Evaluation of OneElectron Properties — oeprop()
¶
Code author: Robert M. Parrish and Andrew C. Simmonett
Section author: Andrew C. Simmonett
 psi4.oeprop(wfn, *args, **kwargs)[source]
Evaluate oneelectron properties.
 Returns
None
 Parameters
wfn (
Wavefunction
) – set of molecule, basis, orbitals from which to compute properties
How to specify args, which are actually the most important
 Parameters
title (str) – label prepended to all psivars computed
wfn (psi4.core.Wavefunction) –
 Examples
>>> # [1] Moments with specific label >>> E, wfn = energy('hf', return_wfn=True) >>> oeprop(wfn, 'DIPOLE', 'QUADRUPOLE', title='H3O+ SCF')
PSI4 is capable of computing a number of oneelectron properties summarized in the table below.
Feature 
Keyword 
Notes 

Electric dipole moment 
DIPOLE 

Electric quadrupole moment 
QUADRUPOLE 
Raw (traced) moments and traceless multipoles 
All moments up order N 
MULTIPOLE(N) 
Only raw (traced) moments. Sets global variables e.g. “DIPOLE”, “32POLE” 
Electrostatic potential, at nuclei 
ESP_AT_NUCLEI 
Sets global variables “ESP AT CENTER n”, n = 1 to natoms 
Electrostatic potential, on grid 
GRID_ESP 
Generates V at each point in grid_esp.dat. See Properties evaluated on a grid 
Electric field, on grid 
GRID_FIELD 
Generates {Ex,Ey,Ez} at each point grid_field.dat. See Properties evaluated on a grid 
Molecular orbital extents 
MO_EXTENTS 

Mulliken atomic charges 
MULLIKEN_CHARGES 

Löwdin atomic charges 
LOWDIN_CHARGES 

Wiberg bond indices 
WIBERG_LOWDIN_INDICES 
Uses (Löwdin) symmetrically orthogonalized orbitals 
Mayer bond indices 
MAYER_INDICES 

Natural orbital occupations 
NO_OCCUPATIONS 

Stockholder Atomic Multipoles 
MBIS_CHARGES 
Generates atomic charges, dipoles, etc. See Minimal Basis Iterative Stockholder 
There are two ways the computation of oneelectron properties can be requested. Firstly, the properties can be evaluated from the last computed oneparticle density, using the following syntax:
oeprop("MO_EXTENTS", "MULTIPOLE(4)", title = "hello!")
Note that it is the user’s responsibility to ensure that the relaxed density matrix is computed using the method of interest, which may require setting additional keywords (see the method’s manual section for details). The named argument, title, is completely optional and is prepended to any globals variables set during the computation. The unnamed arguments are the properties to be computed. These can appear in any order, and multiple properties may be requested, as in the example above. Note that, due to Python syntax restrictions, the title argument must appear after the list of properties to compute. The available properties are shown in the table above.
The syntax above works well for computing properties using the SCF wavefunction, however, may be difficult (or impossible) to use for some of the correlated levels of theory. Alternatively, oneelectron properties can be computed using the builtin properties() function, e.g.:
properties('ccsd', properties=['dipole'])
The properties()
function provides limited functionality, but is a lot easier to
use for correlated methods. For capabilities of properties()
see the
corresponding section of the manual.
Basic Keywords¶
Multipole moments may be computed at any origin, which is controlled by the global PROPERTIES_ORIGIN keyword. The keyword takes an array with the following possible values:
Keyword 
Interpretation 

[x, y, z] 
Origin is at the coordinates, in the same units as the geometry specification 
[“COM”] 
Origin is at the center of mass 
[“NUCLEAR_CHARGE”] 
Origin is at the center of nuclear charge 
Properties evaluated on a grid¶
Certain properties may be evaluated a userspecified grid points. The grid points are completely arbitrary and are specified by providing a file called grid.dat containing the x,y,z values separated with spaces for each point in order:
x1 y1 z1
x2 y2 z2
..........
xn yn zn
The grid.dat file is completely free form; any number of spaces and/or newlines between entries is permitted. The units of the coordinates in grid.dat are the same as those used to specify the molecule’s geometry, and the output quantities are always in atomic units. The requested properties will be written out in the same order as the grid point specification in grid.dat; see the above table for the format and file name of the output.
The grid may be generated in the input file using standard Python loops. By capturing the wavefunction used to evaluate the oneelectron properties, the values at each grid point may be captured as Python arrays in the input file:
E, wfn = prop('scf', properties=["GRID_ESP", "GRID_FIELD"], return_wfn=True)
Vvals = wfn.oeprop.Vvals()
Exvals = wfn.oeprop.Exvals()
Eyvals = wfn.oeprop.Eyvals()
Ezvals = wfn.oeprop.Ezvals()
In this example, the Vvals array contains the electrostatic potential at each grid point, in the order that the grid was specified, while the Exvals, Eyvals and Ezvals arrays contain the x, y and z components of the electric field, respectively; all of these arrays can be iterated and manipulated using standard Python syntax. For a complete demonstration of this utility, see the props4 test case.
Minimal Basis Iterative Stockholder¶
The Minimal Basis Iterative Stockholder (MBIS) method is one of many procedures that partitions a molecular oneparticle density matrix into atomic electron densities. Running MBIS in PSI4 will calculate atomic valence charge widths, volume ratios, atomic charges, as well as dipoles, quadrupoles, and octupoles. Additionally, all expectation values of radial moments of nth order (\(<r^n>\)) are computed up to fourth order. Higher moments can be computed by specifying MAX_RADIAL_MOMENT. The volume ratios are computed as the ratio between the volume of the atomic density (\(<r^3>\)) and the volume of the free atom computed using the same level of theory, but with a potentially unrestricted reference.
The allowed number of iterations and convergence criteria for the stockholder algorithm is controlled by MBIS_MAXITER and MBIS_D_CONVERGENCE. Note that the density is partitioned on a molecular quadrature grid, the details of which can be controlled with the keywords MBIS_RADIAL_POINTS, MBIS_SPHERICAL_POINTS, and MBIS_PRUNING_SCHEME. (Associated Paper: [Verstraelen:2016])