source: ThirdParty/mpqc_open/src/lib/chemistry/qc/dft/functional.h@ 91c409

//
// functional.h --- definition of the dft functional
//
// Copyright (C) 1997 Limit Point Systems, Inc.
//
// Author: Curtis Janssen <cljanss@limitpt.com>
// Maintainer: LPS
//
// This file is part of the SC Toolkit.
//
// The SC Toolkit is free software; you can redistribute it and/or modify
// it under the terms of the GNU Library General Public License as published by
// the Free Software Foundation; either version 2, or (at your option)
// any later version.
//
// The SC Toolkit is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public License
// along with the SC Toolkit; see the file COPYING.LIB.  If not, write to
// the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
//
// The U.S. Government is granted a limited license as per AL 91-7.
//

#ifndef _chemistry_qc_dft_functional_h
#define _chemistry_qc_dft_functional_h

#ifdef __GNUC__
#pragma interface
#endif

#include <util/state/state.h>
#include <math/scmat/vector3.h>
#include <chemistry/qc/wfn/wfn.h>
#include <chemistry/qc/wfn/density.h>

namespace sc {

/** Contains data needed at each point by a DenFunctional. */
struct PointInputData {
    enum {X=BatchElectronDensity::X,
          Y=BatchElectronDensity::Y,
          Z=BatchElectronDensity::Z};
    enum {XX=BatchElectronDensity::XX,
          YX=BatchElectronDensity::YX,
          YY=BatchElectronDensity::YY,
          ZX=BatchElectronDensity::ZX,
          ZY=BatchElectronDensity::ZY,
          ZZ=BatchElectronDensity::ZZ};
    struct SpinData {
        double rho;
        // rho^(1/3)
        double rho_13;

        double del_rho[3];
        // gamma = (del rho).(del rho)
        double gamma;

        // hessian of rho
        double hes_rho[6];
        // del^2 rho
        double lap_rho;
    };
    SpinData a, b;

    // gamma_ab = (del rho_a).(del rho_b)
    double gamma_ab;

    const SCVector3 &r;

    // fill in derived quantities
    void compute_derived(int spin_polarized,
                         int need_gradient,
                         int need_hessian);

    PointInputData(const SCVector3& r_): r(r_) {}
};

/** Contains data generated at each point by a DenFunctional. */
struct PointOutputData {
    // energy at r
    double energy;

    // derivative of functional wrt density
    double df_drho_a;
    double df_drho_b;

    // derivative of functional wrt density gradient
    double df_dgamma_aa;
    double df_dgamma_bb;
    double df_dgamma_ab;
 
  void zero(){energy=df_drho_a=df_drho_b=df_dgamma_aa=df_dgamma_bb=df_dgamma_ab=0.0;}

};

/** An abstract base class for density functionals. */
class DenFunctional: virtual public SavableState {
  protected:
    int spin_polarized_;
    int compute_potential_;
    double a0_;  // for ACM functionals

    void do_fd_point(PointInputData&id,double&in,double&out,
                     double lower_bound, double upper_bound);
  public:
    DenFunctional();
    DenFunctional(const Ref<KeyVal> &);
    DenFunctional(StateIn &);
    ~DenFunctional();
    void save_data_state(StateOut &);

    // Set to zero if dens_alpha == dens_beta everywhere.
    // The default is false.
    virtual void set_spin_polarized(int i);
    // Set to nonzero if the potential should be computed.
    // The default is false.
    virtual void set_compute_potential(int i);

    // Must return 1 if the density gradient must also be provided.
    // The default implementation returns 0.
    virtual int need_density_gradient();
    // Must return 1 if the density hessian must also be provided.
    // The default implementation returns 0.
    virtual int need_density_hessian();

    virtual void point(const PointInputData&, PointOutputData&) = 0;
    void gradient(const PointInputData&, PointOutputData&,
                  double *gradient, int acenter,
                  GaussianBasisSet *basis,
                  const double *dmat_a, const double *dmat_b,
                  int ncontrib, const int *contrib,
                  int ncontrib_bf, const int *contrib_bf,
                  const double *bs_values, const double *bsg_values,
                  const double *bsh_values);

    /// Returns the fraction of Hartee-Fock exchange to be included.
    virtual double a0() const;

    void fd_point(const PointInputData&, PointOutputData&);
    int test(const PointInputData &);
    int test();
};


/** The NElFunctional computes the number of electrons.
    It is primarily for testing the integrator. */
class NElFunctional: public DenFunctional {
  public:
    NElFunctional();
    NElFunctional(const Ref<KeyVal> &);
    NElFunctional(StateIn &);
    ~NElFunctional();
    void save_data_state(StateOut &);

    void point(const PointInputData&, PointOutputData&);
};

/** The SumDenFunctional computes energies and densities
    using the a sum of energy density functions method. */
class SumDenFunctional: public DenFunctional {
  protected:
    int n_;
    Ref<DenFunctional> *funcs_;
    double *coefs_;
  public:
    SumDenFunctional();
    /**
       This KeyVal constructor reads the following keywords:
       <dl>
       <dt><tt>funcs</tt><dd>Specifies an array of DenIntegrator objects.
       <dt><tt>coefs</tt><dd>Specifies the coefficient of each
       DenIntegrator object.
       <dt><tt>a0</tt><dd>Specifies the coefficient of the Hartree-Fock
       exchange.  This is nonzero for hybrid functionals.  The default
       is zero.

       </dl>
       
      For example, the B3LYP functional can be specified
      with the following input:
      <pre>
      functional\<SumDenFunctional\>: (
        a0 = 0.2
        coefs = [ 0.8 0.72 0.19 0.81 ]
        funcs: [
          \<SlaterXFunctional\>:()
          \<Becke88XFunctional\>:()
          \<VWN1LCFunctional\>:( rpa = 1 )
          \<LYPCFunctional\>:()
        ]
      )
      </pre>
     */
    SumDenFunctional(const Ref<KeyVal> &);
    SumDenFunctional(StateIn &);
    ~SumDenFunctional();
    void save_data_state(StateOut &);

    void set_spin_polarized(int);
    void set_compute_potential(int);
    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);

    void print(std::ostream& =ExEnv::out0()) const;

    /** Override the DenFunctional::a0() member, so that a0's in
        contributing functionals can be added in as well. */
    double a0() const;
};

/** The StdDenFunctional class is used to construct the standard density
    functionals.

    The table below lists the functional names and the equivalent
    functionals in other packages.  The Name column gives the name as it is
    given in the input file (this is case sensitive).  Functional names
    with non-alpha-numeric names should be given in double quotes.  The
    description column gives the classes used to build up the functional
    and its coefficient, if it is other than one.  The G98 column lists the
    equivalent functional in Gaussian 98 A.6.  The NWChem column lists the
    equivalent functional in NWChem 3.3.1.

<table>
<tr><td>Name    <td> Description         <td> G98    <td> NWChem 
<tr><td>XALPHA  <td> XalphaFunctional    <td> XALPHA <td>        
<tr><td>HFS     <td> SlaterXFunctional   <td> HFS    <td> slater 
<tr><td>HFB     <td> Becke88XFunctional  <td> HFB    <td> becke88
<tr><td>HFG96   <td> G96XFunctional      <td>        <td>        
<tr><td>G96LYP  <td> G96XFunctional                      
                    +LYPCFunctional      <td> G96LYP <td>         
<tr><td>BLYP    <td> SlaterXFunctional                  
                    +Becke88XFunctional                
                    +LYPCFunctional           <td> BLYP  <td>        
<tr><td>SVWN1   <td> SlaterXFunctional
                    +VWN1LCFunctional         <td>       <td> slater vwn_1 
<tr><td>SVWN1RPA<td> SlaterXFunctional
                    +VWN1LCFunctional(1)      <td>       <td> slater vwn_1_rpa 
<tr><td>SVWN2   <td> SlaterXFunctional
                    +VWN2LCFunctional         <td>       <td> slater vwn_2 
<tr><td>SVWN3   <td> SlaterXFunctional
                    +VWN2LCFunctional         <td>       <td> slater vwn_3 
<tr><td>SVWN4   <td> SlaterXFunctional
                    +VWN4LCFunctional         <td>       <td> slater vwn_4 
<tr><td>SVWN5   <td> SlaterXFunctional
                    +VWN5LCFunctional         <td> SVWN5 <td> slater vwn_5 
<tr><td>SPZ81   <td> SlaterXFunctional
                    +PZ81LCFunctional         <td> SPL   <td>         
<tr><td>SPW92   <td> SlaterXFunctional
                    +PW92LCFunctional         <td>       <td> slater pw91lda 
<tr><td>BP86    <td> SlaterXFunctional
                    +Becke88XFunctional
                    +P86CFunctional
                    +PZ81LCFunctional         <td>       <td> becke88 perdue86 
<tr><td>B3LYP   <td> 0.2 HF-Exchange
                    + 0.8  SlaterXFunctional
                    + 0.72 Becke88XFunctional
                    + 0.19 VWN1LCFunctional(1)
                    + 0.81 LYPCFunctional     <td> B3LYP  <td>   b3lyp 
<tr><td>B3PW91  <td> 0.2 HF-Exchange
                    + 0.8  SlaterXFunctional
                    + 0.72 Becke88XFunctional
                    + 0.19 PW91CFunctional
                    + 0.81 PW92LCFunctional   <td> B3PW91 <td>        
<tr><td>B3P86   <td> 0.2 HF-Exchange
                   + 0.8 SlaterXFunctional
                   + 0.72 Becke88XFunctional
                   + 0.19 P86CFunctional
                   + 0.81 VWN1LCFunctional (1)<td>        <td>          
<tr><td>PBE     <td> PBEXFunctional
                    +PBECFunctional           <td>        <td> xpbe96 cpbe96 
<tr><td>PW91    <td> PW91XFunctional
                    +PW91CFunctional          <td>        <td>           
<tr><td>mPW(PW91)PW91
                <td> mPW91XFunctional(PW91)
                    +PW91CFunctional          <td>PW91PW91<td>       
<tr><td>mPWPW91 <td> mPW91XFunctional(mPW91)
                    +PW91CFunctional          <td>        <td>           
<tr><td>mPW1PW91<td> 0.16 HF-Exchange
                   + 0.84 mPW91XFunctional(mPW91)
                   +PW91CFunctional           <td>        <td>           

</table> */
class StdDenFunctional: public SumDenFunctional {
  protected:
    char *name_;
    void init_arrays(int n);
  public:
    StdDenFunctional();
    /** The <tt>name</tt> keyword is read from the input and is used to
        initialize the functional.  See the general StdDenFunctional
        description for a list of valid values for <tt>name</tt>.
    */
    StdDenFunctional(const Ref<KeyVal> &);
    StdDenFunctional(StateIn &);
    ~StdDenFunctional();
    void save_data_state(StateOut &);

    void print(std::ostream& =ExEnv::out0()) const;
};

/** An abstract base class for local correlation functionals. */
class LSDACFunctional: public DenFunctional {
  protected:
  public:
    LSDACFunctional();
    LSDACFunctional(const Ref<KeyVal> &);
    LSDACFunctional(StateIn &);
    ~LSDACFunctional();
    void save_data_state(StateOut &);

    void point(const PointInputData&, PointOutputData&);
    virtual 
      void point_lc(const PointInputData&, PointOutputData&, 
                    double &ec_local, double &decrs, double &deczeta) = 0;

};


/** Implements the Perdew-Burke-Ernzerhof (PBE) correlation functional.

    John P. Perdew, Kieron Burke, and Yue Wang, Phys. Rev. B, 54(23),
    pp. 16533-16539, 1996.

    John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett.,
    77(18), pp. 3865-3868, 1996.
*/
class PBECFunctional: public DenFunctional {
  protected:
    Ref<LSDACFunctional> local_;
    double gamma;
    double beta;
    void init_constants();
    double rho_deriv(double rho_a, double rho_b, double mdr,
                     double ec_local, double ec_local_dra);
    double gab_deriv(double rho, double phi, double mdr, double ec_local);
  public:
    PBECFunctional();
    PBECFunctional(const Ref<KeyVal> &);
    PBECFunctional(StateIn &);
    ~PBECFunctional();
    void save_data_state(StateOut &);
    int need_density_gradient();
    void point(const PointInputData&, PointOutputData&);
    void set_spin_polarized(int);
  
};

/** The Perdew-Wang 1991 correlation functional computes energies and
    densities using the designated local correlation functional.

    J. P. Perdew, Proceedings of the 75. WE-Heraeus-Seminar and 21st Annual
    International Symposium on Electronic Structure of Solids held in
    Gaussig (Germany), March 11-15, 1991, P. Ziesche and H. Eschrig, eds.,
    pp. 11-20.

    J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson,
    and D. J. Singh, Phys. Rev. B, 46, 6671, 1992.  */
class PW91CFunctional: public DenFunctional {
  protected:
    Ref<LSDACFunctional> local_;
    double a;
    double b;
    double c;
    double d;
    double alpha;
    double c_c0;
    double c_x;
    double nu;
    void init_constants();
    double limit_df_drhoa(double rhoa, double gamma,
                          double ec, double decdrhoa);

  public:
    PW91CFunctional();
    PW91CFunctional(const Ref<KeyVal> &);
    PW91CFunctional(StateIn &);
    ~PW91CFunctional();
    void save_data_state(StateOut &);
    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
    void set_spin_polarized(int);
  
};

/** Implements the Perdew 1986 (P86) correlation functional.

    J. P. Perdew, Phys. Rev. B, 33(12), pp. 8822-8824.

    J. P. Perdew, Phys. Rev. B. 34(10), pp. 7406.
 */
class P86CFunctional: public DenFunctional {
  protected:
    double a_;
    double C1_;
    double C2_;
    double C3_;
    double C4_;
    double C5_;
    double C6_;
    double C7_;
    void init_constants();
  public:
    P86CFunctional();
    P86CFunctional(const Ref<KeyVal> &);
    P86CFunctional(StateIn &);
    ~P86CFunctional();
    void save_data_state(StateOut &);
    int need_density_gradient();
    void point(const PointInputData&, PointOutputData&);
  
};


// The Perdew 1986 (P86) Correlation Functional computes energies and densities
//    using the designated local correlation functional.
class NewP86CFunctional: public DenFunctional {
  protected:
    double a_;
    double C1_;
    double C2_;
    double C3_;
    double C4_;
    double C5_;
    double C6_;
    double C7_;
    void init_constants();
    double rho_deriv(double rho_a, double rho_b, double mdr);
    double gab_deriv(double rho_a, double rho_b, double mdr);

  public:
    NewP86CFunctional();
    NewP86CFunctional(const Ref<KeyVal> &);
    NewP86CFunctional(StateIn &);
    ~NewP86CFunctional();
    void save_data_state(StateOut &);
    int need_density_gradient();
    void point(const PointInputData&, PointOutputData&);
};

/**
   Implements the Slater exchange functional.
*/
class SlaterXFunctional: public DenFunctional {
  protected:
  public:
    SlaterXFunctional();
    SlaterXFunctional(const Ref<KeyVal> &);
    SlaterXFunctional(StateIn &);
    ~SlaterXFunctional();
    void save_data_state(StateOut &);
    void point(const PointInputData&, PointOutputData&);
};

/** An abstract base class from which the various VWN (Vosko, Wilk and
    Nusair) local correlation functional (1, 2, 3, 4, 5) classes are
    derived.

    S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys., 58, pp. 1200-1211,
    1980.
*/
class VWNLCFunctional: public LSDACFunctional {
  protected:
    double Ap_, Af_, A_alpha_;
    double x0p_mc_, bp_mc_, cp_mc_, x0f_mc_, bf_mc_, cf_mc_;
    double x0p_rpa_, bp_rpa_, cp_rpa_, x0f_rpa_, bf_rpa_, cf_rpa_;
    double x0_alpha_mc_, b_alpha_mc_, c_alpha_mc_;
    double x0_alpha_rpa_, b_alpha_rpa_, c_alpha_rpa_;
    void init_constants();

    double F(double x, double A, double x0, double b, double c);
    double dFdr_s(double x, double A, double x0, double b, double c);
  public:
    VWNLCFunctional();
    VWNLCFunctional(const Ref<KeyVal> &);
    VWNLCFunctional(StateIn &);
    ~VWNLCFunctional();
    void save_data_state(StateOut &);

    virtual
      void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};
    
/** The VWN1LCFunctional computes energies and densities using the
    VWN1 local correlation term (from Vosko, Wilk, and Nusair). */
class VWN1LCFunctional: public VWNLCFunctional {
  protected:
    double x0p_, bp_, cp_, x0f_, bf_, cf_;
  public:
    /// Construct a VWN1 functional using Monte-Carlo parameters.
    VWN1LCFunctional();
    /// Construct a VWN1 functional using the RPA parameters.
    VWN1LCFunctional(int use_rpa);
    /** Construct a VWN1 functional using the Monte-Carlo parameters by
        default.  If rpa is set to true, then load the RPA paramenters.
        Furthermore, each value can be overridden by assigning to
        x0p, bp, cp, x0f, bf, and/or cf.
    */
    VWN1LCFunctional(const Ref<KeyVal> &);
    VWN1LCFunctional(StateIn &);
    ~VWN1LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&,
                  double &, double &, double &);
};

/** The VWN2LCFunctional computes energies and densities using the
    VWN2 local correlation term (from Vosko, Wilk, and Nusair). */
class VWN2LCFunctional: public VWNLCFunctional {
  protected:
  public:
    /// Construct a VWN2 functional.
    VWN2LCFunctional();
    /// Construct a VWN2 functional.
    VWN2LCFunctional(const Ref<KeyVal> &);
    VWN2LCFunctional(StateIn &);
    ~VWN2LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};


/** The VWN3LCFunctional computes energies and densities using the
    VWN3 local correlation term (from Vosko, Wilk, and Nusair). */
class VWN3LCFunctional: public VWNLCFunctional {
  protected:
    int monte_carlo_prefactor_;
    int monte_carlo_e0_;
  public:
    VWN3LCFunctional(int mcp = 1, int mce0 = 1);
    VWN3LCFunctional(const Ref<KeyVal> &);
    VWN3LCFunctional(StateIn &);
    ~VWN3LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};

/** The VWN4LCFunctional computes energies and densities using the
    VWN4 local correlation term (from Vosko, Wilk, and Nusair). */
class VWN4LCFunctional: public VWNLCFunctional {
  protected:
    int monte_carlo_prefactor_;
  public:
    VWN4LCFunctional();
    VWN4LCFunctional(const Ref<KeyVal> &);
    VWN4LCFunctional(StateIn &);
    ~VWN4LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};

/** The VWN5LCFunctional computes energies and densities using the
    VWN5 local correlation term (from Vosko, Wilk, and Nusair). */
class VWN5LCFunctional: public VWNLCFunctional {
  protected:
  public:
    VWN5LCFunctional();
    VWN5LCFunctional(const Ref<KeyVal> &);
    VWN5LCFunctional(StateIn &);
    ~VWN5LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};

/** Implements the PW92 local (LSDA) correlation term.  This local
    correlation functional is used in PW91 and PBE.

    J. P. Perdew and Y. Wang.  Phys. Rev. B, 45, 13244, 1992.
*/
class PW92LCFunctional: public LSDACFunctional {
  protected:
    double F(double x, double A, double alpha_1, double beta_1, double beta_2, 
             double beta_3, double beta_4, double p);
    double dFdr_s(double x, double A, double alpha_1, double beta_1, double beta_2, 
             double beta_3, double beta_4, double p);
  public:
    PW92LCFunctional();
    PW92LCFunctional(const Ref<KeyVal> &);
    PW92LCFunctional(StateIn &);
    ~PW92LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};

/** Implements the PZ81 local (LSDA) correlation functional.  This local
   correlation functional is used in P86.

   J. P. Perdew and A. Zunger, Phys. Rev. B, 23, pp. 5048-5079, 1981.
*/
class PZ81LCFunctional: public LSDACFunctional {
  protected:
    double Fec_rsgt1(double rs, double beta_1, double beta_2, double gamma);
    double dFec_rsgt1_drho(double rs, double beta_1, double beta_2, double gamma,
                           double &dec_drs);
    double Fec_rslt1(double rs, double A, double B, double C, double D);
    double dFec_rslt1_drho(double rs, double A, double B, double C, double D,
                           double &dec_drs);
  public:
    PZ81LCFunctional();
    PZ81LCFunctional(const Ref<KeyVal> &);
    PZ81LCFunctional(StateIn &);
    ~PZ81LCFunctional();
    void save_data_state(StateOut &);

    void point_lc(const PointInputData&, PointOutputData&, double &, double &, double &);
};

/** Implements the Xalpha exchange functional */
class XalphaFunctional: public DenFunctional {
  protected:
    double alpha_;
    double factor_;
  public:
    XalphaFunctional();
    XalphaFunctional(const Ref<KeyVal> &);
    XalphaFunctional(StateIn &);
    ~XalphaFunctional();
    void save_data_state(StateOut &);

    void point(const PointInputData&, PointOutputData&);

    void print(std::ostream& =ExEnv::out0()) const;
};

/** Implements Becke's 1988 exchange functional.

    A. D. Becke, Phys. Rev. A, 38(6), pp. 3098-3100, 1988.
 */
class Becke88XFunctional: public DenFunctional {
  protected:
    double beta_;
    double beta6_;
  public:
    Becke88XFunctional();
    Becke88XFunctional(const Ref<KeyVal> &);
    Becke88XFunctional(StateIn &);
    ~Becke88XFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
};

/** Implements the Lee, Yang, and Parr functional.

    B. Miehlich, A. Savin, H. Stoll and H. Preuss, Chem. Phys. Lett.,
    157(3), pp. 200-206, 1989.

    C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B, 37(2), pp 785-789,
    1988.
 */
class LYPCFunctional: public DenFunctional {
  protected:
    double a_;
    double b_;
    double c_;
    double d_;
    void init_constants();
  public:
    LYPCFunctional();
    LYPCFunctional(const Ref<KeyVal> &);
    LYPCFunctional(StateIn &);
    ~LYPCFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
};

/** Implements the Perdew-Wang 1986 (PW86) Exchange functional.

    J. P. Perdew and Y. Wang, Phys. Rev. B, 33(12), pp 8800-8802, 1986.
*/
class PW86XFunctional: public DenFunctional {
  protected:
    double a_;
    double b_;
    double c_;
    double m_;
    void init_constants();
  public:
    PW86XFunctional();
    PW86XFunctional(const Ref<KeyVal> &);
    PW86XFunctional(StateIn &);
    ~PW86XFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
};

/** Implements the Perdew-Burke-Ernzerhof (PBE) exchange functional.

    John P. Perdew, Kieron Burke, and Yue Wang, Phys. Rev. B, 54(23),
    pp. 16533-16539, 1996.

    John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett.,
    77(18), pp. 3865-3868 1996.

    See also the comment and reply discussing the revPBE modification which
    adjusts the value of kappa:

    Yingkai Zhang and Weitao Yang, Phys. Rev. Lett., 80(4), pp. 890, 1998.

    John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett.,
    80(4), pp. 891, 1998.  */
class PBEXFunctional: public DenFunctional {
  protected:
    double mu;
    double kappa;
    void spin_contrib(const PointInputData::SpinData &,
                      double &mpw, double &dmpw_dr, double &dmpw_dg);
    void init_constants();
  public:
    PBEXFunctional();
    PBEXFunctional(const Ref<KeyVal> &);
    PBEXFunctional(StateIn &);
    ~PBEXFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
};

/** The Perdew-Wang 1991 exchange functional computes energies and densities
    using the designated local correlation functional.

    J. P. Perdew, Proceedings of the 75. WE-Heraeus-Seminar and 21st Annual
    International Symposium on Electronic Structure of Solids held in
    Gaussig (Germany), March 11-15, 1991, P. Ziesche and H. Eschrig, eds.,
    pp. 11-20.

    J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson,
    and D. J. Singh, Phys. Rev. B, 46, 6671, 1992.  */
class PW91XFunctional: public DenFunctional {
  protected:
    double a;
    double b;
    double c;
    double d;
    double a_x;
    void spin_contrib(const PointInputData::SpinData &,
                      double &mpw, double &dmpw_dr, double &dmpw_dg);
    void init_constants();
  public:
    PW91XFunctional();
    PW91XFunctional(const Ref<KeyVal> &);
    PW91XFunctional(StateIn &);
    ~PW91XFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
};

/** Implements a modified 1991 Perdew-Wang exchange functional.

    C. Adamo and V. Barone, J. Chem. Phys., 108(2), pp. 664-674, 1998.
*/
class mPW91XFunctional: public DenFunctional {
  protected:
    double b;
    double beta;
    double c;
    double d;
    double a_x;
    double x_d_coef;

    void spin_contrib(const PointInputData::SpinData &,
                      double &mpw, double &dmpw_dr, double &dmpw_dg);
  public:
    enum Func { B88, PW91, mPW91 };

    /// Construct an mPW exchange functional.
    mPW91XFunctional();
    /** Construct an mPW form exchange functional using the given
        functional variant.  The variant can be B88, PW91, or mPW91. */
    mPW91XFunctional(Func variant);
    /** Construct an mPW form exchange functional.
        The following keywords are recognized:
        <dl>

          <dt><tt>constants</tt><dd> This can be B88 to give the Becke88
          exchange functional; PW91, to give results similar to the PW91
          exchange functional; or mPW91, to give the new functional
          developed by Adamo and Barone.

          <dt><tt>b</tt><dd>
          <dt><tt>beta</tt><dd>
          <dt><tt>c</tt><dd> 
          <dt><tt>d</tt><dd>
          <dt><tt>x_d_coef</tt><dd>  The coefficient of \f$x^d\f$,
          where \f$x\f$ is the reduced gradient.
        </dl>

    */
    mPW91XFunctional(const Ref<KeyVal> &);
    mPW91XFunctional(StateIn &);
    ~mPW91XFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);

    void init_constants(Func);
};

/** Implements the Gill 1996 (G96) exchange functional.

    P. M. W. Gill, Mol. Phys., 89(2), pp. 433-445, 1996.
*/
class G96XFunctional: public DenFunctional {
  protected:
    double b_;
    void init_constants();
  public:
    G96XFunctional();
    G96XFunctional(const Ref<KeyVal> &);
    G96XFunctional(StateIn &);
    ~G96XFunctional();
    void save_data_state(StateOut &);

    int need_density_gradient();

    void point(const PointInputData&, PointOutputData&);
};

}

#endif

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