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tddft
Contents
Time dependent DFT/HF calculation. Support Full TDDFT, TDA and RPA.
Quick guides
The following examples give the minimal inputs for starting TD-DFT calculations.
Closed-shell Systems : R-TD-DFT
This gives a R-TD-DFT (imethod=1,itda=0) for singlet-singlet (isf=0) transitions using Davidson iterative diagonalization (idiag=1). In each irreducible representations, the lowest 10 states are calculated.
$TDDFT IMETHOD 1 ISF 0 ITDA 0 IDIAG 1 iexit 10 $END
The algorithm used in TD-DFT is the same as in the ground state calculations. If direct SCF is used.
$xuanyuan ---- /!\ '''Edit conflict - your version:''' ---- ---- /!\ '''End of edit conflict''' ---- directhf $end ...
then TD-DFT also uses direct algorithm. The memory for JK operators can be changed by using MemJKOP.
$TDDFT ... MemJKOP 2048 ... $END
If the ERI is stored, then integral transformation should be carried out before TDDFT
$TRAINT TDDFT (or UTDDFT for RO/U case) ORBI hforb $END
Open-shell Systems : U-TD-DFT and spin-adapted TD-DFT for spin-conserving excitations
Using a UKS reference in SCF, the input for U-TD-DFT reads:
$TDDFT IMETHOD 2 ISF 0 ... $END
Using a ROKS reference in SCF, the input for Spin-adapted TD-DFT (X-TD-DFT) can be set in two ways.
One uses U-TD-DFT solver to solve the X-TD-DFT in spin-orbit basis:
$TDDFT IMETHOD 2 ISF 0 ... icorrect 1 itest 1 itrans 1 $END
The option itrans will transform the eigenvector in CV(aa),CV(bb) basis into CV(0) and CV(1) basis.
The other one uses the original spin-adapted TD-DFT solver to solve the X-TD-DFT in spin-tensor basis:
$TDDFT imethod 3 isf 0 ... itest 1 icorrect 1 $END
These two ways give exactly the same excitation energies. The only different is the representation if "itrans" is not used.
Open-shell Systems : Spin-flip TD-DFT for spin-flip excitations
Although SF-TD-DFT is possible by using isf=3, which calculate a->b and b->a excitation at the same time, however, the TDA version is preferred. This allows separate calculations of a->b and b->a types of excitations.
Using a UKS/ROKS reference in SCF, the input for spin-flip TDA (flip-up) reads:
$TDDFT IMETHOD 2 ISF 1 ... ialda 2 $END
The keyword ialda controls the spin-flip kernel when using GGA functionals in ground state calculations. The option "ialda=2" means a ALDA0 type approximation is used, which always gives numerical stable results.
Flip-down excitations can be calculated by choosing isf=-1.
$TDDFT IMETHOD 2 ISF -1 ... ialda 2 $END
There are spin-adapted versions of flip-down excitations with imethod=3, but they are not thoroughly tested and to be explored in future.
General keywords
imethod
isf
itda
idrpa
ispa
ialda
thrdab
itest
icorrect
itrans
iro
icv
ioo
iksf
iact
elw
eup
idiag
ndiag
aokxc
States specification
iext
next
Save eigenvectors
istore
Integer: specify the file no. to store TDDFT information
lefteig
By default, in TD-DFT the left eigenvector X-Y is also stored.
output eigenvector control
nprt
cthrd
Property evaluation
isoc
=1, Only work for closed-shell case (NOT recommended!)
=2, General SOC state interaction
=3, just print SOC matrix elements between two spin-free states
irsf
Unused.
irso
insf
inso
imatsoc
Define SOC matrices need to be calculated. Input format looks like
$tddft imatsoc ..... 2 0 1 1 2 1 1 2 1 1 2 1 1 ..... $end
In this input, 2 means two set of SOC matrices will be calculate. One set is SOC between state "0 1 1" and "2 1 1". Here, the state is specified by "2S+1 Symm iRoot". "2S+1" is spin multiplet of a state. "Smmy" is symmetry of this state(irreducible irreps of this state). The last "1" means 1st root of the state |2S+1,Symm>. Therefore, the SOC matrices of <011|HSOC|211> (coupling between 1st singlet state and 1st triplet state) are calculated. Notice, the total number of matrix element is "1*3" because of spin multiplets of these states.
imatrsf
Unused.
imatrso
Define transition dipole need to be printed between to states. Input format looks like(notice we omit other input in TDDFT module)
$TDDFT ... irso 1 imatrso 5 1 1 1 2 1 3 1 4 1 5 ... $END
Here, "irso" is set to 1 to enable transition dipole moment calculation. Then, "imatros" is specified to define transition dipole moments need to be printed. The number "5" require transition dipoles between 5-pairs of states to be print. The following 5 lines define which pairs will be printed. Here, we require transition dipoles between the ground state and five low-lying states are printed.
imatnsf
ifgs
nfiles
isgn
ivo
idiag
TD-DFT/SOC can use Davidson's algorithm also, along with a specification for the no. of states by iexit.
iact
=1, allows to use active space specification for the projected active-orbital SOC Hamiltonian (P*HSOC*P), eup can be specified in (eV) to give a cut off to define active physically interested excited states.
Stability analysis
isab
isave
memory control
memjkop
TD-DFT/SOC
SOC计算的输入文件中以$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
$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
Output
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
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
[tddft_soc_final]说明：
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
...
11 3.0881 eV 0.0000 52.9% Spin: |So,1> 2-th A 3.0330 0.0551 3.0947 24960.28这里，ExEnergies列出加入SOC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 !
< 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。