## Jastrow correlation factor

Keyword: JASTROW

Description: This wave function's job is to represent the electron-electron correlations. It is a symmetric function with explicit electron-electron distances. There are three main terms in this function; electron-ion, electron-electron, and electron-electron-ion. In all that follows, the index $\alpha$ stands for the ion (nucleus) coordinate, the indices $i,j$ stand for electron-electron distances, and $k,l,m$ are expansion indices.

Electron-ion. $\sum_{i\alpha} \sum_k c_k a_k (r_{i\alpha})$

Electron-electron. $\sum_{ij} \sum_k c_k b_k (r_{ij})$

Electron-electron-ion. $\sum_{\alpha ij} \sum_{klm} c_{klm} (a_k(r_{i\alpha})a_l(r_{j\alpha}) + a_k(r_{j\alpha})a_l(r_{i\alpha}) ) b_k (r_{ij})$

For efficiency reasons, the Jastrow factor is organized into GROUP sections. Each GROUP can take one of the options listed below.

The ONEBODY, TWOBODY, and THREEBODY sections all accept the FREEZE keyword, in which the ocefficients are held constant during an optimization.

Required keywords

None

Optional keywords

Keyword Type Default Description
OPTIMIZEBASIS flag False Optimize any basis functions present in the expansion.
EIBASIS section empty A section for a Basis function object. This will represent the $a_k$ functions.
EEBASIS section empty A section for a Basis function object. This will represent the $b_k$ functions.
ONEBODY section empty List of expansion coefficients(floats) for the electron-ion terms. There must be one section for each atom type, each beginning with the name of the atom. (for example, COEFFICIENTS { Li 3.4 2.3 }
TWOBODY section empty List of expansion coefficients for the electron-electron terms. For example, COEFFICIENTS { 0.1 0.2 0.3 }.
TWOBODY_SPIN section empty List of expansion coefficients for the electron-electron terms with different spin-dependent terms. For example, LIKE_COEFFICIENTS { 0.1 0.2 0.3 } UNLIKE_COEFFICIENTS { 0.05 0.2 0.3 }.
THREEBODY section empty List of expansion coefficients(floats) for the electron-electron-ion terms. There must be one section for each atom type, each beginning with the name of the atom. (for example, COEFFICIENTS { Li 3.4 2.3 } With the defaults, there are a maximum of 12 parameters they have requirements on the number of basis functions. 3 parms: 1 EE and 1 EI function< 5 parms: 1 EE and 2 EI 7 parms: 2 EE and 2 EI 12 parms: 2 EE and 3 EI

## Pfaffian wave function

Keyword: PFAFFIAN

Description: WARNING. This is a development feature. Make sure you know what you're doing before trying to use Pfaffians. A pfaffian (generalized determinant) or several pfaffians. See Bajdich et al. Phys. Rev. B 77 115112 (2008) for implementation details. Submatrices $\boldsymbol \xi$, $\boldsymbol \Phi$ and $\boldsymbol \varphi$ are defined in Pfaffian group. and ordered according the ORBITAL_ORDER section.

Required keywords

Keyword Type Description
NPAIRS section Number of spin up, spin down, and unpaired electrons. The sum of these 3 numbers defines the Pfaffian matrix.
PFWT section List of the weights of the Pfaffians, for a multi-Pfaffian wave function
PARIING_ORBITAL section Section for Pfaffian group
ORBITALS section Input for a MO Matrix object

Optional keywords

Keyword Type Default Description
ORBITAL_ORDER section ith pairing orbital for ith Pfaffian matrix Contains upper-diagonal of \f( N \times N \f) matrix of pairing occupation numbers
OPTIMIZE_PFWT flag False Optimize the Pfaffian weights

## Slater determinant or sum of determinants

Keyword: SLATER

Description: A Slater determinant or linear combination of several determinants. In this object, a determinant is actually a product of two determinants; one for spin up and one for spin down. The way to think about this is that the orbital object provides a list of $\phi_j$. Each determinant $i$ is defined by the set of orbitals it includes, which is given in STATES. One can think of this as a vector ${\mathbf j}_i$ for each determinant, with the first $n_\uparrow$ elements giving the occupation of the up electrons, and the second $n_\downarrow$ doing the same for the down electrons. There is substantial flexibility in choosing the occupation of these orbitals, which is given in the tutorials. If you are just interested in straightforward ground state calculations, then the converter will probably set this value correctly.

Required keywords

Keyword Type Description
DETWT section List of the weights $c_i$ of the determinants. This can be replaced with CSF.
STATES section List of the occupations of molecular orbitals, first spin up and then spin down. If there is more than one determinant, continue listing up and down occupations. See HOWTOs for methods to modify this section to select states.
ORBITALS/CORBITALS section A Molecular Orbital section.

Optional keywords

Keyword Type Default Description
NSPIN section same as in the Hamiltonian Two integers, the first the number of up electrons, and the second the number of down electrons
OPTIMIZE_DET flag False Optimize the determinantal coefficients. For a single determinant, this does nothing.
CSF section empty This replaces DETWT, and lists configuration state functions to reduce the number of variational parameters. The format is CSF { overallweight weightdet1 weightdet2 ... }. Only the overall weight is optimized. List a separate CSF section for each CSF.
CLARK_UPDATES flag special Force Bryan Clark's updates (J. Chem. Phys 135, 244105 (2011)) of the determinant inverses and values. By default, this is enabled when there is more than one determinant and more than 10 electrons.
SHERMAN_MORRISON flag special Force Sherman-Morrison updates of the determinant inverses and values.

## Slater-Jastrow (multiply two wave functions)

Keyword: SLATER-JASTROW

Description: Multiply two wave functions; that is $\Psi = \Psi_1 \Psi_2$.

Required keywords

Keyword Type Description
WF1 section A section for a Wave function object. Will represent $\Psi_1$
WF2 section A section for a Wave function object. Will represent $\Psi_2$

Optional keywords

None