TD-DFT with SOC: basics

Contents

TD-DFT with SOC: basics

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。

Warning: f-振子强度并没有计算，如需计算需要指定imatrso来计算transition dipole moment !

Example: Calculate (transition) dipole moments with or without including SOC

BASIC Input:

$COMPASS
Title
 ch2s
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
Skeleton
$END

$xuanyuan
scalar
heff
3
soint
hsoc
2
direct
schwarz
$end

$scf
RHF
charge
0
spin
1
THRESHCONV
1.d-12 1.d-10
OPTSCR
1
$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.

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TD-DFT with SOC: basics

Breif description of the flowchart

Example: Print SOC mat and Perform SOC diagonalization

SOC matrix elements

SOC-SI results

Example: Calculate (transition) dipole moments with or without including SOC

Without SOC

With SOC