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.

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] only when selecting a spin-scaled variant or custom scale factors.

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,
)

Legacy .inp

[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

Runnable input: examples/MP2/h2o_ump2_6-31g.oqp or its same-stem legacy .inp companion.

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

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 or its same-stem legacy .inp companion.

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:

[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 energy implementation uses direct per-occupied-MO-pair Coulomb builds through the existing two-electron driver. 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.

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.