The level of the electronic structure calculations can be changed for the different
-body terms in the expansion of the potential. As a consequence, the keywords
`START2D`, `START3D`, `VAR2D` and `VAR3D` exist in full analogy
to the keywords `START1D` and `VAR1D` in standard calculations (see above).
The number always represents the level of the expansion term. Such calculations are termed
multi-level calculations. There does *not* exist a corresponding set of keywords for
the 4-body terms. 4-body terms will always use the variables specified for the 3-body terms.

`MULTI`=*n*- The keywords
`START1D`,`START2D`,`START3D`in combination with the commands`VAR1D`,`VAR2D`and`VAR3D`allow for the calculation of multi-level potential energy surfaces. This would imply in principle that the 1D term of the potential needs to be computed at all three levels and the 2D term at two computational levels. As certain low level results are a byproducts of more sophisticated methods (e.g. the HF energy is a byproduct of an MP2 calculation or the MP2 energy is a byproduct of a CCSD(T) calculation) the computational overhead can be avoided by the`MULTI`option.

`MULTI=1:`This is the default and most expensive choice. The 1D potential will be computed at all 3 levels of theory. Likewise, the 2D potential will be calculated at 2 levels explicitly. An example would be:1D: CCSD(T)/cc-pVTZ 2D: MP4(SDQ)/cc-pVTZ 3D: MP2/cc-pVDZ {SURF,Start1D=label1 VMULT,Start2D=label2,Start3D=label3,Multi=1}

`MULTI=2:`All information is provided by the preceding calculations and thus no part of the potential has to be computed twice. Examples:1D: CCSD(T)/cc-pVTZ 2D: CCSD(T)/cc-pVTZ 3D: MP2/cc-pVTZ {SURF,Start1D=label1 VMULT,Start2D=label1,Start3D=label2 VMULT,Var3D=EMP2,Multi=2}

1D: CCSD(T)/cc-pVTZ 2D: MP2/cc-pVTZ 3D: MP2/cc-pVTZ {SURF,Start1D=label1 VMULT,Start2D=label2,Start3D=label2 VMULT,Var2D=EMP2,Var3D=EMP2,Multi=2}

`MULTI=3:`The 2D potential provides all information for the 3D part while there is no connection between 1D and 2D. Consequently, the 1D contributions need to be computed twice (at the 1D and 2D levels) while all other terms will be computed just once. Examples:1D: CCSD(T)/cc-pVTZ 2D: MP4(SDQ)/cc-pVTZ 3D: MP2/cc-pVTZ {SURF,Start1D=label1 VMULT,Start2D=label2,Start3D=label3 VMULT,Var3D=EMP2,Multi=3}

1D: CCSD(T)/cc-pVTZ 2D: MP4(SDQ)/cc-pVTZ 3D: MP4(SDQ)/cc-pVTZ {SURF,Start1D=label1 VMULT,Start2D=label2,Start3D=label2,Multi=3}

`MULTI=4:`The 1D calculation provides all information for the 2D potential but does not so for the 3D part. Hence, the 1D contribution and the 2D contributions need to be computed twice. Examples:1D: CCSD(T)/cc-pVTZ 2D: CCSD(T)/cc-pVTZ 3D: MP4(SDQ)/cc-pVTZ {SURF,Start1D=label1 VMULT,Start2D=label1,Start3D=label2,Multi=4}

1D: CCSD(T)/cc-pVTZ 2D: MP2/cc-pVTZ 3D: MP2/cc-pVDZ {SURF,Start1D=label1 VMULT,Start2D=label2,Start3D=label3 VMULT,Var2D=EMP2,Multi=4}

In 2D and 4D calculations (i.e.

`NDIM=2,4`) the`VMULT`command can be used as well. In 4D calculations the last level must always be identical to the 3D level. In 2D the meaning of`MULTI=1`and`MULTI=3`is the same. Likewise,`MULTI=2`and`MULTI=4`are the same in case of 2D calculations. `START2D`=*label*`START2D`and`START3D`define labels in the input stream in order to compute the 2D and 3D terms at different levels of electronic structure theory than the 1D terms. The use of the`START2D`and`START3D`commands usually requests the use of`GOTO`commands in the input.`VAR2D`=*variable*- The keywords
`VAR2D`and`VAR3D`are defined in full analogy to the`VAR1D`option. They specify the internal variable (e.g. ENERGY, EMP2, CCSD, ...) to be read out for a given grid point.

The following example shows a 1D:CCSD(T)/cc-pVTZ; 2D:MP4(SDQ)/cc-pVTZ and
3D:MP2/cc-pVTZ multi-level calculation. As the MP2 energy is a byproduct of
the CCSD(T) and MP4(SDQ) calculations only the 1D grid points will be computed
twice (at the CCSD(T) and MP4(SDQ) levels). The 1D and 2D energies will be
obtained from the internal variable `ENERGY` while the 3D energies make
use of the `EMP2` variable.

memory,50,m orient,mass geometry={ 6 Ethene C 0.0000000000 0.0000000000 -0.6685890718 C 0.0000000000 0.0000000000 0.6685890718 H 0.0000000000 -0.9240027061 -1.2338497710 H 0.0000000000 0.9240027061 -1.2338497710 H 0.0000000000 0.9240027061 1.2338497710 H 0.0000000000 -0.9240027061 1.2338497710 } mass,iso basis=vtz logfile,scratch hf ccsd(t) optg freq,symm=auto label1 hf ccsd(t) goto,label4 label2 {hf start,atden} {mp4 notripl} goto,label4 label3 {hf start,atden} mp2 label4 {surf,start1D=label1,sym=auto vmult,start2D=label2,start3D=label3,Var3D=EMP2,Multi=3} vscf vci

molpro@molpro.net 2018-10-21