43.2 Multi-level calculations

VMULT,options

The level of the electronic structure calculations can be changed for the different $i$-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=value

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 byproduct of more sophisticated methods (e.g. the HF energy is a byproduct of a 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
geomtyp=xyz
geometry={ang;mass
6
Ethen
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
}

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