general.h

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/*
 * Copyright University of Reims Champagne-Ardenne
 * Authors and Contributors: Akilan RAJAMANI, Corentin LEFEBVRE, Johanna KLEIN,
 *                           Emmanuel PLUOT, Gaetan RUBEZ, Hassan KHARTABIL,
 *                           Jean-Charles BOISSON and Eric HENON
 * (24/07/2017)
 * jean-charles.boisson@univ-reims.fr, eric.henon@univ-reims.fr
 *
 * This software is a computer program whose purpose is to
 * detect and quantify interactions from electron density
 * obtained either internally from promolecular density or
 * calculated from an input wave function input file. It also
 * prepares for the visualization of isosurfaces representing
 * several descriptors (dg) coming from the IGM methodology.
 *
 * This software is governed by the CeCILL-C license under French law and
 * abiding by the rules of distribution of free software.  You can  use,
 * modify and/ or redistribute the software under the terms of the CeCILL-C
 * license as circulated by CEA, CNRS and INRIA at the following URL
 * "http://www.cecill.info".
 *
 * As a counterpart to the access to the source code and  rights to copy,
 * modify and redistribute granted by the license, users are provided only
 * with a limited warranty  and the software's author,  the holder of the
 * economic rights,  and the successive licensors  have only  limited
 * liability.
 *
 * In this respect, the user's attention is drawn to the risks associated
 * with loading,  using,  modifying and/or developing or reproducing the
 * software by the user in light of its specific status of free software,
 * that may mean  that it is complicated to manipulate,  and  that  also
 * therefore means  that it is reserved for developers  and  experienced
 * professionals having in-depth computer knowledge. Users are therefore
 * encouraged to load and test the software's suitability as regards their
 * requirements in conditions enabling the security of their systems and/or
 * data to be ensured and,  more generally, to use and operate it in the
 * same conditions as regards security.
 *
 * The fact that you are presently reading this means that you have had
 * knowledge of the CeCILL-C license and that you accept its terms.
 *
 * */

 
#ifndef _GENERAL_H_
#define _GENERAL_H_
 
// STL
#include <cmath>
#include<string>
#include <set>
#include <sstream>
#include <iostream>
#include <fstream>
#include <iomanip>
#include <fstream>
#include <cstdlib>
#include <vector>

const double EPS_RHO_PROSELF = 1e-10;
 

//const double  PauliThresh = 1.0E-20; // kcal/mol/bohr^3
const double  PauliThresh = 0.0;

const double  maxElecAccurlev1 = 0.999999;    // default value is 0.999999for ELF, SELF, IGM
const double  maxElecAccurlev2 = 0.9999999;  // value for IBSI   calculations 
const double  maxElecAccurlev3 = 0.999999999; // value for CRITIC calculations 
const double  maxElecAccurlev4 = 0.9999999999999999999; // full accuracy mode              
 
// epsilon in dgscaled = dg/(rho + epsilon)
const double epsrhodgscaled = 0.0005;
 
// dg Threshold used to calculate dg/rho. Only
// those points for which dg > dgThresholdForDGSCALED will be used
// in dg/rho calculations (inter and intra) and then in Pauli calculations also
// to avoid numerical inaccuracy in building dg/rho isosurfaces
//const double dgThresholdForDGSCALED =0.0001; 
const double dgThresholdForDGSCALED =0.00001; 
 
// Rho Threshold used to calculate dg/rho. Only
// those points for which rho > rhoThresholdForDGSCALED will be used
// in dg/rho calculations (inter and intra) and then To project steric repulsion regions 
// to avoid numerical inaccuracy in building dg/rho isosurfaces
const double rhoThresholdForDGSCALED =0.000001; 
 
 
// isovalue for dg/rho isovalues
// Dividing by rho makes the dg/rho scale 
// in the range [0-2.5] (observed so far)
// over the all spectrum of interactions ! (strong or weak) 
const double dgSCALEDisovalue = 0.8;
 
// ED threshold for calculating Pauli repulsion: a grid point enters the SELF analysis
// only if the TOTAL rho is above this value (see NCISolver.cpp, ~line 3362).
//
// The value was 1E-5 as long as SELF took hundreds of seconds, to keep the run short.
// The fast SELFATOMIC routine removed that constraint, so it was measured again in
// August 2026, on test35 (49 atoms) and on a water dimer. Error on iSELF, compared to
// a run with NO threshold at all:
//        1E-4   -0.25 %          1E-6   -0.002 %
//        1E-5   -0.025 %         1E-7   -0.0002 %
// For comparison, going from a 0.20 to a 0.10 Angs grid moves iSELF by 0.004 %. So at
// 1E-5 the threshold was the LARGEST error of the calculation, seven times the grid
// error; at 1E-6 it drops below it. The price is 8 % more grid points, about 5 % of
// run time. 1E-7 gives no visible change and costs twice as much. The atom-pair
// contributions of SELFATOMIC do not move at all between 1E-5 and 1E-6, but they do
// move by up to 2 % at 1E-4.
//
// ! Changing this value and typing "make" rebuilds NOTHING ! The Makefile makes each
// ! object file depend on its own header only, never on general.h. Delete objectFiles
// ! first, or the binary keeps the old threshold and says nothing.
const double PauliRhoThresh = 1E-6;
 
// Local AO overlap (chi_a x chi_b) threshold for calculating Pauli repulsion
const double OV_thresh = 1E-5;
 
// Local AO (chi_a) threshold for calculating Pauli repulsion
const double chi_thresh = 1E-5;
 
 
// range for Pauli exchange repulsion (G - GW)
// so far observed
const double pauliMIN = 0.0;
const double pauliMAX = 2.5;
 
// conversion from Ekin in a.u to kcal/mol
const double ekin2kcal = 627.51;
 
 
// threshold in dg/rho descriptor to integrate pauli repulsion
const double pauliDgOverRhoThreshold = 0.1;
 
// ELF isovalue to draw ELF isosurfaces (default) with VMD
const double elfIsovalue = 0.83;
 
// threshold used to know if the GTO is zero or not
// based on the value of the exponent of the GTO
// -40 is the original value
const double exponThreshold = -40.0;
 
// pda epsilon for cylinder
const double epsCyl = 0.0001;

const double BOHRTOA = 0.52917720859;
 
// MEDIUM grid increments used in the search of critical points with seeds
// found from a promolecular IGM analysis:
const double incrCRITICMEDIUMx = 0.15*BOHRTOA; // in angstroms
const double incrCRITICMEDIUMy = 0.14*BOHRTOA; // no symetrical values are chosen on purpose 
const double incrCRITICMEDIUMz = 0.12*BOHRTOA; // to avoid any problem during the search of qg max values in the grid
 
// FINE grid increments used in the search of critical points with seeds
// found from a promolecular IGM analysis (will take about 4 more times)
const double incrCRITICFINEx = incrCRITICMEDIUMx/1.5874; // in angstroms
const double incrCRITICFINEy = incrCRITICMEDIUMy/1.5874; // no symetrical values are chosen on purpose 
const double incrCRITICFINEz = incrCRITICMEDIUMz/1.5874; // to avoid any problem during the search of qg max values in the grid
 
// ULTRAFINE grid increments used in the search of critical points with seeds
// found from a promolecular IGM analysis (will take about 10 more times)
const double incrCRITICULTRAFINEx = incrCRITICMEDIUMx/2.15443; // in angstroms
const double incrCRITICULTRAFINEy = incrCRITICMEDIUMy/2.15443; // no symetrical values are chosen on purpose 
const double incrCRITICULTRAFINEz = incrCRITICMEDIUMz/2.15443; // to avoid any problem during the search of qg max values in the grid
 
 
// threshold used to filter undesired drifted points during Newton-Raphson procedure for 
// critical points
const double qgThreshNR = 1.3;
 
// lower distance threshold allowed between two critical points
//const double cpSeparationThresh = 0.01;  // in bohr
//MODIF ERIC: 16081023
const double cpSeparationThresh = 0.01;  // in bohr
 
// ED gradient threshold for Newton-Raphson convergence
// MODIF ERIC 16082023
//const double gradThresholdNR = 0.0001;
const double gradThresholdNR = 0.000007;
 
// Displacement threshold for Newton-Raphson convergence
//const double normdisplactThreshNR  = 0.0001;
// MODIF ERIC 16082023
//const double normdisplactThreshNR  = 0.0000001;
const double normdisplactThreshNR  = 0.00000007;
 
// Maximum iteration number allowed for Newton-Raphson convergence
const int niterThreshNR=50;
 
// Epsilon value to perturb a little bit the current position during the Newton-Raphson search
// of critical points of the ED
const double epsXNR = 0.003;
const double epsYNR = 0.006;
const double epsZNR = 0.009;
 
// Threshold for every ED Hessian eigenvalue
const double EVthreshCP=0.00008;
 
// threshold to select those primitive to be used
const double cutoff_pri=1.0e-10; // original value from NCIPlot, save about 30%-40% CPU time
 
// threshold to select those primitive gradient sufficently large 
// to calculate cpsi in IBSI calculations
const double cutoff_gradpri=1.0e-12;
 
// ratio used to determine the isovalue selected to build 3D isosurface
// The isovalue is defined as 40% of the maximum peak height of the signature:
const double ratioPeak = 0.4; 
 
// a threshold value for extracting peaks from dg signatures
const double qgThresh = 1.3;
 
// a threshold to filter peaks in the analysis of dg for the ncc part
const double qgRhoThresh = -0.09;
 
// an espilon value to apply to the qgRhoThresh to estimate the influence of 
// qgRhoThresh on dgAt contribution to NCC
const double EDepsilon = 0.01;
 
// a constant indicating that no CHARGE keyword has been supplied in the param.igm input file
const int NOCHARGE = -99999;
 
 
// upper limit for allowed atomic number for separating core from valence e- 
const int COREAtomLimit= 53; // 0-based numbering -> calculation allowed up to Z=54 (including Xenon)
 
// upper limit for allowed atomic number for HIRSHFELD treatment
const int HIRSHAtomLimit = 17; // 0-based numbering -> calculation allowed up to Z=18 (including Argon)
 
// upper limit to allow critical point search treatment         
const int CRITICPROMOLAtomLimit = 35; // 0-based numbering -> determination of seeds by promol IGM allowed up to Z=36
 
 
// Lower IBSI limit to consider BDA calculation; above this threshold,
// BDA value are considered uncertained (too small covalent character)
const double IBSILimitForBDA = 0.15;
 
// For the BDA calculation the number of core orbital for each atom
// is saved in the ATOM_COREORB array, but fobidden for atoms of periods
// after 5 ==> the constant MAXCORE has been used in the ATOM_COREORB array
// to specify those atoms unallowed
const unsigned int MAXCORE = 1000000000;

//  based on dgpair integration.  In order for this IBSI index to match 1 for H2, Normation
//  coefficient has been computed :
//  (1) for the GTO level at the M062X 6-31G** level of theory
// and with the cylinder increments: Pz=100, Pr=100, Ptheta=50; 
// dist HH        = 0.737309086727
// dg pair (gross)= 0.390519702115
// dg/d^2         = 0.7183627045
const double NormCoeff_deltagd2GTO = 0.7183627045;// (=int_dg/d^2) in the case of H2
//  (2) for the STO level at the M062X/TZP  level of theory (ADF)
// and with the cylinder increments: Pz=100, Pr=100, Ptheta=50; 
// dist HH        = 0.739598965    
// dg pair (gross)= 0.34644146941713405141
// dg/d^2         = 0.63334692753492960460
const double NormCoeff_deltagd2STO = 0.63334692753492960460;// (=int_dg/d^2) in the case of H2
 
 
 
// name of the file containing timing informations 
const std::string runinfo="runinfo";
 
 
// cylindrical grid steps default:
const unsigned int cylPz     = 100;
const unsigned int cylPr     = 100;
const unsigned int cylPtheta =  50; // must be an even number !
 
 
// BDA detection threshold
const double pdaThreshold = 0.005;

const double scoredgThresh = 0.0001;

const double scoredg_over_rhoThresh = 0.0010; // sensible parameter

const double ratioIGMthresholdPRO = 2.0;
const double EDthreshold          = 0.07;
//const double gradrho_over_dgThreshWFN = 3.0;
//const double gradrho_over_dgThreshPRO = 2.0;
//const double gradrho_over_dgInterThreshPRO = 50.0;
 

const double   interacThreshold         = 0.00005;

const unsigned int  NB_KNW_ATMS  = 54;

const double    ALPHA          = 0.16162045967;

const double    ONE_THIRD      = 0.33333333333333;

const double    FOUR_THIRD        = 1.33333333333333;

const double    FIVE_THIRD              = 1.66666666666666;

const double R_MAX              = 20.0;
 
// the threshold used to test if an atom is exactly located on a grid node (in bohr)
const double    R_TRESHOLD      = 0.0000001;

const double    DEFAULT_CUTOFF    = 0.2;

const double    LN_2            = 0.69314718056;

const double    NaN          = 0.0;

const double    PI            = 3.141592653589793;
 
// constant used to obtain the RDG descriptor
//const double constValue = 2.0*std::pow((3.0*std::pow(PI,2)),(ONE_THIRD));
const double constValue = 6.187335452560202;
 

const double   THETA_MAX    = 2*PI;

const double EPSILON_RAD = 0.00055*PI;

const double    PI_2            = 6.28318530718;

const double    PI_4            = 12.5663706144;

const double PI_squared                 = 9.86960440108936;

const double ELF_const                  = 2.871234000188192;// A. Savin, B. Silvi, F. Colonna Can. J. Chem. 74 (1996) 1088-1096 equation [5] independent on the spin.
// equivalent to Thomas Fermi formula : C_F = (3/10)(3pi^2)^2/3 [h/(2pi)]^2 / me
 
 
// =====================================================================
//  Promolecular density — "G2" model: ρ(r) = Σⱼ Pⱼ(u) × exp(-αⱼ·u)
//  with u = r² and Pⱼ(u) = a0 + a2·u + a4·u2 + a6·u3  + a8·u4 (degree 4 in u)
//
//  Indexing convention (per IGMPLOT):
//      atomtype = Z − 1  ∈  [0, PROMOLG2_SIZE_ATOM − 1]
//
//  Storage convention inside the struct:
//      a[t][k] is the coefficient of u^k for the t-th gaussian term,
//      i.e.  a[t][0]=a0 , a[t][1]=a2 , a[t][2]=a4 , a[t][3]=a6,  a[t][4]=a8 .
// =====================================================================
 
constexpr int PROMOLNCI_SIZE_ATOM   = 79;   // H..Au, Z = 1..79  → indices 0..78
constexpr int PROMOLNCI_MAX_TERMS = 6;    // up to 5 gaussian terms per atom
constexpr int PROMOLNCI_DEGREE    = 3;    // P is degree 4 in u = r2 for ALL atoms

struct PromolNCIParams {
    int    n_terms;                                      // number of active gaussians
    double alpha[PROMOLNCI_MAX_TERMS];                    // exponents αⱼ
    double a[PROMOLNCI_MAX_TERMS][PROMOLNCI_DEGREE + 1];   // a[t][k] = coef of u^k
    double r_cutoff99;                                   // radius (bohr) beyond which < 1%    of electrons remain
    double r_cutoff999;                                  // radius (bohr) beyond which < 0.1%  of electrons remain
    double r_cutoff9999;                                 // radius (bohr) beyond which < 0.01% of electrons remain
    double r_neg;                                        // radius beyond which rho becomes asymptotically negative
};
 
// Atoms not listed below are zero-initialized (n_terms = 0) thanks to
// C++ aggregate-initialization rules. Fill them in as the fits become available.
constexpr PromolNCIParams PROMOL_NCI[PROMOLNCI_SIZE_ATOM] = {
 
    // ------------------
    /* idx  0 : Z= 1  H  */ {
    // ------------------
        /* n_terms */ 2,
        /* alpha   */ {
            3.125517633041795e+00,
            2.375433778535769e+00,
            0.0, 0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { -2.996539788984205e+01, -1.454185982818790e+00, 2.291962484694055e+00, 1.358464471368234e+00 }, // term 1
            { 3.021593384989029e+01, -2.045487598139934e+01, 4.065054772036312e+00, -2.535344990947412e-01 }, // term 2
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.258488,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.523262,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.501180,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 7.7527
    }, // end of H
 
    // ------------------
    /* idx  1 : Z= 2  He */ {
    // ------------------
        /* n_terms */ 2,
        /* alpha   */ {
            4.705711621287205e+00,
            1.655770326561886e+00,
            0.0, 0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.853205346296690e+00, -3.447857098049599e+00, 8.256977741615195e+00, -3.932782786240419e+00 }, // term 1
            { 5.668906854064849e-01, -3.336387767475322e-01, 6.573639665172815e-02, -4.332564427129738e-03 }, // term 2
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 2.759013,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 3.567992,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 4.201230,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 5.3752
    }, // end of He
 
 
    // ------------------
    /* idx  2 : Z= 3  Li */ {
    // ------------------
        /* n_terms */ 2,
        /* alpha   */ {
            4.717705166950644e+00,
            1.406215313482279e+00,
            0.0, 0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.149541174973694e+01, 1.514420084220817e-01, -9.874658656932226e+00, 8.286300758187869e+00 }, // term 1
            { -3.251517484384632e-01, 2.137216892282250e-01, -2.905846357305992e-02, 3.989505171416614e-03 }, // term 2
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 7.453021,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 9.991640,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 12.315967,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Li
 
 
    // ------------------
    /* idx  3 : Z= 4  Be */ {
    // ------------------
        /* n_terms */ 2,
        /* alpha   */ {
            8.256825322800806e+00,
            1.948588927387367e+00,
            0.0, 0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.955216175214220e+01, -2.692374141028450e+01, 1.337054914815829e+02, -2.484608728893327e+01 }, // term 1
            { -6.179238019270623e-01, 7.246447171126011e-01, -7.318576555840284e-02, 3.025065328381662e-02 }, // term 2
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 5.548206,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.317529,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.953629,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Be
 
 
    // ------------------
    /* idx  4 : Z= 5  B  */ {
    // ------------------
        /* n_terms */ 2,
        /* alpha   */ {
            1.970840222735338e+01,
            1.987815480577545e+00,
            0.0, 0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 7.621613958426853e+01, 2.454688214888158e+02, 8.604352163820512e-01, 6.012027788549309e+04 }, // term 1
            { -4.111273419327758e-01, 1.355798264696206e+00, -3.138953434236884e-01, 3.676041499653355e-02 }, // term 2
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.756234,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.512518,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.191136,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of B
 
 
    // ------------------
    /* idx  5 : Z= 6  C  */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            4.935208802463244e+00,
            3.523464984605619e+00,
            3.016682413464392e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.417232827843679e+03, 6.084937330221675e+01, -7.133280604989585e+01, -1.019136664754738e+02 }, // term 1
            { -9.999999999549641e+02, 1.079249844497345e+03, -7.809495935640047e+02, 2.353019116877174e+02 }, // term 2
            { -3.553779053361222e+02, 7.791085101168635e+02, -3.695970004220874e+02, 3.847516448799774e+01 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.027189,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.456934,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.697331,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of C
 
    // ------------------
    /* idx  6 : Z= 7  N  */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            1.737431716923670e+01,
            1.904710578978055e+00,
            2.611197547132751e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.586438534305313e+02, 2.668376884541425e+02, 2.128833529772979e+03, -1.586590006213783e+03 }, // term 1
            { 1.278916594518708e-01, 6.251221838119626e+00, -1.406073004402292e+00, 8.377219945524951e-02 }, // term 2
            { 2.428229589129620e+00, -5.002472701626051e+00, -2.730051236824526e+00, -1.016788217261465e+00 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
        }, // end of 'a'
        /* r_cut99   */ 3.474100,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 4.670700,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 5.695800,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of N
 
    // ------------------
    /* idx  7 : Z= 8  O  */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            2.729202256560992e+01,
            3.510900285068801e+00,
            3.114196922719645e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 2.790885795942112e+02, 3.832925793235438e+03, -1.116432174580099e+02, -8.970195794555130e+01 }, // term 1
            { 7.549702381581724e+01, 1.259511475981575e+02, -7.387267341799018e+00, -3.691086871609377e+01 }, // term 2
            { -6.072933573523962e+01, -1.293127040583298e+02, 1.019716439972806e+02, -9.745847798157998e+00 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.163786,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 4.251685,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 5.121890,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 6.7443
    }, // end of O
 
 
 
    // ------------------
    /* idx  8 : Z= 9  F  */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            1.492082891230667e+01,
            2.552710908186560e+00,
            1.513058206999419e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.150524896314547e+02, -8.814147843727217e+01, -6.411938830556404e+02, 4.396042543858071e+02 }, // term 1
            { 7.454485881043989e+00, -1.307393354015624e+01, 2.638447043162817e+00, -6.788768187891444e-01 }, // term 2
            { 4.797782580710073e+00, -1.789665052012564e+00, 2.408379539853601e-01, -1.152845137235171e-02 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 2.863324,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 3.840109,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 4.596365,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 6.1709
    }, // end of F
 
    // ------------------
    /* idx  9 : Z=10  Ne */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            3.193392059178248e+01,
            5.386821612845594e+00,
            3.918917239610918e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 8.299187306208952e+02, 2.704927716722272e+02, 1.248265941846437e+04, 9.740495259747312e+04 }, // term 1
            { -3.821832072953763e+02, 5.115018102118993e+02, 4.064815508692946e+02, 6.269007468694764e+02 }, // term 2
            { 3.985683262815230e+02, -9.999952853701037e+02, 3.975767832801348e+02, -4.197258799533002e+01 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 2.599145,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 3.479554,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 4.180254,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 5.6629
    }, // end of Ne
 
 
    // ------------------
    /* idx 10 : Z=11  Na */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            2.199999999948932e+01,
            6.648018953807128e+00,
            1.461678804374006e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.299460903143946e+03, 3.878928609539038e+03, 1.560321404535262e+03, 4.254257550109087e+02 }, // term 1
            { -8.044396865179552e+01, 2.315268164260275e+02, 8.221689153308314e+01, 3.743259341047210e+01 }, // term 2
            { 4.950393802927862e-01, -3.475602208766879e-01, 8.280721788332199e-02, -1.170846856876532e-04 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
        }, // end of 'a'
        /* r_cut99   */ 6.118500,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 8.654500,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 10.86250,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0   
    }, // end of Na
 
 
    // ------------------
    /* idx 11 : Z=12  Mg */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            2.164284755302462e+01,
            3.723574902194970e+00,
            1.844049821898035e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 6.872919429202409e+02, 2.043261859206392e+02, 4.980105693347653e+03, 1.952205123089008e+04 }, // term 1
            { 5.390714523343194e+01, 1.886434341844081e+02, -8.357963339933005e+01, 7.790777072459775e+01 }, // term 2
            { -6.024507469990663e+01, 3.191544541334905e+01, -5.740541514041333e+00, 3.932518366889246e-01 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 5.433690,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.655407,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 9.644691,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Mg
 
    // ------------------
    /* idx 12 : Z=13  Al */ {
    // ------------------
        /* n_terms */ 3,
        /* alpha   */ {
            2.600000000000000e+01,
            3.381634064880283e+00,
            1.709181052889170e+00,
            0.0, 0.0, 0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.339437149673430e+03, -7.774657538077511e+03, -1.141696102560554e+03, 1.362793475770697e+03 }, // term 1
            { -1.287943633248699e+01, -1.558981052601106e+02, 3.795893023734648e+01, -4.439393303296902e+01 }, // term 2
            { 5.541759630282562e+01, -2.509011132237801e+01, 3.905325355216484e+00, -1.877957113377770e-01 }, // term 3
            { 0.0, 0.0, 0.0, 0.0 },
            { 0.0, 0.0, 0.0, 0.0 }
        }, // end of 'a'
        /* r_cut99   */ 5.349400,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.363000,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.896600,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 11.2604
    }, // end of Al
 
    // ------------------
    /* idx 13 : Z=14  Si */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.465098292646328e+02,
            4.937351992027260e+00,
            3.859286983416000e+00,
            2.062697384942289e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 6.323269339547873e+04, 2.500479099178714e+04, 1.288514662400892e+05, 9.069856745720476e+04 }, // term 1
            { 4.651791758243630e+02, 4.402791311251285e+01, -2.014867539306239e+01, -2.314466682514426e+02 }, // term 2
            { -5.849348771000501e+02, -2.643878842010821e+02, 1.525082014678671e+02, -2.568698980059469e+02 }, // term 3
            { 2.484641612919081e+02, -1.229220162196650e+02, 2.081082636216647e+01, -1.102610370140829e+00 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.763604,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.442788,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.749514,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 9.9885
    }, // end of Si
 
    // ------------------
    /* idx 14 : Z=15  P  */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.017609780297121e+02,
            5.849982493308661e+00,
            4.231921923085189e+00,
            2.410490250382000e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.614773878303076e+04, 5.902068266574021e+03, 1.435068833261286e+05, 2.028879282281589e+05 }, // term 1
            { 2.654947138657883e+02, -5.021327235572019e+01, -2.968283451962907e+02, -6.000623716626154e+02 }, // term 2
            { -9.478458134658875e+02, -9.999999899492340e+02, -1.401916251318781e+02, -6.035541275670705e+02 }, // term 3
            { 8.204747700387694e+02, -4.351909154776381e+02, 7.919214772364640e+01, -4.578530791646235e+00 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.252252,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.695035,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.832822,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.9389
    }, // end of P
 
 
    // ------------------
    /* idx 15 : Z=16  S  */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.090736571339769e+02,
            6.725002931969463e+00,
            4.690938603966750e+00,
            2.580722744751037e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.967036306407420e+04, 1.263766303635186e+05, 8.130681241891781e+04, 1.592022801426488e+05 }, // term 1
            { 2.684910938902691e+02, -1.006273170049298e+02, -6.028035534014535e+02, -6.976976730303206e+02 }, // term 2
            { -8.095620930543886e+02, -9.728239431390086e+02, -2.701306327326059e+02, -8.200281309401330e+02 }, // term 3
            { 7.194262912199570e+02, -4.330156283500661e+02, 8.929216283035348e+01, -5.757923360545031e+00 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.942152,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.270420,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.322604,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.3654
    }, // end of S
 
 
    // ------------------
    /* idx 16 : Z=17  Cl */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.074406470241165e+02,
            5.189062319650679e+00,
            5.122312953547356e+00,
            2.826510725513618e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 7.261082981955828e+04, 1.634170433964407e+05, 2.254111224218435e+05, 2.122868834485046e+05 }, // term 1
            { 7.116824921178939e+01, -1.000000000000000e+03, -4.430749202374029e+02, -2.323945186075172e+02 }, // term 2
            { -8.469654629252728e+02, -9.999999999993234e+02, -2.398453600878386e+01, -9.784491195332934e+02 }, // term 3
            { 9.372839846315730e+02, -6.285726484798477e+02, 1.445150267682523e+02, -1.031727035290172e+01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.634888,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 4.835601,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 5.790276,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 7.7305
    }, // end of Cl
 
    // ------------------
    /* idx 17 : Z=18  Ar */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.279231341919696e+02,
            5.702850369932287e+00,
            4.529393255805360e+00,
            3.205351481933067e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 9.734159688195674e+04, 1.618056853177921e+05, 1.451508540040759e+05, 1.996076617492376e+05 }, // term 1
            { 1.143502477931418e+02, 7.080212266378038e+02, 3.269444756649165e+03, -9.816474694107723e+02 }, // term 2
            { 1.142525148298745e+03, 4.983508983268162e+01, 1.636498540776853e+03, 9.663464340492783e+02 }, // term 3
            { -9.999999425892153e+02, -5.174059781849919e+02, 2.873519853299240e+02, -2.779212193779788e+01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.355968,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 4.439899,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 5.301034,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 7.1571
    }, // end of Ar
 
 
    // ------------------
    /* idx 18 : Z=19  K  */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            4.148296905488644e+01,
            8.507428123859077e+00,
            5.871274330296566e+00,
            1.293788967900932e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 2.256667831694343e+03, 1.341561860850054e+04, 1.182146715380506e+03, -6.825147122433293e+02 }, // term 1
            { 3.010000789825052e+02, -9.668662377365025e+01, 2.484352384985359e-01, -1.527670712870336e+01 }, // term 2
            { -5.423122953785059e+01, -2.894565516581508e+01, 9.633067730193787e+01, 1.987810244750640e+02 }, // term 3
            { 9.048559296554626e-01, -4.744106011389537e-01, 7.774057071519096e-02, -2.720343241120974e-04 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 6.494944,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 9.532443,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 12.083534,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of K
 
 
    // ------------------
    /* idx 19 : Z=20  Ca */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            3.378142050684691e+01,
            1.044324093666313e+01,
            4.865809471562946e+00,
            1.352859165432965e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.935099325203019e+03, -1.302836551654394e+03, 8.801060883807062e+03, 3.356743405233925e+03 }, // term 1
            { 2.166907406643830e+02, 6.519258696966463e+02, -4.572620096832793e+00, -3.899282469804361e+01 }, // term 2
            { 7.175081237229396e+00, -3.328094351489848e+01, 2.391439340759027e+01, 8.629200307586164e+01 }, // term 3
            { -7.285736101949388e-01, 3.777991156410600e-01, -2.049263049085953e-02, 2.480699640246638e-03 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 6.136091,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 8.738770,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 11.108451,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Ca
 
 
    // ------------------
    /* idx 20 : Z=21  Sc */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.606631426627932e+02,
            4.054895019312328e+01,
            2.635228010118652e+00,
            1.678693959184383e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.566216645506153e+04, 5.885940202940742e+02, 7.512190048730324e+03, -8.548885835282898e+02 }, // term 1
            { 1.141995124363607e+04, -1.569799512687506e+03, 8.958508668722089e+02, -1.908342709460376e+02 }, // term 2
            { 6.957464839487028e+01, -2.734755284279715e+01, 2.333153056179162e+01, -7.328720321805725e+00 }, // term 3
            { -3.791912483443785e+01, 2.300150115248174e+01, -4.146118132896609e+00, 2.722555669757267e-01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 5.608865,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 8.093061,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 10.307408,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Sc
 
 
    // ------------------
    /* idx 21 : Z=22  Ti */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.835378211804079e+02,
            6.538847018375490e+01,
            2.963125339630494e+00,
            1.466171954855902e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.041807730389339e+05, -7.173956778830897e+04, -1.424302115393965e+05, -5.200800612208703e+04 }, // term 1
            { 3.646206348047939e+04, 3.507560376208414e+04, -1.929918054711271e+02, -4.867664314238422e+04 }, // term 2
            { 3.466706828512469e+01, -8.866788485642277e+01, 4.046368862616576e+01, -1.660840187230869e+01 }, // term 3
            { 1.394750443874396e+01, -4.959330506257274e+00, 6.370747706485359e-01, -2.431298940873458e-02 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 5.276089,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.681485,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 9.767711,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 15.3484
    }, // end of Ti
 
    // ------------------
    /* idx 22 : Z=23  V  */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            3.679995653671940e+02,
            9.880810735897494e+01,
            2.870355517272690e+00,
            1.902230130344236e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 4.418322062234652e+05, -6.718204481843393e+03, 3.664682836369721e+05, -6.251069825391102e+04 }, // term 1
            { 1.323605240748921e+05, 6.848230816868602e+04, -1.454428579674783e+04, 2.783685434634804e+04 }, // term 2
            { 2.033358405459612e+02, -2.693834116620693e+01, 5.373322465067015e+01, -1.991453006991544e+01 }, // term 3
            { -1.499937272066919e+02, 9.100703604597882e+01, -1.734513424592313e+01, 1.170898361936491e+00 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 5.015878,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.360614,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 9.379945,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */30.0
    }, // end of V
 
    // ------------------
    /* idx 23 : Z=24  Cr */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            3.839812587783138e+02,
            1.273584126782906e+02,
            3.209507654578690e+00,
            1.917662782108202e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 5.759982947337512e+05, 1.625880670237004e+05, -7.778069334416063e+03, -1.028451024947661e+05 }, // term 1
            { 2.792669755325496e+05, -9.299829370923666e+04, -7.308471870313401e+04, -7.576054607802840e+04 }, // term 2
            { 2.351600519800843e+02, -3.431113395117667e+00, 1.274880001032885e+02, -1.050535182603056e+01 }, // term 3
            { -1.569752989295046e+02, 7.801897651472677e+01, -1.331778661128046e+01, 8.236048276946558e-01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.426293,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.663316,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.770517,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Cr
 
 
    // ------------------
    /* idx 24 : Z=25  Mn */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            2.846728397239980e+02,
            4.955604711935337e+01,
            5.698035344140452e+00,
            1.796945795326363e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 5.937460719283020e+04, 9.318326347600608e+04, 1.155166481697692e+04, 2.326006281566359e+04 }, // term 1
            { 1.208492292641235e+04, -3.904846530057479e+02, -8.330518069838480e+01, 3.037598942368552e+02 }, // term 2
            { 2.037307451538520e+02, -3.073705884437762e+02, 5.618695466688815e+01, 3.989336120753417e+02 }, // term 3
            { -6.001049253612496e+00, 4.874064089498819e+00, -1.109676207970691e+00, 1.108009395641731e-01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.661560,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.918425,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.928118,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Mn
 
 
    // ------------------
    /* idx 25 : Z=26  Fe */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.664141158573856e+02,
            3.065750800646249e+02,
            8.285973737654407e+00,
            1.181499443306323e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.095090719668359e+04, 4.382115739352076e+03, 6.012081601478731e+04, -2.580978896444578e+04 }, // term 1
            { 3.713147025998778e+03, 3.547804654858096e+03, 3.044287332008030e+02, 5.690417096341171e+02 }, // term 2
            { 4.239325966193907e+02, -1.201189420188335e+01, 3.398500107582455e+02, 2.457535049702123e+01 }, // term 3
            { 5.142135848909297e-01, -1.190817772509493e-01, 1.222227563895118e-02, -4.997943841395240e-04 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.341823,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.500613,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.409396,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 11.5291
    }, // end of Fe
 
 
    // ------------------
    /* idx 26 : Z=27  Co */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            4.209309812733606e+02,
            8.056073979531172e+01,
            5.157051509863435e+00,
            2.008957447251811e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 6.623776001716487e+05, -4.302218612976634e+05, 5.950484548768046e+04, -1.925016744535210e+05 }, // term 1
            { 5.138339959797909e+04, -1.557529044066435e+03, 5.655664749289082e+02, 3.307502628122907e+02 }, // term 2
            { 2.579473356357865e+02, -6.303303267842897e+02, 7.595865974257897e+02, -1.437110986838784e+02 }, // term 3
            { -1.193949296462547e+01, 1.052195510855963e+01, -2.753675304715103e+00, 2.892637277694303e-01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.069140,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.182010,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.031835,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Co
 
    // ------------------
    /* idx 27 : Z=28  Ni */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.885378966516897e+02,
            1.291742546600151e+02,
            6.178621803761759e+00,
            1.361133033119619e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.425177796872142e+05, 2.293816002490505e+05, 4.011631037491396e+04, 5.374606044452961e+04 }, // term 1
            { 5.281716327743415e+04, -1.193349647749766e+03, 5.019369087075788e+02, -2.097672869795025e+01 }, // term 2
            { 1.892565778590387e+02, 3.605151732175387e+00, 7.847003992083554e+00, 2.333886063180664e+01 }, // term 3
            { 7.775843524604397e-01, -1.969053311393102e-01, 2.710245038547016e-02, -1.414773892954083e-03 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.973332,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.029512,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.845322,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 11.0696
    }, // end of Ni
 
 
    // ------------------
    /* idx 28 : Z=29  Cu */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            1.557017170101405e+02,
            4.639989585117970e+02,
            7.816924982279989e+00,
            1.282232930829049e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 6.425859798180086e+04, 1.581481706839454e+05, -4.559459487132751e+05, 4.195704409802383e+03 }, // term 1
            { 3.958376320129449e+03, 1.333800527670032e+03, 2.092292665859839e+03, -8.756874211861230e+03 }, // term 2
            { 4.767859135155753e+02, -2.262973796192211e+01, -5.975764968734735e+01, 4.577005751928495e+01 }, // term 3
            { 6.803863529173343e-01, -2.013187522241082e-01, 2.395071615277829e-02, -1.011244846677678e-03 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.689878,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.707507,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.650872,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 11.3966
    }, // end of Cu
 
    // ------------------
    /* idx 29 : Z=30  Zn */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            2.044476432323705e+02,
            2.672115467251115e+01,
            4.294698310976129e+00,
            1.657835087140414e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 4.228743463253875e+05, 1.115478626573007e+04, -7.183359966444712e+04, -4.952941965096891e+03 }, // term 1
            { 5.231275228902127e+03, -3.170195526949339e+02, -1.735533550425249e+03, 6.278807441126937e+02 }, // term 2
            { 5.045810977332677e+01, 6.827378332910961e+00, -5.339508062673485e+00, -2.005952330595654e+01 }, // term 3
            { 3.577803339379367e+00, -1.486216293105710e+00, 2.713623474204978e-01, -1.496929647468597e-02 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.751671,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.692201,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.416171,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 11.1436
    }, // end of Zn
 
 
    // ------------------
    /* idx 30 : Z=31  Ga */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            3.383577471767916e+02,
            4.020843798185788e+01,
            3.510001499117459e+00,
            1.926706450742683e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 9.212902154018606e+04, 2.431680792623136e+04, -1.000000000000000e+03, -1.000000000000000e+03 }, // term 1
            { 6.361657700105634e+03, 3.741705925915794e+02, 8.530506956684076e+05, 6.032521259656572e+05 }, // term 2
            { -1.041514291970093e+02, -5.205617778254290e+02, 6.692062578734345e+01, -1.253249657740283e+02 }, // term 3
            { 2.385279269441170e+02, -1.095259415168260e+02, 1.704806866657035e+01, -8.297121971318221e-01 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.231843,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.365122,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.917886,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 10.7662
    }, // end of Ga
 
 
    // ------------------
    /* idx 31 : Z=32  Ge */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            3.576793144593392e+02,
            3.447288588810802e+01,
            3.773368182202734e+00,
            2.087633841408121e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 2.553125746257084e+04, 1.102574632053479e+05, 5.417979314218975e+05, 9.995432914178669e+05 }, // term 1
            { 3.538578819422379e+03, -4.871768260315267e+00, 5.884782014217337e+05, 1.016149741914750e+06 }, // term 2
            { -2.898243147304857e+02, -7.430827763159206e+02, -1.152138365028163e+01, -2.285800685113796e+02 }, // term 3
            { 4.141744495266909e+02, -2.038991427570164e+02, 3.403477761978818e+01, -1.779050908712132e+00 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 4.141137,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.041417,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.445651,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 10.0838
    }, // end of Ge
 
 
    // ------------------
    /* idx 32 : Z=33  As */ {
    // ------------------
        /* n_terms */ 4,
        /* alpha   */ {
            8.862389859509582e+01,
            3.132266867122945e+01,
            4.049619767776894e+00,
            2.214799965723322e+00,
            0.0,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 2.322745554423245e+04, 6.786472671145010e+05, 8.614610153031023e+05, 1.018558747244838e+06 }, // term 1
            { 8.343825531495494e+02, -2.632403331816257e+01, 4.047625317015086e+05, 5.041526206860269e+05 }, // term 2
            { -3.329507170517248e+02, -7.969477151080360e+02, -1.002989485960809e+02, -2.995581021188775e+02 }, // term 3
            { 4.509131288599605e+02, -2.399038067550083e+02, 4.333458513275652e+01, -2.445752920397521e+00 }, // term 4
            { 0.0, 0.0, 0.0, 0.0 }
    }, // end of 'a'
        /* r_cut99   */ 3.930247,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.671792,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.978518,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 9.5123
    }, // end of As
 
 
    // ------------------
    /* idx 33 : Z=34  Se */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            1.890823173598295e+02,
            4.877285870848707e+02,
            7.104465807069148e+01,
            4.047017926301158e+00,
            2.461789509401144e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 7.706671229315954e+05, -2.926751218348644e+04, -3.110573017009450e+04, 7.228082453761069e+04 }, // term 1
            { -7.303834571919909e+02, 8.989132459738852e+01, 7.088487495845964e+02, -2.004111976587150e+01 }, // term 2
            { -3.801642349426786e+01, -5.686734619686415e+01, 6.437485385615983e+00, -3.002883674965500e+00 }, // term 3
            { -1.449935337615875e+03, -2.797665231634578e+03, -1.066646947850083e+02, -7.141063742104517e+02 }, // term 4
            { 1.771176201176940e+03, -8.638936551479381e+02, 1.456163919734339e+02, -7.960025359594623e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.714255,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.250579,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.479071,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.9706
    }, // end of Se
 
 
    // ------------------
    /* idx 34 : Z=35  Br */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            4.543195860781794e+02,
            8.169782147874324e+02,
            2.819194816947872e+01,
            4.200846021062457e+00,
            2.499103432036647e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.224918639819000e+06, 4.642719580897717e+05, 1.118368960582155e+06, 9.615532394974016e+05 }, // term 1
            { 4.315693589606325e+05, 4.108434328582981e+05, 6.059818471575321e+05, 1.113633289234376e+06 }, // term 2
            { 5.215491365176063e+03, 8.067340419010072e+03, 5.618608884755397e+02, 2.584011832756030e+02 }, // term 3
            { -5.306510936379889e+02, -9.999999978779216e+02, -2.549070403312330e+02, -2.232412311004049e+02 }, // term 4
            { 6.776342349572553e+02, -3.685640445362138e+02, 7.037356457335875e+01, -4.295196666012555e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.530009,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 4.952384,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.117383,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.5262
    }, // end of Br
 
 
    // ------------------
    /* idx 35 : Z=36  Kr */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            6.412735184969878e+02,
            4.529650231326018e+02,
            2.489886111648276e+01,
            4.150663490911246e+00,
            2.599086640911890e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 6.194553816911462e+05, 8.067049437189244e+05, 6.376941886839570e+05, 6.517256842992912e+05 }, // term 1
            { 1.050501116313031e+05, 1.122255566772299e+06, 9.351637920233124e+05, 1.219823606418683e+06 }, // term 2
            { 3.003134390416600e+03, 9.152701366867144e+03, -6.814777240927352e+02, 2.891165835648387e+02 }, // term 3
            { -5.459216577610285e+02, -8.978700734515561e+02, -2.634241600582097e+02, -7.854512122744613e+01 }, // term 4
            { 7.037203990619053e+02, -3.873308075504511e+02, 7.590661702863896e+01, -4.809956555499999e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.349165,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 4.684803,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 5.799347,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.1432
    }, // end of Kr
 
 
    // ------------------
    /* idx 36 : Z=37  Rb */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            1.822105946478282e+02,
            9.686800000295705e+01,
            7.977772964979863e+00,
            4.051301274403182e+00,
            1.205856997757515e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.653643406792560e+05, -5.639177963498620e+05, -2.040581414864668e+05, 4.252257664092904e+05 }, // term 1
            { 9.057776804299961e+04, 4.551476689813451e+04, 8.272378745200822e+03, -4.153746920545563e+04 }, // term 2
            { 4.492855458231506e+02, -5.688313435323399e+00, -7.331401076863869e+00, -7.087267289220662e+01 }, // term 3
            { 5.829107696063410e+00, -3.902772596099243e+00, 2.586781574224242e+00, 1.659781928078295e+01 }, // term 4
            { 9.040518381432466e-01, -4.663461202224716e-01, 7.866992643513621e-02, -1.962934225192497e-03 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 5.666690,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 9.169055,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 11.903257,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Rb
 
 
    // ------------------
    /* idx 37 : Z=38  Sr */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            2.126104526023484e+02,
            2.185118012809007e+02,
            1.085012395059580e+01,
            4.253028181626409e+00,
            1.292546479664672e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.443997573796556e+06, -6.229889321908450e+05, -5.464068497557362e+05, 1.256594755890209e+06 }, // term 1
            { 8.551369152816666e+05, 8.187771048231734e+03, 2.105953504677814e+03, 3.718232957810368e+04 }, // term 2
            { 2.611413643854805e+02, -1.139845976809572e+01, 6.480687029780677e+01, -5.537009602100295e+01 }, // term 3
            { 1.252012679470255e+02, -1.081496206479205e+02, -3.550142323019448e+01, 7.249213775064487e+01 }, // term 4
            { -4.990155024583821e-01, 1.562208941966929e-01, 2.435789431734834e-02, -5.362093940255632e-04 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 5.724515,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 8.509172,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 10.925906,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Sr
 
    // ------------------
    /* idx 38 : Z=39  Y  */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            2.835354166250262e+02,
            1.475388102452735e+02,
            1.076385224299804e+01,
            4.039670632644498e+00,
            1.312531160398302e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.680753694181242e+05, -9.999999991236592e+02, -1.000000000000000e+03, 7.036173951576338e+05 }, // term 1
            { 2.565870234898238e+05, 7.749805025339393e+03, 5.831821578917061e+05, 2.820631723613716e+05 }, // term 2
            { 4.796221818007220e+02, -2.539632263769505e+01, 2.198504480166098e+02, -5.257913330780292e+01 }, // term 3
            { 9.176316178617338e+01, -3.355143165357654e+01, -6.446776443217637e+01, 6.580038754566105e+01 }, // term 4
            { -1.883028959174758e+00, 9.545888910967844e-01, -1.025887574239175e-01, 4.236315041476158e-03 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 5.252846,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.745546,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 10.050598,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Y
 
 
   // ------------------
    /* idx 39 : Z=40  Zr */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            3.836025823821367e+02,
            1.195055712676634e+02,
            1.072134098521071e+01,
            3.998734194176778e+00,
            1.513662595040798e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 8.547388901970033e+05, 3.449779863459046e+05, 5.267933306564880e+05, 1.503719916289125e+06 }, // term 1
            { 2.191264435641941e+05, 3.385195696028529e+05, 1.291063075889327e+06, 1.089598004742664e+06 }, // term 2
            { 5.298041982627142e+02, 1.778700220978414e+02, 5.085280856966970e+02, -5.415322510640443e+01 }, // term 3
            { 7.737590586228590e+01, -3.860012227950671e+01, -2.053631203457360e+01, 5.356845893787681e+01 }, // term 4
            { -5.063857955676689e+00, 2.666121975232866e+00, -3.569241627174340e-01, 2.089880561199623e-02 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 4.858277,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 7.204147,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 9.412259,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Zr
 
 
    // ------------------
    /* idx 40 : Z=41  Nb */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            4.082938031393645e+02,
            1.454557526908844e+02,
            1.086283082143797e+01,
            3.307913222778261e+00,
            1.744213744250295e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.067467583477520e+06, 6.147723128194187e+05, 1.032624782962898e+06, 9.518839946852506e+05 }, // term 1
            { 3.036613329402261e+05, 7.781096698877870e+05, 4.947424371364150e+05, 1.005839041988636e+06 }, // term 2
            { 9.408694432456864e+02, -1.398022720189989e+02, -4.427164862515273e+02, -9.507010009077540e+01 }, // term 3
            { 9.094764862178071e+01, 3.313944519976285e+01, 3.671842424314620e+01, 1.822031758427141e+01 }, // term 4
            { -5.419590985705076e+01, 2.516125581079142e+01, -3.840085332410261e+00, 2.199385713387908e-01 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 4.394546,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.598689,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.718929,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Nb
 
    // ------------------
    /* idx 41 : Z=42  Mo */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            2.514325761302984e+02,
            1.347343619673148e+02,
            1.245691358867031e+01,
            2.682042185380089e+00,
            1.904992318668312e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.262124520475954e+06, 7.489251844095874e+05, 9.597580541834604e+05, 5.082508018210163e+05 }, // term 1
            { 1.640358514454804e+05, 1.119868640941791e+06, 4.631941799517832e+05, 5.113349099156424e+05 }, // term 2
            { 1.120607225404626e+03, 1.918682583998441e+02, -2.555780562144827e+02, -6.777173099892150e+01 }, // term 3
            { 2.127985135970862e+02, -4.040048593727899e+01, 3.364958831211862e+01, -1.826314631576733e+01 }, // term 4
            { -1.664375490655018e+02, 1.022877502465713e+02, -1.702865680148093e+01, 9.460843103074035e-01 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 4.141704,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.205254,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.217214,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Mo
 
 
    // ------------------
    /* idx 42 : Z=43  Tc */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            3.572158037626585e+02,
            1.122431001977690e+02,
            1.471395872385304e+01,
            2.835611093455424e+00,
            1.967661292022779e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.077747591896789e+05, 8.876142406750193e+05, 8.925575743811172e+05, 4.143869951879707e+05 }, // term 1
            { 7.429496675450000e+04, 6.756949352488962e+05, 4.591314698249471e+05, 6.495356278025320e+05 }, // term 2
            { 2.003670756544406e+03, 3.970234164798374e+02, -2.619435229341789e+02, 2.212956719916750e+01 }, // term 3
            { 2.143136588789500e+02, -5.228928604816885e+01, 4.388386706467837e+01, -2.405314934755081e+01 }, // term 4
            { -1.590186077580637e+02, 1.089291061495973e+02, -2.058823577696314e+01, 1.327712169169005e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 4.156444,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.328273,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.343068,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg    */  30.0       // bohr
    }, // end of Tc
 
 
 
    // ------------------
    /* idx 43 : Z=44  Ru */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            4.359643548981106e+02,
            1.247544760802347e+02,
            6.636049611431007e+00,
            3.476362393861161e+00,
            1.975034412380370e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.107722471308501e+05, 1.694199143429281e+06, 5.925369154275011e+05, 2.922094372894310e+05 }, // term 1
            { 4.314665344191609e+05, 3.268859173983152e+03, 3.432116990631662e+05, 6.482160058155446e+05 }, // term 2
            { 2.646014302206449e+02, -8.871791976183749e+02, -2.467795509235997e+02, 6.276717770976809e+01 }, // term 3
            { 3.335047479177384e+02, -6.290783681654011e+01, 1.553959580646766e+02, 1.612423707645704e+01 }, // term 4
            { -1.436471016076795e+02, 7.086740547698410e+01, -1.194893323686286e+01, 7.490760183423153e-01 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.865053,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.920665,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.885005,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Ru
 
 
    // ------------------
    /* idx 44 : Z=45  Rh */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            3.767184259685127e+02,
            1.721248535583190e+02,
            1.137817808972690e+01,
            2.984710794169183e+00,
            2.108188595953131e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.832116171027688e+06, 1.137446957796907e+06, 1.467228581925579e+06, 9.316366601569484e+05 }, // term 1
            { 7.152712066708131e+05, 2.822508829701229e+03, 2.986210283592611e+05, 9.799193101060577e+05 }, // term 2
            { 8.940592735534177e+02, -4.113906446781398e+02, -7.056647610139976e+02, 6.629401150127998e+01 }, // term 3
            { 2.517736329703732e+02, -1.525479856678254e+02, 6.125087710370366e+01, -4.702157542833372e+01 }, // term 4
            { -1.680594264059253e+02, 1.610784248668555e+02, -3.398017295055227e+01, 2.304057059072785e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.732396,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.788575,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.724570,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Rh
 
    // ------------------
    /* idx 45 : Z=46  Pd */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            3.790605091407109e+02,
            1.899119624993291e+02,
            1.201201117714957e+01,
            3.108199280863595e+00,
            2.160785972772184e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.538868582997397e+06, 1.217929285224446e+06, 6.081680369571429e+05, 7.403586201785798e+05 }, // term 1
            { 1.168809280837228e+06, 2.286360763873153e+03, 2.860749055502098e+05, 6.764456038515564e+05 }, // term 2
            { 1.224094055058152e+03, -5.586939388670853e+02, -2.166137195722192e+02, 6.355546623308449e+01 }, // term 3
            { 1.861169876417291e+02, -1.010826167605884e+02, 6.321205310464674e+01, -4.161519990588689e+01 }, // term 4
            { -1.218492054080633e+02, 1.116671415036620e+02, -2.352849458624928e+01, 1.568006454705676e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.244287,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.027783,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.887245,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Pd
 
    // ------------------
    /* idx 46 : Z=47  Ag */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            3.800561349293773e+02,
            1.969294857523570e+02,
            1.229173890494504e+01,
            3.202844186629138e+00,
            2.169756918318401e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.988744377431665e+06, 6.810608910066249e+04, 1.291531659450754e+06, 1.291215807648164e+06 }, // term 1
            { 1.338444025281932e+06, 4.471182463500015e+03, 2.496909911732772e+05, 9.114371723526628e+05 }, // term 2
            { 1.288524817305443e+03, -1.889769930225278e+02, -7.062134406415482e+02, 3.587986182007543e+01 }, // term 3
            { 1.896266233131087e+02, -6.901980714020347e+01, 5.798728918285732e+01, -4.555432795653903e+01 }, // term 4
            { -1.341971735995322e+02, 1.232523629081326e+02, -2.852730585916767e+01, 2.183657025443304e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.509034,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.586189,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.490437,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Ag
 
    // ------------------
    /* idx 47 : Z=48  Cd */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            4.239846809918481e+02,
            1.911261686375819e+02,
            1.286540255393204e+01,
            3.189584543291396e+00,
            2.169776199967576e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.180037863061968e+06, 1.780784255552213e+03, 1.883403575273141e+06, 1.376676009572998e+06 }, // term 1
            { 1.065024960202069e+06, 7.061916922500754e+03, 3.392887537058744e+05, 1.894777101419123e+06 }, // term 2
            { 1.728371323379872e+03, -3.164740539028084e+02, -8.971202680190529e+02, 1.150383486361433e+02 }, // term 3
            { 1.378339825949309e+02, -4.948010794246112e+00, 1.180615284792429e+01, -2.511104961246864e+01 }, // term 4
            { -1.055487368703910e+02, 9.263808654461042e+01, -2.108079552242645e+01, 1.644015845764854e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 3.651328,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.586189,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.388960,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of Cd
 
 
    // ------------------
    /* idx 48 : Z=49  In */ {
    // ------------------
        /* n_terms */ 5,
        /* alpha   */ {
            4.341478700970577e+02,
            2.130078441944414e+02,
            1.129546929037459e+01,
            3.062677209218508e+00,
            2.092183700229488e+00,
            0.0
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 8.652835529160596e+05, 1.510840574346172e+03, 1.990568559042664e+06, 1.362813318225479e+06 }, // term 1
            { 2.230372359572058e+06, 9.599038796965226e+03, 4.508007828385527e+05, 2.087606701258378e+06 }, // term 2
            { 1.222725427642879e+03, -1.373979634886840e+02, -7.257139685754012e+02, 7.385987762530350e+01 }, // term 3
            { 7.390527933445888e+01, -8.164659979935833e+01, -6.444020530929873e+01, -3.686174046158256e+01 }, // term 4
            { -5.713354857701304e+01, 1.472234367042772e+02, -4.256777781824670e+01, 3.663937902512499e+00 }, // term 5
    }, // end of 'a'
        /* r_cut99   */ 4.085580,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.549934,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 8.467221,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 30.0
    }, // end of In
 
    // ------------------
    /* idx 49 : Z=50  Sn */ {
    // ------------------
        /* n_terms */ 6,
        /* alpha   */ {
            4.138466372813405e+02,
            2.560602520192794e+02,
            5.967662599558098e+01,
            1.146239410563283e+01,
            2.997304199091875e+00,
            2.080721567717183e+00
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.944692557968491e+06, 4.353403819952226e+05, 1.171768750156853e+06, 1.393775394507077e+06 }, // term 1
            { 2.295407251422541e+05, 7.269918480748729e+05, 1.226518994447893e+06, 4.977404970552641e+05 }, // term 2
            { 1.615441196217320e+04, 3.617510133794803e+01, 2.181684685472328e+02, 1.545033686781014e+02 }, // term 3
            { 1.829782430978784e+03, 8.151380753531969e-01, -1.030894752746840e+01, 1.596396781938975e+01 }, // term 4
            { -4.819035914892549e+02, 2.357554504247813e+02, -1.990314036797938e+02, 1.028281898835555e+02 }, // term 5
            { 3.871079145998077e+02, -2.902286089537633e+02, 5.457432791639454e+01, -2.918774808088296e+00 }, // term 6
    }, // end of 'a'
        /* r_cut99   */ 4.108824,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 6.099242,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 7.561867,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 10.4350
    }, // end of Sn
 
 
    // ------------------
    /* idx 50 : Z=51  Sb */ {
    // ------------------
        /* n_terms */ 6,
        /* alpha   */ {
            4.473578649901836e+02,
            4.131564832186803e+02,
            3.296625217986643e+02,
            1.324021119529086e+01,
            3.469105899528824e+00,
            2.486005670643116e+00
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 2.884536956878446e+05, 1.262395935405997e+06, 1.225402543647633e+06, 7.695622266067440e+05 }, // term 1
            { 1.637819421326813e+06, 9.733850464766740e+05, 9.497193315490221e+05, 1.868971780533742e+06 }, // term 2
            { 1.701574577834392e+04, 4.655546914894258e+01, 2.107733838519138e+02, 1.089953876459621e+02 }, // term 3
            { 1.155219759323437e+03, -3.103644965283792e+01, 1.288068020603342e+01, 4.802186582396089e+01 }, // term 4
            { -6.009390797346223e+02, 1.009769399641189e+03, -2.247712465236667e+02, 4.799900652242957e+02 }, // term 5
            { 5.431909982798429e+02, -9.964140186473296e+02, 2.419536474178813e+02, -1.510576275248690e+01 }, // term 6
    }, // end of 'a'
        /* r_cut99   */ 3.967096,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.566347,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.778966,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 9.4957
    }, // end of Sb
 
 
    // ------------------
    /* idx 51 : Z=52  Te */ {
    // ------------------
        /* n_terms */ 6,
        /* alpha   */ {
            4.040522284757012e+02,
            2.758557407711467e+02,
            3.405275155673196e+01,
            1.049298660507237e+01,
            3.434186919392003e+00,
            2.471385875810073e+00
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 1.528275685988734e+06, 1.939455807950720e+05, 4.904432291846660e+05, 3.073891376433382e+05 }, // term 1
            { 6.610930228283348e+05, 1.548167468161040e+06, 4.184109802246600e+05, 7.258947942372777e+05 }, // term 2
            { 8.787813933121050e+03, 1.045725737731916e+01, 1.046014288729097e+02, 3.604475131350994e+02 }, // term 3
            { 1.332373447542683e+03, 8.795541273418739e-01, -1.170097121665318e+01, 2.071834833015514e+01 }, // term 4
            { -8.381839803806389e+02, 1.080151674915145e+03, -2.998754693618649e+02, 4.430259983244877e+02 }, // term 5
            { 6.476074448973150e+02, -9.999999939165955e+02, 2.366804507086104e+02, -1.491018484680749e+01 }, // term 6
    }, // end of 'a'
        /* r_cut99   */ 3.876391,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.463170,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.663316,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 9.2564
    }, // end of Te
 
    // ------------------
    /* idx 52 : Z=53  I  */ {
    // ------------------
        /* n_terms */ 6,
        /* alpha   */ {
            4.279089130682303e+02,
            3.990094836457029e+02,
            3.834357012973386e+01,
            1.349674443830784e+01,
            3.899191698036487e+00,
            2.704912702020832e+00
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 6.503944241784989e+05, 2.287248625464889e+06, 6.005662863837199e+05, 6.256013914006945e+05 }, // term 1
            { 2.249388698835783e+05, 2.641008376462127e+05, 7.370150596266105e+05, 4.133743956586396e+05 }, // term 2
            { 7.230140818235169e+03, -5.192396916119725e+00, 3.375574460583236e+01, 8.925048309032815e+02 }, // term 3
            { 2.418573269413257e+03, 1.375590474085064e+00, -1.875403523933997e+01, 3.143904848081327e+01 }, // term 4
            { -2.876916847051469e+02, 2.622647897599601e+03, -9.998834052232698e+02, 1.229381004163694e+03 }, // term 5
            { -4.776690240396373e+01, -9.999999997165366e+02, 3.148581318140515e+02, -2.294600167623882e+01 }, // term 6
    }, // end of 'a'
        /* r_cut99   */ 3.752805,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.164975,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.254008,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.6966
    }, // end of I
 
 
    // ------------------
    /* idx 53 : Z=54  Xe */ {
    // ------------------
        /* n_terms */ 6,
        /* alpha   */ {
            4.898281080809339e+02,
            2.082204523786991e+02,
            9.591673131908904e+01,
            1.524494928317407e+01,
            3.874777723885396e+00,
            2.720449565049155e+00
        }, // end of alpha
        /* a       */ {
            //   a0                     a1                     a2                     a3
            { 3.177018638001626e+05, 1.344332062104049e+05, 7.386384362635893e+05, 1.218964655578203e+06 }, // term 1
            { 1.100378643622496e+06, 1.966416246630932e+06, 2.720656790565730e+05, 1.069709947436636e+06 }, // term 2
            { 7.453920738501492e+03, -1.300602206169190e+01, 1.667928854931854e+01, -2.840622965689376e+02 }, // term 3
            { 2.862672695396896e+03, 1.180588270538911e-01, -1.611613778312743e+02, 2.759271687420222e+01 }, // term 4
            { -6.973148030029027e+01, 2.459801376282415e+03, -7.186740327346346e+02, 1.139333237397242e+03 }, // term 5
            { -1.590065302748299e+02, -9.994116551287625e+02, 3.148295426032540e+02, -2.279052064251306e+01 }, // term 6
    }, // end of 'a'
        /* r_cut99   */ 3.634888,  // bohr, int_0^r 4pir2 rho dr >= 0.99 * Z
        /* r_cut999  */ 5.070301,  // bohr, int_0^r 4pir2 rho dr >= 0.999 * Z
        /* r_cut9999 */ 6.176341,  // bohr, int_0^r 4pir2 rho dr >= 0.9999 * Z
        /* r_neg     */ 8.699
    }, // end of Xe
 
}; // end of PROMOL_G2
 
// The cte  in front of the expression of the ED "slater", no unit               
const double    A1[NB_KNW_ATMS] = { //[1:2]   1s 
                                    0.2815, 2.437,                                                                            
                                    //[3:10]  2s 2p
                    11.84, 31.34, 67.82, 120.2,190.9, 289.5, 406.3, 561.3,
                                    //[11:18] 3s 3p
                    760.8, 1016., 1319., 1658., 2042., 2501., 3024., 3625.,
                                    //[19:20] 4s
                    422.685, 328.056,
                                    //[21:30] 3d
                    369.212, 294.479, 525.536, 434.298, 9346.12, 579.606, 665.791, 793.8, 897.784, 1857.03,
                                    //[31:36] 4p
                    898.009, 1001.24, 1101.35, 1272.92, 1333.8, 1459.53, 
                                    //[37:51] 5s NOT AVAILABLE
                                    0.0, 0.0,
                                    //4d NOT AVAILABLE
                                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //[52:54] 5p
                                    0.0, 0.0, 0.0, 457.406, 3.23589, 643.098
};
 
 
// The cte  in front of the expression of the ED "slater", no unit
const double    A2[NB_KNW_ATMS] = { //[1:2]   1s
                                    0.0, 0.0,                                                                               
                                    //[3:10]  2s 2p
                    0.06332, 0.3694, 0.8527, 1.172, 2.247, 2.879, 3.049, 6.984,
                                    //[11:18] 3s 3p
                    22.42, 37.17, 57.95, 87.16, 115.7, 158.0, 205.5, 260.0,
                                    //[19:20] 4s
                    104.678, 48.1693,
                                    //[21:30] 3d
                    66.7813, 64.3627, 97.5552, 37.8524, 166.393, 50.2383, 51.7033, 60.5725, 58.8879, 135.027,
                                    //[31:36] 4p
                    1.10777, 0.855815, 901.893, 1.20778, 1.0722, 1.95028,
                                    //[37:51] 5s NOT AVAILABLE
                                    0.0, 0.0,
                                    //4d NOT AVAILABLE
                                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //[52:54] 5p
                                    0.0, 0.0, 0.0, 0.0648533, 4.1956, 0.133996
};
 
// The cte  in front of the expression of the ED "slater", no unit
const double    A3[NB_KNW_ATMS] = { //1s
                                    0.0, 0.0,                                                                                
                                    //2s 2p
                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //3s 3p
                    0.06358, 0.3331, 0.8878, 0.7888, 1.465, 2.170, 3.369, 5.211,
                                    //4s
                    0.0305251, 0.137293,
                                    //3d
                    0.217304, 0.312378, 0.288164, 0.216041, 0.428442, 0.301226, 0.358959, 0.384414, 0.446463, 0.664027,
                                    //4p
                    0.178217, 0.271045, 1.43271, 0.548474, 1.52238, 3.12305,
                                    //5s NOT AVAILABLE
                                    0.0, 0.0,
                                    //4d NOT AVAILABLE
                                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //5p
                                    0.0, 0.0, 0.0, 0.0273883, 0.0347855, 0.0499776
};
 
// exponent in the expression of the ED "slater", given in bohr^-1 (to be multiplied by the distance 
// between the current grid node and the considered atom --> the distance hs to be expressed in bohr)
const double    B1[NB_KNW_ATMS] = { //1s
                                    1.8910741301059, 2.95945546019532,                                                                                 
                                    //2s 2p
                    5.23012552301255, 7.19424460431655, 9.44287063267233, 11.3122171945701, 13.0378096479791, 14.9476831091181, 16.4473684210526, 18.2149362477231,  
                                    //3s 3p
                    20.1612903225806, 22.271714922049,  24.330900243309, 26.1780104712042, 27.9329608938547, 29.8507462686567, 31.7460317460318, 33.7837837837838,
                                    //4s
                    61.3085, 13.6033,
                                    //3d
                    15.1828, 8.87333, 18.4925, 12.2138, 47.0758, 13.6638, 14.1117, 15.1832, 15.4177, 23.5312,
                                    //4p
                    12.4217, 12.8073, 13.0865, 13.8734, 13.8227, 14.1814,
                                    //5s NOT AVAILABLE
                                    0.0, 0.0,
                                    //4d NOT AVAILABLE
                                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //5p
                                    0.0, 0.0, 0.0, 3.82753, 23.9761, 4.10166 
};
 
// exponent in the expression of the ED "slater", given in bohr^-1 (to be multiplied by the distance 
// between the current grid node and the considered atom --> the distance hs to be expressed in bohr)
const double    B2[NB_KNW_ATMS] = { //1s
                                    1.000000, 1.000000, 
                                    //2s 2p
                    1.00080064051241, 1.43988480921526, 1.88679245283019, 1.82481751824818, 2.20653133274492, 2.51635631605435, 2.50375563345018, 2.90107339715695,  
                                    //3s 3p
                    3.98247710075667, 4.65116279069767, 5.33617929562433, 6.0459492140266, 6.62690523525514, 7.30460189919649, 7.9428117553614, 8.56164383561644,
                                    //4s
                    3.81272, 3.94253,
                                    //3d
                    4.24199, 4.33369, 4.58656, 3.81061, 5.07878, 4.09039, 4.17018, 4.30955, 4.35337, 5.19033,
                                    //4p
                    2.00145, 1.85496, 7.70162, 1.88584, 2.12925, 2.35537,
                                    //5s NOT AVAILABLE
                                    0.0, 0.0,
                                    //4d NOT AVAILABLE
                                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //5p
                                    0.0, 0.0, 0.0, 1.19985, 2.24851, 1.25439 
};
 
// exponent in the expression of the ED "slater", given in bohr^-1 (to be multiplied by the distance 
// between the current grid node and the considered atom --> the distance hs to be expressed in bohr)
const double    B3[NB_KNW_ATMS] = { //1s
                                    1.000000, 1.000000, 
                                    //2s 2p
                    1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 
                                    //3s 3p
                    0.9769441187964, 1.28982329420869, 1.67728950016773, 1.42959256611866, 1.70910955392241, 1.94212468440474, 2.01045436268597, 2.26654578422484,
                                    //4s
                    0.760211, 0.972271,
                                    //3d
                    1.08807, 1.18612, 1.19053, 1.22212, 1.3246, 1.32999, 1.38735, 1.42114, 1.48338, 1.54071,
                                    //4p
                    1.19489, 1.31783, 1.64735, 1.57665, 1.79153, 1.99148,
                                    //5s NOT AVAILABLE
                                    0.0, 0.0,
                                    //4d NOT AVAILABLE
                                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
                                    //5p
                                    0.0, 0.0, 0.0, 0.906738, 0.856995, 1.02511   
};

//const double vdW_VALUES[NB_KNW_ATMS]  = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };

typedef enum PARAM_TYPES
  {
    TYPE_INCREMENTS,
    TYPE_INTERMOLECULAR,
    TYPE_RADIUS,
    TYPE_OUTPUT_NAME,
    TYPE_CUBE,
    TYPE_CUTOFFS,
    TYPE_CUTPLOT,
    TYPE_CUTPLOT_IGM,
    TYPE_VMD_COLRANG_IGM,
    TYPE_LIGAND,
    TYPE_OUTPUT,
    FRAG1,
    FRAG2,
    BONDS,
    IBSI,
    CUBEFRAG,
    //CHARGE,
    HIRSH,
    CRITIC,
    CRITICFINE,
    CRITICULTRAFINE, 
    CRITICaddSEEDS,
    TYPE_PEAKFOCUSINTRA,
    TYPE_PEAKFOCUSINTER,
    ELF, 
    DGSCALED,
    PARSERKF,
    SELF,
    SELFATOMIC,
    FULLAOACC,
    PROSELF,   
    TOPELF,
    SIZE_PARAM
  } param_types_t;

const std::string PARAM_NAMES [] =
  {
    "INCREMENTS",
    "INTERMOLECULAR",
    "RADIUS",
    "ONAME",
    "CUBE",
    "CUTOFFS",
    "CUTPLOT",
    "CUTPLOT_IGM",
    "VMD_COLRANG_IGM",
    "LIGAND",
    "OUTPUT",
    "FRAG1",
    "FRAG2",
    "BONDS",
    "IBSI",
    "CUBEFRAG",
    //"CHARGE",
    "HIRSH",
    "CRITIC",
    "CRITICFINE",
    "CRITICULTRAFINE",
    "CRITICADDSEEDS",
    "PEAKFOCUSINTRA",
    "PEAKFOCUSINTER",
    "ELF",
    "DGSCALED",
    "PARSERKF",
    "SELF",
    "SELFATOMIC",
    "FULLAOACC",
    "PROSELF",
    "TOPELF"
  };
 
                                
typedef struct
{
  double grad;
  
  double gradIGM;

  double gradIGMInter;

  double gradIGMInter2;

  double gradIGMInter3;
}norms_t;

typedef struct
{
  std::string molAFileName;

  std::string molBFileName;

  std::string outputName;

  double radiusRoundLigand;

  double intermolecular;

  int numLigand;

  int nbFiles;

  int outputType;

  double radius[4];

  double cutoffs[2];
  
  double cutplot[2];

  double cutplotIGM[2];

  double vmdcolrangIGM[2];

  double cube[6];

  double increments[3];

  bool cubeUsed;

  bool radiusUsed;
 
  bool cubefrag;

  double bondcut;

  bool paramFound[SIZE_PARAM];

  unsigned int coremo;

  int CHARGE;

  double cutpeakIntra[2];
  double cutpeakInter[2];
 
}param_t;

typedef enum CUBE_TYPES
  {
    TYPE_DELTA_G_INTRA,
    TYPE_DELTA_G_INTER,
    SIZE_CUBE_DELTA,
    TYPE_RHO,
    TYPE_RDG,
    TYPE_DELTA_G_INTRAFC,
    TYPE_DELTA_G_INTERFC
  }cube_types_t;

typedef enum OUTPUT_TYPES
  {
    OUTPUT_NONE,
    OUTPUT_DAT,
    OUTPUT_RHO_RDG,
    OUTPUT_DELTA,
    OUTPUT_PERCENT,
    OUTPUT_ALL
  }output_types_t;

typedef struct
{

  std::pair< unsigned int,  unsigned int> atomPair;

  double length; // in bohr

  double ibsi;  // no unit

  double baf;  // unit of ED gradient

  double ABx,ABy,ABz;
 
}bond_t;

typedef struct
{
  double x;

  double y;

  double z;    
}position_t;
 
/* JC: the definition of axis_t and position_t are similar 
 * but have different documentation ...*/
typedef struct
{
  double x;
  double y;
  double z;    
}axis_t;

typedef struct
{
  double * __restrict xValues;

  double * __restrict yValues;

  double * __restrict zValues;
}positions_t;

typedef struct criticalpoint
  {
      double pos[3], L123[3]; // array containing coordinates of found critical points and ED hessian eigenval.
      double H, V, G, laplac, RHO, GRADRHO;  // and local energy density and kinetic energy density and ED and and ED gradient magn. and laplacian
      double dg, qg; // local dg and qd descriptors
      int type; // -3=NCP, -1=BCP, 1=RCP, 3=CCP
 
  } criticalpoint;
 
 
#endif