Linear response calculations are the most efficient way to predict resonant electronic response frequencies and intensities. QChem can also propagate meanfield theories (HF, DFT) in realtime with and without dissipation and finitetemperature effects. These methods timeevolve the Liouvillevon Neumann equation of motion for a oneparticle density operator, :
(7.93) 
These realtime methods are useful for simulating attosecond to picosecond timescales, density response to multiple or strong applied fields, and timescales of energy relaxation. Symmetry, nonsinglet densities, MetaGGAs and 5thrung functionals are not supported for realtime propagation, and nuclei are fixed. The CPU cost of a single time step is comparable to that of a single SCF cycle, if the modifiedmidpoint unitary transformation (MMUT) propagation algorithm[Li et al.(2005)Li, Smith, Markevitch, Romanov, Lewis, and Schlegel] is employed, and no more than a few times the cost of a single SCF cycle if predictor/corrector algorithms (which facilitate stable time propagation using much larger time steps) are used.[Zhu and Herbert(2018)] Memory costs are similar to those of a groundstate SCF calculation, which for large systems, or those with a large density of states, represents a dramatic reduction in the memory requirement relative to linearreponse TDDFT. The number of required Fockbuild steps can be estimated from the default electronic timestep, which is 0.02 atomic units ( fs). The realtime code exploits realtime sharedmemory parallelism, and the use of 8 or more cores (–nt 8) is suggested. The input file of a basic realtime propagation is relatively simple, but sophisticated jobs require additional input files, and generate additional output.
Example 7.196 QChem Basic RTTDDFT job for BH3.
$molecule 0 1 B 0.000000 0.000000 0.000000 H 1.115609 0.322048 0.260309 H 0.332368 1.137184 0.111382 H 0.782205 0.814474 0.375294 $end $rem SCF_GUESS core GEN_SCFMAN true RTTDDFT 1 BASIS 321g THRESH 10 SCF_CONVERGENCE 9 EXCHANGE b3lyp SYMMETRY false SYM_IGNORE TRUE SCF_ALGORITHM DIIS UNRESTRICTED FALSE MAX_SCF_CYCLES 200 $end
Before executing this job, a directory (/logs) must be made in the output directory of the job to collect most of the results of the propagation. By default, a realtime job begins from the ground state SCF density, applies a weak, brief (0.07 atomic time units) oscillating electric field to the axis of a molecule which excites a superposition of all polarized excited states, and outputs the resulting timedependent dipole moment, energy and other quantities to the logs directory. The parameters of the timedependent run are printed when the propagation begins. During the propagation the state of the molecule and propagation is summarized in the QChem output file, including estimates of the elapsed and remaining simulation walltime. Propagation stops when MaxIter time steps are exceeded, or will stop prematurely if the density matrix becomes nonphysical. The logs directory will be populated by several text, white space delimited tables by default. The ./logs/Pol.csv file is a table consisting of time (in a.u.), , , , total energy, , the gap, the electronic energy, and two unused columns. The ./logs/Fourier_x.csv file contains Fourier transform , in the format of its total value in energy units (eV) followed by its negative imaginary part and then its real part. Analogous files ./logs/Fourier_y.csv and ./logs/Fourier_z.csv are also created.
By adjusting the options of the propagation with a file TDSCF.prm, a much larger amount of output can be generated, including the electron and hole densities at all times as sequential MolDen files (*.mol) viewable with the free package Gabedit (gabedit.sourceforge.net). The *.mol files generated by the realtime code have fractional orbital occupation numbers, and do not render properly in viewers other than Gabedit to our knowledge. So long as the applied field is weak and has short duration the positions at which peaks appear in the Fourier are the same as a linearresponse TDDFTRPA job (note: not the same as a LRTDDFTTDA job), as shown in the sample. In an energyconserving job, the width of the peak is inversely proportional to the duration of the signal sample used to construct the Fourier transform. If the applied field pulse is long ( a.u.), or has strong intensity ( a.u.) nonlinear response can be studied. Nonlinear effects in realtime SCF are an area of active investigation and development.
The absorption crosssection in the direction, , can be obtained from the imaginary part of the frequencydependent polarizability :
(7.94) 
and the rotationallyaveraged absorption spectrum (within the dipole approximation) is
(7.95) 
The frequencydependent polarizability is obtained from the Fourier transform of , for a perturbing field in the direction:[Zhu and Herbert(2018)]
(7.96) 
Thus to compute the spectrum in Eq. eq:RTTDDFT_spectrum, three RTTDDFT simulations are required, perturbing separately in the , , and directions.
Because of the large number of floating point arguments used to control a realtime job, a separate input file TDSCF.prm in the same directory as the QChem input file is used for parameters. The file is two columns of plain text. The first column is a string naming the parameter (which must match the case and spelling printed in the output exactly to be interpreted correctly), and the second column is a floating point number. The number must only be followed by a new line. Several inputs are interpreted as true = 1 or false = 0. The most useful parameters are discussed in this section. The code will signal if this file is not found and default values will be supplied instead.
Example 7.197 QChem Typical TDSCF.prm for a realtime B3LYP calculation.
dt 0.02 Stabilize 0 TCLOn 0 MaxIter 80000 ApplyImpulse 1 ApplyCw 0 FieldFreq 0.7 Tau 0.07 FieldAmplitude 0.001 ExDir 1.0 EyDir 1.0 EzDir 1.0 Print 0 StatusEvery 10 SaveDipoles 1 DipolesEvery 2 SavePopulations 0 SaveFockEnergies 0 WriteDensities 0 SaveEvery 500 FourierEvery 5000 MMUT 1 LFLPPC 0
Parameter String 
Explanation 
dt 
timestep (atomic units) > 0.02 may be unstable. 
Stabilize 
Forces positive occupation numbers. 
MaxIter 
Maximum Timesteps 
ApplyImpulse 
0 = No applied gaussian impulse 
ApplyCw 
0 = No Continuous Wave, 1 = Cosine applied field. 
FieldFreq 
Frequency of applied field (atomic units) 
Tau 
Timevariance of Gaussian Impulse (atomic units) 
FieldAmplitude 
Max. amplitude of field (atomic units) 
ExDir 
Field Polarization Vector (xcomponent) 
EyDir 
Field Polarization Vector (ycomponent) 
EzDir 
Field Polarization Vector (zcomponent) 
Value makes print more debug output. 

StatusEvery 
Iterations between status in output file 
SaveDipoles 
0 = No Pol.csv generated. 
DipolesEvery 
Iterations between samples of Dipole 
SavePopulations 
1 = Saves diagonal of the density 
SaveFockEnergies 
1 = Saves diagonal of the Fock matrix 
WriteDensities 
generates .mol files readable with Gabedit 
SaveEvery 
Iterations between writing of all files in /logs 
FourierEvery 
Iterations between Fourier Transform 
FourierZoom 
A zoom parameter which controls resolution of FT. 
MMUT 
Modified midpoint unitary transform propagator calculation[Li et al.(2005)Li, Smith, Markevitch, Romanov, Lewis, and Schlegel] (default) 
LFLPPC 
Predictor/corrector propagator[Zhu and Herbert(2018)] 
Any undocumented options not discussed above are not officially supported at this time.