saftvrmie.hpp

/***
 
 \brief This file contains the contributions that can be composed together to form SAFT models

*/

#pragma once

#include "nlohmann/json.hpp"
#include "teqp/types.hpp"
#include "teqp/exceptions.hpp"
#include "teqp/constants.hpp"
#include "teqp/math/quadrature.hpp"
#include <optional>

namespace teqp {
namespace SAFTVRMie {

/// Coefficients for one fluid
struct SAFTVRMieCoeffs {
    std::string name; ///< Name of fluid
    double m = -1, ///< number of segments
        sigma_m = -1, ///< [m] segment diameter
        epsilon_over_k = -1, ///< [K] depth of pair potential divided by Boltzman constant
        lambda_a = -1, ///< The attractive exponent (the 6 in LJ 12-6 potential)
        lambda_r = -1; ///< The repulsive exponent (the 12 in LJ 12-6 potential)
    std::string BibTeXKey; ///< The BibTeXKey for the reference for these coefficients
};

/// Manager class for SAFT-VR-Mie coefficients
class SAFTVRMieLibrary {
    std::map<std::string, SAFTVRMieCoeffs> coeffs;
public:
    SAFTVRMieLibrary() {
        insert_normal_fluid("Methane", 1.0000, 3.7412e-10, 153.36, 12.650, 6, "Lafitte-JCP-2001");
        insert_normal_fluid("Ethane", 1.4373, 3.7257e-10, 206.12, 12.400, 6, "Lafitte-JCP-2001");
        insert_normal_fluid("Propane", 1.6845, 3.9056e-10, 239.89, 13.006, 6, "Lafitte-JCP-2001");
    }
    void insert_normal_fluid(const std::string& name, double m, const double sigma_m, const double epsilon_over_k, const double lambda_a, const double lambda_r, const std::string& BibTeXKey) {
        SAFTVRMieCoeffs coeff;
        coeff.name = name;
        coeff.m = m;
        coeff.sigma_m = sigma_m;
        coeff.epsilon_over_k = epsilon_over_k;
        coeff.lambda_r = lambda_r;
        coeff.lambda_a = lambda_a;
        coeff.BibTeXKey = BibTeXKey;
        coeffs.insert(std::pair<std::string, SAFTVRMieCoeffs>(name, coeff));
    }
    const auto& get_normal_fluid(const std::string& name) {
        auto it = coeffs.find(name);
        if (it != coeffs.end()) {
            return it->second;
        }
        else {
            throw std::invalid_argument("Bad name:" + name);
        }
    }
    auto get_coeffs(const std::vector<std::string>& names){
        std::vector<SAFTVRMieCoeffs> c;
        for (auto n : names){
            c.push_back(get_normal_fluid(n));
        }
        return c;
    }
};

/// Things that only depend on the components themselves, but not on composition, temperature, or density
struct SAFTVRMieChainContributionTerms{
    private:
    
    /// The matrix of coefficients needed to evaluate f_k
    const Eigen::Matrix<double, 7, 7> phi{(Eigen::Matrix<double, 7, 7>() <<
        7.5365557, -359.44,  1550.9, -1.19932,  -1911.28,    9236.9,   10,
        -37.60463, 1825.6,   -5070.1, 9.063632,  21390.175, -129430,   10,
        71.745953, -3168.0,  6534.6, -17.9482,  -51320.7,    357230,   0.57,
        -46.83552, 1884.2,   -3288.7, 11.34027,  37064.54,   -315530,   -6.7,
        -2.467982, -0.82376, -2.7171, 20.52142,  1103.742,    1390.2,   -8,
        -0.50272,  -3.1935,  2.0883, -56.6377,  -3264.61,    -4518.2,   0,
        8.0956883, 3.7090,   0,       40.53683,  2556.181,    4241.6,   0 ).finished()};
    
    /// The matrix used to obtain the parameters c_1, c_2, c_3, and c_4 in Eq. A18
    const Eigen::Matrix<double, 4, 4> A{(Eigen::Matrix<double, 4, 4>() <<
         0.81096,  1.7888, -37.578,  92.284,
         1.0205,  -19.341,  151.26, -463.50,
         -1.9057, 22.845,  -228.14,  973.92,
         1.0885,  -6.1962,  106.98, -677.64).finished()};

    // Eq. A48
    auto get_lambda_k_ij(const Eigen::ArrayXd& lambda_k) const{
        Eigen::ArrayXXd mat(N,N);
        for (auto i = 0; i < lambda_k.size(); ++i){
            for (auto j = i; j < lambda_k.size(); ++j){
                mat(i,j) = 3 + sqrt((lambda_k(i)-3)*(lambda_k(j)-3));
                mat(j,i) = mat(i,j);
            }
        }
        return mat;
    }

    /// Eq. A3
    auto get_C_ij() const{
        Eigen::ArrayXXd C(N,N);
        for (auto i = 0; i < N; ++i){
            for (auto j = i; j < N; ++j){
                C(i,j) = lambda_r_ij(i,j)/(lambda_r_ij(i,j)-lambda_a_ij(i,j))*pow(lambda_r_ij(i,j)/lambda_a_ij(i,j), lambda_a_ij(i,j)/(lambda_r_ij(i,j)-lambda_a_ij(i,j)));
                C(j,i) = C(i,j); // symmetric
            }
        }
        return C;
    }
    
    // Eq. A26
    auto get_fkij() const{
        std::vector<Eigen::ArrayXXd> f_(8); // 0-th element is present, but not initialized
        for (auto k = 1; k < 8; ++k){
            f_[k].resize(N,N);
        };
        for (auto k = 1; k < 8; ++k){
            auto phik = phi.col(k-1); // phi matrix is indexed to start at 1, but our matrix starts at 0
            Eigen::ArrayXXd num(N,N), den(N,N); num.setZero(), den.setZero();
            for (auto n = 0; n < 4; ++n){
                num += phik[n]*pow(alpha_ij, n);
            }
            for (auto n = 4; n < 7; ++n){
                den += phik[n]*pow(alpha_ij, n-3);
            }
            f_[k] = num/(1 + den);
        }
        return f_;
    }
    
    /// Eq. A45
    auto get_sigma_ij() const{
        Eigen::ArrayXXd sigma(N,N);
        for (auto i = 0; i < N; ++i){
            for (auto j = i; j < N; ++j){
                sigma(i,j) = (sigma_A(i) + sigma_A(j))/2.0;
                sigma(j,i) = sigma(i,j); // symmetric
            }
        }
        return sigma;
    }
    /// Eq. A55
    auto get_epsilon_ij() const{
        Eigen::ArrayXXd eps_(N,N);
        for (auto i = 0; i < N; ++i){
            for (auto j = i; j < N; ++j){
                eps_(i,j) = (1.0-kmat(i,j))*sqrt(pow(sigma_ij(i,i),3)*pow(sigma_ij(j,j),3)*epsilon_over_k(i)*epsilon_over_k(j))/pow(sigma_ij(i,j), 3);
                eps_(j,i) = eps_(i,j); // symmetric
            }
        }
        return eps_;
    }
    std::size_t get_N(){
        auto sizes = (Eigen::ArrayXd(5) << m.size(), epsilon_over_k.size(), sigma_A.size(), lambda_a.size(), lambda_r.size()).finished();
        if (sizes.mean() != sizes.minCoeff()){
            throw teqp::InvalidArgument("sizes of pure component arrays are not all the same");
        }
        return sizes[0];
    }

    /// Eq. A18 for the attractive exponents
    auto get_cij(const Eigen::ArrayXXd& lambdaij) const{
        std::vector<Eigen::ArrayXXd> cij(4);
        for (auto n = 0; n < 4; ++n){
            cij[n].resize(N,N);
        };
        for (auto i = 0; i < N; ++i){
            for (auto j = i; j < N; ++j){
                using CV = Eigen::Vector<double, 4>;
                const CV b{(CV() << 1, 1.0/lambdaij(i,j), 1.0/pow(lambdaij(i,j),2), 1.0/pow(lambdaij(i,j),3)).finished()};
                auto c1234 = (A*b).eval();
                cij[0](i,j) = c1234(0);
                cij[1](i,j) = c1234(1);
                cij[2](i,j) = c1234(2);
                cij[3](i,j) = c1234(3);
            }
        }
        return cij;
    }
        
    /// Eq. A18 for the attractive exponents
    auto get_canij() const{
        return get_cij(lambda_a_ij);
    }
    /// Eq. A18 for 2x the attractive exponents
    auto get_c2anij() const{
        return get_cij(2.0*lambda_a_ij);
    }
    /// Eq. A18 for the repulsive exponents
    auto get_crnij() const{
        return get_cij(lambda_r_ij);
    }
    /// Eq. A18 for the 2x the repulsive exponents
    auto get_c2rnij() const{
        return get_cij(2.0*lambda_r_ij);
    }
    /// Eq. A18 for the 2x the repulsive exponents
    auto get_carnij() const{
        return get_cij(lambda_r_ij + lambda_a_ij);
    }
    
    template<typename X>
    auto POW2(const X& x) const{
        return forceeval(x*x);
    };
    template<typename X>
    auto POW3(const X& x) const{
        return forceeval(x*POW2(x));
    };
    template<typename X>
    auto POW4(const X& x) const{
        return forceeval(POW2(x)*POW2(x));
    };
    
    public:
    
    // One entry per component
    const Eigen::ArrayXd m, epsilon_over_k, sigma_A, lambda_a, lambda_r;
    const Eigen::ArrayXXd kmat;

    const std::size_t N;

    // Calculated matrices for the ij pair
    const Eigen::ArrayXXd lambda_r_ij, lambda_a_ij, C_ij, alpha_ij, sigma_ij, epsilon_ij; // Matrices of parameters

    const std::vector<Eigen::ArrayXXd> canij, crnij, c2anij, c2rnij, carnij;
    const std::vector<Eigen::ArrayXXd> fkij; // Matrices of parameters

    SAFTVRMieChainContributionTerms(
            const Eigen::ArrayXd& m,
            const Eigen::ArrayXd& epsilon_over_k,
            const Eigen::ArrayXd& sigma_m,
            const Eigen::ArrayXd& lambda_r,
            const Eigen::ArrayXd& lambda_a,
            const Eigen::ArrayXXd& kmat)
    :   m(m), epsilon_over_k(epsilon_over_k), sigma_A(sigma_m*1e10), lambda_a(lambda_a), lambda_r(lambda_r), kmat(kmat),
        N(get_N()),
        lambda_r_ij(get_lambda_k_ij(lambda_r)), lambda_a_ij(get_lambda_k_ij(lambda_a)),
        C_ij(get_C_ij()), alpha_ij(C_ij*(1/(lambda_a_ij-3) - 1/(lambda_r_ij-3))),
        sigma_ij(get_sigma_ij()), epsilon_ij(get_epsilon_ij()),
        crnij(get_crnij()), canij(get_canij()),
        c2rnij(get_c2rnij()), c2anij(get_c2anij()), carnij(get_carnij()),
        fkij(get_fkij())
    {}
    
    /// Eq. A2 from Lafitte
    double get_uii_over_kB(std::size_t i, const double& r) const {
        double rstarinv = sigma_A[i]/r;
        return forceeval(C_ij(i,i)*epsilon_over_k[i]*(::pow(rstarinv, lambda_r[i]) - ::pow(rstarinv, lambda_a[i])));
    }
    
    /// Eq. A9 from Lafitte
    template <typename TType>
    TType get_dii(std::size_t i, const TType &T) const{
        std::function<TType(double)> integrand = [this, i, &T](const double& r){
            return forceeval(1.0-exp(-this->get_uii_over_kB(i, r)/T));
        };
        return quad<30, TType>(integrand, 0.0, sigma_A[i]);
    }
    
    template <typename TType>
    auto get_dmat(const TType &T) const{
        Eigen::Array<TType, Eigen::Dynamic, Eigen::Dynamic> d(N,N);
        // For the pure components, by integration
        for (auto i = 0; i < N; ++i){
            d(i,i) = get_dii(i, T);
        }
        // The cross terms, using the linear mixing rule
        for (auto i = 0; i < N; ++i){
            for (auto j = i+1; j < N; ++j){
                d(i,j) = (d(i,i) + d(j,j))/2.0;
                d(j,i) = d(i,j);
            }
        }
        return d;
    }
    // Calculate core parameters that depend on temperature, volume, and composition
    template <typename TType, typename RhoType, typename VecType>
    auto get_core_calcs(const TType& T, const RhoType& rhomolar, const VecType& molefracs) const{
        
        if (molefracs.size() != N){
            throw teqp::InvalidArgument("Length of molefracs of "+std::to_string(molefracs.size()) + " does not match the model size of"+std::to_string(N));
        }
        
        using FracType = std::decay_t<decltype(molefracs[0])>;
        using NumType = std::common_type_t<TType, RhoType, FracType>;
        
        // Things that are easy to calculate
        // ....
        
        auto dmat = get_dmat(T); // Matrix of diameters of pure and cross terms
        auto rhoN = forceeval(rhomolar*N_A); // Number density, in molecules/m^3
        auto mbar = forceeval((molefracs*m).sum()); // Mean number of segments, dimensionless
        auto rhos = forceeval(rhoN*mbar/1e30); // Mean segment number density, in segments/A^3
        auto xs = forceeval((m*molefracs/mbar).eval()); // Segment fractions
        
        constexpr double MY_PI = static_cast<double>(EIGEN_PI);
        auto pi6 = MY_PI/6;
        
        using TRHOType = std::common_type_t<std::decay_t<TType>, std::decay_t<RhoType>, std::decay_t<decltype(molefracs[0])>, std::decay_t<decltype(m[0])>>;
        Eigen::Array<TRHOType, 4, 1> zeta;
        for (auto l = 0; l < 4; ++l){
            TRHOType summer = 0.0;
            for (auto i = 0; i < N; ++i){
                summer += xs(i)*powi(dmat(i,i), l);
            }
            zeta(l) = forceeval(pi6*rhos*summer);
        }
        
        NumType summer_zeta_x = 0.0;
        TRHOType summer_zeta_x_bar = 0.0;
        for (auto i = 0; i < N; ++i){
            for (auto j = 0; j < N; ++j){
                summer_zeta_x += xs(i)*xs(j)*powi(dmat(i,j), 3)*rhos;
                summer_zeta_x_bar += xs(i)*xs(j)*powi(sigma_ij(i,j), 3);
            }
        }
        
        auto zeta_x = forceeval(pi6*summer_zeta_x); // Eq. A13
        auto zeta_x_bar = forceeval(pi6*rhos*summer_zeta_x_bar); // Eq. A23
        auto zeta_x_bar5 = forceeval(POW2(zeta_x_bar)*POW3(zeta_x_bar)); // (zeta_x_bar)^5
        auto zeta_x_bar8 = forceeval(zeta_x_bar5*POW3(zeta_x_bar)); // (zeta_x_bar)^8
        
        // Coefficients in the gdHSij term, do not depend on component,
        // so calculate them here
        auto X = forceeval(POW3(1.0 - zeta_x)), X3 = X;
        auto X2 = forceeval(POW2(1.0 - zeta_x));
        auto k0 = forceeval(-log(1.0-zeta_x) + (42.0*zeta_x - 39.0*POW2(zeta_x) + 9.0*POW3(zeta_x) - 2.0*POW4(zeta_x))/(6.0*X3)); // Eq. A30
        auto k1 = forceeval((POW4(zeta_x) + 6.0*POW2(zeta_x) - 12.0*zeta_x)/(2.0*X3));
        auto k2 = forceeval(-3.0*POW2(zeta_x)/(8.0*X2));
        auto k3 = forceeval((-POW4(zeta_x) + 3.0*POW2(zeta_x) + 3.0*zeta_x)/(6.0*X3));
        
        // Pre-calculate the cubes of the diameters
        auto dmat3 = dmat.array().pow(3).eval();
        
        NumType a1kB = 0.0;
        NumType a2kB2 = 0.0;
        NumType a3kB3 = 0.0;
        NumType alphar_chain = 0.0;
        
        NumType K_HS = get_KHS(zeta_x);
        NumType rho_dK_HS_drho = get_rhos_dK_HS_drhos(zeta_x);
        
        for (auto i = 0; i < N; ++i){
            for (auto j = i; j < N; ++j){
                NumType x_0_ij = sigma_ij(i,j)/dmat(i, j);
                
                // -----------------------
                // Calculations for a_1/kB
                // -----------------------
                
                auto I = [&x_0_ij](double lambda_ij){
                    return forceeval(-(pow(x_0_ij, 3-lambda_ij)-1.0)/(lambda_ij-3.0)); // Eq. A14
                };
                auto J = [&x_0_ij](double lambda_ij){
                    return forceeval(-(pow(x_0_ij, 4-lambda_ij)*(lambda_ij-3.0)-pow(x_0_ij, 3.0-lambda_ij)*(lambda_ij-4.0)-1.0)/((lambda_ij-3.0)*(lambda_ij-4.0))); // Eq. A15
                };
                auto Bhatij_a = this->get_Bhatij(zeta_x, X, I(lambda_a_ij(i,j)), J(lambda_a_ij(i,j)));
                auto Bhatij_2a = this->get_Bhatij(zeta_x, X, I(2*lambda_a_ij(i,j)), J(2*lambda_a_ij(i,j)));
                auto Bhatij_r = this->get_Bhatij(zeta_x, X, I(lambda_r_ij(i,j)), J(lambda_r_ij(i,j)));
                auto Bhatij_2r = this->get_Bhatij(zeta_x, X, I(2*lambda_r_ij(i,j)), J(2*lambda_r_ij(i,j)));
                auto Bhatij_ar = this->get_Bhatij(zeta_x, X, I(lambda_a_ij(i,j)+lambda_r_ij(i,j)), J(lambda_a_ij(i,j)+lambda_r_ij(i,j)));
                                                 
                auto one_term =  [this, &x_0_ij, &I, &J, &zeta_x, &X](double lambda_ij, const NumType& zeta_x_eff){
                    return forceeval(
                       pow(x_0_ij, lambda_ij)*(
                         this->get_Bhatij(zeta_x, X, I(lambda_ij), J(lambda_ij))
                       + this->get_a1Shatij(zeta_x_eff, lambda_ij)
                       )
                     );
                };
                NumType zeta_x_eff_r = crnij[0](i,j)*zeta_x + crnij[1](i,j)*POW2(zeta_x) + crnij[2](i,j)*POW3(zeta_x) + crnij[3](i,j)*POW4(zeta_x);
                NumType zeta_x_eff_a = canij[0](i,j)*zeta_x + canij[1](i,j)*POW2(zeta_x) + canij[2](i,j)*POW3(zeta_x) + canij[3](i,j)*POW4(zeta_x);
                NumType dzeta_x_eff_dzetax_r = crnij[0](i,j) + crnij[1](i,j)*2*zeta_x + crnij[2](i,j)*3*POW2(zeta_x) + crnij[3](i,j)*4*POW3(zeta_x);
                NumType dzeta_x_eff_dzetax_a = canij[0](i,j) + canij[1](i,j)*2*zeta_x + canij[2](i,j)*3*POW2(zeta_x) + canij[3](i,j)*4*POW3(zeta_x);

                NumType a1ij = 2.0*MY_PI*rhos*dmat3(i,j)*epsilon_ij(i,j)*C_ij(i,j)*(
                    one_term(lambda_a_ij(i,j), zeta_x_eff_a) - one_term(lambda_r_ij(i,j), zeta_x_eff_r)
                ); // divided by k_B
                                    
                NumType contribution = xs(i)*xs(j)*a1ij;
                double factor = (i == j) ? 1.0 : 2.0; // Off-diagonal terms contribute twice
                a1kB += contribution*factor;
                
                // --------------------------
                // Calculations for a_2/k_B^2
                // --------------------------
                
                NumType zeta_x_eff_2r = c2rnij[0](i,j)*zeta_x + c2rnij[1](i,j)*POW2(zeta_x) + c2rnij[2](i,j)*POW3(zeta_x) + c2rnij[3](i,j)*POW4(zeta_x);
                NumType zeta_x_eff_2a = c2anij[0](i,j)*zeta_x + c2anij[1](i,j)*POW2(zeta_x) + c2anij[2](i,j)*POW3(zeta_x) + c2anij[3](i,j)*POW4(zeta_x);
                NumType zeta_x_eff_ar = carnij[0](i,j)*zeta_x + carnij[1](i,j)*POW2(zeta_x) + carnij[2](i,j)*POW3(zeta_x) + carnij[3](i,j)*POW4(zeta_x);
                NumType dzeta_x_eff_dzetax_2r = c2rnij[0](i,j) + c2rnij[1](i,j)*2*zeta_x + c2rnij[2](i,j)*3*POW2(zeta_x) + c2rnij[3](i,j)*4*POW3(zeta_x);
                NumType dzeta_x_eff_dzetax_ar = carnij[0](i,j) + carnij[1](i,j)*2*zeta_x + carnij[2](i,j)*3*POW2(zeta_x) + carnij[3](i,j)*4*POW3(zeta_x);
                NumType dzeta_x_eff_dzetax_2a = c2anij[0](i,j) + c2anij[1](i,j)*2*zeta_x + c2anij[2](i,j)*3*POW2(zeta_x) + c2anij[3](i,j)*4*POW3(zeta_x);
                
                NumType chi_ij = fkij[1](i,j)*zeta_x_bar + fkij[2](i,j)*zeta_x_bar5 + fkij[3](i,j)*zeta_x_bar8;
                auto a2ij = 0.5*K_HS*(1.0+chi_ij)*epsilon_ij(i,j)*POW2(C_ij(i,j))*(2*MY_PI*rhos*dmat3(i,j)*epsilon_ij(i,j))*(
                     one_term(2.0*lambda_a_ij(i,j), zeta_x_eff_2a)
                  -2.0*one_term(lambda_a_ij(i,j)+lambda_r_ij(i,j), zeta_x_eff_ar)
                    +one_term(2.0*lambda_r_ij(i,j), zeta_x_eff_2r)
                ); // divided by k_B^2
                                    
                NumType contributiona2 = xs(i)*xs(j)*a2ij; // Eq. A19
                a2kB2 += contributiona2*factor;
                
                // --------------------------
                // Calculations for a_3/k_B^3
                // --------------------------
                auto a3ij = -POW3(epsilon_ij(i,j))*fkij[4](i,j)*zeta_x_bar*exp(
                     fkij[5](i,j)*zeta_x_bar + fkij[6](i,j)*POW2(zeta_x_bar)
                ); // divided by k_B^3
                NumType contributiona3 = xs(i)*xs(j)*a3ij; // Eq. A25
                a3kB3 += contributiona3*factor;
                
                if (i == j){
                    // ------------------
                    // Chain contribution
                    // ------------------
                    
                    // Eq. A29
                    auto gdHSii = exp(k0 + k1*x_0_ij + k2*POW2(x_0_ij) + k3*POW3(x_0_ij));
                    
                    // The g1 terms
                    // ....
                    
                    // This is the function for the second part (not the partial) that goes in g_{1,ii},
                    // divided by 2*PI*d_ij^3*epsilon*rhos
                    auto g1_term = [&one_term](double lambda_ij, const NumType& zeta_x_eff){
                        return forceeval(lambda_ij*one_term(lambda_ij, zeta_x_eff));
                    };
                    auto g1_noderivterm = -C_ij(i,i)*(g1_term(lambda_a_ij(i,i), zeta_x_eff_a)-g1_term(lambda_r_ij(i,i), zeta_x_eff_r));
                    
                    // Bhat = B*rho*kappa; diff(Bhat, rho) = Bhat + rho*dBhat/drho; kappa = 2*pi*eps*d^3
                    // This is the function for the partial derivative rhos*(da1ij/drhos),
                    // divided by 2*PI*d_ij^3*epsilon*rhos
                    auto rhosda1iidrhos_term = [this, &x_0_ij, &I, &J, &zeta_x, &X](double lambda_ij, const NumType& zeta_x_eff, const NumType& dzetaxeff_dzetax, const NumType& Bhatij){
                        auto I_ = I(lambda_ij);
                        auto J_ = J(lambda_ij);
                        auto rhosda1Sdrhos = this->get_rhoda1Shatijdrho(zeta_x, zeta_x_eff, dzetaxeff_dzetax, lambda_ij);
                        auto rhosdBdrhos = this->get_rhodBijdrho(zeta_x, X, I_, J_, Bhatij);
                        return forceeval(pow(x_0_ij, lambda_ij)*(rhosda1Sdrhos + rhosdBdrhos));
                    };
                    // This is rhos*d(a_1ij)/drhos/(2*pi*d^3*eps*rhos)
                    auto da1iidrhos_term = C_ij(i,j)*(
                         rhosda1iidrhos_term(lambda_a_ij(i,i), zeta_x_eff_a, dzeta_x_eff_dzetax_a, Bhatij_a)
                        -rhosda1iidrhos_term(lambda_r_ij(i,i), zeta_x_eff_r, dzeta_x_eff_dzetax_r, Bhatij_r)
                    );
                    auto g1ii = 3.0*da1iidrhos_term + g1_noderivterm;
                    
                    // The g2 terms
                    // ....
                    
                    // This is the second part (not the partial deriv.) that goes in g_{2,ii},
                    // divided by 2*PI*d_ij^3*epsilon*rhos
                    auto g2_noderivterm = -POW2(C_ij(i,i))*K_HS*(
                       lambda_a_ij(i,j)*one_term(2*lambda_a_ij(i,j), zeta_x_eff_2a)
                       -(lambda_a_ij(i,j)+lambda_r_ij(i,j))*one_term(lambda_a_ij(i,j)+lambda_r_ij(i,j), zeta_x_eff_ar)
                       +lambda_r_ij(i,j)*one_term(2*lambda_r_ij(i,j), zeta_x_eff_2r)
                    );
                    // This is [rhos*d(a_2ij/(1+chi_ij))/drhos]/(2*pi*d^3*eps*rhos)
                    auto da2iidrhos_term = 0.5*POW2(C_ij(i,j))*(
                        rho_dK_HS_drho*(
                            one_term(2.0*lambda_a_ij(i,j), zeta_x_eff_2a)
                            -2.0*one_term(lambda_a_ij(i,j)+lambda_r_ij(i,j), zeta_x_eff_ar)
                            +one_term(2.0*lambda_r_ij(i,j), zeta_x_eff_2r))
                        +K_HS*(
                            rhosda1iidrhos_term(2.0*lambda_a_ij(i,i), zeta_x_eff_2a, dzeta_x_eff_dzetax_2a, Bhatij_2a)
                            -2.0*rhosda1iidrhos_term(lambda_a_ij(i,i)+lambda_r_ij(i,i), zeta_x_eff_ar, dzeta_x_eff_dzetax_ar, Bhatij_ar)
                            +rhosda1iidrhos_term(2.0*lambda_r_ij(i,i), zeta_x_eff_2r, dzeta_x_eff_dzetax_2r, Bhatij_2r)
                            )
                        );
                    auto g2MCAij = 3.0*da2iidrhos_term + g2_noderivterm;
                    
                    auto betaepsilon = epsilon_ij(i,i)/T; // (1/(kB*T))/epsilon
                    auto theta = exp(betaepsilon)-1.0;
                    auto phi7 = phi.col(6);
                    auto gamma_cij = phi7(0)*(-tanh(phi7(1)*(phi7(2)-alpha_ij(i,j)))+1.0)*zeta_x_bar*theta*exp(phi7(3)*zeta_x_bar + phi7(4)*POW2(zeta_x_bar)); // Eq. A37
                    auto g2ii = (1.0+gamma_cij)*g2MCAij;
                    
                    NumType giiMie = gdHSii*exp((betaepsilon*g1ii + POW2(betaepsilon)*g2ii)/gdHSii);
                    alphar_chain -= molefracs[i]*(m[i]-1.0)*log(giiMie);
                }
            }
        }
        
        auto ahs = get_a_HS(rhos, zeta);
        // Eq. A5 from Lafitte, multiplied by mbar
        auto alphar_mono = forceeval(mbar*(ahs + a1kB/T + a2kB2/(T*T) + a3kB3/(T*T*T)));
        
        using dmat_t = decltype(dmat);
        using rhos_t = decltype(rhos);
        using rhoN_t = decltype(rhoN);
        using mbar_t = decltype(mbar);
        using xs_t = decltype(xs);
        using zeta_t = decltype(zeta);
        using zeta_x_t = decltype(zeta_x);
        using zeta_x_bar_t = decltype(zeta_x_bar);
        using alphar_mono_t = decltype(alphar_mono);
        using a1kB_t = decltype(a1kB);
        using a2kB2_t = decltype(a2kB2);
        using a3kB3_t = decltype(a3kB3);
        using alphar_chain_t = decltype(alphar_chain);
        struct vals{
            dmat_t dmat;
            rhos_t rhos;
            rhoN_t rhoN;
            mbar_t mbar;
            xs_t xs;
            zeta_t zeta;
            zeta_x_t zeta_x;
            zeta_x_bar_t zeta_x_bar;
            alphar_mono_t alphar_mono;
            a1kB_t a1kB;
            a2kB2_t a2kB2;
            a3kB3_t a3kB3;
            alphar_chain_t alphar_chain;
        };
        return vals{dmat, rhos, rhoN, mbar, xs, zeta, zeta_x, zeta_x_bar, alphar_mono, a1kB, a2kB2, a3kB3, alphar_chain};
    }
    
    /// Eq. A21 from Lafitte
    template<typename RhoType>
    auto get_KHS(const RhoType& pf) const {
        return forceeval(pow(1.0-pf,4)/(1.0 + 4.0*pf + 4.0*pf*pf - 4.0*pf*pf*pf + pf*pf*pf*pf));
    }
    
    /**
     \f[
      \rho_s\frac{\partial K_{HS}}{\partial \rho_s} = \zeta\frac{\partial K_{HS}}{\partial \zeta}
     \f]
     */
    template<typename RhoType>
    auto get_rhos_dK_HS_drhos(const RhoType& zeta_x) const {
        auto num = -4.0*POW3(zeta_x - 1.0)*(POW2(zeta_x) - 5.0*zeta_x - 2.0);
        auto den = POW2(POW4(zeta_x) - 4.0*POW3(zeta_x) + 4.0*POW2(zeta_x) + 4.0*zeta_x + 1.0);
        return forceeval(num/den*zeta_x);
    }
    
    /// Eq. A6 from Lafitte, accounting for the case of rho_s=0, for which the limit is zero
    template<typename RhoType, typename ZetaType>
    auto get_a_HS(const RhoType& rhos, const Eigen::Array<ZetaType, 4, 1>& zeta) const{
        constexpr double MY_PI = static_cast<double>(EIGEN_PI);
        if (getbaseval(rhos) == 0){
            return forceeval(0.0*rhos*zeta[3]);
        }
        else{
            return forceeval(6.0/(MY_PI*rhos)*(3.0*zeta[1]*zeta[2]/(1.0-zeta[3]) + POW3(zeta[2])/(zeta[3]*POW2(1.0-zeta[3])) + (POW3(zeta[2])/POW2(zeta[3])-zeta[0])*log(1.0-zeta[3])));
        }
    }
    
    /**
    \note Starting from Eq. A12 from Lafitte
     
    Defining:
    \f[
    \hat B_{ij} \equiv \frac{B_{ij}}{2\pi\epsilon_{ij}d^3_{ij}\rho_s} = \frac{1-\zeta_x/2}{(1-\zeta_x)^3}I-\frac{9\zeta_x(1+\zeta_x)}{2(1-\zeta_x)^3}J
    \f]
    */
    template<typename ZetaType, typename IJ>
    auto get_Bhatij(const ZetaType& zeta_x, const ZetaType& one_minus_zeta_x3, const IJ& I, const IJ& J) const{
        return forceeval(
             (1.0-zeta_x/2.0)/one_minus_zeta_x3*I - 9.0*zeta_x*(1.0+zeta_x)/(2.0*one_minus_zeta_x3)*J
        );
    }
    
    /**
    \f[
    B = \hat B_{ij}\kappa \rho_s
    \f]
     \f[
     \left(\frac{\partial B_{ij}}{\partial \rho_s}\right)_{T,\vec{z}} = \kappa\left(\hat B + \zeta_x \frac{\partial \hat B}{\partial \zeta_x}\right)
     \f]
    and thus
     \f[
    \rho_s \left(\frac{\partial B_{ij}}{\partial \rho_s}\right)_{T,\vec{z}} = \hat B + \zeta_x \frac{\partial \hat B}{\partial \zeta_x}
     \f]
    */
    template<typename ZetaType, typename IJ>
    auto get_rhodBijdrho(const ZetaType& zeta_x, const ZetaType& one_minus_zeta_x3, const IJ& I, const IJ& J, const ZetaType& Bhatij) const{
        auto dBhatdzetax = (-3.0*I*(zeta_x - 2.0) - 27.0*J*zeta_x*(zeta_x + 1.0) + (zeta_x - 1.0)*(I + 9.0*J*zeta_x + 9.0*J*(zeta_x + 1.0)))/(2.0*POW4(1.0-zeta_x));
        return forceeval(Bhatij + dBhatdzetax*zeta_x);
    }
    
    /**
     \note Starting from Eq. A16 from Lafitte
     
     \f[
     \hat a^S_{1,ii} = \frac{a^S_{1,ii}}{2\pi\epsilon_{ij}d^3_{ij}\rho_s}
     \f]
     so
     \f[
     a^S_{1,ii} = \kappa\rho_s\hat a^S_{1,ii}
     \f]
    */
    template<typename ZetaType>
    auto get_a1Shatij(const ZetaType& zeta_x_eff, double lambda_ij) const{
        return forceeval(
            -1.0/(lambda_ij-3.0)*(1.0-zeta_x_eff/2.0)/POW3(forceeval(1.0-zeta_x_eff))
        );
    }
    
    /**
     \f[
     \left(\frac{\partial a^S_{1,ii}}{\partial \rho_s}\right)_{T,\vec{z}} = \kappa\left(\hat a^S_{1,ii} + \rho_s\frac{\partial \hat a^S_{1,ii}}{\partial \rho_s} \right)
     \f]
  
     \f[
     \left(\frac{\partial a^S_{1,ii}}{\partial \rho_s}\right)_{T,\vec{z}} = \kappa\left(\hat a^S_{1,ii} + \rho_s\frac{\partial \hat a^S_{1,ii}}{\partial \zeta_{x,eff}}\frac{\partial \zeta_{x,eff}}{\partial \zeta_x}\frac{\partial \zeta_x}{\partial \rho_s} \right)
     \f]
     
     since \f$\rho_s\frac{\partial \zeta_x}{\partial \rho_s}  = \zeta_x\f$
     */
    template<typename ZetaType>
    auto get_rhoda1Shatijdrho(const ZetaType& zeta_x, const ZetaType& zeta_x_eff, const ZetaType& dzetaxeffdzetax, double lambda_ij) const{
        auto zetaxda1Shatdzetax = ((2.0*zeta_x_eff - 5.0)*dzetaxeffdzetax)/(2.0*(lambda_ij-3)*POW4(zeta_x_eff-1.0))*zeta_x;
        return forceeval(get_a1Shatij(zeta_x_eff, lambda_ij) + zetaxda1Shatdzetax);
    }
};

/**
 \brief A class used to evaluate mixtures using the SAFT-VR-Mie model
*/
class SAFTVRMieMixture {
private:
    
    std::vector<std::string> names;
    const SAFTVRMieChainContributionTerms terms;

    void check_kmat(const Eigen::ArrayXXd& kmat, std::size_t N) {
        if (kmat.size() == 0){
            return;
        }
        if (kmat.cols() != kmat.rows()) {
            throw teqp::InvalidArgument("kmat rows and columns are not identical");
        }
        if (kmat.cols() != N) {
            throw teqp::InvalidArgument("kmat needs to be a square matrix the same size as the number of components");
        }
    };
    auto get_coeffs_from_names(const std::vector<std::string> &names){
        SAFTVRMieLibrary library;
        return library.get_coeffs(names);
    }
    auto build_chain(const std::vector<SAFTVRMieCoeffs> &coeffs, const std::optional<Eigen::ArrayXXd>& kmat){
        if (kmat){
            check_kmat(kmat.value(), coeffs.size());
        }
        const std::size_t N = coeffs.size();
        Eigen::ArrayXd m(N), epsilon_over_k(N), sigma_m(N), lambda_r(N), lambda_a(N);
        auto i = 0;
        for (const auto &coeff : coeffs) {
            m[i] = coeff.m;
            epsilon_over_k[i] = coeff.epsilon_over_k;
            sigma_m[i] = coeff.sigma_m;
            lambda_r[i] = coeff.lambda_r;
            lambda_a[i] = coeff.lambda_a;
            i++;
        }
        if (kmat){
            return SAFTVRMieChainContributionTerms(m, epsilon_over_k, sigma_m, lambda_r, lambda_a, std::move(kmat.value()));
        }
        else{
            auto mat = Eigen::ArrayXXd::Zero(N,N);
            return SAFTVRMieChainContributionTerms(m, epsilon_over_k, sigma_m, lambda_r, lambda_a, std::move(mat));
        }
    }
public:
     SAFTVRMieMixture(const std::vector<std::string> &names, const std::optional<Eigen::ArrayXXd>& kmat = std::nullopt) : SAFTVRMieMixture(get_coeffs_from_names(names), kmat){};
    SAFTVRMieMixture(const std::vector<SAFTVRMieCoeffs> &coeffs, const std::optional<Eigen::ArrayXXd> &kmat = std::nullopt) : terms(build_chain(coeffs, kmat)) {};
    
//    PCSAFTMixture( const PCSAFTMixture& ) = delete; // non construction-copyable
    SAFTVRMieMixture& operator=( const SAFTVRMieMixture& ) = delete; // non copyable
    
    const auto& get_terms() const { return terms; }
    auto get_core_calcs(double T, double rhomolar, const Eigen::ArrayXd& mole_fractions) const {
        auto val = terms.get_core_calcs(T, rhomolar, mole_fractions);
        
        auto fromArrayX = [](const Eigen::ArrayXd &x){std::valarray<double>n(x.size()); for (auto i =0; i < n.size(); ++i){ n[i] = x[i];} return n;};
        auto fromArrayXX = [](const Eigen::ArrayXXd &x){
            std::size_t N = x.rows();
            std::vector<std::vector<double>> n; n.resize(x.size());
            for (auto i = 0; i < N; ++i){
                n[i].resize(N);
                for (auto j = 0; j < N; ++j){
                    n[i][j] = x(i,j);
                }
            }
            return n;
        };
        return nlohmann::json{
            {"dmat", fromArrayXX(val.dmat)},
            {"rhos", val.rhos},
            {"rhoN", val.rhoN},
            {"mbar", val.mbar},
            {"xs", fromArrayX(val.xs)},
            {"zeta", fromArrayX(val.zeta)},
            {"zeta_x", val.zeta_x},
            {"zeta_x_bar", val.zeta_x_bar},
            {"alphar_mono", val.alphar_mono},
            {"a1kB", val.a1kB},
            {"a2kB2", val.a2kB2},
            {"a3kB3", val.a3kB3},
            {"alphar_chain", val.alphar_chain}
        };
    }
    
    auto get_m() const { return terms.m; }
    auto get_sigma_Angstrom() const { return (terms.sigma_A).eval(); }
    auto get_sigma_m() const { return terms.sigma_A/1e10; }
    auto get_epsilon_over_k_K() const { return terms.epsilon_over_k; }
    auto get_kmat() const { return terms.kmat; }
    auto get_lambda_r() const { return terms.lambda_r; }
    auto get_lambda_a() const { return terms.lambda_a; }
    
    // template<typename VecType>
    // double max_rhoN(const double T, const VecType& mole_fractions) const {
    //     auto N = mole_fractions.size();
    //     Eigen::ArrayX<double> d(N);
    //     for (auto i = 0; i < N; ++i) {
    //         d[i] = sigma_Angstrom[i] * (1.0 - 0.12 * exp(-3.0 * epsilon_over_k[i] / T));
    //     }
    //     return 6 * 0.74 / EIGEN_PI / (mole_fractions*m*powvec(d, 3)).sum()*1e30; // particles/m^3
    // }
    
    template<class VecType>
    auto R(const VecType& molefrac) const {
        return get_R_gas<decltype(molefrac[0])>();
    }

    template<typename TTYPE, typename RhoType, typename VecType>
    auto alphar(const TTYPE& T, const RhoType& rhomolar, const VecType& mole_fractions) const {
        // First values for the Mie chain with dispersion (always included)
        error_if_expr(T); error_if_expr(rhomolar);
        auto vals = terms.get_core_calcs(T, rhomolar, mole_fractions);
        auto alphar = vals.alphar_mono + vals.alphar_chain;
        return forceeval(alphar);
    }
};

} /* namespace SAFTVRMie */
}; // namespace teqp