Mixing PBC and molecular modules¶
Post-HF methods, as standalone numerical solvers, do not require knowledge of the boundary conditions. Calculations on finite-sized systems and extended systems are distinguished by the boundary conditions of the integrals (and basis). The same post-HF solver can thus be used for both finite-size problems and the periodic boundary problems if they have a compatible Hamiltonian structure.
In PySCF, many molecular post-HF solvers have two implementations: an incore and
outcore version. These differ by the treatment of the 2-electron
integrals. The incore solver takes the
mol_df) from the underlying mean-field object as the two-electron
interaction part of the Hamiltonian while the outcore solver generates the
2-electron integrals (with free boundary conditions) on the fly.
To use the molecular post-HF solvers in PBC code, we need to ensure that the incore
version solver is called.
_eri in a mean-field object is the straightforward way to
trigger the incore post-HF solver. If the allowed memory is large enough to
hold the entire 2-electron integral array, the Gamma point HF solver always
generates and holds this array. A second choice is to set
cell which forces the program to generate and hold
the mean-field object.
If the problem is big,
incore_anyway may overflow the available
Holding the full integral array
_eri in memory limits the problem size
one can treat. Using the density fitting object
with_df to hold the
integrals can overcome this problem. This architecture has been bound to PBC
and molecular mean-field modules. Not all post-HF methods are available with density fitting.
Aside from the 2-electron integrals, there are some attributes and methods
required by the post-HF solver. They are
get_ovlp() for 1-electron integrals,
the numerical integration of DFT exchange-correlation functionals. These are all
overloaded in the PBC mean-field object to produce the PBC integrals.
#!/usr/bin/env python ''' Gamma point post-HF calculation needs only real integrals. Methods implemented in finite-size system can be directly used here without any modification. ''' import numpy from pyscf.pbc import gto, scf cell = gto.M( a = numpy.eye(3)*3.5668, atom = '''C 0. 0. 0. C 0.8917 0.8917 0.8917 C 1.7834 1.7834 0. C 2.6751 2.6751 0.8917 C 1.7834 0. 1.7834 C 2.6751 0.8917 2.6751 C 0. 1.7834 1.7834 C 0.8917 2.6751 2.6751''', basis = '6-31g', verbose = 4, ) mf = scf.RHF(cell).density_fit() mf.with_df.mesh = *3 mf.kernel() # # Import CC, TDDFT module from the molecular implementations # from pyscf import cc, tddft mycc = cc.CCSD(mf) mycc.kernel() mytd = tddft.TDHF(mf) mytd.nstates = 5 mytd.kernel()