linenos: :caption: eda-gks.out WITH BSSE correction: Electrostatic interaction energy: -6.22 kcal/mol Exchange interaction energy: -9.64 kcal/mol Repulsion interaction energy: 15.94 kcal/mol Polarization interaction energy: -2.52 kcal/mol Correlation interaction energy: -0.24 kcal/mol Grimme's dispersion interaction: -1.58 kcal/mol ---------------------------------------------------------------- Total interaction energy: -4.27 kcal/mol We can see that the total interaction energies (with or without BSSE) are the same for both TSO-EDA and GKS-EDA methods, but components are different. As mentioned, Qbics recommends **TSO-EDA** for calculations. This complex is stabilized by ``Electrostatic interaction eneregy``, which is compatible with the chemical intuition that it is stabilized by sigma-hole. Example: MB-EDA for Molecular Cluster (NH\ :sub:`4`:sup:`+`)\ :sub:`2`\ (H\ :sub:`2`\ SO\ :sub:`4`)(HSO\ :sub:`4`:sup:`-`)\ :sub:`2` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The title cluster is composed of two NH\ :sub:`4`:sup:`+` cations, one H\ :sub:`2`\ SO\ :sub:`4` molecules, and two HSO\ :sub:`4`:sup:`-` anions. This cluster is used in the study of atmopheric chemistry.We can do MB-EDA calculation by the following input: .. code-block:: bash :linenos: :caption: eda-2.inp basis def2-svp end scf charge 0 # Total charge. spin2p1 1 type U end grimmedisp type bj end eda type mb_tso mb_level 4 frag +1 1 1-5 # NH4+ frag +1 1 6-10 # NH4+ frag 0 1 11-17 # H2SO4 frag -1 1 18-23 # HSO4- frag -1 1 24-29 # HSO4- end mol N 0.13124700 -1.86033100 -1.49054300 H -0.68471400 -1.96085700 -0.84840100 H 0.16284500 -2.63375000 -2.14527600 H -0.00155300 -0.97157900 -1.98611500 H 1.02982000 -1.79400200 -0.97437700 N -1.89606400 2.02266900 1.95536400 H -2.33766600 1.07911300 1.78190600 H -1.20423600 1.92734800 2.69193100 H -1.40455300 2.34660500 1.08417600 H -2.60508400 2.69280200 2.23215700 S 3.40269500 -0.73966700 0.43845300 O 4.56636300 -1.26003200 1.03924300 O 2.66268100 -1.55477200 -0.49575900 O 2.42657400 -0.30120000 1.56959800 O 3.78755300 0.58843400 -0.27018200 H 2.99297400 1.01172300 -0.68798600 H 1.56137200 -0.00498400 1.17228000 S -3.05756300 -0.82805000 0.17173500 O -2.21824200 -1.98280100 -0.09354400 O -3.00471800 -0.39464500 1.56194000 O -2.90973700 0.26502300 -0.77053900 O -4.55472700 -1.30387800 -0.08712900 H -4.73898300 -2.05912100 0.48328300 H -1.51856700 0.72871100 -1.53329100 S 0.24159900 1.52238500 -0.65825900 O -0.59336700 0.90131200 -1.85962900 O 1.55183900 1.72430300 -1.22252400 O -0.45708500 2.72297400 -0.23978600 O 0.20716100 0.49864900 0.39894800 end task eda b3lyp end The atom indices are shown below, which is used to define the fragments ``frag``: .. figure:: figs/eda-1.jpg The results are: .. code-block:: bash :linenos: :caption: eda-2.out Table 5. Summary (kcal/mol). --------------------------------------------------------------------------------------------------------------------------------- Interactions delE_el delE_xc delE_pl delE_ct delE_bsse delE_disp delE_tot --------------------------------------------------------------------------------------------------------------------------------- SUM of 2-body -3.51853640E+02 1.04231044E+02 -5.50310217E+01 -9.70290703E+01 4.35696096E+01 -1.98079059E+01 -3.75920984E+02 SUM of 3-body 1.72107484E-09 1.45358519E+00 2.82254671E+01 2.81735373E+01 -1.24450163E+01 1.01531078E-02 4.54177264E+01 SUM of 4-body -4.14670076E-09 1.70212282E-02 -2.25462767E+00 -5.15894065E+00 1.89758583E+00 2.28017787E-05 -5.49893846E+00 Remain 7.51748885E-09 -8.58522126E-04 6.43113307E-02 4.30266615E-01 -1.22896862E-01 5.97720460E-07 3.70823167E-01 --------------------------------------------------------------------------------------------------------------------------------- SUM -3.51853640E+02 1.05700792E+02 -2.89958710E+01 -7.35842070E+01 3.28992822E+01 -1.97977294E+01 -3.35631373E+02 --------------------------------------------------------------------------------------------------------------------------------- We can see that the total interaction energy is -335.63 kcal/mol, which is decomposed into 2-body, 3-body, 4-body, and remaining terms. The 2-body term is the most important one (-375.92 kcal/mol), while the 3-body term is also significant, but **anti-cooperative** (destablizing the complex) (+45.42 kcal/mol). The 4-body term is small (-5.50 kcal/mol, slightly cooperative). The remaining term (sum of 5- and 6-body) is very small (+0.37 kcal/mol) and can be ignored. We can also see that the electrostatic and exchange energy are highly **additive**, while the polarization and charge-transfer energy are **non-additive**. For different kinds of clusters, the 3-body effects (many-body interactions) can be quite different, see `Phys. Chem. Chem. Phys. 2024, 26, 17549 `_ for more information.