MP2¶

OpenQP supports standalone second-order Moller-Plesset ground-state correlation with [input] method=mp2. The calculation first converges an HF reference, then adds the MP2 correlation energy and reports the correlated E(HF+MP2) total.

MP2 is currently an energy-only post-SCF workflow:

Use runtype=energy.
Leave [input] functional empty. MP2 on Kohn-Sham references is rejected.
Use [scf] type=rhf, uhf, or rohf for the reference.
Use [mp2] only when selecting a spin-scaled variant or custom scale factors.

Energy¶

Input File Style¶

[input]
system=
 8   0.000000000   0.000000000  -0.041061554
 1  -0.533194329   0.533194329  -0.614469223
 1   0.533194329  -0.533194329  -0.614469223
charge=0
runtype=energy
method=mp2
functional=
basis=6-31g

[guess]
type=huckel

[scf]
type=uhf
multiplicity=1
conv=1.0e-10

[mp2]
variant=mp2

Pythonic Style¶

from oqp.openqp import OpenQP

job = OpenQP("h2o_mp2", silent=1)
job.molecule(geometry="water", charge=0, multiplicity=1)
job.theory.mp2(basis="6-31g", reference="uhf", variant="mp2", conv=1.0e-10)

mol = job.run()
print("MP2 total energy:", mol.get_results()["energy"])

For custom spin scaling in Python, pass the scale factors through the same helper:

job.theory.mp2(
    basis="6-31g",
    reference="uhf",
    variant="custom",
    same_spin_scale=0.50,
    opposite_spin_scale=1.10,
)

Runnable input: examples/MP2/h2o_ump2_6-31g.inp.

For the H2O / 6-31G example, the validated installed-package run reports:

Quantity	Value (Ha)
`E(MP2, correlation)`	`-0.1278307451`
`E(MP2, total)`	`-76.1121207760`

Spin-Scaled Variants¶

The native MP2 kernel computes same-spin and opposite-spin components separately. Named presets choose scale factors for

E(MP2) = c_ss * (E_aa + E_bb) + c_os * E_ab

Variant	Same-spin scale `c_ss`	Opposite-spin scale `c_os`
`mp2`, `conventional`	`1.0`	`1.0`
`scs-mp2`, `scs`	`1.0 / 3.0`	`1.2`
`sos-mp2`, `sos`	`0.0`	`1.3`
`os-mp2`, `os`, `opposite-spin`	`0.0`	`1.0`
`ss-mp2`, `ss`, `same-spin`, `sss-mp2`, `sss`	`1.0`	`0.0`
`scs-mi-mp2`, `scs-mi`	`1.29`	`0.40`

For any other literature parameterization, use variant=custom:

[mp2]
variant=custom
same_spin_scale=0.50
opposite_spin_scale=1.10

Named presets overwrite same_spin_scale and opposite_spin_scale. Set variant=custom when the numeric scales should be read directly.

Implementation Notes¶

OpenQP assembles the MP2 energy in spin-blocked form on semicanonicalized orbitals. ROHF references are semicanonicalized before the correlation step so the denominator expression is well defined.

The current implementation uses direct per-occupied-MO-pair Coulomb builds through the existing two-electron driver. It does not store a full fourth-order MO integral tensor. A guard limits the number of pair builds; if a job aborts with OQP_MP2_MAX_JBUILDS, reduce the basis/problem size or raise that guard only after checking the expected runtime and memory cost.

Derivative workflows are not implemented for MP2 yet. Use HF/DFT or response methods for gradients, Hessians, optimization, NACME, SOC, PCM, NMR, IR, and Raman workflows until MP2-specific derivatives are added.

See References for the MP2 and spin-component-scaling papers behind the supported presets.