Tip

All input files can be downloaded: Files.

eda

This keyword defines how to perform an energy decomposition analysis (EDA) calculation.

Options 

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.
	`mseda` for multi-state energy decomposition analysis (MS-EDA) for exciplexes.
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.

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 scfguess.

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.

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.

mb_level

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.

orb1

Must be given for type mseda calculations. This defines the orbital partition of diabatic excited state of fragment 1. The format is:

orb num_electrons spin_multiplicity alpha_MO_indices : beta_MO_indices

There can be arbitrary number of orb1, but all orbitals must be included once and only once. They are the same as orb in scfguess. See scfguess.

orb2: Must be given for type mseda calculations. This defines the orbital partition of diabatic excited state of fragment 2.

orb: Must be given for type mseda calculations. This defines the orbital partition of excited state of the whole molecule.

Theoretical Background 

Hint

If you use tso and mb_tso, please cite the following reference:

If you use gks and mb_gks, please cite the following reference:

If you use mseda, please cite the following reference:

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):

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:

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

The terms higher than \(\Delta E^{(2)}\) is the many-body interaction term. Usually the most important one is the three-body effect \(\Delta E^{(3)}\), the effects of which can be decomposed into three ones:

\(\Delta E^{(3)} < 0\): 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.
\(\Delta E^{(3)} > 0\): 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.
\(\Delta E^{(3)} \approx 0\): 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:

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

Usually, electrostatic and exchange terms are highly additive, while polarization and charge transfer terms are non-additive. The dispersion term is always additive.

Multi-State EDA for Exciplexes 

This method is developed in JACS Au 2023, 3, 1800-1819. and J. Phys. Chem. Lett. 2023, 14, 2917-2926. and is used to analyze the nature of exciplexes. We will calculate the following 4 energy components:

\(\Delta E_{\text{Lint}}\): Local interaction energy between the two fragments.
\(\Delta E_{\text{exciton}}\): The local exciton energy of the fragments of the exciplex.
\(\Delta E_{\text{superexchange}}\): The charge transfer effect between the two fragments.
\(\Delta E_{\text{OCD}}\): The oribtal-configuration delocalization (OCD) effects over the whole molecule.

The exact mathematical expressions can be found in JACS Au 2023, 3, 1800-1819. Below is a graph to show how the calculate each term, althgouth they can be automatically done by Qbics.

\(\Delta E_{\text{Lint}}\): For the complex AB, we calculate the diabatic state [A][B], where the wave functions are localized on each fragment. Its calculation by TSO-DFT can be found in scfguess and TSO-DFT (2): Diabatic States.
\(\Delta E_{\text{exciton}}\): Two states [A][B*] and [A*][B] are calculated (assigned by orb1 and orb2). For [A][B*], A is in the ground state and B is in the excited state. [A*][B] is in the same way. They are the so-called local exciton states. They can be combined by NOSI method to get exciton state a[A][B*]+b[A*][B].
\(\Delta E_{\text{superexchange}}\): Two charge transfer states [A⁺][B^-] and [A^-][B⁺] are calculated. They can be combined by NOSI method with the exciton state to get the superexchange state a[A][B*]+b[A*][B]+c[A⁺][B^-]+d[A^-][B⁺].
\(\Delta E_{\text{OCD}}\): The standard excited state. It can be calculated by TSO-DFT with the orbital partition orb. Examples are shown in TSO-DFT (1): Excited States.

Here, we give a brief list to show how to use these energies to identify the nature of exciplexes:

\(\Delta E_{\text{superexchange}}\approx 0,\Delta E_{\text{OCD}}\approx 0\): The exciplex is called encounter exciplex. This means that the exciplex is actually a combination of two fragments, and one fragment is excited while the other is not.
\(\Delta E_{\text{superexchange}} < -1\) eV: The exciplex is called charge-transfer exciplex. This means that in this exciplex, one electron of one fragment is transferred to the other fragment.
\(\Delta E_{\text{OCD}} > 0.4\) eV: The exciplex is called intimate exciplex. This means that in this exciplex, the two fragments are strongly coupled, and the electronic wavefunction is delocalized over the whole molecule.

While type mseda in Qbics is quite automatic, unfortunately, you have to design the intermediate diabatic excited state manually and carefully.

Input Examples 

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

For the complex GeH₃F-NCH, we can do EDA calculation by the following input:

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:

The results are:

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

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 (NH₄⁺)₂(H₂SO₄)(HSO₄^-)₂ 

The title cluster is composed of two NH₄⁺ cations, one H₂SO₄ molecules, and two HSO₄^- anions. This cluster is used in the study of atmopheric chemistry.We can do MB-EDA calculation by the following input:

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:

The results are:

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.

Example: MS-EDA for Excited State of (H₂O)₂ 

Tip

For a complete tutorial of MS-EDA, please refer to:

Multi-State Energy Decomposition Analysis for Exciplexes

Here, we give an exmaple to show how to use MS-EDA to analyze the nature of excited state of (H₂O)₂.

eda-3.inp

mol
O            2.25695562672726        4.09092939425841        1.44708469612963
H            2.60549948258352        4.95596113201443        1.66737912969664
H            1.70005657505238        3.82479696706390        2.19401386768222
O            0.46185891193345        3.08059831055055        3.39436520556125
H            0.75871260498951        2.17908731297165        3.53934447614016
H           -0.35008320128635        3.03362688314125        2.88381262479031
end

basis
    cc-pvdz
end

scf
    charge  0
    spin2p1 1
    type    u
end

eda
    type mseda
    frag 0 1 1-3
    frag 0 1 4-6
    # Orbital partition for fragment 1
    orb1 10 1 1-4 6-24 : 1-23
    orb1  0 1        5 : 24
    orb1 10 1    25-48 : 25-48
    # Orbital partition for fragment 2
    orb2 10 1        1-24 : 1-24
    orb2 10 1 25-28 30-48 : 25-47
    orb2  0 1          29 : 48
    # Orbital partition for the whole molecule
    orb 20 1 1-9 11-48 : 1-47
    orb  0 1        10 : 48
end

task
    eda m062x
end

Let’s explain the input file:

type mseda: Use MS-EDA.
frag 0 1 1-3: This is the fragment assignment for fragment 1.
frag 0 1 4-6: This is the fragment assignment for fragment 2.

The following 3 lines indicate a diabatic state that fragment 1 is in the excited state and fragment 2 is in the ground state.

orb1 10 1 1-4 6-24 : 1-23
orb1  0 1        5 : 24
orb1 10 1    25-48 : 25-48

The orbital occupation of the diabatic ground state [H₂O][H₂O] is shown in the left panel, which is caculated automatically by Qbics. Then, the local exciton (diabatic excited state) state [H₂O*][H₂O], where the first water is excited (5 → 6) while the second one is in the ground state, assigned by orb1, is shown in the right panel.

The another local exciton state [H₂O][H₂O*], where the second water is excited while the first one is in the ground state, assigned by orb2.

Finally, the standard excited state (H₂O)₂* (10 → 11) is assigned by orb. The charge transfer states will be calculated automatically by Qbics.

Now, after calculation, the results are:

eda-4.out

---- NOSI Results ----
======================
   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
       0   -152.49573626      0.00000000      0.00000000  71.07190 190.55904 130.28574
       1   -152.49513363      0.01639767      0.00021144   0.37783   0.89791   0.32667
       2   -152.46935243      0.71790407      0.00000000   0.00000   0.00000   0.00000
       3   -152.46845033      0.74245017      0.00000000  -0.00000  -0.00000  -0.00000

---- NOSI State Identification (Coefficients) ----
==================================================
State |0> = +0.239 |eda-3-Ax.B.mwfn> -0.239 |spin_flip_eda-3-Ax.B.mwfn> +0.666 |eda-3-A.Bx.mwfn> -0.666 |spin_flip_eda-3-A.Bx.mwfn>
State |1> = +0.666 |eda-3-Ax.B.mwfn> -0.666 |spin_flip_eda-3-Ax.B.mwfn> -0.239 |eda-3-A.Bx.mwfn> +0.239 |spin_flip_eda-3-A.Bx.mwfn>
State |2> = -0.681 |eda-3-Ax.B.mwfn> -0.681 |spin_flip_eda-3-Ax.B.mwfn> -0.189 |eda-3-A.Bx.mwfn> -0.189 |spin_flip_eda-3-A.Bx.mwfn>
State |3> = -0.190 |eda-3-Ax.B.mwfn> -0.190 |spin_flip_eda-3-Ax.B.mwfn> +0.681 |eda-3-A.Bx.mwfn> +0.681 |spin_flip_eda-3-A.Bx.mwfn>
--omitted--
E[exciton]: You will have to manually select from "NOSI Results" according to "NOSI State Identification (Coefficients)".
--omitted--
---- NOSI Results ----
======================
   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
       0   -152.49716659      0.00000000      0.00000000  71.72102 192.27664 131.05811
       1   -152.49623624      0.02531483      0.00046202  -0.38016  -1.04711  -0.50330
       2   -152.47228961      0.67690257      0.00000000   0.00000   0.00000   0.00000
       3   -152.46913953      0.76261617      0.00000000  -0.00000   0.00000   0.00000
       4   -152.40168515      2.59804997      0.00000000  -0.00000  -0.00000   0.00000
       5   -152.37292576      3.38059283      0.11715904  -1.09643  -1.11179   0.63183
       6   -152.37106237      3.43129579      0.00000000  -0.00000  -0.00000   0.00000
       7   -152.27658033      6.00215210      0.03076888  -0.44092  -0.37968   0.28486

---- NOSI State Identification (Coefficients) ----
==================================================
State |0> = -0.607 |eda-3-Ax.B.mwfn> +0.607 |spin_flip_eda-3-Ax.B.mwfn> -0.324 |eda-3-A.Bx.mwfn> +0.324 |spin_flip_eda-3-A.Bx.mwfn> -0.079 |eda-3-A+.B-.mwfn> +0.079 |spin_flip_eda-3-A+.B-.mwfn>
State |1> = +0.325 |eda-3-Ax.B.mwfn> -0.325 |spin_flip_eda-3-Ax.B.mwfn> -0.611 |eda-3-A.Bx.mwfn> +0.611 |spin_flip_eda-3-A.Bx.mwfn>
State |2> = -0.669 |eda-3-Ax.B.mwfn> -0.669 |spin_flip_eda-3-Ax.B.mwfn> -0.098 |eda-3-A.Bx.mwfn> -0.098 |spin_flip_eda-3-A.Bx.mwfn> +0.122 |eda-3-A+.B-.mwfn> +0.122 |spin_flip_eda-3-A+.B-.mwfn>
State |3> = +0.101 |eda-3-Ax.B.mwfn> +0.101 |spin_flip_eda-3-Ax.B.mwfn> -0.676 |eda-3-A.Bx.mwfn> -0.676 |spin_flip_eda-3-A.Bx.mwfn> -0.070 |eda-3-A-.B+.mwfn> -0.070 |spin_flip_eda-3-A-.B+.mwfn>
State |4> = +0.272 |eda-3-A.Bx.mwfn> +0.272 |spin_flip_eda-3-A.Bx.mwfn> -0.702 |eda-3-A-.B+.mwfn> -0.702 |spin_flip_eda-3-A-.B+.mwfn>
State |5> = +0.200 |eda-3-Ax.B.mwfn> -0.200 |spin_flip_eda-3-Ax.B.mwfn> -0.711 |eda-3-A+.B-.mwfn> +0.711 |spin_flip_eda-3-A+.B-.mwfn>
State |6> = -0.234 |eda-3-Ax.B.mwfn> -0.234 |spin_flip_eda-3-Ax.B.mwfn> -0.703 |eda-3-A+.B-.mwfn> -0.703 |spin_flip_eda-3-A+.B-.mwfn>
State |7> = -0.280 |eda-3-A.Bx.mwfn> +0.280 |spin_flip_eda-3-A.Bx.mwfn> +0.775 |eda-3-A-.B+.mwfn> -0.775 |spin_flip_eda-3-A-.B+.mwfn>
--omitted--
E[SE]: You will have to manually select from "NOSI Results" according to "NOSI State Identification (Coefficients)".
--omitted--
---- NOSI Results ----
======================
   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
       0   -152.78958902      0.00000000      0.00000000  71.76585 191.51356 130.39299
       1   -152.50815639      7.65778183      0.00000000  -0.00000  -0.00000   0.00000
       2   -152.48459764      8.29881531      0.02202111  -0.38172   0.19276  -0.18544

---- NOSI State Identification (Coefficients) ----
==================================================
State |0> = -1.000 |eda-3-AB.mwfn>
State |1> = -0.707 |eda-3-ABx.mwfn> +0.707 |spin_flip_eda-3-ABx.mwfn>
State |2> = +0.707 |eda-3-ABx.mwfn> +0.707 |spin_flip_eda-3-ABx.mwfn>
--omitted--
E[es]: You will have to manually select from "NOSI Results" according to "NOSI State Identification (Coefficients)".
--omitted--
MS-EDA Results
==============
E[A]+E[B] = -152.77690444 Hartree ->  0.00000 eV (as reference)
E[A.B]    = -152.78247691 Hartree -> -0.15163 eV
E[A+.B-]  = -152.38240651 Hartree -> +10.73484 eV
E[A-.B+]  = -152.36309839 Hartree -> +11.26024 eV
E[Ax.B]   = -152.48224465 Hartree -> +8.01810 eV
E[A.Bx]   = -152.48208951 Hartree -> +8.02232 eV
E[AB]     = -152.78958934 Hartree -> -0.34517 eV
E[ABx]    = -152.49637681 Hartree -> +7.63355 eV

      delta E_Lint =          E[A.B]-(E[A]+E[B]) = -0.00557247 Hartree = -0.15163 eV
      delta E_exciton =       E[exciton]-E[A.B]
delta delta E_superexchange = E[SE]-E[exciton]
delta delta E_OCD =           E[es]-E[SE]

Below:

Line 63-70: The TSO-DFT energy of the diabatic state ([A.B]), charge transfer (like [A+.B-]), local exciton (like [A.Bx]), and standard ground ([AB]) and excited state ([ABx]).
Line 72-75: \(\Delta E_{\text{Lint}}\), \(\Delta E_{\text{exciton}}\), \(\Delta E_{\text{superexchange}}\), and \(\Delta E_{\text{OCD}}\). Some energies are not calculated because the NOSI solution of exciton, superexchange, and OCD are multiple, and there are some degrees of freedom to choose. One principle is to choose the singlet state with the lowest energy.
- To choose E[exciton], check Lines 3-15. State 2 is a singlet state of the combination of [A*][B] and [A][B*], so its energy is E[exciton] = -152.46935243 Hartree (Line 7).
- To choose E[SE], check Lines 17-29. State 2 is a singlet state of the combination of [A*][B], [A][B*] and [A⁺][B^-], so its energy is E[SE] = -152.47228961 Hartree (Line 25).
- To choose E[es], check Lines 45-57. State 2 is a singlet excited state, so its energy is E[es] = -152.48459764 Hartree (Line 51).

Tip

Usually, the singlet state is that the coefficients of the wave function and its spin-flip one have the same sign.

Now, the energies can be calculated:

E_Lint = -0.15 eV
E_exciton = (-152.46935243-( -152.78247691))*27.21 = +8.52 eV
E_superexchange = (-152.47228961-( -152.46935243))*27.21 = -0.08 eV
E_OCD = (-152.48459764-( -152.47228961))*27.21 = -0.33 eV

Therefore, the excited state of (H₂O)₂ is a typical encounter exciplex. It almost has no charge transrfer effect, but has a small OCD effect, due to the formation of hydrogen bond in the dimer.

Tip

In Multi-State Energy Decomposition Analysis for Exciplexes, we will show more examples and some other types of exciplexes.

Besides the output file, you can also find some MWFN files corresponding to the diabatic (eda-3-A.B.mwfn), dibatic excited (eda-3-Ax.B.mwfn, eda-3-A.Bx.mwfn), charge-transfer (eda-3-A+.B-.mwfn, eda-3-A-.B+.mwfn), and standard ground (eda-3-AB.mwfn) and excited state (eda-3-ABx.mwfn).