6.9 Maximum Physical Regularisation Perturbation Theory 6.9.1 Introduction 6.10 Direct Random Phase Approximation Methods

6.9.2 MPR-BWs2 Job Control

(May 21, 2025)

MPR-BWs2 has been implemented as a specific partition of the RI-BW-s2 program. It is invoked by setting METHOD = RIBWS2 in the $rem section and writing METHOD = MPR-BWS2 in the $bws2 section. Iterative and non-iterative parameters as well as additional variables to control the convergence behaviour of the iterative method are also defined in the $bws2 section. See 6.8 for variables unrelated to MPR-BWs2

METHOD
       Defines the correlation energy expression to be used.
INPUT SECTION: $bws2
TYPE:
       STRING
DEFAULT:
       BWS2
OPTIONS:
       MPR-BWS2
RECOMMENDATION:
       In order to activate MPR-BWs2, the method keyword has to be set to MPR-BWS2 or MPRBWS2

MPR_A0
       Controls the value of the $A_{0}$ parameter.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       1000
OPTIONS:
       $n$ where $n/1000$ is the value of $A_{0}$ .
RECOMMENDATION:
       Since $A_{0}$ is equal to $\alpha$ in BW-s2 theory, its standard value is set to $\alpha=A_{0}=1$ and recreates BW-s2. If both MPR_A0 and ALPHA are defined in the input file, the last read takes priority.

MPR_A1
       Controls the value of the $A_{1}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $A_{1}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_A2
       Controls the value of the $A_{2}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $A_{2}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_A3
       Controls the value of the $A_{3}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $A_{3}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_A4
       Controls the value of the $A_{4}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $A_{4}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_B0
       Controls the value of the $B_{0}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $B_{0}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_B1
       Controls the value of the $B_{1}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $B_{1}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_B3
       Controls the value of the $B_{3}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $B_{3}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_B4
       Controls the value of the $B_{4}$ parameter..
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the value of $B_{4}$ .
RECOMMENDATION:
       Large values lead to convergence issues.

MPR_A0_NONITER
       Controls the value of the $A_{0}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $A_{0}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_A1_NONITER
       Controls the value of the $A_{1}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $A_{1}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_A2_NONITER
       Controls the value of the $A_{2}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $A_{2}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_A3_NONITER
       Controls the value of the $A_{3}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $A_{3}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_A4_NONITER
       Controls the value of the $A_{4}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $A_{4}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_B0_NONITER
       Controls the value of the $B_{0}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $B_{0}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_B1_NONITER
       Controls the value of the $B_{1}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $B_{1}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_B3_NONITER
       Controls the value of the $B_{3}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $B_{3}$ .
RECOMMENDATION:
       Arbitrary values are possible.

MPR_B4_NONITER
       Controls the value of the $B_{4}$ parameter for non-iterative contributions.
INPUT SECTION: $bws2
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       $n$ where $n/1000$ is the non-iterative value of $B_{4}$ .
RECOMMENDATION:
       Arbitrary values are possible.

PARAM_GRADIENT
       Controls whether or not to compute the derivative of the energy with respect to parameters.
INPUT SECTION: $bws2
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Computes the iterative and non-iterative parameter gradient. FALSE Does not compute the parameter gradient.
RECOMMENDATION:
       If required, set to TRUE.

Example 6.23 MPR-BWs2 calculation on formaldehyde with $A_{0}=1$ and $B_{0}=-1$ .

$comment
    Standard MPR-BWs2 calculation
$end

$molecule
0 1
C   0.0000      0.0000      0.0000
O   0.0000      0.0000     -1.2195
H   0.9391      0.0000      0.5422
H  -0.9391      0.0000      0.5422
$end

$rem
JOBTYPE             SP
METHOD              RIBWS2              ! activate RI-BWS2 driver
BASIS               DEF2-SVP
AUX_BASIS           RIMP2-DEF2-SVP      ! auxilliary basis is required
SYM_IGNORE          TRUE
SYMMETRY            FALSE
$end

$bws2
METHOD              MPR-BWS2            ! activate MPR-BWs2
MPR_A0              1000                ! A_0 = 1.0
MPR_B0              -1000               ! B_0 = -1.0
MAX_CYCLES          50
$end

Example 6.24 MPR-BWs2 calculation on formaldehyde with non-iterative contributions.

$comment
    MPR-BWs2 calculation with non-iterative contributions
$end

$molecule
0 1
C   0.0000      0.0000      0.0000
O   0.0000      0.0000     -1.2195
H   0.9391      0.0000      0.5422
H  -0.9391      0.0000      0.5422
$end

$rem
JOBTYPE             SP
METHOD              RIBWS2              ! activate RI-BWS2 driver
BASIS               DEF2-SVP
AUX_BASIS           RIMP2-DEF2-SVP      ! auxilliary basis is required
SYM_IGNORE          TRUE
SYMMETRY            FALSE
$end

$bws2
METHOD              MPR-BWS2            ! activate MPR-BWs2
MPR_A0              500                 ! A_0 = 0.5
MPR_B1_NONITER      -1500               ! non-iterative B_0 = -1.5
MAX_CYCLES          50
$end

Example 6.25 MPR-BWs2 calculation on formaldehyde including the parameter gradient.

$comment
    MPR-BWs2 calculation with parameter gradient
$end

$molecule
0 1
C   0.0000      0.0000      0.0000
O   0.0000      0.0000     -1.2195
H   0.9391      0.0000      0.5422
H  -0.9391      0.0000      0.5422
$end

$rem
JOBTYPE             SP
METHOD              RIBWS2              ! activate RI-BWS2 driver
BASIS               DEF2-SVP
AUX_BASIS           RIMP2-DEF2-SVP      ! auxilliary basis is required
SYM_IGNORE          TRUE
SYMMETRY            FALSE
$end

$bws2
METHOD              MPR-BWS2            ! activate MPR-BWs2
MPR_A0              1500                ! A_0 = 1.5
MAX_CYCLES          50
PARAM_GRADIENT      TRUE                ! activate parameter gradient
$end

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6.9.2 MPR-BWs2 Job Control