Example (GAMESSUS): Excited H₂O⁺ in external electric field (BO+FSSH)

This example describes the interaction of a water molecule ion in a time-dependent electric field. See directory:

Examples/xpyder/h2o+_field/

Preparation

Set your environment variable CDTK_GAMESSUS to the path of the gamessus directory. For example:
```
export CDTK_GAMESSUS=$HOME/gamess/
```
Instead of ‘$HOME/gamess/’ insert the actual path of your gamess installation.
Depending on your gamess installation, output is written to the scratch file folder. This is configured in the rungms script in your gamess installation. Edit the script rungms accordingly so that the output is written in the current working directory. You may want to comment out the lines set SCR=~/gamess/restart and #set USERSCR=~/gamess/restart, instead, set the SCR and USERSCR environment variables to .. For example:
```
export SCR=.
export USERSCR=.
```

Note that the local directory in which the simulation is run should be a rapidly accessible disk (i.e., a local folder or ramdisk) - otherwise there will be huge performance losses.

Run the BO dynamics

To run the example, execute:

xpyder -i input_bo_es -d bo_es

Details of the Inputfile

The file input_bo_es is the input file used for the calculation:

$SYSTEM
    qchemistry  = gamess
    xunit       = an
$END

$gamess
    memddi = 2
    mwords = 2
    gbasis = CCD
    icharg = 1
    mult = 2
    ncore = 1
    nact = 4
    nels = 7
    wstate = 1.0,1.0
    nstate = 4
    sz = 0.5
    mxxpan = 100
    fullnr = .false.
$end

$trajectory
    dt = 0.5   fs
    tf = 40.0   fs
$end

$quantum
    type    = bo
    istate  = 1
    nstates = 2
$end

$cartPOS
 O    0.0   0.0        0.0
 H    0.0   0.757215   0.5865358
 H    0.0  -0.7572157  0.5865358
$end

$cartVEL
 O  0.0  0.0  0.0
 H  0.0  0.0  0.0
 H  0.0  0.0  0.0
$end


$efield
    envelope =  gaussian
    omega =     4000.0   cm-1
    fwhm =      10      fs
    phase =     0.5
    center =    15 fs
    amplitude = 0.104   au
    #amplitude = 0.0   au
    polarization = 0.0  0.0  1.0
$end

The section $SYSTEM
- qchemistry = gamess specifies the quantum chemistry tool. (One can also give “molcas”, but remember that field induced dynamics cannot be done using MOLCAS with the current version of CDTK).
- xunit = an specifies the unit in the coordinates of the atom is specified. “an” refers to Angstrom and one can give “au” for atomic units.
$gamess
- this gives the input detials such as the basis used, active space etc., for the electronic structure calculation.
$trajectory - “dt” specifies the time step used for the calculation (in fs). - “tf” specifies the final time ie., the time till the calculation will last (in fs).
quantum
- type = bo specifies Born-Oppenheimer dynamics. That means we stay at a fixed
- istate and nstate gives the initial state at which the trajectory present and the nomber of states respectively.
cartPOS and cartVEL. This gives the intial position and velicity of the atoms.
$efield specifies an electric field.
- envelope gives the shape of the envelope. Currently, the only possible value is “gaussian”
- omega secifies the central frequency
- amplitude, fwhm, phase, and center specify the temporal width as the full width at half maximum $t_\mathrm{FWHM}$ , the phase $\phi$ (in rad), and the temporal center $t_0$ , such that the temporal envelope of the electric field is given by
  
  $\frac{\mathcal{E}}{\sqrt{2 \pi } \sigma} \exp( - \frac{(t-t_0)^2}{2\sigma^2} ) \cos(\omega t + \phi)$
  
  with $\sigma = t_\mathrm{FWHM} / (2 \sqrt{2} \ln 2)$ and $\mathcal{E}$ is the amplitude of the electric field.
- polarization specifies the polarization (x, y, z, value)

Output data

The folder bo_es contains all the output files.

R.log gives the position of the atoms: The first column is time; the following columns coordinates (x,y,z) for each atom. All columns are in atomic units.
V.log gives the velocity of the atoms: The first column is time; the following columns velocities (x,y,z) for each atom. All columns are in atomic units.
E.log contains 4 columns (all in atomic units): The first column gives the time, the second column gives the kinetic energy, the third column gives the potential energy, and the fourth column the total energy (sum of kinetic and potenital energy) of the simulation trajectory.
field.log contains 3 columns: First column time (in atomic units), second column the amplitude of the electric field (in atomic units) and the third column gives the temporal envelope of the electric field pulse (in atomic units).

You can convert the trajectory information into .vtf format or .xyz format by executing either an_traj2vtf or cdtk2xyz.

Electric field, total molecular energy, potential and kinetic energy as a function of time.

Animation of water molecule cation exposed to time dependent electric field.

As one can see, in the ionized and excited state the water molecule strongly vibrates. The external field along the z direction pushes and pulls the water molecule and thus modifies the vibration. As a consequence the total energy of the molecule after the pulse is somewhat altered. It turns out, the total energy can be increased by the pulse, when the electric field pushes the hydrogen atoms along the vibration, or it can be decreased by the pulse, when the electric field pushes the hydrogen atoms against the vibration:

Electric field, total molecular energy, potential and kinetic energy as a function of time. Here a lower frequency :math:`2000 \mathrm{cm}^{-1}` has been used and a phase of :math:`\phi=0.2`. — Electric field, total molecular energy, potential and kinetic energy as a function of time. Here a frequency of $2000 \mathrm{cm}^{-1}$ has been used and a phase of $\phi=0.2$ .

Electric field, total molecular energy, potential and kinetic energy as a function of time. Here a frequency of $2000 \mathrm{cm}^{-1}$ has been used and a phase of $\phi=0.2$ .

Running the dynamics using fewest switches surface hopping

A variant for this example employing fewest switches surface hopping can be found here:

Examples/xpyder/h2o+_field/input_fssh

Compared to the earlier example, the input file is changed in the section:

$gamess
   memddi = 2
   mwords = 2
   gbasis = CCD
   icharg = 1
   mult = 2
   ncore = 1
   nact = 4
   nels = 7
   wstate = 1.0,1.0,1.0,1.0
   nstate = 4
   sz = 0.5
   mxxpan = 100
   fullnr = .false.
$end

altering the GAMESS calculation parameters and in the section:

$quantum
   type    = fssh
   istate  = 1
   nstates = 4
$end

switching on the surface hopping. Moreover, the polarization of the electric field is changed and now in the x-axis direction:

$efield
   envelope =  gaussian
   omega =     4000.0   cm-1
   fwhm =      10      fs
   phase =     0.5
   center =    15 fs
   amplitude = 0.104   au
   polarization = 1.0  0.0  0.0
$end

Run the FSSH dynamics

To run the example, execute:

xpyder -i input_fssh -d fssh

For comparison you may also run the example without any external field (amplitude set to zero):

xpyder -i input_fssh_nofield -d fssh_nofield

Output data

The folders fssh fssh_nofield contain all the output files. In addition to the earlier example, these are

P.log contains the electronic populations as a function of time.
C.log contains the electronic state coefficients as a function of time.
S.log contains the active state as a function of time
V_ad.log contains the adiabatic potential energies as a function of time.

Results
Without electric field	With electric field

The figures show how the electric field enables non-adiabatic transitions: In the trajectory with electric field, the active potential energy surface changes at time t=7fs.

Further example

Further examples with CO₂ can be found here:

Examples/xpyder/co2_field/

Example (GAMESSUS): Excited H2O+ in external electric field (BO+FSSH)

Preparation

Run the BO dynamics

Details of the Inputfile

Output data

Running the dynamics using fewest switches surface hopping

Run the FSSH dynamics

Output data

Further example

Example (GAMESSUS): Excited H₂O⁺ in external electric field (BO+FSSH)