5. CheMPS2::Hamiltonian

There are several ways to feed matrix elements to CheMPS2. They are explained below in detail. Because CheMPS2 is a spin-adapted code, it can only handle spatial orbitals. It is hence not possible to use different orbitals for \(\uparrow\) and \(\downarrow\) electrons.

1. The CheMPS2::Hamiltonian object is able to read in FCIDUMP files. The fcidump plugin to psi4 allows to generate such FCIDUMP files.

2. The savehdf plugin to psi4 fills a CheMPS2::Hamiltonian object, and saves the matrix elements to disk in HDF5 format, taking into account their eightfold permutation symmetry.

3. Users can also generate matrix elements themselves, and feed them to the CheMPS2::Hamiltonian object.

5.1. psi4 fcidump plugin

The CheMPS2::Hamiltonian object is able to read in FCIDUMP files:

CheMPS2::Hamiltonian::Hamiltonian( const string filename, const int psi4groupnumber )

The variable filename should contain the path to the FCIDUMP file, and the variable psi4groupnumber should be the group number of the abelian point group with real-valued character table as defined in psi4. The conversion table is provided here:

Group name	c1	ci	c2	cs	d2	c2v	c2h	d2h
Group number	0	1	2	3	4	5	6	7

FCIDUMP files can for example be generated by molpro, or by a plugin to psi4. The plugin has been tested on psi4-0.5 (released February 17, 2016).

To make use of this feature, build psi4 with the plugin option ENABLE_PLUGINS=ON, and then run:

$ cd /mypsi4plugins
$ psi4 --new-plugin fcidump
$ cd fcidump

Now, replace the file fcidump.cc with /sourcefolder/chemps2/integrals/psi4plugins/fcidump.cc. To compile the plugin, run:

$ make

An example input file to generate a FCIDUMP file:

molecule N2 {
   N       0.0000   0.0000   0.0000
   N       0.0000   0.0000   2.1180
units au
}

sys.path.insert(0, './..')
import fcidump

set basis cc-pVDZ
set reference rhf
set scf_type PK
set e_convergence 1e-12
set d_convergence 1e-12
set ints_tolerance 0.0

set fcidump dumpfilename N2.ccpvdz.fcidump

energy('fcidump')

This file (N2.fcidump.in) should be placed in the folder /mypsi4plugins/fcidump/. The FCIDUMP file can then be generated with:

$ cd /mypsi4plugins/fcidump
$ psi4 N2.fcidump.in N2.fcidump.out
$ less N2.CCPVDZ.FCIDUMP

Examples of output generated with this plugin can be found in /sourcefolder/chemps2/tests/matrixelements/.

5.2. psi4 savehdf plugin

The CheMPS2::Hamiltonian object is able to read in HDF5 files generated by a plugin to psi4. The plugin has been tested on psi4-0.5 (released February 17, 2016). It stores all unique matrix elements (remember that there is eightfold permutation symmetry) in binary form with HDF5.

To make use of this feature, build psi4 with the plugin option ENABLE_PLUGINS=ON, and then run:

$ cd /mypsi4plugins
$ psi4 --new-plugin savehdf
$ cd savehdf

Now, replace the file savehdf.cc with /sourcefolder/chemps2/integrals/psi4plugins/savehdf.cc. To compile the plugin, the Makefile should be adjusted. Change the line

$(CXX) $(LDFLAGS) -o $@ $^ $(CXXDEFS)

to

$(CXX) $(LDFLAGS) -o $@ $^ $(CXXDEFS) -lchemps2

Remember to add the library and include paths to the Makefile as well, if libchemps2 is not installed in a standard location. For debian/sid, the HDF5 headers are located in the folder /usr/include/hdf5/serial/. It might be necessary to add it to the INCLUDES variable in the Makefile. To compile the plugin, run:

$ make

An example input file to use the savehdf plugin:

molecule N2 {
   N       0.0000   0.0000   0.0000
   N       0.0000   0.0000   2.1180
units au
}

sys.path.insert(0, './..')
import savehdf

set basis cc-pVDZ
set reference rhf
set scf_type PK
set e_convergence 1e-12
set d_convergence 1e-12
set ints_tolerance 0.0

energy('savehdf')

This file (N2.savehdf.in) should be placed in the folder /mypsi4plugins/savehdf/. The matrix elements can then be saved to disk in binary form with HDF5 by running:

$ cd /mypsi4plugins/savehdf
$ psi4 N2.savehdf.in N2.savehdf.out
$ ls *.h5

The plugin generates three files:

/mypsi4plugins/CheMPS2_Ham_parent.h5
/mypsi4plugins/CheMPS2_Ham_Tmat.h5
/mypsi4plugins/CheMPS2_Ham_Vmat.h5

which allow to create an instance of the CheMPS2::Hamiltonian object:

CheMPS2::Hamiltonian::Hamiltonian( const bool fileh5, const string main_file, const string file_tmat, const string file_vmat )

The variable fileh5 should be true, and the three strings should contain the paths to the three files listed above, in the same respective order.

5.3. Custom matrix elements

It is also possible to create a CheMPS2::Hamiltonian object with your own matrix elements. Please consult the CheMPS2::Hamiltonian class in the doxygen html output, and more specifically the functions:

CheMPS2::Hamiltonian::Hamiltonian( const int Norbitals, const int nGroup, const int * OrbIrreps )
void CheMPS2::Hamiltonian::setEconst( const double val )
void CheMPS2::Hamiltonian::setTmat( const int index1, const int index2, const double val )
void CheMPS2::Hamiltonian::setVmat( const int index1, const int index2, const int index3, const int index4, const double val )

The variable Norbitals should be the total number of orbitals in the active space. The variable nGroup should be the group number of the abelian point group with real-valued character table as defined in psi4. The array OrbIrreps of length Norbitals contains for each orbital its irreducible representation number as defined in psi4. The conversion table is provided here:

Group / Irreps	0	1	2	3	4	5	6	7
0: c1	A
1: ci	Ag	Au
2: c2	A	B
3: cs	A’	A’’
4: d2	A	B1	B2	B3
5: c2v	A1	A2	B1	B2
6: c2h	Ag	Bg	Au	Bu
7: d2h	Ag	B1g	B2g	B3g	Au	B1u	B2u	B3u

Two important remarks:

1. On creation of the CheMPS2::Hamiltonian object, every matrix element is set to zero.

2. Physics notation is used for the two-electron integrals in CheMPS2: \(V_{ij;kl} = ( ik \mid jl )\) or CheMPS2::Hamiltonian::setVmat( i, j, k, l, (ik|jl) ).