MP2

Source access and public downloads

Repository paths identify files in the licensed engine source; they are not public downloads. For freely downloadable .oqp inputs and results, see Worked Examples.

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.

The available workflows depend on the HF reference:

• RHF supports energy, the analytic grad calculation, and the gradient-driven optimize, ts, mep, and irc calculations.
• UHF and ROHF support energy only. Their gradient requests stop explicitly; OpenQP does not apply the restricted formula to an open-shell reference.
• Leave input.functional empty. MP2 on Kohn-Sham references is rejected.
• Use scf.type=rhf, uhf, or rohf for the reference.
• Use mp2 when selecting spin scaling or an energy transformation.

Energy

.oqp

mp2(reference=uhf)/6-31g scf(conv=1e-10)
geom="../geometries/H2O-0381125c86f2.xyz"

The reference route option accepts rhf, rohf, or uhf and lowers to scf.type. It is separate from the mp2 spin-scaling section.

Python

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,
)

Canonical .oqp input

mp2(reference=uhf)/6-31g scf(conv=1e-10)
geom="""
8   0.000000000   0.000000000  -0.041061554
1  -0.533194329   0.533194329  -0.614469223
1   0.533194329  -0.533194329  -0.614469223
"""

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

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

Energy Transformation

The default transform=auto chooses direct Coulomb builds for small bases and packed AO-to-MO transformations above 120 basis functions or when the pair-build count exceeds its guard. To request the packed form on a small molecule:

mp2(reference=uhf,transform=n5)/6-31g scf(conv=1e-10)
geom="../geometries/H2O-0381125c86f2.xyz"

job.theory.mp2(reference="uhf", basis="6-31g", conv=1e-10)
job.settings.mp2(transform="n5")

In legacy input, add mp2.transform=n5. Explicit n5 can fall back from full to occupied-virtual storage, but stops if neither packed form succeeds. Explicit direct retains OQP_MP2_MAX_JBUILDS and stops when its count is exceeded. Automatic selection retains the guarded direct fallback after packed failure. See transform for the complete selection and memory behavior. The setting does not select the analytic-gradient assembly.

The small UHF H2O/6-31G input is examples/MP2/h2o_ump2_n5_6-31g.oqp. Its geometry, reference, SCF settings and committed energy reference are shared with the conventional example above.

Analytic RHF Gradient

The RHF derivative is evaluated from a stationary MP2 Lagrangian. It includes the relaxed one-particle density, the amplitude-linear two-particle density, and the coupled-perturbed RHF orbital response. No finite-difference gradient is substituted. The same equations use the selected same-spin and opposite-spin coefficients, so conventional MP2, SCS-MP2, SOS-MP2, and custom spin scaling all have analytic gradients.

.oqp

mp2/6-31g grad(S0) scf(conv=1e-10,incremental=false)
geom="../geometries/H2O-0381125c86f2.xyz"

Runnable input: examples/MP2/h2o_rmp2_6-31g_grad.oqp

Python

from oqp.openqp import OpenQP

job = OpenQP("h2o_rmp2_grad", silent=1)
job.molecule(geometry="water", charge=0, multiplicity=1)
job.theory.mp2(basis="6-31g", reference="rhf", variant="scs-mp2")
job.workflow.gradient(state=0)

mol = job.run()
print(mol.get_grad())

The same analytic gradient supplies the native geometry workflows. For a minimum search, replace job.workflow.gradient(state=0) with job.workflow.optimize(istate=0) or use opt(S0) in concise input.

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:

rhf/6-31g* mp2(variant=custom,same_spin_scale=0.5,opposite_spin_scale=1.1)
geom="molecule.xyz"

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 energy calculation uses direct Coulomb builds or packed AO-to-MO transformations according to transform. A guard limits direct pair builds; packed transformations check available memory and allocation status. If a job stops at the direct-build guard, use auto or n5, reduce the basis/problem size, or raise the guard only after checking runtime and memory requirements.

The first analytic-gradient implementation forms dense AO and MO four-index quantities and therefore has fourth-power memory growth. It stops above 60 basis functions by default. OQP_MP2_GRAD_MAX_NBF can raise that limit after the required memory has been checked. The gradient supports Cartesian and pure spherical shells. MP2 Hessians, open-shell MP2 gradients, NACME, SOC, PCM, NMR, IR, and Raman derivatives are not implemented.

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

Scientific references

MP2 and Spin-Scaled MP2.