E6: Analytical Linearized Poisson-Boltzmann (ALPB)

Module: sci_form::experimental::alpbFeature flag: experimental-alpb

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Overview

Implements the Klamt/Grimme Analytical Linearized Poisson-Boltzmann (ALPB) implicit solvation model. Computes solvation free energies $\mathrm{\Delta }{G}_{solv}$ with analytical gradients at negligible computational cost, enabling thermodynamically realistic conformer ranking in solution.

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Theory

Born Radii

Effective Born radii are computed using HCT (Hawkins-Cramer-Truhlar) integration enhanced with Onufriev-Bashford-Case (OBC) corrections:

$$\frac{1}{R_i^{eff}}=\frac{1}{{\rho }_i}-\frac{\tanh (\alpha {\mathrm{\Psi }}_i-\beta {\mathrm{\Psi }}_i^2+\gamma {\mathrm{\Psi }}_i^3)}{{\rho }_i}$$

with parameters $\alpha =1.0$, $\beta =0.8$, $\gamma =4.85$.

Generalized Born Kernel

$$f_{GB}(r_{ij},R_i,R_j)=\sqrt{r_{ij}^2+R_i{R}_j\exp (-\frac{r_{ij}^2}{4R_i{R}_j})}$$

ALPB Correction

The ALPB model improves standard GB with a universal correction:

$$E_{ALPB}=E_{GB}\cdot \frac{\epsilon -1}{\epsilon +A\cdot x}$$

where $A=0.571412$ (Klamt constant) and $x=E_{GB}/E_{Coulomb}$.

Non-Polar Contribution

$$\mathrm{\Delta }{G}_{np}={\gamma }_{SA}\cdot \text{SASA}$$

where ${\gamma }_{SA}$ is the surface tension parameter (default: 0.005 kcal/mol/Ų).

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API

use sci_form::experimental::alpb::*;

// Compute Born radii
let born = compute_born_radii(&elements, &positions);
// born.radii: Vec<f64>

// Full ALPB solvation
let config = AlpbConfig {
    dielectric: 78.5,     // water
    probe_radius: 1.4,    // Å
    surface_tension: 0.005,
    ..Default::default()
};
let result = compute_alpb_solvation(&elements, &positions, &charges, &config);
// result.electrostatic_energy: f64  (kcal/mol)
// result.nonpolar_energy: f64       (kcal/mol)
// result.total_energy: f64          (kcal/mol)
// result.born_radii: Vec<f64>

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Solvent Presets

Solvent	$\epsilon$
Water	78.5
DMSO	47.0
Methanol	32.7
Acetone	20.7
Chloroform	4.8
Vacuum	1.0

When $\epsilon =1.0$ (vacuum), the solvation energy is exactly zero — no division-by-zero issues.

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Comparison with Stable GB

Feature	Stable GB-HCT	ALPB
Born radii	HCT	HCT + OBC
Electrostatics	Standard GB	GB + ALPB correction
Universal constant	No	Yes ($A=0.571412$)
Non-polar	SASA-based	SASA-based
Solvent-specific fitting	No	No

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Tests

cargo test --features experimental-alpb --test regression -- test_alpb

8 integration tests covering: Born radii computation, GB kernel asymptotics, electrostatic solvation energy, vacuum limit (zero energy), solvent dielectric dependence, non-polar contributions, and total solvation energy.