excel lambda functions

pair_potentials.txt

// Dispersion force Models
// See <https://arxiv.org/pdf/1910.05746.pdf>
// In these expressions, the unit of length is /sigma, the interparticle
// distance where the potential changes sign and the unit of energy is
// /epsilon, the well depth.
// 

/* Lennard-Jones Potential
Inputs:
    rs: separation
    sigma: interparticle distance where the potential changes sign
    epsilon: well depth
Return:
    The potential
*/
LJ = LAMBDA(rs, sigma_, epsilon_,
    4 * epsilon_ * ((sigma_ / rs) ^ 12 - (sigma_ / rs) ^ 6)
);
 
/* Coefficient that ensures the depth of the attractive well is -epsilon
Inputs:
    rs: separation
    sigma: interparticle distance where the potential changes sign
    epsilon: well depth
*/
alpha = LAMBDA(rc_, sigma_,
    2 * (rc_ / sigma_) ^ 2 *
        (3 / (2 * ((rc_ / sigma_) ^ 2 - 1))) ^ 3
);

rmin = LAMBDA(rc_, sigma_,
    rc_ * (3 / (1 + 2 * (rc_ / sigma_) ^ 2)) ^ 0.5
);

/* Alternative to LJ potential
Inputs:
    rs_: separation
    sigma_: interparticle distance where the potential changes sign
    epsilon_: well depth
    rc_: Cut off
Return:
    Modified potential with cutoff at rc_
*/
phi = LAMBDA(rs_, sigma_, epsilon_, rc_,
    LET(
        alpha_, alpha(rc_, sigma_),
        return_, epsilon_ * alpha_ *
            ((sigma_ / rs_) ^ 2 - 1) *
            ((rc_ / rs_) ^ 2 - 1) ^ 2,
        IF(rs_ <= rc_, return_, 0)
    )
);