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182
docs/methods/post_hartree_fock/mp2.md
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@ -6,13 +6,20 @@ $$
E^{(2)} = - \sum_{ijab} \frac{(ia|jb)[2(ia|jb)-(ib|ja)]}{\epsilon_{a}+\epsilon_{b}-\epsilon_{i}-\epsilon_{j}}
$$
with the GPW method as described in [](#DelBen2012) and [](#DelBen2013). CP2K also implements double-hybrid functionals.
with the GPW method as described in [](#DelBen2012) and [](#DelBen2013). CP2K also implements
double-hybrid functionals.
CP2K provides three different implementations: A canonical implementation, a GPW-based implementation and a RI-based implementation. Different functionals require rescaling of different contributions (singulet, triplet). This is achieved using the keywords [SCALE_S](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_S) and [SCALE_T](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_T) for all implementations.
CP2K provides three different implementations: A canonical implementation, a GPW-based
implementation and a RI-based implementation. Different functionals require rescaling of different
contributions (singulet, triplet). This is achieved using the keywords
[SCALE_S](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_S) and
[SCALE_T](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_T) for all implementations.
## Canonical Implementation
The canonical implementation is available for GPW and GAPW reference calculations and thus allows for core-corrections. It is the most costly implementation. Gradients (Nuclear forces, stress tensors) are not analytically available. A simple WF_CORRELATION section looks like
The canonical implementation is available for GPW and GAPW reference calculations and thus allows
for core-corrections. It is the most costly implementation. Gradients (Nuclear forces, stress
tensors) are not analytically available. A simple WF_CORRELATION section looks like
```none
&WF_CORRELATION
@ -30,7 +37,9 @@ The canonical implementation is available for GPW and GAPW reference calculation
## GPW-based Implementation
The MP2-based implementation is available only for GPW calculations.[](#DelBen2012) It is the cheaper than the canonical implementation. Gradients (Nuclear forces, stress tensors) are not analytically available. A simple WF_CORRELATION section looks like
The MP2-based implementation is available only for GPW calculations.[](#DelBen2012) It is the
cheaper than the canonical implementation. Gradients (Nuclear forces, stress tensors) are not
analytically available. A simple WF_CORRELATION section looks like
```none
&WF_CORRELATION
@ -53,7 +62,10 @@ The MP2-based implementation is available only for GPW calculations.[](#DelBen20
## RI-based Implementation
The RI-based implementation is the most affordable MP2-implementation.[](#DelBen2013) Analytical gradients are available for GPW-based integrals (not for GAPW reference calculations).[](#DelBen2015b) MME-integration does not support stress tensor calculations, Obara-Saika integration does not implement any gradients. A simple WF_CORRELATION section looks like
The RI-based implementation is the most affordable MP2-implementation.[](#DelBen2013) Analytical
gradients are available for GPW-based integrals (not for GAPW reference
calculations).[](#DelBen2015b) MME-integration does not support stress tensor calculations,
Obara-Saika integration does not implement any gradients. A simple WF_CORRELATION section looks like
```none
&WF_CORRELATION
@ -71,13 +83,167 @@ The RI-based implementation is the most affordable MP2-implementation.[](#DelBen
&RI_MP2
# Larger block sizes require more memory but reduce communication, -1 (default) let CP2K choose it
BLOCK_SIZE 2
# This keyword determines how many copies of the rank-three tensor are kept in the memory of all CPUs. Large number of groups increasethe memory demands but reduce communication (default: -1, automatic determination)
# This keyword determines how many copies of the rank-three tensor are kept in the memory of all CPUs. Large number of groups increase the memory demands but reduce communication (default: -1, automatic determination)
NUMBER_INTEGRATION_GROUPS 2
&END
&END
```
## RI-MP2 Gradient Calculations
Analytical gradients (nuclear gradients, stress tensors) are available for RI-MP2 and related
double-hybrid functionals.[](#DelBen2015b),[](#Stein2022) HF calculations may also be accelerated by
the ADMM approximation which is recommended if very diffuse basis functions are included. The
computational costs of the MP2 part is 2-3 times as high as for energy-only calculations. A typical
input file of a RI-MP2 calculation using ADMM-accelerated HF is
```none
&GLOBAL
PRINT_LEVEL LOW
PROJECT example
RUN_TYPE FORCE_EVAL
&END GLOBAL
&FORCE_EVAL
METHOD Quickstep
&DFT
# This file contains basis sets for common elements (H, C, N, O; for F, Al, Cl, Si, P, S only TZ basis sets)
BASIS_SET_FILE_NAME BASIS_RI_cc-TZ
BASIS_SET_FILE_NAME BASIS_ADMM
POTENTIAL_FILE_NAME POTENTIAL
# Plug in your preconverged wfn file here
WFN_RESTART_FILE_NAME ./example_HF.wfn
# Use if no RI basis set is available (possible values: SMALL, MEDIUM, LARGE, HUGE)
AUTO_BASIS RI_AUX LARGE
&AUXILIARY_DENSITY_MATRIX_METHOD
# Purification is not implemented
ADMM_PURIFICATION_METHOD NONE
# Try different options (check with reference values or use the default)
EXCH_CORRECTION_FUNC PBEX
# other methods are not implemented
METHOD BASIS_PROJECTION
&END AUXILIARY_DENSITY_MATRIX_METHOD
&MGRID
# Adjust as usual
CUTOFF 600
REL_CUTOFF 50
&END MGRID
&POISSON
PERIODIC XYZ
POISSON_SOLVER WAVELET
&END POISSON
&QS
# Choose as tight as necessary
EPS_DEFAULT 1.0E-10
METHOD GPW
&END QS
&SCF
# Choose as tight as necessary
EPS_SCF 1.0E-8
MAX_SCF 100
SCF_GUESS RESTART
&END SCF
&XC
&HF
FRACTION 1.0000000
&INTERACTION_POTENTIAL
# Adjust the cutoff radius according to your cell
CUTOFF_RADIUS 1.5
POTENTIAL_TYPE TRUNCATED
T_C_G_DATA t_c_g.dat
&END INTERACTION_POTENTIAL
&SCREENING
# Tune these parameters
EPS_SCHWARZ 1.0E-10
EPS_SCHWARZ_FORCES 1.0E-5
SCREEN_ON_INITIAL_P .FALSE.
&END SCREENING
&END HF
&WF_CORRELATION
MEMORY 500
NUMBER_PROC 1
&CANONICAL_GRADIENTS
# The default is usually good enough
EPS_CANONICAL 1E-6
# This is the option which should always work
# Try to set it to .TRUE. (may segfault)
FREE_HFX_BUFFER .FALSE.
&CPHF
# Choose as tight as necessary
EPS_CONV 1.0E-6
# Smaller values of EPS_CONV may require more iterations
MAX_ITER 10
&END CPHF
&END CANONICAL_GRADIENTS
&INTEGRALS
&WFC_GPW
# Adjust these parameters to your needs of accuracy
CUTOFF 200
EPS_FILTER 1.0E-12
EPS_GRID 1.0E-8
REL_CUTOFF 50
&END WFC_GPW
&END INTEGRALS
&RI_MP2
# Determine an automatic block size, if memory is low, set it to 1
BLOCK_SIZE -1
&END RI_MP2
&END WF_CORRELATION
&XC_FUNCTIONAL NONE
&END XC_FUNCTIONAL
&END XC
&END DFT
&PRINT
&FORCES
&END FORCES
&END PRINT
&SUBSYS
# Adjust cell information and coordinations as necessary
&CELL
ABC [angstrom] 5.0 5.0 5.0
PERIODIC XYZ
&END CELL
&COORD
O 0.000000 0.000000 -0.211000
H 0.000000 -0.844000 0.495000
H 0.000000 0.744000 0.495000
&END COORD
&KIND H
# orbital and RI basis set should match
BASIS_SET cc-TZ
BASIS_SET RI_AUX RI_TZ
# Use the largest affordable one
BASIS_SET AUX_FIT cpFIT3
POTENTIAL GTH-HF-q1
&END KIND
&KIND O
BASIS_SET cc-TZ
BASIS_SET RI_AUX RI_TZ
BASIS_SET AUX_FIT cpFIT3
POTENTIAL GTH-HF-q6
&END KIND
&TOPOLOGY
&CENTER_COORDINATES
&END CENTER_COORDINATES
&END TOPOLOGY
&END SUBSYS
&END FORCE_EVAL
```
A few more words are required regarding systems with many degenerate occupied orbital pairs as they
are found in structures with many symmetry-equivalent atoms. In that case, non-diagonal elements of
the density matrix of almost degenerate occupied-orbital pairs have to be calculated explicitly for
numerical reason. This is significantly more expensive than for non-degenerate orbital pairs. This
behavior can be tuned using the
[EPS_CANONICAL](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.EPS_CANONICAL)
keyword.
## Performance Considerations
MP2-calculations are generally very expensive for large systems due to their quintical scaling with respect to the number of atoms. Thus, for larger systems, one should switch to the cheaper RPA or SOS-MP2 methods.
CP2K employs local matrix-matrix multiplications for contractions. These can be accelerated with the SpLA library if CP2K was linked against it. In that way, GPU acceleration is possible if no GPU-accelerated DGEMM implementation is available and SpLA was configured accordingly.
MP2-calculations are generally very expensive for large systems due to their quintical scaling with
respect to the number of atoms. Thus, for larger systems, one should switch to the cheaper RPA or
SOS-MP2 methods. CP2K employs local matrix-matrix multiplications for contractions. These can be
accelerated with the SpLA library if CP2K was linked against it. In that way, GPU acceleration is
possible if no GPU-accelerated DGEMM implementation is available and SpLA was configured
accordingly.

92
docs/methods/post_hartree_fock/preliminaries.md
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@ -1,48 +1,99 @@
# Preliminaries
Here, we explain the relevant preparation steps and things to consider with all post-Hartree-Fock methods regarding choice of basis sets and pseudopotentials. Because of the different building blocks, we have to distinguish at least two kinds of basis sets: the primary basis set (PBS) to represent the orbital functions and the RI basis set to expand products of PBS functions into a set of auxiliary functions such that the four-center electron repulsion integrals (in Mulliken-notation) are approximated by
Here, we explain the relevant preparation steps and things to consider with all post-Hartree-Fock
methods regarding choice of basis sets and pseudopotentials. Because of the different building
blocks, we have to distinguish at least two kinds of basis sets: the primary basis set (PBS) to
represent the orbital functions and the RI basis set to expand products of PBS functions into a set
of auxiliary functions such that the four-center electron repulsion integrals (in Mulliken-notation)
are approximated by
$$
(ia|jb)=\sum_{PQ}(ia|P) (P|Q)^{-1} (Q|jb)
$$
On top of the PBS and the RI basis set, the ADMM approximation of HF may introduce a third kind of basis set (see there for further information).
On top of the PBS and the RI basis set, the ADMM approximation of HF may introduce a third kind of
basis set (see there for further information).
## Step 1: Choice of Primary Basis Sets
Because of the slow convergence of the calculated properties from post-Hartree-Fock calculations with respect to the size of the PBS, post-Hartree-Fock methods demand for larger PBSs than ordinary hybrid DFT or HF calculations and for very accurate results a basis set convergence scheme employing consistent PBS for accurate results. For this purpose, post-Hartree-Fock calculations are commonly performed with correlation-consistent (cc)-basis sets. Without an extrapolation scheme, we recommend basis sets of at least triple-zeta (cc-TZ) or augmented double-zeta (aug-cc-DZ) quality. With an extrapolation scheme, one needs a second basis set for each atom kind of different size. The usual extrapolation formula for correlation energies is given by
Because of the slow convergence of the calculated properties from post-Hartree-Fock calculations
with respect to the size of the PBS, post-Hartree-Fock methods demand for larger PBSs than ordinary
hybrid DFT or HF calculations and for very accurate results a basis set convergence scheme employing
consistent PBS for accurate results. For this purpose, post-Hartree-Fock calculations are commonly
performed with correlation-consistent (cc)-basis sets. Without an extrapolation scheme, we recommend
basis sets of at least triple-zeta (cc-TZ) or augmented double-zeta (aug-cc-DZ) quality. With an
extrapolation scheme, one needs a second basis set for each atom kind of different size. The usual
extrapolation formula for correlation energies is given by
$$
E(X) = A + \frac{B}{X^3}
$$
with $X$ being 2, 3 or 4 in case of DZ, TZ or QZ zeta basis sets, respectively. If possible, one should refrain from non-augmented DZ basis sets as their results are usually not converged enough for extrapolation. Suitable basis sets can be found in the `BASIS_RI_cc-TZ` and `BASIS_ccGRB` basis set files in the data directory.
with $X$ being 2, 3 or 4 in case of DZ, TZ or QZ zeta basis sets, respectively. If possible, one
should refrain from non-augmented DZ basis sets as their results are usually not converged enough
for extrapolation. Suitable basis sets can be found in the `BASIS_RI_cc-TZ` and `BASIS_ccGRB` basis
set files in the data directory.
## Step 2: Choice of RI Basis Sets (Only for RI-based Methods)
The RI approximation asks for an additional auxiliary basis set. They are usually specified as [BASIS_SET RI_AUX](#CP2K_INPUT.FORCE_EVAL.SUBSYS.KIND.BASIS_SET) in the input file. CP2K provides several options to find suitable RI basis sets:
- For a few main group elements, the `BASIS_RI_cc-TZ` file contains RI basis sets for the given PBSs. The literature may help with missing elements.
- Optimize RI basis sets yourself. This is recommended if a larger number of calculations is required to reduce the computational costs significantly. Check the [OPT_RI_BASIS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI.OPT_RI_BASIS) and the regtest suite (QS/regtest-ri-opt) fur further information.
- In all other cases, CP2K can generate RI basis sets automatically (see the [AUTO_BASIS RI_AUX](#CP2K_INPUT.FORCE_EVAL.DFT.AUTO_BASIS). These basis sets provide a decent accuracy but are roughly twice as large as optimized basis sets.
The RI approximation asks for an additional auxiliary basis set. They are usually specified as
[BASIS_SET RI_AUX](#CP2K_INPUT.FORCE_EVAL.SUBSYS.KIND.BASIS_SET) in the input file. CP2K provides
several options to find suitable RI basis sets:
- For a few main group elements, the `BASIS_RI_cc-TZ` file contains RI basis sets for the given
PBSs. The literature may help with missing elements.
- Optimize RI basis sets yourself. This is recommended if a larger number of calculations is
required to reduce the computational costs significantly. Check the
[OPT_RI_BASIS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI.OPT_RI_BASIS) and the regtest suite
(QS/regtest-ri-opt) fur further information.
- In all other cases, CP2K can generate RI basis sets automatically (see the
[AUTO_BASIS RI_AUX](#CP2K_INPUT.FORCE_EVAL.DFT.AUTO_BASIS). These basis sets provide a decent
accuracy but are roughly twice as large as optimized basis sets.
## Step 3: Pseudopotentials
Pseudopotentials should reflect the underlying hybrid or HF calculation used to determine orbitals and orbital energies (see the respective sections).
Pseudopotentials should reflect the underlying hybrid or HF calculation used to determine orbitals
and orbital energies (see the respective sections).
## Step 4: Preoptimize Reference Orbitals
It is recommended to restart the orbital calculation step from preoptimized HF or hybrid orbitals. This reduces computational costs because DFT and HF calculations do not perform well in case of the large number of CPU cores required for post-Hartree-Fock methods.
It is recommended to restart the orbital calculation step from preoptimized HF or hybrid orbitals.
This reduces computational costs because DFT and HF calculations do not perform well in case of the
large number of CPU cores required for post-Hartree-Fock methods.
## Step 5: Setup of Integral Calculation Step
The integration step is setup with the [INTEGRALS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS) section. Because most densities occurring in the formalisms of the post-Hartree-Fock methods have a zero net-charge, such that the Coulomb operator does not need to be truncated it is required by HF. CP2K has its own integration routines for post-Hartree-Fock methods exploiting this circumstance. The available integration methods (compare the [ERI_METHOD](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS.ERI_METHOD) keyword) are Gaussian-Plane-Wave integration (GPW), Minimax-Ewald integration (MME) and Obara Saika integration (OS).
The integration step is setup with the
[INTEGRALS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS) section. Because most densities
occurring in the formalisms of the post-Hartree-Fock methods have a zero net-charge, such that the
Coulomb operator does not need to be truncated it is required by HF. CP2K has its own integration
routines for post-Hartree-Fock methods exploiting this circumstance. The available integration
methods (compare the [ERI_METHOD](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS.ERI_METHOD)
keyword) are Gaussian-Plane-Wave integration (GPW), Minimax-Ewald integration (MME) and Obara Saika
integration (OS).
GPW is fully supported, MME does not implement stress tensors and does not support short-ranged operators (truncated Coulomb, erfc-Coulomb, ...), OS implements gradients only in case of low scaling methods and does not support automatically generated RI basis sets. The GPW and MME integration methods are further configured in the respective [WFC_GPW](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS.WFC_GPW) and [ERI_MME](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS.ERI_MME) sections. In case of the GPW integration method, the respective CUTOFF parameters should be tuned as known from ordinary G(A)PW integrations in CP2K although the primary cutoff parameter can be chosen much smaller (150-300 Ry) then usual.
GPW is fully supported, MME does not implement stress tensors and does not support short-ranged
operators (truncated Coulomb, erfc-Coulomb, ...), OS implements gradients only in case of low
scaling methods and does not support automatically generated RI basis sets. The GPW and MME
integration methods are further configured in the respective
[WFC_GPW](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS.WFC_GPW) and
[ERI_MME](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.INTEGRALS.ERI_MME) sections. In case of the
GPW integration method, the respective CUTOFF parameters should be tuned as known from ordinary
G(A)PW integrations in CP2K although the primary cutoff parameter can be chosen much smaller
(150-300 Ry) then usual.
The RI metric can be set by the user with the [RI](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI) section. In case of low scaling methods (with activated [LOW_SCALING](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.LOW_SCALING) section), the metric is by default the overlap metric, else it will be the potential operator will be used. If the default is not requested, the RI section should be set.
The RI metric can be set by the user with the [RI](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI)
section. In case of low scaling methods (with activated
[LOW_SCALING](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.LOW_SCALING) section), the metric is by
default the overlap metric, else it will be the potential operator will be used. If the default is
not requested, the RI section should be set.
## General Structure of Post-Hartree-Fock Methods
The general structure is very similar. Each post-Hartree-Fock method has its own section which has to be activated to start the respective calculation. Each section has subsections to further configure the respective kind of calculation. Most post-Hartree-Fock calculations require the following structure
The general structure is very similar. Each post-Hartree-Fock method has its own section which has
to be activated to start the respective calculation. Each section has subsections to further
configure the respective kind of calculation. Most post-Hartree-Fock calculations require the
following structure
```none
&WF_CORRELATION
@ -80,7 +131,12 @@ The general structure is very similar. Each post-Hartree-Fock method has its own
## Gradient Calculations
Gradient calculations are available for RI-MP2, RI-RPA and RI-SOS-MP2 calculations. In case of low-scaling implementations, consult the [CPHF](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.LOW_SCALING.CPHF) section in the LOW_SCALING section, otherwise the [CANONICAL_GRADIENTS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS) section for further information. The setup of the CANONICAL_GRADIENTS section islooks like
Gradient calculations are available for RI-MP2, RI-RPA and RI-SOS-MP2 calculations. In case of
low-scaling implementations, consult the
[CPHF](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.LOW_SCALING.CPHF) section in the LOW_SCALING
section, otherwise the
[CANONICAL_GRADIENTS](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS) section for
further information. The setup of the CANONICAL_GRADIENTS section islooks like
```none
&CANONICAL_GRADIENTS
@ -98,4 +154,8 @@ Gradient calculations are available for RI-MP2, RI-RPA and RI-SOS-MP2 calculatio
## Basis Set Superposition Error (BSSE)
Energy calculations using post-Hartree-Fock methods suffer from severe basis set superposition error (BSSE). In CP2K, this is enhanced by the many different basis sets in use. Check the [BSSE](#CP2K_INPUT.FORCE_EVAL.BSSE) section for further information on the automatic setup of BSSE calculations and the [GHOST](#CP2K_INPUT.FORCE_EVAL.SUBSYS.KIND.GHOST) for the manual setup of BSSE calculations.
Energy calculations using post-Hartree-Fock methods suffer from severe basis set superposition error
(BSSE). In CP2K, this is enhanced by the many different basis sets in use. Check the
[BSSE](#CP2K_INPUT.FORCE_EVAL.BSSE) section for further information on the automatic setup of BSSE
calculations and the [GHOST](#CP2K_INPUT.FORCE_EVAL.SUBSYS.KIND.GHOST) for the manual setup of BSSE
calculations.

62
docs/methods/post_hartree_fock/rpa.md
View file

@ -14,20 +14,31 @@ E^{LT-RI-SOS-MP2} &= - \int_{0}^{\infty}d\tau\text{Tr}\left(\overline{Q}(\tau)^2
\overline{Q}_{RS}(\tau) &= \sum_{ia}B_{iaR}e^{-\left(\epsilon_a-\epsilon_i\right)\tau}B_{iaS}
$$
as implemented in [](#DelBen2013). The integration is performed numerically. Double-hybrid functionals are available in CP2K.
as implemented in [](#DelBen2013). The integration is performed numerically. Double-hybrid
functionals are available in CP2K.
CP2K provides two different implementations: a quartically-scaling and a low-scaling cubically-scaling implementation. Different functionals require rescaling which is achieved using the keywords [SCALE_RPA](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.SCALE_RPA) in case of RPA and [SCALE_S](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_S) in case of LT-RI-SOS-MP2.
CP2K provides two different implementations: a quartically-scaling and a low-scaling
cubically-scaling implementation. Different functionals require rescaling which is achieved using
the keywords [SCALE_RPA](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.SCALE_RPA) in case of
RPA and [SCALE_S](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_S) in case of LT-RI-SOS-MP2.
Here, we will focus on the quartically-scaling implementation only.
## RI-dRPA
CP2K implements two quadrature schemes: Clenshaw-Curtis and Minimax. The first requires 30-40 quadrature points, the latter 6-8 quadrature points. Minimax quadrature rules have to be preoptimized such that not all possible numbers of quadrature points are available.
CP2K implements two quadrature schemes: Clenshaw-Curtis and Minimax. The first requires 30-40
quadrature points, the latter 6-8 quadrature points. Minimax quadrature rules have to be
preoptimized such that not all possible numbers of quadrature points are available.
RPA correlation energies are usually combined with exact exchange energies. In CP2K, this is available by activating the [HF](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.HF) section which is setup like an ordinary HF section.
RPA correlation energies are usually combined with exact exchange energies. In CP2K, this is
available by activating the [HF](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.HF) section
which is setup like an ordinary HF section.
Several Beyond-RPA schemes are available: The Renormalized Screened Exchange (RSE) correction, the Approximate Exchange Kernel (AXK) and the Second-Order Screened Exchange corrections (SOSEX). These are enabled with the [RSE](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.RSE) keyword and the [EXCHANGE_CORRECTION](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.EXCHANGE_CORRECTION) section.
This results into the following possible RPA section
Several Beyond-RPA schemes are available: The Renormalized Screened Exchange (RSE) correction, the
Approximate Exchange Kernel (AXK) and the Second-Order Screened Exchange corrections (SOSEX). These
are enabled with the [RSE](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.RSE) keyword and the
[EXCHANGE_CORRECTION](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.EXCHANGE_CORRECTION)
section. This results into the following possible RPA section
```none
&RI_RPA
@ -52,12 +63,24 @@ This results into the following possible RPA section
## RI-dRPA Gradient Calculations
Analytical gradients are only available for RPA calculations using a minimax grid, but not for the beyond-RPA methods (RSE, AXK, SOSEX). The general setup is similar to RI-MP2 gradients. In addition, there are two more relevant keywords: [DOT_PRODUCT_BLKSIZE](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.DOT_PRODUCT_BLKSIZE) and [MAX_PARALLEL_COMM](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.MAX_PARALLEL_COMM). The first splits the contraction along the auxiliary index to improve numerical stability. By default, this feature is turned off. The second keyword determines the number of parallel communication channels for non-blocking communication. Larger numbers allow more overlap but increase the memory requirements. Larger values than 3 are commonly not necessary.
Analytical gradients are only available for RPA calculations using a minimax grid, but not for the
beyond-RPA methods (RSE, AXK, SOSEX).[](#Stein2024) The general setup is similar to RI-MP2
gradients. In addition, there are two more relevant keywords:
[DOT_PRODUCT_BLKSIZE](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.DOT_PRODUCT_BLKSIZE)
and
[MAX_PARALLEL_COMM](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.MAX_PARALLEL_COMM).
The first splits the contraction along the auxiliary index to improve numerical stability. By
default, this feature is turned off. The second keyword determines the number of parallel
communication channels for non-blocking communication. Larger numbers allow more overlap but
increase the memory requirements. Larger values than 3 are commonly not necessary.
## LT-RI-SOS-MP2
CP2K implements two quadrature schemes only the Minimax scheme requiring usually 6-8 quadrature points. Minimax quadrature rules have to be preoptimized such that not all possible numbers of quadrature points are available. Scaling of the energy contribution is possible with the [SCALE_S](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_S) keyword which is also used by MP2 calculations.
The input is simpler than in the RPA-case
CP2K implements two quadrature schemes only the Minimax scheme requiring usually 6-8 quadrature
points.[](#DelBen2013) Minimax quadrature rules have to be preoptimized such that not all possible
numbers of quadrature points are available. Scaling of the energy contribution is possible with the
[SCALE_S](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.SCALE_S) keyword which is also used by MP2
calculations. The input is simpler than in the RPA-case
```none
&RI_SOS_MP2
@ -70,10 +93,25 @@ The input is simpler than in the RPA-case
## LT-RI-SOS-MP2 Gradient Calculations
Analytical gradients are available and work similarly to RI-MP2 calculations and RI-RPA calculations. As in case of RI-MP2, it makes use of the [EPS_CANONICAL](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.EPS_CANONICAL) keyword. Larger values improve the numerical accuracy but increase the computational costs significantly because CP2K assumes that the number of relevant pairs is negligible.
Analytical gradients are available and work similarly to RI-MP2 calculations and RI-RPA
calculations. As in case of RI-MP2, it makes use of the
[EPS_CANONICAL](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.CANONICAL_GRADIENTS.EPS_CANONICAL)
keyword. Larger values improve the numerical accuracy but increase the computational costs
significantly because CP2K assumes that the number of relevant pairs is negligible.
## Performance Considerations
Without employing the low-scaling implementation, RI-RPA and RI-SOS-MP2 calculations scale quartically with respect to the number of atoms. The implementation relies on parallel matrix-matrix multiplications. Their costs can be reduced with the COSMA library and accelerated on GPUs if COSMA was configured accordingly.
Without employing the low-scaling implementation, RI-RPA and RI-SOS-MP2 calculations scale
quartically with respect to the number of atoms. The implementation relies on parallel matrix-matrix
multiplications. Their costs can be reduced with the COSMA library and accelerated on GPUs if COSMA
was configured accordingly.
HF calculations may be accelerated using ADMM which is recommended if very diffuse basis functions are employed. The RSE correction employs the same HF section as for the calculation of the HF exchange energy. The costs of AXK and SOSEX depend on the implementation in use. The HF-based implementation is cheaper for larger systems. Its performance depends on the available memory per process group (see [GROUP_SIZE](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.GROUP_SIZE) and [MAX_MEMORY](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.HF.MEMORY.MAX_MEMORY)). The costs becomes neglegible for large systems. Without the HF implementation, CP2K relies on SpLA-accelerated local matrix-matrix multiplications. These become the bottleneck for larger systems but introduce less numerical noise than the HF-based implementation.
HF calculations may be accelerated using ADMM which is recommended if very diffuse basis functions
are employed. The RSE correction employs the same HF section as for the calculation of the HF
exchange energy. The costs of AXK and SOSEX depend on the implementation in use. The HF-based
implementation is cheaper for larger systems. Its performance depends on the available memory per
process group (see [GROUP_SIZE](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.GROUP_SIZE) and
[MAX_MEMORY](#CP2K_INPUT.FORCE_EVAL.DFT.XC.WF_CORRELATION.RI_RPA.HF.MEMORY.MAX_MEMORY)). The costs
becomes neglegible for large systems. Without the HF implementation, CP2K relies on SpLA-accelerated
local matrix-matrix multiplications. These become the bottleneck for larger systems but introduce
less numerical noise than the HF-based implementation.

43
src/common/bibliography.F
View file

@ -91,7 +91,8 @@ MODULE bibliography
Rycroft2009, Thomas2015, Brehm2018, Brehm2020, Shigeta2001, Heinecke2016, &
Brehm2021, Bussy2021a, Bussy2021b, Ditler2021, Ditler2022, Mattiat2019, &
Mattiat2022, Belleflamme2023, Knizia2013, Musaelian2023, Eriksen2020, &
Bussy2023, Wang2018, Zeng2023, Graml2024, Solca2024, Freeman1977, Gruneis2009
Bussy2023, Wang2018, Zeng2023, Graml2024, Solca2024, Freeman1977, Gruneis2009, &
Stein2022, Stein2024
CONTAINS
@ -5031,7 +5032,7 @@ CONTAINS
CALL add_reference(key=Gruneis2009, ISI_record=s2a( &
"TY JOUR", &
"AU Grüneis, Andreas", &
"AU Grueneis, Andreas", &
" Marsman, Martijn", &
" Harl, Judith", &
" Schimka, Laurids", &
@ -5050,6 +5051,44 @@ CONTAINS
"ER"), &
DOI="10.1063/1.3250347")
CALL add_reference(key=Stein2022, ISI_record=s2a( &
"TY JOUR", &
"AU Stein, Frederick", &
"AU Hutter, Juerg", &
"TI Double-hybrid density functionals for the condensed phase: ", &
" Gradients, stress tensor, and auxiliary-density matrix method acceleration", &
"PY 2022", &
"Y1 2022/02/17", &
"JO The Journal of Chemical Physics", &
"JA J. Chem. Phys.", &
"VL 156", &
"IS 7", &
"SP 074107", &
"SN 0021-9606", &
"Y2 6/13/2024", &
"UR https://doi.org/10.1063/5.0082327", &
"ER"), &
DOI="10.1063/5.0082327")
CALL add_reference(key=Stein2024, ISI_record=s2a( &
"TY JOUR", &
"AU Stein, Frederick", &
"AU Hutter, Juerg", &
"TI Massively parallel implementation of gradients within the random ", &
" phase approximation: Application to the polymorphs of benzene", &
"PY 2024", &
"Y1 2024/01/12", &
"JO The Journal of Chemical Physics", &
"JA J. Chem. Phys.", &
"VL 160", &
"IS 2", &
"SP 024120", &
"SN 0021-9606", &
"Y2 6/13/2024", &
"UR https://doi.org/10.1063/5.0180704", &
"ER"), &
DOI="10.1063/5.0180704")
END SUBROUTINE add_all_references
END MODULE bibliography

11
src/input_cp2k_mp2.F
View file

@ -14,7 +14,7 @@
MODULE input_cp2k_mp2
USE bibliography, ONLY: &
Bates2013, DelBen2012, DelBen2013, DelBen2015, DelBen2015b, Rybkin2016, Wilhelm2016a, &
Wilhelm2016b, Wilhelm2017, Wilhelm2018
Wilhelm2016b, Wilhelm2017, Wilhelm2018, Stein2022, Stein2024, Bussy2023
USE cp_eri_mme_interface, ONLY: create_eri_mme_section
USE cp_output_handling, ONLY: add_last_numeric, &
cp_print_key_section_create, &
@ -81,7 +81,8 @@ CONTAINS
"RI-MP2, RI-SOS-MP2, RI-RPA and GW (inside RI-RPA). ", &
n_keywords=4, n_subsections=7, repeats=.TRUE., &
citations=(/DelBen2012, DelBen2013, DelBen2015, DelBen2015b, Rybkin2016, &
Wilhelm2016a, Wilhelm2016b, Wilhelm2017, Wilhelm2018/))
Wilhelm2016a, Wilhelm2016b, Wilhelm2017, Wilhelm2018, Stein2022, &
Stein2024, Bussy2023/))
NULLIFY (keyword, subsection)
@ -442,7 +443,8 @@ CONTAINS
CALL section_create(section, __LOCATION__, name="CANONICAL_GRADIENTS", &
description="Parameters influencing gradient calculations of canonical RI methods. "// &
"Ignored if the IM_TIME section is set.", &
n_keywords=3, n_subsections=1, repeats=.FALSE.)
n_keywords=3, n_subsections=1, repeats=.FALSE., &
citations=(/DelBen2015b, Rybkin2016, Stein2022, Stein2024/))
NULLIFY (subsection, keyword)
CALL create_cphf(subsection)
@ -1484,7 +1486,8 @@ CONTAINS
description="Cubic scaling RI-RPA, GW and Laplace-SOS-MP2 method using the imaginary time formalism. "// &
"EPS_GRID in WFC_GPW section controls accuracy / req. memory for 3-center integrals. "// &
"SORT_BASIS EXP should be specified in DFT section.", &
n_keywords=12, n_subsections=2, repeats=.FALSE.)
n_keywords=12, n_subsections=2, repeats=.FALSE., &
citations=(/Wilhelm2016b, Wilhelm2018, Bussy2023/))
NULLIFY (keyword)
CALL keyword_create(keyword, __LOCATION__, name="_SECTION_PARAMETERS_", &

8
src/mp2.F
View file

@ -17,9 +17,12 @@ MODULE mp2
admm_uncorrect_for_eigenvalues
USE atomic_kind_types, ONLY: atomic_kind_type,&
get_atomic_kind_set
USE bibliography, ONLY: DelBen2012,&
USE bibliography, ONLY: Bussy2023,&
DelBen2012,&
DelBen2015b,&
Rybkin2016,&
Stein2022,&
Stein2024,&
cite_reference
USE cp_blacs_env, ONLY: cp_blacs_env_type
USE cp_control_types, ONLY: dft_control_type
@ -239,6 +242,9 @@ CONTAINS
IF (calc_forces) THEN
CALL cite_reference(DelBen2015b)
CALL cite_reference(Rybkin2016)
CALL cite_reference(Stein2022)
CALL cite_reference(Bussy2023)
CALL cite_reference(Stein2024)
!Gradients available for RI-MP2, and low-scaling Laplace MP2/RPA
IF (.NOT. (mp2_env%method == ri_mp2_method_gpw .OR. mp2_env%method == ri_rpa_method_gpw .OR. mp2_env%method == ri_mp2_laplace)) THEN
CPABORT("No forces/gradients for the selected method.")