# What are the default units for the core hamiltonian and the density AO matrices in CP2K?

I have a few questions about default units. I am trying to find the default units for the density matrix and the core hamiltonian. I am assuming they are in e/(bohr)$$^3$$ and Hartrees respectively. I am also trying to determine which units are being used in my input file for the Electric field intensity as they change based on the periodicity of the system. Is it in W/cm$$^2$$ or in a.u? I have used the PERIODIC NONE keyword for the cell so I am thinking it is in a.u.

My input file is as follows:

&GLOBAL
PROJECT BENZENE-UNPERTURBED
RUN_TYPE ENERGY_FORCE
PRINT_LEVEL low
&END GLOBAL
&FORCE_EVAL
METHOD QS
&SUBSYS
&KIND H
POTENTIAL GTH-PBE-q1
&END KIND
&KIND C
POTENTIAL GTH-PBE-q4
&END KIND
&KIND N
POTENTIAL GTH-PBE-q5
&END KIND
&CELL
ABC 30.0 30.0 30.0
PERIODIC NONE
&END CELL
&TOPOLOGY
COORD_FILE_NAME benzene.xyz
COORD_FILE_FORMAT xyz
&CENTER_COORDINATES
&END CENTER_COORDINATES
&END TOPOLOGY
&END SUBSYS
&DFT
BASIS_SET_FILE_NAME ./BASIS_SET
POTENTIAL_FILE_NAME ./POTENTIALS
&QS
EPS_DEFAULT 1.0E-10
&END QS
&POISSON
PERIODIC NONE
POISSON_SOLVER wavelet
&WAVELET
SCF_TYPE 100
&END WAVELET
&END POISSON
&MGRID
CUTOFF 800
NGRIDS 6
&END MGRID
&SCF
SCF_GUESS RESTART
EPS_SCF 1.0E-10
MAX_SCF 100
&DIAGONALIZATION T
ALGORITHM STANDARD
&END DIAGONALIZATION
&END SCF
&XC
&XC_FUNCTIONAL PBE
&END XC_FUNCTIONAL
&END XC
&REAL_TIME_PROPAGATION
INITIAL_WFN SCF_WFN
EPS_ITER 1E-9
MAX_ITER 10
MAT_EXP TAYLOR
DELTA_PULSE_DIRECTION 0 0 1
#  DENSITY_PROPAGATION .TRUE.
&END REAL_TIME_PROPAGATION
&EFIELD
INTENSITY 1E10
POLARISATION 1.0000000000000000 0.0000000000000000 0.0000000000000000
WAVELENGTH [nm] 1E6
&CONSTANT_ENV
START_STEP 0
END_STEP 1
&END CONSTANT_ENV
&END EFIELD
&PRINT
&AO_MATRICES
DENSITY .TRUE.
CORE_HAMILTONIAN
NDIGITS 30
&END AO_MATRICES
&END PRINT
&END DFT
&END FORCE_EVAL


Thank you, Jason Gray

• +1. Thanks again for joining the site and contributing your questions here! Just please look at the edits I made to this question, and keep it in mind for future questions here :) – Nike Dattani Oct 22 '20 at 21:53
• Thank you, I will try to format them accordingly in the future. – Jason M Gray Oct 22 '20 at 23:04
• The Hamiltonian is quite certainly in Hartree. Why would the density matrix not be dimensionless? Does the wavefunction have units? If not, then why would the density matrix have units? As for the electric field intensity, since it depends on the input file, have you run the input file and looked at the output file? Maybe you can do that and paste the output file here as long as it's less than 1000 lines? – Nike Dattani Oct 22 '20 at 23:12
• My input file is around 170,000 lines so I am going to rerun the simulation printing the electric field in a cube format. If the input units are au, I would expect the value of the resultant electric field to be similar to the initial field close to the boundary of my box if there is no unit discrepancy. If the input units are not in au I would expect this value to be very different. I am assuming that the electric field will not change very much "far away" from the molecule. – Jason M Gray Oct 23 '20 at 0:01
• Files of that size can be uploaded here: github.com/HPQC-LABS/Modeling_Matters in a folder called 3586 (since as you can see in the URL for this question, it says that this is post # 3586). – Nike Dattani Oct 23 '20 at 0:33

I have yet to find an explicit place where this is stated in the documentation, but the default unit for energy, and thus the core Hamiltonian, seems to be a.u., that is, hartree. Similarly, the default length unit seems to be angstroms, so the density matrix elements are likely in angstroms$$^{-3}$$.
From the CP2K Documentation the E-Field is given in units of $$\mathrm{W}\cdot\mathrm{cm}^{-2}$$ when the Intensity keyword is specified and you are performing Real-time propagation.