# sc_MBPT2_R12 - Man Page

The MBPT2_R12 class implements several linear R12 second-order perturbation theory methods.

## Synopsis

`#include <mbptr12.h>`

Inherits **sc::MBPT2**.

### Public Member Functions

**MBPT2_R12** (**StateIn** &)**MBPT2_R12** (const **Ref**< **KeyVal** > &)

The **KeyVal** constructor.

void **save_data_state** (**StateOut** &)

Save the base classes (with save_data_state) and the members in the same order that the **StateIn** CTOR initializes them. **Ref**< **GaussianBasisSet** > **aux_basis** () const**Ref**< **GaussianBasisSet** > **vir_basis** () const

bool **gbc** () const

bool **ebc** () const

LinearR12::ABSMethod **abs_method** () const

LinearR12::StandardApproximation **stdapprox** () const

bool **spinadapted** () const**R12IntEvalInfo::StoreMethod r12ints_method** () const

const std::string & **r12ints_file** () const

double **corr_energy** ()

double **r12_corr_energy** ()**RefSymmSCMatrix density** ()

Returns the **SO** density.

void **obsolete** ()

Marks all results as being out of date.

int **gradient_implemented** () const

int **value_implemented** () const

Information about the availability of values, gradients, and hessians.

void **print** (std::ostream &o=**ExEnv::out0**()) const

Print information about the object.

Public Member Functions inherited from **sc::MBPT2****MBPT2** (**StateIn** &)**MBPT2** (const **Ref**< **KeyVal** > &)

The **KeyVal** constructor.

void **save_data_state** (**StateOut** &)

Save the base classes (with save_data_state) and the members in the same order that the **StateIn** CTOR initializes them. **Ref**< **SCF** > **ref** ()

double **ref_energy** ()

double **corr_energy** ()**RefSCVector ref_energy_gradient** ()**RefSCVector corr_energy_gradient** ()

int **nelectron** ()

Returns the number of electrons.

int **nfzcore** () const

int **nfzvirt** () const**RefSymmSCMatrix density** ()

Returns the **SO** density.

int **spin_polarized** ()

Return 1 if the alpha density is not equal to the beta density.

int **gradient_implemented** () const

int **value_implemented** () const

Information about the availability of values, gradients, and hessians.

void **symmetry_changed** ()

Call this if you have changed the molecular symmetry of the molecule contained by this **MolecularEnergy**.

void **obsolete** ()

Marks all results as being out of date.

void **print** (std::ostream &o=**ExEnv::out0**()) const

Print information about the object.

Public Member Functions inherited from **sc::Wavefunction****Wavefunction** (**StateIn** &)**Wavefunction** (const **Ref**< **KeyVal** > &)

The **KeyVal** constructor.

void **save_data_state** (**StateOut** &)

Save the base classes (with save_data_state) and the members in the same order that the **StateIn** CTOR initializes them.

double **density** (const **SCVector3** &)

double **density_gradient** (const **SCVector3** &, double *)

double **natural_orbital** (const **SCVector3** &r, int iorb)

double **natural_orbital_density** (const **SCVector3** &r, int orb, double *orbval=0)

double **orbital** (const **SCVector3** &r, int iorb, const **RefSCMatrix** &orbs)

double **orbital_density** (const **SCVector3** &r, int iorb, const **RefSCMatrix** &orbs, double *orbval=0)

double **charge** ()

Returns the charge.

virtual int **nelectron** ()=0

Returns the number of electrons.

virtual **RefSymmSCMatrix density** ()=0

Returns the **SO** density.

virtual **RefSymmSCMatrix ao_density** ()

Returns the AO density.

virtual **RefSCMatrix natural_orbitals** ()

Returns the natural orbitals.

virtual **RefDiagSCMatrix natural_density** ()

Returns the natural density (a diagonal matrix).

virtual int **spin_polarized** ()=0

Return 1 if the alpha density is not equal to the beta density.

virtual **RefSymmSCMatrix alpha_density** ()

Return alpha electron densities in the **SO** basis.

virtual **RefSymmSCMatrix beta_density** ()

Return beta electron densities in the **SO** basis.

virtual **RefSymmSCMatrix alpha_ao_density** ()

Return alpha electron densities in the AO basis.

virtual **RefSymmSCMatrix beta_ao_density** ()

Return beta electron densities in the AO basis.

virtual **RefSCMatrix nao** (double *atom_charges=0)

returns the ao to nao transformation matrix

virtual **RefSymmSCMatrix overlap** ()

Returns the **SO** overlap matrix.

virtual **RefSymmSCMatrix core_hamiltonian** ()

Returns the **SO** core Hamiltonian.

virtual double **nuclear_repulsion_energy** ()

Returns the nuclear repulsion energy.

void **nuclear_repulsion_energy_gradient** (double *g)

Computes the nuclear repulsion gradient.

virtual void **nuclear_repulsion_energy_gradient** (double **g)

Computes the nuclear repulsion gradient. **RefSCDimension ao_dimension** ()

Atomic orbital dimension. **RefSCDimension so_dimension** ()

Symmetry adapted orbital dimension. **RefSCDimension oso_dimension** ()

Orthogonalized symmetry adapted orbital dimension. **Ref**< **SCMatrixKit** > **basis_matrixkit** ()

Matrix kit for AO, **SO**, orthogonalized **SO**, and MO dimensioned matrices. **Ref**< **Molecule** > **molecule** () const

Returns the **Molecule**. **Ref**< **GaussianBasisSet** > **basis** () const

Returns the basis set. **Ref**< **GaussianBasisSet** > **atom_basis** () const

Returns the basis set describing the nuclear charge distributions.

const double * **atom_basis_coef** () const

Returns the coefficients of the nuclear charge distribution basis functions. **Ref**< **Integral** > **integral** ()

Returns the integral evaluator.

void **symmetry_changed** ()

Call this if you have changed the molecular symmetry of the molecule contained by this **MolecularEnergy**. **RefSCMatrix so_to_orthog_so** ()

Returns a matrix which does the default transform from **SO**'s to orthogonal **SO**'s. **RefSCMatrix so_to_orthog_so_inverse** ()

Returns the inverse of the transformation returned by so_to_orthog_so. **OverlapOrthog::OrthogMethod orthog_method** () const

Returns the orthogonalization method.

void **set_orthog_method** (const **OverlapOrthog::OrthogMethod** &)

(Re)Sets the orthogonalization method and makes this obsolete

double **lindep_tol** () const

Returns the tolerance for linear dependencies.

void **set_lindep_tol** (double)

Re(Sets) the tolerance for linear dependencies.

void **obsolete** ()

Marks all results as being out of date.

void **print** (std::ostream &=**ExEnv::out0**()) const

Print information about the object.

Public Member Functions inherited from **sc::MolecularEnergy****MolecularEnergy** (const **MolecularEnergy** &)**MolecularEnergy** (const **Ref**< **KeyVal** > &)

The **KeyVal** constructor. **MolecularEnergy** (**StateIn** &)

void **save_data_state** (**StateOut** &)

Save the base classes (with save_data_state) and the members in the same order that the **StateIn** CTOR initializes them.

void **set_checkpoint** ()

Set up checkpointing.

void **set_checkpoint_file** (const char *)

void **set_checkpoint_freq** (int freq)

bool **if_to_checkpoint** () const

Check if need to checkpoint.

const char * **checkpoint_file** () const

int **checkpoint_freq** () const**MolecularEnergy** & **operator=** (const **MolecularEnergy** &)

virtual double **energy** ()

A wrapper around **value()**;.

virtual **Ref**< **Molecule** > **molecule** () const

virtual **RefSCDimension moldim** () const

void **guess_hessian** (**RefSymmSCMatrix** &)**Compute** a quick, approximate hessian. **RefSymmSCMatrix inverse_hessian** (**RefSymmSCMatrix** &)**RefSymmSCMatrix hessian** ()

If a molecule hessian object is given, it will be used to provide a hessian.

int **hessian_implemented** () const

void **set_x** (const **RefSCVector** &)

Set and retrieve the coordinate values. **RefSCVector get_cartesian_x** ()

Return the cartesian coordinates. **RefSCVector get_cartesian_gradient** ()

Return the cartesian gradient. **RefSymmSCMatrix get_cartesian_hessian** ()

Return the cartesian hessian. **Ref**< **MolecularCoor** > **molecularcoor** ()

virtual void **symmetry_changed** ()

Call this if you have changed the molecular symmetry of the molecule contained by this **MolecularEnergy**. **Ref**< **NonlinearTransform** > **change_coordinates** ()

An optimizer can call change coordinates periodically to give the function an opportunity to change its coordinate system.

void **print_natom_3** (const **RefSCVector** &, const char *t=0, std::ostream &o=**ExEnv::out0**()) const

Nicely print n x 3 data that are stored in a vector.

void **print_natom_3** (double **, const char *t=0, std::ostream &o=**ExEnv::out0**()) const

void **print_natom_3** (double *, const char *t=0, std::ostream &o=**ExEnv::out0**()) const

virtual void **print** (std::ostream &=**ExEnv::out0**()) const

Print information about the object.

Public Member Functions inherited from **sc::Function**

virtual **RefSCVector gradient** ()

int **gradient_needed** () const

int **do_gradient** (int)

virtual void **set_desired_gradient_accuracy** (double)

virtual double **actual_gradient_accuracy** () const

virtual double **desired_gradient_accuracy** () const**AccResultRefSCVector** & **gradient_result** ()

int **hessian_needed** () const

int **do_hessian** (int)

virtual void **set_desired_hessian_accuracy** (double)

virtual double **actual_hessian_accuracy** () const

virtual double **desired_hessian_accuracy** () const**AccResultRefSymmSCMatrix** & **hessian_result** ()**RefSCVector get_x** () const

const **RefSCVector** & **get_x_no_copy** () const**Function** ()**Function** (**StateIn** &)**Function** (const **Function** &)**Function** (const **Ref**< **KeyVal** > &, double funcacc=DBL_EPSILON, double gradacc=DBL_EPSILON, double hessacc=DBL_EPSILON)

The keyval constructor reads the following keywords:

virtual **~Function** ()**Function** & **operator=** (const **Function** &)**Ref**< **SCMatrixKit** > **matrixkit** () const

Return the **SCMatrixKit** used to construct vectors and matrices. **RefSCDimension dimension** () const

Return the **SCDimension** of the problem.

virtual double **value** ()

Return the value of the function.

int **value_needed** () const

Returns nonzero if the current value is not up-to-date.

int **do_value** (int)

If passed a nonzero number, compute the value the next time **compute()** is called. **AccResultdouble** & **value_result** ()

virtual void **set_desired_value_accuracy** (double)

Set the accuracy to which the value is to be computed.

virtual double **actual_value_accuracy** () const

Return the accuracy with which the value has been computed.

virtual double **desired_value_accuracy** () const

Return the accuracy with which the value is to be computed.

Public Member Functions inherited from **sc::SavableState****SavableState** & **operator=** (const **SavableState** &)

void **save_state** (**StateOut** &)

Save the state of the object as specified by the **StateOut** object.

void **save_object_state** (**StateOut** &)

This can be used for saving state when the exact type of the object is known for both the save and the restore.

virtual void **save_vbase_state** (**StateOut** &)

Save the virtual bases for the object.

virtual void **save_data_state** (**StateOut** &)

Save the base classes (with save_data_state) and the members in the same order that the **StateIn** CTOR initializes them.

Public Member Functions inherited from **sc::DescribedClass****DescribedClass** (const **DescribedClass** &)**DescribedClass** & **operator=** (const **DescribedClass** &)**ClassDesc** * **class_desc** () const throw ()

This returns the unique pointer to the **ClassDesc** corresponding to the given type_info object.

const char * **class_name** () const

Return the name of the object's exact type.

int **class_version** () const

Return the version of the class.

virtual void **print** (std::ostream &=**ExEnv::out0**()) const

Print the object.

Public Member Functions inherited from **sc::RefCount**

int **lock_ptr** () const

Lock this object.

int **unlock_ptr** () const

Unlock this object.

void **use_locks** (bool inVal)

start and stop using locks on this object

refcount_t **nreference** () const

Return the reference count.

refcount_t **reference** ()

Increment the reference count and return the new count.

refcount_t **dereference** ()

Decrement the reference count and return the new count.

int **managed** () const

void **unmanage** ()

Turn off the reference counting mechanism for this object.

int **managed** () const

Return 1 if the object is managed. Otherwise return 0.

Public Member Functions inherited from **sc::Identity****Identifier identifier** ()

Return the **Identifier** for this argument.

virtual void **obsolete** ()

Marks all results as being out of date.

### Protected Member Functions

void **compute** ()

Recompute at least the results that have compute true and are not already computed.

Protected Member Functions inherited from **sc::MBPT2**

void **init_variables** ()

void **compute** ()

Recompute at least the results that have compute true and are not already computed.

void **eigen** (**RefDiagSCMatrix** &vals, **RefSCMatrix** &vecs, **RefDiagSCMatrix** &occs)

void **compute_hsos_v1** ()**distsize_t compute_v2_memory** (int ni, int nfuncmax, int nbfme, int nshell, int ndocc, int nsocc, int nvir, int nproc)

void **compute_hsos_v2** ()

void **compute_hsos_v2_lb** ()

int **compute_cs_batchsize** (size_t mem_static, int nocc_act)**distsize_t compute_cs_dynamic_memory** (int ni, int nocc_act)

int **make_cs_gmat** (**RefSymmSCMatrix** &Gmat, double *DPmat)

int **make_cs_gmat_new** (**RefSymmSCMatrix** &Gmat, const **RefSymmSCMatrix** &DPmat)

void **form_max_dens** (double *DPmat, signed char *maxp)

int **init_cs_gmat** ()

void **done_cs_gmat** ()

int **make_g_d_nor** (**RefSymmSCMatrix** &Gmat, double *DPmat, const double *mgdbuff)

void **cs_cphf** (double **scf_vector, double *Laj, double *eigval, **RefSCMatrix** &P2aj)

void **s2pdm_contrib** (const double *intderbuf, double *PHF, double *P2AO, double **hf_ginter, double **ginter)

void **hcore_cs_grad** (double *PHF, double *PMP2, double **hf_ginter, double **ginter)

void **overlap_cs_grad** (double *WHF, double *WMP2, double **hf_ginter, double **ginter)

void **compute_cs_grad** ()

Protected Member Functions inherited from **sc::Wavefunction**

double **min_orthog_res** ()

double **max_orthog_res** ()

void **copy_orthog_info** (const **Ref**< **Wavefunction** > &)

Protected Member Functions inherited from **sc::MolecularEnergy**

void **failure** (const char *)

virtual void **set_energy** (double)

This is just a wrapper around set_value().

virtual void **set_gradient** (**RefSCVector** &)

These are passed gradients and hessian in cartesian coordinates.

virtual void **set_hessian** (**RefSymmSCMatrix** &)

void **x_to_molecule** ()

void **molecule_to_x** ()

Protected Member Functions inherited from **sc::Function**

virtual void **set_value** (double)

virtual void **set_matrixkit** (const **Ref**< **SCMatrixKit** > &)

Set the **SCMatrixKit** that should be used to construct the requisite vectors and matrices.

virtual void **set_dimension** (const **RefSCDimension** &)

virtual void **set_actual_value_accuracy** (double)

virtual void **set_actual_gradient_accuracy** (double)

virtual void **set_actual_hessian_accuracy** (double)**RefSCVector** & **get_x_reference** ()

Get read/write access to the coordinates for modification.

void **do_change_coordinates** (const **Ref**< **NonlinearTransform** > &)

Change the coordinate system and apply the given transform to intermediates matrices and vectors.

Protected Member Functions inherited from **sc::SavableState****SavableState** (const **SavableState** &)**SavableState** (**StateIn** &)

Each derived class **StateIn** CTOR handles the restore corresponding to calling save_object_state, save_vbase_state, and save_data_state listed above.

Protected Member Functions inherited from **sc::RefCount****RefCount** (const **RefCount** &)**RefCount** & **operator=** (const **RefCount** &)

virtual void **compute** ()=0

Recompute at least the results that have compute true and are not already computed.

### Additional Inherited Members

Static Public Member Functions inherited from **sc::SavableState**

static void **save_state** (**SavableState** *s, **StateOut** &)

static **SavableState** * **restore_state** (**StateIn** &si)

Restores objects saved with save_state.

static **SavableState** * **key_restore_state** (**StateIn** &si, const char *keyword)

Like restore_state, but keyword is used to override values while restoring.

static **SavableState** * **dir_restore_state** (**StateIn** &si, const char *objectname, const char *keyword=0)

Protected Attributes inherited from **sc::MBPT2****Ref**< **SCF** > **reference_****Ref**< **MemoryGrp** > **mem**

int **nfzc**

int **nfzv**

size_t **mem_alloc**

double **cphf_epsilon_**

int **eliminate_in_gmat_**

const double * **intbuf_****Ref**< **TwoBodyInt** > **tbint_****Ref**< **TwoBodyInt** > * **tbints_****Ref**< **TwoBodyDerivInt** > * **tbintder_**

int **nbasis**

int **noso****Ref**< **MessageGrp** > **msg_**

int **nvir**

int **nocc**

int **nsocc****Ref**< **ThreadGrp** > **thr_**

int **dynamic_**

double **print_percent_**

int **max_norb_**

int * **symorb_irrep_**

int * **symorb_num_**

char * **method_**

char * **algorithm_**

int **do_d1_**

int **do_d2_**

int **nfuncmax**

double **hf_energy_****RefSCVector hf_gradient_**

double **restart_ecorr_**

int **restart_orbital_v1_**

int **restart_orbital_memgrp_**

Protected Attributes inherited from **sc::Wavefunction**

int **debug_**

Protected Attributes inherited from **sc::MolecularEnergy****Ref**< **PointGroup** > **initial_pg_**

int **print_molecule_when_changed_**

Protected Attributes inherited from **sc::Function****Ref**< **SCMatrixKit** > **matrixkit_**

Used to construct new matrices. **RefSCVector x_**

The variables. **RefSCDimension dim_**

The dimension of x_. **AccResultdouble value_**

The value of the function at x_. **AccResultRefSCVector gradient_**

The gradient at x_. **AccResultRefSymmSCMatrix hessian_**

The hessian at x_.

## Detailed Description

The **MBPT2_R12** class implements several linear R12 second-order perturbation theory methods.

## Constructor & Destructor Documentation

### sc::MBPT2_R12::MBPT2_R12 (const Ref< KeyVal > &)

The **KeyVal** constructor.

- gbc
This boolean specifies whether Generalized Brillouin Condition (GBC) is assumed to hold. The default is 'true'. This keyword is only valid if stdapprox=A'. The effect of setting this keyword to true is rather small -- hence it is not recommended to use this keyword.

- ebc
This boolean specifies whether Extended Brillouin Condition (EBC) is assumed to hold. The default is 'true'. This keyword is only valid if stdapprox=A'. The effect of setting this keyword to true is rather small -- hence it is not recommended to use this keyword.

- stdapprox
This gives a string that must take on one of the values below. The default is A'.

- A
Use second order Mo/ller-Plesset perturbation theory with linear R12 terms in standard approximation A (MP2-R12/A). Only energies can be computed with the MP2-R12/A method.

- A'
Use second order Mo/ller-Plesset perturbation theory with linear R12 terms in standard approximation A' (MP2-R12/A'). This will cause MP2-R12/A energies to be computed also. Only energies can be computed with the MP2-R12/A' method.

- B
Use second order Mo/ller-Plesset perturbation theory with linear R12 terms in standard approximation B. This method is not implemented yet.

- spinadapted
This boolean specifies whether to compute spin-adapted or spin-orbital pair energies. Default is to compute spin-adapted energies.

- aux_basis
This specifies the auxiliary basis to be used for the resolution of the identity. Default is to use the same basis as for the orbital expansion.

- vir_basis
This specifies the basis to be used for the virtual orbitals. Default is to use the same basis as for the orbital expansion.

- include_mp1
This specifies whether to compute MP1 correction to the MP2 and MP2-R12 energies. This option only has effect if vir_basis is not the same as basis. MP1 correction is a perturbative estimate of the difference between the HF energy computed in vir_basis and basis. Usually, it is a very poor estimate -- therefore this keyword should be avoided by non-experts. Default is false.

- abs_method
This string specifies whether the old ABS method, introduced by Klopper and Samson, or the new ABS variant, CABS, introduced by Valeev, should be used. Valid values are 'ABS' (Klopper and Samson), 'ABS+', 'CABS', and 'CABS+', where the '+' labels a method where the union of OBS and ABS is used to construct the RI basis. The default is 'ABS'. The default in 2.3.0 and later will be 'CABS+'.

- lindep_tol
The tolerance used to detect linearly dependent basis functions in the RI basis set. The precise meaning depends on the orthogonalization method. The default value is 1e-8.

- r12ints
This specifies how to store transformed MO integrals. Valid values are:

- mem-posix
Store integrals in memory for single-pass situations and in a binary file on task 0's node using POSIX I/O for multipass situations.

`posix`

is usually less efficient than`mpi`

for distributed parallel multipass runs since the I/O is performed by one task only. However, this method is guaranteed to work in all types of environments, hence`mem-posix`

is the default.- posix
Store integrals in a binary file on task 0's node using POSIX I/O. This method is different from

`mem-posix`

in that it forces the integrals out to disk even if they could be stored in memory.`posix`

should only be used for benchmarking and testing purposes.- mem-mpi
Store integrals in memory for single-pass situations and in a binary file using MPI-I/O for multipass situations. This method assumes the availability of MPI-I/O.

`mem-mpi`

is the preferred choice in distributed environments which have MPI-I/O available.- mpi
Store integrals in a binary file using MPI-I/O. This method is different from

`mem-mpi`

in that it forces the integrals out to disk even if they could be stored in memory.`mpi`

should only be used for benchmarking and testing purposes.- mem
Store integrals in memory. Can only be used with single-pass transformations for MP2-R12/A and MP2-R12/A' methods. This method should only be used for testing purposes.

If `r12ints`

is not specified, then `mem-posix`

method will be used. If user wishes to use MPI-I/O, pending its availability, for higher parallel efficiency, `r12ints`

should be explicitly set to `mem-mpi`

.

- r12ints_file
This specifies the prefix for the transformed MO integrals file if

`r12ints`

is set to`posix`

,`mpi`

,`mem-posix`

or`mem-mpi`

is used. Default is './<i>inputbasename</i>.r12ints', where*inputbasename*is the name of the input file without '.in'. If MPI-I/O is used then it is user's responsibility to ensure that the file resides on a file system that supports MPI-I/O.- twopdm_grid_aa
This optional keyword specifies a

**TwoBodyGrid**object which to use for coordinates at which to compute alpha-alpha part of 2-PDM.- twopdm_grid_ab
This optional keyword specifies a

**TwoBodyGrid**object which to use for coordinates at which to compute alpha-beta part of 2-PDM.

## Member Function Documentation

### void sc::MBPT2_R12::compute () [protected], [virtual]

Recompute at least the results that have compute true and are not already computed. This should only be called by **Result**'s members.

Reimplemented from **sc::MBPT2**.

### RefSymmSCMatrix sc::MBPT2_R12::density () [virtual]

Returns the **SO** density.

Reimplemented from **sc::MBPT2**.

### int sc::MBPT2_R12::gradient_implemented () const [virtual]

Reimplemented from **sc::MBPT2**.

### void sc::MBPT2_R12::obsolete () [virtual]

Marks all results as being out of date. Any subsequent access to results will cause **Compute::compute()** to be called.

Reimplemented from **sc::MBPT2**.

### void sc::MBPT2_R12::print (std::ostream & = ExEnv::out0()) const [virtual]

Print information about the object.

Reimplemented from **sc::MBPT2**.

### void sc::MBPT2_R12::save_data_state (StateOut &) [virtual]

Save the base classes (with save_data_state) and the members in the same order that the **StateIn** CTOR initializes them. This must be implemented by the derived class if the class has data.

Reimplemented from **sc::MBPT2**.

### int sc::MBPT2_R12::value_implemented () const [virtual]

Information about the availability of values, gradients, and hessians.

Reimplemented from **sc::MBPT2**.

## Author

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