MPPT — Multipartitioning perturbation theory#
MPPT / Electronic-structure calculations
Multipartitioning
perturbation theory
Quasi-degenerate multireference perturbation theory for incomplete model spaces, with spin–orbit coupling and GRECP / GRPP relativistic pseudopotentials.
A custom PySCF interface connected to MPPT’s
Fortran and C++ computational core.
Diagrammatic MRPT
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Methods and capabilities
Determinant selection
Incomplete
model spaces
CIPSIXX builds selected or complete determinant spaces. Selection reduces the cost of both the variational calculation and the subsequent perturbative treatment.
Selection algorithmThe MPPT formulation
Multipartitioning
perturbation theory
- Multiple partitionings. Each model determinant defines its own zeroth-order Hamiltonian.
- Density-based denominators. Auxiliary-state density and Fock-like matrices give separate electron-removal and attachment energies: an IP/EA-like construction.
- Wave-function relaxation. Diagonalize → perturb → diagonalize updates the state mixing, as well as the energies.
GRECP / GRPP
Relativistic
spin–orbit calculations
GRECP, also called GRPP, accounts for scalar-relativistic effects and spin–orbit coupling. Suitable Gatchina pseudopotential parameter sets also incorporate Breit and QED contributions, including self-energy and vacuum polarization.
Relativistic formulationOrbital generation / PySCF interface
Orbitals for compact
model spaces
Computed virtual orbitals can be spatially delocalized: the local atomic character of interest is spread across many MOs. AO projections identify linear combinations that concentrate this character in a few orbitals, giving a more compact representation of the corresponding excitation channel.
Orbital generation and projectionsDelocalized virtual MOs
Character spread over many MOs
Rotated virtual MOs
Character concentrated in a few MOs
PySCF preparation.
MPPT calculations.
A custom YAML interface wraps PySCF for SCF and CASSCF, with AVAS initial guesses and reusable orbital checkpoints.
MPPT’s own Fortran and C++ programs perform determinant selection, correlation and spin–orbit calculations. Run the stages separately through a shared HDF5 file or enable the complete workflow in one input.
ce.yaml / input and basis from the quick start
# Prepare the reference; stop before MPPT
pyscf2mppt ce.yaml \
--output-dir runs/ce-reference \
--stop-after dump
# Read saved orbital checkpoints
pyscf2mppt --inspect-checkpoint \
runs/ce-reference/checkpointsExisting HDF5 / enabled native stages only
# Selection → scalar MPPT → spin–orbit levels
pyscf2mppt ce.yaml \
--from-hdf5 runs/ce-reference/data/ce.h5 \
--output-dir runs/ce-levelsOnly the mppt section is used. The saved HDF5 is updated in place; PySCF is not rerun.
runs/ce-levels/
summary.md run status
run.log complete output
logs/ per-stage diagnostics
data/ Hamiltonians and eigenvectors
reports/ levels and propertiesFrom SCF to
spin–orbit energy levels
The Ce³⁺ example takes you from reference orbitals to correlated, relativistic spin–orbit-split levels. Run preparation and downstream stages separately, then use one input for the complete calculation.
pyscf2mppt ce.yaml --output-dir runs/ce-fullFirst result: runs/ce-full/summary.md
Diagrammatic formulation
of MPPT
The diagrammatic formulation connects general model spaces, determinant-specific partitionings and a second-order effective Hamiltonian. The literature guide follows the method from its foundations to relativistic applications.
Equations and literatureA Quasirelativistic Perturbation Theory As a Tool for Modeling f–f and f–d Transitions in Lanthanide Ions
M. M. Seregin, I. O. Glebov, N. S. Mosyagin,
A. V. Oleynichenko & A. V. Zaitsevskii
Mikhail Seregin · diploma thesis
Manuscript link to be added.
PlaceholderMulti-partitioning quasidegenerate perturbation theory
A. Zaitsevskii & J.-P. Malrieu
Diagrammatic formulation of the second-order many-body multipartitioning perturbation theory
A. Zaitsevskii & R. Cimiraglia