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extending our previous approach for bcc [14]. As a first step, we match the peak liquid structure factor properties of the two-mode PFC model to the standard expression from classical DFT. The expression for the PFC liquid structure factor is obtained by varying ψ around its liquid value, ψ = ¯ ψ$_{l}$ + δψ , and evaluating the corresponding variation Δ F of the dimensional free-energy difference between solid and liquid using Eqs. (2) and (4), and the relation (15) between φ and ψ . Dropping terms of δψ higher than quadratic order, we obtain 

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Substituting the Fourier transform, 

we obtain 

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A second expression for the free-energy of a spatially in- homogeneous liquid is obtained from classic DFT 

where 

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and 

is the Fourier transform of the direct correlation function. Fourier transforming again, we obtain 

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Equating Δ F PFC = Δ F DFT and using the expression for the liquid structure factor S ( k ) = 1 / (1 − C ( k )), we obtain 

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By evaluating the above expression at the peak of the liquid structure factor, we obtain 

or, using Eq. (11) and the relationship ¯ ψ$_{l}$ = ψ$_{c}$ϵ 1 / $^{2}$, 

A second relation is now needed to determine ϵ and λ independently. To obtain it, we substitute Eq. (58) into the relation C ( k ) = ( S ( k ) − 1) /S ( k ) and compute the second derivative of C ( k ) evaluated at the peak of the liquid structure factor to obtain 

Eqs. (60) and (61) combined now give 

and 

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In addition, the relation (55) between the real and di- mensionless densities expresses 

in terms of the solid amplitude A$_{s}$ of the first q$_{0}$ -mode. The two solid amplitudes A$_{s}$ and B$_{s}$ can be computed for a given R by using the scaling relations A$_{s}$ = ϵ 1 / $^{2}$A and B$_{s}$ = ϵ 1 / $^{2}$B where A and B are the equilibrium values of the scaled amplitudes in solid. The latter are obtained, together with ψ$_{c}$ (Fig. 9), by using the conditions (46) and (47) with Δ F AE defined by Eq. (45). 

For a given R , Eqs. (62), (63), and (64) fix the three parameters ϵ , λ , and g of the PFC model uniquely in terms of peak liquid structure factor properties, S ( q$_{0}$ ) and C ′′ ( q$_{0}$ ), where q$_{0}$ = | ⃗ K$_{111}$ | here, and the solid density wave amplitude u$_{s}$ = u$_{111}$ . This still leaves the freedom to vary R within the range where fcc is stable with re- spect to bcc (Fig. 9). Varying R changes the shape of the liquid structure factor as shown in Fig. 12 and de- creasing R below some threshold produces a second peak at q$_{1}$ = | ⃗ K$_{200}$ | , and generally increases the contribution of the second mode. Thus decreasing R increases the am- plitude of the second mode u$_{200}$ as shown in Fig. 11. For 

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