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To use the finite difference approach, '''nosym''' must be used to avoid the rotation of molecules. Currently, only C(1) group is permitted. For the example considered above, it turns out that the first two ^1^A2 excited states are the 1st and 4th excited states. However, if only use '''iexit=4''' with iterative diagonalization, the initialization based on orbital energy difference (IPA) will miss the 2rd excited states, as its IPA is very large, viz., {{{ No. Pair ExSym ExEnergies f D<S^2> Dominant Excitations IPA Ova En-E1 1 A 2 A 4.3504 eV 0.0000 0.0000 88.9% CV(0): A( 8 )-> A( 9 ) 15.558 0.476 0.0000 2 A 3 A 9.3394 eV 0.0008 0.0000 92.4% CV(0): A( 6 )-> A( 9 ) 21.045 0.546 4.9890 3 A 4 A 9.3480 eV 0.1782 0.0000 85.8% CV(0): A( 7 )-> A( 9 ) 17.814 0.822 4.9975 4 A 5 A 11.3372 eV 0.0000 0.0000 92.3% CV(0): A( 5 )-> A( 9 ) 22.197 0.535 6.9868 5 A 6 A 11.6654 eV 0.3266 0.0000 92.9% CV(0): A( 8 )-> A( 10 ) 18.527 0.461 7.3150 }}} Thus, '''iexit=5''' is used in the following inputs: {{{ $COMPASS Title nh3 Basis 6-31GP Geometry C 0.00000000 -0.00000000 -0.53964037 O 0.00000000 0.00000000 0.68767663 H 0.00000000 0.93940400 -1.13178537 H 0.00000000 -0.93940400 -1.13178537 End geometry skeleton group c(1) nosym $END $xuanyuan direct schwarz $end $scf RHF charge 0 spin 1 THRESHCONV 1.d-10 1.d-8 OPTSCR 1 $end $tddft imethod 1 isf 0 iexit 5 itda 0 idiag 1 istore 1 crit_e 1.d-10 crit_vec 1.d-8 lefteig DirectGrid $end $resp iprt 1 QUAD FNAC double pairs 1 1 1 1 1 1 4 norder 1 method 2 nfiles 1 ignore 0 noresp $end }}} |
First-order nonadiabatic couplings
The calculations of first-order nonadiabatic couplings (NAC) between ground and excited-states (<0|Dx|Sn>), and those between the excited-states (<Sm|Dx|Sn> or <Tm|Dx|Tn>) at the TD-DFT/TDA level can be achieved by generalizing the standard linear and quadratic response theories, for details, see
Zhendong Li and Wenjian Liu, "First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels", J. Chem. Phys. 141, 014110 (2014).
For convenience, however, in the input they are both specified by the QUAD keyword with single and double, respectively. Either analytic derivative or finite difference approach can be used. The latter is only allowed for C(1) symmetry, and for molecules without orbital degeneracy!
Analytic derivative approach
NAC between two 1A2 states of CH2O:
$COMPASS Title nh3 Basis 6-31GP Geometry C 0.00000000 -0.00000000 -0.53964037 O 0.00000000 0.00000000 0.68767663 H 0.00000000 0.93940400 -1.13178537 H 0.00000000 -0.93940400 -1.13178537 End geometry skeleton $END $xuanyuan direct schwarz $end $scf RHF charge 0 spin 1 THRESHCONV 1.d-10 1.d-8 OPTSCR 1 $end $tddft imethod 1 isf 0 nexit 0 2 0 0 itda 0 idiag 1 istore 1 crit_e 1.d-10 crit_vec 1.d-8 lefteig DirectGrid $end $resp iprt 1 QUAD FNAC double pairs 1 1 2 1 1 2 2 norder 1 method 2 nfiles 1 ignore 0 noresp $end
Finite difference approach
To use the finite difference approach, nosym must be used to avoid the rotation of molecules. Currently, only C(1) group is permitted. For the example considered above, it turns out that the first two 1A2 excited states are the 1st and 4th excited states. However, if only use iexit=4 with iterative diagonalization, the initialization based on orbital energy difference (IPA) will miss the 2rd excited states, as its IPA is very large, viz.,
No. Pair ExSym ExEnergies f D<S^2> Dominant Excitations IPA Ova En-E1 1 A 2 A 4.3504 eV 0.0000 0.0000 88.9% CV(0): A( 8 )-> A( 9 ) 15.558 0.476 0.0000 2 A 3 A 9.3394 eV 0.0008 0.0000 92.4% CV(0): A( 6 )-> A( 9 ) 21.045 0.546 4.9890 3 A 4 A 9.3480 eV 0.1782 0.0000 85.8% CV(0): A( 7 )-> A( 9 ) 17.814 0.822 4.9975 4 A 5 A 11.3372 eV 0.0000 0.0000 92.3% CV(0): A( 5 )-> A( 9 ) 22.197 0.535 6.9868 5 A 6 A 11.6654 eV 0.3266 0.0000 92.9% CV(0): A( 8 )-> A( 10 ) 18.527 0.461 7.3150
Thus, iexit=5 is used in the following inputs:
$COMPASS Title nh3 Basis 6-31GP Geometry C 0.00000000 -0.00000000 -0.53964037 O 0.00000000 0.00000000 0.68767663 H 0.00000000 0.93940400 -1.13178537 H 0.00000000 -0.93940400 -1.13178537 End geometry skeleton group c(1) nosym $END $xuanyuan direct schwarz $end $scf RHF charge 0 spin 1 THRESHCONV 1.d-10 1.d-8 OPTSCR 1 $end $tddft imethod 1 isf 0 iexit 5 itda 0 idiag 1 istore 1 crit_e 1.d-10 crit_vec 1.d-8 lefteig DirectGrid $end $resp iprt 1 QUAD FNAC double pairs 1 1 1 1 1 1 4 norder 1 method 2 nfiles 1 ignore 0 noresp $end
$COMPASS Title nh3 Basis sto-3g Geometry C 0.00000000 -1.20809142 -1.14173975 C 0.00000000 -1.20797607 0.25342015 C 0.00000000 0.00000000 0.95085852 C -0.00000000 1.20797607 0.25342015 C -0.00000000 1.20809142 -1.14173975 C 0.00000000 0.00000000 -1.83922155 H 0.00000000 -2.16045397 -1.69142002 H 0.00000000 -2.16044427 0.80300713 H -0.00000000 2.16044427 0.80300713 H -0.00000000 2.16045397 -1.69142002 H 0.00000000 0.00000000 -2.93882555 F 0.00000000 0.00000000 2.30085848 End geometry skeleton group c(1) nosym $END $xuanyuan direct schwarz $end $scf RHF charge 0 spin 1 THRESHCONV 1.d-10 1.d-8 OPTSCR 1 iaufbau 0 $end $tddft imethod 1 isf 0 iexit 2 itda 1 idiag 1 istore 1 crit_e 1.d-10 crit_vec 1.d-8 lefteig AOKXC DirectGrid $end $resp iprt 1 QUAD FNAC single states 1 1 1 2 double pairs 1 1 1 1 1 1 2 norder 1 method 2 nfiles 1 FDIF step 0.001 ignore 1 noresp $end
To use finite-difference, a script fdiff.py should be used as
./fbdiff.py run.sh input.inp > log
After the calculation is done, an output file input.out will present in the current directory. The log file saves the information during the calculations.
Note: If FDIF is omitted, the analytic calculation will be carried out by simply using the run.sh script.