9.3 How to Prepare and Perform MP2 Calculations

Prerequisites

Calculations with mpgrad, ricc2 or pnoccsd require

• a converged SCF calculation with the one-electron density convergence threshold set to $denconv 1.d-7 or less
• the maximum core memory the program is allowed to allocate should be defined in the data group $maxcor (in MB); the recommended value is ca. 3/4 of the available (physical) core memory at most.
• orbitals to be excluded from the correlation treatment have to be specified in the data group $freeze
• for mpgrad the calculation of gradients is omitted by adding the flag $mp2energy to the control file; in this case only the MP2 energy is calculated.

Calculations with ricc2 and pnoccsd moreover use

• an auxiliary basis defined in the data groups $atoms and $cbas. If not specified before the start of ricc2 or pnoccsd the programs will assign the default auxiliary basis sets which have the same names as the one-electron basis sets and will try to extract them from the TURBOMOLE basis set library. If this succeeds the assignment and auxiliary basis sets are stored in the control file else the programs will stop.

This is not needed for mpgrad, but here one needs

• a specification for scratch files and their size in data group $mointunit (see Section 20.2.18)
• and the number of passes for integral evaluations and transformations in data group $traloop

For explicitly-correlated MP2-F12 calculations one needs—depending the details of the applied approximations—additionally a so-called complementary auxiliary basis set (CABS, defined in $cabs) and a RI-SCF auxiliary basis set defined in $jkbas.

Calculations with ricc2 and pnoccsd

1.

RI-MP2 calculations require the specification of auxiliary basis sets ($cbas) and a converged SCF calculation with the one-electron density convergence threshold set to $denconv 1.d-7 or less. In addition, the options $freeze (frozen core approximation) and $maxcor (maximum core memory usage) should be set. All these settings can be done during the input generation with the program define under the entries mp2/cc or pnocc of the last main menu.

2.

The ricc2 program requires the data group:
$ricc2
  mp2 
  geoopt model=mp2
(Where the last line should only be included if the calculation of gradients is needed e.g. in geometry optimizations.) This can be prepared with define in the menu cc.

3.

The pnoccsd program does not require any special input for a MP2 calculation with default thresholds but it is recommended to specify the PNO truncation threshold explicitly in the data group:
$pnoccsd
  mp2 
  tolpno= 1.0E-7 
This can be prepared with define in the menu pnocc.

4.

For explicitly-correlated MP2-F12 calculations with ricc2 or pnoccsd also the data groups $rir12 and $lcg are needed.

5.

Start a single ricc2 and pnoccsd calculations respectively with the commands ricc2 and pnoccsd.

6.

For optimisation of structure parameters at the RI-MP2 level with ricc2 use the command jobex -level cc2. For geometry optimizations with RI-JK-SCF as reference for RI-MP2 with the ridft and ricc2 binaries the additional option -rijk has to be given.

7.

The combination of RI-MP2 with RI-JK-SCF can lead to significant computational savings in particular for geometry optimizations for small and medium sized molecules with large basis sets (quadruple-ζ and beyond) or basis sets with diffuse functions (e.g. the aug-cc-pVXZ basis set families). For large molecules with TZVPP or similar basis sets, conventional direct SCF calculations are usually more efficient.

8.

With ricc2 and pnoccsd spin-component scaled SCS- or SOS-RI-MP2 calculations can be carried out by adding in the $ricc2 (for ricc2) or $pnoccsd (for pnoccsd data group the line

scs  cos=1.2d0 css=0.3333d0

where the two parameters are the scaling factors for, respectively, the opposite- and same-spin contribution. The specification of the scaling factors is optional; the default values are cos=6/5 and css=1/3 as recommended by S. Grimme in J. Chem. Phys. 118 (2003) 9095. The abbreviation sos can be used for SOS-MP2 calculations with cos=1.3 and css=0.0 (Y., Jung, R.C. Lochan, A.D. Dutoi, and M. Head-Gordon, J. Chem. Phys. 121 (2004) 9793.). SOS-MP2 is in ricc2 implemented with (⁴) scaling costs. For such calculations the data group $laplace has to be added.

9.

For technical recommendations and additional options for parallel RI-MP2 and PNO-MP2 calculations with the ricc2 and pnoccsd programs see Secs. 3.2 and 10.6 and 9.7.

MP2 calculations with a ROHF reference state

With the program ricc2 it is possible to compute MP2 (and spin-component scaled) MP2 energies with single-determinant restricted open-shell reference wavefunctions. No additional input is required apart from the usual ROHF input for the dscf and ridft programs and a standard MP2 input for ricc2.

TURBOMOLEs Hartree-Fock codes can handle within the ROHF framework many cases, which include beside common high- and low-spin configuration state functions also weighted averages of high-spin CSFs (see Sec. 6.3 for further details). The Møller-Plesset perturbation theory and coupled cluster functionalities implemented in ricc2 require a single-determinant reference state and can thus only deal with high-spin open-shell cases (not averaged):

• The spins of all n_open unpaired electrons are parallel (α spin will be assumed) so that the ROHF reference state has the spin multiplicity n_open + 1.
• There must be only one type of open shells and all orbitals in this shell must have the occupation number 1.
• For the single electron case (i.e. doublets) the Roothaan parameters are a = b = 0, for high-spin cases with more than one unpaired electron the Roothaan parameters must be set to a = 1 and b = 2.

For non-abelian points groups this implies that shells with degenerate orbitals (as e.g. t₁ in point group I) must be half-filled. An average over the different (symmetry-equivalent or inequivalent) high-spin determinants that are obtained when a shell of degenerate orbitals is less than or more than half-filled is not possible with single-point ricc2 calculations.

For states with less than or more than half-filled shells of degenerate orbitals the calculations half to be done in a point group that lifts the degeneracy such that it becomes possible to assign integer occupation numbers. A symmetry-breaking of the orbitals can be avoided by doing the Hartree-Fock calculation in the full point group. The input (and MO coefficients) can then be transformed to a lower point group using define only for the ricc2 calculation.

Calculations with mpgrad

1.

Add $denconv 1.d-7 to the control file and perform a dscf run.

2.

If any orbitals are decided to be excluded from MP2 treatment, add data group $freeze manually to the control file, see also Section 20.2.18.

3.

For preparation of an mpgrad run use the script Mp2prep:
mp2prep -e/g -m memory -p discspace [scratch file directory]
As an example, with the command
mp2prep -e -m 100 -p 1000 /work
an MP2-energy calculation is prepared, the amount of available core memory is restricted to 100 MB, the MOs are blocked, so that integral scratch files—located in the directory /work—do not need more than 1000 Mb. The number of blocks, i.e. the number of passes with repeated integral evaluations, is written to the control file ($traloop) as well as the specification of scratch files ($mointunit, see Section 20.2.18). Note: less disc space means more passes and thus lower efficiency of mpgrad, but due the technical limitations discspace should be limited to values < 16Gb to avoid integer overflow errors. Settings obtained by mp2prep may be changed manually. You may change the number of passes in $traloop by editing the control file (e.g. if the originally intended disc space is not available). To adapt the size of scratch files add $statistics mpgrad to control file and start an mpgrad statistics run with the command mpgrad.

4.

Start a single mpgrad calculation with the command mpgrad.

5.

For optimisation of structure parameters at the (non-RI-) MP2 level use the command jobex -level mp2. Note, that the frozen core approximation is ignored in this case.