Trying to evaluate performance of SOC calculations in TD-DFT methods

Hello,

We are currently trying to perform SOC computation on silicon quantum dots with the TD-DFT method and we wanted to evaluate the soundness of the results.

After trying a calculation using the B3LYP/def2-SVP method on a Ca atom and comparing it to the NIST values, the results appear to be quite bad.

This is the input we’ve used for the calculation:

$molecule
   0 1
Ca 0.0 0.0 0.0
$end

$rem
   MEM_TOTAL            1000
   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

This is the output of the calculation:

 ----------------------------------------------------------------
             Standard Nuclear Orientation (Angstroms)
    I     Atom           X                Y                Z
 ----------------------------------------------------------------
    1      Ca      0.0000000000     0.0000000000     0.0000000000
 ----------------------------------------------------------------
 Molecular Point Group                 Kh    NOp =***
 Largest Abelian Subgroup              D2h   NOp =  1
 Nuclear Repulsion Energy =           0.00000000 hartrees
 There are       10 alpha and       10 beta electrons
 Requested basis set is def2-SVP
 There are 10 shells and 24 basis functions

 Total QAlloc Memory Limit   1000 MB
 Mega-Array Size       196 MB
 MEM_STATIC part       200 MB
 A cutoff of  1.0D-11 yielded     55 shell pairs
 There are       329 function pairs (       390 Cartesian)
 Smallest overlap matrix eigenvalue = 1.22E-01

 Scale SEOQF with 1.000000e-01/1.000000e-01/1.000000e-01

 Standard Electronic Orientation quadrupole field applied
 Guess from superposition of atomic densities
 Warning:  Energy on first SCF cycle will be non-variational
 SAD guess density has 20.000000 electrons

 -----------------------------------------------------------------------
  General SCF calculation program by
  Eric Jon Sundstrom, Paul Horn, Yuezhi Mao, Dmitri Zuev, Alec White,
  David Stuck, Shaama M.S., Shane Yost, Joonho Lee, David Small,
  Daniel Levine, Susi Lehtola, Hugh Burton, Evgeny Epifanovsky,
  Bang C. Huynh
 -----------------------------------------------------------------------
 Exchange:     0.2000 Hartree-Fock + 0.0800 Slater + 0.7200 B88
 Correlation:  0.1900 VWN1RPA + 0.8100 LYP
 Using SG-1 standard quadrature grid
 using 2 threads for integral computing
 -------------------------------------------------------
 OpenMP Integral computing Module                
 Release: version 1.0, May 2013, Q-Chem Inc. Pittsburgh 
 -------------------------------------------------------
 A restricted SCF calculation will be
 performed using DIIS
 SCF converges when DIIS error is below 1.0e-08
 ---------------------------------------
  Cycle       Energy         DIIS error
 ---------------------------------------
    1    -677.4893010978      4.24e-03  
    2    -677.4910087559      2.49e-04  
    3    -677.4910160572      2.93e-05  
    4    -677.4910161880      1.33e-06  
    5    -677.4910161882      4.10e-09  Convergence criterion met
 ---------------------------------------
 SCF time:   CPU 0.60s  wall 1.00s 
 SCF   energy in the final basis set =     -677.4910161882
 Total energy in the final basis set =     -677.4910161882
 
 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
 Triplet excitation energies requested
 Singlet excitation energies requested
 CIS energy converged when residual is below 10e- 6
 ---------------------------------------------------
 Iter    Rts Conv    Rts Left    Ttl Dev     Max Dev
 ---------------------------------------------------
   1         0           5      0.002607    0.000521
   2         0           5      0.000161    0.000032
   3         0           5      0.000007    0.000001
   4         5           0      0.000000    0.000000    Roots Converged
 ---------------------------------------------------
 Triplets done: starting singlet calculation
 ---------------------------------------------------
 Iter    Rts Conv    Rts Left    Ttl Dev     Max Dev
 ---------------------------------------------------
   5         0           5      0.005365    0.001073
   6         0           5      0.000724    0.000145
   7         0           5      0.000013    0.000003
   8         5           0      0.000000    0.000000    Roots Converged
 ---------------------------------------------------
 
 ---------------------------------------------------
         TDDFT/TDA Excitation Energies              
 ---------------------------------------------------

 Excited state   1: excitation energy (eV) =    1.7838
 Total energy for state  1:                  -677.42546272 au
    Multiplicity: Triplet
    Trans. Mom.:  0.0000 X   0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    2) amplitude =  0.9999

 Excited state   2: excitation energy (eV) =    1.7838
 Total energy for state  2:                  -677.42546272 au
    Multiplicity: Triplet
    Trans. Mom.:  0.0000 X   0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    1) amplitude =  0.9999

 Excited state   3: excitation energy (eV) =    1.7838
 Total energy for state  3:                  -677.42546272 au
    Multiplicity: Triplet
    Trans. Mom.:  0.0000 X   0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    4) amplitude =  0.9999

 Excited state   4: excitation energy (eV) =    1.7838
 Total energy for state  4:                  -677.42546272 au
    Multiplicity: Triplet
    Trans. Mom.:  0.0000 X   0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    3) amplitude =  0.9999

 Excited state   5: excitation energy (eV) =    1.7838
 Total energy for state  5:                  -677.42546272 au
    Multiplicity: Triplet
    Trans. Mom.:  0.0000 X   0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    5) amplitude =  0.9999

 Excited state   6: excitation energy (eV) =    2.2924
 Total energy for state  6:                  -677.40677104 au
    Multiplicity: Singlet
    Trans. Mom.: -0.0000 X  -0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    1) amplitude =  0.9985

 Excited state   7: excitation energy (eV) =    2.2924
 Total energy for state  7:                  -677.40677104 au
    Multiplicity: Singlet
    Trans. Mom.:  0.0000 X  -0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    2) amplitude =  0.9985

 Excited state   8: excitation energy (eV) =    2.2924
 Total energy for state  8:                  -677.40677104 au
    Multiplicity: Singlet
    Trans. Mom.:  0.0000 X   0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    3) amplitude =  0.9985

 Excited state   9: excitation energy (eV) =    2.2924
 Total energy for state  9:                  -677.40677104 au
    Multiplicity: Singlet
    Trans. Mom.:  0.0000 X   0.0000 Y  -0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    4) amplitude =  0.9985

 Excited state  10: excitation energy (eV) =    2.2924
 Total energy for state 10:                  -677.40677104 au
    Multiplicity: Singlet
    Trans. Mom.:  0.0000 X  -0.0000 Y   0.0000 Z
    Strength   :     0.0000000000
    D(   10) --> V(    5) amplitude =  0.9985
 
 ---------------------------------------------------
  SETman timing summary (seconds)
  CPU time                 1.09s
  System time              0.00s
  Wall time                0.66s



*********SPIN-ORBIT COUPLING JOB BEGINS HERE*********


=======================================================================================
    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  +  0.000000i    cm-1
T2(ms=0)      0.000000  +  0.000000i    cm-1
T3(ms=0)      0.000000  +  -0.000000i    cm-1
T4(ms=0)      0.000000  +  0.000000i    cm-1
T5(ms=0)      0.000000  +  0.000000i    cm-1
SOC between the singlet ground state and excited triplet states (ms=1):
T1(ms=1)      -0.000000  + (-0.000000i)    cm-1
T2(ms=1)      -0.000000  + (-0.000000i)    cm-1
T3(ms=1)      -0.000000  + (0.000000i)    cm-1
T4(ms=1)      0.000000  + (0.000000i)    cm-1
T5(ms=1)      0.000000  + (-0.000000i)    cm-1
SOC between the singlet ground state and excited triplet states (ms=-1):
T1(ms=-1)     -0.000000  - (-0.000000i)    cm-1
T2(ms=-1)     -0.000000  - (-0.000000i)    cm-1
T3(ms=-1)     -0.000000  - (0.000000i)    cm-1
T4(ms=-1)     0.000000  - (0.000000i)    cm-1
T5(ms=-1)     0.000000  - (-0.000000i)    cm-1
Total SOC between the singlet ground state and excited triplet states:
T1      0.000000    cm-1
T2      0.000000    cm-1
T3      0.000000    cm-1
T4      0.000000    cm-1
T5      0.000000    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)      -39.185965  + (0.000091i)    cm-1
T3(ms=1)      -0.000179  + (-21.540613i)    cm-1
T4(ms=1)      0.000001  + (0.000345i)    cm-1
T5(ms=1)      17.901179  + (-0.000003i)    cm-1
SOC between the T1 (ms=0) state and excited triplet states (ms=-1):
T2(ms=-1)     39.185965  + (0.000091i)    cm-1
T3(ms=-1)     0.000179  + (-21.540613i)    cm-1
T4(ms=-1)     -0.000001  + (0.000345i)    cm-1
T5(ms=-1)     -17.901179  + (-0.000003i)    cm-1
SOC between the T1 (ms=1) state and excited triplet states (ms=0):
T2(ms=0)      39.185965  + (0.000091i)    cm-1
T3(ms=0)      0.000179  + (-21.540613i)    cm-1
T4(ms=0)      -0.000001  + (0.000345i)    cm-1
T5(ms=0)      -17.901179  + (-0.000003i)    cm-1
SOC between the T1 (ms=1) state and excited triplet states (ms=1):
T2(ms=1)      0.000000  + (-0.000048i)    cm-1
T3(ms=1)      0.000000  + (0.000519i)    cm-1
T4(ms=1)      0.000000  + (30.463028i)    cm-1
T5(ms=1)      0.000000  + (-0.000056i)    cm-1
SOC between the T1 (ms=-1) state and excited triplet states (ms=0):
T2(ms=0)      -39.185965  + (0.000091i)    cm-1
T3(ms=0)      -0.000179  + (-21.540613i)    cm-1
T4(ms=0)      0.000001  + (0.000345i)    cm-1
T5(ms=0)      17.901179  + (-0.000003i)    cm-1
SOC between the T1 (ms=-1) state and excited triplet states (ms=-1):
T2(ms=-1)     0.000000  + (0.000048i)    cm-1
T3(ms=-1)     0.000000  + (-0.000519i)    cm-1
T4(ms=-1)     0.000000  + (-30.463028i)    cm-1
T5(ms=-1)     0.000000  + (0.000056i)    cm-1
Total SOC between the T1 state and excited triplet states:
T2      78.371931    cm-1
T3      43.081227    cm-1
T4      43.081227    cm-1
T5      35.802358    cm-1



SOC between the T2 (ms=0) state and excited triplet states (ms=1):
T3(ms=1)      -0.000014  + (-0.000581i)    cm-1
T4(ms=1)      0.000103  + (-35.095859i)    cm-1
T5(ms=1)      -0.000013  + (0.000060i)    cm-1
SOC between the T2 (ms=0) state and excited triplet states (ms=-1):
T3(ms=-1)     0.000014  + (-0.000581i)    cm-1
T4(ms=-1)     -0.000103  + (-35.095859i)    cm-1
T5(ms=-1)     0.000013  + (0.000060i)    cm-1
SOC between the T2 (ms=1) state and excited triplet states (ms=0):
T3(ms=0)      0.000014  + (-0.000581i)    cm-1
T4(ms=0)      -0.000103  + (-35.095859i)    cm-1
T5(ms=0)      0.000013  + (0.000060i)    cm-1
SOC between the T2 (ms=1) state and excited triplet states (ms=1):
T3(ms=1)      0.000000  + (-5.784285i)    cm-1
T4(ms=1)      0.000000  + (0.000086i)    cm-1
T5(ms=1)      0.000000  + (0.000273i)    cm-1
SOC between the T2 (ms=-1) state and excited triplet states (ms=0):
T3(ms=0)      -0.000014  + (-0.000581i)    cm-1
T4(ms=0)      0.000103  + (-35.095859i)    cm-1
T5(ms=0)      -0.000013  + (0.000060i)    cm-1
SOC between the T2 (ms=-1) state and excited triplet states (ms=-1):
T3(ms=-1)     0.000000  + (5.784285i)    cm-1
T4(ms=-1)     0.000000  + (-0.000086i)    cm-1
T5(ms=-1)     0.000000  + (-0.000273i)    cm-1
Total SOC between the T2 state and excited triplet states:
T3      8.180214    cm-1
T4      70.191717    cm-1
T5      0.000406    cm-1



SOC between the T3 (ms=0) state and excited triplet states (ms=1):
T4(ms=1)      -21.540613  + (-0.000156i)    cm-1
T5(ms=1)      0.000068  + (0.000415i)    cm-1
SOC between the T3 (ms=0) state and excited triplet states (ms=-1):
T4(ms=-1)     21.540613  + (-0.000156i)    cm-1
T5(ms=-1)     -0.000068  + (0.000415i)    cm-1
SOC between the T3 (ms=1) state and excited triplet states (ms=0):
T4(ms=0)      21.540613  + (-0.000156i)    cm-1
T5(ms=0)      -0.000068  + (0.000415i)    cm-1
SOC between the T3 (ms=1) state and excited triplet states (ms=1):
T4(ms=1)      0.000000  + (-0.000145i)    cm-1
T5(ms=1)      0.000000  + (-60.650855i)    cm-1
SOC between the T3 (ms=-1) state and excited triplet states (ms=0):
T4(ms=0)      -21.540613  + (-0.000156i)    cm-1
T5(ms=0)      0.000068  + (0.000415i)    cm-1
SOC between the T3 (ms=-1) state and excited triplet states (ms=-1):
T4(ms=-1)     0.000000  + (0.000145i)    cm-1
T5(ms=-1)     0.000000  + (60.650855i)    cm-1
Total SOC between the T3 state and excited triplet states:
T4      43.081227    cm-1
T5      85.773262    cm-1



SOC between the T4 (ms=0) state and excited triplet states (ms=1):
T5(ms=1)      0.000001  + (24.985452i)    cm-1
SOC between the T4 (ms=0) state and excited triplet states (ms=-1):
T5(ms=-1)     -0.000001  + (24.985452i)    cm-1
SOC between the T4 (ms=1) state and excited triplet states (ms=0):
T5(ms=0)      -0.000001  + (24.985452i)    cm-1
SOC between the T4 (ms=1) state and excited triplet states (ms=1):
T5(ms=1)      0.000000  + (0.001022i)    cm-1
SOC between the T4 (ms=-1) state and excited triplet states (ms=0):
T5(ms=0)      0.000001  + (24.985452i)    cm-1
SOC between the T4 (ms=-1) state and excited triplet states (ms=-1):
T5(ms=-1)     0.000000  + (-0.001022i)    cm-1
Total SOC between the T4 state and excited triplet states:
T5      49.970904    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  +  0.000001i    cm-1
T2(ms=0)      0.000000  +  -0.000026i    cm-1
T3(ms=0)      0.000000  +  5.990486i    cm-1
T4(ms=0)      0.000000  +  -0.000012i    cm-1
T5(ms=0)      0.000000  +  -0.000007i    cm-1
SOC between the S1 state and excited triplet states (ms=1):
T1(ms=1)      (40.587926)  + (0.000004i)    cm-1
T2(ms=1)      (0.000100)  + (0.000058i)    cm-1
T3(ms=1)      (0.000021)  + (-0.000547i)    cm-1
T4(ms=1)      (0.000009)  + (-36.352013i)    cm-1
T5(ms=1)      (-0.000059)  + (0.000103i)    cm-1
SOC between the S1 state and excited triplet states (ms=-1):
T1(ms=-1)    -(40.587926)  + (0.000004i)    cm-1
T2(ms=-1)    -(0.000100)  + (0.000058i)    cm-1
T3(ms=-1)    -(0.000021)  + (-0.000547i)    cm-1
T4(ms=-1)    -(0.000009)  + (-36.352013i)    cm-1
T5(ms=-1)    -(-0.000059)  + (0.000103i)    cm-1
Total SOC between the S1 state and excited triplet states:
T1      57.399996    cm-1
T2      0.000166    cm-1
T3      5.990486    cm-1
T4      51.409510    cm-1
T5      0.000168    cm-1



SOC between the S2 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  0.000010i    cm-1
T2(ms=0)      0.000000  +  0.000045i    cm-1
T3(ms=0)      0.000000  +  -0.000513i    cm-1
T4(ms=0)      0.000000  +  -31.553085i    cm-1
T5(ms=0)      0.000000  +  0.000106i    cm-1
SOC between the S2 state and excited triplet states (ms=1):
T1(ms=1)      (0.000103)  + (0.000017i)    cm-1
T2(ms=1)      (-40.588156)  + (0.000106i)    cm-1
T3(ms=1)      (-0.000178)  + (-22.311401i)    cm-1
T4(ms=1)      (-0.000016)  + (0.000272i)    cm-1
T5(ms=1)      (18.541737)  + (0.000006i)    cm-1
SOC between the S2 state and excited triplet states (ms=-1):
T1(ms=-1)    -(0.000103)  + (0.000017i)    cm-1
T2(ms=-1)    -(-40.588156)  + (0.000106i)    cm-1
T3(ms=-1)    -(-0.000178)  + (-22.311401i)    cm-1
T4(ms=-1)    -(-0.000016)  + (0.000272i)    cm-1
T5(ms=-1)    -(18.541737)  + (0.000006i)    cm-1
Total SOC between the S2 state and excited triplet states:
T1      0.000148    cm-1
T2      57.400320    cm-1
T3      31.553085    cm-1
T4      31.553085    cm-1
T5      26.221975    cm-1



SOC between the S3 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  31.553085i    cm-1
T2(ms=0)      0.000000  +  0.000047i    cm-1
T3(ms=0)      0.000000  +  0.000056i    cm-1
T4(ms=0)      0.000000  +  0.000010i    cm-1
T5(ms=0)      0.000000  +  -0.000617i    cm-1
SOC between the S3 state and excited triplet states (ms=1):
T1(ms=1)      (-0.000002)  + (-0.000200i)    cm-1
T2(ms=1)      (-0.000094)  + (36.351693i)    cm-1
T3(ms=1)      (22.311401)  + (0.000169i)    cm-1
T4(ms=1)      (-0.000157)  + (0.000147i)    cm-1
T5(ms=1)      (-0.000005)  + (25.879506i)    cm-1
SOC between the S3 state and excited triplet states (ms=-1):
T1(ms=-1)    -(-0.000002)  + (-0.000200i)    cm-1
T2(ms=-1)    -(-0.000094)  + (36.351693i)    cm-1
T3(ms=-1)    -(22.311401)  + (0.000169i)    cm-1
T4(ms=-1)    -(-0.000157)  + (0.000147i)    cm-1
T5(ms=-1)    -(-0.000005)  + (25.879506i)    cm-1
Total SOC between the S3 state and excited triplet states:
T1      31.553085    cm-1
T2      51.409057    cm-1
T3      31.553085    cm-1
T4      0.000304    cm-1
T5      36.599148    cm-1



SOC between the S4 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  0.000316i    cm-1
T2(ms=0)      0.000000  +  -5.991263i    cm-1
T3(ms=0)      0.000000  +  -0.000013i    cm-1
T4(ms=0)      0.000000  +  0.000174i    cm-1
T5(ms=0)      0.000000  +  62.821123i    cm-1
SOC between the S4 state and excited triplet states (ms=1):
T1(ms=1)      (0.000011)  + (22.311401i)    cm-1
T2(ms=1)      (0.000046)  + (0.000346i)    cm-1
T3(ms=1)      (-0.000157)  + (0.000017i)    cm-1
T4(ms=1)      (-22.311401)  + (0.000003i)    cm-1
T5(ms=1)      (0.000056)  + (0.000248i)    cm-1
SOC between the S4 state and excited triplet states (ms=-1):
T1(ms=-1)    -(0.000011)  + (22.311401i)    cm-1
T2(ms=-1)    -(0.000046)  + (0.000346i)    cm-1
T3(ms=-1)    -(-0.000157)  + (0.000017i)    cm-1
T4(ms=-1)    -(-22.311401)  + (0.000003i)    cm-1
T5(ms=-1)    -(0.000056)  + (0.000248i)    cm-1
Total SOC between the S4 state and excited triplet states:
T1      31.553085    cm-1
T2      5.991263    cm-1
T3      0.000224    cm-1
T4      31.553085    cm-1
T5      62.821123    cm-1



SOC between the S5 state and excited triplet states (ms=0):
T1(ms=0)      0.000000  +  0.000050i    cm-1
T2(ms=0)      0.000000  +  0.000282i    cm-1
T3(ms=0)      0.000000  +  -62.821197i    cm-1
T4(ms=0)      0.000000  +  0.001054i    cm-1
T5(ms=0)      0.000000  +  0.000013i    cm-1
SOC between the S5 state and excited triplet states (ms=1):
T1(ms=1)      (-18.542239)  + (0.000007i)    cm-1
T2(ms=1)      (0.000007)  + (0.000063i)    cm-1
T3(ms=1)      (0.000006)  + (-0.000434i)    cm-1
T4(ms=1)      (-0.000006)  + (-25.879056i)    cm-1
T5(ms=1)      (0.000003)  + (0.000089i)    cm-1
SOC between the S5 state and excited triplet states (ms=-1):
T1(ms=-1)    -(-18.542239)  + (0.000007i)    cm-1
T2(ms=-1)    -(0.000007)  + (0.000063i)    cm-1
T3(ms=-1)    -(0.000006)  + (-0.000434i)    cm-1
T4(ms=-1)    -(-0.000006)  + (-25.879056i)    cm-1
T5(ms=-1)    -(0.000003)  + (0.000089i)    cm-1
Total SOC between the S5 state and excited triplet states:
T1      26.222686    cm-1
T2      0.000296    cm-1
T3      62.821197    cm-1
T4      36.598512    cm-1
T5      0.000126    cm-1






            *********SOC CODE ENDS HERE*********




                    STATE-TO-STATE TRANSITION MOMENTS


    Electron Dipole Moments of Ground State
 -----------------------------------------------------
   State     X           Y           Z(a.u.) 
 -----------------------------------------------------
       0    -0.000000    0.000000   -0.000000
 -----------------------------------------------------

 Within CIS/TDA Excited States:

    Electron Dipole Moments of Triplet Excited State
 -----------------------------------------------------
   State     X           Y           Z(a.u.) 
 -----------------------------------------------------
       1    -0.000000    0.000000   -0.000000
       2    -0.000000    0.000000   -0.000000
       3    -0.000000   -0.000000   -0.000000
       4    -0.000000   -0.000000   -0.000000
       5    -0.000000   -0.000000   -0.000000
 -----------------------------------------------------

                Transition Moments Between Ground and Triplet Excited States
 --------------------------------------------------------------------------------
    States   X          Y          Z           Strength(a.u.)
 --------------------------------------------------------------------------------
    0    1   0.000000   0.000000   0.000000              0
    0    2   0.000000   0.000000   0.000000              0
    0    3   0.000000   0.000000   0.000000              0
    0    4   0.000000   0.000000   0.000000              0
    0    5   0.000000   0.000000   0.000000              0
 --------------------------------------------------------------------------------

                Transition Moments Between Triplet Excited States
 --------------------------------------------------------------------------------
    States   X          Y          Z           Strength(a.u.)
 --------------------------------------------------------------------------------
    1    2  -0.000000  -0.000000  -0.000000   6.494388E-40
    1    3   0.000000   0.000000  -0.000000    1.10427E-38
    1    4  -0.000000  -0.000000   0.000000    7.99723E-39
    1    5   0.000000  -0.000000  -0.000000   1.467804E-39
    2    3   0.000000   0.000000   0.000000   9.336752E-39
    2    4  -0.000000  -0.000000  -0.000000   1.075217E-39
    2    5   0.000000  -0.000000   0.000000   3.514127E-40
    3    4  -0.000000   0.000000  -0.000000   6.911698E-40
    3    5   0.000000   0.000000   0.000000   4.094268E-41
    4    5   0.000000   0.000000   0.000000   1.029034E-40
 --------------------------------------------------------------------------------

 Within CIS/TDA Excited States:

    Electron Dipole Moments of Singlet Excited State
 -----------------------------------------------------
   State     X           Y           Z(a.u.) 
 -----------------------------------------------------
       6     0.000000    0.000000   -0.000000
       7     0.000000    0.000000   -0.000000
       8    -0.000000    0.000000   -0.000000
       9     0.000000    0.000000   -0.000000
      10     0.000000    0.000000   -0.000000
 -----------------------------------------------------

                Transition Moments Between Ground and Singlet Excited States
 --------------------------------------------------------------------------------
    States   X          Y          Z           Strength(a.u.)
 --------------------------------------------------------------------------------
    0    6  -0.000000  -0.000000   0.000000   5.094332E-31
    0    7   0.000000  -0.000000   0.000000   7.969081E-30
    0    8   0.000000   0.000000   0.000000   1.876901E-30
    0    9   0.000000   0.000000  -0.000000   6.654994E-30
    0   10   0.000000  -0.000000   0.000000   9.193339E-31
 --------------------------------------------------------------------------------

                Transition Moments Between Singlet Excited States
 --------------------------------------------------------------------------------
    States   X          Y          Z           Strength(a.u.)
 --------------------------------------------------------------------------------
    6    7   0.000000   0.000000   0.000000   4.688525E-41
    6    8  -0.000000   0.000000   0.000000   4.849869E-41
    6    9   0.000000  -0.000000  -0.000000   3.004411E-40
    6   10  -0.000000  -0.000000   0.000000    1.64474E-40
    7    8   0.000000   0.000000  -0.000000   2.337829E-40
    7    9  -0.000000   0.000000  -0.000000   4.067484E-40
    7   10   0.000000   0.000000   0.000000   3.948606E-40
    8    9   0.000000  -0.000000   0.000000   2.348509E-40
    8   10   0.000000  -0.000000  -0.000000   1.870286E-40
    9   10  -0.000000  -0.000000  -0.000000   3.826249E-43
 --------------------------------------------------------------------------------

                    END OF TRANSITION MOMENT CALCULATION

 STSman time:  CPU 0.01 s  wall 0.01 s

 
 --------------------------------------------------------------
 
                    Orbital Energies (a.u.)
 --------------------------------------------------------------
 
 Alpha MOs
 -- Occupied --
******** -15.4574 -12.5920 -12.5920 -12.5920  -1.8342  -1.1075  -1.1075
 -1.1075  -0.1551
 -- Virtual --
 -0.0277  -0.0277  -0.0277  -0.0277  -0.0277  -0.0111  -0.0111  -0.0111
  0.0254   0.1680   0.1680   0.1680   0.1680   0.1680
 --------------------------------------------------------------
 
          Ground-State Mulliken Net Atomic Charges

     Atom                 Charge (a.u.)
  ----------------------------------------
      1 Ca                   -0.000000
  ----------------------------------------
  Sum of atomic charges =     0.000000

 -----------------------------------------------------------------
                    Cartesian Multipole Moments
 -----------------------------------------------------------------
    Charge (ESU x 10^10)
                -0.0000
    Dipole Moment (Debye)
         X       0.0000      Y      -0.0000      Z       0.0000
       Tot       0.0000
    Quadrupole Moments (Debye-Ang)
        XX     -23.7775     XY       0.0000     YY     -23.7775
        XZ       0.0000     YZ       0.0000     ZZ     -23.7775
    Octopole Moments (Debye-Ang^2)
       XXX       0.0000    XXY      -0.0000    XYY       0.0000
       YYY      -0.0000    XXZ       0.0000    XYZ       0.0000
       YYZ       0.0000    XZZ       0.0000    YZZ      -0.0000
       ZZZ       0.0000
    Hexadecapole Moments (Debye-Ang^3)
      XXXX     -85.6082   XXXY       0.0000   XXYY     -28.5361
      XYYY       0.0000   YYYY     -85.6082   XXXZ       0.0000
      XXYZ       0.0000   XYYZ       0.0000   YYYZ       0.0000
      XXZZ     -28.5361   XYZZ       0.0000   YYZZ     -28.5361
      XZZZ       0.0000   YZZZ       0.0000   ZZZZ     -85.6082
 -----------------------------------------------------------------

 STANDARD THERMODYNAMIC QUANTITIES AT   298.15 K  AND     1.00 ATM

   Translational Enthalpy:        0.889 kcal/mol
   Rotational Enthalpy:           0.000 kcal/mol
   Vibrational Enthalpy:          0.000 kcal/mol
   gas constant (RT):             0.592 kcal/mol
   Translational Entropy:        36.984  cal/mol.K
   Rotational Entropy:            0.000  cal/mol.K
   Vibrational Entropy:           0.000  cal/mol.K

   Total Enthalpy:                1.481 kcal/mol
   Total Entropy:                36.984  cal/mol.K

 -----------------------------------------------------------------

After diagonalising the full SOC matrix QCHEM gave me, this is what I’ve obtained:

----------------------------------------------------
              Relativistic states list                        
----------------------------------------------------
Number    Label     Energy (Ha)     Energy (cm-1) 
----------------------------------------------------
0         E0        0.00000e+00     0.0000           
1         E1        6.51318e-02     14294.7851     
2         E2        6.51331e-02     14295.0705      
3         E3        6.51357e-02     14295.6412     
4         E4        6.54081e-02     14355.4093       
5         E5        6.54139e-02     14356.6914      
6         E6        6.54139e-02     14356.6964    
7         E7        6.54146e-02     14356.8542       
8         E8        6.54146e-02     14356.8542      
9         E9        6.58251e-02     14446.9322      
10        E10       6.58257e-02     14447.0634       
11        E11       6.58284e-02     14447.6556    
12        E12       6.58304e-02     14448.1132     
13        E13       6.58310e-02     14448.2433    
14        E14       6.58310e-02     14448.2433      
15        E15       6.58310e-02     14448.2433      
16        E16       8.42507e-02     18490.8840      
17        E17       8.42507e-02     18490.8979     
18        E18       8.42507e-02     18490.8984       
19        E19       8.42508e-02     18490.9198      
20        E20       8.42509e-02     18490.9269       
----------------------------------------------------

Now compare to the values available on the NIST website which are the following:

Configuration  Term  J   Level  (cm-1)  Uncertainty (cm-1)   Reference 
  	  	  	  	  	 
3p64s2  	 1S  	 0  	  0.000          	   	 L7185 
  	  	  	  	  	 
3p64s4p  	 3P°  	 0  	  15 157.901          	   	 L7185 
  	              	 1  	  15 210.063          	   	 L7185 
     	  	         2  	  15 315.943          	   	 L7185 
  	  	  	  	  	 
3p63d4s  	 3D  	 1  	  20 335.360          	   	 L7185 
  	            	 2  	  20 349.260          	   	 L7185 
            	  	 3  	  20 371.000          	   	 L7185 
  	  	  	  	  	 
3p63d4s  	 1D  	 2  	  21 849.634          	   	 L7185 
  	  	  	  	  	 
3p64s4p  	 1P°  	 1  	  23 652.304          	   	 L7185 
  	  	  	  	  	 
3p64s5s  	 3S  	 1  	  31 539.495          	   	 L7185 
  	  	  	  	  	 
3p64s5s  	 1S  	 0  	  33 317.264          	   	 L7185 
  	  	  	  	  	 
3p63d4p  	 3F°  	 2  	  35 730.454          	   	 L7185 
  	             	 3  	  35 818.713          	   	 L7185 
  	            	 4  	  35 896.889          	   	 L7185 
  	  	  	  	  	 
3p63d4p  	 1D°  	 2  	  35 835.413          	   	 L7185 

Source: NIST ASD Levels Output

As you can see, there is quite a big difference between the two sets of results. If we take a look at the difference between the J=0 and J=2 states of the P triplet, we have for the NIST results a value of 158.042 cm-1 whereas QCHEM gives us less than 2 cm-1.

Now this isn’t a strike against QCHEM, as ORCA gave us similar results for the same method. We just want to understand why that is and how confident we can be in those results.

Thank you very much for your help!

Best regards!

Iacobellis Nicolas, Ph.D. Student

Hello Iacobellis,

Thank you for the information. The default of TDDFT SOC only includes one-electron operator. The numbers obtained from both one-electron and two-electron operators (ORCA) are roughly 0.6 smaller than the numbers obtained from Q-Chem 5.4. However, we have added two-electron operator (mean field) in Q-Chem 6.0. Acoording to the internal testing, the numbers using Q-Chem 6.0 beta agrees with the numbers obtained from ORCA. We would encrouage you to run the calculation again after Q-Chem 6.0 is released.

Edit: to the best of my knowledge, the SOC have been used to predict the phosphorescence rates. It’s unclear to me if they can be interpreted in terms of atomic spectra.

Hello,

Thank you for your answer. ORCA and Q-CHEM already gave me close results so that wasn’t my main concern but glad to hear that Q-CHEM wil get even better!

I also asked this question on the ORCA forums and someone gave me this answer:

The first problem is you are not comparing the experimental results properly with the Orca calculations.
A 3P0 term is undegenerated (2J+1=1), while the 3P1 is triple degenerated (2J+1=3) and finally a 3P2 is 5th degenerated (2J+1=5). (…)

Being the ≈160cm-1 the difference between 1 and 5-9 and not the diference on the triplet.

Secondly, for the previous point, you can check your TDDFT electronic structure is very bad, because you are not obtaining the first 3P0 state, your states are the GS, an (2S+1)L1 and a (2S+1)L2 beeing miss the first (2S+1)L0.

What I don’t understand is why some states would be “missed” during calculation, especially the lower ones?

Thank you for your help,

Best regards,

Iacobellis Nicolas, Ph.D. Student