RPABFeeBreakup< T > Struct Template Reference

Collaboration diagram for RPABFeeBreakup< T >:

Public Member Functions
	RPABFeeBreakup ()
void	reset (ParticleSet &ref)
void	reset (ParticleSet &ref, T rs)
T	operator() (T r, T rinv) const
T	df (T r) const
T	Fk (T k, T rc) const
T	Xk (T k, T rc) const
T	integrate_r2 (T rc) const
T	Uk (T kk) const
	return RPA value at |k| More...
T	derivUk (T kk) const
	return d u(k)/d rs More...
T	urpa (T q) const
T	Dlindhard (T q, T w) const
T	Dlindhardp (T q, T w) const

Public Attributes
T	Rs
T	kf
T	kfm [2]
T	Density
T	volume
T	hbs2m
int	nelec
int	nspin
int	nppss [2]

Detailed Description

template<class T = double>
struct qmcplusplus::RPABFeeBreakup< T >

Definition at line 489 of file LRBreakupUtilities.h.

Constructor & Destructor Documentation

RPABFeeBreakup()

RPABFeeBreakup ( )

inline

Definition at line 500 of file LRBreakupUtilities.h.

{}

Member Function Documentation

derivUk()

T derivUk ( T  kk ) const

inline

return d u(k)/d rs

Implement a correct one

Definition at line 606 of file LRBreakupUtilities.h.

{ return 0.0; }

df()

T df ( T  r ) const

inline

Definition at line 547 of file LRBreakupUtilities.h.

{ return 0.0; }

Dlindhard()

T Dlindhard ( T  q, T  w  ) const

inline

Definition at line 620 of file LRBreakupUtilities.h.

References qmcplusplus::abs(), RPABFeeBreakup< T >::hbs2m, RPABFeeBreakup< T >::kfm, qmcplusplus::log(), RPABFeeBreakup< T >::nspin, and qmcplusplus::sqrt().

Referenced by RPABFeeBreakup< T >::Xk().

  {
    T xd1, xd2, small = 0.00000001, xdummy, rq1, rq2;
    T res = 0.0;
    for (int i = 0; i < nspin; i++)
    {
      if (kfm[i] > 0.0)
      {
        T xq = q / kfm[i];
        if (xq < small)
          xq = small;
        T om = w / (kfm[i] * kfm[i] * hbs2m * 2.0);
        xd1  = om / xq - xq / 2.0;
        xd2  = om / xq + xq / 2.0;
        if (std::abs(xd1 - 1.0) <= small)
        {
          if (xd1 >= 1.0)
            xd1 = 1.0 + small;
          else
            xd1 = 1.0 - small;
        }
        else if (std::abs(xd2 - 1.0) <= small)
        {
          if (xd2 >= 1.0)
            xd2 = 1.0 + small;
          else
            xd2 = 1.0 - small;
        }
#if OHMMS_DIM == 3
        rq1    = std::log(std::abs(1.0 + xd1) / std::abs(1.0 - xd1));
        rq2    = std::log(std::abs(1.0 + xd2) / std::abs(1.0 - xd2));
        xdummy = -1.0 + 0.5 * (1.0 - xd1 * xd1) / xq * rq1 - 0.50 * (1.0 - xd2 * xd2) / xq * rq2;
        xdummy *= kfm[i] / (8.0 * M_PI * M_PI * hbs2m);
#elif OHMMS_DIM == 2
        T sd1, sd2;
        if (std::abs(xd1) < small)
          sd1 = 0.0;
        else
          sd1 = xd1 / std::abs(xd1);
        if (std::abs(xd2) < small)
          sd2 = 0.0;
        else
          sd2 = xd2 / std::abs(xd2);
        if (xd1 * xd1 - 1.0 > 1.0)
          rq1 = std::sqrt(xd1 * xd1 - 1.0) * sd1;
        else
          rq1 = 0.0;
        if (xd2 * xd2 - 1.0 > 1.0)
          rq2 = std::sqrt(xd2 * xd2 - 1.0) * sd2;
        else
          rq2 = 0.0;
        xdummy = -(xq + rq1 - rq2) / (4.0 * M_PI * xq * hbs2m);
#endif
        res += xdummy;
      }
    }
    return res;
  }

Dlindhardp()

T Dlindhardp ( T  q, T  w  ) const

inline

Definition at line 680 of file LRBreakupUtilities.h.

References qmcplusplus::abs(), RPABFeeBreakup< T >::hbs2m, RPABFeeBreakup< T >::kfm, qmcplusplus::log(), RPABFeeBreakup< T >::nspin, and qmcplusplus::sqrt().

Referenced by RPABFeeBreakup< T >::Xk().

  {
    T xd1, xd2, small = 0.00000001, xdummy, rq1, rq2;
    T res = 0.0;
    for (int i = 0; i < nspin; i++)
    {
      if (kfm[i] > 0.0)
      {
        T xq = q / kfm[i];
        if (xq < small)
          xq = small;
        T om = w / (kfm[i] * kfm[i] * hbs2m * 2.0);
        xd1  = om / xq - xq / 2.0;
        xd2  = om / xq + xq / 2.0;
        if (std::abs(xd1 - 1.0) <= small)
        {
          if (xd1 >= 1.0)
            xd1 = 1.0 + small;
          else
            xd1 = 1.0 - small;
        }
        else if (std::abs(xd2 - 1.0) <= small)
        {
          if (xd2 >= 1.0)
            xd2 = 1.0 + small;
          else
            xd2 = 1.0 - small;
        }
#if OHMMS_DIM == 3
        rq1    = std::log(std::abs(1.0 + xd1) / std::abs(1.0 - xd1));
        rq2    = std::log(std::abs(1.0 + xd2) / std::abs(1.0 - xd2));
        xdummy = -xd1 / (xq * kfm[i] * kfm[i] * 2.0 * hbs2m) * rq1 + xd2 / (xq * kfm[i] * kfm[i] * 2.0 * hbs2m) * rq2;
        xdummy *= kfm[i] / (8.0 * M_PI * M_PI * hbs2m * xq);
#elif OHMMS_DIM == 2
        T sd1, sd2;
        if (std::abs(xd1) < small)
          sd1 = 0.0;
        else
          sd1 = xd1 / std::abs(xd1);
        if (std::abs(xd2) < small)
          sd2 = 0.0;
        else
          sd2 = xd2 / std::abs(xd2);
        if (xd1 * xd1 - 1.0 > 1.0)
          rq1 = sd1 * xd1 / std::sqrt(xd1 * xd1 - 1.0);
        else
          rq1 = 0.0;
        if (xd2 * xd2 - 1.0 > 1.0)
          rq2 = sd2 * xd2 / std::sqrt(xd2 * xd2 - 1.0);
        else
          rq2 = 0.0;
        xdummy = -(rq1 - rq2) / (8.0 * M_PI * (xq * kfm[i] * hbs2m) * (xq * kfm[i] * hbs2m));
#endif
        res += xdummy;
      }
    }
    return res;
  }

Fk()

T Fk ( T  k, T  rc  ) const

inline

Definition at line 549 of file LRBreakupUtilities.h.

References RPABFeeBreakup< T >::Xk().

{ return -Xk(k, rc); }

integrate_r2()

T integrate_r2 ( T  rc ) const

inline

Definition at line 595 of file LRBreakupUtilities.h.

{ return 0.0; }

operator()()

T operator() ( T  r, T  rinv  ) const

inline

Definition at line 545 of file LRBreakupUtilities.h.

{ return 0.0; }

reset() [1/2]

void reset ( ParticleSet &  ref )

inline

Definition at line 503 of file LRBreakupUtilities.h.

References RPABFeeBreakup< T >::Density, ParticleSet::first(), ParticleSet::getLattice(), ParticleSet::getTotalNum(), ParticleSet::groups(), RPABFeeBreakup< T >::hbs2m, RPABFeeBreakup< T >::kf, RPABFeeBreakup< T >::kfm, ParticleSet::last(), RPABFeeBreakup< T >::nelec, RPABFeeBreakup< T >::nppss, RPABFeeBreakup< T >::nspin, OHMMS_DIM, qmcplusplus::pow(), RPABFeeBreakup< T >::Rs, and RPABFeeBreakup< T >::volume.

  {
    volume = ref.getLattice().Volume;
    nspin  = ref.groups();
    for (int i = 0; i < nspin; ++i)
      nppss[i] = ref.last(i) - ref.first(i);
    Density = ref.getTotalNum() / ref.getLattice().Volume;
    Rs      = std::pow(3.0 / (4.0 * M_PI * Density), 1.0 / 3.0);
    nelec   = ref.getTotalNum();
    hbs2m   = 0.5;
    kf      = 0.0;
    kfm[0] = kfm[1] = 0.0;
    for (int i = 0; i < nspin; i++)
    {
      T a3   = 3.0 * volume / (4.0 * M_PI * nppss[i]);
      kfm[i] = std::pow(9.0 * M_PI / (2.0 * a3), 1.0 / OHMMS_DIM);
      kf += kfm[i] * nppss[i] / ref.getTotalNum();
    }
  }

reset() [2/2]

void reset ( ParticleSet &  ref, T  rs  )

inline

Definition at line 524 of file LRBreakupUtilities.h.

References RPABFeeBreakup< T >::Density, ParticleSet::first(), ParticleSet::getLattice(), ParticleSet::getTotalNum(), ParticleSet::groups(), RPABFeeBreakup< T >::hbs2m, RPABFeeBreakup< T >::kf, RPABFeeBreakup< T >::kfm, ParticleSet::last(), RPABFeeBreakup< T >::nelec, RPABFeeBreakup< T >::nppss, RPABFeeBreakup< T >::nspin, OHMMS_DIM, qmcplusplus::pow(), RPABFeeBreakup< T >::Rs, and RPABFeeBreakup< T >::volume.

  {
    Density = ref.getTotalNum() / ref.getLattice().Volume;
    volume  = ref.getLattice().Volume;
    nspin   = ref.groups();
    for (int i = 0; i < nspin; ++i)
      nppss[i] = ref.last(i) - ref.first(i);
    Rs     = rs;
    nelec  = ref.getTotalNum();
    hbs2m  = 0.5;
    kf     = 0.0;
    kfm[0] = kfm[1] = 0.0;
    for (int i = 0; i < nspin; i++)
    {
      T a3   = 3.0 * volume / (4.0 * M_PI * nppss[i]);
      kfm[i] = std::pow(9.0 * M_PI / (2.0 * a3), 1.0 / OHMMS_DIM);
      kf += kfm[i] * nppss[i] / ref.getTotalNum();
    }
  }

Uk()

T Uk ( T  kk ) const

inline

return RPA value at |k|

Parameters

kk

|k|^2

Definition at line 600 of file LRBreakupUtilities.h.

{ return 0.0; }

urpa()

T urpa ( T  q ) const

inline

Definition at line 608 of file LRBreakupUtilities.h.

References RPABFeeBreakup< T >::Density, RPABFeeBreakup< T >::hbs2m, and qmcplusplus::sqrt().

Referenced by RPABFeeBreakup< T >::Xk().

  {
    T a = 0.0, vkbare;
    if (q > 0.0)
    {
      vkbare = 4.0 * M_PI / (q * q);
      a      = 2.0 * Density * vkbare / (hbs2m * q * q);
    }
    return -0.5 + 0.5 * std::sqrt(1.0 + a);
  }

Xk()

T Xk ( T  k, T  rc  ) const

inline

Definition at line 551 of file LRBreakupUtilities.h.

References qmcplusplus::asin(), RPABFeeBreakup< T >::Density, RPABFeeBreakup< T >::Dlindhard(), RPABFeeBreakup< T >::Dlindhardp(), RPABFeeBreakup< T >::hbs2m, RPABFeeBreakup< T >::kfm, RPABFeeBreakup< T >::nelec, RPABFeeBreakup< T >::nppss, RPABFeeBreakup< T >::nspin, OHMMS_DIM, qmcplusplus::pow(), qmcplusplus::sqrt(), RPABFeeBreakup< T >::urpa(), and RPABFeeBreakup< T >::volume.

Referenced by RPABFeeBreakup< T >::Fk().

  {
    T u    = urpa(k) * volume / nelec;
    T eq   = k * k * hbs2m;
    T vlr  = u * u * 2.0 * Density * eq;
    T vq   = (2.0 * M_PI * (OHMMS_DIM - 1.0)) / (std::pow(k, OHMMS_DIM - 1.0));
    T veff = vq - vlr;
    T op2  = Density * 2.0 * vq * eq;
#if OHMMS_DIM == 3
    //    T op2kf=Density*2.0*(2.0*M_PI*(OHMMS_DIM-1.0))*hbs2m;
    T op = (op2 + 1.2 * (kfm[0] * kfm[0] + kfm[1] * kfm[1]) * eq * hbs2m + eq * eq);
#elif OHMMS_DIM == 2
    //    T op2kf=Density*2.0*(2.0*M_PI*(OHMMS_DIM-1.0))*std::pow(kf,3.0-OHMMS_DIM)*hbs2m;
    T op = (op2 + 1.5 * (kfm[0] * kfm[0] + kfm[1] * kfm[1]) * hbs2m * eq + eq * eq);
#endif
    op      = std::sqrt(op);
    T denom = 1.0 / veff - Dlindhard(k, -eq);
    T dp    = -Dlindhardp(k, -eq);
    T s0 = 0.0, ss = 0.0;
    for (int i = 0; i < nspin; i++)
    {
      if (nppss[i] > 0)
      {
        T y = 0.5 * k / kfm[i];
        if (y < 1.0)
        {
#if OHMMS_DIM == 3
          ss = 0.5 * y * (3.0 - y * y);
#elif OHMMS_DIM == 2
          ss = (2.0 / M_PI) * (std::asin(y) + y * std::sqrt(1.0 - y * y));
#endif
        }
        else
        {
          ss = 1.0;
        }
        s0 += nppss[i] * ss / nelec;
      }
    }
    T yq = s0 * s0 / (4.0 * k * k) * (1.0 / (eq * denom) + dp / (denom * denom)) +
        2.0 * hbs2m * vlr / (op * (std::sqrt(op2) + eq));
    return yq / volume;
  }

Member Data Documentation

Density

T Density

Definition at line 494 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::reset(), RPABFeeBreakup< T >::urpa(), and RPABFeeBreakup< T >::Xk().

hbs2m

T hbs2m

Definition at line 496 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::Dlindhard(), RPABFeeBreakup< T >::Dlindhardp(), RPABFeeBreakup< T >::reset(), RPABFeeBreakup< T >::urpa(), and RPABFeeBreakup< T >::Xk().

kf

T kf

Definition at line 492 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::reset().

kfm

T kfm[2]

Definition at line 493 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::Dlindhard(), RPABFeeBreakup< T >::Dlindhardp(), RPABFeeBreakup< T >::reset(), and RPABFeeBreakup< T >::Xk().

nelec

int nelec

Definition at line 497 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::reset(), and RPABFeeBreakup< T >::Xk().

nppss

int nppss[2]

Definition at line 499 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::reset(), and RPABFeeBreakup< T >::Xk().

nspin

int nspin

Definition at line 498 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::Dlindhard(), RPABFeeBreakup< T >::Dlindhardp(), RPABFeeBreakup< T >::reset(), and RPABFeeBreakup< T >::Xk().

Rs

T Rs

Definition at line 491 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::reset().

volume

T volume

Definition at line 495 of file LRBreakupUtilities.h.

Referenced by RPABFeeBreakup< T >::reset(), and RPABFeeBreakup< T >::Xk().

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The documentation for this struct was generated from the following file:

• /home/pk7/projects/qmc/for_cron_doxygen/qmcpack/src/QMCWaveFunctions/Jastrow/LRBreakupUtilities.h