Exponential-6 + Reaction Field¶

Description¶

The exp6rf_compute_force operator adds an exponential-6 term and a reaction-field electrostatic term:

\[ E(r) = E_{\mathrm{exp6}}(r) + E_{\mathrm{RF}}(r) \]

with

\[ E_{\mathrm{exp6}}(r) = \begin{cases} A\,e^{-Br} - \dfrac{C}{r^{6}} + D\left(\dfrac{12}{B\,r}\right)^{12} - E_{\mathrm{shift}} & r \le r_{\mathrm{exp6}} \\ 0 & r > r_{\mathrm{exp6}} \end{cases} \qquad E_{\mathrm{RF}}(r) = \begin{cases} \dfrac{q_i q_j}{4\pi\varepsilon_0}\left[\dfrac{1}{r} + k_{\mathrm{rf}} r^2 - C_{\mathrm{rf}}\right] & r \le r_{\mathrm{rf}} \\ 0 & r > r_{\mathrm{rf}} \end{cases} \]

\(E_{\mathrm{shift}}\) is the exponential-6 energy at \(r_{\mathrm{exp6}}\), so that this term is zero at its cutoff. \(k_{\mathrm{rf}}\) and \(C_{\mathrm{rf}}\) are defined on the reaction field page. The charges \(q_i\), \(q_j\) are the species charges.

Parameter	Units	Description
`exp6_rcut`	distance	Cutoff \(r_{\mathrm{exp6}}\) of the exponential-6 term (0 or missing disables it)
`exp6.A`	energy	Amplitude of the exponential repulsion
`exp6.B`	1/distance	Inverse range of the exponential
`exp6.C`	energy·distance\(^6\)	Dispersion coefficient
`exp6.D`	energy	Amplitude of the short-range wall
`rf.epsilon`	—	Dielectric constant of the surrounding continuum
`rf.rc`	distance	Cutoff \(r_{\mathrm{rf}}\) of the reaction field
`rcut`	distance	Cutoff radius of the pair potential, at least \(\max(r_{\mathrm{exp6}}, r_{\mathrm{rf}})\)

YAML syntax¶

exp6rf_compute_force:
  rcut: VALUE UNITS
  parameters:
    exp6_rcut: VALUE UNITS
    exp6: { A: VALUE UNITS , B: VALUE UNITS , C: VALUE UNITS , D: VALUE UNITS }
    rf: { epsilon: VALUE , rc: VALUE UNITS }

VALUE = Physical value of the intended parameter.
UNITS = Units of the provided value that will be passed to the conversion helper for internal units conversion.

Usage examples¶

Systems with a single atomic specy

# Default variant
exp6rf_compute_force:
  rcut: 12.5 ang
  parameters:
    exp6_rcut: 11.0 ang
    exp6: { A: 107023.9 Da*kcal/g , B: 3.6405 1/ang , C: 554.01 Da*kcal*ang^6/g , D: 5.0e-5 Da*kcal/g }
    rf: { epsilon: 100. , rc: 12.5 ang }

# Symetric variant
exp6rf_compute_force_symetric:
  rcut: 12.5 ang
  parameters:
    exp6_rcut: 11.0 ang
    exp6: { A: 107023.9 Da*kcal/g , B: 3.6405 1/ang , C: 554.01 Da*kcal*ang^6/g , D: 5.0e-5 Da*kcal/g }
    rf: { epsilon: 100. , rc: 12.5 ang }

Systems with multiple atomic species

exp6rf_multi_force:
  rcut: 12.5 ang
  common_parameters: { rf: { epsilon: 100. , rc: 12.5 ang } , exp6_rcut: 12.5 ang , exp6: { A: 37111.29 Da*kcal/g , B: 3.4635 1/ang , C: 484.30 Da*kcal*ang^6/g , D: 5.0e-5 Da*kcal/g } }
  parameters:
    - { type_a: C , type_b: C , rcut: 12.5 ang , parameters: { rf: { epsilon: 100. , rc: 12.5 ang } , exp6_rcut: 11.0 ang , exp6: { A: 107023.9 Da*kcal/g , B: 3.6405 1/ang , C: 554.01 Da*kcal*ang^6/g , D: 5.0e-5 Da*kcal/g } } }
    - { type_a: C , type_b: N , rcut: 12.5 ang , parameters: { rf: { epsilon: 100. , rc: 12.5 ang } , exp6_rcut: 12.5 ang , exp6: { A: 37111.29 Da*kcal/g , B: 3.4635 1/ang , C: 484.30 Da*kcal*ang^6/g , D: 5.0e-5 Da*kcal/g } } }