Wavefunction

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. $\Psi = \sum_i c_i \left|\phi_{j(i)}^\uparrow(r_k^\uparrow)\right|\left|\phi_{j(i)}^\downarrow(r_k^\downarrow)\right|$ 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