Calculations of SOC with TDDFT and a triplet ground state

Hello,

We are currently trying to perform SOC computation with the TD-DFT method but with a triplet ground state. Here is the relevant input for the Si17H36 molecule:

$molecule
   0 3
 Si        4.565393568581     -3.816245866555      5.990644702250
 Si        3.715364211679     -5.801154961144      5.089950779278
 Si        2.226464673811      3.826347417073     -1.276591968872
 Si        0.533512423306      2.927148468449     -2.654709961282
 Si        1.720565928981      1.643844904805     -4.240474917713
 Si        4.788263741870     -6.611619522210      3.175342851592
 Si       -1.388209882214      4.902940846827      0.942260662361
 Si       -2.371687978534      2.920665358924      0.120741521407
 Si       -2.803610397138      1.658144688051      2.068499291880
 Si        2.990185118353     -7.407803537822      6.628269725755
 Si       -0.520922178516      4.672605195735     -3.847435178496
 Si       -4.418324225520      3.545789847515     -0.880252986201
 Si       -1.006205314266      1.695810610037     -1.361119034378
 Si       -2.964897459008      0.327708763241     -4.455648408618
 Si       -0.347501374067     -1.883732402407     -2.688212353730
 Si       -3.638252125680     -1.258044211807     -1.082410290589
 Si       -1.972873004289     -0.199661053143     -2.377462345094
 H         3.629824295869     -3.292088221649      7.015318174775
 H         5.891375860046     -4.015053457925      6.631712127621
 H         4.717764974383     -2.805073734483      4.916275188529
 H         1.689351207448      4.771104542081     -0.269871770134
 H         2.932399217250      2.731402883087     -0.567113598649
 H         3.208040143124      4.552104166118     -2.121521209486
 H         0.822290739155      0.961182773262     -5.200646114645
 H         2.599664296434      2.569966157775     -4.997966376863
 H         2.572924210751      0.630334999468     -3.574142812025
 H         3.978780395982     -7.697762483907      2.571182360423
 H         4.938908607136     -5.516789281168      2.186083132653
 H         6.139033648735     -7.152972257180      3.477159773743
 H        -1.002009968763      5.833849204438     -0.143543685508
 H        -2.393113073652      5.577130478411      1.802493725150
 H        -0.193289926457      4.602825815606      1.766765720897
 H        -3.551057512201      0.412605401862      1.777575736216
 H        -1.525161697788      1.297912529132      2.729118627498
 H        -3.608282830942      2.476350100854      3.010397857086
 H         2.235178183410     -8.471081246576      5.921580466099
 H         4.123293658870     -8.044569631435      7.348913099747
 H         2.101575296780     -6.772995938046      7.631951746334
 H        -1.487824314943      4.109047355641     -4.821007148452
 H        -1.250095928509      5.580863036682     -2.930978267864
 H         0.491887526048      5.464192755053     -4.590830611706
 H        -5.149691296758      2.360073486518     -1.385933886159
 H        -5.275964052154      4.242908572555      0.111457974723
 H        -4.167342802471      4.465340337599     -2.016834903731
 H        -3.489951466751     -0.905292862752     -5.095221893970
 H        -4.091031884163      1.271969875412     -4.254577366777
 H        -1.983066466057      0.953692601419     -5.372505558250
 H        -0.999568965113     -3.088676839998     -3.260122172834
 H         0.734521923757     -1.459471706889     -3.606798798433
 H         0.256840574148     -2.248285613910     -1.383434021800
 H        -4.179387760370     -2.384856150508     -1.883508192523
 H        -3.068828830530     -1.807102195382      0.171413096670
 H        -4.755251706653     -0.345530008307     -0.744232509010
$end

$rem
   MEM_TOTAL            8000
   MEM_STATIC           200
   JOBTYPE              sp
   EXCHANGE             b3lyp
   BASIS                def2-svp
   SCF_ALGORITHM        diis
   MAX_SCF_CYCLES       100
   CIS_N_ROOTS          5
   CIS_SINGLETS         true
   CIS_TRIPLETS         true
   STS_MOM              true
   CALC_SOC             true
   IQMOL_FCHK           True
$end

The output seems rather weird though. Only 5 states have been computed with no information about their multiplicity instead of the 5 singlets and 5 triplets we were expecting:

 Direct TDDFT/TDA calculation will be performed
 Exchange:     0.2000 Hartree-Fock + 0.0800 Slater + 0.7200 B88
 Correlation:  0.1900 VWN1RPA + 0.8100 LYP
 Using SG-1 standard quadrature grid
 CIS energy converged when residual is below 10e- 6
 ---------------------------------------------------
 Iter    Rts Conv    Rts Left    Ttl Dev     Max Dev
 ---------------------------------------------------
   1         0           5      0.000365    0.000141
   2         2           3      0.000134    0.000046
   3         2           3      0.000053    0.000019
   4         2           3      0.000024    0.000009
   5         2           3      0.000011    0.000004
   6         0           5      0.000199    0.000098
   7         3           2      0.000142    0.000070
   8         3           2      0.000054    0.000027
   9         3           2      0.000019    0.000009
  10         3           2      0.000013    0.000006
  11         3           2      0.000011    0.000005
  12         3           2      0.000006    0.000003
  13         5           0      0.000003    0.000001    Roots Converged
 ---------------------------------------------------
 
 ---------------------------------------------------
         TDDFT/TDA Excitation Energies              
 ---------------------------------------------------

 Excited state   1: excitation energy (eV) =    3.0143
 Total energy for state  1:                 -4941.62726973 au
    <S**2>     :  2.0245
    Trans. Mom.: -0.0432 X   0.0312 Y  -0.1381 Z
    Strength   :     0.0016183467
    D(  136) --> S(    1) amplitude =  0.9799 beta

 Excited state   2: excitation energy (eV) =    3.0155
 Total energy for state  2:                 -4941.62722621 au
    <S**2>     :  2.0245
    Trans. Mom.: -0.0191 X  -0.1450 Y  -0.0257 Z
    Strength   :     0.0016298610
    D(  135) --> S(    1) amplitude =  0.9799 beta

 Excited state   3: excitation energy (eV) =    3.2014
 Total energy for state  3:                 -4941.62039347 au
    <S**2>     :  2.0240
    Trans. Mom.: -0.1229 X   0.0095 Y   0.0406 Z
    Strength   :     0.0013217838
    S(    2) --> V(    1) amplitude =  0.9898 alpha

 Excited state   4: excitation energy (eV) =    3.5809
 Total energy for state  4:                 -4941.60644691 au
    <S**2>     :  2.0244
    Trans. Mom.: -0.0468 X   0.1468 Y  -0.1788 Z
    Strength   :     0.0048872767
    S(    2) --> V(    2) amplitude = -0.9662 alpha
    S(    2) --> V(    3) amplitude =  0.1511 alpha

 Excited state   5: excitation energy (eV) =    3.5817
 Total energy for state  5:                 -4941.60641768 au
    <S**2>     :  2.0244
    Trans. Mom.: -0.0630 X  -0.1826 Y  -0.1377 Z
    Strength   :     0.0049392705
    S(    2) --> V(    2) amplitude =  0.1512 alpha
    S(    2) --> V(    3) amplitude =  0.9660 alpha
 
 ---------------------------------------------------
  SETman timing summary (seconds)
  CPU time              1590.58s
  System time              0.00s
  Wall time              207.14s

On top of that, the SOC results section mentions a singlet ground state as well as the usual 5 triplet and 5 singlet excited states:

=======================================================================================
    SPIN-ORBIT COUPLING BETWEEN THE SINGLET GROUND STATE AND EXCITED TRIPLET STATE
=======================================================================================

SOC between the singlet ground state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  -0.868171i    cm-1
T2(ms=0)      0.000000  +  7.229184i    cm-1
T3(ms=0)      0.000000  +  0.753279i    cm-1
T4(ms=0)      0.000000  +  -15.820413i    cm-1
T5(ms=0)      0.000000  +  40.114332i    cm-1
SOC between the singlet ground state and excited triplet states (ms=1):
T1(ms=1)      -5.348454  + (-0.620998i)    cm-1
T2(ms=1)      -0.781414  + (1.631144i)    cm-1
T3(ms=1)      0.119509  + (-1.432836i)    cm-1
T4(ms=1)      -29.475830  + (-6.004400i)    cm-1
T5(ms=1)      -12.466265  + (8.382454i)    cm-1
SOC between the singlet ground state and excited triplet states (ms=-1):
T1(ms=-1)     -5.348454  - (-0.620998i)    cm-1
T2(ms=-1)     -0.781414  - (1.631144i)    cm-1
T3(ms=-1)     0.119509  - (-1.432836i)    cm-1
T4(ms=-1)     -29.475830  - (-6.004400i)    cm-1
T5(ms=-1)     -12.466265  - (8.382454i)    cm-1
Total SOC between the singlet ground state and excited triplet states:
T1      7.664002    cm-1
T2      7.668349    cm-1
T3      2.168417    cm-1
T4      45.387666    cm-1
T5      45.392800    cm-1




=======================================================================================
                     SPIN-ORBIT COUPLING BETWEEN EXCITED TRIPLET STATES
=======================================================================================

SOC between the T1 (ms=0) state and excited triplet states (ms=1):
T2(ms=1)      0.034530  + (-0.436316i)    cm-1
T3(ms=1)      1.296887  + (-0.030390i)    cm-1
T4(ms=1)      0.481655  + (1.528259i)    cm-1
T5(ms=1)      -0.455493  + (-2.799411i)    cm-1
SOC between the T1 (ms=0) state and excited triplet states (ms=-1):
T2(ms=-1)     -0.034530  + (-0.436316i)    cm-1
T3(ms=-1)     -1.296887  + (-0.030390i)    cm-1
T4(ms=-1)     -0.481655  + (1.528259i)    cm-1
T5(ms=-1)     0.455493  + (-2.799411i)    cm-1
SOC between the T1 (ms=1) state and excited triplet states (ms=0):
T2(ms=0)      -0.034530  + (-0.436316i)    cm-1
T3(ms=0)      -1.296887  + (-0.030390i)    cm-1
T4(ms=0)      -0.481655  + (1.528259i)    cm-1
T5(ms=0)      0.455493  + (-2.799411i)    cm-1
SOC between the T1 (ms=1) state and excited triplet states (ms=1):
T2(ms=1)      0.000000  + (0.204354i)    cm-1
T3(ms=1)      0.000000  + (-0.533557i)    cm-1
T4(ms=1)      0.000000  + (0.300910i)    cm-1
T5(ms=1)      0.000000  + (2.172311i)    cm-1
SOC between the T1 (ms=-1) state and excited triplet states (ms=0):
T2(ms=0)      0.034530  + (-0.436316i)    cm-1
T3(ms=0)      1.296887  + (-0.030390i)    cm-1
T4(ms=0)      0.481655  + (1.528259i)    cm-1
T5(ms=0)      -0.455493  + (-2.799411i)    cm-1
SOC between the T1 (ms=-1) state and excited triplet states (ms=-1):
T2(ms=-1)     0.000000  + (-0.204354i)    cm-1
T3(ms=-1)     0.000000  + (0.533557i)    cm-1
T4(ms=-1)     0.000000  + (-0.300910i)    cm-1
T5(ms=-1)     0.000000  + (-2.172311i)    cm-1
Total SOC between the T1 state and excited triplet states:
T2      0.921834    cm-1
T3      2.701986    cm-1
T4      3.232858    cm-1
T5      6.450936    cm-1



SOC between the T2 (ms=0) state and excited triplet states (ms=1):
T3(ms=1)      -0.371124  + (-0.434865i)    cm-1
T4(ms=1)      -0.910824  + (3.068900i)    cm-1
T5(ms=1)      -0.672726  + (1.022898i)    cm-1
SOC between the T2 (ms=0) state and excited triplet states (ms=-1):
T3(ms=-1)     0.371124  + (-0.434865i)    cm-1
T4(ms=-1)     0.910824  + (3.068900i)    cm-1
T5(ms=-1)     0.672726  + (1.022898i)    cm-1
SOC between the T2 (ms=1) state and excited triplet states (ms=0):
T3(ms=0)      0.371124  + (-0.434865i)    cm-1
T4(ms=0)      0.910824  + (3.068900i)    cm-1
T5(ms=0)      0.672726  + (1.022898i)    cm-1
SOC between the T2 (ms=1) state and excited triplet states (ms=1):
T3(ms=1)      0.000000  + (-1.742617i)    cm-1
T4(ms=1)      0.000000  + (-0.579546i)    cm-1
T5(ms=1)      0.000000  + (-1.480097i)    cm-1
SOC between the T2 (ms=-1) state and excited triplet states (ms=0):
T3(ms=0)      -0.371124  + (-0.434865i)    cm-1
T4(ms=0)      -0.910824  + (3.068900i)    cm-1
T5(ms=0)      -0.672726  + (1.022898i)    cm-1
SOC between the T2 (ms=-1) state and excited triplet states (ms=-1):
T3(ms=-1)     0.000000  + (1.742617i)    cm-1
T4(ms=-1)     0.000000  + (0.579546i)    cm-1
T5(ms=-1)     0.000000  + (1.480097i)    cm-1
Total SOC between the T2 state and excited triplet states:
T3      2.716761    cm-1
T4      6.454668    cm-1
T5      3.221320    cm-1



SOC between the T3 (ms=0) state and excited triplet states (ms=1):
T4(ms=1)      -10.790625  + (-1.527163i)    cm-1
T5(ms=1)      -2.677706  + (3.223598i)    cm-1
SOC between the T3 (ms=0) state and excited triplet states (ms=-1):
T4(ms=-1)     10.790625  + (-1.527163i)    cm-1
T5(ms=-1)     2.677706  + (3.223598i)    cm-1
SOC between the T3 (ms=1) state and excited triplet states (ms=0):
T4(ms=0)      10.790625  + (-1.527163i)    cm-1
T5(ms=0)      2.677706  + (3.223598i)    cm-1
SOC between the T3 (ms=1) state and excited triplet states (ms=1):
T4(ms=1)      0.000000  + (-3.240925i)    cm-1
T5(ms=1)      0.000000  + (14.578591i)    cm-1
SOC between the T3 (ms=-1) state and excited triplet states (ms=0):
T4(ms=0)      -10.790625  + (-1.527163i)    cm-1
T5(ms=0)      -2.677706  + (3.223598i)    cm-1
SOC between the T3 (ms=-1) state and excited triplet states (ms=-1):
T4(ms=-1)     0.000000  + (3.240925i)    cm-1
T5(ms=-1)     0.000000  + (-14.578591i)    cm-1
Total SOC between the T3 state and excited triplet states:
T4      22.272999    cm-1
T5      22.255727    cm-1



SOC between the T4 (ms=0) state and excited triplet states (ms=1):
T5(ms=1)      2.055651  + (-27.803903i)    cm-1
SOC between the T4 (ms=0) state and excited triplet states (ms=-1):
T5(ms=-1)     -2.055651  + (-27.803903i)    cm-1
SOC between the T4 (ms=1) state and excited triplet states (ms=0):
T5(ms=0)      -2.055651  + (-27.803903i)    cm-1
SOC between the T4 (ms=1) state and excited triplet states (ms=1):
T5(ms=1)      0.000000  + (12.977354i)    cm-1
SOC between the T4 (ms=-1) state and excited triplet states (ms=0):
T5(ms=0)      2.055651  + (-27.803903i)    cm-1
SOC between the T4 (ms=-1) state and excited triplet states (ms=-1):
T5(ms=-1)     0.000000  + (-12.977354i)    cm-1
Total SOC between the T4 state and excited triplet states:
T5      58.702251    cm-1







=======================================================================================
         SPIN-ORBIT COUPLING BETWEEN EXCITED SINGLET STATES AND TRIPLET STATES
=======================================================================================

SOC between the S1 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  -56.659477i    cm-1
T2(ms=0)      0.000000  +  42.781833i    cm-1
T3(ms=0)      0.000000  +  1493.109352i    cm-1
T4(ms=0)      0.000000  +  -8.858243i    cm-1
T5(ms=0)      0.000000  +  543.068930i    cm-1
SOC between the S1 state and excited triplet states (ms=1):
T1(ms=1)      (59.329289)  + (96.344346i)    cm-1
T2(ms=1)      (-74.008877)  + (-32.065249i)    cm-1
T3(ms=1)      (2527.113936)  + (-234.019029i)    cm-1
T4(ms=1)      (875.541078)  + (1143.586386i)    cm-1
T5(ms=1)      (-121.083032)  + (78.645564i)    cm-1
SOC between the S1 state and excited triplet states (ms=-1):
T1(ms=-1)    -(59.329289)  + (96.344346i)    cm-1
T2(ms=-1)    -(-74.008877)  + (-32.065249i)    cm-1
T3(ms=-1)    -(2527.113936)  + (-234.019029i)    cm-1
T4(ms=-1)    -(875.541078)  + (1143.586386i)    cm-1
T5(ms=-1)    -(-121.083032)  + (78.645564i)    cm-1
Total SOC between the S1 state and excited triplet states:
T1      169.748907    cm-1
T2      121.824764    cm-1
T3      3887.353218    cm-1
T4      2036.860935    cm-1
T5      580.186447    cm-1



SOC between the S2 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  580.679793i    cm-1
T2(ms=0)      0.000000  +  145.807004i    cm-1
T3(ms=0)      0.000000  +  4028.593601i    cm-1
T4(ms=0)      0.000000  +  2984.376246i    cm-1
T5(ms=0)      0.000000  +  4517.408835i    cm-1
SOC between the S2 state and excited triplet states (ms=1):
T1(ms=1)      (-217.979192)  + (-15.281831i)    cm-1
T2(ms=1)      (119.665658)  + (-42.321260i)    cm-1
T3(ms=1)      (2530.462315)  + (-69.709131i)    cm-1
T4(ms=1)      (-3317.881746)  + (-410.606102i)    cm-1
T5(ms=1)      (230.375815)  + (-633.405052i)    cm-1
SOC between the S2 state and excited triplet states (ms=-1):
T1(ms=-1)    -(-217.979192)  + (-15.281831i)    cm-1
T2(ms=-1)    -(119.665658)  + (-42.321260i)    cm-1
T3(ms=-1)    -(2530.462315)  + (-69.709131i)    cm-1
T4(ms=-1)    -(-3317.881746)  + (-410.606102i)    cm-1
T5(ms=-1)    -(230.375815)  + (-633.405052i)    cm-1
Total SOC between the S2 state and excited triplet states:
T1      657.788680    cm-1
T2      231.260892    cm-1
T3      5389.412231    cm-1
T4      5591.097825    cm-1
T5      4616.874758    cm-1



SOC between the S3 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  -15.454128i    cm-1
T2(ms=0)      0.000000  +  75.941387i    cm-1
T3(ms=0)      0.000000  +  117.840024i    cm-1
T4(ms=0)      0.000000  +  -291.642814i    cm-1
T5(ms=0)      0.000000  +  404.329379i    cm-1
SOC between the S3 state and excited triplet states (ms=1):
T1(ms=1)      (191.354980)  + (19.459601i)    cm-1
T2(ms=1)      (212.198388)  + (-15.474412i)    cm-1
T3(ms=1)      (-782.562538)  + (-400.317989i)    cm-1
T4(ms=1)      (-750.661399)  + (655.131050i)    cm-1
T5(ms=1)      (651.265325)  + (-61.137335i)    cm-1
SOC between the S3 state and excited triplet states (ms=-1):
T1(ms=-1)    -(191.354980)  + (19.459601i)    cm-1
T2(ms=-1)    -(212.198388)  + (-15.474412i)    cm-1
T3(ms=-1)    -(-782.562538)  + (-400.317989i)    cm-1
T4(ms=-1)    -(-750.661399)  + (655.131050i)    cm-1
T5(ms=-1)    -(651.265325)  + (-61.137335i)    cm-1
Total SOC between the S3 state and excited triplet states:
T1      272.451168    cm-1
T2      310.326152    cm-1
T3      1248.680707    cm-1
T4      1438.900271    cm-1
T5      1009.579537    cm-1



SOC between the S4 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  -469.758518i    cm-1
T2(ms=0)      0.000000  +  -200.118790i    cm-1
T3(ms=0)      0.000000  +  -117.217263i    cm-1
T4(ms=0)      0.000000  +  -771.627013i    cm-1
T5(ms=0)      0.000000  +  2399.756612i    cm-1
SOC between the S4 state and excited triplet states (ms=1):
T1(ms=1)      (-43.251288)  + (62.646067i)    cm-1
T2(ms=1)      (-159.913351)  + (-61.825560i)    cm-1
T3(ms=1)      (1918.387972)  + (-599.643933i)    cm-1
T4(ms=1)      (-2679.518534)  + (2156.726787i)    cm-1
T5(ms=1)      (-553.453193)  + (752.108116i)    cm-1
SOC between the S4 state and excited triplet states (ms=-1):
T1(ms=-1)    -(-43.251288)  + (62.646067i)    cm-1
T2(ms=-1)    -(-159.913351)  + (-61.825560i)    cm-1
T3(ms=-1)    -(1918.387972)  + (-599.643933i)    cm-1
T4(ms=-1)    -(-2679.518534)  + (2156.726787i)    cm-1
T5(ms=-1)    -(-553.453193)  + (752.108116i)    cm-1
Total SOC between the S4 state and excited triplet states:
T1      481.937208    cm-1
T2      314.383348    cm-1
T3      2844.874409    cm-1
T4      4925.239919    cm-1
T5      2739.121375    cm-1



SOC between the S5 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  -151.707114i    cm-1
T2(ms=0)      0.000000  +  -664.882667i    cm-1
T3(ms=0)      0.000000  +  -2721.119681i    cm-1
T4(ms=0)      0.000000  +  -492.444125i    cm-1
T5(ms=0)      0.000000  +  596.019004i    cm-1
SOC between the S5 state and excited triplet states (ms=1):
T1(ms=1)      (-91.581712)  + (-63.116183i)    cm-1
T2(ms=1)      (1.398841)  + (-97.320193i)    cm-1
T3(ms=1)      (-1269.027401)  + (-1857.767239i)    cm-1
T4(ms=1)      (-99.357495)  + (-695.899219i)    cm-1
T5(ms=1)      (738.690940)  + (-1485.437547i)    cm-1
SOC between the S5 state and excited triplet states (ms=-1):
T1(ms=-1)    -(-91.581712)  + (-63.116183i)    cm-1
T2(ms=-1)    -(1.398841)  + (-97.320193i)    cm-1
T3(ms=-1)    -(-1269.027401)  + (-1857.767239i)    cm-1
T4(ms=-1)    -(-99.357495)  + (-695.899219i)    cm-1
T5(ms=-1)    -(738.690940)  + (-1485.437547i)    cm-1
Total SOC between the S5 state and excited triplet states:
T1      218.533232    cm-1
T2      678.981086    cm-1
T3      4186.639659    cm-1
T4      1109.412676    cm-1
T5      2420.664511    cm-1

Do we need to specify some additional parameters in the input file? Are we missing something?

Thank you very much for your help!

Best regards!

Iacobellis Nicolas, Ph.D. Student

Dear Lacobellis,

Hello. To my knowledge, (charge, multiplicity)=(0,3) overrides
CIS_SINGLETS=TRUE. In other words, QChem will find the lowest
5 excited states, regardless of spin multiplicities. In your output
“<S**2> : 2.0245” means the state is triplet as there are two
independent spins.

In the case you are in need of singlet excited state, you may just
increase CIS_N_ROOTS to 10 or larger and
observe any states that show <S**2> : 0.00 (or close to null).

Besides, overall SOC output looks ok to my evaluation, aside from
physical/chemical soundness. :slight_smile:

Best,
Jiyong