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. 1101 and 717 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