****Iteration 0**** <<< Triplet sigma vectors requested >>> Memory handling for direct AO based CIS: Memory per vector needed ... 1 MB Memory needed ... 0 MB Memory available ... 512 MB Number of vectors per batch ... 512 Number of batches ... 1 [...]
打印激发对状态的贡献
1 2 3 4 5 6 7 8 9 10 11
------------------------------------ TD-DFT/TDA EXCITED STATES (TRIPLETS) ------------------------------------
the weight of the individual excitations are printed if larger than 1.0e-02
STATE 1: E= 0.123186 au 3.352 eV 27036.2 cm**-1 <S**2> = 2.000000 7a -> 8a : 0.996653 (c= 0.99832517)
STATE 2: E= 0.219375 au 5.969 eV 48147.2 cm**-1 <S**2> = 2.000000 6a -> 8a : 0.993680 (c= -0.99683484)
GBW file ... form.gbw Input density ... form.cisp0 Output integrals ... form.cis Operator type ... Mean-field/Effective potential One-Electron Terms ... 1 Coulomb Contribution ... 2 Exchange Contribution ... 3 Correlation Contribution ... 0 Maximum number of centers ... 4 [...]
The calculation of these integrals can take some time. For larger systems, one can use the RI-SOMF(1X) on the main input, that will invoke the use of RI for the Coulomb part. This will accelerate the calculation significantly with only a small error associated
This is expected from the analysis of the components of these states. The T1T1 is mostly composed of a HOMO-LUMO transition, which makes it a n−π∗n−π∗ excited state. A transition from that to the ground state involves a change of angular momentum, which then facilitates the change of spin state by increasing the SOC
x下一部分是由SOC引起的基态稳定能量和新混合SOC状态的能量l列表：
1 2 3 4 5 6 7 8 9
SOC stabilization of the ground state: -0.2024 cm-1 Eigenvalues of the SOC matrix:
The second SOC state now, is a mixture of two spin sublevels of the first triplet (Root 1), those with angular momentum -1 and +1 in spherical harmonics. The third state is a similar mixture, the fourth state is again basically the S1S1, and so on.
Now let’s come back to the aforementioned example of a phosphorescent Iridium(III) complex. That is a case when the SOC is so strong that there are no clear singlets or triplets anymore, and the excited change change drastically due to coupling.
The first step is to optimize this heavy metal complex. We will look after the fac-Ir(ppy)3, for we have plenty of experimental data to compare with for that isomer. The optimization can be done running:
Here we use the B3LYP functional with the DEF2-TZVP basis, which in practice uses a pseudo-potential for heavy atoms such as Ir. This helps to accelerate the calculation and also somewhat accounts for the relativistic effects on the geometry, since the pseudo-potential are fitted to relativistic calculations.
We also use larger grids, which is important and such heavy atoms are present, together with CPCM for a solvation correction and the D4 for the dispersion interaction. The result is:
1 2 3 4 5 6 7 8
!B3LYP ZORA ZORA-DEF2-TZVP SARC/J CPCM(CH2CL2) RI-SOMF(1X) %TDDFT NROOTS 25 DOSOC TRUE TDA FALSE END %BASIS NEWGTO IR "SARC-ZORA-TZVP" END END * XYZFILE 0 1 fac-Irppy_optimized.xyz
Now we do a full calculation with Relativistic corrections, using ZORA and its required basis. Note that we also need to specify the SARC-ZORA-TZVP basis for the Ir, as there is no simple ZORA-DEF2-TZVP for that. Here we added the RI-SOMF(1X) to accelerate the SOC integrals and choose the TDA FALSE to compute a full TD-DFT calculation, for later comparison.
In contrast to the formaldehyde, that had no heavy atom, the SOC matrix elements are much larger now:
The ground SOC state is still essentially the DFT ground state, as the energy differences are still high. However, the first SOC state is already a hybrid of many. It is not a simple triplet, but a mixture of T1 to T9, with various amounts and spin components. That shows the impact of the SOC on these cases!
The closest state to a singlet now is the SOC state 10:
which has 34% of S1 and 2% of S6, but there is nothing like a pure state anymore.
The approximate zero-field splitting (ZFS), obtained as the energy difference between SOC state 3 and SOC state 1 is of about 70cm−170cm−1, in quite good agreement with the experimental value of 85−170cm−1
From the oscillator strengths it is also possible to predict the phosphorescence lifetime for these complexes, and the calculated value using Eq. 4 from the same reference, is about 1.17μs1.17μs, also close to the 1.6−1.8μs1.6−1.8μs from measurements.
Using a very simplistic approach, if one takes the energy difference from the S1S1 to the ground state and assumes a ZPE difference of 2000cm−12000cm−1, the expected emission color would be blue. Even using the T1T1 energy alone, it would be green, but not yellow enough. Now using the SOC state 1, the color at about 532nm532nm matches the yellow-green emission color of this complex quite well:
SOC with other methods
The inclusion of SOC can be done through ORCA in many other theory levels such as CASSCF, ROCIS, STEOM and MRCI. The input is somewhat different, depending on the method, but the output in general is the same. For more detailed information on these other methods, please check the ORCA manual.
# fac-Ir(ppy)3 - C3 symmetry C 3.393895879 -0.289566719 2.776304932 C 4.076284431 -1.374299959 2.244246939 C 3.562788518 -2.026286944 1.144617313 C 2.365194919 -1.600441421 0.563698783 C 1.656920791 -0.490717084 1.087023288 C 2.209908242 0.138316955 2.204838066 C 1.779556093 -2.262575837 -0.593808565 C 2.310998596 -3.397126504 -1.214621244 C 1.678633212 -3.946679457 -2.310344980 C 0.513725976 -3.353425417 -2.779039051 C 0.041132843 -2.238327622 -2.115943483 N 0.643735830 -1.703611386 -1.062120264 C -3.228320892 -2.843015891 2.244246939 C -1.947720074 -2.794416690 2.776304932 C -0.985168124 -1.982995155 2.204838066 C -1.253433856 -1.189576955 1.087023288 C -2.568620388 -1.248098174 0.563698783 C -3.536210228 -2.072321893 1.144617313 C -2.849226199 -0.409852865 -0.593808565 N -1.797238653 0.294314111 -1.062120264 C -1.959015004 1.083541724 -2.115943483 C -3.161014589 1.231812963 -2.779039051 C -4.257241276 0.519600723 -2.310344980 C -4.097497151 -0.302820240 -1.214621244 C -0.403486935 1.680294039 1.087023288 C -1.224740118 1.844678200 2.204838066 C -1.446175805 3.083983409 2.776304932 C -0.847963539 4.217315849 2.244246939 C -0.026578290 4.098608837 1.144617313 C 0.203425469 2.848539595 0.563698783 C 1.069670107 2.672428702 -0.593808565 C 1.786498555 3.699946745 -1.214621244 C 2.578608064 3.427078734 -2.310344980 C 2.647288613 2.121612454 -2.779039051 C 1.917882161 1.154785898 -2.115943483 N 1.153502823 1.409297275 -1.062120264 Ir 0.000000000 0.000000000 0.043448572 H 3.792342787 0.222162593 3.641507453 H 5.002872009 -1.707739869 2.689139743 H 4.102575829 -2.869480849 0.738507580 H 1.696641422 0.983426029 2.641159087 H 3.213678708 -3.847263406 -0.836341679 H 2.081671478 -4.823466100 -2.794933558 H -0.013921102 -3.747584685 -3.633027960 H -0.865398626 -1.751267403 -2.451342694 H -3.980382114 -3.478744318 2.689139743 H -1.703772945 -3.395346490 3.641507453 H 0.003351213 -1.961047587 2.641159087 H -4.536331226 -2.118194464 0.738507580 H -1.083942747 1.625090897 -2.451342694 H -3.238542989 1.885848371 -3.633027960 H -5.218079916 0.608952668 -2.794933558 H -4.938667199 -0.859495698 -0.836341679 H -1.699992635 0.977621558 2.641159087 H -2.088569843 3.173183897 3.641507453 H -1.022489895 5.186484186 2.689139743 H 0.433755396 4.987675313 0.738507580 H 1.724988490 4.706759104 -0.836341679 H 3.136408438 4.214513433 -2.794933558 H 3.252464091 1.861736314 -3.633027960 H 1.949341373 0.126176507 -2.451342694
