Tip

All input files can be downloaded: Files.

Tip

For more information of this section, please refer to these keywords:

Multi-State Energy Decomposition Analysis for Exciplexes

This tutorial will lead you step by step to do multi-state energy decomposition analysis (MS-EDA) for exciplexes using Qbics.

Hint

If you use Qbics to do MS-EDA in you paper, please cite the following references:

Theory: How to Decompose the Exciplex Energy

Input

Below, we consider 3 exciplexes: (MeOCH=CH2)(TCNE), acetone dimer, and (C6H6)-(cis-2-butadiene).

../_images/a57.png

Their input files are shown below:

tn.inp
 1mol
 2C      -0.198382       0.676975        0.839378
 3C      -1.315863       0.038931        0.405996
 4C      -2.225365       0.670286        -0.508436
 5N      -2.959552       1.174482        -1.247154
 6C      -1.634267       -1.289698       0.850726
 7N      -1.901673       -2.352749       1.221105
 8C      0.723624        0.024005        1.725081
 9N      1.483401        -0.507944       2.417545
10C      0.131547        2.005023        0.406927
11N      0.406859        3.079229        0.077027
12C      -0.018608       -1.360064       -2.097094
13C      1.086004        -1.277514       -1.352322
14H      -0.458263       -2.333443       -2.305731
15H      -0.471114       -0.462748       -2.522620
16H      1.590935        -2.157076       -0.934177
17O      1.621801        -0.078506       -1.011442
18C      2.981195        -0.123945       -0.597217
19H      3.629890        -0.409943       -1.438672
20H      3.239414        0.887438        -0.263120
21H      3.112168        -0.831294       0.237956
22end
23
24basis
25    cc-pvdz
26end
27
28scf
29    charge  0
30    spin2p1 1
31    type    u
32end
33
34eda
35    type mseda
36    frag 0 1  1-10
37    frag 0 1 11-20
38    # Orbital partition for fragment 1
39    orb1 64 1 1-31 33-140 : 1-139
40    orb1  0 1          32 : 140
41    orb1 32 1     141-226 : 141-226
42    # Orbital partition for fragment 2
43    orb2 64 1       1-140 : 1-140
44    orb2 32 1     141-155 157-226 : 141-225
45    orb2  0 1                 156 : 226
46    # Orbital partition for the whole molecule
47    orb 96 1 1-47 49-226 : 1-225
48    orb  0 1          48 : 226
49end
50
51task
52    eda m062x
53end

We will take one example to explain the input, i.e., (MeOCH=CH2)(TCNE).

Before proceeding, you should have read TSO-DFT (1): Excited States to understand how to use TSO-DFT to get the excited states.

For the exciplex, we will use type mseda to do MS-EDA, and the fragments should be given by frag option. This is the same as the eda keyword in eda.

Now, we will use orb option to set the excited state of the whole exciplex. See Line 47-48. This is a 48 → 49 (HOMO → LUMO) singlet excited state. We partition the oribtals into 2 subspaces. By putting alpha 48 and beta 226 into a subspace with zero electrons, the Aufbau occupation of the first subspace naturally leads to the HOMO-LUMO transition. Of course, you can consider other excitations.

../_images/a58.png

Then, we will use orb1 and orb2 options to set the diabatic excited states (MeOCH=CH2*)(TCNE) and (MeOCH=CH2)(TCNE*). See Line 39-41 and 43-45.

Below, in the left panel, we show the diabatic state of (MeOCH=CH2*)(TCNE), where the wave functions are localized on its own fragment. This state is assigned by frag automatically. In the right panel, we show the diabatic excited state of (MeOCH=CH2*)(TCNE). We partition the orbitals into 3 subspaces. By putting alpha 32 and beta 140 into a subspace with zero electrons, the Aufbau occupation of the first subspace naturally leads to the HOMO-LUMO transition of MeOCH=CH2. For the third subspace, we keep it unchanged as in the diabatic state, so TCNE is in the ground state.

../_images/a59.png

By the same logic, we can set the diabatic excited state of (MeOCH=CH2)(TCNE*) using orb2 option. See Line 43-45.

../_images/a60.png

Finally, we can calculate the exciplex energy using eda m062x in the task section.

Here, we want to study the relationship between the HOMO-LUMO transition of the exciplex and the HOMO-LUM transition of the fragments. You can set orb1 and orb2 options to use other excited states.

For the other two exciplexes, the input files are written in the same way.

Output

After running the calculation, we will get the following output files. We again take (MeOCH=CH2)(TCNE) as an example.

tn.out
 1---- NOSI Results ----
 2======================
 3   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
 4               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
 5       0   -640.36742765      0.00000000      0.00000000  -0.96550   0.43709   0.00378
 6       1   -640.32444246      1.16962698      0.00000331  -0.01186  -0.00940  -0.00159
 7       2   -640.25510627      3.05626471      0.00000000   0.00000   0.00000   0.00000
 8       3   -640.15547535      5.76722204      0.00000000   0.00000   0.00000   0.00000
 9
10---- NOSI State Identification (Coefficients) ----
11==================================================
12State |0> = +0.707 |tn-Ax.B.mwfn> -0.707 |spin_flip_tn-Ax.B.mwfn>
13State |1> = -0.707 |tn-A.Bx.mwfn> +0.707 |spin_flip_tn-A.Bx.mwfn>
14State |2> = -0.698 |tn-Ax.B.mwfn> -0.698 |spin_flip_tn-Ax.B.mwfn> +0.111 |tn-A.Bx.mwfn> +0.111 |spin_flip_tn-A.Bx. mwfn>
15State |3> = +0.111 |tn-Ax.B.mwfn> +0.111 |spin_flip_tn-Ax.B.mwfn> +0.698 |tn-A.Bx.mwfn> +0.698 |spin_flip_tn-A.Bx. mwfn>
16--omitted--
17---- NOSI Results ----
18======================
19   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
20               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
21       0   -640.36749379      0.00000000      0.00000000  -0.98365   0.43935   0.01448
22       1   -640.34091881      0.72310508      0.00000000   0.00000  -0.00000  -0.00000
23       2   -640.33660378      0.84051710      0.00145069   0.28743  -0.09118  -0.22446
24       3   -640.32372617      1.19091695      0.00009900   0.05373  -0.03170  -0.05398
25       4   -640.25509855      3.05827441      0.00000000   0.00000   0.00000   0.00000
26       5   -640.15527583      5.77445072      0.00000000   0.00000   0.00000   0.00000
27       6   -640.07534938      7.94924924      0.00077286  -0.02996   0.05389   0.06448
28       7   -640.07504770      7.95745814      0.00000000   0.00000  -0.00000  -0.00000
29
30---- NOSI State Identification (Coefficients) ----
31==================================================
32State |0> = -0.706 |tn-Ax.B.mwfn> +0.706 |spin_flip_tn-Ax.B.mwfn>
33State |1> = +0.705 |tn-A-.B+.mwfn> +0.705 |spin_flip_tn-A-.B+.mwfn>
34State |2> = -0.152 |tn-A.Bx.mwfn> +0.152 |spin_flip_tn-A.Bx.mwfn> -0.688 |tn-A-.B+.mwfn> +0.688 |spin_flip_tn-A-.B +.mwfn>
35State |3> = +0.691 |tn-A.Bx.mwfn> -0.691 |spin_flip_tn-A.Bx.mwfn> -0.168 |tn-A-.B+.mwfn> +0.168 |spin_flip_tn-A-.B +.mwfn>
36State |4> = +0.698 |tn-Ax.B.mwfn> +0.698 |spin_flip_tn-Ax.B.mwfn> -0.111 |tn-A.Bx.mwfn> -0.111 |spin_flip_tn-A.Bx. mwfn>
37State |5> = +0.111 |tn-Ax.B.mwfn> +0.111 |spin_flip_tn-Ax.B.mwfn> +0.699 |tn-A.Bx.mwfn> +0.699 |spin_flip_tn-A.Bx. mwfn>
38State |6> = +0.707 |tn-A+.B-.mwfn> -0.707 |spin_flip_tn-A+.B-.mwfn>
39State |7> = +0.707 |tn-A+.B-.mwfn> +0.707 |spin_flip_tn-A+.B-.mwfn>
40--omitted--
41---- NOSI Results ----
42======================
43   State   NOSI Energies  Excited Energy       Osc. Str.        DX        DY        DZ
44               (Hartree)            (eV)                    (a.u.)    (a.u.)    (a.u.)
45       0   -640.46151149      0.00000000      0.00000000  -1.39398   0.68556   0.39128
46       1   -640.34568876      3.15153658      0.00000000   0.00019   0.00008  -0.00003
47       2   -640.33525702      3.43538409      0.16461516  -1.15897   0.76059   1.41473
48
49---- NOSI State Identification (Coefficients) ----
50==================================================
51State |0> = -1.000 |tn-AB.mwfn>
52State |1> = -0.711 |tn-ABx.mwfn> +0.711 |spin_flip_tn-ABx.mwfn>
53State |2> = +0.703 |tn-ABx.mwfn> +0.703 |spin_flip_tn-ABx.mwfn>
54--omitted--
55MS-EDA Results
56==============
57E[A]+E[B] = -640.44244734 Hartree -> 0.00000 eV (as reference)
58E[A.B]    = -640.45105170 Hartree -> -0.23414 eV
59E[A+.B-]  = -640.07545516 Hartree -> 9.98637 eV
60E[A-.B+]  = -640.33851873 Hartree -> 2.82804 eV
61E[Ax.B]   = -640.31003238 Hartree -> 3.60319 eV
62E[A.Bx]   = -640.24118378 Hartree -> 5.47666 eV
63E[AB]     = -640.46138548 Hartree -> -0.51533 eV
64E[ABx]    = -640.34047390 Hartree -> 2.77484 eV
65
66      delta E_Lint =          E[A.B]-(E[A]+E[B]) = -0.00860437 Hartree = -0.23414 eV
67      delta E_exciton =       E[exciton]-E[A.B]
68delta delta E_superexchange = E[SE]-E[exciton]
69delta delta E_OCD =           E[es]-E[SE]
70
71For E[es], E[SE], and E[exciton], you will have to manually select from "NOSI Results" according to "NOSI State Identification (Coefficients)".

For tn.out, we list the results of TSO-DFT for the diabatic and dibatic excited states. The E[exciton], E[SE], and E[es] have to be selected from the NOSI energies, like shown in Line 5-8, 21-28, and 45-47. In most cases, you should choose the lowest singlet states, where the coefficients of the wave function and its spin-flip one have the same sign. The selected states are highlighted. For example, for exciton, we choose State 2 (Line 14), it is a combination of local exciton state [A*][B] and [A][B*], its energy is given in Line 7. For SE, we choose State 1 (Line 33), it is a state of [A-][B+] and has little contributions from other states. For es, we choose State 3 (Line 47), it is the target excited state.

Tip

In principle, you can choose other intermediate excited states to see the SE or exciton effects, but you should be absolutely sure what you intend to do.

Now we can do the calculations accoding to the equations given in Line 66-69.

  • delta E_Lint = E[A.B]-(E[A]+E[B]) = -0.23 eV

  • delta E_exciton = E[exciton]-E[A.B] = (-640.25510627–640.45105170)*27.21 = +5.33 eV

  • delta delta E_superexchange = E[SE]-E[exciton] = (-640.34091881–640.25510627)*27.21 = -2.33 eV

  • delta delta E_OCD = E[es]-E[SE] = (-640.33525702–640.34091881)*27.21 = +0.15 eV

For other exciplexes, the calculations are done in the same way. The results are shown below:

Type

(MeOCH=CH2)(TCNE)

acetone dimer

(C6H6)-(cis-2-butadiene)

\(\Delta E_{\text{Lint}}\)

-0.23 eV

-0.14 eV

-0.08 eV

\(\Delta E_{\text{exciton}}\)

+5.33 eV

+3.24 eV

+7.10 eV

\(\Delta \Delta E_{\text{superexchange}}\)

-2.33 eV

-0.06 eV

-0.12 eV

\(\Delta \Delta E_{\text{OCD}}\)

+0.15 eV

+0.02 eV

+0.85 eV

We can see that:

  • (MeOCH=CH2)(TCNE) has a very large \(\Delta\Delta E_{\text{superexchange}}\), so it is a charge transfer excipler;

  • Acetone dimer has very small \(\Delta\Delta E_{\text{superexchange}}\) and \(\Delta\Delta E_{\text{OCD}}\), so it is an encounter excipler;

  • (C6H6)-(cis-2-butadiene) has a large \(\Delta E_{\text{OCD}}\), so it is a intimate excipler. This is not unexpected, since a Dield-Alder reaction is about to occur between the two fragments upon photochemical ways, thus there should be considerable orbital overlap, leading to a large \(\Delta\Delta E_{\text{OCD}}\).

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