Пример #1
0
def trans_e1_outcore(mol, mo, ncore, ncas, erifile, max_memory=None, level=1, verbose=logger.WARN):
    time0 = (time.clock(), time.time())
    if isinstance(verbose, logger.Logger):
        log = verbose
    else:
        log = logger.Logger(mol.stdout, verbose)
    log.debug1("trans_e1_outcore level %d  max_memory %d", level, max_memory)
    nao, nmo = mo.shape
    nao_pair = nao * (nao + 1) // 2
    nocc = ncore + ncas

    _tmpfile1 = tempfile.NamedTemporaryFile()
    faapp_buf = h5py.File(_tmpfile1.name)
    feri = h5py.File(erifile, "w")

    mo_c = numpy.asarray(mo, order="C")
    mo = numpy.asarray(mo, order="F")
    pashape = (0, nmo, ncore, ncas)
    papa_buf = numpy.zeros((nao, ncas, nmo * ncas))
    j_pc = numpy.zeros((nmo, ncore))
    k_pc = numpy.zeros((nmo, ncore))

    mem_words = int(max(2000, max_memory - papa_buf.nbytes / 1e6) * 1e6 / 8)
    aobuflen = mem_words // (nao_pair + nocc * nmo) + 1
    shranges = outcore.guess_shell_ranges(mol, aobuflen, aobuflen, "s4")
    ao2mopt = _ao2mo.AO2MOpt(mol, "cint2e_sph", "CVHFnr_schwarz_cond", "CVHFsetnr_direct_scf")
    ao_loc = numpy.array(mol.ao_loc_nr(), dtype=numpy.int32)
    log.debug("mem cache %.8g MB", mem_words * 8 / 1e6)
    ti0 = log.timer("Initializing trans_e1_outcore", *time0)
    nstep = len(shranges)
    paapp = 0
    maxbuflen = max([x[2] for x in shranges])
    bufs1 = numpy.empty((maxbuflen, nao_pair))
    bufs2 = numpy.empty((maxbuflen, nmo * ncas))
    bufs3 = numpy.empty((maxbuflen, nao * ncore))

    # fmmm, ftrans, fdrv for level 1
    fmmm = _fpointer("MCSCFhalfmmm_nr_s2_ket")
    ftrans = _fpointer("AO2MOtranse1_nr_s4")
    fdrv = getattr(libmcscf, "AO2MOnr_e2_drv")
    for istep, sh_range in enumerate(shranges):
        log.debug("[%d/%d], AO [%d:%d], len(buf) = %d", istep + 1, nstep, *(sh_range[:3]))
        buf = bufs1[: sh_range[2]]
        _ao2mo.nr_e1fill_("cint2e_sph", sh_range[:3], mol._atm, mol._bas, mol._env, "s4", 1, ao2mopt, buf)
        if log.verbose >= logger.DEBUG1:
            ti1 = log.timer("AO integrals buffer", *ti0)
        bufpa = bufs2[: sh_range[2]]
        _ao2mo.nr_e1_(buf, mo, pashape, "s4", "s1", vout=bufpa)
        # jc_pp, kc_pp
        if level == 1:  # ppaa, papa and vhf, jcp, kcp
            if log.verbose >= logger.DEBUG1:
                ti1 = log.timer("buffer-pa", *ti1)
            buf1 = bufs3[: sh_range[2]]
            fdrv(
                ftrans,
                fmmm,
                buf1.ctypes.data_as(ctypes.c_void_p),
                buf.ctypes.data_as(ctypes.c_void_p),
                mo.ctypes.data_as(ctypes.c_void_p),
                ctypes.c_int(sh_range[2]),
                ctypes.c_int(nao),
                ctypes.c_int(0),
                ctypes.c_int(nao),
                ctypes.c_int(0),
                ctypes.c_int(ncore),
                ctypes.POINTER(ctypes.c_void_p)(),
                ctypes.c_int(0),
            )
            p0 = 0
            for ij in range(sh_range[0], sh_range[1]):
                i, j = _ao2mo._extract_pair(ij)
                i0 = ao_loc[i]
                j0 = ao_loc[j]
                i1 = ao_loc[i + 1]
                j1 = ao_loc[j + 1]
                di = i1 - i0
                dj = j1 - j0
                if i == j:
                    dij = di * (di + 1) // 2
                    buf = numpy.empty((di, di, nao * ncore))
                    idx = numpy.tril_indices(di)
                    buf[idx] = buf1[p0 : p0 + dij]
                    buf[idx[1], idx[0]] = buf1[p0 : p0 + dij]
                    buf = buf.reshape(di, di, nao, ncore)
                    mo1 = mo_c[i0:i1]
                    tmp = numpy.einsum("uvpc,pc->uvc", buf, mo[:, :ncore])
                    tmp = pyscf.lib.dot(mo1.T, tmp.reshape(di, -1))
                    j_pc += numpy.einsum("vp,pvc->pc", mo1, tmp.reshape(nmo, di, ncore))
                    tmp = numpy.einsum("uvpc,uc->vcp", buf, mo1[:, :ncore])
                    tmp = pyscf.lib.dot(tmp.reshape(-1, nmo), mo).reshape(di, ncore, nmo)
                    k_pc += numpy.einsum("vp,vcp->pc", mo1, tmp)
                else:
                    dij = di * dj
                    buf = buf1[p0 : p0 + dij].reshape(di, dj, nao, ncore)
                    mo1 = mo_c[i0:i1]
                    mo2 = mo_c[j0:j1]
                    tmp = numpy.einsum("uvpc,pc->uvc", buf, mo[:, :ncore])
                    tmp = pyscf.lib.dot(mo1.T, tmp.reshape(di, -1))
                    j_pc += numpy.einsum("vp,pvc->pc", mo2, tmp.reshape(nmo, dj, ncore)) * 2
                    tmp = numpy.einsum("uvpc,uc->vcp", buf, mo1[:, :ncore])
                    tmp = pyscf.lib.dot(tmp.reshape(-1, nmo), mo).reshape(dj, ncore, nmo)
                    k_pc += numpy.einsum("vp,vcp->pc", mo2, tmp)
                    tmp = numpy.einsum("uvpc,vc->ucp", buf, mo2[:, :ncore])
                    tmp = pyscf.lib.dot(tmp.reshape(-1, nmo), mo).reshape(di, ncore, nmo)
                    k_pc += numpy.einsum("up,ucp->pc", mo1, tmp)
                p0 += dij
            if log.verbose >= logger.DEBUG1:
                ti1 = log.timer("j_cp and k_cp", *ti1)

        if log.verbose >= logger.DEBUG1:
            ti1 = log.timer("half transformation of the buffer", *ti1)

        # ppaa, papa
        faapp_buf[str(istep)] = bufpa.reshape(sh_range[2], nmo, ncas)[:, ncore:nocc].reshape(-1, ncas ** 2).T
        p0 = 0
        for ij in range(sh_range[0], sh_range[1]):
            i, j = _ao2mo._extract_pair(ij)
            i0 = ao_loc[i]
            j0 = ao_loc[j]
            i1 = ao_loc[i + 1]
            j1 = ao_loc[j + 1]
            di = i1 - i0
            dj = j1 - j0
            if i == j:
                dij = di * (di + 1) // 2
                buf1 = numpy.empty((di, di, nmo * ncas))
                idx = numpy.tril_indices(di)
                buf1[idx] = bufpa[p0 : p0 + dij]
                buf1[idx[1], idx[0]] = bufpa[p0 : p0 + dij]
            else:
                dij = di * dj
                buf1 = bufpa[p0 : p0 + dij].reshape(di, dj, -1)
                mo1 = mo[j0:j1, ncore:nocc].copy()
                for i in range(di):
                    pyscf.lib.dot(mo1.T, buf1[i], 1, papa_buf[i0 + i], 1)
            mo1 = mo[i0:i1, ncore:nocc].copy()
            buf1 = pyscf.lib.dot(mo1.T, buf1.reshape(di, -1))
            papa_buf[j0:j1] += buf1.reshape(ncas, dj, -1).transpose(1, 0, 2)
            p0 += dij
        if log.verbose >= logger.DEBUG1:
            ti1 = log.timer("ppaa and papa buffer", *ti1)

        ti0 = log.timer("gen AO/transform MO [%d/%d]" % (istep + 1, nstep), *ti0)
    buf = buf1 = bufs1 = bufs2 = bufs3 = bufpa = None
    time1 = log.timer("mc_ao2mo pass 1", *time0)

    log.debug1("Half transformation done. Current memory %d", pyscf.lib.current_memory()[0])

    nblk = int(max(8, min(nmo, max(2000, max_memory * 1e6 / 8 - papa_buf.size) / (ncas ** 2 * nmo))))
    log.debug1("nblk for papa = %d", nblk)
    dset = feri.create_dataset("papa", (nmo, ncas, nmo, ncas), "f8")
    for i0, i1 in prange(0, nmo, nblk):
        tmp = pyscf.lib.dot(mo[:, i0:i1].T, papa_buf.reshape(nao, -1))
        dset[i0:i1] = tmp.reshape(i1 - i0, ncas, nmo, ncas)
    papa_buf = tmp = None
    time1 = log.timer("papa pass 2", *time1)

    tmp = numpy.empty((ncas ** 2, nao_pair))
    p0 = 0
    for istep, sh_range in enumerate(shranges):
        tmp[:, p0 : p0 + sh_range[2]] = faapp_buf[str(istep)]
        p0 += sh_range[2]
    nblk = int(max(8, min(nmo, max(2000, max_memory * 1e6 / 8 - tmp.size) / (ncas ** 2 * nmo) - 1)))
    log.debug1("nblk for ppaa = %d", nblk)
    dset = feri.create_dataset("ppaa", (nmo, nmo, ncas, ncas), "f8")
    for i0, i1 in prange(0, nmo, nblk):
        tmp1 = _ao2mo.nr_e2_(tmp, mo, (i0, i1 - i0, 0, nmo), "s4", "s1", ao_loc=ao_loc)
        tmp1 = tmp1.reshape(ncas, ncas, i1 - i0, nmo)
        for j in range(i1 - i0):
            dset[i0 + j] = tmp1[:, :, j].transpose(2, 0, 1)
    tmp = tmp1 = None
    time1 = log.timer("ppaa pass 2", *time1)

    faapp_buf.close()
    feri.close()
    _tmpfile1 = None
    time0 = log.timer("mc_ao2mo", *time0)
    return j_pc, k_pc
Пример #2
0
def half_e1(mol, mo_coeffs, swapfile,
            intor='cint2e_sph', aosym='s4', comp=1,
            max_memory=2000, ioblk_size=256, verbose=logger.WARN, compact=True,
            ao2mopt=None):
    r'''Half transform arbitrary spherical AO integrals to MO integrals
    for the given two sets of orbitals

    Args:
        mol : :class:`Mole` object
            AO integrals will be generated in terms of mol._atm, mol._bas, mol._env
        mo_coeff : ndarray
            Transform (ij|kl) with the same set of orbitals.
        swapfile : str or h5py File or h5py Group object
            To store the transformed integrals, in HDF5 format.  The transformed
            integrals are saved in blocks.

    Kwargs
        intor : str
            Name of the 2-electron integral.  Ref to :func:`getints_by_shell`
            for the complete list of available 2-electron integral names
        aosym : int or str
            Permutation symmetry for the AO integrals

            | 4 or '4' or 's4': 4-fold symmetry (default)
            | '2ij' or 's2ij' : symmetry between i, j in (ij|kl)
            | '2kl' or 's2kl' : symmetry between k, l in (ij|kl)
            | 1 or '1' or 's1': no symmetry
            | 'a4ij' : 4-fold symmetry with anti-symmetry between i, j in (ij|kl) (TODO)
            | 'a4kl' : 4-fold symmetry with anti-symmetry between k, l in (ij|kl) (TODO)
            | 'a2ij' : anti-symmetry between i, j in (ij|kl) (TODO)
            | 'a2kl' : anti-symmetry between k, l in (ij|kl) (TODO)

        comp : int
            Components of the integrals, e.g. cint2e_ip_sph has 3 components.
        verbose : int
            Print level
        max_memory : float or int
            The maximum size of cache to use (in MB), large cache may **not**
            improve performance.
        ioblk_size : float or int
            The block size for IO, large block size may **not** improve performance
        verbose : int
            Print level
        compact : bool
            When compact is True, depending on the four oribital sets, the
            returned MO integrals has (up to 4-fold) permutation symmetry.
            If it's False, the function will abandon any permutation symmetry,
            and return the "plain" MO integrals
        ao2mopt : :class:`AO2MOpt` object
            Precomputed data to improve perfomance

    Returns:
        None

    '''
    time0 = (time.clock(), time.time())
    if isinstance(verbose, logger.Logger):
        log = verbose
    else:
        log = logger.Logger(mol.stdout, verbose)

    ijsame = compact and iden_coeffs(mo_coeffs[0], mo_coeffs[1])

    nmoi = mo_coeffs[0].shape[1]
    nmoj = mo_coeffs[1].shape[1]
    nao = mo_coeffs[0].shape[0]
    aosym = _stand_sym_code(aosym)
    if aosym in ('s4', 's2ij'):
        nao_pair = nao * (nao+1) // 2
    else:
        nao_pair = nao * nao

    if compact and ijsame and aosym in ('s4', 's2ij'):
        log.debug('i-mo == j-mo')
        ijmosym = 's2'
        nij_pair = nmoi*(nmoi+1) // 2
        moij = numpy.asarray(mo_coeffs[0], order='F')
        ijshape = (0, nmoi, 0, nmoi)
    else:
        ijmosym = 's1'
        nij_pair = nmoi*nmoj
        moij = numpy.asarray(numpy.hstack((mo_coeffs[0],mo_coeffs[1])), order='F')
        ijshape = (0, nmoi, nmoi, nmoj)

    e1buflen, mem_words, iobuf_words, ioblk_words = \
            guess_e1bufsize(max_memory, ioblk_size, nij_pair, nao_pair, comp)
# The buffer to hold AO integrals in C code, see line (@)
    aobuflen = int((mem_words - iobuf_words) // (nao_pair*comp))
    shranges = guess_shell_ranges(mol, e1buflen, aobuflen, aosym)
    if ao2mopt is None:
        if intor == 'cint2e_sph':
            ao2mopt = _ao2mo.AO2MOpt(mol, intor, 'CVHFnr_schwarz_cond',
                                     'CVHFsetnr_direct_scf')
        else:
            ao2mopt = _ao2mo.AO2MOpt(mol, intor)

    log.debug('step1: tmpfile %.8g MB', nij_pair*nao_pair*8/1e6)
    log.debug('step1: (ij,kl) = (%d,%d), mem cache %.8g MB, iobuf %.8g MB',
              nij_pair, nao_pair, mem_words*8/1e6, iobuf_words*8/1e6)

    if isinstance(swapfile, str):
        fswap = h5py.File(swapfile, 'w')
    else:
        fswap = swapfile
    for icomp in range(comp):
        g = fswap.create_group(str(icomp)) # for h5py old version

    # transform e1
    ti0 = log.timer('Initializing ao2mo.outcore.half_e1', *time0)
    nstep = len(shranges)
    maxbuflen = max([x[2] for x in shranges])
    bufs1 = numpy.empty((comp*maxbuflen,nao_pair))
    bufs2 = numpy.empty((comp*maxbuflen,nij_pair))
    for istep,sh_range in enumerate(shranges):
        log.debug('step 1 [%d/%d], AO [%d:%d], len(buf) = %d', \
                  istep+1, nstep, *(sh_range[:3]))
        buflen = sh_range[2]
        iobuf = bufs2[:comp*buflen].reshape(comp,buflen,nij_pair)
        nmic = len(sh_range[3])
        p0 = 0
        for imic, aoshs in enumerate(sh_range[3]):
            log.debug1('      fill iobuf micro [%d/%d], AO [%d:%d], len(aobuf) = %d', \
                       imic+1, nmic, *aoshs)
            buf = bufs1[:comp*aoshs[2]] # (@)
            _ao2mo.nr_e1fill_(intor, aoshs, mol._atm, mol._bas, mol._env,
                              aosym, comp, ao2mopt, out=buf)
            buf = _ao2mo.nr_e1_(buf, moij, ijshape, aosym, ijmosym)
            iobuf[:,p0:p0+aoshs[2]] = buf.reshape(comp,aoshs[2],-1)
            p0 += aoshs[2]
        ti2 = log.timer('gen AO/transform MO [%d/%d]'%(istep+1,nstep), *ti0)

        e2buflen, chunks = guess_e2bufsize(ioblk_size, nij_pair, buflen)
        for icomp in range(comp):
            _transpose_to_h5g(fswap, '%d/%d'%(icomp,istep), iobuf[icomp],
                              e2buflen, None)
        ti0 = log.timer('transposing to disk', *ti2)
    bufs1 = bufs2 = None
    if isinstance(swapfile, str):
        fswap.close()
    return swapfile
Пример #3
0
def light_e1_outcore(mol, mo, ncore, ncas,
                     max_memory=None, approx=1, verbose=logger.WARN):
    time0 = (time.clock(), time.time())
    if isinstance(verbose, logger.Logger):
        log = verbose
    else:
        log = logger.Logger(mol.stdout, verbose)
    nao, nmo = mo.shape
    nao_pair = nao*(nao+1)//2
    nocc = ncore + ncas
    aapp_buf = numpy.empty((nao_pair,ncas,ncas))
    appa_buf = numpy.zeros((ncas,nao,nmo*ncas))
    max_memory -= (aapp_buf.nbytes+appa_buf.nbytes) / 1e6

    mo = numpy.asarray(mo, order='F')
    nao, nmo = mo.shape
    pashape = (0, nmo, ncore, ncas)
    if approx == 1:
        jc = numpy.empty((nao,nao,ncore))
        kc = numpy.zeros((nao,nao,ncore))
    else:
        dm_core = numpy.dot(mo[:,:ncore], mo[:,:ncore].T) * 2
        jc = numpy.zeros((nao,nao))
        kc = numpy.zeros((nao,nao))
    max_memory -= (jc.nbytes+kc.nbytes) / 1e6

    mem_words = int(max(1000,max_memory)*1e6/8)
    aobuflen = mem_words//(nao_pair+nocc*nmo) + 1
    shranges = outcore.guess_shell_ranges(mol, aobuflen, aobuflen, 's4')
    ao2mopt = _ao2mo.AO2MOpt(mol, 'cint2e_sph',
                             'CVHFnr_schwarz_cond', 'CVHFsetnr_direct_scf')
    ao_loc = numpy.array(mol.ao_loc_nr(), dtype=numpy.int32)
    log.debug('mem cache %.8g MB', mem_words*8/1e6)
    ti0 = log.timer('Initializing light_e1_outcore', *time0)
    nstep = len(shranges)
    paapp = 0
    maxbuflen = max([x[2] for x in shranges])
    bufs1 = numpy.empty((maxbuflen, nao_pair))
    bufs2 = numpy.empty((maxbuflen, pashape[1]*pashape[3]))
    bufs3 = numpy.empty((maxbuflen, nao*ncore))
    for istep,sh_range in enumerate(shranges):
        log.debug('[%d/%d], AO [%d:%d], len(buf) = %d',
                  istep+1, nstep, *(sh_range[:3]))
        buf = bufs1[:sh_range[2]]
        _ao2mo.nr_e1fill_('cint2e_sph', sh_range[:3],
                          mol._atm, mol._bas, mol._env, 's4', 1, ao2mopt, buf)
        if log.verbose >= logger.DEBUG1:
            ti1 = log.timer('AO integrals buffer', *ti0)
        bufpa = bufs2[:sh_range[2]]
# jc_pp, kc_pp
        if approx == 1: # aapp, appa and vhf, jcp, kcp
            _ao2mo.nr_e1_(buf, mo, pashape, 's4', 's1', vout=bufpa)
            if log.verbose >= logger.DEBUG1:
                ti1 = log.timer('buffer-pa', *ti1)
            buf1 = bufs3[:sh_range[2]]
            fmmm = _fpointer('MCSCFhalfmmm_nr_s2_ket')
            ftrans = _fpointer('AO2MOtranse1_nr_s4')
            fdrv = getattr(libmcscf, 'AO2MOnr_e2_drv')
            fdrv(ftrans, fmmm,
                 buf1.ctypes.data_as(ctypes.c_void_p),
                 buf.ctypes.data_as(ctypes.c_void_p),
                 mo.ctypes.data_as(ctypes.c_void_p),
                 ctypes.c_int(sh_range[2]), ctypes.c_int(nao),
                 ctypes.c_int(0), ctypes.c_int(nao),
                 ctypes.c_int(0), ctypes.c_int(ncore),
                 ctypes.POINTER(ctypes.c_void_p)(), ctypes.c_int(0))
            p0 = 0
            for ij in range(sh_range[0], sh_range[1]):
                i,j = _ao2mo._extract_pair(ij)
                i0 = ao_loc[i]
                j0 = ao_loc[j]
                i1 = ao_loc[i+1]
                j1 = ao_loc[j+1]
                di = i1 - i0
                dj = j1 - j0
                if i == j:
                    dij = di * (di+1) // 2
                    buf = numpy.empty((di,di,nao*ncore))
                    idx = numpy.tril_indices(di)
                    buf[idx] = buf1[p0:p0+dij]
                    buf[idx[1],idx[0]] = buf1[p0:p0+dij]
                    buf = buf.reshape(di,di,nao,ncore)
                    jc[i0:i1,j0:j1] = numpy.einsum('uvpc,pc->uvc', buf, mo[:,:ncore])
                    kc[j0:j1] += numpy.einsum('uvpc,uc->vpc', buf, mo[i0:i1,:ncore])
                else:
                    dij = di * dj
                    buf = buf1[p0:p0+dij].reshape(di,dj,nao,ncore)
                    jc[i0:i1,j0:j1] = numpy.einsum('uvpc,pc->uvc', buf, mo[:,:ncore])
                    jc[j0:j1,i0:i1] = jc[i0:i1,j0:j1].transpose(1,0,2)
                    kc[j0:j1] += numpy.einsum('uvpc,uc->vpc', buf, mo[i0:i1,:ncore])
                    kc[i0:i1] += numpy.einsum('uvpc,vc->upc', buf, mo[j0:j1,:ncore])
                p0 += dij
            if log.verbose >= logger.DEBUG1:
                ti1 = log.timer('jc and kc buffer', *ti1)
        elif approx == 2: # aapp, appa, vhf
            fdrv = libmcscf.MCSCFnrs4_aapp_jk
            fdrv(buf.ctypes.data_as(ctypes.c_void_p),
                 bufpa.ctypes.data_as(ctypes.c_void_p),
                 mo.ctypes.data_as(ctypes.c_void_p),
                 dm_core.ctypes.data_as(ctypes.c_void_p),
                 jc.ctypes.data_as(ctypes.c_void_p),
                 kc.ctypes.data_as(ctypes.c_void_p),
                 ctypes.c_int(sh_range[0]), ctypes.c_int(sh_range[1]-sh_range[0]),
                 ctypes.c_int(pashape[0]), ctypes.c_int(pashape[1]),
                 ctypes.c_int(pashape[2]), ctypes.c_int(pashape[3]),
                 ao_loc.ctypes.data_as(ctypes.c_void_p),
                 ctypes.c_int(mol.nbas))
            if log.verbose >= logger.DEBUG1:
                ti1 = log.timer('bufpa + core vj and vk', *ti1)
        else: # aapp, appa
            _ao2mo.nr_e1_(buf, mo, pashape, 's4', 's1', vout=bufpa)

# aapp, appa
        aapp_buf[paapp:paapp+sh_range[2]] = \
                bufpa.reshape(sh_range[2],nmo,ncas)[:,ncore:nocc]
        paapp += sh_range[2]
        p0 = 0
        for ij in range(sh_range[0], sh_range[1]):
            i,j = _ao2mo._extract_pair(ij)
            i0 = ao_loc[i]
            j0 = ao_loc[j]
            i1 = ao_loc[i+1]
            j1 = ao_loc[j+1]
            di = i1 - i0
            dj = j1 - j0
            if i == j:
                dij = di * (di+1) // 2
                buf1 = numpy.empty((di,di,nmo*ncas))
                idx = numpy.tril_indices(di)
                buf1[idx] = bufpa[p0:p0+dij]
                buf1[idx[1],idx[0]] = bufpa[p0:p0+dij]
                buf1 = buf1.reshape(di,-1)
            else:
                dij = di * dj
                buf1 = bufpa[p0:p0+dij].reshape(di,dj,-1)
                mo1 = mo[j0:j1,ncore:nocc].copy()
                for i in range(di):
                    appa_buf[:,i0+i] += pyscf.lib.dot(mo1.T, buf1[i])
                buf1 = bufpa[p0:p0+dij].reshape(di,-1)
            mo1 = mo[i0:i1,ncore:nocc].copy()
            appa_buf[:,j0:j1] += pyscf.lib.dot(mo1.T, buf1).reshape(ncas,dj,-1)
            p0 += dij
        if log.verbose >= logger.DEBUG1:
            ti1 = log.timer('aapp and appa buffer', *ti1)

        ti0 = log.timer('gen AO/transform MO [%d/%d]'%(istep+1,nstep), *ti0)
    bufs1 = bufs2 = bufs3 = None

    aapp_buf = pyscf.lib.transpose(aapp_buf.reshape(nao_pair,-1))
    aapp = _ao2mo.nr_e2_(aapp_buf, mo, (0,nmo,0,nmo), 's4', 's1', ao_loc=ao_loc)
    aapp = aapp.reshape(ncas,ncas,nmo,nmo)
    aapp_buf = None
    if nao == nmo:
        appa = appa_buf
    else:
        appa = numpy.empty((ncas,nao,nmo*ncas))
    for i in range(ncas):
        appa[i] = numpy.dot(mo.T, appa_buf[i].reshape(nao,-1))
    appa = appa.reshape(ncas,nmo,nmo,ncas)
    appa_buf = None

    if approx == 1:
        vhf_c = numpy.einsum('ijc->ij', jc)*2 - numpy.einsum('ijc->ij', kc)
        vhf_c = reduce(numpy.dot, (mo.T, vhf_c, mo))
        j_cp = numpy.dot(mo.T, jc.reshape(nao,-1)).reshape(nao,nao,ncore)
        j_cp = numpy.einsum('pj,jpi->ij', mo, j_cp)
        k_cp = numpy.dot(mo.T, kc.reshape(nao,-1)).reshape(nao,nao,ncore)
        k_cp = numpy.einsum('pj,jpi->ij', mo, k_cp)
    elif approx == 2:
        jc = pyscf.lib.hermi_triu(jc, hermi=1, inplace=True)
        kc = pyscf.lib.hermi_triu(kc, hermi=1, inplace=True)
        vhf_c = reduce(numpy.dot, (mo.T, jc-kc*.5, mo))
        j_cp = k_cp = None
    elif approx == 3:
        vhf_c = j_cp = k_cp = None

    time0 = log.timer('mc_ao2mo', *time0)
    return vhf_c, j_cp, k_cp, aapp, appa