Functional Control Parameters
These are switches that control the density functional equations being studied
for a given case. The functional switches are separated into hard sphere,
attractive, Coulombic, and polymer functionals.
- Type_func(int): Hard sphere functional type (for HS perturbation calculations). Options are:
- -1: NONE: no hard sphere functionals. Set this for ideal gases, Poisson-Boltzman electrolytes, or CMS polymers.
- 0: FMT1: original FMT functional developed by Rosenfeld (Phys Rev Lett, v.63, p.980, 1989).
- 1: FMT2: FMT with corrected zero dimensional crossover behavior (Rosenfeld et.al., Phys. Rev. E., v.55, p.4245, 1997 and Rosenfeld et.al., J. Phys. Cond. Matt., v.8, p.L577, 1996).
- 2: FMT3: White Bear Functional (Roth et.al., J. Phys. Cond. Matt., v.14, p.12063, 2002)
- Type_hsdiam(int): Type of hard sphere diameter to be used in FMT functional. Options are:
- 0: use Sigma_ff parameters as the hard sphere diameter in FMT functionals.
- 1: use Barker-Henderson approach to set hard sphere diameters in FMT functionals.
- Type_attr(int): Define longer range (often but not always attractive) interactions. if Type_attr> -1, then Type_pairPot must be defined. Options are:
- -1: NONE: no longer range interactions.
- 0: MFPAIR1: Strict mean field interactions (e.g. Lennard-Jones or Yukawa) will be added to the free energy functional. (see Frink and Frischknecht, Phys.Rev.E, v.72, p.041923, 2005
for an example of how this has been implemented for CMS-DFT)
- 2: MF_VARIABLE: Strict mean field interactions (e.g. Lennard-Jones or Yukawa) will be included in the functional, but a new field variable will be introduced into the matrix solve. This allows the matrix entries associated with the pair potential (which are constants) to be separated from the fill of the Euler-Lagrange (density) equations. When optimized Schur solvers are used, this approach reduces the number of nonzeros in the A22 block of the matrix which can speed computations considerably. The densities and energies obtained from this method should be identical to those obtained with Type_attr=0.
- Type_pairPot(int): Type of potential to be used for calculation with a strict mean field extended interactions. The specific function associated with each type of potential
can be found in Tramonto/src/dft_pairPot_potID.c, where potID depends on the potential of interest.
- 0: PAIR_LJ12_6_CS: Cut and shifted 12-6 Lennard-Jones potential. WCA approximation with integrals take from r=0 to r=rcut, and u=u_min for all r
- 1: PAIR_COULOMB_CS: Cut and shifted Coulomb potential (note ... this is generally a bad idea - turn on Type_coul instead to preserve charge neutrality.
- 2: PAIR_COULOMB: Full Coulomb potential used in forming integration stencils. (note ... this is still approximate and a bad idea - again turn on Type_coul instead to preserve charge neutrality.
- 3: PAIR_YUKAWA_CS: Cut and shifted Yukawa potential (defined as in Egorov, Phys.Rev.E., v.70, p.031402, 2004).
- 4: PAIR_LJ12_6_SIGTORCUT_CS: Cut and shifted 12-6 Lennard-Jones potential. Integrals taken from r=sigma to r=r_cut only.
- 5: PAIR_EXP_CS: Cut and shifted exponential potential.
- 6: PAIR_SW: Square well interaction potential.
- Type_coul(int): Type of potential to be used to treat electrostatics for cases where the electrostatic potential is introduced into the
system of equations, and Poisson's equation is solved simultaneously with the DFT Euler-Lagrange equations.
- -1: NONE: turn off Poisson Terms. Do this for neutral systems or for Type_pairPot=1 or 2.
- 0: BARE: Mean field electrostatics based on point charges only (no other correlations included).
- 1: DELTAC: Mean field electrostatics for point charges plus a 2nd order correction based on an analytical solution for the RPM
using the mean spherical approximation (MSA) for the special case of a restricted primitive model (RPM) where all charged species have identical
size. (see Tang and Davis, J. Chem. Phys., 97:9258, 1992).
- 2: POLARIZE: Electrostatics for a polarizeable fluid. Preliminary 1D implementation only in both the 2007 release of Tramonto-2.1 and 2009 release of Trmaonto-3.0.
- Type_poly(int): The type of functional to be used to describe bonded systems. Note that long range interactions and electrostatics
can be turned on in conjunction with bonded systems by turning on Type_attr and/or Type_coul as described above. Furthermore note that
the WTC and WJDC polymers (options 2-5) also require a selection for the reference hard sphere fluid type using Type_func above. Options for Type_poly are:
- -1: NONE: No polymer functionals. No bonds.
- 0: CMS: Chandler-McCoy-Singer DFT (J.Chem.Phys., v.85, p. 5971, 1986; v.85, p.5977, 1986; v. 87, p.4853, 1987) based
on freely-jointed chains where the single chain part of the functional is evaluated
numerically as described by Doneley et.al. (see Doneley et.al. J. Chem. Phys., v.103, p.5061, 1995; and Frischknecht et.al., J. Chem. Phys., v. 117, 10385, 2002).
- 1: CMS_SCFT: This option simplifies the CMS theory to reproduce polymer Self-Consistent Field Theory.
Note that the algorithms in Tramonto are not optimal for SCFT. Rather this approach serves as a test
and a point of comparison with work in the SCFT community. This option is not fully implemented as
of the 2007 release of Tramonto v2.1.
- 2: WTC: Tripathi-Chapman functionals based on a Wertheim's theory approach in the limit
of infinitely strong associations (see Tripathi and Chapman, Phys. Rev. Lett., v.94, p. 087801, 2005 and J. Chem. Phys., v.122, p.094506, 2005).
- 3: WJDC: Jain-Dominik-Chaman functionals based on a Wertheim's theory approach (see J. Chem. Phys., 127:244904, 2007). This implementation treats both the densities and the effective fields as segment based variables explicitly. It may be used in conjunction with Schur solvers.
- 4: WJDC2: Jain-Dominik-Chaman functionals based on a Wertheim's theory approach (see J. Chem. Phys., 127:244904, 2007). This implementation treats the densities segment based variable but the effective field as a component (segment type) based variable. It may NOT be used in conjunction with Schur solvers.
- 5: WJDC3: Jain-Dominik-Chaman functionals based on a Wertheim's theory approach (see J. Chem. Phys., 127:244904, 2007). This implementation treats both the densities and the effective fields as component (segment type) based variables. It may be used in conjunction with Schur solvers, and is considered the optimal implementation of the WJDC functional from a performance perspective.