Time-Resolved Photoelectron Spectroscopy
To calculate a time-resolved photo-electron spectrum, it is necessary to set up the system with both the neutral and ion states and then include the pump and probe pulses in the operator. The ion states include the free electron continua. The method is based on the method of Seel and Domcke JCP (91) 95: 7806 adapted for MCTDH. It was first used in energy resolved photoelectron spectra in Worth et al Chem. Phys. (07) 338: 220. Please cite these papers if you use the method. The input for the 3-mode model of pyrazine used by Seel and Domcke requires the following files:
In the input file, the important point is that the electronic states are defined as:
el elcont 5 3
Elcont sin 113 0.0, ev 3.75, ev
This specifies that the are 5 electronic states, the first 3 of which are bound and states 4 and 5 are continua. The Elcont defines that a sin DVR is used to define the continua, with 113 points from 0 to 3.75 eV
The wavefunction in the continuum is then defined by a set of SPFs in the usual way in the SPF-BASIS-SECTION and INIT-WF-SECTION - in thsi example the initial function is a Gaussian centred around 1 eV, but as the continua are initially unoccupied the initial function chosen does not play a role.
In the operator, the Time degree of freedom needs to be included and the pulses defined, here by
dip_b2u*s1*C/width1 |1 S1&3 |5 cosom1*pulse1*step1*rstep1 dip_b2u*s2*C/width2 |1 S1&3 |5 cosom2*pulse2*step2*rstep2 dipi*s1*C/width1 |1 CS4&2 |5 cosom1*pulse1*step1*rstep1 dipi*s2*C/width2 |1 CS4&2 |5 cosom2*pulse2*step2*rstep2
The pulse is a combination of a cos function (cosom) with a Gaussian envelope (pulse) and a step function to ensure the pulse is really 0 when off. The constants define the pulse strength and dipole coupling. The first 2 lines define the excitation out of the ground-state, the latter lines excitation out of the S1 into the ion states. Note that the coupling to the ion states is defined by CS4&2 rather than the S4&2 operator that couples bound states.
The cmd file makes use of the MCTDH command line input to run a set of calculations with different time delays. The -p option changes the parameter in the program - here the t2 parameter governing the centre of the second pulse. The -D option writes the jobs to different directories. Note that the first job is with the pump pulse only to give the background signal. There is an analysis program tdpespecXXX that will plot the time-resolved electron KE populations, i.e. the photoelectron spectrum. It reads the gridpop files in the set of directories and requires the gridpop=el keyword in the RUN-SECTION to ensure the grid densities for each molecular state are stored separately (the default is to sum the densities). If the file stem is pyr_3d then type
tdpespec101 -w -inter pyr3_tdto access the plot menu.