def prod(ij):
i, j = divmod(ij, nao)
rhoR = aoR_k1[:, i] * aoR_k2[:, j].conj()
rhoG = tools.fftk(rhoR, cell.gs, expmikr)
vG = coulG * rhoG
vR = tools.ifftk(vG, cell.gs, expmikr.conj())
return vR
def get_vkR_(mf, cell, aoR_k1, aoR_k2, kpt1, kpt2):
'''Get the real-space 2-index "exchange" potential V_{i,k1; j,k2}(r).
Kwargs:
kpts : (nkpts, 3) ndarray
The sampled k-points; may be required for G=0 correction.
Returns:
vR : (ngs, nao, nao) ndarray
The real-space "exchange" potential at every grid point, for all
AO pairs.
Note:
This is essentially a density-fitting or resolution-of-the-identity.
The returned object is of size ngs*nao**2 and could be precomputed and
saved in vhfopt.
'''
coords = pyscf.pbc.dft.gen_grid.gen_uniform_grids(cell)
ngs, nao = aoR_k1.shape
coulG = tools.get_coulG(cell, kpt1-kpt2, exx=True, mf=mf)
vR = np.zeros((ngs,nao,nao), dtype=np.complex128)
for i in range(nao):
for j in range(nao):
rhoR = aoR_k1[:,i] * aoR_k2[:,j].conj()
rhoG = tools.fftk(rhoR, cell.gs, coords, kpt1-kpt2)
vG = coulG*rhoG
vR[:,i,j] = tools.ifftk(vG, cell.gs, coords, kpt1-kpt2)
return vR
def prod(ij):
i, j = divmod(ij, nao)
rhoR = aoR_k1[:,i] * aoR_k2[:,j].conj()
rhoG = tools.fftk(rhoR, cell.gs, expmikr)
vG = coulG*rhoG
vR = tools.ifftk(vG, cell.gs, expmikr.conj())
return vR
def get_vkR(mydf, cell, aoR_k1, aoR_k2, kpt1, kpt2, coords, gs, exxdiv):
'''Get the real-space 2-index "exchange" potential V_{i,k1; j,k2}(r)
where {i,k1} = exp^{i k1 r) |i> , {j,k2} = exp^{-i k2 r) <j|
Kwargs:
kpt1, kpt2 : (3,) ndarray
The sampled k-points; may be required for G=0 correction.
Returns:
vR : (ngs, nao, nao) ndarray
The real-space "exchange" potential at every grid point, for all
AO pairs.
Note:
This is essentially a density-fitting or resolution-of-the-identity.
The returned object is of size ngs*nao**2
'''
ngs, nao = aoR_k1.shape
expmikr = np.exp(-1j * np.dot(kpt1 - kpt2, coords.T))
mydf.exxdiv = exxdiv
coulG = tools.get_coulG(cell, kpt1 - kpt2, True, mydf, gs)
aoR_k1 = np.asarray(aoR_k1.T, order='C')
aoR_k2 = np.asarray(aoR_k2.T, order='C')
vR = np.empty((nao, nao, ngs), dtype=np.complex128)
for i in range(nao):
rhoR = aoR_k1 * aoR_k2[i].conj()
rhoG = tools.fftk(rhoR, gs, expmikr)
vG = rhoG * coulG
vR[:, i] = tools.ifftk(vG, gs, expmikr.conj())
vR = vR.transpose(2, 0, 1)
if aoR_k1.dtype == np.double and aoR_k2.dtype == np.double:
return vR.real
else:
return vR
def get_vkR(mydf, cell, aoR_k1, aoR_k2, kpt1, kpt2, coords, gs, exxdiv):
"""Get the real-space 2-index "exchange" potential V_{i,k1; j,k2}(r)
where {i,k1} = exp^{i k1 r) |i> , {j,k2} = exp^{-i k2 r) <j|
Kwargs:
kpt1, kpt2 : (3,) ndarray
The sampled k-points; may be required for G=0 correction.
Returns:
vR : (ngs, nao, nao) ndarray
The real-space "exchange" potential at every grid point, for all
AO pairs.
Note:
This is essentially a density-fitting or resolution-of-the-identity.
The returned object is of size ngs*nao**2
"""
ngs, nao = aoR_k1.shape
expmikr = np.exp(-1j * np.dot(kpt1 - kpt2, coords.T))
mydf.exxdiv = exxdiv
coulG = tools.get_coulG(cell, kpt1 - kpt2, True, mydf, gs)
aoR_k1 = np.asarray(aoR_k1.T, order="C")
aoR_k2 = np.asarray(aoR_k2.T, order="C")
vR = np.empty((nao, nao, ngs), dtype=np.complex128)
for i in range(nao):
rhoR = aoR_k1 * aoR_k2[i].conj()
rhoG = tools.fftk(rhoR, gs, expmikr)
vG = rhoG * coulG
vR[:, i] = tools.ifftk(vG, gs, expmikr.conj())
vR = vR.transpose(2, 0, 1)
if aoR_k1.dtype == np.double and aoR_k2.dtype == np.double:
return vR.real
else:
return vR