9.4 General Comments on MP2 Calculations, Practical Hints
- It is well-known, that perturbation theory yields reliable results only, if the
perturbation is small. This is also valid for MP2, which means, that MP2 improves
HF results only, if HF already provides a fairly good solution to the problem. If HF
fails, e.g. in case of partially filled d-shells, MP2 usually will also fail and should not
be used in this case.
- MP2 results are known to converge very slowly with increasing basis sets, in particular
slowly with increasing l-quantum number of the basis set expansion. Thus for reliable
results the use of TZVPP basis sets (or higher) is recommended. When using SVP
basis sets a qualitative trend can be expected at the most. Basis sets much larger
than TZVPP usually do not significantly improve geometries of bonded systems, but
still can improve the energetic description. For non–bonded systems larger basis sets
(especially, with more diffuse functions) are needed.
- It is recommended to exclude all non-valence orbitals from MP2 calculations, as
neither the TURBOMOLE standard basis sets SVP, TZVPP, and QZVPP nor the
cc-pVXZ basis set families (with X=D,T,Q,5,6) are designed for correlation treatment
of inner shells (for this purpose polarisation functions for the inner shells are needed).
The default selection for frozen core orbitals in Define (orbitals below -3 a.u. are
frozen) provides a reasonable guess. If core orbitals are included in the correlation
treatment, it is recommended to use basis sets with additional tight correlation
functions as e.g. the cc-pwCVXZ and cc-pCVXZ basis set families.
- RI-MP2: We strongly recommend the use of auxiliary basis sets optimized for the
corresponding (MO) basis sets.
RI-MP2 calculations with the ricc2 program:
All what is needed for a RI-MP2 gradient calculation with the ricc2 program is a $ricc2 data
group with the entry geoopt model=mp2. If you want only the RI-MP2 energy for a single point
use as option just mp2. To activate in MP2 energy calculations the evaluation of the D1 diagnostic
(for details see Sec. 10.1). use instead mp2 d1diag. (Note that the calculation of the D1
diagnostic increases the costs compared to a MP2 energy evaluation by about a factor of
Comments on the Output
- Most important output for ricc2, pnoccsd, and mpgrad are of course the MP2(+HF)
energies (written to standard output and additionally to the file energy) and
MP2(+HF) gradients (written to the file gradient).
- In case of MP2 gradient calculations the modules also calculate the MP2 dipole
moment from the MP2 density matrix (note, that in case of mpgrad a frozen core
orbital specification is ignored for gradient calculations and thus for MP2 dipole
Further output contains indications of the suitability of the (HF+MP2) treatment.
- As discussed above, reliable (HF+MP2) results are in line with small MP2 corrections.
The size of the MP2 correction is characterised by the t-amplitudes, as evident from
the above equations. mpgrad by default plots the five largest t-amplitudes as well as
the five largest norms of t-amplitudes for fixed i and j, rimp2 does the same upon
request, if $tplot is added to control file. More or less than five t-amplitudes will
be plotted for $tplot n, where n denotes the number of largest amplitudes to be
plotted. It is up to the user to decide from these quantities, whether the (SCF+MP2)
treatment is suited for the present problem or not. Unfortunately, it is not possible
to define a threshold, which distinguishes a "good" and a "bad" MP2-case, since the
value of individual t-amplitudes are not orbital-invariant, but depend on the orbital
basis (and thereby under certain circumstances even on the orientation). Example:
the largest norm of t-amplitudes for the Cu-atom (d10s1, "good" MP2-case) amounts
to ca. 0.06, that of the Ni-atom (d8s2, "bad" MP2 case) is ca. 0.14.
- A more descriptive criterion may be derived from the MP2 density matrix. The
eigenvalues of this matrix reflect the changes in occupation numbers resulting from
the MP2 treatment, compared to the SCF density matrix, where occupation numbers
are either one (two for RHF) or zero. Small changes mean small corrections to HF
and thus suitability of the (HF+MP2) method for the given problem. In case of
gradient calculations rimp2 displays by default the largest eigenvalue of the MP2
density matrix, i.e. the largest change in occupation numbers (in %). All eigenvalues
are shown, if $mp2occ is added to the control file. For main group compounds largest
changes in occupation numbers of ca. 5 % or less are typical, for d10 metal compounds
somewhat higher values are tolerable.
- A similar idea is pursued by the D2 and D1 diagnostics [120,121] which is implemented
in ricc2. D2 is a diagnostic for strong interactions of the HF reference state with
doubly excited determinants, while D1 is a diagnostic for strong interactions with
singly excited determinants.