12.16 The Many-Body Expansion Method 12.16.1 Introduction 12.17 Ab Initio Frenkel Davydov Exciton Model (AIFDEM)

12.16.2 Job Control

(February 4, 2022)

A MBE( $n$ ) calculation is requested by setting MANY_BODY_INT = TRUE in the $rem section. The level of theory used for the fragments will be whatever is specified in the $rem section. Researchers who use Q-Chem’s MBE code are asked to cite Ref. 969, 637. In addition, please cite Ref. 967 for the MBCP( $n$ ) method.

MANY_BODY_INT

MANY_BODY_INT
       Perform a MBE calculation.
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Perform a MBE calculation. FALSE Do not perform a MBE calculation.
RECOMMENDATION:
       NONE

Additional MBE-specific options, such as the order of the expansion ( $n$ ), are specified in a $mbe input section, as described below.

Order
       Specifies the order of the many-body expansion.
INPUT SECTION: $mbe
TYPE:
       INTEGER
DEFAULT:
       None
OPTIONS:
       $n$ Perform an MBE( $n$ ) calculation.
RECOMMENDATION:
       Orders $n\leq 5$ are available.

Embed
       Specifies the embedding method for EE-MBE( $n$ ).
INPUT SECTION: $mbe
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       None Do not use embedding. Charges Use atomic point charges. Density Full Coulomb embedding using monomer densities.
RECOMMENDATION:
       Use of atomic point charges requires a $mbe_charges section to specify the charges.

Q-Chem’s implementation of EE-MBE( $n$ ) with atomic point charges is designed to use with a $mbe_charges input section to specify fixed embedding charges. (Use of these charges is intended to accelerate convergence of the MBE by capturing many-body polarization effects and thus making the higher-order $n$ -body terms smaller, although three- and four-body terms remain non-negligible even with embedding charges.^{637, 706}) The format of the $mbe_charges section is simply a list of charges in the same order as the atoms in the $molecule section. An example is provided below.

Many-body counterpoise corrections are requested with two keywords in the $mbe input section: BSSE_Type and BSSE_Order. These have only been implemented up to $n=3$ , as the $n=2$ terms make by far the most significant contribution.⁷⁰⁶

BSSE_Order
       Perform a many-body counterpoise correction of the MBCP( $n$ ) or VMFC( $n$ ) variety.
INPUT SECTION: $mbe
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not perform a counterpoise correction. $n$ Perform a counterpoise correction truncated at order $n$ .
RECOMMENDATION:
       Orders $n\leq 3$ are available. Use the keyword BSSE_Type to choose between MBCP and VMFC.

BSSE_Type
       Select the type of many-body counterpoise correction, MBCP( $n)$ or VMFC( $n$ ).
INPUT SECTION: $mbe
TYPE:
       STRING
DEFAULT:
       MBCP
OPTIONS:
       MBCP Use MBCP( $n$ ). VMFC Use VMFC( $n$ ).
RECOMMENDATION:
       The two methods are equivalent for $n=2$ but different for $n\geq 3$ . MBCP( $n$ ) contains fewer terms but generally provides comparable results as compared to the formally more complete VMFC( $n$ ) approach.

Example 12.40 Example showing a EE-MBE(3) calculation using TIP3P charges.

$molecule
0 1
--
   0 1
   O -1.126149 -1.748387 -0.423240
   H -0.234788 -1.493897 -0.661862
   H -1.062789 -2.681331 -0.218819
--
   0 1
   O -0.254210 1.611495 -1.293845
   H -1.001520 1.163510 -1.690129
   H -0.153399 2.411746 -1.809248
--
   0 1
   O 1.694541 -0.226287 1.705739
   H 0.785920 0.073487 1.677909
   H 2.047134 0.150917 2.511706
--
   0 1
   O -0.864533 0.522472 1.218817
   H -0.694120 1.093542 0.469789
   H -1.131418 -0.310426 0.829702
$end

$rem
   SYM_IGNORE        true
   METHOD            B3LYP
   BASIS             cc-pVDZ
   MANY_BODY_INT     true
   THRESH            14
   SCF_CONVERGENCE   7
$end

$mbe
  order 3
  embed charges
$end

$mbe_charges
  -0.834
   0.417
   0.417
  -0.834
   0.417
   0.417
  -0.834
   0.417
   0.417
  -0.834
   0.417
   0.417
$end

View output

Example 12.41 Example of a MBCP(3) calculation.

$molecule
0 1
--
   0 1
   O -1.126149 -1.748387 -0.423240
   H -0.234788 -1.493897 -0.661862
   H -1.062789 -2.681331 -0.218819
--
   0 1
   O -0.254210  1.611495 -1.293845
   H -1.001520  1.163510 -1.690129
   H -0.153399  2.411746 -1.809248
--
   0 1
   O  1.694541 -0.226287  1.705739
   H  0.785920  0.073487  1.677909
   H  2.047134  0.150917  2.511706
--
   0 1
   O -0.864533  0.522472  1.218817
   H -0.694120  1.093542  0.469789
   H -1.131418 -0.310426  0.829702
$end

$rem
   MANY_BODY_INT     TRUE
   METHOD            B3LYP
   BASIS             cc-pVDZ
   THRESH            12
   SCF_CONVERGENCE   6
$end

$mbe
  BSSE_Order 3
  BSSE_Type MBCP ! this is the default
$end

View output

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12.16.2 Job Control