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9.8 Nonadiabatic Couplings and Optimization of Minimum-Energy Crossing Points

9.8.2 Job Control and Examples

(November 19, 2024)

In order to perform nonadiabatic coupling calculations, the $derivative_coupling section must be given:

$derivative_coupling
<one line comment>
i, j, k, ...
$end

Nonadiabatic couplings will then be computed between all pairs of the states i,j,k,…; use “0” to request the HF or DFT reference state, “1” for the first excited state, etc. Note that the derivative couplings are have dimensions of inverse length and are printed in atomic units, i.e., bohr-1.

CALC_NAC

CALC_NAC
       Determines whether we are calculating nonadiabatic couplings.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Calculate nonadiabatic couplings. FALSE Do not calculate nonadiabatic couplings.
RECOMMENDATION:
       None.

CIS_DER_NUMSTATE

CIS_DER_NUMSTATE
       Determines among how many states we calculate nonadiabatic couplings. These states must be specified in the $derivative_coupling section.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not calculate nonadiabatic couplings. n Calculate n⁢(n-1)/2 pairs of nonadiabatic couplings.
RECOMMENDATION:
       None.

SET_QUADRATIC

SET_QUADRATIC
       Determines whether to include full quadratic response contributions for TDDFT.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       TRUE Include full quadratic response contributions for TDDFT. FALSE Use pseudo-wave function approach.
RECOMMENDATION:
       The pseudo-wave function approach is usually accurate enough and is free of accidental singularities. Consult Refs.  1434 Zhang X., Herbert J. M.
 J. Chem. Phys.
 (2015), 142, pp. 064109. Link and 959 Ou Q. et al.
 J. Chem. Phys.
 (2015), 142, pp. 064114. Link for additional guidance.

Example 9.23  Nonadiabatic couplings among the lowest five singlet states of ethylene, computed at the TD-B3LYP level using the pseudo-wave function approach.

$molecule
   0 1
   C    1.85082356   -1.78953123    0.00000000
   H    2.38603593   -2.71605577    0.00000000
   H    0.78082359   -1.78977646    0.00000000
   C    2.52815456   -0.61573833    0.00000000
   H    1.99294220    0.31078621    0.00000000
   H    3.59815453   -0.61549310    0.00000000
$end

$rem
   EXCHANGE           b3lyp
   BASIS              6-31G*
   CIS_N_ROOTS        4
   CIS_TRIPLETS       false
   MAX_CIS_CYCLES     50
   CIS_DER_NUMSTATE   5
   CALC_NAC           true
$end

$derivative_coupling
   0 is the reference state
   0 1 2 3 4
$end

View output

Example 9.24  Nonadiabatic couplings between S1 and S3 states of ethylene using BH&HLYP and spin-flip TDDFT.

$molecule
   0 3
   C    1.85082356   -1.78953123    0.00000000
   H    2.38603593   -2.71605577    0.00000000
   H    0.78082359   -1.78977646    0.00000000
   C    2.52815456   -0.61573833    0.00000000
   H    1.99294220    0.31078621    0.00000000
   H    3.59815453   -0.61549310    0.00000000
$end

$rem
   EXCHANGE           bhhlyp
   BASIS              6-31G*
   SPIN_FLIP          true
   UNRESTRICTED       true
   CIS_N_ROOTS        4
   CIS_TRIPLETS       false
   MAX_CIS_CYCLES     50
   CIS_DER_NUMSTATE   2
   CALC_NAC           true
$end

$derivative_coupling
   comment
   1 3
$end

View output

Example 9.25  Nonadiabatic couplings between S1 and S2 states of ethylene computed via quadratic response theory at the TD-B3LYP level.

$molecule
   0 1
   C    1.85082356   -1.78953123    0.00000000
   H    2.38603593   -2.71605577    0.00000000
   H    0.78082359   -1.78977646    0.00000000
   C    2.52815456   -0.61573833    0.00000000
   H    1.99294220    0.31078621    0.00000000
   H    3.59815453   -0.61549310    0.00000000
$end

$rem
   EXCHANGE          b3lyp
   BASIS             6-31G*
   CIS_N_ROOTS       4
   CIS_TRIPLETS      false
   RPA               true
   MAX_CIS_CYCLES    50
   CIS_DER_NUMSTATE  2
   CALC_NAC          true
   SET_QUADRATIC     true ! include full quadratic response
$end

$derivative_coupling
   comment
   1 2
$end

View output