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kohn-sham_random-phase_approximation [2026/02/05 16:04] – dollkohn-sham_random-phase_approximation [2026/02/05 16:10] (current) – doll
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 ===== Random-phase approximation (RPATDDFT) program ===== ===== Random-phase approximation (RPATDDFT) program =====
  
-The random-phase approximation program (''rpatddft'') can be used to calculate RPA correlation energies after a SCF calculation. Additionnally, it can be used to calculate dynamic dipole polarizabilities, C$_6$ dispersion coefficients, and excitation energies. The program currently works without point-group symmetry.+The random-phase approximation program (''rpatddft'') can be used to calculate RPA correlation energies after a SCF calculation. Additionally, it can be used to calculate dynamic dipole polarizabilities, C$_6$ dispersion coefficients, and excitation energies. The program currently works without point-group symmetry.
  
 List of the main keywords: List of the main keywords:
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   * **''TDA''** Tamm-Dancoff approximation for ''EXCIT'' and ''PROPERTIES''.   * **''TDA''** Tamm-Dancoff approximation for ''EXCIT'' and ''PROPERTIES''.
   * **''NOMP2''** The MP2 energy is calculated in certain situations where it is available almost for free, provided that some matrices are allocated. This behavior can be switched off by this ''NOMP2'' keyword.   * **''NOMP2''** The MP2 energy is calculated in certain situations where it is available almost for free, provided that some matrices are allocated. This behavior can be switched off by this ''NOMP2'' keyword.
-  * **''NOSPINBLOCK''** For spin-unrestricted calculations, use a formalism where matrices are of $\alpha\alpha+\alpha\beta+\beta\alpha+\beta\beta$ dimensions (the default is to use a formalism with a nospinflip/splinflip block structure)+  * **''NOSPINBLOCK''** For spin-unrestricted calculations, use a formalism where matrices are of $\alpha\alpha+\alpha\beta+\beta\alpha+\beta\beta$ dimensions (the default is to use a formalism with a nospinflip/spinflip block structure)
   * **''NOSPINFLIP''** Exclude spin-flip dimensions of unrestricted RPA calculations that use the ''NOSPINBLOCK'' formalism (not suitable for all RPA variants).   * **''NOSPINFLIP''** Exclude spin-flip dimensions of unrestricted RPA calculations that use the ''NOSPINBLOCK'' formalism (not suitable for all RPA variants).
   * **''WRITEFILE''** Write files with eigenvalues, virtual orbital energies, dipole moments, dipole velocities, dipole accelerations and amplitudes from a TDA calculation   * **''WRITEFILE''** Write files with eigenvalues, virtual orbital energies, dipole moments, dipole velocities, dipole accelerations and amplitudes from a TDA calculation
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   * **''%%CORE,<core>%%''** Specify core orbitals (default: last specified core orbitals or, if none, atomic inner shells)   * **''%%CORE,<core>%%''** Specify core orbitals (default: last specified core orbitals or, if none, atomic inner shells)
   * **''%%PRINT,<nbr>%%''** Level of print expected from the output (from 0(default) to 3).   * **''%%PRINT,<nbr>%%''** Level of print expected from the output (from 0(default) to 3).
-  * **''%%PRINT_INT,<nbr>%%''** Level of print of integrals (AO,MO,Orbtials,...), from 0 to 4.+  * **''%%PRINT_INT,<nbr>%%''** Level of print of integrals (AO,MO,Orbitals,...), from 0 to 4.
   * **''%%PRINT_TIME,<nbr>%%''** If greater or equal to 1, will print out information on time spent in routines.   * **''%%PRINT_TIME,<nbr>%%''** If greater or equal to 1, will print out information on time spent in routines.
  
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 </code> </code>
 Calculation of properties, excitation energies and oscillator strengths\\ Calculation of properties, excitation energies and oscillator strengths\\
-''%%EXCIT, METHOD=<method>%%'' The ''EXCIT'' calculations output shows the excitation energies in ua, eV and nm, the oscillator strengths in length and velocity gauge, as well as the major excitations involved in each mode. The methods available are:+''%%EXCIT, METHOD=<method>%%'' The ''EXCIT'' calculations output shows the excitation energies in au, eV and nm, the oscillator strengths in length and velocity gauge, as well as the major excitations involved in each mode. The methods available are:
  
   * **''DRPA''** Direct random-phase approximation (or time-dependent Hartree).   * **''DRPA''** Direct random-phase approximation (or time-dependent Hartree).
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 The RIRPA and URIRPA programs allow non-self-consistent spin-restricted and spin-unrestricted resolution of identity (RI) random phase approximation (RPA) [1-3] and σ-functional [4-6] calculations. These methods should be used in conjunction with conventional Kohn-Sham (KS) density functional theory (DFT) calculations, i.e. data from a preceding KS DFT calculation should be provided. Conventional KS DFT means calculations with LDA, GGA and hybrid exchange-correlation functionals. The RIRPA and URIRPA programs allow non-self-consistent spin-restricted and spin-unrestricted resolution of identity (RI) random phase approximation (RPA) [1-3] and σ-functional [4-6] calculations. These methods should be used in conjunction with conventional Kohn-Sham (KS) density functional theory (DFT) calculations, i.e. data from a preceding KS DFT calculation should be provided. Conventional KS DFT means calculations with LDA, GGA and hybrid exchange-correlation functionals.
  
-**Bibilography:**\\+**Bibliography:**\\
 **RPA:**\\ **RPA:**\\
 [1] F. Furche, [[https://dx.doi.org/10.1103/PhysRevB.64.195120|Phys. Rev. B]], 195120 (2001)\\ [1] F. Furche, [[https://dx.doi.org/10.1103/PhysRevB.64.195120|Phys. Rev. B]], 195120 (2001)\\
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 The ''SCEXX'' and ''USCEXX'' programs allow self-consistent exact-exchange calculations for closed-shell and open-shell systems. The ''SCEXX'' and ''USCEXX'' programs allow self-consistent exact-exchange calculations for closed-shell and open-shell systems.
  
-**Bibilography:**\\+**Bibliography:**\\
 [1] A. Heßelmann, A.W. Götz, F. Della Sala, A. Görling [[https://doi.org/10.1063/1.2751159|J. Chem. Phys.]] 127, 054102 (2007)\\ [1] A. Heßelmann, A.W. Götz, F. Della Sala, A. Görling [[https://doi.org/10.1063/1.2751159|J. Chem. Phys.]] 127, 054102 (2007)\\
 [2] E. Trushin, A. Görling, [[https://aip.scitation.org/doi/full/10.1063/5.0056431|J. Chem. Phys.]] 155, 054109 (2021)\\ [2] E. Trushin, A. Görling, [[https://aip.scitation.org/doi/full/10.1063/5.0056431|J. Chem. Phys.]] 155, 054109 (2021)\\
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 The ''SCRPA'' and ''USCRPA'' programs allow spin-restricted and spin-unrestricted self-consistent random phase approximation calculations. The ''SCRPA'' and ''USCRPA'' programs allow spin-restricted and spin-unrestricted self-consistent random phase approximation calculations.
  
-**Bibilography:**\\+**Bibliography:**\\
 [1] A. Heßelmann, A.W. Götz, F. Della Sala, A. Görling [[https://doi.org/10.1063/1.2751159|J. Chem. Phys.]] 127, 054102 (2007)\\ [1] A. Heßelmann, A.W. Götz, F. Della Sala, A. Görling [[https://doi.org/10.1063/1.2751159|J. Chem. Phys.]] 127, 054102 (2007)\\
 [2] E. Trushin, A. Görling, [[https://aip.scitation.org/doi/full/10.1063/5.0056431|J. Chem. Phys.]] 155, 054109 (2021)\\ [2] E. Trushin, A. Görling, [[https://aip.scitation.org/doi/full/10.1063/5.0056431|J. Chem. Phys.]] 155, 054109 (2021)\\
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-Below is an example input file for spin-restricted calculations for the hygrogen molecule. Note that the input record from a preceding calculation is mandatory for initialization of orbitals and eigenvalues as starting point for RPA calculation, whereas it can come from HF or DFT calculations with maxit=0.+Below is an example input file for spin-restricted calculations for the hydrogen molecule. Note that the input record from a preceding calculation is mandatory for initialization of orbitals and eigenvalues as starting point for RPA calculation, whereas it can come from HF or DFT calculations with maxit=0.
  
 <code - examples/h2_scrpa.inp> <code - examples/h2_scrpa.inp>
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   * **nquadint** number of logarithmically spaced intervals for frequency integration (default ‘1’)   * **nquadint** number of logarithmically spaced intervals for frequency integration (default ‘1’)
   * **nquad** number of points per interval for frequency integration (default '20')   * **nquad** number of points per interval for frequency integration (default '20')
-  * **w0** caling factor for rational the function mapping the Gauss–Legendre quadrature for the interval [−1, 1] to the interval [0, ∞], see Eqs. 37-38 in Ref. [4] for details (default: ‘2.5’)+  * **w0** scaling factor for rational the function mapping the Gauss–Legendre quadrature for the interval [−1, 1] to the interval [0, ∞], see Eqs. 37-38 in Ref. [4] for details (default: ‘2.5’)
   * **vc_scal** scaling factor for the Coulomb kernel, which can be used to mimic the effect of the inclusion of the exact-exchange kernel. In the special case of non-spin-polarized two-electron systems, the RPA calculation with a Coulomb kernel scaled by 1/2 is equivalent to including of the exact-exchange kernel. Implemented only in `SCRPA` (default: ‘1d0’)   * **vc_scal** scaling factor for the Coulomb kernel, which can be used to mimic the effect of the inclusion of the exact-exchange kernel. In the special case of non-spin-polarized two-electron systems, the RPA calculation with a Coulomb kernel scaled by 1/2 is equivalent to including of the exact-exchange kernel. Implemented only in `SCRPA` (default: ‘1d0’)
   * **vref_fa** if set to $\neq$ 0, enable the use of the Fermi-Amaldi potential as reference potential. Otherwise, the reference potential is constructed according to Eq. (45) of Ref. [2] (default: '1')     * **vref_fa** if set to $\neq$ 0, enable the use of the Fermi-Amaldi potential as reference potential. Otherwise, the reference potential is constructed according to Eq. (45) of Ref. [2] (default: '1')