Table of contents
Details
The RT
input section includes all specifications for realtime electron dynamics calculations. This section is required for all calculations where QM.JOB
is RT
. The defaults are suitable for most applications, although the time step and simulation length must be specified by the user.
Keywords
Keyword  Type  Description  Default  Required? 

TMAX 
Double precision float  Maximum time to which to propagate in A.U.  N/A  Yes 
DELTAT 
Double precision float  Time between each propagation step in A.U.  N/A  Yes 
INTALG 
String  Propagation algorithm  MMUT 
No 
FIELD 
Multiline string  Timedependent fields during propagation  None  No 
RESTARTSTEP 
String  Algorithm to use for MMUT restart step  MAGNUS2 
No 
IRSTRT 
String  Number of steps between MMUT restart steps  50 
No 
SAVESTEP 
Integer  Number of steps between saving to the binary file  50 
No 
RESTART 
Boolean  Whether or not to restart propagation from the binary file  FALSE 
No 
SCFFIELD 
Boolean  Whether or not to use the time independent field from the SCF calculation during the RT calculation  TRUE 
No 
INTALG
Keyword
The The integration algorithm used to propagate the density matrix. The currently available methods are both 2^{nd} order integrators based on the Magnus expansion,^{1} specifically MMUT
and MAGNUS2
. The default algorithm is MMUT
due to its lower cost (single Fock formation and diagonalization per step)
and superior performance for oscillatory solutions.
MMUT
: The Modified Midpoint Unitary Transform (MMUT) propagator^{2}
MMUT is a "leapfrog" integrator in which the density from the previous time step is propagated to the next time step based on the Fock matrix of the current time step.
\mathbf{P}(t_{k+1}) = \mathbf{U}(t_k) \mathbf{P}(t_{k1}) \mathbf{U}^\dag(t_k)
The propagator, \mathbf{U}
is an exponential based on the Fock matrix at the current time.
\mathbf{U}(t_k) = e^{2i\Delta t \mathbf{F}(t_k)}
Currently, this expression is evaluated through explicit diagonalization of the time dependent Fock matrix. Other methods for evaluating the matrix exponential are possible and are being implemented.
MAGNUS2
: A second order, trapezoidal approximation to the Magnus expansion^{3}
The 2nd order, explicit Magnus propagator is a single step integrator, propagating the density from the current step to the next step.
\mathbf{P}(t_{k+1}) = \mathbf{U}(t_k) \mathbf{P}(t_k) \mathbf{U}^\dag(t_k)
Where the propagator is based on the Fock matrix at the current time step and the next time step.
\mathbf{U}(t_k) = e^{\frac{i\Delta t}{2} (\mathbf{F}(t_k) + \mathbf{F}(t_{k+1}))}
Currently, the Fock matrix at the next time step is obtained through a forward Euler propagation of the density.
FIELD
Keyword
The The FIELD
keyword specifies a timedependent electromagnetic perturbation for the realtime electron dynamics simulation. The specification of the RT field is very similar to that of the SCF.FIELD
, with a few caveats:
 One must specify a timedependent envelope and
 Multiple fields may be specified.
Thus, the total field at a given time is given by
E(t) = \sum_k e_k(t) a_{kj} O_j
Where e_k
is the envelope for the k
th field, O_j
is some multipole operator and a_{kj}
is the amplitude of
O_j
for the k
th field.
In general, this may be specified as
Field:
<ENVELOPE> <FIELD TYPE> <AMPLITUDES>
<ENVELOPE> <FIELD TYPE> <AMPLITUDES>
<ENVELOPE> <FIELD TYPE> <AMPLITUDES>
The <FIELD TYPE>
and <AMPLITUDES>
follow the same rules as SCF.FIELD
. The <ENVELOPE>
specification may be given (in general) as,
<ENVELOPE NAME>(<ENVELOPE PARAM>)
Where <ENVELOPE PARAM>
is a comma separated list of envelope parameters (see table). As of 10/2/2020, ChronusQ supports the following envelopes:
Envelope  Description  Parameters 

StepField 
Step function  Time on (A.U.), Time off (A.U.) 
Note: Currently, ChronusQ only supports Electric Dipole fields in realtime electron dynamics.
RESTARTSTEP
and IRSTRT
Keywords
The When using the MMUT algorithm to propagate the density, single step methods must be used to start the algorithm. Furthermore, if allowed to propagate for long time frames, the branches of the MMUT algorithm with even and odd steps can diverge, leading to a highly oscillatory solution. This can be remedied by using a single step method to periodically restart the MMUT algorithm.
IRSTRT
controls the number of MMUT steps between the single step propagator.
For RESTARTSTEP
, both MAGNUS2
and FORWARDEULER
are accepted, but the FORWARDEULER
restart step may introduce significant error and should not be used. It is included for the sake of backward compatibility.
RESTART
Keyword
The RESTART
will trigger an attempt to restart from the last recorded checkpoint on the binary ChronusQ file. It will load the last time dependent density saved and propagate to the final time. RESTART
cannot currently be used to extend the simulation time specified in the original input file. If this is important for your work, please open an issue!
Examples
Propagation after a "delta kick"
The absorption spectrum of a system can be extracted by analyzing the dipole oscillations after an instantaneous "kick" from an external field.^{1} One of the required simulations for this process can be achieved in ChronusQ with the following input.
[RT]
TMAX = 620.15
DELTAT = 0.005
FIELD:
StepField(0.,0.00001) Electric 0. 0.001 0.
Propagation after SCF in a field
Real time electron dynamics can also be used to study molecular plasmons.^{4} In this case, one performs an optimization of the molecular wavefunction in a static electric field, but then removes the electric field for the propagation. This may be achieved (combined with the required SCF field) with the following RT
input.
[RT]
TMax = 1000.
DeltaT = 0.005
SCFField = False
References

Goings, J. J., Lestrange, P. J., & Li, X. (2018). Real‐time time‐dependent electronic structure theory. Wiley Interdisciplinary Reviews: Computational Molecular Science, 8(1), e1341.
↩ 
Li, X., Smith, S. M., Markevitch, A. N., Romanov, D. A., Levis, R. J., & Schlegel, H. B. (2005). A timedependent Hartree–Fock approach for studying the electronic optical response of molecules in intense fields. Physical Chemistry Chemical Physics, 7(2), 233239.
↩ 
Blanes, S., & Casas, F. (2017). A concise introduction to geometric numerical integration. CRC press.
↩ 
Ding, F., Guidez, E. B., Aikens, C. M., & Li, X. (2014). Quantum coherent plasmon in silver nanowires: A realtime TDDFT study. The Journal of chemical physics, 140(24), 244705.
↩