eda

This keyword specifies the method used to perform an Energy Decomposition Analysis (EDA) calculation.

Options

Theoretical Background

TSO-EDA

TSO-EDA is based on the Target State Optimization self-consistent field method (J. Chem. Theory Comput. 2023, 19, 1777) and decomposes the total interaction energy into five terms: electrostatic, exchange, polarization, charge transfer, and dispersion energies. The sum of electrostatic and exchange energy is referred to as the Heitler–London term (Phys. Chem. Chem. Phys. 2024, 26, 17549).

The energy terms in TSO-EDA are defined as follows:

• Electrostatic term: Represents the semiclassical Coulombic interaction between charged particles from different monomers.
• Exchange term: Accounts for quantum effects arising from the antisymmetric nature of the electronic wavefunction and the Pauli exclusion principle.
• Polarization term: Describes the polarization of the electron density of one monomer due to the presence of another.
• Charge transfer term: Represents the transfer of electronic charge between monomers.
• Dispersion term: Represents dispersion (van der Waals) interactions between monomers.

The basis set superposition error (BSSE) is included in the charge transfer term. All of the above energy components can be found in the Qbics output.

Many-Body TSO-EDA

This method, developed in Phys. Chem. Chem. Phys. 2024, 26, 17549, is used to analyze many-body effects in molecular clusters. The total interaction energy is decomposed into two-body, three-body, and higher-order contributions, as follows:

$$\Delta E^{\text{int}} = \frac{1}{2!} \sum_{I_1 \neq I_2}^{N} \Delta E_{I_1 I_2}^{(2)} +\frac{1}{3!} \sum_{I_1 \neq I_2 \neq I_3}^{N} \Delta E_{I_1 I_2 I_3}^{(3)} + \cdots + \frac{1}{n!} \sum_{I_1 \neq \cdots \neq I_n}^{N} \Delta E_{I_1 \cdots I_n}^{(n)} + \cdots + \Delta E_{I_1 \cdots I_N}^{(N)} \equiv \sum_{n=2}^{N} \Delta E^{(n)}$$

Terms beyond \( \Delta E^{(2)} \) represent many-body interaction effects. Among these, the three-body term \( \Delta E^{(3)} \) is usually the most significant. Its behavior can be categorized into three types:

• \( \Delta E^{(3)} < 0 \): Indicates a cooperative effect among monomers. The many-body interaction stabilizes the cluster. This is commonly observed in hydrogen-bonded systems, such as water clusters.
• \( \Delta E^{(3)} > 0 \): Indicates an anti-cooperative effect. The many-body interaction destabilizes the cluster. This often occurs in clusters of charged species, such as ionic liquid clusters. (See discussion below.)
• \( \Delta E^{(3)} \approx 0 \): Indicates a non-cooperative effect. There is minimal many-body interaction in the system. This is typical for clusters without significant charge or hydrogen bonding.

Each order can be decomposed into electrostatic, exchange, polarization, charge transfer, and dispersion components.

$$\Delta E_X^{(n)} = \Delta E_X^{(n)\text{-el}} + \Delta E_X^{(n)\text{-ex/xc}} + \Delta E_X^{(n)\text{-pl}} + \Delta E_X^{(n)\text{-ct}} + \Delta E_X^{(n)\text{-disp}}$$

Electrostatic and exchange terms are typically highly additive, whereas polarization and charge transfer terms are non-additive. The dispersion term is consistently additive.

Input Examples

Example: EDA for GeH₃F-NCH Complex by B3LYP-D3BJ/def2-SVP

For the GeH₃F–NCH complex, an EDA calculation can be performed using the following input:

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:

The results are:

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

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

The total interaction energies—both with and without BSSE correction—are identical for the TSO-EDA and GKS-EDA methods, although their individual energy components differ. As noted earlier, Qbics recommends using TSO-EDA. In this complex, stabilization is dominated by the electrostatic term, which accords with the chemical intuition that σ-hole interactions are responsible for its binding.

Example: MB-EDA for Molecular Cluster (NH₄⁺)₂(H₂SO₄)(HSO₄^-)₂

The cluster of interest contains two NH₄⁺ cations, one H₂SO₄ molecule, and two HSO₄⁻ anions. This ion–molecule assembly is frequently investigated in atmospheric-chemistry studies. An MB-EDA analysis can be launched with the following input:

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 listed below are used to define the frag fragments.

The results are as follows:

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
---------------------------------------------------------------------------------------------------------------------------------

The total interaction energy is −335.63 kcal mol⁻¹, resolved into two-, three-, four-, and higher-order contributions:

• Two-body: −375.92 kcal mol⁻¹ — the dominant, stabilising term.
• Three-body: +45.42 kcal mol⁻¹ — substantial yet anti-cooperative, thus destabilising the complex.
• Four-body: −5.50 kcal mol⁻¹ — small and slightly cooperative.
• Five- plus six-body (remainder): +0.37 kcal mol⁻¹ — negligible.

Electrostatic and exchange contributions are strongly additive, whereas polarization and charge-transfer contributions are distinctly non-additive. The magnitude and sign of three-body (many-body) effects vary markedly across different cluster types; see Phys. Chem. Chem. Phys. 2024, 26, 17549 for details.