ElectrostaticEnergetics.jl

import Base: +, *

# Vacuum permittivity eps0 = 8.854187817e-12 # C^2/(J-m)
# 1 m = 1e10 A, 1 e = 1.602176e-19 C, kb = 1.3806488e-23 J/K
# 8.854187817e-12 C^2/(J-m) [1 m / 1e10 A] [1 e / 1.602176e-19 C]^2 [kb = 1.3806488e-23 J/K]
const ϵ₀ = 8.854187817e-12 / (1.602176565e-19 ^ 2) / 1.0e10 * 1.3806488e-23  # \epsilon_0 vacuum permittivity units: electron charge^2 /(A - K)
const FOUR_π_ϵ₀ = 4.0 * π * ϵ₀

mutable struct EwaldSum
    sr::Float64 # short-range
    lr::Float64 # long-range
end
+(e1::EwaldSum, e2::EwaldSum) = EwaldSum(e1.sr + e2.sr, e1.lr + e2.lr)
*(a::Float64, ews::EwaldSum) = EwaldSum(a * ews.sr, a * ews.lr)
total(ews::EwaldSum) = ews.sr + ews.lr
EwaldSum() = EwaldSum(0.0, 0.0)

mutable struct GGEwaldSum # for guest-guest interactions
    sr::Float64 # short-range sum
    lr_excluding_own_images::Float64 # long-range sum, excluding contribution from own periodic images
    lr_own_images::Float64 # long-range sum, contribution from own periodic images only
    self::Float64 # spurious self-interaction
    intra::Float64 # intramolecular interactions
end
total(ews::GGEwaldSum) = ews.sr + ews.lr_excluding_own_images + ews.lr_own_images + ews.self + ews.intra
+(e1::GGEwaldSum, e2::GGEwaldSum) = GGEwaldSum(e1.sr                      + e2.sr,
                                               e1.lr_excluding_own_images + e2.lr_excluding_own_images,
                                               e1.lr_own_images           + e2.lr_own_images,
                                               e1.self                    + e2.self,
                                               e1.intra                   + e2.intra)
*(a::Float64, ews::GGEwaldSum) = GGEwaldSum(a * ews.sr,
                                            a * ews.lr_excluding_own_images,
                                            a * ews.lr_own_images,
                                            a * ews.self,
                                            a * ews.intra)
GGEwaldSum() = GGEwaldSum(0.0, 0.0, 0.0, 0.0, 0.0)

"""
Data structure for a k-vector replication, although the reciprocal lattice is needed to
specify the exact k-vector. This data structure stores the weight determining the
contribution of kvector (ka, kb, kc) (all Int's) to the Fourier component of the Ewald sum.
Precomputing this weight saves computation time. So Ewald sums work with an array of
`Kvecvtors`'s.
"""
struct Kvector
    ka::Int
    kb::Int
    kc::Int

    wt::Float64
end

"Data structure for storing Ewald summation settings"
struct EwaldParams
    "number of replications in k-space in a, b, c directions"
    kreps::Tuple{Int, Int, Int}
    "Ewald summation convergence parameter (units: inverse Å)"
    α::Float64
    "short-range cutoff radius (units: Å)"
    sr_cutoff_r::Float64
    "list of k-vectors and pre-computed weights in long-range sum"
    kvecs::Array{Kvector, 1}
end

function Base.print(io::IO, eparams::EwaldParams)
    @printf(io, "\tEwald summation parameters:\n")
    @printf(io, "\t\tk-replication factors: %d %d %d\n", eparams.kreps[1], eparams.kreps[2], eparams.kreps[3])
    @printf(io, "\t\tEwald convergence param. α = %f\n", eparams.α)
    @printf(io, "\t\tshort-range cutoff radius (Å): %f\n", eparams.sr_cutoff_r)
    @printf(io, "\t\t%d kvectors\n", length(eparams.kvecs))
end

# it is super important for speed to type-assert these in this complicated way.
# pre-allocate memory for e^{i k vec(k) ⋅ r}. Don't put these in EwaldParams for speed,
#  so they are passed as reference. These are OffsetArrays, which changes indexing scheme.
# different sizes for guest-guest and guest-host
"""
    eikr = Eikr(eikar, eikbr, eikcr)

mutable struct for holding the eikr vectors

# Attributes
- `eikar::OffsetArray{Complex{Float64}}`: array for storing e^{i * ka ⋅ r}; has indices
    0:kreps[1] and corresponds to recip. vectors in a-direction
- `eikbr::OffsetArray{Complex{Float64}}`: array for storing e^{i * kb ⋅ r}; has indices
    -kreps[2]:kreps[2] and corresponds to recip. vectors in b-direction
- `eikcr::OffsetArray{Complex{Float64}}`: array for storing e^{i * kc ⋅ r}; has indices
    -kreps[2]:kreps[1] and corresponds to recip. vectors in c-direction
"""
mutable struct Eikr
    eikar::OffsetArray{Complex{Float64}, 2, Array{Complex{Float64}, 2}}
    eikbr::OffsetArray{Complex{Float64}, 2, Array{Complex{Float64}, 2}}
    eikcr::OffsetArray{Complex{Float64}, 2, Array{Complex{Float64}, 2}}
end
Eikr(n_charges::Int, kreps::Tuple{Int, Int, Int}) = Eikr(
        OffsetArray{Complex{Float64}}(undef, 1:n_charges, 0:kreps[1]), # remove negative kreps[1] and take advantage of symmetry
        OffsetArray{Complex{Float64}}(undef, 1:n_charges, -kreps[2]:kreps[2]),
        OffsetArray{Complex{Float64}}(undef, 1:n_charges, -kreps[3]:kreps[3])
    )
Eikr(framework::Framework, eparams::EwaldParams) = Eikr(framework.charges.n_charges, eparams.kreps)
Eikr(molecule::Molecule, eparams::EwaldParams) = Eikr(molecule.charges.n_charges, eparams.kreps)

"""
    α, max_mag_k_sqrd = determine_ewald_params(sr_cutoff_r, ϵ)

Compute the Ewald summation convergence parameter α and the cutoff value for |k|² in the
reciprocal space.

# Arguments
- `sr_cutoff_r::Float64`: cutoff-radius (units: Å) for short-range contributions to Ewald
sum. This must be consistent with the number of replication factors used to apply the
nearest image convention, so typically this is chosen to be the same as for short-range
van-der Waals interactions.
- `ϵ::Float64`: desired level of precision. Typical value is 1e-6, but this does not
guarentee this precision technically since that depends on the charges in the system, but
it is very helpful to think of this as the weight on contributions near the edge of the
short-range cutoff radius or max |k|².

# Returns
- `α::Float64`: Ewald sum convergence parameter (units: inverse Å)
- `max_mag_k_sqrd::Float64`: cutoff for |k|², where k is a k-vector, in the Fourier sum.
"""
function determine_ewald_params(sr_cutoff_r::Float64, ϵ::Float64)
    # α is Ewald sum convergence parameter. It determines how fast the long- and short-
    #  range interactions decay with r in the Fourier and real space sum, respectively.
    #    erfc(α * r) / r dependence for short-range
    #    exp(-mag_k_squared / (4α²)) / mag_k_squared dependence for long-range
    #   as α increases, short-range contributions decays with r more quickly;
    #   thus need smaller sr_cutoff. but long-range decays more slowly with r with larger
    #   α. thus would need more kevectors.
    #      this approach is similar to DLPoly according to here:
    #       http://www.cse.scitech.ac.uk/ccg/software/DL_POLY_CLASSIC/FAQ/FAQ2.shtml
    # solve for α to allow short-range interactions to decay beyond the cutoff radius.
    sr_error(α) = erfc(sr_cutoff_r * α) / sr_cutoff_r - ϵ
    α = fzero(sr_error, 0.0, 25.0) # 25.0 should be safe bracket.
    # solve for the max squre norm of the k-vectors required to allow long-range
    #   interactions in Fourier space to decay beyond for k-vectors longer than this.
    lr_error(mag_k_sqrd) = 2 * exp(- mag_k_sqrd / (4.0 * α ^ 2)) / mag_k_sqrd - ϵ
    max_mag_k_sqrd = fzero(lr_error, 0.0, 100.0)
    return α, max_mag_k_sqrd
end

"""
    kreps = required_kreps(box, max_mag_k_sqrd)

Determine replications of k-vectors in Fourier sum, `kreps`, a Tuple of Ints, required to
assert all k-vectors with square magnitude less than |k|² (`max_mag_k_sqrd`) are included.

# Arguments
- `box::Box`: the simulation box containing the reciprocal lattice.
- `max_mag_k_sqrd::Float64`: cutoff value for |k|² in reciprocal space sum.

# Returns
- `kreps::Tuple{Int, Int, Int}`: number of k-vector replications required in a, b, c
directions.
"""
function required_kreps(box::Box, max_mag_k_sqrd::Float64)
    # fill in later
    kreps = [0, 0, 0]
    for abc = 1:3
        n = [0, 0, 0]
        while true
            n[abc] += 1
            # compute reciprocal vector, k. rows are the reciprocal lattice vectors
            k = transpose(box.reciprocal_lattice) * n
            # if we reached a k-vector with sq. mag. g.t. max_mag_k_sqrd...
            #   we have enough kreps
            if dot(k, k) > max_mag_k_sqrd
                kreps[abc] = n[abc] - 1
                break
            end
        end
    end
    return (kreps[1], kreps[2], kreps[3])
end

"""
    kvectors = precompute_kvec_wts(kreps, box, α, max_mag_k_sqrd=Inf)

For speed, pre-compute the weights for each reciprocal lattice vector for the Ewald sum in
Fourier space. This function takes advantage of the symmetry:
    cos(-k⋅(x-xᵢ)) + cos(k⋅(x-xᵢ)) = 2 cos(k⋅(x-xᵢ))

If `max_mag_k_sqrd` is passed, k-vectors with a magnitude greater than `max_mag_k_sqrd` are
not included.

# Arguments
- `kreps::Tuple{Int, Int, Int}`: number of k-vector replications required in a, b, c
- `box::Box`: the simulation box containing the reciprocal lattice.
- `α::Float64`: Ewald sum convergence parameter (units: inverse Å)
- `max_mag_k_sqrd::Float64`: cutoff for |k|² in Fourier sum; if passed, do not include
k-vectors with magnitude squared greater than this.

# Returns
- `kvectors::Array{Kvector, 1}`: array of k-vectors to include in the Fourier sum and their
corresponding weights indicating the contribution to the Fourier sum.
"""
function precompute_kvec_wts(kreps::Tuple{Int, Int, Int}, box::Box, α::Float64,
                             max_mag_k_sqrd::Float64=Inf)
    kvecs = Kvector[]
    # take advantage of symmetry. cos(k ⋅ dx) = cos( (-k) ⋅ dx)
    #   don't include both [ka kb kc] [-ka -kb -kc] for all kb, kc
    #   hence ka goes from 0:k_repfactors[1]
    for ka = 0:kreps[1], kb = -kreps[2]:kreps[2], kc=-kreps[3]:kreps[3]
        # don't include the home unit cell
        if (ka == 0) && (kb == 0) && (kc == 0)
            continue
        end
        # if ka == 0, don't include both [0 1 x] and [0 -1 -x]
        #  but need [0 1 x] [0 1 -x]
        if (ka == 0) && (kb < 0)
            continue
        end
        # don't include both [0 0 1] and [0 0 -1]
        if (ka == 0) && (kb == 0) && (kc < 0)
            continue
        end

        # compute reciprocal vector, k; rows are the reciprocal lattice vectors
        k = transpose(box.reciprocal_lattice) * [ka, kb, kc]
        # |k|²
        mag_k_sqrd = dot(k, k)

        # factor of 2 from cos(-k⋅(x-xᵢ)) + cos(k⋅(x-xᵢ)) = 2 cos(k⋅(x-xᵢ))
        #  and how we include ka>=0 only and the two if statements above
        if mag_k_sqrd < max_mag_k_sqrd
            wt = 2.0 * exp(-mag_k_sqrd / (4.0 * α ^ 2)) / mag_k_sqrd / ϵ₀ / box.Ω
            push!(kvecs, Kvector(ka, kb, kc, wt))
        end
    end
    return kvecs
end

"""
    eparams = setup_Ewald_sum(box, sr_cutoff_r; ϵ=1e-6, verbose=false)

Given the short-range cutoff radius and simulation box, automatically compute Ewald
convergence parameter and number of k-vector replications in Fourier space required for a
given precision. Constructs and returns Ewald parameters data type with this information.

Also, pre-compute weights on k-vector contributions to Ewald sum in Fourier space.

Also, allocate OffsetArrays for storing e^{i * k ⋅ r} where r = x - xⱼ and k is a reciprocal
lattice vector.

# Arguments
- `box::Box`: the simulation box containing the reciprocal lattice.
- `sr_cutoff_r::Float64`: cutoff-radius (units: Å) for short-range contributions to Ewald
- `ϵ::Float64`: desired level of precision. Typical value is 1e-6, but this does not
- `verbose::Bool`: If `true` will print results

# Returns
- `eparams::EwaldParams`: data structure containing Ewald summation settings
corresponding weights indicating the contribution to the Fourier sum.
"""
function setup_Ewald_sum(box::Box, sr_cutoff_r::Float64;
                         ϵ::Float64=1e-6, verbose::Bool=false)
    # determine Ewald convergence parameter and cutoff for |k|² for sum in Fourier space
    α, max_mag_k_sqrd = determine_ewald_params(sr_cutoff_r, ϵ)
    # determine kreps required to assert all k-vectors with magnitude less than |k|² are included.
    kreps = required_kreps(box, max_mag_k_sqrd)
    # pre-compute weights associated with each k-vector in sum in Fourier space.
    #  discards k-vector replications whose |k|² > max_mag_k_sqrd for efficiency.
    kvecs = precompute_kvec_wts(kreps, box, α, max_mag_k_sqrd)
    # construct Ewald parameters
    eparams = EwaldParams(kreps, α, sr_cutoff_r, kvecs)
    if verbose
        print(eparams)
        @printf("\t\t(calculated with specified precision %e)\n", ϵ)
    end
    return eparams
end

"""
    fill_eikr!(eikr, k_dot_dx, krep, include_neg_reps)

Given k ⋅ r, where r = x - xⱼ, compute e^{i n k ⋅ r} for n = 0:krep to fill the OffsetArray
`eikr`. If `include_neg_reps` is true, also compute n=-krep:-1.

columns of eikr correspond to different k's; rows are charges

# Arguments
- `eikr::OffsetArray{Complex{Float64}, 2, Array{Complex{Float64}, 2}}: An offset array containing charges, then kreps, then abc (direction)
- `k_dot_dc::Array{Float64, 1}`: k ⋅ r, where r = x - xⱼ
- `krep::Int`: number of k-vector replications required in a, b or c
- `include_neg_reps::Bool`: If `true` will include negative replications
"""
@inline function fill_eikr!(eikr::OffsetArray{Complex{Float64}, 2, Array{Complex{Float64}, 2}},
                            k_dot_dx::Array{Float64, 1}, krep::Int, incl_neg_reps::Bool)
    # explicitly compute for k = 1, k = 0
    @inbounds eikr[:, 0] .= exp(0.0 * im)
    @inbounds eikr[:, 1] .= exp.(im * k_dot_dx)
    # recursion relation for higher frequencies to avoid expensive computing of cosine.
    #  e^{3 * i * k_dot_r} = e^{2 * i * k_dot_r} * e^{ i * k_dot_r}
    for k = 2:krep
        @inbounds eikr[:, k] .= eikr[:, k - 1] .* eikr[:, 1]
    end
    # negative kreps are complex conjugate of positive ones.
    #  e^{2 * i * k_dot_r} = conj(e^{-2 * i * k_dot_dr})
    if incl_neg_reps
        for k = -krep:-1
            @inbounds eikr[:, k] .= conj.(eikr[:, -k])
        end
    end
    return nothing
end
"""
    ϕ = electrostatic_potential_energy(framework, molecule, eparams, eikr)


Compute the electrostatic potential energy of a molecule inside a framework.

The electrostatic potential is created by the point charges assigned to the framework
atoms in `framework.charges`. Periodic boundary conditions are applied through the Ewald
summation. The spurious self-interaction term is neglected here because we are looking at
*differences* in energy in a Monte Carlo simulation.

Warning: it is assumed that the framework is replicated enough such that the nearest
image convention can be applied for the short-range cutoff radius supplied in
`eparams.sr_cutoff_r`.

# Arguments
- `framework::Framework`: Crystal structure (see `framework.charges` for charges)
- `molecule::Molecule`: The molecule being compared to the atoms in the framework.
- `eparams::EwaldParams`: data structure containing Ewald summation settings
- `eikr::Eikr`: Stores the eikar, eikbr, and eikcr OffsetArrays used in this calculation.

# Returns
- `pot::EwaldSum`: Electrostatic potential between `framework` and `molecule` (units: K)
"""
function electrostatic_potential_energy(framework::Framework,
                                        molecule::Molecule,
                                        eparams::EwaldParams,
                                        eikr::Eikr)
    pot = EwaldSum()
    # loop over charges of the molecule
    for c = 1:molecule.charges.n_charges
        # compute electrostatic potential generated by framework at molecule's charge location
        @inbounds pot += molecule.charges.q[c] * _ϕ(framework.charges, molecule.charges.xf[:, c], eparams, framework.box, eikr)
    end
    return pot::EwaldSum
end

"""
Electrostatic potential at point x due to charges
"""
@inline function _ϕ(charges::Charges, xf::Array{Float64, 1}, eparams::EwaldParams, box::Box, eikr::Eikr)
    pot = EwaldSum()
    @inbounds dxf = broadcast(-, charges.xf, xf)

    ###
    #   Long-range sum
    ###
    @inbounds k_dot_dx = (box.reciprocal_lattice * box.f_to_c) * dxf # 3 by n_charges

    fill_eikr!(eikr.eikar, k_dot_dx[1, :], eparams.kreps[1], false)
    fill_eikr!(eikr.eikbr, k_dot_dx[2, :], eparams.kreps[2], true)
    fill_eikr!(eikr.eikcr, k_dot_dx[3, :], eparams.kreps[3], true)

    # loop over kevectors
    for kvec in eparams.kvecs
        kvec_pot = 0.0 # total ϕ arising from this k-vector. multiply by shared kvector weight later.
        # cos( i * this_k * r) = real part of:
        #     e^{i ka r * vec(ka)} *
        #     e^{i kb r * vec(kb)} *
        #     e^{i kb r * vec(kc)} where r = x - xᵢ
        #   and eikar[ka], eikbr[kb], eikcr[kc] contain exactly the above components.
        @simd for c = 1:charges.n_charges
            @inbounds kvec_pot += charges.q[c] * real(eikr.eikar[c, kvec.ka] * eikr.eikbr[c, kvec.kb] * eikr.eikcr[c, kvec.kc])
        end
        pot.lr += kvec.wt * kvec_pot
    end

    ###
    #   Short-range sum
    ###
    nearest_image!(dxf)
    dxf .= box.f_to_c * dxf
    dxf .= dxf .^ 2
    # convert to Cartesian coords
    for c = 1:charges.n_charges
        @fastmath @inbounds r = sqrt(dxf[1, c] + dxf[2, c] + dxf[3, c])
        if r < eparams.sr_cutoff_r
            @inbounds @fastmath pot.sr += charges.q[c] / r * erfc(r * eparams.α) / FOUR_π_ϵ₀
        end
    end
    return pot::EwaldSum
end

# spurious self-interaction in EWald sum
function _spurious_self_interaction_energy(molecule::Molecule, eparams::EwaldParams)
    return -eparams.α / sqrt(π) / FOUR_π_ϵ₀ * sum(molecule.charges.q .^ 2)
end

# intramolecular interaction (these are implicitly included in the reciprocal space terms)
# allows molecule to be split accross periodic boundary by applying nearest image convention
function _intramolecular_energy(molecule::Molecule, eparams::EwaldParams, box::Box)
    ϕ_intra = 0.0
    for i = 1:molecule.charges.n_charges
        for j = (i + 1):molecule.charges.n_charges
            dxf = molecule.charges.xf[:, i] - molecule.charges.xf[:, j]
            nearest_image!(dxf)
            dx = box.f_to_c * dxf
            r = sqrt(dx[1] * dx[1] + dx[2] * dx[2] + dx[3] * dx[3])
            ϕ_intra -= molecule.charges.q[i] * molecule.charges.q[j] * erf(eparams.α * r) / r
        end
    end
    return ϕ_intra / FOUR_π_ϵ₀
end

"""
    ϕ = electrostatic_potential_energy(molecules, eparams, box, eikr)

Compute the electrostatic potential energy of a system comprised of an array of `Molecule`s.

The EWald summation is used here in a double for loop; do not use this function for Monte
Carlo simulations because it is computationally expensive.

Returns an `EwaldSum` type containing short-range and long-range contributions to the Ewald
sum as well as the spurious self-interaction and intramolecular interactions. Access via
(ϕ.sr, ϕ.lr, ϕ.self, ϕ.intra).

Units of energy: Kelvin

# Arguments
- `molecules::Array{Molecules, 1}`: array of molecules comprising the system.
- `eparams::EwaldParams`: data structure containing Ewald summation settings
- `box::Box`: the box the energy is being computed in
- `eikr::Eikr`: Stores the eikar, eikbr, and eikcr OffsetArrays used in this calculation.

# Returns
- `ϕ::GGEwaldSum`: The total electrostatic potential energy
"""
function electrostatic_potential_energy(molecules::Array{Molecule, 1},
                                        eparams::EwaldParams, box::Box,
                                        eikr::Eikr)
    ϕ = GGEwaldSum()
    for i = 1:length(molecules)
        for j = 1:length(molecules)
            for c = 1:molecules[j].charges.n_charges
                # view here is that charges in molecules[i] create a potential field for charges in molecules[j]
                ϕ_with_i = molecules[j].charges.q[c] * _ϕ(molecules[i].charges,
                    molecules[j].charges.xf[:, c], eparams, box, eikr)
                ###
                #  Long-range contribution
                ###
                if i == j
                    ϕ.lr_own_images += ϕ_with_i.lr
                else
                    ϕ.lr_excluding_own_images += ϕ_with_i.lr
                end

                ###
                #  Short range contribution
                ###
                if i != j
                    ϕ.sr += ϕ_with_i.sr
                end
            end # charge c in molecule j
        end # molecule j
    end # molecule i
    ϕ.sr /= 2.0 # two to avoid double-counting
    ϕ.lr_excluding_own_images /= 2.0
    ϕ.lr_own_images /= 2.0

    for molecule in molecules
        ###
        #  Spurious self-interaction of point charge with Gaussian charge
        ###
        ϕ.self += _spurious_self_interaction_energy(molecule, eparams)

        ###
        #  Intramolecular interactions
        #    this function allows the molecule to be split apart across a periodic boundary
        ###
        ϕ.intra += _intramolecular_energy(molecule, eparams, box)
    end

    return ϕ::GGEwaldSum
end

# for use in MC simulations
# V(entire system (incl. molecule i)) - V(entire system (excl. molecule i))
function electrostatic_potential_energy(molecules::Array{Molecule, 1},
                                        molecule_id::Int,
                                        eparams::EwaldParams,
                                        box::Box,
                                        eikr::Eikr)
    ϕ = GGEwaldSum()
    for c = 1:molecules[molecule_id].charges.n_charges
        for other_molecule_id = 1:length(molecules)
            # view here is the molecules[other_molecule_id] creates potential field for
            #   charge cof molecules[molecule_id]
            ϕ_with_other_molecule_id = molecules[molecule_id].charges.q[c] * _ϕ(
                molecules[other_molecule_id].charges, molecules[molecule_id].charges.xf[:, c],
                eparams, box, eikr)

            if other_molecule_id != molecule_id
                ϕ.sr += ϕ_with_other_molecule_id.sr
                ϕ.lr_excluding_own_images += ϕ_with_other_molecule_id.lr
            else
                # yes, allow interaction with its own periodic image.
                ϕ.lr_own_images += 0.5 * ϕ_with_other_molecule_id.lr
            end
        end
    end

    # for insertions, need to include spurious self-interaction and intramolecular interaction
    #   as well as interactio with own periodic images
    ϕ.self += _spurious_self_interaction_energy(molecules[molecule_id], eparams)
    ϕ.intra += _intramolecular_energy(molecules[molecule_id], eparams, box)
    return ϕ::GGEwaldSum
end

# incremented
"""
    total_ϕ = total_electrostatic_potential_energy(molecules, eparams, box, eikr)


Calculates the total electrostatic potential energy of an array of `Molecule`s using a Grand Canonical Monte Carlo (GCMC) algorithm.
#TODO add to this

# Arguments
- `molecules::Array{Molecule, 1}`: The molecules comprising the system.
- `eparams::EwaldParams`: data structure containing Ewald summation settings
- `box::Box`: The box the energy is being computed in.
- `eikr::Eikr`: Stores the eikar, eikbr, and eikcr OffsetArrays used in this calculation.

# Returns
- `ϕ::GGEwaldSum`: The total electrostatic potential energy
"""
function total_electrostatic_potential_energy(molecules::Array{Molecule, 1},
                                              eparams::EwaldParams,
                                              box::Box,
                                              eikr::Eikr)
    ϕ = GGEwaldSum()
    for i = 1:length(molecules)
        ϕ += electrostatic_potential_energy(molecules, i, eparams, box, eikr)
    end
    ϕ.sr /= 2.0 # avoid double-counting
    ϕ.lr_excluding_own_images /= 2.0
    # intra, spurious self, and interaction with own periodic images are not divided by 2
    return ϕ::GGEwaldSum
end

"""
    total_ϕ = total_electrostatic_potential_energy(framework, molecules, eparams, eikr)


Explanation of total_electrostatic_potential_energy that uses framework

# Arguments
- `framework::Framework`: Crystal structure (see `framework.charges` for charges)
- `molecules::Array{Molecule, 1}`: The molecules comprising the system.
- `eparams::EwaldParams`: data structure containing Ewald summation settings
- `eikr::Eikr`: Stores the eikar, eikbr, and eikcr OffsetArrays used in this calculation.
"""
function total_electrostatic_potential_energy(framework::Framework,
                                              molecules::Array{Molecule, 1},
                                              eparams::EwaldParams,
                                              eikr::Eikr)
    ϕ = EwaldSum()
    for molecule in molecules
        ϕ += electrostatic_potential_energy(framework, molecule, eparams,
                                            eikr)
    end
    return ϕ::EwaldSum
end