# Properties¶

## Overview¶

Properties can be calculated for both the Hartree-Fock and DFT wave functions. The properties that are available are:

• Natural bond analysis
• Dipole, quadrupole, and octupole moment
• Mulliken population analysis and bond order analysis
• Electrostatic potential (diamagnetic shielding) at nuclei
• Electric field and field gradient at nuclei
• Electric field gradients with relativistic effects
• Electron and spin density at nuclei
• NMR shielding (GIAO method)
• NMR hyperfine coupling (Fermi-Contact and Spin-Dipole expectation values)
• NMR indirect spin-spin coupling
• Gshift
• Response to electric and magnetic fields (static and dynamic)
• Raman

The properties module is started when the task directive TASK property is defined in the user input file. The input format has the form:

 PROPERTY
[property keyword]
[CENTER ((com || coc || origin || arb <real x y z>) default coc)]
END


Most of the properties can be computed for Hartree-Fock (closed-shell RHF, open-shell ROHF, and open-shell UHF), and DFT (closed-shell and open-shell spin unrestricted) wavefunctions. The NMR hyperfine and indirect spin-spin coupling require a UHF or ODFT wave function.

## Vectors keyword¶

 VECTORS [ (<string input_movecs >)]


The VECTORS directive allows the user to specify the input molecular orbital vectors for the property calculation

## Property keywords¶

Each property can be requested by defining one of the following keywords:

 NBOFILE
DIPOLE
OCTUPOLE
MULLIKEN
ESP
EFIELD
GSHIFT
ELECTRONDENSITY
HYPERFINE [<integer> number_of_atoms <integer> atom_list]
SHIELDING [<integer> number_of_atoms <integer> atom_list]
SPINSPIN [<integer> number_of_pairs <integer> pair_list]
RESPONSE [<integer> response_order <real> frequency]
AIMFILE
MOLDENFILE
ALL


The ALL keyword generates all currently available properties.

### NMR and EPR¶

Both the NMR shielding and spin-spin coupling have additional optional parameters that can be defined in the input. For the shielding the user can define the number of atoms for which the shielding tensor should be calculated, followed by the list of specific atom centers. In the case of spin-spin coupling the number of atom pairs, followed by the atom pairs, can be defined (i.e., spinspin 1 1 2 will calculate the coupling for one pair, and the coupling will be between atoms 1 and 2).

For both the NMR spin-spin and hyperfine coupling the isotope that has the highest abundance and has spin, will be chosen for each atom under consideration.

#### Calculating EPR and paramagnetic NMR parameters¶

The following tutorial illustrates how to combine the hyperfine, gshift and shielding to calculate the EPR and paramagnetic NMR parameters of an open-shell system. All calculations are compatible with the ZORA model potential approach.

For theoretical and computational details, please refer to references123.

#### NMR: Input Example¶

geometry  nocenter
C    0.00000000    0.00000000    0.00000000
O    1.18337200    0.00000000    0.00000000
H    -.63151821    0.94387462    0.00000000
end

basis
"*" library 6-311G**
end
property
shielding 2 1 2
hyperfine 2 1 3
gshift
end

relativistic
zora on
zora:cutoff_NMR 1d-8
zora:cutoff 1d-30
end

dft
mult 2
xc becke88 perdew86
end



### CENTER: Center of expansion for multipole calculations¶

The user also has the option to choose the center of expansion for the dipole, quadrupole, and octupole calculations.

   [CENTER ((com || coc || origin || arb <real x y z>) default coc)]


com is the center of mass, coc is the center of charge, origin is (0.0, 0.0, 0.0) and arb is any arbitrary point which must be accompanied by the coordinated to be used. Currently the x, y, and z coordinates must be given in the same units as UNITS in GEOMETRY.

### Response Calculations¶

Response calculations can be calculated as follows:

property
response  1 7.73178E-2   # response order and frequency in Hartree energy units
velocity                 # use modified velocity gauge for electric dipole
orbeta                   # calculate optical rotation 'beta' directly [^4]
giao                     # GIAO optical rotation [^5][^6][^7], forces orbeta
bdtensor                 # calculates B-tilde of Refs. [^5][^7]
analysis                 # analyze response in terms of MOs [^7]
damping 0.007            # complex response functions with damping, Ref [^8]
convergence 1e-4         # set CPKS convergence criterion (default 1e-4)
end


Response calculations are currently supported only for

• order 1 (linear response),
• single frequency,
• electric field,
• mixed electric-magnetic field perturbations.

The output consists of the electric polarizability and optical rotation tensors (alpha, beta for optical rotation) in atomic units.
The response keyword requires two arguments: response order and frequency in Hartree energy units (the aoresponse keyword can be used with same effect as the response keyword).
If the velocity or giao keywords are absent, the dipole-length form will be used for the dipole integrals. This is a bit faster.
The isotropic optical rotation is origin independent when using the velocity gauge (by means of velocity keyword) or with GIAOs 5 (by means of the giao keyword).
With the keyword bdtensor, a fully origin-invariant optical rotation tensor is calculated 57.
Note that velocity and orbeta are incompatible.
The input line

set prop:newaoresp 0


outside of the properties block forces the use of an older version of the response code, which has fewer features (in particular, no working GIAO optical rotation) but which has been tested more thoroughly. In the default newer version you may encounter undocumented features (bugs).
The keyword analysis triggers an analysis of the response tensors in terms of molecular orbitals.
If the property input block also contains the keyword pmlocalization, then the analysis is performed in terms of Pipek-Mezey localized MOs, otherwise the canonical set is used (this feature may currently not work, please check the sum of the analysis carefully). See Ref. [6] for an example. Works with HF and density functionals for which linear response kernels are implemented in NWChem.

Please refer to papers546987 for further details:

### Raman¶

Raman calculations can be performed by specifying the Raman block. These calculations are performed in conjunction with polarizability calculations. Detailed description of input parameters at https://pubs.acs.org/doi/10.1021/jp411039m#notes-1

RAMAN
[ (NORMAL | | RESONANCE) default NORMAL ]
[ (LORENTZIAN | | GAUSSIAN) default LORENTZIAN ]
[ LOW <double low default 0.0> ]
[ HIGH <double high default highest normal mode> ]
[ FIRST <integer first default 7> ]
[ LAST < integer last default number of normal modes > ]
[ WIDTH <double width default 20.0> ]
[ DQ <double dq default 0.01> ]
END


or

task dft raman numerical


Sample input block:

property
response 1 8.8559E-2
damping 0.007
end
raman
normal
lorentzian
end


#### Raman Keywords¶

• NORMAL and RESONANCE: Type of Raman plot to make.
• LORENTZIAN and GAUSSIAN: Generation of smoothed spectra (rather than sticks) using either a Lorentzian function or a Gaussian function. The default is LORENTZIAN.
• LOW and HIGH: The default range in which to generate the Raman spectrum plot is (0.0, highest wavenumber normal mode) cm-1. The LOW and HIGH keywords modify the frequency range.
• FIRST and LAST: The default range of indices of normal modes used in the plot is (7, number of normal modes). The FIRST and LAST keywords modify the range of indices.
• WIDTH: Controls the width in the smoothed peaks, using Lorentzians or Gaussians, in the plot. The default value for WIDTH is 20.0.
• DQ: Size of the steps along the normal modes. The default value for DQ is 0.01. It is related to the step size dR used in numerical evaluation of polarizability derivative

#### Raman Output¶

Raman spectrum in stick format and smoothed using Lorentzians or Gaussians stored in a filename with format [fname].normal.
The number of points is 1000 by default. This value can be changed by adding the following SET directive to the input file

set raman:numpts <integer>


#### Raman References¶

Please refer to papers1011 for further details:

### Polarizability computed with the Sum over Orbitals method¶

As an alternative to the linear response method, the Sum over Orbitals (SOO) method is available to compute polarizabilities. Results of these method are much less accurate than linear response calculations, with values off by a factor of 2-4x. However, the qualitative nature of this results can be used to compute Raman frequencies when coupled with QMD, as described in references 1213.

Sample input computing polarizability both with the SOO method and the linear response method:

property
polfromsos
end

property
response 1 0
end


### Nbofile¶

The keyword NBOFILE does not execute the Natural Bond Analysis code, but simply creates an input file to be used as input to the stand-alone NBO code. All other properties are calculated upon request.

Following the successful completion of an electronic structure calculation, a Natural Bond Orbital (NBO) analysis may be carried out by providing the keyword NBOFILE in the PROPERTY directive. NWChem will query the rtdb and construct an ASCII file, file_prefix.gen, that may be used as input to the stand alone version of the NBO program, GenNBO. file_prefix is equal to string following the START directive. The input deck may be edited to provide additional options to the NBO calculation, (see the NBO user’s manual for details.)

Users that have their own NBO version can compile and link the code into the NWChem software. See the INSTALL file in the source for details.

## Gaussian Cube Files¶

Electrostatic potential (keyword esp) and the magnitude of the electric field (keyword efield) on the grid can be generated in the form of the Gaussian Cube File. This behavior is triggered by the inclusion of grid keyword as shown below

 grid [pad dx [dy dz]] [rmax x y z] [rmin x y z] [ngrid nx [ny nz]] [output filename]


where

• pad dx [dy dz] - specifies amount of padding (in angstroms) in x,y, and z dimensions that will be applied in the automatic construction of the rectangular grid volume based on the geometry of the system. If only one number is provided then the same amount of padding will be applied in all dimensions. The default setting is 4 angstrom padding in all dimensions.

• rmin x y z - specifies the coordinates (in angstroms) of the minimum corner of the rectangular grid volume. This will override any padding in this direction.

• rmax x y z - specifies the coordinates (in angstroms) of the maximum corner of the rectangular grid volume. This will override any padding in this direction.

• ngrid nx [ny nz] - specifies number of grid points along each dimension. If only one number is provided then the same number of grid points are assumed all dimensions. In the absence of this directive the number of grid points would be computed such that grid spacing will be close to 0.2 angstrom, but not exceeding 50 grid points in either dimension.

• output filename - specifies name of the output cube file. The default behavior is to use prefix-elp.cube or prefix-elf.cube file names for electrostatic potential or electric field respectively. Here prefix denotes the system name as specified in start directive. Note that Gaussian cube files will be written in the run directory (where the input file resides).

Example input file

  echo
start nacl

geometry nocenter noautoz noautosym
Na                   -0.00000000     0.00000000    -0.70428494
Cl                    0.00000000    -0.00000000     1.70428494
end

basis
* library 6-31g*
end

#electric field would be written out to nacl.elf.cube file
#with
#ngrid     : 20 20 20
#rmax      : 4.000     4.000     5.704
#rmin      :-4.000    -4.000    -4.704

property
efield
end

#electrostatic potential would be written to esp-pad.cube file
# with the same parameters as above

property
esp
end

#illustrating explicit specification of minumum box coordinates

property
esp
grid pad 4.0 rmax 4.000 4.000 5.704 ngrid 20
end



## Aimfile¶

This keyword generates AIM Wavefunction files. The resulting AIM wavefunction file (.wfn/.wfx) can be post-processed with a variety of codes, e.g.

WARNING: Since we have discovered issues in generating .WFN files with this module (e.g. systems with ECPs), the recommended method for generating .WFN file is to first generate a Molden file with the Moldenfile option, then convert the Molden file into a WFN file by using the Molden2AIM program.

## Moldenfile¶

MOLDENFILE
MOLDEN_NORM (JANPA | | NWCHEM || NONE)


This keyword generates files using the Molden format. The resulting Molden file (.molden) should compatible with a variety of codes that can input Molden files, e.g.

the MOLDEN_NORM option allows the renormalization of the basis set coefficients. By default, the coefficient values from input are not modified. Using the JANPA value coefficients are normalized following JANPA‘s convention (where basis coefficients are normalized to unity), while the NWCHEM will produce coefficients normalized according to NWChem’s convention. Using MOLDEN_NORM equal NONE will leave the input coefficients unmodified.
It is strongly recommended to use spherical basis set when using the NWChem Molden output for JANPA analysis

Example input file for a scf calculation. The resulting Molden file will be named h2o.molden

 start heat

geometry; he 0. 0. 0.; end

basis spherical; * library 6-31g ; end

property
vectors heat.movecs
moldenfile
molden_norm janpa
end



Then, the resulting h2o.molden file can be post processed by Janpa with the following command

java -jar janpa.jar h2o.molden > h2o.janpa.txt


## Localization¶

Localized molecular orbitals can be computed with the localization keyword.

property localization (( pm || boys || ibo) default pm) end

The following methods are available:

• Pipek-Mezey14, pm keyword (default)
• Foster-Boys15, boys keyword
• IAO/IBO1617, ibo keyword

## References¶

1. Autschbach, J.; Patchkovskii, S.; Pritchard, B. Calculation of Hyperfine Tensors and Paramagnetic NMR Shifts Using the Relativistic Zeroth-Order Regular Approximation and Density Functional Theory. Journal of Chemical Theory and Computation 2011, 7 (7), 2175–2188. https://doi.org/10.1021/ct200143w

2. Aquino, F.; Pritchard, B.; Autschbach, J. Scalar Relativistic Computations and Localized Orbital Analyses of Nuclear Hyperfine Coupling and Paramagnetic NMR Chemical Shifts. Journal of Chemical Theory and Computation 2012, 8 (2), 598–609. https://doi.org/10.1021/ct2008507

3. Aquino, F.; Govind, N.; Autschbach, J. Scalar Relativistic Computations of Nuclear Magnetic Shielding and <i>g</i>-Shifts with the Zeroth-Order Regular Approximation and Range-Separated Hybrid Density Functionals. Journal of Chemical Theory and Computation 2011, 7 (10), 3278–3292. https://doi.org/10.1021/ct200408j

4. Autschbach. Computation of Optical Rotation Using Timedependent Density Functional Theory. Computing Letters 2007, 3 (2), 131–150. https://doi.org/10.1163/157404007782913327

5. Autschbach, J. Time-Dependent Density Functional Theory for Calculating Origin-Independent Optical Rotation and Rotatory Strength Tensors. ChemPhysChem 2011, 12 (17), 3224–3235. https://doi.org/10.1002/cphc.201100225

6. Krykunov, M.; Autschbach, J. Calculation of Optical Rotation with Time-Periodic Magnetic-Field-Dependent Basis Functions in Approximate Time-Dependent Density-Functional Theory. The Journal of Chemical Physics 2005, 123 (11), 114103. https://doi.org/10.1063/1.2032428

7. Moore, B.; Srebro, M.; Autschbach, J. Analysis of Optical Activity in Terms of Bonds and Lone-Pairs: The Exceptionally Large Optical Rotation of Norbornenone. Journal of Chemical Theory and Computation 2012, 8 (11), 4336–4346. https://doi.org/10.1021/ct300839y

8. Krykunov, M.; Kundrat, M. D.; Autschbach, J. Calculation of Circular Dichroism Spectra from Optical Rotatory Dispersion, and Vice Versa, as Complementary Tools for Theoretical Studies of Optical Activity Using Time-Dependent Density Functional Theory. The Journal of Chemical Physics 2006, 125 (19), 194110. https://doi.org/10.1063/1.2363372

9. Hammond, J. R.; Govind, N.; Kowalski, K.; Autschbach, J.; Xantheas, S. S. Accurate Dipole Polarizabilities for Water Clusters n=212 at the Coupled-Cluster Level of Theory and Benchmarking of Various Density Functionals. The Journal of Chemical Physics 2009, 131 (21), 214103. https://doi.org/10.1063/1.3263604

10. Mullin, J. M.; Autschbach, J.; Schatz, G. C. Time-Dependent Density Functional Methods for Surface Enhanced Raman Scattering (SERS) Studies. Computational and Theoretical Chemistry 2012, 987, 32–41. https://doi.org/10.1016/j.comptc.2011.08.027

11. Aquino, F. W.; Schatz, G. C. Time-Dependent Density Functional Methods for Raman Spectra in Open-Shell Systems. The Journal of Physical Chemistry A 2014, 118 (2), 517–525. https://doi.org/10.1021/jp411039m

12. Fischer, S. A.; Ueltschi, T. W.; El-Khoury, P. Z.; Mifflin, A. L.; Hess, W. P.; Wang, H.-F.; Cramer, C. J.; Govind, N. Infrared and Raman Spectroscopy from Ab Initio Molecular Dynamics and Static Normal Mode Analysis: The C-H Region of DMSO as a Case Study. The Journal of Physical Chemistry B 2015, 120 (8), 1429–1436. https://doi.org/10.1021/acs.jpcb.5b03323

13. Aprà, E.; Bhattarai, A.; Baxter, E.; Wang, S.; Johnson, G. E.; Govind, N.; El-Khoury, P. Z. Simplified Ab Initio Molecular Dynamics-Based Raman Spectral Simulations. Applied Spectroscopy 2020, 74 (11), 1350–1357. https://doi.org/10.1177/0003702820923392

14. Pipek, J.; Mezey, P. G. A Fast Intrinsic Localization Procedure Applicable for Ab Initio and Semiempirical Linear Combination of Atomic Orbital Wave Functions. The Journal of Chemical Physics 1989, 90 (9), 4916–4926. https://doi.org/10.1063/1.456588

15. Foster, J. M.; Boys, S. F. Canonical Configurational Interaction Procedure. Reviews of Modern Physics 1960, 32 (2), 300–302. https://doi.org/10.1103/revmodphys.32.300

16. Knizia, G. Intrinsic Atomic Orbitals: An Unbiased Bridge Between Quantum Theory and Chemical Concepts. Journal of Chemical Theory and Computation 2013, 9 (11), 4834–4843. https://doi.org/10.1021/ct400687b

17. Knizia, G.; Klein, J. E. M. N. Electron Flow in Reaction Mechanisms-Revealed from First Principles. Angewandte Chemie International Edition 2015, 54 (18), 5518–5522. https://doi.org/10.1002/anie.201410637