Skip to content

GitLab

  • Menu
Projects Groups Snippets
    • Loading...
  • Help
    • Help
    • Support
    • Community forum
    • Submit feedback
    • Contribute to GitLab
  • Sign in
  • chronusq_public chronusq_public
  • Project information
    • Project information
    • Activity
    • Labels
    • Planning hierarchy
    • Members
  • Repository
    • Repository
    • Files
    • Commits
    • Branches
    • Tags
    • Contributors
    • Graph
    • Compare
  • Issues 1
    • Issues 1
    • List
    • Boards
    • Service Desk
    • Milestones
  • Merge requests 0
    • Merge requests 0
  • CI/CD
    • CI/CD
    • Pipelines
    • Jobs
    • Schedules
  • Deployments
    • Deployments
    • Environments
    • Releases
  • Monitor
    • Monitor
    • Incidents
  • Analytics
    • Analytics
    • Value stream
    • CI/CD
    • Repository
  • Wiki
    • Wiki
  • Snippets
    • Snippets
  • Activity
  • Graph
  • Create a new issue
  • Jobs
  • Commits
  • Issue Boards
Collapse sidebar
  • ChronusQ
  • chronusq_publicchronusq_public
  • Wiki
  • Examples
  • Model Order Reduction of TDDFT

Last edited by Andrew Wildman Dec 08, 2020
Page history

Model Order Reduction of TDDFT

Model Order Reduction or MOR is a general linear algebra technique that allows for a reduction in dimension of a linear system solver while retaining high accuracy, ubiquitous in many scientific domains.

For our purposes, we will can use MOR in ChronusQ to compute the one-electron absorption cross section over an arbitrary energy range for the TDHF or TDDFT response matrices. The frequency (\omega) dependent absorption cross section1 is defined as

{\boldsymbol \sigma}(\omega) = \omega \text{Im}\left[ \text{Tr} \left( {\boldsymbol \alpha}(\tilde{\omega}) \right) \right]

where {\boldsymbol \alpha}(\tilde{\omega}) is the dynamic polarizabilty tensor, and \tilde{\omega} = \omega + i \eta, where \eta is a small positive damping factor to numerically converge resonant excitations.

Luckily, we can use a frequency dependent response (FDR) calculation to compute {\boldsymbol \alpha}(\tilde{\omega}), which is detailed in the example: Frequency Dependent TDHF.

Input

The MOR absorption cross section job only requires a small modification to the input file in the Frequency dependent TDHF example.

[Molecule]                                                                                                            
charge = 0                                                                                                            
mult = 1                                                                                                              
geom:                                                                                                                 
 Cl   0.0   0.0   0.0                                                                                                 
 H    0.0   0.0   1.27                                                                                                
                                                                                                                      
[QM]                                                                                                                  
reference = RB3LYP                                                                                                    
job = resp                                                                                                            
                                                                                                                      
[BASIS]                                                                                                               
basis = cc-pvdz                                                                                                       
                                                                                                                      
[RESPONSE]                                                                                                            
type = mor                                                                                                            
damp = 0.01
bfreq = range(0.15,300,0.01)                                                                                          
bops  = edl md                                                                                                        
dofull = true

[MOR]
refine = true

The main difference from the FDR job input file is in the [RESPONSE] section and the additional [MOR] section. First, we specify that the additional MOR absorption cross section is to be computed with type = mor in the [RESPONSE] section. Additionally, we sample 300 different frequencies bfreq = range(0.15,300,0.01) to have good resolution for the output MOR spectrum.

Next, the damp parameter is required. This is a user choice that is equivalent to dressing a typical TDDFT stick spectra with a lorentzian where the width is chosen by said damp parameter. In this case damp = 0.01 Hartrees.

Finally there's an optional parameter refine in the optional section [MOR]. This method is turns on an adaptive scheme for the MOR method,2 reducing computational overhead, and is recommended for large and dense spectra.

Output

For the output file of an MOR spectrum TDDFT job, we see the typical polarizabilties that are produced by the FDR portion.

FREQUENCY DEPENDENT RESPONSE RESULTS


* RESPONSE FUNCTIONS (POLARIZABILITIES)


  Electric Dipole - Electric Dipole (Length) : - Re [<< r_i; r_j >>] (AU)


                         { << X; X >>, << X; Y >>, << X; Z >> }
                         { << Y; X >>, << Y; Y >>, << Y; Z >> }
                         { << Z; X >>, << Z; Y >>, << Z; Z >> }

    W(AU) = 0.1500      6.68923e+00    0.00000e+00    0.00000e+00
                        0.00000e+00    6.68923e+00    0.00000e+00
                        0.00000e+00    0.00000e+00    1.38417e+01

    W(AU) = 0.1600      6.72890e+00    0.00000e+00    0.00000e+00
                        0.00000e+00    6.72890e+00    0.00000e+00
                        0.00000e+00    0.00000e+00    1.39914e+01
.
.
.

However, below all the polarizabilities, the absorption cross section {\boldsymbol \sigma}(\omega) at each frequency is reported in the following format:

* OBSERVABLES


  ONE-PHOTON ABSORPTION CROSS-SECTION (EDA)

    * SIGMA(W) = 4 * PI * W / C * IM[ALPHA(-W,W)]
    * ALPHA(-W,W) = TR[ << r; r >>(W) ]



                            W           SIGMA(W) (AU)
             1.5000000000e-01         3.0037708606e-03
             1.6000000000e-01         3.5462240120e-03
             1.7000000000e-01         4.1741142323e-03
             1.8000000000e-01         4.9075595328e-03
             1.9000000000e-01         5.7753132370e-03
.
.
.

where W is the frequency and SIGMA(W) is the absorption cross section. Using this data, the absorption spectrum can be easily plotted with your favorite plotting software. For this example, the spectrum looks like the following:

HCl MOR Spectrum

References

  1. Oddershede, J., & Jørgensen, P. & Yeager, D. L. (1984). Polarization Propagator Methods in Atomic and Molecular Calculations. Computer Physics Reports, 33-92. ↩

  2. Van Beeumen, R., & Williams-Young, D. B., & Kasper, J. M., & Yang, C., & Ng, E. G., & Li, X. (2017). Model Order Reduction Algorithm for Estimating the Absorption Spectrum. Journal of Chemical Theory and Computation, 13(10), 4950-4961. ↩

Clone repository

Overview and Features

Getting ChronusQ

Running ChronusQ

Input sections

     Overview
     QM and PROTQM
     Molecule
     Basis and DFBasis
     Ints
     DFTInts
     SCF
     RT
     Response
     CC
     MCSCF
     Misc

FAQ

Examples

     HF energy
     Relativistic DFT Energy
     Linear Response TDDFT
     Frequency dependent TDHF
     Model Order Reduction of TDDFT
     Electron dynamics

Keyword Reference

Binary Reference