TD-DFT with SOC: basics
Contents
TD-DFT based state interaction with SOC. For details, see
Zhendong Li, Bingbing Suo, Yong Zhang, Yunlong Xiao, and Wenjian Liu, “Combining spin-adapted open-shell TD-DFT with spin-orbit coupling”, Mol. Phys. 111, 3741 (2013).
Breif description of the flowchart
SOC计算的输入文件中以$section name ... $end符号为划分分为6段:
$compass 为基组和坐标控制（如果要计算其他化合物，选用其他基组，可修改这一段）；
$xuanyuan 为积分控制，基本不需要改动，除非需要使用cam-b3lyp这段要加入两行：RS和0.33d0，控制计算新的积分;
$scf为计算方法控制，可选用不同泛函；
$tddft isf=0 ... 这一段(isf=0)表示计算singlet
$tddft isf=1 ... 计算triplet
$tddft isoc=2 ...根据前面两个计算的结果来计算soc state interaction，imatsoc为控制打印旋轨耦合矩阵元，格式如下：
IMATSOC
n
fileA symA stateA fileB symB stateB
fileA' symA' stateA' fileB' symB' stateB'
...
...其中，IMATSOC下参数说明如下：
1. "n" - 代表要打印"几个旋轨耦合矩阵元<A|hso|B>"，接着后面(fileA symA stateA fileB symB stateB等)为要打印矩阵元两个态的描述，共n行。
2. 每一行"fileA symA stateA fileB symB stateB"代表一个矩阵元<A|hso|B>，每个态由(file,sym,state)3个量表示。
3. 整数file － 表示前面第几个tddft计算的文件。
4. 整数sym － 表示该计算中第几个不可约表示，这取决于分子的对称性。可以从“SCF段”输出的occupation出查看不可约表示顺序。
5. 整数state － 表示该不可约表示里的第几个态，这取决于前面"TD-DFT段"计算出的激发态。
特殊说明：
1. 计算必须按照isf=0,isf=1的顺序进行。
2. 基态用(0,0,0)表示。
例子：
输入文件中"0，0，0，2，1，1"表示基态(000)和file2即triplet，sym＝1的第一个态(即211对应1T1，因为此时对称性为C1)之间的旋轨耦合矩阵元。
Some common questions about SOC
Example: Print SOC mat and Perform SOC diagonalization
Input:
$COMPASS Title ir1 Basis IRCOMPLEX Geometry Ir -0.0117154745 0.02136826 -0.1871622466 C -1.590674169 0.7736105591 0.850482009 C -4.0103593084 1.6631710744 2.0881698872 C -1.587030516 1.6064254297 1.9846531563 C -2.8754743453 0.4162567381 0.3762778017 C -4.0684588604 0.8406678872 0.9653728357 C -2.7652566303 2.0433988261 2.5945234724 H -0.633533598 1.9127046365 2.4024890794 H -5.031807216 0.5389051931 0.5644872718 H -2.7118027246 2.6839610147 3.4712663621 H -4.9285536031 2.0014173162 2.5588819363 C 1.4053272337 1.0109349589 0.8613594531 C 3.3836289249 2.6234305864 2.1354680771 C 2.0771460677 0.5800974992 2.0211645669 C 1.7631262545 2.2970140474 0.3585152663 C 2.7411852479 3.0844966855 0.9939992732 C 3.044957901 1.3650101996 2.6469305081 H 1.8305785647 -0.3881315485 2.4444240781 H 3.0042061929 4.0630294704 0.6010854425 H 3.5407187868 0.9959817385 3.5420383099 H 4.1379887938 3.2338708527 2.6233130653 C 0.1111675725 -1.7119838156 0.8795182027 C 0.5294631611 -4.2465845213 2.136544371 C 1.0417183334 -2.6652412426 0.4024936912 C -0.6004107662 -2.1019903883 2.028797446 C -0.4006210626 -3.3384592866 2.6477946425 C 1.2608503358 -3.9079720636 1.0002003463 H -1.3244348019 -1.413608967 2.4531282601 H -0.9731808696 -3.5946754614 3.5357463104 H 1.9890357565 -4.6057356294 0.596753782 H 0.6876544671 -5.2085686031 2.6147222734 N -1.7055918832 -0.7893527004 -1.3058124454 C -1.9722242221 -1.5767164653 -2.3518797181 C -3.3612772292 -1.7339951323 -2.5010242321 C -3.9194938069 -0.9920736156 -1.4729787184 N -2.8999954385 -0.434228237 -0.7703095731 N 1.5150714233 -1.0583114657 -1.2825131804 C 2.3138081406 -0.9142123699 -2.3433358371 C 3.1082799478 -2.0614459074 -2.5127910698 C 2.7399679653 -2.9098550697 -1.4816601802 N 1.779892419 -2.2802990117 -0.7566347846 H -1.1601491745 -1.9907288667 -2.9313421992 H 3.089224611 -3.8952971699 -1.2184247348 H 3.8501674705 -2.2464169166 -3.2743336863 H -3.8863865729 -2.3105313491 -3.2470045506 H -4.9492341453 -0.8290099882 -1.1983109053 H 2.2814545468 -0.0015798294 -2.9198044757 C 0.5167706643 4.2876200227 -2.6332627231 C -0.4153270812 3.3663568698 -3.1195481682 C -0.5686406908 2.1688169354 -2.4341135463 N 0.1409383672 1.8631654694 -1.3352631181 C 1.05542065 2.7471949823 -0.8428699526 C 1.2493629941 3.9769776219 -1.4963443658 H 0.6676353447 5.2385692731 -3.1359337322 H -1.011339893 3.5685529446 -4.0026032407 H -1.276466123 1.413706092 -2.7596936709 H 1.9731120675 4.6831024371 -1.1074561222 End geometry GROUP C(1) Skeleton $END $XUANYUAN scalar heff 3 soint hsoc 2 Direct Schwarz $END $SCF RKS DFT functional B3lyp $END $TDDFT IMETHOD 1 ISF 0 ITDA 0 IDIAG 1 istore 1 iexit 10 AOKXC MemJKOP 2048 crit_e 1.d-4 $END $TDDFT IMETHOD 1 ISF 1 ITDA 0 IDIAG 1 istore 2 iexit 10 AOKXC MemJKOP 2048 crit_e 1.d-4 $END $TDDFT isoc 2 nfiles 2 ifgs 1 imatsoc 1 0 0 0 2 1 1 $END
NOTE: If isoc=3, no diagonalization of Hsoc will be performed.
Output:
SOC matrix elements
Print selected matrix elements of [Hsoc] < 0 0 0 |Hso| 2 1 1 > mi/mj ReHso(au) cm^-1 ImHso(au) cm^-1 1 1 0.0003219734 70.6650036601 0.0009582030 210.3012602778 1 2 0.0000000000 0.0000000000 -0.0006544171 -143.6279497862 1 3 0.0003219734 70.6650036601 -0.0009582030 -210.3012602778
这里计算<S0|Hso|T1>分别给出其实部ReHso和虚部ImHso。因为S0只有一个分量，mi为1。T1(spin S=1)有3个分量(Ms=-1,0,1), mj编号这3个分量。
Warning: 在不同程序结果对比时需要注意：这里给出的时所谓spherical tensor，而不是cartesian tensor，即T1是T_{-1},T_{0},T_{1}，不是Tx,Ty,Tz，两者之间存在酉变换。
SOC-SI results
*** List of SOC-SI results ***
Totol No. of States: 41
No. ExEnergies f Dominant Excitations Esf dE Eex(eV) (cm^-1)
1 -0.0066 eV 0.0000 99.8% Spin: |Gs,1> 0-th A 0.0000 -0.0066 0.0000 0.00
2 2.5694 eV 0.0000 44.1% Spin: |S+,2> 1-th A 2.6425 -0.0731 2.5760 20776.65
3 2.5727 eV 0.0000 32.8% Spin: |S+,3> 1-th A 2.6425 -0.0698 2.5793 20803.69
4 2.5908 eV 0.0000 31.8% Spin: |S+,1> 1-th A 2.6425 -0.0517 2.5974 20949.77
5 2.7010 eV 0.0000 31.1% Spin: |So,1> 1-th A 2.9592 -0.2583 2.7076 21837.87
6 2.8740 eV 0.0000 19.9% Spin: |S+,1> 2-th A 2.9081 -0.0340 2.8806 23233.61
7 2.8794 eV 0.0000 27.0% Spin: |S+,2> 2-th A 2.9081 -0.0287 2.8859 23276.69
8 2.9589 eV 0.0000 22.8% Spin: |S+,1> 3-th A 2.9849 -0.0261 2.9655 23917.99
9 3.0395 eV 0.0000 26.0% Spin: |S+,2> 2-th A 2.9081 0.1314 3.0461 24568.13
10 3.0631 eV 0.0000 38.7% Spin: |S+,2> 3-th A 2.9849 0.0782 3.0697 24758.84
11 3.0881 eV 0.0000 52.9% Spin: |So,1> 2-th A 3.0330 0.0551 3.0947 24960.28
12 3.1239 eV 0.0000 30.7% Spin: |So,1> 1-th A 2.9592 0.1647 3.1305 25249.42
13 3.1328 eV 0.0000 21.9% Spin: |S+,2> 5-th A 3.1710 -0.0382 3.1394 25320.98
14 3.1334 eV 0.0000 20.5% Spin: |S+,3> 4-th A 3.1640 -0.0305 3.1400 25325.94
15 3.1455 eV 0.0000 33.3% Spin: |S+,2> 4-th A 3.1640 -0.0185 3.1521 25423.24
16 3.1489 eV 0.0000 24.5% Spin: |S+,2> 5-th A 3.1710 -0.0221 3.1555 25450.64
17 3.1546 eV 0.0000 17.0% Spin: |S+,3> 4-th A 3.1640 -0.0094 3.1612 25496.52
18 3.1580 eV 0.0000 34.2% Spin: |S+,3> 5-th A 3.1710 -0.0130 3.1646 25524.02
19 3.1866 eV 0.0000 17.4% Spin: |S+,2> 7-th A 3.2865 -0.1000 3.1932 25754.60
20 3.2140 eV 0.0000 28.2% Spin: |S+,3> 6-th A 3.2065 0.0074 3.2206 25975.68
21 3.2174 eV 0.0000 48.4% Spin: |S+,2> 6-th A 3.2065 0.0109 3.2240 26003.33
22 3.2435 eV 0.0000 38.0% Spin: |So,1> 3-th A 3.2231 0.0204 3.2501 26213.63
23 3.2627 eV 0.0000 20.7% Spin: |S+,3> 6-th A 3.2065 0.0562 3.2693 26368.83
24 3.2725 eV 0.0000 30.0% Spin: |S+,2> 7-th A 3.2865 -0.0140 3.2791 26447.54
25 3.3035 eV 0.0000 45.4% Spin: |So,1> 3-th A 3.2231 0.0804 3.3101 26697.85
26 3.3651 eV 0.0000 23.9% Spin: |So,1> 4-th A 3.5132 -0.1481 3.3717 27194.63
27 3.3945 eV 0.0000 31.5% Spin: |S+,1> 8-th A 3.4260 -0.0315 3.4011 27431.99
28 3.4070 eV 0.0000 31.1% Spin: |S+,1> 9-th A 3.4454 -0.0384 3.4136 27532.74
29 3.4308 eV 0.0000 31.7% Spin: |S+,3> 8-th A 3.4260 0.0047 3.4374 27724.20
30 3.4465 eV 0.0000 19.7% Spin: |S+,2> 8-th A 3.4260 0.0204 3.4531 27850.76
31 3.4518 eV 0.0000 55.5% Spin: |S+,2> 8-th A 3.4260 0.0257 3.4583 27893.46
32 3.4658 eV 0.0000 43.7% Spin: |S+,2> 9-th A 3.4454 0.0204 3.4724 28006.99
33 3.4764 eV 0.0000 24.6% Spin: |S+,1> 10-th A 3.4870 -0.0106 3.4830 28092.46
34 3.5252 eV 0.0000 68.4% Spin: |S+,2> 10-th A 3.4870 0.0382 3.5318 28485.50
35 3.6092 eV 0.0000 49.3% Spin: |So,1> 4-th A 3.5132 0.0960 3.6158 29163.42
36 3.6402 eV 0.0000 60.5% Spin: |So,1> 6-th A 3.5920 0.0482 3.6468 29413.12
37 3.6508 eV 0.0000 48.8% Spin: |So,1> 5-th A 3.5648 0.0859 3.6574 29498.52
38 3.6609 eV 0.0000 47.4% Spin: |So,1> 7-th A 3.6206 0.0403 3.6675 29580.42
39 3.6684 eV 0.0000 43.5% Spin: |So,1> 8-th A 3.6288 0.0396 3.6750 29640.60
40 3.7293 eV 0.0000 83.7% Spin: |So,1> 9-th A 3.6898 0.0395 3.7359 30131.95
41 3.7898 eV 0.0000 90.1% Spin: |So,1> 10-th A 3.7487 0.0411 3.7964 30620.26
[tddft_soc_final]这里，ExEnergies列出考虑SOC后的激发能。Esf为原始不考虑SOC时的激发能。
激发态表示用"Spin: |S,M> n-th sym"来表示，自旋|Gs,1>，空间对称性为sym的第n个态。例如，|Gs,1>代表基态，|So,1>表示总自旋和基态相同的激发态，|S+,2>表示总自旋加1的激发态。M为自旋投影的第几个分量(in total 2S+1)。
Warning: f-振子强度并没有计算，如需计算需要指定imatrsf来计算transition dipole moment !
Example: Calculate (transition) dipole moments with or without including SOC
BASIC Input:
$COMPASS Title nh3 Basis aug-cc-pvtz Geometry C 0.000000 0.000000 -1.039839 S 0.000000 0.000000 0.593284 H 0.000000 0.932612 -1.626759 H 0.000000 -0.932612 -1.626759 End geometry $END $xuanyuan scalar heff 3 soint hsoc 2 $end $scf RHF charge 0 spin 1 THRESHCONV 1.d-12 1.d-10 OPTSCR 1 $end $traint tddft orbi hforb $end $tddft imethod 1 isf 0 idiag 1 iexit 10 itda 1 istore 1 $end $tddft imethod 1 isf 1 itda 1 idiag 1 iexit 10 istore 2 $end
Without SOC
If we only want to calculate (transition) dipole moments between spin-free states, a new section could be added as
$tddft nfiles 2 ifgs 1 imatrsf -1 # selected printing will be implemented in future #3 #0 0 0 1 2 1 #1 1 1 1 2 1 #2 2 1 2 2 1 $end
Output:
>>> Print (transition) dipole moments :
Ground state dipole moment (in Debye)
(ifile,irep,istate|state2) <I|X|J> <I|Y|J> <I|Z|J>
DipPair= 0 0 0 0 0 0 -0.0000 0.0000 2.2128
Ground state to Excited state transition dipole moments
(ifile,irep,istate|state2) <I|X|J> <I|Y|J> <I|Z|J>
DipPair= 0 0 0 1 1 1 0.0000 -0.0000 -3.6211
DipPair= 0 0 0 1 1 2 0.0000 -0.0000 0.9935
DipPair= 0 0 0 1 1 3 -0.0000 -0.0000 0.6184
...
APPROXIMATE excited state to excited state (transition) dipole moments
(ifile,irep,istate|state2) <I|X|J> <I|Y|J> <I|Z|J>
ifile = 1
DipPair= 1 1 1 1 1 1 -0.0000 -0.0000 1.3886
DipPair= 1 1 2 1 1 1 -0.0000 0.0000 -0.0598
DipPair= 1 1 3 1 1 1 -0.0000 0.0000 0.2098
...
With SOC
However, if the (transition) dipole moments between SOC-coupled states, the SOC-SI calculation must be performed first and then use the imatrso keywords:
$tddft isoc 2 nprt 10 nfiles 2 ifgs 1 #imatsoc #1 #0 0 0 1 2 1 imatrso 6 1 1 1 2 1 3 1 4 1 5 1 6 $end
Output:
[tddft_soc_matrso]: Print selected matrix elements of [dpl]
autodebye= 2.5417649999999998
No. ( I , J ) |rij|^2 E_J-E_I fosc rate
---------------------------------------------------------------------
1 1 1 0.757E+00 -0.0004 -0.667E-05 -0.374E-04
Details of transition dipole moment with SOC (in a.u.):
<I|X|J> <I|Y|J> <I|Z|J> (also in debye)
Real= 0.136E-16 -0.512E-17 0.870E+00 0.0000 -0.0000 2.2121
Imag= -0.410E-35 -0.117E-34 -0.299E-34 -0.0000 -0.0000 -0.0000
Norm= 0.136E-16 0.512E-17 0.870E+00
No. ( I , J ) |rij|^2 E_J-E_I fosc rate
---------------------------------------------------------------------
2 1 2 0.166E-05 1.9361 0.788E-07 0.128E+02
Details of transition dipole moment with SOC (in a.u.):
<I|X|J> <I|Y|J> <I|Z|J> (also in debye)
Real= -0.127E-02 0.776E-14 0.476E-17 -0.0032 0.0000 0.0000
Imag= 0.229E-03 0.273E-13 0.310E-16 0.0006 0.0000 0.0000
Norm= 0.129E-02 0.284E-13 0.313E-16
...Note that for the diagonal term (<1|r|1>), we have the dipole moment of state 1, while the off-diagonal term (<1|r|2>) gives the transition dipole moments.