Skip to content

7.2 Correlation energy with MP2 and CCSD(T)

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

7.2.1 Model, units and provenance

Geometry in Å; electronic energy in hartree; vibrational wavenumbers in cm⁻¹. Check each printed field and keep thermal and standard-state terms distinct.

Shared inputs, conventions and evidence

Original schematic: Correlation energy with MP2 and CCSD(T). No numerical results are claimed.
Original schematic: Correlation energy with MP2 and CCSD(T). No numerical results are claimed.

7.2.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

7.2.2.1 Input block 1

%chk=g26_water_mp2_dz.chk
%mem=4GB
%nprocshared=2
#p MP2(FC)/cc-pVDZ SP SCF=Tight

Water frozen core MP2 fixed geometry

0 1
O  0.000000  0.000000  0.000000
H  0.758000  0.000000  0.586000
H -0.758000  0.000000  0.586000

7.2.3 Worked investigation

7.2.3.1 Intuition and prerequisites

Mean-field electrons respond to an average environment. Post-HF methods add electron correlation beyond that reference. In a small closed-shell molecule near equilibrium, MP2 and coupled-cluster calculations let you isolate this improvement while also seeing why basis convergence becomes more demanding. Use a fixed water geometry so structural changes do not contaminate the first comparison. This is a method-learning exercise; CCSD(T) is not an automatic oracle, especially for substantial multireference character. Prerequisites: HF convergence, basis-family tests, and enough local memory/disk quota.

See input block 1 above.

Separate copies use HF/cc-pVDZ, CCSD(T,FC)/cc-pVDZ, and MP2(FC)/cc-pVTZ; give every copy its own checkpoint. The FC option makes the frozen-core intention explicit. Check the local revision's accepted coupled-cluster syntax before a costly submission, and verify frozen/active occupied orbitals from its output. /

7.2.3.2 Workflow

  1. Establish a tightly converged HF reference in each basis. Keep exactly the same nuclear coordinates.
  2. Read the post-HF total energy from the correct method-specific final record. The preceding SCF Done is the HF reference, not the MP2 or CCSD(T) total.
  3. Calculate Ecorr(method)=Etotal(method)−EHF at the same geometry and basis. Retain hartree and optionally convert a difference to kJ mol−1.
  4. Compare MP2 DZ→TZ changes with HF DZ→TZ changes. A small HF basis increment does not establish convergence of correlated energy.
  5. Inspect iterative convergence and reported diagnostics for CCSD; archive warnings, amplitudes/diagnostics available in the log, and the correlation treatment.
  6. For a reaction extension, repeat the entire balanced species set at matched geometry convention, basis, and core treatment.

7.2.3.3 Interpret check and limits

The label “correlation energy” is method-defined here and should not be confused with an experimental binding energy. MP2 can be unreliable when orbital gaps are small, and CCSD(T) can fail near dissociation or other strongly multiconfigurational situations. Diagnostics are warning tools, not universal binary certificates. Frozen-core and all-electron correlation cannot be mixed casually in small reaction differences. A basis without diffuse functions may inadequately describe anions or weak interactions even if correlation converges numerically. Scaling estimates are qualitative; actual performance depends on implementation, memory, disk, and hardware.

Exercise Build a table whose entries require method, basis, core treatment, geometry source, HF energy, correlated energy, and termination status. Explain why “CCSD(T) energy” without these qualifiers is incomplete.

7.2.5 Sources and further reading