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E Capabilities of pcksdisp program

This Appendix contains a more detailed description of the program pcksdisp. In the pEDI.X scripts, this program is used to calculate the CHF static and dynamic susceptibility functions of the monomers. In addition, both these objects can also be calculated at the UCHF level. The CHF and UCHF induction and dispersion energies are also reported. The uncoupled (UCHF) dispersion and induction energies are equivalent to E_disp⁽²⁰⁾ and E_ind⁽²⁰⁾ SAPT corrections, respectively. At the CHF level, the induction energy is equal to E_ind,resp⁽²⁰⁾. The CHF dispersion is equivalent to the so-called RPA dispersion (see Ref. 39 for examples). The RPA dispersion energy is currently not computed by the regular (non-parallel) SAPT algorithms. Two other quantities that can be obtained using pcksdisp are the static/dynamic dipole-dipole polarizability tensor and the isotropic C₆ dispersion asymptotic coefficient (for the interaction of identical monomers), both at the UCHF and CHF levels.

The pcksdisp program uses the transformed intra- and intermonomer integrals (i.e., the MO representation) as generated by the ptran module. Therefore, within a script like pEDI.X, it should be run after the SCF and transformation programs. Note that currently pcksdisp assumes all integrals to be located in a single file f2e.000.001. Thus, all such files have to be properly merged after a parallel ptran run. This task is accomplished with the help of the program tmerge. To ensure that ptran generates all the integrals necessary for pcksdisp, the namelist INPUTCOR in the nameP.data file should contain the directives

The actual control parameters for pcksdisp are collected in the namelist INPUT, which should be appended to nameP.data (the scripts pEDI.X do this automatically) and look similar to

The meaning of the options is as follows:

• Main Control flags:
  • ISITCASPOL : (T/F) Set if this is a Casimir-Polder dispersion calculation.
  • ISITINDUCT : (T/F) Set if this is an induction calculation.
  • ISITPROP : (T/F) Set if a properties calculation needs to be performed.
  • ISITSOSDISP : (T/F) Set to perform the regular sum-over-states (SOS) E_disp⁽²⁰⁾ calculation.
• Propagator Type (only one can be selected):
  • ISITCKS : (T/F) Set to T if the propagator is to be computed in the CHF approximation, otherwise – set to F.
  • ISITUCKS : (T/F) Set to T if the UCHF approximation is to be used, otherwise – set to F.
• Properties calculation options:
  • ISITPOL : (T/F) Set if the frequency-dependent dipole polarizability tensor α_xy(ω) is to be computed. The frequencies at which the computation will be made are set by the input keywords NUMFREQ and FREQ<#> (see below). The dipole integrals are needed for this calculation.
  • ISITC6DISP : (T/F) Set if the C₆ dispersion coefficient is to be computed. At the moment the program outputs only the isotropic coefficient.
• USESUMN6 : (T/F) Sets the o³v³ summation algorithm in a Casimir-Polder dispersion calculation. Set this to T unless you want to use the old o⁴v⁴ summation algorithm.
• MAKEH1H2 : (T/F) Set to enable construction of the Electric and Magnetic Hessians (the H⁽¹⁾ and H⁽²⁾ matrices) in the CHF approximation. Transformed integrals of certain types are required for this option. If this option is set to F, then the H⁽¹⁾ and H⁽²⁾ matrices must be read in from a file in either the CHF or CKS approximation.
• NUMFREQ and FREQ1, FREQ2,...,FREQ8 : NUMFREQ is the number of frequencies at which a frequency-dependent polarization calculation is to be made. This should be less than or equal to 8. The variables FREQ1, FREQ2,...,FREQ8 contain the frequencies. If complex frequencies are required, set a negative frequency. These variables override the quadrature scheme described below.
• IQUADTYP and NQUAD : The type of quadrature scheme to be used in performing the ω-integral in the Casimir-Polder dispersion calculation and in the calculation of the C₆ dispersion coefficient:
  • IQUADTYP=1 sets the Gauss-Legendre quadrature with the transformation ω = ω₀.
  • IQUADTYP=2 sets the Gauss-Legendre quadrature with the transformation ω = ω₀ tan(t).
  • IQUADTYP=3 sets the Gauss-Laguerre quadrature scheme.

  The variable NQUAD sets the number of quadrature points to be used for the integration.

• OMEGA0 and ALPHA : The transformation used in the Gauss-Legendre quadrature schemes involves a constant ω₀. The namelist variable OMEGA0 allows one to set this constant. It is typically between 0.3 and 0.5. The Gauss-Laguerre quadrature scheme involves the constant α. For the integrals encountered here, one should set ALPHA=0.0.
• Debugging levels : There are many debugging levels built into the code. These can be activated by setting the relevant combination of debugging flags to T. Nota bene: large matrices may be printed out at certain levels. Here is a list of current debugging levels:
  • DEBUG1 : (T/F) Test the quadrature grid.
  • DEBUG2 : (T/F) Use the un-coupled propagator in the coupled propagator route. This is very useful when testing the code as the dispersion energy obtained this way should be the same as the value of E_disp⁽²⁰⁾ obtained from the SOS formula.
  • DEBUG3 : (T/F) Print out all matrices in the construction of the coupled propagator.
  • DEBUG4 : (T/F) Print out all 2-electron integrals read in.
  • DEBUG5 : (T/F) Print out information in the N⁶ summation algorithm (subroutine SUMN6).
  • DEBUG6 : (T/F) Print out information in the PROPERTIES and C6DISP routines.
  • DEBUG7 : (T/F) Print out integrals, etc. Used in computing the H⁽¹⁾ and H⁽²⁾ matrices in the CHF approximation.
  • DEBUG8 : (T/F) Print out information in the induction module. Integrals and intermediates are printed. This can generate a very large output.