9.7 Nonadiabatic Couplings and Optimization of Minimum-Energy Crossing Points

9.7.2 Job Control and Examples

In order to perform non-adiabatic 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.

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

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

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. Zhang:2015a and Ou:2015 for additional guidance.

Example 9.15  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
   CIS_N_ROOTS        4
   CIS_TRIPLETS       false
   SET_ITER           50
   CIS_DER_NUMSTATE   5
   CALC_NAC           true
   EXCHANGE           b3lyp
   BASIS              6-31G*
$end

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

Example 9.16  Nonadiabatic couplings between S0 and S1 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
   SPIN_FLIP          true
   UNRESTRICTED       true
   CIS_N_ROOTS        4
   CIS_TRIPLETS       false
   SET_ITER           50
   CIS_DER_NUMSTATE   2
   CALC_NAC           true
   EXCHANGE           bhhlyp
   BASIS              6-31G*
$end

$derivative_coupling
   comment
   1 3
$end

Example 9.17  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
   CIS_N_ROOTS       4
   CIS_TRIPLETS      false
   RPA               true
   SET_ITER          50
   CIS_DER_NUMSTATE  2
   CALC_NAC          true
   EXCHANGE          b3lyp
   BASIS             6-31G*
   SET_QUADRATIC     true #include full quadratic response
$end

$derivative_coupling
   comment
   1 2
$end