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howto:rtp_field_xas [2023/10/11 09:43] – [CP2K input] glebretonhowto:rtp_field_xas [2023/10/16 16:15] – oschuett
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 In this tutorial, we will present a simulation of resonant X-Ray excitation of an isolated carbon monoxide in real-time using a time-dependent field.  In this tutorial, we will present a simulation of resonant X-Ray excitation of an isolated carbon monoxide in real-time using a time-dependent field. 
 On this page, you will find an overview of the method, some equations, and the CP2K input file.  On this page, you will find an overview of the method, some equations, and the CP2K input file. 
-A longer version is available in the form of a jupyter notebook file in {{:howto:rtp_field_xas.zip | this zip file}} along with the simulated data so that you do not need to run this calculation yourself to perform the analysis.+A longer version is available in the form of a jupyter notebook file in {{ :howto:rtp_field_xas.zip | this zip file}} along with the simulated data so that you do not need to run this calculation yourself to perform the analysis.
 This kind of calculation is not easy to grasp: do not hesitate to have a first look before diving into the equations and details!  This kind of calculation is not easy to grasp: do not hesitate to have a first look before diving into the equations and details! 
 This tutorial is connected to this article REF where you can find complementary information.  This tutorial is connected to this article REF where you can find complementary information. 
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 </code> </code>
  
-We will not detail all the parameters and instead focus on the one related to the dynamics itself, the field, and the time-dependent projection part.+We will not detail all the parameters and instead focus on the one related to the real-time propagation, the field, and the time-dependent projection part.
  
 == Real-Time Propagation parameters == == Real-Time Propagation parameters ==
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 INITIAL_WFN SCF_WFN INITIAL_WFN SCF_WFN
 </code> </code>
-Therefore, before the Real-Time Propagation, a ground state calculation will be performed. +Before the Real-Time Propagation starts, a ground state calculation will thus be performed. 
 We use a Molecular Orbital-based description of the wave function for the propagation along with the Arnoldi approach to compute the exponential: We use a Molecular Orbital-based description of the wave function for the propagation along with the Arnoldi approach to compute the exponential:
  
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 </code> </code>
  
-Note that for very large systems, the density-based method can be used for linear scaling (see the DENSITY_PROPAGATION keyword). +Note that for extensive systems, the density-based method can be used for linear scaling (see the DENSITY_PROPAGATION keyword). 
 For each time step, the AERTS algorithm is used with a convergence threshold defined by  For each time step, the AERTS algorithm is used with a convergence threshold defined by 
  
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 The time-dependent electric field is defined for both gauges in the EFIELD section. It should be noted that one can define several EFIELD sections to apply several fields within the same simulation.  The time-dependent electric field is defined for both gauges in the EFIELD section. It should be noted that one can define several EFIELD sections to apply several fields within the same simulation. 
  
-The field is defined by its envelope, its intensity (in W.cm$^{-2}$), its polarization along the laboratory x,y, and z-axis, its wavelength (in nanometer), and the original phase. Several types of field envelopes can be used. Here we use a Gaussian one with a width of $\sigma=0.3073$ fs and centered at $T0=1.3190$ fs. The intensity used is 4.08E+13 W.cm$^{-2}$. Along with a carrying frequency of 529 ev (approximately 2.34374655955 nm), it should promote about $10^{-3}$ from the Oxygen 1s to the first available excited state. See {{:howto:rtp_field_xas.zip |the jupyter notebook tutorial}} for more information about how to choose these parameters depending your system.  +The field is defined by its envelope, its intensity, its polarization along the laboratory x, y, and z-axis, its wavelength, and the original phase. Several types of field envelopes can be used. Here we use a Gaussian one with a width of $\sigma=0.3073$ fs and centered at $T0=1.3190$ fs. The intensity used is 4.08E+13 W.cm$^{-2}$. Along with a carrying frequency of 529 ev (approximately 2.34374655955 nm), it should promote about $10^{-3}$ from the Oxygen 1s to the first available excited state. See {{:howto:rtp_field_xas.zip |the jupyter notebook tutorial}} for more information about how to choose these parameters depending on your system.  
  
 <code> <code>
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 All the time-dependent Molecular Orbitals are projected (TD_MO_INDEX = -1) and these projections are stored separately (SUM_ON_ALL_TD .FALSE.). This calculation is spin-independent so one does not have to define the spin of the MO to project.  All the time-dependent Molecular Orbitals are projected (TD_MO_INDEX = -1) and these projections are stored separately (SUM_ON_ALL_TD .FALSE.). This calculation is spin-independent so one does not have to define the spin of the MO to project. 
-The reference to projected on is loaded from the file RTP-RESTART.wfn, which is the ground state obtained after the SCF cycles. Note that you can define a wave-function that is not the ground state as long as the wave-function description (basis set, number of electrons...) is the same as the one used for the real-time propagation. The 'type' of reference is the default one, REFERENCE_TYPE SCF. All the molecular orbitals available in this reference wave-function will be used as a reference for the projection (REF_MO_INDEX -1 ), and stored in separate files (SUM_ON_ALL_REF .FALSE.). The projection will be computed at each time step.+The reference to projected to is loaded from the file RTP-RESTART.wfn, which is the ground state obtained after the SCF cycles. Note that you can define a wave-function that is not the ground state as long as the wave-function description (basis set, number of electrons...) is the same as the one used for the real-time propagation. The 'type' of the reference file is the default one, REFERENCE_TYPE SCF. All the molecular orbitals available in this reference wave-function will be used as a reference for the projection (REF_MO_INDEX -1 ), and stored in separate files (SUM_ON_ALL_REF .FALSE.). The projection will be computed at each time step.
  
-There are $N_e/2 = 7$ molecular orbitals for carbon monoxide. There are thus 7 time dependent MOs (the $i$) and 7 reference MO (the $j$), so that there will be $7x7=49$ projection per time step: +There are $N_e/2 = 7$ molecular orbitals for carbon monoxide. There are thus 7 time-dependent MOs (the $i$s) and 7 reference MO (the $j$s), so that there will be $7x7=49$ projection per time step: 
  
 $$ $$
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 $$ $$
  
-Now, let us focus on the second and third projections which can be viewed as excited-state projections: +Now, let us focus on the second and third projections which can be viewed as projections toward excited-states: 
  
 <code> <code>
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 </code> </code>
  
-In this case, all the time-dependent MO are involved in the projection and stored separately. This time, the reference wave function is supposed to be from an XAS_TDP calculation, see XAS_TDP%PRINT%RESTART_WFN section or the Linear Response input file in the {{:howto:rtp_field_xas.zip |tutorial archive}}. Running with the proper parameters, this XAS_TDP run produces a .wfn file per excited state: it is the $|\omega>$ presented before. Thus, using  REFERENCE_TYPE XAS_TDP automatically looks for the  $|\omega>$ saved in the .wfn file and performs the projection toward it: +In this case, all the time-dependent MO are involved in the projection and stored separately. This time, the reference wave function is supposed to be from an XAS_TDP calculation, see XAS_TDP%PRINT%RESTART_WFN section or the Linear Response input file in the {{:howto:rtp_field_xas.zip |tutorial archive}}. Running with the proper parameters, this XAS_TDP run saves one .wfn file per excited state: it is the $|\omega>$ presented before. Using REFERENCE_TYPE XAS_TDP, the projection uses automatically the $|\omega>$ saved in the .wfn file as the reference file: 
  
 $$ $$
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 Where $c_\omega^a$ is the $a^{\text{th}}$ atomic coefficient of the excited state found in the XAS_TDP module. Where $c_\omega^a$ is the $a^{\text{th}}$ atomic coefficient of the excited state found in the XAS_TDP module.
-There will thus be 7 projections per time step in this case. The excited state population associated to this state is:+There will be 7 projections per time step in this case: one for each time-dependent MO. The excited state population associated with this excited state is:
  
 $$ $$
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 $$ $$
  
-The carbon monoxide molecule has a rotational symmetry along its CO bond: if one notes this axis $z$, then the $x$ and $y$-axis are equivalent by symmetry. It happens that the first available excited state for the Oxygen 1s is degenerate: there are two available states orthogonal in the $xy$-plane.  That is why ta third projection is requested: it uses the other excited state proposed by the XAD_TDP module which has the exact same frequency as the first one. +The carbon monoxide molecule has a rotational symmetry along its CO bond. If one notes this axis $z$, then the $x$ and $y$-axis are equivalent by symmetry. It happens that the first available excited state for the Oxygen 1s is degenerate: there are two available excited states orthogonal in the $xy$-plane.  That is why a third projection is requested which uses the other excited state proposed by the XAD_TDP module.
  
-Therefore, the excited state should be understood as the some over these two frequency equivalent state: +Therefore, the excited state should be understood as the sum over the two equivalent excited states:
  
 $$ $$
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 $$ $$
  
-Where $\omega'$ stands for the other equivalent excited state. +Where $\omega'$ stands for the other equivalent excited state, with $\omega=\omega'=529$ ev. 
  
  
howto/rtp_field_xas.txt · Last modified: 2024/02/24 10:02 by oschuett