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

$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.